Which expression is equivalent to (2x^2 + 4x – 7)(x – 3)?
A. x(2x^2 + 4x – 7) + 3(2x^2 + 4x – 7)
B. x(2x^2 + 4x – 7) – 3
C. –3x(2x^2 + 4x – 7)
D. (2x^2 + 4x – 7)(x) + (2x^2 + 4x – 7)(–3)
The expression (2x² + 4x – 7)(x – 3) is equivalent to the expression (2x² + 4x – 7)(x) + (2x² + 4x – 7)(–3) option (D) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
= (2x² + 4x – 7)(x – 3)
After using the distributive property:
= (2x² + 4x – 7)(x) + (2x² + 4x – 7)(–3)
Distributed the whole term (2x² + 4x – 7) with (x - 3)
Thus, the expression (2x² + 4x – 7)(x – 3) is equivalent to the expression (2x² + 4x – 7)(x) + (2x² + 4x – 7)(–3) option (D) is correct.
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Find the slope of the line on the graph. Write your answer as a fraction or a whole number, not a mixed number or decimal.
Answer: -3
Step-by-step explanation:
The points (1,1) (2,-2) plugged into slope formula m = y2 - y2/x2 - x1
-2 is y2
1 is y1
2 is x2
1 is x1
Subtract and simplify
HELP Please THANKS (;
What is the fifth term in the expansion of (3x - 3y)7?
__ x3y4
Answer:
76545
Step-by-step explanation:
got it write on edge :)
If one honey bee makes 1/2 teaspoon of honey during its lifetime, how many honey bees are needed to make 1/2 teaspoon of honey
equations that look different but have the same solution are said to be
a. equivalent
b. expressions
c. equals
d. similar
e. radical
the question is............
a triangle has two sides of lengths 7 and 9.what value could the length of the third side be?
Answer:
13, 10, 8, 5
Step-by-step explanation:
2+7=9 9=9 the requirment is it has to be greater than the third length not equal to
A parent rewards a child with 50 cents for each correctly solved mathematics problem and fines the child 30 cents for each incorrectly solved problem. if the child nets $22.00 after 100 problems. how many problems were solved correctly?
x = correct answer
y = incorrect answer
0.50x-0.30(100-x)=22.00
0.50x-30.00+0.30x=22.00
0.80x=22.00+30.00
0.80x=52.00
x=52.00/0.80
x= 65
y=100-65 = 35
0.5x65 = 32.50
35*0.30=10.5
32.5-10.5 = 22
there were 65 correct answers
Answer:
65 problems were solved correctly, 35 incorrecly.
Step-by-step explanation:
1. Data:
Total answers= 100
50 cent = $0.50 for each correct answer
-30 cent = -$0.30 for each incorrect answer
Net reward= $22.00
2. Define Variables:
x= Correct answers
y= Incorrect answers
3. Formulate the Equations
Total number of answers (Eq 1)
[tex]x+y=100\\y=100-x[/tex]
Net reward (Eq 2)
[tex]0.50*x-0.30*y=22.00[/tex]
4. Solve by replaccing the Eq 1 in Eq 2 as follows:
[tex]0.50*x-0.30*y=22.00\\0.50*x-0.30*(100-x)=22.00[/tex]
5. Apply distrivutive property and operate:
[tex]0.50x-(0.30*100)+(0.30*x)=22.00\\0.50x-30.00+0.30x=22.00[/tex]
6. Separate numbers and variables on each side of the equation and solve
[tex]0.50x+0.30x=22.00+30.00\\0.80x=52.00[/tex]
7. Solve x
[tex]x=\frac{52.00}{0.8} \\x=65[/tex]
Now you know that correct answers are equal to 65
8. Find Incorrect Answers with Eq 1.
[tex]y=100-x\\y=100-65\\y=35[/tex]
Now you know that incorrect answers are equal to 35
9. Answer
65 problems were solved correctly, 35 incorrecly.
