Omar is hiring a painting company to paint the interior of his house. The table represents prices the painting company quoted Omar.

Write a two-variable linear equation to represent the total cost, c, given the square feet, s, of the house.
A: c=2.25s+1347.85
B: c=2.25s+2847.85
C: c=2.25s+4047.85
D: c=2.25s+7654.60

Sorrel has 19 yellow beads.

Fraction is a ratio of two integers.

Fraction is divided into two section by a dividing line and these sections are numerator and denominator.

Fractions are of different types: proper fraction, improper fraction and mixed numbers.

Total number of beads =54

if 16 are red, the remaining beads would be ( 54 - 16) = 38

Half of the remaining are yellow = 1/2 x 38

Then number of yellow beads = 19

And number of green beads = 38 - 19

                                                = 19

In conclusion, the total number of yellow beads is 19

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The x-intercept of the function represented on the graph is 3

The graph represents the given parameters

To determine the x-intercept of the graph, we set y = 0

This means that the x-intercept of the graph is the point, where the line of the graph crosses the x-axis

For the graph, we have

When y = 0, the function has a value of 3

This means that

x-intercept is 3

Hence, the x-intercept of the graph is 7

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Answer:

Step-by-step explanation:

yes Saab do

The possible value of x which the two triangles are similar is x=60°.

What do you mean by triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Method:

Given that two angles of the triangle are specified, the triangles can be

similar for only one value of x.

According to the given data in the question,

The two triangles are similar when we have;

x + 10° = 2x - 50°

Which gives;

2x - x = 50° + 10° = 60°

x = 60°

Checking gives;

x + 10° = 2·x - 50° = 70°

Two angles of the first triangle are 70° and 60°

Then, the third angle of the first triangle is (180° - (70° + 60°)) = 50°

The three angles of the first triangle are therefore; 70°, 60° and 50°.

Two angles of the second triangle are 70° and 70°.

The third angle of the second triangle is (180° - (70° + 70°)) = 40°

The three angles of the second triangle are therefore; 70°, 70° and 40°

Therefore, the two triangles are similar by AAA similarity.

The two triangles are similar when, x = 60°

When x = 50°, we have;

x + 10° gives;

50° + 10° = 60°

∴ ∠(x + 10°) = 60°

The two angles of the first triangle are; 60° and 50°

The third angle on the second triangle is 180° - (60° + 50°) = 70°

On the second triangle, we have;

2·x - 50° gives;

2 × 50° - 50° = 50°

∴∠(2·x - 50°) = 50°

Therefore, the two angles of the second triangle are 70° and 50°

The third angle on the second triangle is 180° - (70° + 50°) = 60°

Therefore, the two triangles are not similar when x = 50°

Similarly, the two triangles are not similar when x + 10° = 50°

Hence, the possible value of x which the two triangles are similar is x = 60°.

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The required price of almond and expression are $32.75 and c= $7.25P - $3.5 respectively.

Pound is unit used to measure weight of quantity. It is used by the English speaking peoples.It equal to the 16 ounces and 0.454 kilogram.

Alonso has a coupon of $3.5, let us consider P pound of almond. And price per pound of almond is $7.25

So, equation for the cost,

Cost(c) = $7.25P - $3.5

Then, the price of 5 pound of almond = $7.25×5 - $3.5

⇒ $36.25 - $3.5 = $32.75

Thus, the price of 5 pounds of almond is $32.75.

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The value of x is 32.5°(degree) when isosceles triangle has a base angle of (4x-3)degrees and non base angle is 54 degrees.

We know that an isosceles triangles is composed of a vertex angle and two base angles. The base angles are congruent to each other. We also know that the sum of a triangle's angles is 180°(degrees).

According to given data,

⇒ 180 - {(4x-3)+54}= 0

⇒180 - 4x + 3 - 54 = 0

⇒130 = 4x

∴ x = 32.5°(degree).

That means that each base angle is 32.5°(degree).

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Answer: False

Step-by-step explanation:

Can not divide a number by 0.

