Find the sum and express it in simplest form.
(2y2 +9y + 4) + (-3y² - 3y)
Exponent (^)
Enter the correct answer.
Answers
Answer:
To find the sum of the two expressions, we can combine like terms. In this case, we have two terms with a coefficient of -3y² and two terms with a coefficient of -3y, so we can combine them to get:
(-3y² + -3y²) + (-3y + -3y) + (2y² + 9y + 4)
Simplifying the expression gives us:
-6y² - 6y + 2y² + 9y + 4
Combining the like terms again gives us:
-4y² + 15y + 4
Therefore, the sum of the two expressions is -4y² + 15y + 4. This is already in simplest form.
Related Questions
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
The three (3) statements which are true include the following:
A. The radius of the circle is 3 units.
B. The center of the circle lies on the x-axis.
D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r² ....equation 1.
Where:
h and k represents the coordinates at the center of a circle.
r represents the radius of a circle.
From the information provided above, we have the following equation of a circle:
x² + y² – 2x – 8 = 0 ......equation 2.
In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:
x² – 2x + y² = 8 = 0
x² – 2x + (2/2)² + y² = 8 + (2/2)²
x² – 2x + 1 + y² = 8 + 1
(x – 1)² + (y - 0)² = 9 .......equation 3.
Comparing equation 1 and equation 3, we have the following:
Center (h, k) = (1, 0)
Radius (r) = 3
Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).
(x – 0)² + (y - 0)² = 3²
x² + y² = 9.
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The magnitude of the electrostatic force between two point charges Q and q of the same sign is given by F(x)
, where x is the distance between the charges and k is a physical constant (C stands for coulomb, the unit of charge; N stands for newton, the unit of force). Use this information to answer parts (a) through (c) below.
Answers
Answer:
The electrostatic force between two charges Q1 and q is given by
where
ke is the Coulomb's constant
Q1 is the first charge
q is the second charge
r is the distance between the two charges
Re-arranging the formula, we have
and since we know the value of the force F, of the charge Q1 and the distance r between the two charges, we can calculate the value of q:
And since the force is attractive, the two charges must have opposite sign, so the charge q must have negative sign
Step-by-step explanation:
And since the force is attractive, the two charges must have opposite sign, so the charge q must have negative sign.
What is the answer please help no links I will report
Answers
Answer:
Step-by-step explanation:
The answer is False
1. UV = 8 and WX = 5
TU=
WU=
TX=
TV=
Answers
All sides of a rhombus have equal measures, so TU = 8. Since a rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other, WU = 10. The diagonals of a rhombus are also perpendicular, meaning they form right angles. Using the Pythagorean theorem, you can find the length of TX. (TX)^2 + (WX)^2 = (WT)^2. Substituting in known values, (TX)^2 + 25 = 64. Solving gives you TX = the square root of 39. TV is double the length of TX, so TV = 2 times the square root of 39.
What is best estimate mass of a base ball. A-15kilograms B-150grams. C-150kilograms D-15grams
Answers
Answer:
B if not sorry
Step-by-step explanation:
2/3 + (-5/6) - (-1/2)
Answers
The answer would be 0.03
solve by completing the square:
x^2+3x-70=0 (Answer: -10, 7)
x^2=-10x-30 (Answer: { })
help and with explanation; will give brainliest
Answers
Answer:
Step-by-step explanation:
x² + 3x - 70 = 0
x² + 3x = 70
x² + 3x + (3/2)² = 70 + (3/2)²
(x + 3/2)² = 70 + 9/4 = 289/4 = (17/2)²
so
x + 3/2 = ±17/2
x = ±17/2 - 3/2
x₁ = 17/2 - 3/2 = 14/2 = 7
x₂ = -17/2 - 3/2 = -20/2 = -10
x² = -10x - 30
x² + 10x = -30
x² + 10x + (10/2)² = -30 + (10/2)²
x² + 10x + 25 = -30 + 25 = -5
(x + 5)² = -5
\(x+5 = \pm\sqrt{-5}\\x + 5 = \pm i \sqrt{5}\\x = -5\pm i \sqrt{5}\\\\x_1 = -5+ i \sqrt{5}\\\\x _2= -5- i \sqrt{5}\\\)
please give me right answer.
Answers
Answer:
32² = 1024
35² = 1225
71² = 5041
46² = 2116
Step-by-step explanation:
Atmospheric pressure decreases by about 12% for every kilometer you climb. The pressure at sea levelis about 1013 atmospheres.20. Construct a model to represent the atmospheric pressure at a given altitude in kilometers.21. How many atmospheres of pressure will you feel at 5.895 km? (Top of Mt. Kilimanjaro) (round to the nearestatmosphere)22. How many atmospheres of pressure will you feel at 8.848 km? (Top of Mt. Everest) (round to the nearestatmosphere)23. How many atmospheres of pressure will you feel at 0.383 km? (highest point in Indiana) (round to the nearestatmosphere)
Answers
20) We have to model the variation of the atmospheric pressure with the height.
