Question 8 of 10
What are the zeros of f(x) = x² − 8x + 16?
A. x= -4 and x = 4
B. x=-2 and x = 8
C. x = 4 only
D. x = -4 only
Answer:
c ×=4, only
Step-by-step explanation:
4*-8×+16=0
16-32=-16
-16=-16
Answer:
D. x=4 only
Step-by-step explanation:
You can solve using the quadratic equation which is [tex]x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}[/tex]
where in this case a=1, b=-8, and c=16. But there is any easier way to solve the equation. You can solve by completing the square which consists of moving the constant to the right side and then adding [tex](\frac{b}{2})^2[/tex]. To both sides that way you can rewrite the left side as a perfect square binomial. This is because [tex](x+b)^2[/tex] will expand to [tex]x^2 + 2xb + b^2[/tex]. So when you add [tex](\frac{b}{2})^2[/tex] to both equations. You're able to rewrite the left side as [tex](x+(\frac{b}{2}))^2[/tex]. Because once you expand it out, it becomes [tex]x^2 + 2(\frac{b}{2})x + (\frac{b}{2})^2[/tex]. Which simplifies to [tex]x^2 + bx + (\frac{b}{2})^2[/tex] which is the original equation. In this case there is no need to move the constant, which in this case is 16, to the other side. Since if you calculate the value of (-8/2)^2 it's equal to 16! So this can already be written as a perfect square binomial.
So the equation becomes
[tex]0 = (x+\frac{b}{2})^2[/tex]
Plug values in
[tex]0 = (x+(-\frac{8}{2}))^2[/tex]
Simplify
[tex]0 = (x-4)^2[/tex]
Take the square root of both sides
[tex]0 = x-4[/tex]
Add 4 to both sides
[tex]4 = x[/tex]
What is the decimal multiplier to increase by 93%?
Answer:
0.93
Step-by-step explanation:
15 points for this need help badly
Answer:
check image below
Step-by-step explanation:
What is the length of the missing side of this triangle?
A
2
B
10
C
50
D
100
top side is 26 bottom side is 24 left side is whats missing
Answer:
B
Step-by-step explanation:
pythagorus theorem
a² + b² = c²
c² - b² = a²
26² - 24² = a²
676 - 576 = a²
a² = 100
a = 10
A classroom monitors chicken eggs in various temperatures. The table shows the class's recorded results. Using the data in the table, a conclusion is made by calculating probabilities related to a randomly selected egg.
(see attachment for table)
Based on the information, which statement about the eggs is correct?
Given the egg has _______, the egg was kept warmer than room temperature.
answer choices for blank: hatched, not hatched
Given the egg has hatched, the egg was kept warmer than room temperature.
Given:Cool Room temperature Warm Total
Hatched 5 16 21 42
Unhatched 18 10 4 32
Total 23 26 25 74
To fill the blank we need to analyse the temperature carefully if see the table then cool hatched eggs are 5 , unhatched cool eggs are 18, eggs on room temperature and hatched are 16, eggs on room temperature and unhatched are 10, warm hatched eggs are 21 and warm unhatched eggs
So we can notice that hatched eggs are more in room temperature.
Hence hatched eggs are more in room temperature.
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Answer:
Given the egg has hatched the egg was kept warmer than room temperature.
Hope this helped!
hii can someone help thank you
two number cubes are rolled. Deterimine the number of ways that you could get a sum that is less than 5. The number cube is out of 6
Answer: six ways
Step-by-step explanation: The pairs when the cube is rolled that are less than five would be; (1,1), (1,2), (1,3), (2,1), (2,2), (3,1) since each cube is out of six.
Hii! would anyone mind helping me out?
Find the center of this hyperbola
[tex]\large\boldsymbol{9x^2-y^2-72x+8y+119=0}[/tex]
[tex]\bigstar[/tex]
[tex]\underbrace[/tex]
Answer:
(4, 4)
Step-by-step explanation:
This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.
[tex]\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1[/tex]
Match the values in this hyperbola to those of the standard form. The variable h represents the x-offset from the origin, k represents the y-offset from origin, a.
a = 1
b = 3
k = 4
h = 4
Thus,
[tex](x-4)^2 - \frac{(y-4)^2}{9} = 1[/tex]
The center of a hyperbola follows the form of (h, k). Substitute in the values of h and k.
