How to find the product of rational expressions
Which number belongs to the solution set of the equation below? x - 7 = 35
A) 22
B) 28
C) 42
D) 41
21. The Johnsons framed a family picture to hang on the wall. The perimeter of the frame is 72 inches. Use the formula P = 2 l + 2 w to find the length of the frame if the width is 14 inches. 21. The Johnsons framed a family picture to hang on the wall. The perimeter of the frame is 72 inches. Use the formula P = 2 l + 2 w to find the length of the frame if the width is 14 inches.
How many regions would a net for a three-dimensional solid like the one shown have?
Answer:
A
Step-by-step explanation:
A 16 ounce jar of peanut butter costs $1.98. What is the price per ounce, rounded to the nearest hundredths place?
60 is 300% of what number
7.What are the steps that you would follow to recreate a triangle using a protractor, a string, and the AAS Congruence Theorem?
ANSWER:
To construct a triangle given one side and the angle at each end of it with compass and straightedge or ruler. It works by first copying the line segment to form one side of the triangle, then copy the two angles on to each end of it to complete the triangle. Follow these steps to draw the recreate a triangle using a protector, a string and angle, angle side congruence theorem.
STEP-BY-STEP EXPLANATION:
Step 1: You will need to choose two angle and one length for both triangle. Noted that the two angle and one length must be the same for both triangle.
Step 2: Draw a long line on a paper
Step 3: Use a ruler to measure the length ,and then make a mark on the string.
Step 4: Use the string to mark on the long line.
Step 5: Use a protractor to measure
Step 6: Use AAS Congruence Theorem to prove that both triangle are congruent.
The size S of a tumor in mm cubed is given by S=2^t, where t is the number of months since the tumor was discovered a: what is the total change in the size of the tumor during the first 6 months?
and b: what is the average rate of change in the size of the tumor during the first 6 months?
and c: estimate the rate at which the tumor is growing at t=6?
a. the total change in the size of the tumor during the first 6 months is 64 - 1 = 63 mm³.
b. the average rate of change in the size of the tumor during the first 6 months is 10.5 mm³ per month.
c. the estimated rate at which the tumor is growing at t = 6 is approximately 44.352 mm³ per month.
a) Total change in the size of the tumor during the first 6 months:
To find the total change in the size of the tumor, we need to subtract the initial size from the size after 6 months. Since [tex]\( S = 2^t \)[/tex], we can calculate the size at t = 6 by plugging in t = 6 into the equation. Then, we can subtract the initial size from this value.
[tex]\[ S(6) = 2^6 = 64 \][/tex]
The initial size is given by [tex]\( S(0) = 2^0 = 1 \).[/tex]
So, the total change in the size of the tumor during the first 6 months is 64 - 1 = 63 mm³.
b) Average rate of change in the size of the tumor during the first 6 months:
The average rate of change is given by the total change divided by the number of months. We already found the total change (63 mm³), and the number of months is 6.
[tex]\[ \text{Average rate of change} = \frac{\text{Total change}}{\text{Number of months}} = \frac{63}{6} = 10.5 \][/tex]
So, the average rate of change in the size of the tumor during the first 6 months is 10.5 mm³ per month.
c) Estimate the rate at which the tumor is growing at t = 6:
To estimate the rate at which the tumor is growing at t = 6, we can use calculus to find the derivative of the function [tex]\( S(t) = 2^t \)[/tex] with respect to t. The derivative represents the rate of change of S with respect to t at any given time.
[tex]\[ \frac{dS}{dt} = \frac{d}{dt} (2^t) = (\ln 2) \cdot (2^t) \][/tex]
Now, plug in t = 6 to find the rate of change at that specific time.
[tex]\[ \frac{dS}{dt}\bigg|_{t=6} = (\ln 2) \cdot (2^6) \][/tex]
[tex]\[ \frac{dS}{dt}\bigg|_{t=6} = (\ln 2) \cdot 64 \][/tex]
Since [tex]\( \ln 2 \approx 0.693 \)[/tex], we have:
[tex]\[ \frac{dS}{dt}\bigg|_{t=6} \approx 0.693 \cdot 64 \approx 44.352 \][/tex]
So, the estimated rate at which the tumor is growing at t = 6 is approximately 44.352 mm³ per month.
