2x to the fourth power + 5x squared + 3, factored
The m6 = (11x + 8)° and m7 = (12x – 4)° What is the measure of 4? m4 = 40° m4 = 48° m4 = 132° m4 = 140°
The measure of angle 4 is 40°. That is, m4 = 40°. The correct option is the first option m4 = 40°
From the diagram, we can observe that angles 6 and 7 are vertically opposite angles.
From one of the angle theorems, we have that vertically opposite angles are equal
That means,
measure of ∠ 6 = measure of ∠ 7
From the question,
we have that, m6 = (11x + 8)° and m7 = (12x – 4)°
Since, the measures of angles 6 and 7 are equal, then we can write that
(11x + 8)° = (12x – 4)°
Now, determine the value of x, we will solve the equation
11x + 8 = 12x – 4
First, subtract 11x from both sides
11x - 11x + 8 = 12x - 11x - 4
8 = x - 4
Now, add 4 to both sides
8 + 4 = x -4 +4
12 = x
∴ x = 12
Now, we will determine the measure of ∠6
m ∠6 = (11x + 8)°
Put x = 12
∴ m ∠6 = (11(12) + 8)°
m ∠6 = (132 + 8)°
m ∠6 = 140°
To determine the measure of ∠4, m4, we will first determine the measure of ∠8.
From the diagram,
m ∠6 + m ∠8 = 180° (Sum of angles on a straight line)
∴ 140° + m ∠8 = 180°
Then,
m ∠8 = 180° - 140°
m ∠8 = 40°
From the diagram, we can observe that angles 4 and 8 are corresponding angles.
Also, from one of the angle theorems, we have that corresponding angles are equal.
Hence, the measure of ∠ 4 equals the measure of ∠ 8.
From above, m ∠8 = 40°
∴ m ∠4 = 40°
Hence, the measure of angle 4 is 40°. That is, m4 = 40°. The correct option is the first option m4 = 40°
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What's the ordered pair ?
decimals between 3.0 and 3.8 with an interval of 0.2 between each pair of decimals
Answer:
Decimals between 3.0 and 3.8 with an interval of 0.2 between each pair of decimals are:
3.2,3.4 and 3.6
Step-by-step explanation:
We have to find decimals between 3.0 and 3.8 with an interval of 0.2 between each pair of decimals
3.0
3.0+0.2= 3.2
3.2+0.2= 3.4
3.4+0.2= 3.6
3.6+0.2= 3.8
Hence, decimals between 3.0 and 3.8 with an interval of 0.2 between each pair of decimals are:
3.2,3.4 and 3.6
A family is comparing different car seats. One car seat is designed for a child up to and including 30 lb. Another car seat is designed for a child between 15 lb and 40 lb. A third car seat is designed for a child between 30 lb and 85 lb, inclusive. Model these ranges on a number line. Represent each range of weight using interval notation. Which car seats are appropriate for a 32-lb child?
The interval notation is:
0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;
The second and third car seats are suitable.
The number lines shows the weights of the car seats which is designed for in comparison the weight of the 32lb child.
Three car seats are designed as follows:
The car seat made for children upto 30lb. The seat for children between 15lbs and 40lbs andThe seat designed for a child between 30 lb and 85 lbAs the seat designed for a child upto and including 30 lb would not be suitable for 32 lb child. Because 32lb is more than the 30 lb.
Now, the seat designed for a child between 30 lb and 85 lb, 30lbs and 85lbs would be suitable as the child is within these weight ranges that is 32lb.
The interval notation is:
0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;
The second and third car seats are suitable.
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Carl, Brian, Dave, and Ashley want to attend the same university. Unfortunately only two spots remain and these four friends have the same GPA, as well as virtually identical community service and leadership experiences. Therefore, the two spots will be determined by their SAT and ACT scores. Carl scored 1,280 on the SAT, while Brian scored 1,325. Dave scored 28 on the ACT, while Ashley scored 30. Use z-scores to determine which two students should be admitted. The mean SAT score was 1,000 with a standard deviation of 175 and the mean ACT score was 20.6 with a standard deviation of 5.2 Both tests are normally distributed.
In a company, it takes 4 employees 4 days to complete a task. It would take 2 employees 8 days to complete the same task. Which function can be used to represent e, the number of employees working on the task, and d, the number of days it takes them to complete that task?
