Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q4

The mechanic charges $24 per hour. Also, labour was charged for 1 3/4 hours. Therefore, the total labour cost is,

Now, the total bill is,

Therefore, the total bill is $67.79.

ANSWER

• slope: 3

• y-intercept: 6

• equation: y = 3x + 6

EXPLANATION

The slope-intercept form of the equation of a line is,

Where m is the slope and b is the y-intercept.

The slope of a line passing through points (x₁, y₁) and (x₂, y₂) is,

In this case, to find the slope we have to take two pairs of values from the table. Using the points (1, 9) and (0, 6) we have,

Hence, the slope is 3.

The y-intercept is the value of y where the line intersects the y-axis. This always occurs at x = 0, so the y-intercept is shown in the table as the value of y for x = 0,

Hence, the y-intercept is 6.

Finally, we have to substitute m and b with the slope and y-intercept found to write the equation for this function. Hence, the equation is y = 3x + 6.

Given

Find

Rewrite it into standard form and identify vertex and all its intercepts.

Explanation

standard form =

where (h , k) be the vertex

so ,

so vertex be

for intercept put f(x) = 0

so , x - intercept = (1 , 0) and (2 , 0)

for y- intercept put x =0

y - intercept (0 , 2)

Final Answer

Therefore , vertex is (3/2,-1/4)

x - intercept = (1 , 0) and (2 , 0) and y - intercept (0 , 2)

1% of 7,281 is 72.81, you need to compare that value with the one you obtained in answer a

and say if it's greater, equal or less than that

You can do something similar to solve question a

Answer:

907.2 grams

Explanation:

We were given that:

A can of fruit contains 32 OZ. Of pineapples

1 ounce = 28.35 grams

The number of grams in the can of fruit is calculated using simple proportion as shown below:

Therefore, there are 907.2 grams in a can of fruit

Given -

4x² - 20x + 25 = 10

To Find -

Solutions to the equation =?

Step-by-Step Explanation -

We have to rearrange the equation first

4x² - 20x + 25 = 10

4x² - 20x + 25 - 10 = 0

4x² - 20x + 15 = 0

Here a = 4, b = -20, c = 15

Now, we put it in equation:

Final Answer -

x = (5 + √10)/2 and

x = (5 - √10)/2

Answer:

[tex]x=\dfrac{5\pm\sqrt{10}}{2}[/tex]

Step-by-step explanation:

[tex]4x^2-20x+25=10\\(2x)^2-2\cdot2x\cdot5+5^2=10\\(2x-5)^2=10\\2x-5=\pm\sqrt{10} \\2x=5\pm\sqrt{10} \\x=\dfrac{5\pm\sqrt{10}}{2} \\\\x_1=\dfrac{5-\sqrt{10}}{2}; \ x_2=\dfrac{5+\sqrt{10}}{2}[/tex]

Write an equation in slope-intercept form for the situation shown in the image

The slope-intercept form of a line is:

y = mx + b

On Phill's Frozen Yogurt Shop, Phill charges $3.00 for a medium cup of frozen yogurt and $0.50 for each topping.

Let's call x=number of toppings selected for the yogurt.

Since each topping costs $0.50, the x toppings cost 0.50x. The total cost (y) is calculated as:

y = 0.50x + 3

For Frank's Pizzeria, the cost (y) of a medium pizza is

y = 10 + 1.75x

Where x is the number of toppings.

To write this equation in slope-intercept form, we only need to rearrange it as follows:

y = 1.75x + 10

ANSWER

False

EXPLANATION

The equation of a circle is:

Where (x0, y0) is the center of the circle and r is the radius.

If we have the equation of a circle:

x0 = 0 and y0 = 2. Therefore the center of the circle is at point (0, 2). Also, we have that:

Solving for r, the radius of this circle is:

Therefore, it is false that the radius of the given circle is 12.

Answer:

1/221 or 0.005

Explanation:

• The number of aces in a standard 52-cards deck = 4

• The total number of cards = 52

The probability of drawing two cards (Aces) without replacement is given below:

Therefore, the probability that all cards are aces is:

The probability is 1/221 (as a fraction) and 0.005 (as a decimal correct to 3 decimal places).

ANSWER :

t - 3 < 26

EXPLANATION :

From the problem, the initial temperature is t degrees.