Let w represent the possible weights of boxes on a delivery truck. For this type of delivery, the weight of the box must be within 8 pounds of a standard lifting weight of 48 pounds. Write an inequality to describe the possible weights of boxes.
A. |w – 48| ≥ 8
B. |w – 48| ≤ 8
C. |w – 48| < –8
D. |w – 48| > –8
Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natural gas, y.
750x + 17y = 141.61
300x + 30y = 75.90
Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y. Which statement explains Karina’s solution?
a. The cost of electricity is $0.17 per unit.
b. The cost of natural gas is $0.20 per unit.
c. The cost of electricity is $0.72 per unit.
d. The cost of natural gas is $0.83 per unit.
D: The cost of natural gas is $0.83 per unit.
Answer:
Option d is correct
The cost of natural gas (y) = $0.83 per unit
Step-by-step explanation:
Given the system of equation:
750x + 17y = 141.61 ......[1]
300x + 30y =75.90 ......[2]
where x is the cost of electricity and y is the costs of natural gas.
Multiply equation [1] by 30 and equation [2] by 75 we get;
[tex]30 \cdot (750x + 17y) = 30 \cdot 141.61[/tex]
Simplify:
22500x + 510y = 4248.3 ......[3]
[tex]75 \cdot (300x + 30y) = 75 \cdot 75.90[/tex]
Simplify:
22500x + 2250y = 5692.5 .......[4]
Subtract equation [3] from [4] we get;
1740 y = 1444.2
Divide by 15 both sides, we get
116 y = 96.28
Since, Katrina solves the above system using linear equation and arrives at the equation :
116 y = 96.28
Division property of equality states that divide the same number to both sides of an equation:
Divide by 116 to both sides of an equation, to solve for y;
[tex]\frac{116 y}{116} =\frac{96.28}{116}[/tex]
Simplify:
y = 0.83 where y represents the cost of natural gas
Therefore, the cost of natural gas y ,is, $ 0.83 per unit.
Ryan throws a tennis ball straight up into the air. The ball reaches its maximum height at 2 seconds. The approximate height of the ball x seconds after being thrown is shown in the table.
y = –17(x)(x – 4)
y = –16(x)(x – 4)
y = –16(x – 2)^2 + 68
y = –17(x – 2)^2 + 68
Answer: C - Y = -16(x- 2)^2 + 68
Step-by-step explanation:
Edge 2023
Final answer:
The correct quadratic equation that models the ball's vertical motion is y = –16(x – 2)² + 68, since it reflects the ball reaching its maximum height at 2 seconds and the vertex of the parabola being the highest point of the ball's path.
Explanation:
The question involves finding an equation that models the height of a tennis ball thrown straight up into the air after a certain number of seconds. Given that the ball reaches its maximum height at 2 seconds, we can determine which equation best describes the ball's vertical motion. The correct equation will show the ball peaking at 2 seconds and then descending symmetrically in a parabolic path.
The equation that correctly models the motion of the ball in this context is y = –16(x – 2)² + 68. This quadratic equation is in the vertex form of a parabola, where the maximum height is represented by the vertex point (2, 68), and the vertex is the highest point of the parabola since the coefficient of the squared term is negative.
When x is 2 seconds, the equation simplifies to y = –16(0)²+ 68, which results in y = 68, demonstrating that the maximum height of 68 is indeed reached at 2 seconds after the ball is thrown, thus supporting that this is the correct quadratic equation for the scenario.
What is the length of the altitude of the equilateral triangle below
Answer
Find out the altitude of the equilateral triangle .
To proof
By using the trignometric identity.