The function representing the relationship between the number of employees and the number of days it takes to complete the task is[tex]\[ e \times d = 16 \][/tex].
To represent the relationship between the number of employees (e) and the number of days (d) it takes to complete a task, we can use the formula:
[tex]\[ e \times d = k \][/tex]
where k is a constant representing the amount of work to be done.
Given the information that 4 employees complete the task in 4 days, and 2 employees complete it in 8 days, we can set up two equations using the formula:
[tex]\[ 4 \times 4 = k \][/tex]
[tex]\[ 2 \times 8 = k \][/tex]
Now, solve each equation for ( k):
[tex]\[ 4 \times 4 = 16 \][/tex]
[tex]\[ 2 \times 8 = 16 \][/tex]
Since both equations give us the same constant ( k ), we can conclude that:
[tex]\[ e \times d = 16 \][/tex]
Therefore, the function representing the relationship between the number of employees and the number of days it takes to complete the task is:
[tex]\[ e \times d = 16 \][/tex]
Which will result in a difference of squares? (–7x + 4)(–7x + 4) (–7x + 4)(4 – 7x) (–7x + 4)(–7x – 4) (–7x + 4)(7x – 4)
Answer:
(–7x + 4)(–7x – 4) Sign changes in the middle of both parenthesis , so this will result in difference of squares
Step-by-step explanation:
The formula for difference of squares
[tex]a^2 - b^2 =(a+b)(a-b)[/tex]
(–7x + 4)(–7x + 4) both parenthesis having same terms so this will not result in difference of squares
(–7x + 4)(4 – 7x) both parenthesis having same terms so this will not result in difference of squares
(–7x + 4)(–7x – 4) Sign changes in the middle of both parenthesis , so this will result in difference of squares
(–7x + 4)(7x – 4) sign changes for both terms in both parenthesis so this will not result in difference of squares
Kate earns $8.50 per hour. How much money will she earn after working 8 hours? She will earn $.
relative maxima and relative minima are called relative_____.
Hint: first 2 letters are ex
Relative maxima and relative minima are called relative extrema.
Given:
The given statement is:
Relative maxima and relative minima are called relative_____.
To find:
The correct word to fill the given blank.
Explanation:
Relative maxima: If the function changes from increasing to decreasing, then the turning point is known as relative maxima.
Relative minima: If the function changes from decreasing to increasing, then the turning point is known as relative minima.
Relative extrema: The turning points relative maxima and relative minima are known as relative extrema.
Therefore, the relative maxima and relative minima are called relative extrema.
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Ricarda earns a $25 allowance each week. How much allowance will she earn after 7 weeks. Explain how to use mental math to solve.
2. Consider the function . a.) Find the inverse of f(x) and name it g(x). Show and explain your work. b.) Use composition to show that f(x) and g(x) are inverses of each other. c.) Draw the graphs of f(x) and g(x) on the same coordinate plane. Explain what about your graph shows that the functions are inverses of each other.
First correct answer will get 25 pts and brainliest!!!! So please help! :D
What is a quick way to determine which savings account will pay the most interest?
1) which expression forms an equation with the given expression?
18-4•3=______
A. 8•4÷4
B. 14-11•2
C. 3(12-9)
D. 12÷3+3
2) choose the expression that completes the equation
24÷6+20=_____
A. 3(7+1)
B. 2(7+10)
C. 4(4+3)
D. 3(7+7)
HELP PLEASEEE
If George received $ 78.00 for his work at Weaver's Store, and he was paid $ 6.00 per hour, how many hours did he work?
Add -12+20, Then divide the sum by -4
if f(x)=2x-4 find f(q+1)
The value of f(q+1) is 2(q-1).
What is a function?A relation or expression involving one or more variables.
Given that, f(x) = 2x - 4
When x = q+1
f(q+1) = 2(q+1) - 4
f(q+1) = 2q + 2 - 4
f(q+1) = 2q - 2
f(q+1) = 2(q-1)
Hence, the value of f(x) when x = (q+1) is 2(q-1)
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what is 6 divided by 46.8
Which irrational number can be multiplied by negative square root of 41 to get a product that equals 1?