We know that it is 1013 atm at sea level and it decreases by 12% for every kilometer climbed.
Then, we can consider the sea level to be h = 0.
We then will have a pressure P(0) = 1013.
We can also relate the pressures with one kilometer of difference as:
\(\begin{gathered} P(h+1)=P(h)-0.12P(h) \\ P(h+1)=(1-0.12)\cdot P(h) \\ P(h+1)=0.88\cdot P(h) \\ \frac{P(h+1)}{P(h)}=0.88 \end{gathered}\)We can model this type of relations with an exponential model:
\(P(h)=A\cdot b^h\)We then have to find the values of parameters A and b.
We then start with A, that will correspond to the initial value of P, as:
\(P(0)=A\cdot b^0=A=1013\)Then, we can calculate b as:
\(\begin{gathered} \frac{P(h+1)}{P(h)}=0.88 \\ \frac{A\cdot b^{h+1}}{A\cdot b^h}=0.88 \\ b^{h+1-h}=0.88 \\ b^1=0.88 \end{gathered}\)Then, b = 0.88 and we can write the model as:
\(P(h)=1013\cdot0.88^h\)21) We can calculate the pressure when h = 5.895 km using the model as:
\(\begin{gathered} P(5.895)=1013\cdot0.88^{5.895} \\ P(5.895)\approx1013\cdot0.4707 \\ P(5.895)\approx477 \end{gathered}\)22) We now have to calculate the pressure for the top of the Mt. Everest (h = 8.848 km):
\(\begin{gathered} P(8.848)=1013\cdot0.88^{8.848} \\ P(8.848)\approx1013\cdot0.3227 \\ P(8.848)\approx327 \end{gathered}\)23) We finally have to calcualte the pressure for h = 0.383:
\(\begin{gathered} P(0.383)=1013\cdot0.88^{0.383} \\ P(0.383)\approx1013\cdot0.9522 \\ P(0.383)\approx965 \end{gathered}\)Answer:
20) The model is P(h) = 1013*0.88
What is the image point of (3,-4) after a translation left 2 units and up 5 units?
Answers
Answer:
(1,1)
Step-by-step explanation:
3-2=1
-4+5=1
The image point of (3,-4) after a translation left 2 units and up 5 units is (1,1).
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
We are given that;
Point= (3,-4)
Now,
To find the image point of a translation, we can use the following rule:
To translate a point left or right, add or subtract the horizontal distance to the x-coordinate of the point.
To translate a point up or down, add or subtract the vertical distance to the y-coordinate of the point.
In this case, we have a translation left 2 units and up 5 units. This means that we need to subtract 2 from the x-coordinate and add 5 to the y-coordinate of the point (3,-4). Therefore, the image point is:
(3−2,−4+5)
(1,1)
Therefore, by the graph the answer will be (1,1)
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Determine whether the sequence is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or geometric, give the next term in the sequence. 4096, 1024, 256, 64, 16,...
Answers
Answer: geometric series
Step-by-step explanation:
If it is arithmetic, the difference from each term to the next will always be the same.
4096 - 1024 = 3072; 1024 - 256 = 768
3072 ≠ 768. so not arithmetic
If it is geometric, the ratio of each term to the next will always be the same.
4096/1024 = 4
1024/256 = 4
256/64 = 4
64/16 = 4
This is a geometric series. Each term (after the first) is (1/4) of the term before.
Hope this helps.
For homework, a student had to complete 54 problems total. If she finished 9 problems in
class, what is the ratio of problems she still needs to complete to problems that she's
already finished?
Answers
Answer:
10
Step-by-step explanation:
Answer:
45:9
Step-by-step explanation:
Suppose a pizza was cut into 12 equal sized slices. 3/4 of the pizza is left. How many slices are left?
Answers
Answer:
9 Slices
Step-by-step explanation:
multiply each side of the equation by 12x to eliminate the fractions while keeping the equation balanced
12x3/4= 9
I cant solve please help me
Answers
Answer:
Let us set up a ratio to find the relationship between side lengths of the two triangles.
25:10
5:2
We can divide both sides by two, but there's no need as the smaller triangle has multiples of two.
So, if XZ is 6, let's place it into the ratio and find what "x" is.
5(3) : 2(3)
15 : 6
x = 15
HELP PLEASE whats the number for this answer?
ASAP
Answers
Answer:
68°
Step-by-step explanation:
Total angle in a quadrant = 90°
x + 22° = 90°
x = 90 - 22
x = 68°
Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the following exercise.
