Determine the quadratic function of the form f(x) = a(x - h)² + k whose graph is given on
the right.
f(x) =
(Do not simplify.)

Answer:

A) 25% or 1/4

B) 5% or 1/20

Step-by-step explanation:

Part A)

Divide the down payment by the total purchase price to find the percent:

[tex]60,000/240,000=1/4=0.25[/tex]

Part B)

Divide the new down payment by the total purchase price to find the percent:

[tex]12,000/240,000=1/20=0.05[/tex]

Answer:

$8.75

Step-by-step explanation:

$4.50 × 2.5 = $11.25

$20.00 - $11.25 = $8.75 change

Answer: negative

Step-by-step explanation:

When graphing the points on a coordinate plane, the line falls as it moves from left to right. This means that the line has a negative slope.

Answer:

negative

Step-by-step explanation:

If jenny and penny play on the same basketball team last season a combined total of 485 points. Jenny scored 192 of points then the points penny scored is 293.

Jenny and penny play on the same basketball team last season a combined total of 485 points.

Individually Jenny scored 192 of points.

Let the score of penny on the same basketball team last season be x

Then the equation which represents the combined score of Jenny and Penny is

x + 192 = 485

x = 485 - 192

x = 293

The score of penny on the same basketball team last season is 293 points.

Therefore, if  jenny and penny play on the same basketball team last season a combined total of 485 points. Jenny scored 192 of points then the points penny scored is 293.

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Answer:

7+w

Step-by-step explanation:

I think this is the answer hope it helped

The correct answer is the first option.

We can show that the 2 triangles are congruent by using vertical angles, to prove that m∠DCA = m∠TCS

Then by Alternating Interior Triangles, m∠A = m∠T and m∠D = m∠S

And finally, the sides AC and CS are equal, and DC = CT

Then we have 3 pairs of congruent corresponding sides and 3 pairs of congruent corresponding angles, which is the first option.

A sequence of transformations that would not return a shape to its original position is: 'Translate 3 unit left, then 3 units down.'

1. Reflect over line x, and over x again.

These transformations are direct opposite and will cancel out one another. Hence, the shape will return to its initial position.

2. Translate 1 unit up, then 4 units down, then 3 units up.

This transformation will return a shape to its original position.

3. Rotate 270° counterclockwise around center C, then rotate 90° counterclockwise around C again.

This means, rotate object by 360° counterclockwise around C.

And this sequence of  transformations will return a shape to its original position.

4. Translate 3 unit left, then 3 units down.

These sequence of transformations would not make a shape go back to its original position.

Therefore, a sequence of transformations that would not return a shape to its original position is: 'Translate 3 unit left, then 3 units down.'

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{2}x+1\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{2\implies \cfrac{2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{2}}}[/tex]

so we're really looking for the equation of a line with a slope of -1/2 and that it passes through (4 , 6)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{1}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y-6=- \cfrac{1}{2}x+2\implies {\Large \begin{array}{llll} y=- \cfrac{1}{2}x+8 \end{array}}[/tex]

At x=1 in the domain f(x)=0.

The entire range of independent variable values is the domain of a function.

This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.

Keep in mind that a fraction's denominator (bottom) cannot be zero when determining the domain.

A square root must have a positive number under it.

At the points where the function's graph and the x-axis connect, f(x)=0.

You can see from the diagram that the function's graph crosses the x-axis three times:

1)between -3 and -2

2)between -1 and 0;

3)at x=1.

Since x=1 is the value of x from the domain, then correct choice is option C.

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Answer: -6

Step-by-step explanation:

Given: y = 100 - 2x

New: y = 100 - 2(x + 3)

          = 100 - 2x - 6

          = 94 - 2x

The original equation had a y-intercept of 100.  The new equation has a y-intercept of 94.  The y-value changes by -6 units.

The correct option is option: rotation 90°counterclockwise about the origin.

What is transformation?

A transformation is generally the shifting of the picture for manipulating the shape or position of a point, a line, or a geometric figure.

Transformation is a process by which the orientation or size of a given picture is changed without any effect on the shape.

A rotation is one kind of transformation in which the object rotates about a fixed point or line. The direction of rotation is clockwise or anticlockwise.

It is clear from the figure that

the triangle ∆ABC is mapped over triangle ∆A'B'C' by rotating every point 90° from 2nd quadrant to 3rd quadrant by the rotation of  90° counterclockwise about the origin.

Therefore triangle is rotated 90°counterclockwise about the origin.

Answer:

Step-by-step explanation:

Answer:log_3 (3) + log_3(x)

=log_3(36)

Step-by-step explanation:log_3 (3) + log_3(x)

=log_3(36)log_3 (3) + log_3(x)

=log_3(36)

Answer:

For two functions to be equal, the arguments of each must be equal.

x=12

Step-by-step explanation:

Answer:

a)77/100 b)7/10 c)7/100

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the lowest price per ounce, we must find the unit rate (how much does it cost to buy 1 unit of something).