For this case we define the following variable:
x: unknown number
We then have the following equation:
[tex]- \sqrt {41} x = 1[/tex]
From here, we clear the value of x.
We have then:
[tex]x = - \frac {1} {\sqrt {41}}[/tex]
Answer:
An irrational number that can be multiplied by negative square root of 41 to get a product that equals 1 is:
[tex]x = - \frac {1} {\sqrt {41}}[/tex]
after 5 years what is the total amount of a compound interest investment of 32,000 at 3% interest, compounded quarterly
A.57.795.56
B.32,426.67
C.43,099.36
D.37,157.89
Which of the following statements describes the process for solving 4x ≥ -24?
Divide both sides of the inequality by -24 and flip the symbol.
Divide both sides of the inequality by -24 but don't flip the symbol.
Divide both sides of the inequality by 4 and flip the symbol.
Divide both sides of the inequality by 4 but don't flip the symbol.
Answer:
Your answer would be D.
Step-by-step explanation:
"you buy a baseball bat and a ball for $1.10. the baseball bat costs $1.00 more than the ball. how much did the ball cost?"
Which property can be used to remove the parentheses in the expression 1.7(x+9)
Circle J and circle K are shown in the diagram below.
What is the total number of lines of tangency that are common to circle J and circle K?
3
2
4
1
Thank you!
If (1, 2) and (3, 4) lie on the same line, give the slope-intercept equation of the line.
Final answer:
The slope-intercept equation of the line that passes through (1, 2) and (3, 4) is y = x + 1, with a slope of 1 and a y-intercept of 1.
Explanation:
To find the slope-intercept equation of a line that passes through the points (1, 2) and (3, 4), we first need to determine the slope of the line. We use the formula for the slope (m) given by the change in y over the change in x, or Δy/Δx. Calculating the slope, we get:
m = (4 - 2) / (3 - 1) = 2 / 2 = 1.
Now we have the slope, we can use the slope-intercept form of the line, which is y = mx + b, where m is the slope and b is the y-intercept. Plugging in one of the points, say (1, 2), into this equation gives us:
2 = (1)(1) + b
Which simplifies to:
b = 2 - 1 = 1
So the y-intercept (b) is 1. Therefore, the slope-intercept equation of the line is:
y = x + 1
What is the slope ? Simplify your answer and write it as a proper fraction improper fraction or integer
Suppose f(x) = x2 and g(x) = 4x2. Which statement best compares the graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) vertically compressed by a factor of 4.
B. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 4.
C. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 4.
D. The graph of g(x) is the graph of f(x) shifted 4 units left.
Determine whether 2y=3x-1 represents a direct variation. if it does, find the constant of variation.
The equation 2y=3x-1 does not represent a direct variation in its strict definition, as it includes a y-intercept. If the y-intercept is ignored, the constant of variation would be k = 3/2.
The equation 2y=3x-1 represents a direct variation if it can be written in the form y = kx, where k is the constant of variation. To determine if this equation represents a direct variation, we can solve it for y:
Divide both sides of the equation by 2 to isolate y:
y = (3/2)x - 1/2.
Since we can express y as an equation of the form y = kx + b, with b being a constant, it does not represent a pure direct variation, as direct variation should have a form y = kx without the constant term.
However, if the question is interpreted to include such linear relationships as direct variations despite the y-intercept, then the constant of variation would be k = 3/2.
How would you graph the solution set of ≤ -18?
closed circle on -3 and shaded to the right
closed circle on -3 and shaded to the left
closed circle on -108 and shaded to the right
closed circle on -108 and shaded to the left
Answer:
Closed circle on -108 and shaded to the left, I took the same lesson and got 100%
Step-by-step explanation:
But your missing part of the question, it's how would you graph the solution set of x/-6 ≤ -18?
Which equation is the inverse of y = x2 – 36?
Answer:
The given equation of the curve is
y= x² - 36
To find it's inverse we have to convert y in terms of x.
So, adding 36 to both sides of equation
→ y + 36=x² -36 + 36
→ y + 36 = x²
→ x² = y+ 36
→ x =[tex]\pm[/tex][tex]\sqrt{y+36}[/tex]
Now, to find inverse you can replace x by y, so by replacing x by y, the above equation becomes
y =[tex]\pm\sqrt{x+36}[/tex]
Second option is correct.