Find the following sums without using a calculator or a formula. Hint: Apply the procedure used by Gauss. (See the Math Matters on page 31.)
+393 +394 + 395
(a) 1+2+3+4+...+392
(b) 1+2+3+4
x
546 + 547 +548 + 549
(c) 2+4+6+8+...+76 + 78 + 80 +82
Answers
(a) The sum of the series 1+2+3+4+...+392 is 77,028.
(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).
(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.
To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.
(a) For the series 1+2+3+4+...+392:
Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.
(b) For the series 1+2+3+4...x:
To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).
(c) For the series 546 + 547 + 548 + 549:
Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.
The final answer for each part is:
(a) The sum of the series 1+2+3+4+...+392 is 77,028.
(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).
(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.
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Elroy bought a $4210 custom video gam e/ virtual sound system on a special no-interest plan. He made
Answers
The amount of the last payment that Elroy will make is $710, which includes the $200 monthly payment and a balance of $510.
How is the last payment determined?The last payment amount is the result of the mathematical operations of subtraction and multiplication.
The first mathematical operation was the subtraction of the down payment from the total cost of the video game system.
Using multiplication, the monthly payments are determined to be $3,400 for 17 months. This is subtracted from the remaining balance to obtain the last payment amount.
The cost of a custom video game/virtual sound system = $4,210
Down payment = $100
The remaining balance for monthly payment = $4,110 ($4,210 - $100)
Payment period = 18 months (1¹/₂ years)
Monthly payments = $200
Payment for the first 17 months = $3,400 (17 x 200)
Last payment = $710 ($4,110 - $3,400)
Thus, if Elroy makes the minimum monthly payment of $200 till the last payment, then he will pay $710 to settle the account.
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Question Completion:He made a $100 down payment and agreed to pay the entire purchase off in 1 1/2 years The minimum monthly payment is $200 if he makes the minimum monthly payment up until the last payment what will be the amount of his last payment?
The size of a rectangular television screen is usually given by its diagonal measurement. If a flat television screen is 20 inches high and 25 inches wide, what is its size rounded to the nearest inch?
Answers
Answer:
32 inches Aprox
Step-by-step explanation:
To find the size of a rectangular television screen given its height and width, we can use the Pythagorean theorem. The diagonal measurement (size) is the hypotenuse of a right triangle formed by the height and width.
Given:
Height of the television screen (h) = 20 inches
Width of the television screen (w) = 25 inches
Using the Pythagorean theorem:
diagonal² = height² + width²
diagonal² = 20² + 25²
diagonal² = 400 + 625
diagonal² = 1025
Taking the square root of both sides:
diagonal ≈ √1025
diagonal ≈ 32.02
Rounding to the nearest inch, the size of the television screen is approximately 32 inches.
Therefore, the size of the rectangular television screen, rounded to the nearest inch, is 32 inches.
Can anyone tell me how to do this? Step by step
Answers
Step-by-step explanation:
f(x)=x^2-4x-9
g(x)=-3x-5
so when f(g(x)) that x is a number
-3x-5 equals the number in f(x) so that x is -3x-5
f(-3x-5) and if f(x)=x^2-4x-9
then inserting in -3x-5 for x in f(x) and distrubute
(-3x-5)^2-4(-3x-5)-9
9x^2+42x+36
I hope that helps :)
Answer:
9x^2 + 42x + 16
Step-by-step explanation:
f(g(x))
Plug in the expression for g(x)
f(g(x)) = f(-3x - 5)
f(x) = x^2 - 4x - 9
For every x in f(x) replace it with -3x - 5
f(-3x - 5) = (-3x - 5)^2 - 4(-3x -5) -9
Expand
f(-3x - 5) = (9x^2 + 30x + 25) + (12x + 20) - 9
Combine like terms
f(-3x - 5) = 9x^2 + 42x + 16
f(g(x)) = 9x^2 + 42x + 16
An ice cream house has a total of 10 different flavors. They are running a special where you can get 3 sciops for the price of one. How many ways can you order 3 different flavored scoops?
Answers
Answer:
3ways
Step-by-step explanation:
It will be in three ways
Select the correct answer.
Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina?
A.
The equation that represents this situation is t − 3 = 18. Tina is 21.
B.
The equation that represents this situation is t + 3 = 18. Tina is 15.
C.
The equation that represents this situation is 3 − t = 18. Tina is 21.
D.
The equation that represents this situation is -3 − t = 18. Tina is 15.
Answers
Answer:
A is correct.
Isabella earned $129.60 at her job when she worked for 6 hours. How much money
did she earn each hour?
Answers
Answer:
21.6
Step-by-step explanation:
you divide 129.60 by 6 and you get 21.6.
