Use right triangle trigonometry and the Pythagorean theorem to solve for all angles and sides of triangle DEF. Please help!
Answers
To solve triangle DEF, use Pythagorean theorem and right triangle trigonometry: find third side using \($c^2 = a^2 + b^2$\), and find all angles using \($\tan C = \frac{b}{a}$\), \($\sin C = \frac{b}{c}$\), \($\cos C = \frac{a}{c}$\).
To solve for all angles and sides of triangle DEF using right triangle trigonometry and the Pythagorean theorem, we need to know the lengths of all sides of the triangle. Let's assume that we have the lengths of two sides of the triangle and call them a and b.
If we know a and b, we can use the Pythagorean theorem to find the length of the third side c:
\($c^2 = a^2 + b^2$\)
Once we have the length of all sides, we can use right triangle trigonometry to find all angles. For example, if we have the lengths of sides a and b, we can use the tangent function to find angle C:
\($\tan C = \frac{b}{a}$\)
Similarly, we can use the sine and cosine functions to find the other angles:
\($\sin C = \frac{b}{c}$\)
\($\cos C = \frac{a}{c}$\)
So, if we know two sides of the triangle, we can use the Pythagorean theorem to find the third side and then use right triangle trigonometry to find all angles.
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Related Questions
Please help me
Thank you ;)
Answers
Explanation:
SAS = side angle side
The tickmarks tell us which sides are congruent to one another. This forms one S of SAS.
The other S would be the shared overlapping sides between the triangles. We're using the reflexive property here.
The marked angles in red are congruent to one another, which refers to the 'A' in SAS. We have two pairs of congruent sides, and a pair of congruent angles between those sides. This allows us to use the SAS rule.
SSS can't be used since we don't know anything about the third pair of sides.
The total cost of a cab from downtown to the airport is $80.20. If you give the driver a 25 percent tip for getting to the airport early, how much will the gratuity be? Use the diagram to solve.
A 2-column table with 5 rows. Column 1 has entries 25 percent, 25 percent, 25 percent, 25 percent, Total 100 percent. Column 2 has entries blank, blank, blank, blank, Total 80 dollars and 20 cents.
You would tip the driver $
.
Answers
Answer:
$20.50!
Step-by-step explanation:
Answer:
its 20.05. just took the assignment.
Step-by-step explanation:
just took the assignment.
Given: DF and DE are midsegments of ∆ABC Prove: DE= 1/2 AC (PLEASE HELP)
Answers
Answer:
The correct answer is D because we proved that the triangles ΔDBE and ΔADF are congruent so that means that DE = segment A F because of CPCTC.
Answer:
The correct answer is D because we proved that the triangles ΔDBE and ΔADF are congruent so that means that DE = segment A F because of CPCTC.
Step-by-step explanation:
for a posttest following anova, there are four different treatment groups. how many pairwise comparisons must be made to gain a complete understanding of which treatment effects differ significantly from others? a. 4 b. 6 c. 12 d. 24
Answers
There are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.
In order to determine which treatment effects differ significantly from others, we need to make pairwise comparisons between all possible pairs of treatment groups. Let's consider an example with four treatment groups labeled A, B, C, and D.
To determine which treatment effects differ significantly from others, we need to compare the mean scores of each treatment group with the mean scores of every other treatment group. This means we need to make the following pairwise comparisons:
A vs B
A vs C
A vs D
B vs C
B vs D
C vs D
Therefore, there are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.
It's worth noting that when making multiple pairwise comparisons, there is an increased risk of making a Type I error (i.e., rejecting the null hypothesis when it is actually true) due to the multiple testing problem. To control for this, researchers may choose to adjust the significance level or use methods such as the Bonferroni correction to adjust the p-values of the individual tests.
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What additional information is needed to prove the triangles are congruent by side-angle-side?
Answers
The corresponding angles and sides of the two triangles need to be given in order to prove congruence by side-angle-side.
In order to prove congruence by side-angle-side, the corresponding angles and sides of the two triangles must be given. The sides must be proportional, which means that two sides of one triangle must be equal to two sides of the other triangle, and the angles between these two sides must also be equal. In other words, if two sides of one triangle are equal to two sides of the other triangle, and the angle between those two sides is also equal, then the two triangles are congruent. This can be expressed as “If two sides and the included angle of one triangle are equal to the corresponding sides and angle of a second triangle, then the two triangles are congruent.” In order to prove congruence by side-angle-side, all of the corresponding sides and angles must be given in order to show that they are equal.