If the temperature falls by 3 more degrees, which means 3 degrees subtracted from t degrees (t - 3), it will break the record low temperature (26 degrees)

It means that the temperature passes the 26 degrees mark, so the temperature must be less than 26 degrees to break the record.

That will be :

In order to find the coordinates of the vertex T', M' and Q', use the following transformation:

T(x,y) => T'(x , -(y - 1) + 1)

Then, for the given points T, M and Q, you obtain:

T(-4 , 1) => T'(-4, -(1 - 1) + 1) = T'(4 , 1)

M(-1 , 3) => M'(-1, -(3 - 1) + 1) = M'(1 , -1)

Q(2 , -3) => Q'(2 , -(-3 -1) + 1) = Q'(2 , 5)

Hence, the coordinates ofthe point Q' are (2 , 5)

2(4−x) − 3(x+3) = −11

First open the parenthesis

8 - 2x - 3x - 9 = -11

8 - 5x -9 = -11

Rearrange

8 - 9 - 5x = - 11

-1 - 5x = -11

Add one to both-side of the equation

-5x = -11+ 1

-5x = -10

Divide both-side of the equation by -5

x = 2

Factor each completely:

5. m^3 - m ^2 + 2 m - 2

m ^2 ( m - 1 ) + 2 ( m - 1 )

= ( m - 1 ) ( m^2 + 2 )

1)

The property not preserved under line reflection is orientation.

Option g

(Note: Dilation, rotation and translation are preserved under line reflection).

2)

A congruence transformation is also known as isometry or rigid transformation.

Option e.

3)

A --- invloves three reflections

4)

Since reflection does not preserve orientation, the reflection of quadrilateral does not preserve orientaion

Option g.

5)

The equaivalent of three reflections in parallel lines is a reflection

Option l

6)

In reflection, the figure is flipped over a line.

Option o

7)

A figure with rotational symmetry can be mapped onto itself by a rotation of 180 degree or less.

Option j.

8) Transformation that change the position of a figure without changing its shape and size is known as translation.

Option m

9)

Moving a figure to the right or left and up or down without flipping is

translation.

Option m

10)

In translation, a point, line or image is slided to a new position without any change in shape or size without any flipping.

Option m

Question clarified:

The slope tells you how much the y-value of a point changes each time the x-value increases by 1 unit. This is called the ____________ (1).

When one quantity changes at a ____________ (2) rate relative to another, there is a ____________ (3) relationship between the quantities, which is graphed as a ____________ (4).

Some basic explanation:

Line is a points connected that goes in both directions infinitely. Basically:

It has slope. Which is the rate of change of y with respect to x.

Line is a linear curve.

Now, the first part tells us the rate of change of y with x, so blank (1) would be rate of change.

Let's look at the second part now:

When y and x changes at a constant rate (constant slope), it will be a line. Otherwise, it is a curve.

Hence, blank (2) is "constant".

The relationship is linear, that is blank "3".

Of course, when graphed, it creates a "line".

That's blank number 4.

Final answer:

The slope tells you how much the y-value of a point changes each time the x-value increases by 1 unit. This is called the rate of change (1).

When one quantity changes at a constant (2) rate relative to another, there is a linear (3) relationship between the quantities, which is graphed as a line (4).

We have that angle BAD is an exterior angle of the circle, then, we have the following general equation:

where BD and BC are the measures of their respective arc.

In this case,we have the following:

then, using the equation and solving for BD, we get:

therefore, the measure of arc BD is 110 degrees

we place the t's on the same side and the other nombers on the other side

now do the operations

then solve t

the value of t is 3.5 so the rigth option is D

Given:

The angle is 166 degree.

Explanation:

The coterminal angle can be determined by adding and substracting 360 from the given angle 166 degree.

Determine the positive and negative coterminal angle.

For positive coterminal angle:

For negative coterminal angle:

Thus positive and negative coterminal angles are 526 degree and -194 degree.

In general, the simple interest formula is

Where t is given in years.

And the interest is given by

Let B the initial amount Lisa invested in the 10% interest account and C the amount she invested in the 8% account.

Therefore,

Expanding the second equation,

The system of equations becomes

From the first equation, B=30000-C. Substitute into the second equation as shown below

And

Therefore, she invested $12000 in the 10% account and $18000 in the 8% account.

