5. What is the solution to the system? *
Captionless Image
6. Explain what your solution means in terms of the scenario. *

Answer:

[tex]\frac{11}{5}[/tex]

Step-by-step explanation:

Using the section formula

[tex]y_{P}[/tex] = [tex]\frac{3(5)+7(1)}{3+7}[/tex] = [tex]\frac{15+7}{10}[/tex] = [tex]\frac{22}{10}[/tex] = [tex]\frac{11}{5}[/tex]

Answer:

Option 3

Step-by-step explanation:

y is less than the y values on the red line and greater than the y values on the blue line.

Equation of the red line:

y-intercept is clearly 3

using (0,3) & (-2,2)

Slope = (y2-y1)/(x2-x1)

= (3-2)/(0-(-2)) = 1/2

y = (1/2)x + 3

Equation of the blue line:

y-intercept is clearly -2

Using (0,-2) & (1,1)

Slope = (1-(-2))/(1-0) = 3/1 = 3

y = 3x - 2

y < (1/2)x + 3 & y > 3x - 2

The graph shows the solution for the following inequalities; C. y ≥ 3x - 2 and y ≤ -1/2(x) + 3.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

[tex]y - y_1 = m(x - x_1)[/tex]

Where:

First of all, we would determine the slope for the red line by using these points (2, 4) and (0, 3);

[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope (m) = (3 - 4)/(0 - 2)

Slope (m) = 1/2

At point (0, 3) and a slope of 1/2, an inequality for this line can be calculated by using the point-slope form as follows:

y - 3= 1/2(x - 0)  

y = 1/2(x) + 3

y ≤ 1/2(x) + 3 (since the solid line is shaded below).

At point (0, -2) and a slope of 3, an inequality for this line can be calculated by using the point-slope form as follows:

y + 2= 1/2(x - 0)  

y = 3(x) - 2

y ≥ 3x - 2 (since the solid line is shaded below).

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Answer:

$127.40

Step-by-step explanation:

$98-30%=$127.4

Answer:

(-8, -5)

Step-by-step explanation:

I plotted  the equation on a graph and looked at the reflection and got that.

Answer:

[tex]\$4,400[/tex]

Step-by-step explanation:

Let

x ----> the original price of the furniture

Remember that

[tex]100\%-20\%=80\%=80/100=0.80[/tex]

we know that

The original price multiplied by 0.80 must be equal to the cost of the furniture after a 20% reduction

so

The linear equation that  represent this situation is

[tex]0.80x=3,520.00[/tex]

solve for x

Divide by 0.80 both sides

[tex]x=\$4,400[/tex]

Answer:

4.00

Step-by-step explanation:

Step-by-step explanation:

BOTH TRIANGLES ARE SIMILAR BY THE AA SIMILARITY POSTULATE.

In first triangle:

Remaining angle = 180° - (70° + 30°)= 80°

In second triangle:

Remaining angle = 180° - (80° + 30°)= 70°

Hence, all the angles of first triangle are congruent to the corresponding angles of the second triangle.

Thus, both the triangles are similar by

THE AA SIMILARITY POSTULATE

The complete factorized form for the given expression is [tex]\left(9 x^{4}+1\right)\left(3 x^{2}+1\right)\left(3 x^{2}-1\right)[/tex]

Step-by-step explanation:

Step 1: Given expression:

              [tex]81 x^{8}-1[/tex]

Step 2: Trying to factor as a Difference of Squares

Factoring [tex]81 x^{8}-1[/tex]

As we know the theory that the difference of two perfect squares, [tex]A^{2}-B^{2}[/tex]  can be factored into (A+B) (A-B)

from this, when analysing, 81 is the square of 9, [tex]x^{8}[/tex] is the square of [tex]x^{4}[/tex]. Hence, we can write the given expression as,

            [tex]\left(9 x^{4}\right)^{2}-1^{2}[/tex]

By using the theory, we get

           [tex]\left(9 x^{4}+1\right)\left(9 x^{4}-1\right)[/tex]

Again, we can further factorise the term [tex]\left(9 x^{4}-1\right)[/tex]

[tex]9 x^{4}[/tex] is the square of [tex]3 x^{2}[/tex]. Therefore, it can be expressed as below