= (4, 4)
A recipe calls for 4 1/2 cups of flour. if you only make half of the recipe, then how many cups of flour do you need? express your answer as a mixed number. please help
Answer:
2 1/4
Step-by-step explanation:
Half of 4 is 2 and half of 1/2 is 1/4 so half of 4 1/2 is 2 1/4
PLease help due today! I will give brainliest!!
Select the correct answer.
Simplify the expression.
[tex][tex]\sqrt[5]{224x^{11}yx^{8} }[/tex][/tex]
The water was pumped out of a backyard pond what is the domain of the graph that 70 time 6
The domain of the given graph is the set of all real numbers from 0 to 8.
How to find the domain of a Graph?The graph showing the water depth on the y-axis in inches against the time in minutes on the x-axis has been attached.
Now, domain is the set of all possible input values and from the graph we see that the set of all possible input values are between 0 and 8.
Thus, we can conclude that the domain of the given graph is the set of all real numbers from 0 to 8.
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A. Does the relationship of weeks passed and total number of followers represent a linear function? (0.5 points) B. What is the independent variable in the situation(0.5 points) C. What is the dependent variable in the situation? (0.5 points ) D. What is the slope of the line ? What does the slope represent in this scenario ? (0.5 points) E. What is the y-intercept of the line? What does the y intercept represent in this scenario? (0.5 points) F. Write the equation in slope intercept form that represents the situation (points ) G. What is the domain ? (Inequality notation ) (0.5 points) H. What is the range ? ( Inequality notation ) (0.5 points) How many weeks would it take Jorge to get 100 followers ? (points ) J. How many followers will Jorge have after 12 weeks ? (0.5 points)
The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
a) Yes it does, because the graph of their relationship is a Straight line
b) Independent variables are variables whose variation does not depend on another. Number of works does not depend on followers. Therefore, it is independent
C)number of followers depend on the number of locks passing. It is dependent.
D) Slope = (Y₂- Y₁)/(x₂-x₁) = (100-82)/ (3-0) = 18/3 = 6
It represents the increase in number of followers per week,
E) y-intercept is value of y when x=0
y-intercept = 82. It means his initial number of followers
F) Slope-intercept form → y = mx + c m = slope горе C = y-intercept y = no of followers x= weeks.
Y=6x+82
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I know it’s simple but I’ve never been good at this topic please help —— 1232÷14
Answer:
88
Step-by-step explanation:
Write the number in standard notation: 5.32 x 106?
Answer:
5.32⋅10−6
Step-by-step explanation:
Answer:
5320000
Step-by-step explanation:
standard notation form : 5320000
Is the following statement a good definition? Why? An integer is divisible by 100 if and only if its last two digits are zeros. No, it is not. When the definition is separated into two conditional statements, one of the statements is false. Yes, it is. When the definition is separated into two conditional statements, one of the statements is true. Yes, it is. When the definition is separated into two conditional statements, both of the statements are true. No, it is not. When the definition is separated into two conditional statements, both of the statements are false.
The given statement is An integer is divisible by 100 if and only if its last two digits are zeros.
The two conditional statements that can be made are:
1) If an integer is divisible by 100 its last two digits are zeros.
This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have the last two digits zeros.
What happen when last two digit of the number are 0?
2) If the last two digits of an integer are zeros, it is divisible by 100.
This is also true. If the last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.
Therefore, the two conditional statements that are formed are both true.
So, option A is the correct answer.
Yes, it is. When the definition is separated into two conditional statements, both of the statements are true.
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The given statement is An integer is divisible by 100 if and only if its last two digits are zeros.
What is Integers?An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.
The two conditional statements that can be made are:
1) If an integer is divisible by 100 its last two digits are zeros.
This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have the last two digits zeros.
2) If the last two digits of an integer are zeros, it is divisible by 100.
This is also true. If the last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.
Therefore, the two conditional statements that are formed are both true.
So, option A is the correct answer.
Yes, it is. When the definition is separated into two conditional statements, both of the statements are true.
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Carly will be going to college in 3 years. she anticipates that she will need $12,000 to pay for the first year. she currently has $2,900 in a savings account. without including any interest earned, what is a reasonable estimate of the amount carly needs to deposit into the savings account per month over the next 3 years to be able to pay for her first year of college? $150 $250 $350 $450
The estimate of the amount carly needs to deposit into the savings account per month over the next 3 years to be able to pay for her first year of college is $250
SavingsAmount needed = $12,000Amount available = $2,900Number of months in three years = 12 × 3 = 36Amount of savings per week = x12,000 = 2900 + 36x
12,000 - 2900 = 36x
9,100 = 36x
x = 9100 / 36
x = 252.777777777777
Approximately,
$250
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Answer:
The answer is B. $250
Step-by-step explanation:
At a track meet, the height of John's high jump was within 6 inches of the track record of 76 inches. What is
the range of heights for John's jump?