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The additional information that is needed to prove the triangles are congruent by Side-Angle -Side us that the corresponding angles and sides of the two triangles need to be given .
What is Side-Angle-Side Congruence ?
The Two Triangles can be called as Congruent by Side-Angle-Side rule if any 2 sides and angle included between sides of one triangle is equivalent to corresponding 2 sides and angle between sides of second triangle .
In order to prove the Congruence by Side-Angle-Side, the corresponding angles and the sides of the 2 triangles must be given.
The sides must also be in proportional, that means that the two sides of one triangle must be equal to two sides of other triangle, and
the angles between these two sides of the triangle must be equal.
So , In order to prove a triangle congruent by Side-Angle-Side, all of the corresponding sides and angles must be given in order to prove that they are equal.
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A vase contains 9 balls: 3 blue, 3 red and 3 green ones. Draw 3 random balls from the vase and don't put them back in. Consider the events: A = the 3 balls drawn have the same color, B = the 3 balls drawn have different colors.
a) Calculate P(A).
b) Calculate P(B).
c) Are A and B independent?
Answers
a)The probability that 3 balls drawn have the same color=1/28.
b)The probability that 3 balls drawn have different colors= 3/14.
c)A and B are mutually exclusive events.
Explanation:
Given that a vase contains 9 balls: 3 blue, 3 red, and 3 green ones. Three random balls are drawn from the vase and are not put back in.
The events that are considered are: A = the 3 balls drawn to have the same color. B = the 3 balls drawn have different colors.
(a) Calculation of P(A), We need to find the probability that 3 balls drawn have the same color.
P(A) = probability of getting 3 blue balls + probability of getting 3 red balls + probability of getting 3 green balls.
The probability of getting 3 blue balls is 3/9 × 2/8 × 1/7 = 1/84.
The probability of getting 3 red balls is 3/9 × 2/8 × 1/7 = 1/84.
The probability of getting 3 green balls is 3/9 × 2/8 × 1/7 = 1/84
Therefore, P(A) = 1/84 + 1/84 + 1/84 = 3/84 = 1/28.
(b) Calculation of P(B), We need to find the probability that 3 balls drawn have different colors.
P(B) = probability of getting one ball of each color + probability of getting 2 balls of one color and one ball of another color.
The probability of getting one ball of each color is 3/9 × 3/8 × 3/7 = 27/252
The probability of getting 2 balls of one color and one ball of another color is 3(3/9 × 2/8 × 3/7) = 27/252
Therefore, P(B) = 27/252 + 27/252 = 54/252 = 3/14.
(c) Finding if are A and B independent,
A and B are not independent as P(A) = 1/28 and P(B) = 3/14.
The probability of both A and B occurring together is zero, as it is impossible to draw 3 balls that are of the same color and 3 balls of different colors at the same time. Hence, A and B are mutually exclusive events.
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a) The probability that the 3 balls drawn have the same color:
P(A) = 0.0095 or 0.95%
b) The probability that the 3 balls drawn have different colors:
P(B) = 0.2143 or 21.43%
c) A and B are not independent.
Explanation:
a)
P(A) = (3/9) × (2/8) × (1/7) + (3/9) × (2/8) × (1/7) + (3/9) × (2/8) × (1/7)
= 0.0095 or 0.95%
Note: In the first fraction, the numerator is 3 because there are three blue balls. The denominator is 9 because there are 9 balls in total.
Since the first ball has been drawn, there are only 8 balls left, hence 2/8 in the second fraction. And so on.
b)
P(B) = (3/9) × (3/8) × (3/7) + (3/9) × (3/8) × (3/7) + (3/9) × (3/8) × (3/7)
= 0.2143 or 21.43%
Note: In the first fraction, the numerator is 3 because there are three blue balls. The denominator is 9 because there are 9 balls in total.
Since the first ball has been drawn, there are only 8 balls left, hence 3/8 in the second fraction. And so on.
c)
P(A)P(B) = 0.0095 × 0.2143
= 0.00204
≈ 0.2%
P(A ∩ B) = 0 (because if you have 3 balls of different colors, then you cannot have 3 balls of the same color at the same time)
Therefore, A and B are not independent.
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1. which is the product of these numbers, to the appropriate number of significant digits? 56.2 × 9.2057 = a. 517 b. 517.4 c. 517.36 d. 517.00
Answers
The product of 56.2 and 9.2057 to the appropriate number of significant digits is 517.00.
