Given:
Angle BAC is 15x-2 degree.
Angle DAC is 7x+4 degree.
The objective is to find the measure of each angle.
Since the given triangle is a right angled triangle.
So the sum of the angles in a right angle is a complementary angle 90 degree.
Then, the value of x can be calculated as,
\(\begin{gathered} 15x-2+7x+4=90^0 \\ 22x+2=90^0 \\ 22x=90-2 \\ 22x=88 \\ x=\frac{88}{22} \\ x=4 \end{gathered}\)Substitute the value of x in each angle.
The measure of angle BAC is,
\(\begin{gathered} \angle BAC=(15x-2)^0 \\ =15(4)^0-2^0 \\ =60^0-2^0 \\ =58^0 \end{gathered}\)The measure of angle DAC is,
\(\begin{gathered} \angle DAC=(7x+4)^0 \\ =7(4)^0+4^0 \\ =28^0+4^0 \\ =32^0 \end{gathered}\)Hence, measure of anlge BAC is 58 degree and the measure of angle CAD is 32 degree.
-12 -9 (t-3) = 78
t=?
Answer:
equals -43
Step-by-step explanation:
Can someone help me with this please?
Answer:
The triangles are similar.
Explanation:
Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.
Can you explain to me how did we get the answer
The end behavior of the polynomials are as follows;
(a) y = x³ - 9·x² + 8·x - 14
End behavior; y → ∞ as x → ∞
\({}\) y → -∞ as x → -∞
(b) y = -8·x⁴ + 13·x + 800
End behavior; y → -∞ as x → -∞
\({}\) y → -∞ as x → ∞
What is the end behavior of a a polynomial?The end behavior of a polynomial is the characteristics of the graph of the polynomial as the input (x-values), tends to plus and minus infinity.
The factors that effect the end behavior of a polynomial are;
The degree of the polynomial, (even or odd)
The sign of the leading coefficient of the polynomial (positive or negative)
The leading coefficient is the coefficient of the term with the highest degree.
(a) The polynomial, function, y = x³ - 9·x² + 8·x - 14
The specified polynomial is a third degree polynomial, with a positive leading coefficient of 1, the end behavior is therefore;
y tends to positive infinity as x tends to positive infinity
y tends to negative infinity as x tends to negative infinity
End behavior;
y → ∞ as x → ∞
y → -∞ as x → -∞
(b) The polynomial function can be expressed as follows;
y = -8·x⁴ + 13·x + 800
The above polynomial of degree 4 is an even degree polynomial
The leading coefficient of the polynomial is -8, therefore, the leading coefficient is negative
The shape of the graph of the polynomial is therefore ∩ shaped, such that the end behavior is as follows;
y-values approaches negative infinity as x approaches negative infinity
y-values approaches negative infinity as x approaches positive infinity
End behavior;
y → -∞ as x → -∞
y → -∞ as x → ∞
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A bag contains quarters and dimes. You are given the number
and the ratio of dimes to quarters. Draw and use a tape diagram to find the
number of quarters.
The tape diagram below can be used to represent the ratio of dimes to quarters.
How to use tape diagram to represent ratio?let
Number of quarters = xNumber of dimes = 15
Ratio of dimes to quarters = 3 : 2
Number of quarters:
3 : 2 = 15 : x
3/2 = 15/x
cross product
3 × x = 15 × 2
3x = 30
x = 30/3
x = 10 quarters
Number of dimes = 8
Ratio of dimes to quarters = 1 : 4
1:4 = 8 : x
1/4 = 8/x
cross product
1 × x = 8 × 4
x = 32 quarters
Number of dimes = 28
Ratio of dimes to quarters = 4 : 3
4 : 3 = 28 : x
4/3 = 28/x
cross product
4 × x = 28 × 3
4x = 84
x = 84/4
x = 21 quarters
Therefore, tape diagram is a diagram that can be used for visual representation of ratio
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Which ordered pairs to the equation 5x+12y=15 (5,-5/6) (-3,5/2) ( -6,15/4) (-5,10/3)
Answer:
All of them
Step-by-step explanation:
All we have to do is replace the x and y with their following coordinates
A.(5, -5/6) - - > 5(5) + 12(-5/6) = 25 + (-10) = 15
15 = 15
Yes
B. ( -3, 5/2) - - > 5(-3) + 12(5/2) = -15 + 30 = 15
15 = 15
Yes
C. (-6, 15/4) - - > 5(-6) + 12(15/4) = -30 + 45 = 15
15 = 15
Yes
D. (-5, 10/3) - - > 5(-5) + 12(10/3) = -25 + 40 = 15
15 = 15
Yes
Please answer this question
Answer:
$40.00 is the answer
Step-by-step explanation:
also can you mark me as a brainlist if you get a chance
Answer: $40.00
Step-by-step explanation:
12 is 30% of 40
If you share seven apples equally with three people, there are 2 1/3 first complete the sentence then briefly explain what a whole number to the denominator of three and the numerator one mean in this problem
The meaning is that "If you share seven apples equally with three people, there are 2 1/3 apples for each person."