The range:
[tex]{x|70\leq x\leq 82[/tex]
What is the factored form for the quadratic function below?
y = x² + 9x + 8
Oy=(x-9)(x - 1)
Oy=(x-8)(x - 1)
Oy= (x + 9) (x + 1)
Oy= (x + 8) (x + 1)
Answer:
D. y = (x + 8) (x + 1)
Explanation:
[tex]\sf y = x^2 + 9x + 8[/tex]
[tex]\rightarrow \sf y = x^2 + 9x + 8[/tex]
middle term split
[tex]\rightarrow \sf y = x^2 + 8x +x + 8[/tex]
factor the common terms
[tex]\rightarrow \sf y = x(x + 8) + 1(x + 8)[/tex]
collect into groups
[tex]\rightarrow \sf y = (x + 1)(x + 8)[/tex]
Option D
What is the speed of a wave with a wavelength of 10 meters
Any wave's speed is equal to its frequency times wavelength. Now, the question doesn't specifically state what kind of wave it is. Thus, there might be two distinct scenarios: If the wave is elastic (sound is an example), you can't calculate its speed unless you also know its frequency and wavelength. However, the speed in vacuum is constant (3*108 m/s) if the wave is electromagnetic (for instance, light). In order to maintain constant velocity, frequency must shift in response to variations in wavelength. The frequency of light rays is constant in all other optical media (apart from vacuum and air), although their velocity and wavelength change correspondingly. However, that is not the case here since if it must be an EM wave with a wavelength of 10 m, then it must be a radio wave that travels uniformly through all medium at a speed of 3*108 m/s.
Use the Factor Theorem to determine whether x + 1 is a factor of P(x) = 2x³+4x²–2x−8.
Specifically, evaluate P at the proper value, and then determine whether x + 1 is a factor.
Answer: [tex]2x^2+2x-4-\frac{4}{x+1}[/tex]
Not a factor because there is a remainder.
Step-by-step explanation:
Let's use synthetic division to solve this..
-1 ║ 2 | 4 | -2 | -8
║ | -2| -2 | 4
║ 2 | 2| -4 | -4
[tex]2x^2+2x-4-\frac{4}{x+1}[/tex]
PS: if anyone knows a better way to do a synthetic division chart please let me know.
Suppose f(x) = x² and g(x)= (1/5x)^2
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) shifted units left.
B. The graph of g(x) is the graph of f(x) vertically stretched by a
factor of 5.
OC. The graph of g(x) is the graph of f(x) horizontally stretched by a
factor of 5.
D. The graph of g(x) is the graph of f(x) horizontally compressed by a
factor of 5.
Answer:
B. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.
What is the equation of the line that passes through the point (5,-2) and has a
slope of -2/5
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = -2/5x}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Passes through (5, -2) and slope of -2/5}[/tex]
Find: [tex]\textsf{The equation that follows the details provided}[/tex]
Solution: We first need to plug into the point-slope form and after simplifying, distributing, and solving for y we will complete our equation.
Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-2) = -2/5(x - 5)}[/tex]Distribute and simplify
[tex]\textsf{y + 2 = -2/5(x - 5)}[/tex][tex]\textsf{y + 2 = (-2/5 * x) + (-2/5 * (-5))}[/tex][tex]\textsf{y + 2 = -2/5x + 2}[/tex]Subtract 2 from both sides
[tex]\textsf{y + 2 - 2 = -2/5x + 2 - 2}[/tex][tex]\textsf{y = -2/5x + 2 - 2}[/tex][tex]\textsf{y = -2/5x}[/tex]Therefore, the final equation that follows the information that was provided is y = -2/5x.
The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square bas-
is x units.
Which expression represents the volume of the prism, in cubic units?
x³ +9
x³ + 3x²
x³ + 3x + 3
x³ + 6x² + 9x
Answer:
College dropout is the greatest album of all-time
This week, Marie trimmed 61% of the bushes in her yard. Katie trimmed 7/20 of the bushes in her yard. Who has trimmed a greater percentage of her bushes?