The significant digits in a number are the digits that contribute to its precision. When multiplying numbers, the result should be rounded to the same number of significant digits as the factor with the least number of significant digits.
In this case, 56.2 has three significant digits, and 9.2057 has five significant digits. The factor with the least number of significant digits is 56.2. Therefore, the product should be rounded to three significant digits.
Multiplying 56.2 by 9.2057 gives 517.38134. Rounding this result to three significant digits gives us 517.00. The trailing zeros after the decimal point are significant in this case as they indicate the precision of the result. Hence, the correct answer is 517.00.
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What are homoskedasticity and heteroskedasticity in multiple linear regression? How would you check for heteroskedasticity in a multiple linear regression model?
Answers
Homoskedasticity and heteroskedasticity are terms used to describe the variability of errors in a multiple linear regression model.
To check for heteroskedasticity in a multiple linear regression model, there are several diagnostic tests and graphical methods that can be used: Residual plot, Breusch-Pagan test, White's test, Goldfeld-Quandt test,
Homoskedasticity refers to a situation where the variance of the errors (residuals) is constant across all levels of the independent variables. This means that the spread of the residuals is the same throughout the range of predicted values. In other words, the variability of the errors is consistent and does not change systematically.
Heteroskedasticity, on the other hand, occurs when the variance of the errors is not constant across all levels of the independent variables. In this case, the spread of the residuals tends to vary as the predicted values change. Heteroskedasticity implies that the variability of the errors is not consistent and may exhibit patterns or trends.
To check for heteroskedasticity in a multiple linear regression model, there are several diagnostic tests and graphical methods that can be used: Residual plot, Breusch-Pagan test, White's test, Goldfeld-Quandt test,
Residual plot: Plotting the residuals against the predicted values or the independent variables can reveal patterns or trends in the spread of the residuals. If the spread of the residuals appears to fan out or there is a clear pattern, it suggests the presence of heteroskedasticity.
Breusch-Pagan test: This is a statistical test that formally tests for heteroskedasticity in the residuals. The test assesses the relationship between the squared residuals and the independent variables. If the test result is statistically significant, it indicates the presence of heteroskedasticity.
White's test: Similar to the Breusch-Pagan test, White's test also examines the relationship between the squared residuals and the independent variables. It is another statistical test commonly used to detect heteroskedasticity in regression models.
Goldfeld-Quandt test: This test divides the data into two groups based on a selected independent variable and compares the variances of the residuals between the two groups. If the variances significantly differ, it suggests the presence of heteroskedasticity.
By conducting these tests and examining the graphical plots, one can assess whether heteroskedasticity is present in the multiple linear regression model. If heteroskedasticity is detected, it may be necessary to address the issue by using heteroskedasticity-robust standard errors, transforming variables, or considering alternative regression techniques designed to handle heteroskedastic data.
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A fisherman can row upstream at 5 mph and downstream at 10 mph. He started rowing upstream until he got tired and then rowed downstream to his starting point. How far did the fisherman row if the entire trip took 6 hours?
Answers
Given:
R, S, T are midpoints of , , and .
If the perimeter (distance around) of ABC is 20, then the perimeter of RST is
5
10
15
Answers
Answer:
10 since its half of the original
Three students were asked to use estimation strategies to find a reasonable
solution to this question:
A cashier is ringing up a stove for $484 and a dishwasher for $503. What is the
total that is owed for the appliances?
Answers
The estimated amount that is owed for the appliances is about $1000.
What is Estimation Strategies?Estimation strategies are strategies used to do an operation in order for the operation to be predictable and easy.
Given question is,
A cashier is ringing up a stove for $484 and a dishwasher for $503.
If we are doing it the normal way,
Total amount owed = $484 + $503
= $987.
If we using estimation to find the total amount, estimate the amount for the stove being $500 and estimate the amount for the dishwasher being $500.
Total amount owed = $500 + $500 = $1000
Hence the total amount owed is about $1000 but is the overestimated value.