The camera melissa wanted for her birthday is on sale at 27%off the usual price. theamount of the discount is $99.90.what was the original price of the camera?$nothing
divide the discount by the percentage off
so:
99.90/0.27 = 370
the original price was 370 dollars
If a cone and a sphere have the same radius and the same height what is the relationship among the volumes of the two shapes
Answer:
the volume of the sphere will be 4 times the volume of the cone;
Step-by-step explanation:
The question is on volume comparison
Volume of a sphere=4/3 ×r³
Volume of a cone= /3×r²h
where r is the radius and h is the height
Apply the condition
If r=h=1 unit
Then volume of sphere will be= 4/3 × ×1³ = 4/3
And volume of the cone will be= /3 ×1²×1 =/3
We can see the volume of the sphere will be 4 times the volume of the cone;
4/3 = 4×/3
If tan y = 3 over y and cos x = y over z what is the value of sin x??
A. sin x = 3/z
B. sin x = 3y
C. sin x = z/3
D. sin x = 3z
Answer: (A) sin x° = 3/z
Step-by-step explanation: i couldnt find it anywhere else but i figured it out and dont worry i got it right on the quiz
Someone help me please !
AE x BE = DE x CE
6x5 = 30
6 x DE = 30
DE = 30/6 =5
DC = DE +CE = 5+6 =11
Answer is C) 11
2x^3y + 18xy - 10x^2y - 90y Part A: Rewrite the expression so that the GCF is factored completely. (3 points)
To factor 2x^3y + 18xy - 10x^2y - 90y, find the GCF of the terms, rewrite the expression, factor out the GCF from the terms inside the parentheses, and simplify the expression.
Explanation:To factor the expression 2x^3y + 18xy - 10x^2y - 90y, we can begin by finding the greatest common factor (GCF) of the terms. The GCF of the coefficients is 2, and the GCF of the variables is y.
So, we can rewrite the expression as 2y(x^3 + 9x - 5x^2 - 45).
Next, we can factor out the GCF from the terms inside the parentheses. The GCF of x^3, 9x, -5x^2, and -45 is x. Factoring out x, we get x(x^2 + 9 - 5x - 45).
Finally, we simplify the expression inside the parentheses. Rearranging the terms, we have x(x^2 - 5x + 9 - 45). Combining like terms, we get x(x^2 - 5x - 36).
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a hot air balloon holds 3,249 cubic meters kf helium. the density of the helium is 0.1785 kilograms per cubic meter. how many kilograms of helium does the balloon contain, round to the nearest tenth of a kilogram?
Use the drop-down menus to complete each statement to show why √65 is between 12 and 18.
Answer:
12 < 6√5 < 18
Step-by-step explanation:
It has been given in the question 4 < 5 < 9 and we have to show 6√5 is between 12 and 18.
For box number 1.
4 < 5 < 9 ⇒ √4 < √5 < √9
For the box number 2.
√4 < √5 < √9 ⇒ 2 < √5 < 3
For the box number 3.
we multiply the inequality by 6.
6×(2 < √5 < 3) ⇒ 6×2 < 6×√5 < 6×3
Therefore final answer is 6×2 < 6×√5 < 6×3 ⇒ 12 < 6√5 < 18
The square root of 65 (√65) falls between 8 and 9, as these are the square roots of the closest perfect square numbers (64 and 81 respectively). The range of 12 to 18 provided in the question seems incorrect.
Explanation:The student's question is referring to the mathematical concept of square roots of numbers. The square root of a number is a value which, when multiplied by itself, yields the original number. In the case of √65, we need to locate it between two perfect square numbers, which are 64 (8^2) and 81(9^2). As a result, √65 should fall between 8 and 9.
However, the interval of 12 and 18 as stated in the question seems to be a mistake, as they are not the correct boundaries for the value of √65. Please verify the numbers in your question.
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Show that the equation is not an identity by finding a value of x for which both sides are defined but not equal. cos x - cos x sinx = cos3 x
Answer:
The answer is pi/4
Step-by-step explanation:
You substitute each x for "pi/4", you will see that the equation is incorrect, the two values are no longer equal.
The equation is not an identity. Value of x = nπ, where n∈I , I → set of integers, for which both sides are defined but not equal.
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
We have the equation,
cos x - (cos x) (sin x) = cos³x
Simplifying,
cos x [ 1 - (sin x) ] = cos²x (cos x)
1 - sinx = cos²x
1 - sinx = 1 - sin²x
1 - sinx = 1² - sin²x
1 - sinx = (1 - sinx)(1 +sinx)
1 = 1 + sinx
sinx = 0
x = nπ, where n∈I , I → set of integers.
