What is the value of the x-coordinate of the vertex of the function shown below?
f(x)=(x+4)(x-2)
...?
Find the GCF of the following literal terms.
m^7n^4p^3 and mn^12p^5
What forms of measurement of length, width, height, and distance are forms of what measurement?
The measurement of length and distance in mathematics, including the SI unit meter, different units, and measurement systems.
Measurement of Length, Width, Height, and Distance
Length is the measurement of the extent along the greatest dimension. The SI unit of length is the meter (m). Units of length include kilometers (km), millimeters, and micrometers.
Distance is a quantity arrived at by measurements with material or optical apparatus. It is commonly measured in meters, kilometers, feet, yards, etc. in various systems of measurement.
Customary and Metric Systems are two different systems used for measuring length and distance.
Find the point on the line 6x+y=9 that is closest to the point (-3,1).
Convert the line equation to 'y = mx + c' form. We calculate the orthogonal distance from the point to a generic point on the line using the formula 'd = |Ax1 + By1 + C| / sqrt(A^2 + B^2)'. Solve the line equation for 'y' using the computed 'd'. This yields the point closest to (-3,1) on the line.
Explanation:The subject of the question involves the algebra of straight lines, specifically finding points on lines. The given line in the question is '6x + y = 9'. We want to find the point along this line that is closest to a given point (-3,1).
First, rewrite the equation in slope-intercept form: y = -6x + 9. Now recall the formula for the shortest distance from a point to a line, d = |Ax1 + By1 + C| / sqrt(A^2 + B^2), where 'A', 'B' and 'C' are the coefficients in the equation of the line, and '(x1, y1)' is the point.
In this case, A = -6, B = 1, C = -9, and the point is (-3,1). If we plug these into the formula, we can solve for 'd'. Then we solve the given equation for 'y' using the resulting 'd' value and we get the point which is closest to (-3,1) on the line '6x + y = 9'.
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What is 1/50 as a percent and decimal?
The fraction 1/50 is equivalent to 0.02 as a decimal.
To convert 1/50 to a percent, we multiply the fraction by 100:
= 1/50 x 100
= 2%
Therefore, 1/50 is equivalent to 2% as a percent.
To convert 1/50 to a decimal, we divide the numerator (1) by the denominator (50):
= 1 ÷ 50
= 0.02
Therefore, 1/50 is equivalent to 0.02 as a decimal.
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Rewrite 5x(12+7) using distributive property
To rewrite 5x(12+7) using the distributive property, we distribute the 5x to both terms inside the parentheses. The final answer is 95.
Explanation:To rewrite 5x(12+7) using the distributive property, we need to distribute the 5x to both terms inside the parentheses.
First, let's distribute the 5 to the 12:
5 x 12 = 60
Next, let's distribute the 5 to the 7:
5 x 7 = 35
Putting it all together, we have:
5x(12+7) = 5x12 + 5x7 = 60 + 35 = 95
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The correct rewritten expression using the distributive property is [tex]\( 5x \times 12 + 5x \times 7 \).[/tex]
To rewrite the expression 5x(12+7) using the distributive property, one must multiply the term outside the parentheses, 5x , by each term inside the parentheses.
The distributive property states that a(b+c) = ab + ac
Applying this property to the given expression, we have:
[tex]\[ 5x(12+7) = 5x \times 12 + 5x \times 7 \][/tex]
Now, we can simplify the expression by performing the multiplication:
[tex]\[ 5x \times 12 = 60x \][/tex]
[tex]\[ 5x \times 7 = 35x \][/tex]
Combining these results, we get the final simplified expression:
[tex]\[ 60x + 35x = 95x \][/tex]
Therefore, the expression 5x(12+7) simplifies to 95x when the distributive property is applied and the multiplication is carried out.
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What are the factors of 16x^4 ? Select all that apply.
5
16
7
x^3
264 shared in ratio 2:3:1
How much water does a rectangular tank with a square base of 2.5 yards and a height of 4 yards hold?
how many inches are in a foot then converted into millimeters
(6.6x10^4)(7x10^3 sientific notation
7 × (–3) × (–2)2 =
a. 84b. –84c. 48d. –48
What are the domain, range, and asymptote of h(x) = (0.5)x – 9?
domain: {x | x > 9}; range: {y | y is a real number}; asymptote: y = 9
domain: {x | x > –9}; range: {y | y is a real number}; asymptote: y = –9
domain: {x | x is a real number}; range: {y | y > 9}; asymptote: y = 9
domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9
Answer:
Option 4 - domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9
Step-by-step explanation:
Given : [tex]h(x)=(0.5)^x-9[/tex]
To find : What are the domain, range, and asymptote of h(x) ?
Solution :
Domain of the function is where the function is defined
The given function [tex]h(x)=(0.5)^x-9[/tex] is an exponential function
So, the domain of the function is,
[tex]D=(-\infty,\infty) , x|x\in \mathbb{R}[/tex]
i.e, The set of all real numbers.
Range is the set of value that corresponds to the domain.
Let [tex]y=(0.5)^x-9[/tex]
If [tex]x\rightarrow \infty , y\rightarrow -9[/tex]
If [tex]x\rightarrow -\infty , y\rightarrow \infty[/tex]
So, The range of the function is
[tex]R=(-9,\infty) , y|y>-9[/tex]
The asymptote of the function,
Exponential functions have a horizontal asymptote.