Answer:

For y = 72 and x = 3

k = 1/24

For y = 20 and x = 12

k = 3/5

For y = 45 and x = 40

k = 8/9

Explanation:

Given that x and y are proportional,

Then

For y = 72 and x = 3

k = 3/72 = 1/24

For y = 20 and x = 12

k = 12/20 = 3/5

For y = 45 and x = 40

k = 40/45 = 8/9

Given B = (5,-4) and C = (-3,8)

M is the midpoint of BC

So,

M = 0.5 [ B + C ]

= 0.5 * [ (5,-4) + (-3,8) ]

= 0.5 * ( 5 - 3 , -4 + 8 )

= 0.5 ( 2 , 4)

= (1 , 2 )

So, M = (1,2)

Answer:

y = -12

Explanation:

The first step is to subtract 12 from both sides of the equation to get:

Finally, multiplying both sides by 6 gives

which is our answer!

Given, that a polynomial has the following:

The degree = 6

The leading coefficient = 1

The zeros are as follows:

-3 as a zero of multiplicity 3 ⇒ The corresponding factor = (x+3)

0 as a zero of multiplicity 2 ⇒ The corresponding factor = x

3 as a zero of multiplicity 1 ⇒ The corresponding factor = (x-3)

So, the equation of the polynomial written in factor form will be as follows:

Expand the polynomial:

Combine the like terms:

So, the answer will be:

The given coordinate is E(-5,0).

The dilation factor is 3.

The translation is (x-3,y-1).

First, we apply the dilation

Then, we translate the point

For the linear equation given;

It is important to note that whatever we do on the right side, we must do the same on the left side.

The Left side is;

While the Right side is;

To calculate the unknown variable, which in this case is x, we would first of all isolate any term(s) that inculdes x, as shown below;

Remember however that one rule we must never forget is that whatever you do on the left you must do the same on the right, and vice versa. Therefore, our first step would be,

"Add 9 to both sides of the equation."

Where we have -9 + 9 (or +9 - 9) that equals zero. Hence;

Next we try to isolate x by removing -4, as follows;

We are dividing here because -4x is actually -4 times x. The opposite of multiplication is division, the same way the opposite of addition is subtraction.

We can now complete the solution as shown below;

ANSWER:

x = 11

If we have the system:

and we don't want the system to have a solution we need that one equation contradicts the other. For example if we choose a=3, b=1 and c=3, we have the system:

notice that the left side on both equations is the same, whereas the right side is not the same; this means that the second equation contradicts the first one, hence the system does not have a solution.

This form of choosing a, b and c can be extend to and infinite number of systems if we only change the value of c, that is, as long as a=3, b=1 and that c is not -2 the sytem will not have a solution.

Given:

a.) Ishi walked a total of 2 1/2 miles on a treadmill.

b.) He walked at a constant rate of 4 miles per hour.

For us to be able to determine how long, in minutes, Ishi walked on the treadmill, we will be using the following formula:

We get,

Therefore, the answer is letter B.

When you translate G' coordinate becomes (0, -1)

F' coordinates becomes (0, -6)

H' coordinates becomes ( -9, -1)

The graph will be atteached below:

Rotation of 180

Explanation

Step 1

Plot segment AB

let's check every option

Step 2

a) 90°

To rotate triangle ABC about the origin 90° clockwise we would follow the rule (x,y) → (y,-x)

so,let's check

those are not the coordinates of A'B' hence we can discard the rotation of 90°

b)180 °

The rule for a rotation by 180° about the origin is (x,y)→(−x,−y)

so

we can see that those are the coordinates of A'B'

hence

the answer is

Rotation of 180

I hope this helps you

Given:

Volume of cylinder, V = 90π cm³

Radius, r = 3 cm

Let's find the height of the cylinder.

To find the height, given the volume, apply the formula for the volume of a cylinder:

Where h is the height.

Let's rewrite the formula for h to solve for h.

Re-arrange the equation:

Divide both sides by πr²:

Now, substitute values into the equation and solve for h.

Where:

V = 90π

r = 3

We have:

Therefore, the height of the cylinder is 10 cm.

ANSWER:

D. 10 cm