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If marc r v = marc v u , what is marc v u ?a. 47° b. 52° c. 64° d. 87°
Answers
If marc r v = marc v u , the value of marc v u is given as 64°.
mArc R V = mArc V U, Angle S O R = 13 x degrees and angle T O U = 15 x - 8 degrees
∠SOR = ∠TOU (Vertically opposite angles are equal). Therefore:
13 x = 15x - 8
solving by calculating the value of x to satisfy the equation: Subtracting 13x from both sides
13x - 13x = 15x - 8 - 13x
0 = 15x - 13x - 8
2x - 8 = 0
Adding 8 to both sides:
2x - 8 + 8 = 0 + 8
2x = 8
2x/2 = 8/2
x = 4
∠SOR = 13x = 13(4) = 52°
∠TOU = 15x - 8 = 15(4) - 8 = 60 - 8 = 52°
Let a = mArc R V = mArc V U
Therefore:
mArc R V + mArc V U + ∠TOU = 180 (sum of angles on a straight line)
Substituting:
a + a + 52 = 180
2a = 180-52
2a = 128
a = 128/2
a= 64°
mArc R V = mArc V U = 64°
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Jadd buys a blouse and a skirt for 3/4 of their original price. She pays a total of $31.50 for the two items. If the original price of the blouse is $18, Jade buys a blouse and a skirt for what is the original price of the skirt?
Answers
Answer:
$13.50
Step-by-step explanation:
$31.50-$18= $13.50
The price of the two items - the known price which is the blouse
It is given that AB CD Identify the postulate that proves the triangles are congruent
Answers
Answer:
i can't see the multiple choice
Step-by-step explanation:
angle c and b are equal
angle a and d are equal
and you have a common angle o
and ab = cd
The triangles ΔAOB and ΔDOC are congruent to each other by SSS and SAS postulates. Then the correct option is A.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
It is given that AB || CD. The side AB is congruent to the side CD.
The line AD and BC intersect at the mid-point. Then the line segment AO and OD will be congruent and the line segment CO and OB will be congruent.
And the angle ∠AOB and ∠COD will be congruent because they are vertically opposite angles.
The triangles ΔAOB and ΔDOC are congruent to each other by SSS and SAS postulates. Then the correct option is A.
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what points satisfy 2x-6y=12 (i need 3)
Answers
Answer:
(0,-2),(3,-1),(6,0)
Step-by-step explanation:
Plug in a number into x or y and solve the equation for the other variable. Or just use Desmos to graph it real quick and see the points.
I NEED HELP ASAP
The volume of paint used, V liters, is directly proportional to the area, A square feet, that the paint can cover. 5 liters of paint can cover a wall with an area of 75 square feet.
a) What is the constant of proportionality? Tell how you found it.
b) Write an equation relating V and A.
c) How much paint would be needed to cover an area of 180 square feet? Show your work.
Whoever answers me correctly first will get extra points after this!
Answers
Hey! I believe this is the answer you're looking for:
https://brainly.com/question/16663256
Step-by-step explanation:
The volume of paint used, V liters, is directly proportional to the area, A square feet, that the paint can cover.
This is written as:
\begin{gathered}V \propto A\\V=kA,$ where k is the constant of proportionality\end{gathered}
(a)5 liters of paint can cover a wall with an area of 75 square feet.
V=5 liters, A=75 square feet.
Substitution into V=kA
5=75k
k=5/75
\text{Constant of proportionality, k}=\dfrac{1}{15}Constant of proportionality, k=151
(b)Substitution of k=\dfrac{1}{15}k=151 into V=kA
The equation relating V and A is:
V=\frac{1}{15}AV=151A
(c)If A=180 Square feet
Volume of paint needed,
\begin{gathered}V=\frac{1}{15} X 180\\=12$ liters\end{gathered}
A car that costs $14000 without tax costs 14700 with tax. What is the sales tax percent
Answers
Answer
5%
Explanation
The answer is 5% increase because you have to subtract 14700 and 14000 which gets you 700 and then you divide 700 by 14000 (the original price) which gets you 0.05 and then you multiply that by 100 which then gets you 5%
(x-2)(x-1)= in standard form
Answers
Answer:
\(x^{2} -3x+2\)
Step-by-step explanation:
Her sister is twice as old as Cheryl. Find her sister's age in terms of x.
Answers
Her sister is twice as old as Cheryl ,her sister's age in terms of x is 2x years old.