It is not an identity equation.
cos x - (cos x) (sin x) ≠ cos³x
Therefore, both sides are defined but not equal.
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Solve 3x2 + 2x + 7 = 0. Round solutions to the nearest hundredth. (5 points)
x ≈ −1.90 and x ≈ 1.23
x ≈ −1.23 and x ≈ 1.90
x ≈ −0.44 and x ≈ −3.56
No real solutions
Answer:
The answer is No Solutions Look Below
Step-by-step explanation:
How many different 1010-letter permutations can be formed from 88 identical h's and two identical t's?
A right triangle has a side with length 12 in and a hypotenuse with length 20 in. find the length of the second leg (in inches). (round to the nearest hundredth if needed)
Jamie has invested $1500 in a savings account. Each month the account pays an interest of 3.8%. How much money will she have in her account 4 years later if she does not make any deposits or withdrawals (round to the nearest dollar)?
A) $1,257
B) $1,557
C) $1,559
D) $2,341
Answer:
$4236.
Step-by-step explanation:
We have been given that Jamie has invested $1500 in a savings account. Each month the account pays an interest of 3.8%. We are asked to find the total amount Jamie will have in her account after 4 years.
We will use simple interest formula to solve our given problem.
[tex]A=P(1+rt)[/tex], where,
A = Final amount after t years,
P = Principal amount,
r = Interest rate in decimal form,
t = Number of years.
Let us convert our given rate in decimal form.
[tex]3.8\%=\frac{3.8}{100}=0.038[/tex]
Since the we have been given monthly interest rate, so we will convert the given rate to annual interest rate by multiplying 0.038 by 12.
Upon substituting our given values in above formula we will get,
[tex]A=\$1500(1+0.038*12*4)[/tex]
[tex]A=\$1500(1+1.824)[/tex]
[tex]A=\$1500(2.824)[/tex]
[tex]A=\$4236[/tex]
Therefore, Jamie will have $4236 in her account after 4 years.
Jacob and Isaiah are brothers. Their combined ages are 63. Jacob is 7 years older than Isaiah. How old are each of the boys?
Final answer:
To solve this problem, set up a system of equations and solve for the variables. Isaiah is 28 years old and Jacob is 35 years old.
Explanation:
To solve this problem, we can set up a system of equations.
Let's say Isaiah's age is represented by x. Jacob's age is then represented by x + 7, since he is 7 years older than Isaiah.
We know that the sum of their ages is 63, so we can set up the equation: x + (x + 7) = 63.
Simplifying the equation gives us: 2x + 7 = 63.
Subtracting 7 from both sides of the equation gives us: 2x = 56.
Dividing both sides of the equation by 2 gives us: x = 28.
So, Isaiah is 28 years old, and Jacob is 28 + 7 = 35 years old.
Charmaine pays $848 for landscaping rocks for a project. The cost per pound is 32 cents. How many pounds did she purchase?
Answer:
D
Step-by-step explanation:
Find the area of the square.
Why is 8.8 classified as a rational number?
John's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs John $4.70 per pound, and type B coffee costs $5.90 per pound. This month, John made 181 pounds of the blend, for a total cost of $967.10 . How many pounds of type A coffee did he use?
A +B = 181
A=181-B
4.70A+5.90B= 967.10
4.70(181-B) +5.90B =967.10
850.70-4.70B+5.90B=967.10
850.70+1.2B =967.10
1.2B=116.40
B =116.40/1.2 = 97
A=181-97 = 84 pounds of type A coffee
In a plane, line N is parallel to line O, Line O is parallel to P, and line L is perpendicular to line N. Which must be true?
A) N||L
B) N||P
C) L||O
D) P||L
Answer:
The correct answer is option B) N || P
Step-by-step explanation:
N || P.
As it is given, in a plane, line N is parallel to line O, Line O is parallel to P, and line L is perpendicular to line N.
Since, N is parallel to O, and O is parallel to P, then N must be parallel to P.
So, option B is correct.
The sum of three numbers is 91 . the third number is 2 times the first. the first number is 9 more than the second. what are the numbers?
You are taking a multiple-choice test that has 10 questions. each of the questions has four answer choices, with one correct answer per question. if you select one of these four choices for each question and leave nothing blank, in how many ways can you answer the questions?
The sum of three consecutive odd integers is 207. What are the integers?