How to explain the fraction with a denominator of 3In this context, a "whole number to the denominator of three and the numerator one" refers to the fact that when the seven apples are divided equally among the three people, each person receives a whole number of apples, plus a fraction.
The denominator of the fraction is three because there are three people sharing the apples,
Tthe numerator of the fraction is one because each person receives one of the three equal parts.
The fraction 1/3 represents the amount of the seventh apple that each person receives. So, each person receives 2 whole apples and 1/3 of another apple, for a total of 2 1/3 apples.
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Why did my question, "Describe the effects of the 2009 Samoa earthquake and tsunami" get deleted?
it may be because you put it for math
S vi) The temperature in Gulmerg in Kashmir was-10°C in January and it rose by 44°c to reach the maximum temperature during summer. The maximum temperature during summer in that year was
The maximum temperature during summer in that year was 34°C.
It's not possible for the maximum temperature in Gulmarg, Kashmir to rise by 44°C during the summer.
A temperature rise of that magnitude would be extremely unusual and potentially dangerous.
However, assuming that the question meant to ask about the difference between the minimum temperature in January and the maximum temperature in summer, we can proceed with the calculation.
The minimum temperature in January was -10°C, and if we add 44°C to it, we get:
-10°C + 44°C = 34°C
Therefore, the maximum temperature during summer in that year was 34°C.
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Solve the equation using the quadratic formula. Please help !
Answer:
decimal
x = 5.284 or 0.284
fraction
x = (21.136) / 4 or (1.136) / 4
Step-by-step explanation:
2x² - 10x - 3 = 0
x = [-b ± √b² - 4(a)(c)] / 2(a)
x = {-(-10) ± √[(-10)² - 4(2)(-3)]} / 2(2)
x = [10 ± √(100 + 24)] / 4
x = (10 ± √124) / 4
x = (10 ± 11.136) / 4
x = (21.136) / 4 or (1.136) / 4
x = 5.284 or 0.284
Solve the following equation: -3x + 10 = 21 *
1 point
x = 11/3
x = -11/3
x = 16/3
x = -16/3
x = 3
x = -3
x = 17
x = -17
please help with this.. thankyou
When a system of equations has no solutions, it is referred to as an inconsistent system.
What is equation?An equation is a mathematical statement that two expressions are equal. It consists of two expressions, one on each side of an equal sign. Equations are used to solve problems in mathematics, chemistry, physics, engineering, and other sciences. They can also be used to define relationships between different variables or constants. Equations are an important tool for understanding the world around us.
This means that there is no solution that can satisfy all of the equations at the same time. This can happen when the equations are contradictory, or when one equation is an exact multiple of the other equation. In some cases, a system of equations may have infinitely many solutions, meaning that there are an infinite number of solutions that satisfy the equations. However, in the case of an inconsistent system, no solutions exist.
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Answer:
there is no solution
Step-by-step explanation:
giving brainliest !!!!
Answer:
It is A or D but mostly A is correct.
Step-by-step explanation:
give brainliest
what is 1*5+89 20 points
Answer:
your answer is going to be 94
Step-by-step explanation:
1×5=5
5+89=94
Answer: 1*5+89 = 94
The answer is 94
The price of a computer component is decreasing at a rate of 10% per year. State whether this decrease is linear or
exponential. If the component costs $80 today, what will it cost in three years?
A computer component's price is coming down by 10% annually, which implies that the decrease is exponential.
What distinguishes linear from exponential growth?When the x-values rise by a certain amount, the y-values change in different ways for linear and exponential relationships: The y-values in a linear connection differ by an equal amount. The y-values have identical ratios in an exponential relationship.