The equation of the horizontal asymptote is when
[tex]x\rightarrow \infty[/tex]
[tex]y=(0.5)^\infty-9[/tex]
[tex]y=-9[/tex]
Therefore, Option 4 is correct.
Domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9
write 14/5 as a mixed number in simplest terms.
Answer: 2 and 4/5
Step-by-step explanation: To write an improper fraction as a mixed number, divide the denominator into the numerator.
[tex]\sqrt[5]{14}[/tex] = 2 with a remainder of 4
Therefore, 14/5 can be written as the mixed number 2 and 4/5.
Solve for x.
x/36= 16/24
16
24
36
54
What is ��1.95 x 6thanks?
Divide 9 by z expression
Which type of transformation does NOT result in a figure that is congruent to the original one?
Answer:
Rotations, reflections, and translations are isometric. That means that these transformations do not change the size of the figure. If the size and shape of the figure is not changed, then the figures are congruent.
Step-by-step explanation:
Please Help!!!!!
The function q(w)=3+5(w−1) represents the number of quarters in a bowl on week w.
What does the value 5 represent in this situation?
Quarters were added to the bowl for 5 weeks.
Five quarters are added to the bowl every week.
There were 5 quarters in the bowl on Week 1.
The value of the quarters in the bowl on Week 1 was $5.
The function p(t) represents the population of a certain town t years after 2010.
p(t)=3476(0.97)^t
What does the value 3476 represent in this situation?
Every year after 2010, the population increases by 3476.
Every year after 2010, the population decreases by 3476.
The population of the town in 2010 is 3476.
The population t years after 2010 is 3476.
Answer:
For number 2:
Step-by-step explanation:
Whick is the shorter distance 9/10 or 10/9
1. Write the statement in parentheses as a converse and provide the truth value (2 points). "An angle that measures 90° is a right angle."
2. Write the statement in parentheses as an inverse and provide the truth value (2 points). "An angle that measures 90° is a right angle."
3. Write the statement in parentheses as a contrapositive and provide the truth value (2 points). "An angle that measures 90° is a right angle."
Perform the indicated operation.
5/4 + 7/9
a. 4/9
b.2 and 4/9
c.2 and 1/36
Answer:
c.
Step-by-step explanation:
[tex]\frac{5}{4}+\frac{7}{9} = \frac{5*9+7*4}{4*9} = \frac{45+28}{36} = \frac{73}{36}[/tex]
and [tex]\frac{73}{36}= 2(36) + 1 = 2\frac{1}{36}[/tex]
The sum of negative eighteen and a number is eleven. what is the number? which equation could be used to solve the problem? x - 18 = 11 18 - x = 11 -x 18 = 11 x 18 = 11 user: solve for y. y - 12 = -10 y = 22 y = -22 y = -2 y = 2
how do you solve ky-bf=fy/m?
Final answer:
To solve the equation ky - bf = fy/m, you need to isolate the variable y. The steps are to distribute the k, add kf to both sides, and factor out y. The solution is y = (fy/m + kf)/k.
Explanation:
To solve the equation ky - bf = fy/m, we first want to isolate the variable y. Here are the steps:
Distribute the k to both terms in the equation: ky - bf = fy/m becomes ky - kf = fy/m.
Add kf to both sides of the equation: ky - kf + kf = fy/m + kf simplifies to ky = fy/m + kf.
Factor out y on the left side of the equation: y(k) = fy/m + kf becomes y = (fy/m + kf)/k.
So, the solution is y = (fy/m + kf)/k.
Solve the system and explain what the results mean according to your scenario.
2x + y = 9
3x + 4y = 26
...?
Four students took a national standardized test for which the mean was 500 and the standard deviation was 100. If a student’s z-value was 1.75 on the test, what was the student’s score?
z = (x - 500) / 100
1.75 = (x - 500) / 100
175 = x - 500
675 = x
Answer:
A, 675
Step-by-step explanation:
Zinnia and Ruby earn $58 per week for delivering pizzas. Zinnia worked for x weeks and earned an additional total bonus of $13. Ruby worked for y weeks. Which expression shows the total money, in dollars, that Zinnia and Ruby earned for delivering pizzas? (5 points)
71x + 58y
58x − 13 + 58y
58x + 71y
58x + 13 + 58y
Answer:
Total money Zinnia and Ruby earned for delivering pizzas is 58x + 13 + 58y .
Step-by-step explanation:
As given
Zinnia and Ruby earn $58 per week for delivering pizzas.
Zinnia worked for x weeks and earned an additional total bonus of $13.
Ruby worked for y weeks.
Thus
Money Zinnia earns = Money earns per week × Number of weeks + Additional total bonus .
Put all the values in the above
Money Zinnia earns = 58 × x + 13
Money Zinnia earns = 58x + 13
Thus
Money Ruby earns = Money earns per week × Number of weeks
Put all the values in the above
Money Ruby earns = 58 × y
Money Ruby earns = = 58y
Thus
Total Zinnia and Ruby earned for delivering pizzas = Money Zinnia earns + Money Ruby earns
Total Zinnia and Ruby earned for delivering pizzas = 58x + 13 + 58y
Therefore the total money Zinnia and Ruby earned for delivering pizzas is 58x + 13 + 58y .
30 : 48 as a ratio in simplest form
F(x) = 2x2 – 3x 7 for the input value 2.what is the value of the function when x = 2?
two cassettes and three CDs cost $175 while four cassettes and one cd cost $125. Given that one cassette costs 5x and one cd costs 5y , write two equations in x and y to represent the information.