For a biology experiment, students labeled the plants in a greenhouse in order to track their heights over the next few weeks. The greenhouse contained ROSES labeled 1, 2, 3, 4, 5, 6, LILIES labeled 1, 2, 3, 4, 5, and VIOLETS labeled 1, 2, 3, 4. If a single flower is picked at random, what is the probability that the flower is NOT A ROSE?
Using it's concept, it is found that there is a 0.6 = 60% probability that the flower is NOT A ROSE.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 6 + 5 + 4 = 15 flowers, out of which 5 + 4 = 9 are not roses, hence the probability is given by:
p = 9/15 = 0.6 = 60%.
0.6 = 60% probability that the flower is NOT A ROSE.
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A group of friends wants to go to the amusement park. They have no more than $280 to spend on parking and admission. Parking is $19.50, and tickets cost $33.75 per person, including tax. Which inequality can be used to determine semanticsp, the maximum number of people who can go to the amusement park?
The number of people who can go to the amusement park is 8.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given: the group of friends had $280.
For parking= $19.50
Remaining will be,
=$(280-19.50)
= $ 260.5
Cost of ticket per person = $33.75
Thus, number of tickets they can buy
=260.5 / 33.75
=7.718 = 8 peoples
Hence, number of people who can go to the amusement park is 8.
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explain this please thanks.
Answer:
Step-by-step explanation:
Two possible patters of sitting:
⇒ [tex]I) M W M W M W[/tex]
⇒ [tex]II) W M W M W M[/tex]
⇒ Three ways can be used to seat each set of three people, for a total of six.
⇒ There are two groups
2 × 3 = 6 (ways in six groups.)
*The two options can be distributed in two groups.
⇒ Total methods are equal to 6 * 6 * 2 = 72 ways.
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Fill in the missing work and justification for step 5 when solving 4(x + 1) = 8.
Step Work Justification
1 4(x + 1) = 8 Given
2 4x + 4 = 8 Distributive Property
3 4x + 4 − 4 = 8 − 4 Subtraction Property of Equality
4 4x = 4 Simplify
5
6 x = 1 Simplify
A 4x − 4 = 4 − 4; Subtraction Property of Equality
B 4x + 4 = 4 + 4; Addition Property of Equality
c Four times x over four equals four over four; Division Property of Equality
d 4x(4) = 4(4); Multiplication Property of Equality
Answer:
c) Four times x over four equals four over four; Division Property of Equality===========================
Given equation and steps to solve it:
4(x + 1) = 84x + 4 = 84x + 4 - 4 = 8 - 44x = 44x/4 = 4/4 This is the missing stepx = 1All steps given above including the missing one. As we can see, we divided both sides by 4, so the justification for this step is Division Property of Equality.
Hence, the correct choice is C.
Answer:
Four times x over four equals four over four; Division Property of Equality
Option CStep-by-step explanation:
See on antepenultimate step
4x=4Now for getting x we have to divide each side by 4
We get.
4x)4=4/4x=1What is the equation of the line that passes through the point (8,4) and has an undefined slope?
Answer:
x = 8
Step-by-step explanation:
An undefined slope indicates that the line is vertical and parallel to the y- axis with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (8, 4 ) with x- coordinate 8 , then
x = 8 ← equation of line
4
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9 to the power of - half is equal to (as a fraction) 27 to the power of a quarter over 3 to the power of x-1
whats x?
9^(-1/2) = ((27^(1/4))/(3^(x-1)))
Answer:
[tex]x=\dfrac{11}{4}[/tex]
Step-by-step explanation:
Given:
[tex]9^{-\frac{1}{2}}=\dfrac{27^{\frac{1}{4}}}{3^{(x-1)}}[/tex]
Rewrite 9 as 3² and 27 as 3³:
[tex]\implies (3^2)^{-\frac{1}{2}}=\dfrac{(3^3)^{\frac{1}{4}}}{3^{(x-1)}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{-1}=\dfrac{3^{\frac{3}{4}}}{3^{(x-1)}}[/tex]
Multiply both sides by [tex]3^{(x-1)}[/tex] :
[tex]\implies 3^{-1} \cdot 3^{(x-1)}=3^{\frac{3}{4}}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies 3^{(-1+x-1)}=3^{\frac{3}{4}}[/tex]
[tex]\implies 3^{(x-2)}=3^{\frac{3}{4}}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]
[tex]\implies x-2=\dfrac{3}{4}[/tex]
[tex]\implies 4(x-2)=3[/tex]
[tex]\implies 4x-8=3[/tex]
[tex]\implies 4x=11[/tex]
[tex]\implies x=\dfrac{11}{4}[/tex]