Why is it twice age?Your sister is 11 years older than you since she was twice as old as you when you were 11 (she was 112 = 22 years old).Add your age at the time of your daughter's birth to the day of her birth. For instance, if your daughter was born on January 1, 2010, and you were 25 at the time, you will be double her age on that day in 2035.If one's age is x now, one's age will be nx in the future. Age n years from now equals x + n if the age at currently is x. Age n years ago equals x - n if the current age is x.To learn more about twice age refer to:
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In your reservoir, you have a production well which flows for 48 hours at 200 STB/day, and then shut-in for 24 hours. The following additional data are given : Pi = 3100 psi Ct = 15x10^-6 psi^-1 Bo = 1.3 bbl/STB ϕ = 15% μ=1.2 cp K = 45 md and h = 60 ft
a-) Calculate the pressure in this production well at 12 hours of shut in
b-) Explain how can you use superposition in time to analyze a pressure build-up test.
Answers
a) To calculate the pressure at 12 hours of shut-in:
substitute the given values into the pressure buildup equation and solve for P(t=12).
b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.
We have,
a) To calculate the pressure in the production well at 12 hours of a shut-in, we can use the equation for pressure transient analysis during shut-in periods, known as the pressure buildup equation:
P(t) = Pi + (Q / (4πKh)) * log((0.14ϕμCt(t + Δt)) / (Bo(ΔP + Δt)))
Where:
P(t) = Pressure at time t
Pi = Initial reservoir pressure
Q = Flow rate
K = Permeability
h = Reservoir thickness
ϕ = Porosity
μ = Viscosity
Ct = Total compressibility
t = Shut-in time (12 hours)
Δt = Time since the start of the flow period
Bo = Oil formation volume factor
ΔP = Pressure drop during the flow period
Given:
Pi = 3100 psi
Q = 200 STB/day
K = 45 md
h = 60 ft
ϕ = 15%
μ = 1.2 cp
Ct = 15x10^-6 psi^-1
Bo = 1.3 bbl/STB
t = 12 hours
Δt = 48 hours
ΔP = Pi - P(t=Δt) = Pi - (Q / (4πKh)) * log((0.14ϕμCt(Δt + Δt)) / (Bo(ΔP + Δt)))
Substituting the given values into the equation:
ΔP = 3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15x\(10^{-6}\) * (48 + 48)) / (1.3 * (3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15 x \(10^{-6}\) * (48 + 48)) / (1.3 * (0 + 48))))))
After evaluating the equation, we can find the pressure in the production well at 12 hours of shut-in.
b) Superposition in time is a principle used in pressure transient analysis to analyze and interpret pressure build-up tests.
It involves adding or superimposing the responses of multiple transient tests to simulate the pressure behavior of a reservoir.
The principle of superposition states that the response of a reservoir to a series of pressure changes is the sum of the individual responses to each change.
Superposition allows us to combine the information obtained from multiple tests and obtain a more comprehensive understanding of the reservoir's behavior and properties.
It is a powerful technique used in reservoir engineering to optimize production strategies and make informed decisions regarding reservoir management.
Thus,
a) To calculate the pressure at 12 hours of shut-in:
substitute the given values into the pressure buildup equation and solve for P(t=12).
b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.
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Which equation has exactly one solution in common with the equation y=6x-2?
A. 18x - 3y = 6
B. 1/2y = 3x - 2
C. 2y = 4x - 12
D. 18x - 12 = 3y
Answers
Answer:
A. 18x - 3y = 6
Step-by-step explanation:
By taking 3 common from the terms 18x and 3y we get,
3 (6x-3y) = 6
or, 6x - y = 6/3
or, 6x - y = 2
And,
The equation becomes,
y = 6x - 2
The equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.
What is a system of equations?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
By taking 3 commons from the terms 18x and 3y we get,
3 (6x-3y) = 6
6x - y = 6/3
6x - y = 2
The equation becomes,
y = 6x - 2
Therefore, the equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.
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86, 82, 78, 74 , what is the 40th term
Answers
Answer:
Step-by-step explanation:
its subtracting 4 each time
HELP THIS IS DUE TONIGHT AT 12!!!
Answers
Marcus is skiing. He is 869 1/10 get up the mountain. He descends to 450 7/10 feet. What is his change in elevation
Answers
Answer:
418 4/10
Step-by-step explanation:
To answer this we subtract 450 7/10 from 869 1/10.
We must borrow a '1' from 869 1/10: 868 11/10
Now subtract 450 7/10 from 868 11/10:
418 4/10 (CHANGE IN ELEVATION)
This reduces to 418 2/5.
andrew wants the average of his five tests in science to be a 93. what score must he earn on the fifth test if his first four test grades are 87, 89, 97, and 95?
Answers
Andrew needs to score 99 on his fifth science test in order to have an average of 93 across all five tests.