The way to do this is divide the price by the quantity.

Option 1) [tex]\frac{1.65}{26/5} = 1.65 * 5/26 = 8.25/26 = 33/104[/tex]

For the first option, every ounce costs $33/104.

Option 2) [tex]\frac{10.4}{26} = 0.4 = \frac{4}{10}[/tex]

For the second option, every ounce costs $4/10.

Since we know that 33/104 is less than 4/10, option 1 is more worth it as every ounce costs less than option 2.

Hey, this question lacks the statement, answer choices, and pictures...etc

I can't answer unless you give more details.

Answer:

Technically, there is a proportionality because there will always be more road bikes than mountain bikes rented, but the proportionality is not completely constant as the ratio is 300/425 which is 0.75 compared to 575/680 which is 0.84.

The y-intercept of the equation is 4.

The equation of a line is

y = mx + c

x, y is the point on the line

m = slope of a line

c = y-intercept

As the equation of a line is 3x + 2y = 8.

We have to find the y-intercept of the equation.

3x + 2y = 8

2y = -3x + 8

y = -3/2x + 4

y = mx + c

So from this, we get the y-intercept

c = 4

Therefore the y-intercept of the equation is 4.

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If Lamont withdraws $2,750 monthly, he will be 66 years old (after 134.326 months) when the money runs out.

We can calculate the number of monthly withdrawals using an online finance calculator.

It determines the number of periods it will take for the investment to be exhausted, given an interest rate of 3.8%.

I/Y (Interest per year) = 3.8%

PV (Present Value) = $300,500

PMT (Periodic Payment) = $-2750

FV (Future Value) = $0

Results:

N = 134.326 months

Years = 11 years (134.326/12)

Age at FV = $0 is 66 years (55 + 11)

Sum of all periodic payments = $-369,397.09 (134.326 x $-2,750)

Total Interest = $68,897.09

Thus, making a monthly withdrawal of $2,750 will exhaust the investment when Lamont turns 66.

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Ok, so

First of all, remember that a line can be described by two forms:

1. y = mx+b, where m is the slope and b is the y - intercept-

2. We would have the general equation for a line, which is:

Ax + By + C = 0

Where m(slope) is -A/B and the intercept (b) is -C/B.

Now, let's find the slope and y - intercept for each line here below.

a. y = 5 - 6x

Here we have a line which has the first form (1). So, if we rewrite:

y = - 6x + 5.

So, If we compare with the first equation, we notice that m = -6 and b = 5

or, m = -6 and b = (0,5)

b. y = (5/6)x + 1

Here we have a line which has the first form (1).

So, if we compare, we notice that m = 5/6 and b = 1, or, m = 5/6 and b = (0,1)

c. 5x - 6y = 6

If we rewrite the equation:

5x - 6y - 6 = 0

Here we have a line which has the second form (2).

We know that

A = 5

B = -6

C = -6

If we replace, m = -A/B, which is -(5) / (-6) , and this is 5/6.

And, y intercept will occurs at y = -C/B, which is -(-6) / -6, which is 6/-6, or -1.

So, the slope will be 5/6 and y-intercept (0,-1).

m = 5/6 and b = (0,-1)

d. 5x + 6y = 6

If we rewrite the equation:

5x + 6y - 6 = 0

Here we have a line which has the second form (2).

We know that:

A = 5

B = 6

C = -6

If we replace, m = -A/B, which is -(5) / 6, so, m = -5/6

And, y intercept will occurs at y = -C/B, which is -(-6) / 6, so, b = 1

Finally, m = -5/6, and b = (0,1)

The simplified fraction is  [tex]\frac{7}{90}[/tex]

How are the fractions multiplied?

[tex]\frac{2}{15} *\frac{7}{12} \\\\=\frac{7}{15*6} \\\\=\frac{7}{90}[/tex]

What is product of fractions?

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7/90 is the simple fraction.

2/15*7/12

=7/15*6

=7/90

The fractions can be made more simpler before being multiplied by removing common components from the numerator and denominator.

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the linear equation has solution b=3x+9y/a

what is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. the equation can be represented as Ax+ By= C,

x, y are variable, A,B, C are constant.

so given equation

x+3y=ab/3

multiply 3 on both side

⇒ ab=3x+9y

⇒b= 3x+9y/a

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the answer should be 6, 12, 18. 24

The value of a, b and c in Y=ax²+bx+c are 3, -5 and 1 respectively.

As it is provided that the quadratic equation Y=ax²+bx+c goes through the coordinates  (-2, 23), (-1, 9), and (4, 29).

One of the method of solving quadratic is by putting the points,

So, it means that these coordinates will satisfy the equation,

So, putting the coordinates in the equation one by one,

First putting (-2,23)

We get,

(23) = a(-2)²+b(-2)+c

23 = 4a-2b+c

Now, putting, (-1,9)

We get,

(9) = a(-1)²+b(-1)+c

9 = a-b+c

From here, we get,

c = 9-a+b.