           [tex]\left(3 x^{2}+1\right)\left(3 x^{2}-1\right)[/tex]

Now, we can not factorise further the term [tex]\left(3 x^{2}-1\right)[/tex]. Because it will come as [tex]\sqrt{3} x[/tex] (3 is not a square term). Thereby concluding that the complete factorisation for the given expression is [tex]\left(9 x^{4}+1\right)\left(3 x^{2}+1\right)\left(3 x^{2}-1\right)[/tex]

Answer:

The y-intercept is where an equation's graph hits the y-axis. It represents the constant value, when x=0, the intercept is the constant

Step-by-step explanation:

The y-intercept indicates the vertical position where the line or curve intersects the y-axis

The y-intercept refers to the point where a line or curve intersects the y-axis on a graph.

It is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

In the equation of a line in slope-intercept form (y = mx + b), where m represents the slope of the line and b represents the y-intercept, the y-intercept is the constant term (b).

The y-intercept represents the value of the dependent variable (y) when the independent variable (x) is not present or equal to zero.

It is the initial value or starting point of the function or graph.

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Answer:

ideas and conflict and maybe elements depending on the story

Answer:

  see below for a graph

Step-by-step explanation:

It is convenient to use a point-slope form of the equation of a line for graphing, since we know the slope is -12 m/min and the point is (30, 0) at sea level.

The horizontal axis is minutes; the vertical axis is meters above sea level. The graph cannot extend below -413 meters from sea level, as that is the lowest place on earth.

Answer:

87.5%

Step-by-step explanation:

35/40=7/8=0.875=87.5%

Answer:

Step-by-step explanation:

9

Final answer:

Multiplying the dimensions of a rectangle by 3 increases its area by a factor of 9, which is the square of 3. The area of the rectangle goes from 14 cm^2 to 126 cm^2.

Explanation:

When the dimensions of a rectangle are multiplied by a certain factor, the area of the rectangle is affected by the square of that factor. Initially, the area of a 7-cm by 2-cm rectangle is 14 cm2. When the dimensions are each multiplied by 3, the new dimensions become 21 cm by 6 cm. Therefore, the new area is 21 cm  imes 6 cm = 126 cm2. The area scales in proportion to the square of the linear dimensions. If we compare the new area to the old area, we see that 126 cm2 / 14 cm2 equals 9, meaning the area has increased by a factor of 9, which is 32, since we multiplied the dimensions by 3. This principle applies generally: when a rectangle's dimensions are scaled by a factor, its area is scaled by the square of that factor.

Answer:

3*(5*x-7)-(15*x-21)=0

Step-by-step explanation:

3 • (5x - 7) -  (15x - 21)  = 0

Step  2  :

Equation at the end of step  2  :

 0  = 0

Step  3  :

Equations which are always true :

Answer:

52

Step-by-step explanation:

65 dollar is price so it has 20 percent discount so,

65× 20% = 13

so,

65- 13

52 dollars

Answer:

see explanation

Step-by-step explanation:

Using the Cosine rule

a² = b² + c² - 2abcosA ← Rearranging for cosA gives

cosA = [tex]\frac{b^2+c^2-a^2}{2ab}[/tex]

(a)

let a = 10, b = 7, c = 8 and A = α, then

cosα = [tex]\frac{7^2+8^2-10^2}{2(7)(8)}[/tex] = [tex]\frac{49+64-100}{112}[/tex] = [tex]\frac{13}{112}[/tex], thus

α = [tex]cos^{-1}[/tex]( [tex]\frac{13}{112}[/tex] ) ≈ 83° ( to the nearest degree )

(b)

let the angle opposite side 7 be x

Using the Sine rule

[tex]\frac{10}{sin83}[/tex] = [tex]\frac{7}{sinx}[/tex] ( cross- multiply )

10sinx = 7sin83 ( divide both sides by 10 )

sinx = [tex]\frac{7sin83}{10}[/tex] , thus

x = [tex]sin^{-1}[/tex] ( [tex]\frac{7sin83}{10}[/tex] ) = 44°

The third angle can be found using the sum of angles in a triangle

third angle = 180° - (83 + 44)° = 180° - 127° = 53°

The 3 angles are 83°, 44°, 53°

Answer:

-1.5

Step-by-step explanation:

The value of x is -3/2 or -1.5.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

4x²+12x+9 =0

Now, the solution for the expression is

4x²+12x+9 =0

4x²+6x+ 6x +9 =0

2x( 2x + 3)+ 3 (2x+ 3)= 0

(2x+ 3) (2x+ 3) = 0

x= -3/2, x= -3/2

Hence, the value of x is -3/2 or -1.5.