[tex]tan\theta = \frac{Perpendicular}{base}[/tex]
As shown in the diagram
and putting the values of the angles , base and perpendicular
[tex]tan 60^{\circ} = \frac{a}{4\sqrt{3}}[/tex]
[tex]tan 60^{\circ} = \sqrt{3}[/tex]
solving
[tex]\sqrt{3} = \frac{a}{4\sqrt{3}}[/tex]
[tex]a = \sqrt{3}\times 4 \sqrt{3}[/tex]
As
[tex]\sqrt{3}\times \sqrt{3} = 3[/tex]
put in the above
a = 4 × 3
a = 12 units
The length of the altitude of the equilateral triangle is 12 units .
Option (F) is correct .
Hence proved
Answer:
F. 12
Step-by-step explanation:
We have been given an image of a triangle and we are asked to find the length of the altitude of our given triangle.
Since we know that altitude of an equilateral triangle splits it into two 30-60-90 triangle.
We will use Pythagoras theorem to solve for the altitude of our given triangle.
[tex]\text{Leg}^2+\text{Leg}^2=\text{Hypotenuse}^2[/tex]
Upon substituting our given values in above formula we will get,
[tex](4\sqrt{3})^2+a^2=(8\sqrt{3})^2[/tex]
[tex]16*3+a^2=64*3[/tex]
[tex]48+a^2=192[/tex]
[tex]48-48+a^2=192-48[/tex]
[tex]a^2=144[/tex]
Upon taking square root of both sides we will get,
[tex]a=\sqrt{144}[/tex]
[tex]a=12[/tex]
Therefore, the length of the altitude of our given equilateral triangle is 12 units and option F is the correct choice.
25% of what number is 17
The daily rainfall during a two week period in April was: 1, 0.5, 0.3, 0, 0 ,0, 1.2, 3, 0, 1.1, 0.7, 2, 1.3, 2 inches. What was the mode during this two week period?
Answer: 0.3 is the mode
Step-by-step explanation: The mode is what number shows up the most and 0.3 shows up 3 times.
0 shows up twice
Percent change 74 to 85
Which equation is satisfied by all of the plotted points?
A. y = 2x
B. y = x + 3
C. y = 2x + 1
D. y = -2x
E. y = x
F. y = 3x -3
The answer is y= -2x
The perimeter of the rectangle below is 128 units. Find the length of side VW .
Write your answer without variables.
3 times a number divided by 2
Expand 2x (3x+2y) Thanks
how to write 2/5 as a decimal
Write 702,001 in Expanded Form. (No spaces in answer) ...?
Jim Debt was reviewing the total accounts receivable. This month he received $80,000 from Credit customers. This represented 40 percent of all receivables due. The total amount of accounts receivable is ...?
40% = 80,000
20% = 40,000
x5 = 100% = 200,000
How many times does 59 go into 295?
9x-3y=3; 3x+8y=-17
I want to know the steps and answers
You roll 1 red and 1 white dice. What is the probability that the number on the red die is larger than the number on the white die?
can anyone help me?:( ...?
Which answer is an equation in point-slope form for the given point and slope? Point: (1,9); Slope:5
y - 1 = 5(x + 9)
y + 9 = 5(x - 1)
y - 9 = 5(x - 1)
y - 9 = 5(x + 1)
Think the answer is C. DO NOT JUST AGREE WITH ME I think I'm wrong.
Thanks to whoever is going to answer. I will be marking the best answer the brainliest answer.
The answer is indeed C.
point slope form is: y - y1=m(x - x1)
we substitute the values in; y1= 9; x1=1
and of course, the slope is 5
which gives us
y-9=5(x - 1)
Solve for x.
−5x−4(x−6)=−3
Enter your answer in the box.
x =
how do u right this Seven less than the quotient of x and 9
Answer:
(x÷9)−7 is your answer.
your new cell phone plan charges $50 per month for 400 minutes of talk time. the plan charges $0.10 for each additional minute you talk. you use 50 additional minutes this month. what is your bill for the month?
Answer:
$55
Step-by-step explanation:
What is the equation in point-slope form of the line passing through (−1, 3) and (1, 7)
y − 7 = 4(x − 1)
y − 7 = 2(x − 1)
y − 3 = 2(x − 1)
y − 3 = 4(x + 1)