When a price decreases initially at a constant pace throughout time, it is considered to be exponential.
It decreases exponentially in this problem.
If the component is now $80,
Its cost after a year is 80x (88/100).
Its cost after the second year is 80x (88/100)x(88/100).
Cost after the third year is equal to 80 x (88/100 x 88/100) = $54.52.
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The Fahrenheit temperature readings on 66 Spring mornings in New York City are
summarized in the table below. Construct and label a frequency histogram of the data
with an appropriate scale.
Temp (°F) Number of Days.
30-39
2
40-49
26
50-59
28
60-69
8
70-79
2
Graph answer Click and drag to make a rectangle. Click a rectangle to delete it.
To construct a frequency histogram based on the given temperature data, we will use the temperature ranges as the x-axis and the number of days as the y-axis.
The temperature ranges and their corresponding frequencies are as follows:
30-39: 2 days
40-49: 26 days
50-59: 28 days
60-69: 8 days
70-79: 2 days
To create the histogram, we will represent each temperature range as a bar and the height of each bar will correspond to the frequency of days.
Using an appropriate scale, we can label the x-axis with the temperature ranges (30-39, 40-49, 50-59, 60-69, 70-79) and the y-axis with the frequency values.
Now, we can draw rectangles (bars) on the graph, with the base of each rectangle corresponding to the temperature range and the height representing the frequency of days. The height of each bar will be determined by the corresponding frequency value.
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Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
Find the 13th term of the geometric sequence 3 -15 75
Answer:
732,421,875
Step-by-step explanation:
You have to find the pattern which in this case is just multiplying by 5 every absolute number. the negatives are only every other one. from knowing this you just have to find all the numbers until 13 and the 13th term in this sequence is 732,421,875
16+(16∠−50)(5+j12)
R=_____ +j____
Answer:
214.504 +j62.132
Step-by-step explanation:
You want the value of the complex expression 16+(16∠−50°)(5+j12).
EvaluateIf you're evaluating expressions like this, you're in a course that allows (or requires) a suitable scientific calculator. The result of using a calculator to evaluate this expression is shown in the attachment. (You can see that the angle mode is set to degrees.)
R = 214.504 +j62.132
GIVING BRAINLIEST
_____ is the use of force to move or change the position or motion of an object.
Work
Acceleration
Friction
Inertia
4.
Choose the best answer.
A(n) _____ is the point that a lever pivots.
bar
pulley
wheel and axle
fulcrum
5.
Choose the best answer.
A(n) _____ is a machine that makes work easier and has no or few moving parts.
complex machine
compound machine
simple machine
easy machine
6.
Choose the best answer.
A(n) _____ is made of two or more simple machines.
complex machine
scientific machine
compound machine
electric machine
7.
Which of these is an example of work being done?
A child pushes a toy car across the floor.
A woman opens a door.
A soccer player hits a ball in the air with his head, and its direction changes.
All of these
8.
Choose the best answer.
A(n) _____ is made of a round shape that rolls and a rod that it turns around.
wheel and axle
fulcrum
pulley
lever
9.
Choose the best answer.
A(n) _____ is made of a bar that pivots at a fixed point.
lever
wheel and axle
pulley
fulcrum
10.
Choose the best answer.
A(n) _____ is an inclined plane wrapped around a post.
lever
screw
wedge
pulley
11.
Choose the best answer.
A(n) _____ is two inclined planes placed back to back.
wedge
pulley
screw
lever
12.
Choose the best answer.
A(n) _____ looks like a ramp.
screw
inclined plane
wedge
pulley
13.
The words that can be used to fill in the blanks are;
3) Work
4) fulcrum
5) simple machine
6) compound machine
7) All of these
8) pulley
9) wheel and axle
10) screw
11) wedge
12) inclined plane
What is force?We know that the term force has to do with a push or a pull force has to do with that which could cause an object to move some distance in the direction of the force that has been applied.
There are several kinds of simple machine. Let us recall that a machine has to do with any material that eases our work. It is the material that helps us to exert a lesser effort in order to move a heavier load.
The various kinds of simple machines that we have are;
LeverWheel and axlePulleyScrew jackThe Lever is a simple machine that is composed of the load, the fulcrum and the effort.