To find out what score Andrew needs to earn on his fifth science test, we can use the concept of averages. The average of a set of numbers is calculated by adding up all the numbers and then dividing the sum by the total number of values.
Andrew has already taken four science tests, and their scores are given as 87, 89, 97, and 95. To calculate the average, we add up these four scores: 87 + 89 + 97 + 95 = 368.
Now, we need to consider the fifth test score that Andrew needs to achieve. Let's call it x. To have an average of 93 across all five tests, we need to divide the sum of all the scores (including the fifth test score) by 5 (the total number of tests): (368 + x) / 5 = 93.
We can solve this equation for x by isolating it on one side. Multiplying both sides by 5 gives us 368 + x = 465. By subtracting 368 from both sides, we find x = 465 - 368 = 97.
Therefore, Andrew needs to score 97 on his fifth science test to have an average of 93 across all five tests.
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Principal Evans has 24 baby chicks.She shared the chicks among 5 classrooms.Each class gets at least 4 chicks.There can be no more than 3 chicks in each cage.
Answers
(7w^2-6w-6) - (4w^2+4w 6)
What’s the constant?
Answers
Answer:
2
Step-by-step explanation:
(7w^2-6w-6)-(4w^2+4w+6)
3w^2-2w
w(3w-2)
Choose all the numbers that are common multiples of 4 and 5.
25
40
50
60
75
80
Answers
Answer:
40
Step-by-step explanation:
it would be 20 too but there is no opition for this i hope i helped
i hope this helps
jane is 3 times as old as kate. in 5 years jane's age will be 2 less than twice kate's. how old are the girls now
Answers
Answer:
Kate is 3 years old, Jane is 9 years old
Step-by-step explanation:
1.) First, assign variables to all of their ages. If we say Kate's age is x, Jane's age is 3 times this, which can be written as j, is 3x.
2.) Jane's age is also 2 less than twice of Kate's in 5 years. This means that her age is also 2(x+5) - 2 = j + 5. With a little simplification, you get that 2x + 8 = j + 5.
3.) Since j, Jane's age, is also 3x, we can substitute 3x in for j in the second equation. If you do this, you get 2x + 8 = 3x + 5.
4.) By moving the x onto one side and the numbers onto another, you get x = 3. X was Kate's age, meaning that Kate is 3 years old.
5.) Finally, since Jane's age is 3 times Kate's age, Jane's age is 3 * 3, which is 9. Jane is 9 years old.
Jane is 9 years old and Kate is 3 years old.To solve the problem, let's first establish variables for Jane and Kate's ages.
Let J represent Jane's age and K represent Kate's age.
According to the student question, Jane is 3 times as old as Kate, which can be represented as:
J = 3K
In 5 years, Jane's age will be 2 less than twice Kate's age, which can be represented as:
J + 5 = 2(K + 5) - 2
Now we can solve the equations step by step:
Substitute the first equation into the second equation to eliminate one of the variables:
3K + 5 = 2(K + 5) - 2
Distribute the 2 on the right side of the equation:
3K + 5 = 2K + 10 - 2
Simplify the equation by combining like terms:
3K + 5 = 2K + 8
Move the 2K term to the left side of the equation:
K = 3
now we know that Kate is currently 3 years old.
Substitute K's value back into the first equation to find Jane's age:
J = 3K
J = 3(3)
Simplify to find Jane's age:
J = 9
So, Jane is currently 9 years old.
Jane is 9 years old and Kate is 3 years old.
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What are independent variables and dependent variables when
conducting a research design to investigate the impact of a school
nutrition program on grade performance of students at high
school?
Answers
Independent variables are the factors that are manipulated or controlled by the researcher in a study. In the context of investigating the impact of a school nutrition program on grade performance of high school students, the independent variable would be the school nutrition program itself.
The researcher would design and implement the program, and this variable would be under their control.
Dependent variables, on the other hand, are the outcomes or variables that are measured in a study and are expected to change as a result of the independent variable. In this case, the dependent variable would be the grade performance of the students. The researcher would collect data on the grades of the students before and after the implementation of the nutrition program, and this would be the variable that is expected to be influenced by the independent variable.
In summary, the independent variable in this research design is the school nutrition program, while the dependent variable is the grade performance of the students. The researcher would manipulate the independent variable (implement the nutrition program) and then measure the dependent variable (student grades) to determine if there is an impact of the program on grade performance.
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