Now, putting (4,29)

We get,

(29) = a(4)²+b(4)+c

29 = 16a+4b+c

Now, putting c = 9-a+b, in 29 = 16a+4b+c  and 23 = 4a-2b+c,

we get,

29 = 16a+4b+9-a+b

20 = 15a + 5b

dividing by 5,

4 = 3a+b ….. Equation (1)

Now,

c = 9-a+b in 23 = 4a-2b+c,

23 = 4a-2b+9-a+b

14 = 3a-b ….. Equation (2)

Adding equation 1 and 2,

18 = 6a

a = 3,

Putting a = 3 in equation 1,

4 = 3(3)+b

b = -5

We know,

c = 9-a+b

c = 9-3+(-5)

c = 1

So, a = 3, b = -5 and c = 1.

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A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it.

A % is a number without dimensions and without a standard measurement.

How many students were on the honor roll overall as a percentage increase?

In response: The circumstances we are aware of, boys: 144 * 1+25% =144 * 1.25=180 girls: 75 * 1+16% =75 * 1.16=87 144+75. There were 75 females and 144 guys on the honor list at a particular high school last year. In comparison to last year, there were 25% more males and 16% more girls on the honor roll this year.

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Answer: x=3

Step-by-step explanation:

[tex]g(x)=x^3-3\\\\g(x)=24\\\\Hence,\\\\x^3-3=24\\\\x^3-3+3=24+3\\\\x^3=27\\\\x^3=3^3\\\\Thus,\\\\x=3[/tex]

The simplification of the given expression is [tex]2^{\frac{1}{12} }[/tex].

Given expression:

[tex]\frac{8^{\frac{1}{4} }*4^{\frac{1}{6} }}{2^{\frac{1}{6} }}[/tex]

Exponents

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself. For example, 8 is multiplied by itself 3 times, i.e. 8 × 8 × 8. This can be written as [tex]8^3[/tex]. Here, 3 is the exponent and 8 is the base. This can be read as 8 is raised to power 3.

We know that,

8 is the cube of 2 and 4 is the square of 2, hence, we can write,

[tex]\frac{(2^3)^{\frac{1}{4} }*(2^2)^{\frac{1}{6} }}{2^{\frac{1}{6} }}[/tex]

Using the properties of exponents, we can write,

[tex]\frac{(2)^{\frac{3}{4} }*(2)^{\frac{2}{6} }}{2^{\frac{1}{6} }}[/tex]

Simplifying this further, we can write,

[tex]\frac{2^{(\frac{3}{4}*\frac{2}{6}) }}{2^{\frac{1}{6} }} = \frac{2^{\frac{1}{4} }}{2^{\frac{1}{6} }} = 2^{\frac{1}{4}-\frac{1}{6} }=2^{\frac{3-2}{12} }=2^{\frac{1}{12}}[/tex]

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The class interval of the histogram based on the information will lie between B. 150 ≤ h < 165.

It should be noted that a histogram simply means a graph that is used to show the data given. It helps with the distribution of data.

In this case, the histogram shows the heights of the students.

It should be noted that the median simply means the number in the middle. In this case, the median will be between 150 and 165 based on the diagram.

In conclusion, the correct option is B.

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x^2+4x-5>0 is the required quadratic inequality which is represented in the graph

Quadratic inequality: A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. Examples of quadratic inequalities are: x2 – 6x – 16 ≤ 0, 2x2 – 11x + 12 > 0, x2 + 4 > 0, x2 – 3x + 2 ≤ 0 etc. Solving a quadratic inequality in Algebra is similar to solving a quadratic equation

as per the shaded region we can consider a number line from (-5,0) to(,1,0)

where x lies between the two points as per the given question

-5<x<1

which gives x>-5 and x<1

in the shaded region f(x)>0

so we can directly write that ,

(x+5)(x-1)>0

x^2-x+5x-5>0

x^2+4x-5>0

x^2+4x-5>0 is the required quadratic inequality which is represented in the graph

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The range of values of T is the domain and the range of values of W is the domain, then the,

Domain : Number of minutes water has been added ( 0 , 60 )

Range : Amount of water in the pond (in liters) ( 0 , 2800 )

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

The range is the difference between the highest and lowest values in a set of numbers. To find it, subtract the lowest number in the distribution from the highest.

Consider the relation {(0,7),(0,8),(1,7),(1,8),(1,9),(2,10)} . Here, the relation is given as a set of ordered pairs. The domain is the set of x -coordinates, {0,1,2} , and the range is the set of y -coordinates, {7,8,9,10} .

The range of values of T is the domain is,

T = ( 0 , 60 )

The range of values of W is the domain is,

W = ( 0 , 35T+700 )

0 ≤ 35T+700

Then,

We can substitute T value,

0 ≤ 35T+700 ≤ 35*60 + 700

0 ≤ 35T+700 ≤  2800

Therefore,

Domain : Number of minutes water has been added ( 0 , 60 )

Range : Amount of water in the pond (in liters) ( 0 , 2800 )

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