Reflection at point y = -6 will have coordinates as

preimage      image

Q(0, -9)          Q' (0, -6)

R(4, -9)           R' (4, -6)

S(6, -8)           S' (6, -5)

T(2, -8)           T' (2, -5)

The transformation involve is reflection and this is a type of transformation that produces the mirror image of the preimage

The transformation rule to get the mirror image is (x, y) → (x, y + 3)

The coordinates are applied as follows

Q(0, -9) → (0, -9 + 3) → Q' (0, -6)

R(4, -9) → (4, -9 + 3) → R' (4, 6)

S(6, -8) → (6, -8 + 3) → S' (6, -5)

T(2, -8) → (2, -8 + 3) → T' (2, -5)

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Answer:

x = 9/5 y - 4/5

Step-by-step explanation:

Make x the subject:

9y - 5x =4

Subtract 9y from each side

9y-9y - 5x =-9y+4

-5x = -9y +4

Divide each side by -5

-5x/-5 = -9y/-5 + 4/-5

x = 9/5 y - 4/5

Answer:

x = (9/5)y - (4/5)

Step-by-step explanation:

Given equation,

→ 9y - 5x = 4

Solving for the required value of x,

→ 9y - 5x = 4

→ -5x = -9y + 4

→ x = (-9y + 4)/-5

→ [ x = (9/5)y - (4/5) ]

Hence, value of x = (9/5)y - (4/5).

They will require 4 (4/11) days to complete the remaining work together.

Time is the duration during which any activity or work happens or continues.  Work is a task or set of activities to achieve a certain result

It takes Ann alone 10 days to translate a document.

Ann's work in one day = 1/10

In 2 days = 2 / 10

Work left = 8 / 10

Ben alone now takes 12 days to translate a document.

Ben's work in one day = 1/12

We will now use addition.

Combined work of both Ann and Ben in 1 day = 1 / 10 + 1 / 12 = 11 / 60

Time taken to complete the rest of the work = 8 / 10 ÷ 11 / 60

= 48 / 11 = 4.4 days.

As a result, they need 4 (4/11) days to finish the remaining work together.

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The sum of a number w is more than -12 becomes w > -12

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

We have been given that the sum of a number w is more than -12.

Now the sum of a number = w

It is more than -12 means the inequality form as;

w > -12

Therefore, the overall expression becomes w > -12

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Answer:2

Step-by-step explanation:

2*4=8

2*25=50

Applying the transformation rule (x - 2.y + 4) and using the scale factor k = 3 for dilation gives

preimage      translation image     Dilation image

A (1.-2)             A' (-1, 2)                   A'' (-3, 6)  

B (4,-1)             B' (2, 3)                    B'' (6, 9)

C (5.-3)            C' (3, 1)                     C'' (9, 3)

Transformation is a term used in mathematics to refer to the movements made by objects.

Translation refers to a type of transformation that involve a linear movement.

Applying the transformation rule (x - 2.y + 4 ) gives

A (1.-2) = (1 - 2, -2 + 4) = (-1, 2)

B (4,-1) = (4 - 2, -1 + 4) = (2, 3)

C (5.-3) = (5 - 2, -3 + 4) = (3, 1)

preimage        image

A (1.-2)             A' (-1, 2)

B (4,-1)             B' (2, 3)

C (5.-3)            C' (3, 1)

Dilation involves making the image bigger or smaller. In this case K > 1 hence the image is bigger

Using the scale factor k = 3 for dilation rule (kx, ky) gives

A' (-1, 2) = (-1 * 3, 2 * 3) = (-3, 6)

B' (2, 3) = (2 * 3, 3 * 3) = (6, 9)

C' (3, 1) = (3 * 3, 1 * 3) = ( 9, 3)

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The proof that show show how ΔTRS ≅ ΔQRP by SAS congruence theorem is explained below.

The SAS congruence theorem states that if two triangles have one pair of corresponding included angles that are congruent, and two pairs of corresponding sides that are also congruent, then both triangles are congruent to each other.