(5+5)x2-12 divided by 4
Answers
Answer:
(5+5)x2-12 = 8
Step-by-step explanation:
5+5=10, 10×2= 20-12 = 8
PLEASE RESPOND FAST I NEED IT ANSWERED
The data set lists the ages of the cast members of a recent children’s play. Find the median age. {14, 11, 8, 12, 5, 3, 17, 10, 8, 11}
Answers
Answer:
Mean: 9.9
Median: 10.5
Step-by-step explanation:
PLS HELP WILL MARK BRAINIEST!!!!TY
Answers
Answer:
19
Step-by-step explanation:
Notice that these two triangles are comprised of the same two lines. Because of this we can assume that \(39 = (2x+1)\)
We can proceed from here.
The parentheses are unnecessary on the right side of the equation because there is nothing else on that side. Lets remove them
\(39=2x+1\)
Now remember that we must do OPPOSITES. do the opposite on both sides. For example lets get rid of the 1. The opposite of 1 is negative 1. So subtract 1 from both sides. We get
\(38=2x\)
now we are making progress.....
the opposite of 2 times x is 2 divided by x. Lets divide 2 from both sides.
\(19=x\)
SUCCESS!
Frances had no money in her checking account. She writes 3 checks for $35 each. The bank imposes a $15 penalty because she has overdrawn her account. How much money is in her account now?
Answers
The money in Frances' account is - $ 120 after the 3 checks and the penalty.
We are given that:
Frances has no money in her account.
Current balance of her account = $ 0
Now she wrote 3 checks of $ 35 each.
Amount written = 3 × $ 35 = $ 105
Now, the balance in her account will be = $ 0 - $ 105 = - $ 105
Also, the bank has imposed a penalty of $ 15 as she has overdrawn her account.
So, the balance now will become:
Balance = - $ 105 - $ 15 = - $ 120
Therefore, the money in Frances' account is - $ 120 after the 3 checks and the penalty.
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Which of the following describes how to calculate net pay?
A)Subtract the total deductions from the net pay.
B)Add the total deductions to the gross pay.
C)Subtract the total deductions from the gross pay.
D) Subtract the total deductions from the take-home pay.
Answers
Answer: C
Step-by-step explanation: The answer is C because it is.
Is my answer correct or incorrect? True or false
Answers
Answer:
Youre correct
Step-by-step explanation:
Answer:
it is true
Step-by-step explanation:
Solve the following inequality:
Answers
Answer:
\(r \geqslant - 16\)
Step-by-step explanation:
\( \frac{ - 10 + r}{2} \geqslant - 13\)
multiply both sides by 2:
\( - 10 + r \geqslant - 26\)
add 10 on both sides:
\(r \geqslant - 16\)
Answer:
\(r \ge -16\)
Step-by-step explanation:
To solve any equation/inequality:
1. get the variable to show up exactly once
2. isolate it
\(\frac{-10+r}{2} \ge -13\)
Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)
\(\frac{-10+r}{2} *2 \ge -13 *2\)
\(-10+r \ge -26\)
Add 10 to both sides, and simplify
\((-10+r)+10 \ge (-26)+10\)
\(r \ge -16\)
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, s shown below. A: 12, 11, 09, 0.4 C 1.0, 1.5, 1.1, 1.3 B: 2.3, 2.1,1.9, 1.6 D0.8,1.3, 1.1, 0.7 The ressults of the analysis are Sumarized in the following ANOVA table F P-value 1818 1.0606 Neighbarhood Error Total 0001 12 4.3644 (a) (Spt) Fill in the blanks in the ANOVA table. (Show your steps for partial credits (b) (2pt) Bsed on the P-value in the ANOVA, you should rejesct) Hp then conclude thnt (reject or not (c) (2pt) The realtor decided to compare the 4 population mes by using the a multiple comparison procedure. In this case, you prefer to uTukey or Bonferroni) because (d) (1pt) Given the multiple comparison procesdr comparisons that can be made in (c), there are
Answers
The solutions are,
(a) 1.1825
(b) 0.0985
(c) Reject the null hypothesis since the test's p-value (0.001) is less than 0.05. One might draw the conclusion that there is evidence of a difference in the mean ratios for the 4 neighborhoods based on the sample data.
Given data,
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood ;
(a) The within-group sum of squares for this analysis will be
4.3644 - 3.1819 = 1.1825
Hence, within the group sum of squares for this analysis is 1.1825.
(b) There are four groups so df for within groups is 12 so the within-group mean squares for this analysis will be,
\(\frac{1.1825}{12}=0.0985\)
(c) Since the p-value of the test (0.001) is less than 0.05, reject the null hypothesis. That is based on sample evidence one can conclude that there is evidence of a difference in the mean ratios for the 4 neighborhoods.
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