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Y (4)
+4y ′′
+4y=0 A general solution with x as the independent variable is y(x)=
Answer:
Step-by-step explanation:
We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.
For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,
y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0
(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.
Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get
yp″=a1+2a2x....yp‴=2a2+3a3x+....
Substituting the general solution into the non-homogeneous equation, we get
a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)
So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:
a(n+1)=Y(n-2)/n^2
From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.
a hikers map has a scale of 3 inches to 10 miles. the trail is 4 inches long on the map. how long is the actual hike?
Answer:
13 1/3 miles
Step-by-step explanation:
inches/miles = inches/miles
3/10 = 4/x
3x = 40
x = 13 1/3
Unit conversion is the conversion of one unit to another unit with its standard conversion.
3 inches = 10 miles
4 inches = 13.33 miles
The actual length of the trial is 13.33 miles.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
1 hour = 60 minutes
1 minute = 60 seconds
1 km = 1000 m
1 m = 100 cm
We have,
Scale factor:
3 inches = 10 miles
Map:
Length of the trial = 4 inches
The actual length of the trail.
3 inches = 10 miles
Multiply both sides by 4/3.
4/3 x 3 inches = 4/3 x 10 miles
4 inches = 13.33 miles
Thus,
The actual length of the trial is 13.3 miles
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Please help this is for a grade and I need it answered soon
Answer:
option D
Step-by-step explanation:
5c(3c²)³
5c(27c^6)
135c^7
2. The client wants the four kitchen windows to be framed with a special molding. If the
windows are 22 inches by 24 inches , how many total inches of molding are needed fo
the kitchen windows?
Answer:
2,112 inches
Step-by-step explanation:
4 kitchen windows
1 window (22 x 24)
4(22 x 24)
multiplying the brackets by 4 for the 4 windows
4(22 x 24) = 2,112
differentiate y = 8x/ 3 − tan(x)
Answer:
\(\frac{dy}{dx}=\frac{8(xsec^2(x)-tan(x)+3)}{(3-tan(x))^2}\)
Step-by-step explanation:
\(y=\frac{8x}{3-tan(x)}\\ \\\frac{dy}{dx}=\frac{(3-tan(x))(\frac{d}{dx}8x)-(\frac{d}{dx}(3-tan(x)))(8x)}{(3-tan(x))^2}\\ \\ \frac{dy}{dx}=\frac{(3-tan(x))(8)-(-sec^2(x))(8x)}{(3-tan(x))^2}\\ \\ \frac{dy}{dx}=\frac{24-8tan(x)+8xsec^2(x)}{(3-tan(x))^2}\\ \\ \frac{dy}{dx}=\frac{8xsec^2(x)-8tan(x)+24}{(3-tan(x))^2}\\\\ \frac{dy}{dx}=\frac{8(xsec^2(x)-tan(x)+3)}{(3-tan(x))^2}\)
Remember to use the Quotient Rule
What does c equal in the picture?
Answer:8
Step-by-step explanation:
write 5040 in scientific notation
5.04 × 10³
This is the scientific notation.
Answer:
5.04*10³
Step-by-step explanation:
5.04*10³
Evaluate the following expression.
3 to power of 1
Answer:
3
Step-by-step explanation:
it is 3 3x1 is 3
Find
-/16. (4 points)
a
-4
ob
4
Ос
+4
Od
-8
Answer:
4i
Step-by-step explanation:
I hope its not too complicated
\(\sqrt{-16} \\\\\mathrm{Apply\:radical\:rule}:\quad \sqrt{-a}=\sqrt{-1}\sqrt{a}\\\\\sqrt{-16}=\sqrt{-1}\sqrt{16}\\\\\mathrm{Apply\:imaginary\:number\:rule}:\quad \sqrt{-1}=i\\\\=\sqrt{16}i\\\\\sqrt{16}=4\\\\=4i\)
HELP!!
Construct the graph of the direct proportion y=kx for k=1
3,3
Pretty simple.
1 x 3 = 3
The graph of the direct proportion y = kx for k=1 is shown in figure.
What is linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The direct proportion is defined as,
⇒ y = kx
Now, The equation for k = 1 is,
⇒ y = kx
⇒ y = 1x
⇒ y = x
Clearly, It represent the straight line.
Hence, The graph of y = x is shown in figure.
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