Using the SAS, the proof that shows both triangles are congruent is explained below.

Statements                        Reasons                                          

1. SR ≅ PR                          1. Given

2. SP bisects TQ               2. Given

3. TR ≅ QR                        3. Definition of bisection

4. ∠TRS ≅ ∠QRP              4. Vertical ∠s theorem

5. ΔTRS ≅ ΔQRP              5. SAS congruence theorem

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The person who runs fastest is Zach.

Ron runs 9 feet per second: 9 ft/s

Zach runs 410 feet in 49 seconds:

410/49 ft/s

=8.36 ft/s

= 8.4 ft/s (Approximately)

Katie runs 1 mile in 412 seconds:

1 mile = 5280 ft

5280/412 ft/s

=12.8 ft/s

Noah  runs 870 feet in 1 minute:  

= 870/60 ft/s

= 14.5 ft/s

Hence,

Ron 9 feet per seconds

Zach 8.4 feet per seconds

Katie  12.8 feet per seconds

Noah 14.5 feet per seconds

So, Zach is the fastest.

Therefore the fastest is Zach.

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The equation of line: y = 2x - 9

slope = 2

y-intercept = (0, -9)

The graph of the line y = 2x - 9 is as shown below.

In this question we have been given a point (6, 3) and slope m = 2

We need to find an equation of line passing through (6, 3) with slope m = 2

Using formula of the point-slope form:

(y - y1) = m(x - x1)

(y - 3) = 2(x - 6)

y - 3 = 2x - 12

y = 2x - 12 + 3

y = 2x - 9

This is slope-intercept form of equation of line.

slope = 2

y-intercept = -9

Therefore, the equation of line: y = 2x - 9

slope = 2

y-intercept = (0, -9)

The graph of the line y = 2x - 9 is as shown below.

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The degree measure of each angle in the triangle is

∠H = 59°

∠F = 39°

Angle sum property of triangle says that sum of all the triangle is always equal to 180°

∠G is given to us as 90°

So by applying the property we an say that

90 + (3x - 14) + (5x - 16) = 180

8x = 180 - 90 + 14 + 16

8x = 120

x = 15

∠H =  5x - 16

∠H = 5*15 - 16

∠H = 75 - 16

∠H = 59°

∠F = 3x - 14

∠F = 3*15 - 14

∠F = 45 - 14

∠F = 39°

Therefore ∠H = 59° and ∠F = 39°

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The formula for the cost if the line rental is £20 and the price of calls made is £15 will be 20 + 15p.

It should be noted that an expression is used to illustrate the relationship given between the variables.

In this case, the monthly phone contract is made up of the fixed line rental and the price represented by p.

The appropriate expression to illustrate this information will be:

= Fixed cost + Calls made

= 20 + 15(p)

= 20 + 15p

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Answer:

(- 8, 0 )

Step-by-step explanation:

under a reflection in the line y = x

a point (x, y ) → (y, x ) , then

(0, - 8 ) → (- 8, 0 )

Answer:

C) 9 hours

Step-by-step explanation:

as per your picture the equation is

D(t) = 0.75×cos(pi/6 × t) + 1.5

the function cosine continuously "waves" from +1 to -1 and back.

the lowest value of this function for the first time after t>0 is when the cosine part reaches -1 the first time.

that is at 270° or 3pi/2.

so,

pi/6 × t = 3pi/2

1/6 × t = 3/2

t = 3×6/2 = 3×3 = 9

A system of linear inequalities that represents this scenario is given by:

p + s ≥ 10

5.50p + 3.50s ≤ 117

An inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

In order to write a system of linear inequalities to represent the scenario, we would assign variables to the cost of the beginner class and advanced class, and then translate the word problem into algebraic equation as follows:

Since Latisha cannot buy more than (≥) 10 vegetables, the inequality to represent this is as follows:

p + s ≥ 10

Since Latisha's budget cannot exceed (≤) $117, the inequality to represent this is as follows:

5.50p + 3.50s ≤ 117

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The spreadsheet that shows the distances between the cities, indicates that the distances between the cities are as follows;

a) From Hereford to Chester, the distance is 95 miles

b) Chester is the town that is 99 miles from Kendal

c) Ellen will have driven 201 miles if she drives from Kendal to Hereford through Chester

A spreadsheet application is used for the storage analysis, organization, and computation of data.

The interpretation of the distances in the chart which is in the form of a spreadsheet are;

The value in the cell corresponding to the distance from Kendal to Chester that is the cell which is on the same column as Kendal and on the same row as Chester is 99

Therefore, the distance from Kendal to Chester is 99 miles

The value in the cell that directly links Chester to Hereford that is the cell which is on the same column as Chester and on the same row as Hereford is 95

Therefore, the distance from Chester to Hereford is 95 miles

The value in the cell that connects Kendal to Hereford, that is the cell which is on the same column as Kendal and which is on the same row as Hereford is 201

Therefore the distance from Kendal to Hereford is 201 miles

a) The distance from Hereford to Chester is 95 miles

b) The town that is 99 miles from Kendal is Chester

c) The distance Ellen will have driven if she drives from Kendal to Hereford via Chester is 201 miles

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The total number of oranges in the pyramidal stack is 78.

The oranges are stacked by the grocer in a pyramid like shape,

The base of the pyramid is rectangular with a size of 5 by 8 oranges,

So, total number of oranges in the base can be found as,

= 5 x 8

= 40 oranges.

One orange has four oranges below it. So, if there are 40 oranges in the base, the upper layer will have one row of oranges reduced from each side of the rectangular base.

So, every next level will have (L-1)(B-1) oranges, where L and B are the length and breadth of every preceding rectangle.

Hence, Oranges in level 1 = 4x8

Oranges in level 2 = 3x7

Oranges in level 3 = 2x6

Oranges in level 4 = 1x5

Hence, total oranges are, (40+21+12+5) oranges.

Total oranges stacked are 78 oranges.

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The probability that no one enters between 12:00 and 12:05 is 0.082.

The probability that at least 4 people enter the casino during that time is 0.242

Given that people enter the casino at the rate of 1 every 2 minutes. A random variable X is defined as the number of people entering the casino between the time period of 12:00 and 12:05. Since we are given in the question that people enter the casino at the rate of 1 every minute, hence in the given time period they enter at the rate of 2.5.

P(X=0) = [tex]e^{-2.5}[/tex] = 0.082

Hence the probability that no one enters between 12:00 and 12:05 is 0.082.

The required probability is simply

P(X≥4) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=3)

= 1 - [tex]e^{-2.5}[/tex] - 2.5[tex]e^{-2.5}[/tex] - (((2.5)² / 2)[tex]e^{-2.5}[/tex] ) - (((2.5³)/3!)[tex]e^{-2.5}[/tex])

= 0.242

Hence, the probability that at least 4 people enter the casino during that time is 0.242

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The solutions for the quadratic equation:

2x^2 + 12x + 18 = 0

are:

x₋ =  -5.55

x₊  = -0.4

Remember that for a general quadratic equation:

a*x^2 +b*x + c = 0

The solutions are of the form:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Here we have the quadratic:

2x^2 + 12x + 18 = 0

Then using the formula for the solutions we will get:

[tex]x = \frac{-12 \pm \sqrt{12^2 - 4*2*18} }{2*2} \\\\x = \frac{-12 \pm 10.2}{4}[/tex]

The two solutions of the quadratic equation are:

x₋ = (-12 - 10.2)/4 =  -5.55

x₊ = (-12 + 10.2)/4 = -0.4

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f(x+9) = 3x + 26.

Given equation:

f(x)=3x-1

f(x+9) = 3(x+9) - 1

= 3x + 3*9 - 1

= 3x + 27 - 1

= 3x + 26.

Therefore f(x+9) = 3x + 26.

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