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Answer:

−2k=k−7−8

−2k=k+−7+−8

−2k=(k)+(−7+−8)(Combine Like Terms)

−2k=k+−15

−2k=k−15

Step 2: Subtract k from both sides.

−2k−k=k−15−k

−3k=−15

Step 3: Divide both sides by -3.

−3k

−3

=

−15

−3

k=5

Step-by-step explanation:

Answer:

Part 1) [tex]\frac{5}{2}[/tex]  or  [tex]5:2[/tex]

Part 2) [tex]\frac{8}{1}[/tex]  or  [tex]8:1[/tex]

Step-by-step explanation:

Write the ratio as a fraction in simplest form

Part 1) 15 girls to 6 boys

we know that

To find out the ratio, divide the number of girls by the number of boys

so

[tex]\frac{15}{6}[/tex]

Simplify

Divide by 3 both numerator and denominator

[tex]\frac{5}{2}\ \frac{girls}{boys}[/tex]

Part 2) 24 plays for 3 teams

we know that

To find out the ratio, divide the number of plays by the number of teams

so

[tex]\frac{24}{3}[/tex]

Simplify

Divide by 3 both numerator and denominator

[tex]\frac{8}{1}\ \frac{plays}{team}[/tex]

Final answer:

To simplify the ratios 15 girls : 6 boys and 24 plays : 3 teams, find the greatest common factor and divide both parts of the ratio by it, resulting in the simplest forms  rac{5}{2} and 8, respectively.

Explanation:

To write the ratios as fractions in simplest form for the given scenarios:

For the ratio of 15 girls to 6 boys, the fraction would be  rac{15}{6}. To simplify, divide both the numerator and the denominator by their greatest common factor (GCF), which is 3. Thus, the simplest form is  rac{15 \/ 3}{6 \/ 3} =  rac{5}{2}.

For the ratio of 24 plays for 3 teams, the fraction is  rac{24}{3}. Again, to simplify, divide both the numerator and the denominator by the GCF, which is 3 in this case. The simplest form is  rac{24 \/ 3}{3 \/ 3} =  rac{8}{1}, which can also be written simply as 8 since a denominator of 1 implies the value is a whole number.

Answer:

Divide it all by 3, then put it outside the parentheses.

3(2x+5)

Step-by-step explanation:

The requried factors of the given expression are given as 3[x + 5].

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

here,
The distributive property is given as,
a[b + c] = ab + bc

Now,
the given expression performing the distributive property in a way given as,
ab + bc = a[b + c]

Given expression,
= 6x + 15
= 3 × 2x + 3 × 5
= 3 [2x + 5]

Thus, the requried factors of the given expression are given as 3[x + 5].

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To determine how many ways to paint the buildings, we consider the choices for each building sequentially, considering the constraints. There are either 36 or 24 combinations, depending on the colors chosen for the first and last buildings. A step-by-step count confirms this range of possibilities.

A systematic approach gives us the general formula: 4 choices for the first building × 3 choices for the second building × 3 choices for the third building × (2 or 3) choices for the fourth building, depending on the first color chosen. This results in a total of 36 or 24 possible combinations, depending on the first and last color's relationship. A careful count avoiding the restrictions on the colors confirms this.

Answer:

The answer is true.

I took the quiz! :)

Answer:

The volume of the actual house is 1,324.94 cubic meters

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Height of the scale model = 53 cm

Height of the actual house = 624 cm

Scale of the model = 642/53 = 11.77

Volume of the scale model = 0.8125 cubic meters

2. What is the volume of the house?

For answering the question we have to find the width and the length of the model, then use the scale of the model for calculating the volume of the actual house, this way:

Volume of the scale model = 0.8125 cubic meters

Area of the scale model = Volume of the model/Height of the model

Area of the scale model = 0.8125/0.53

Area of the scale model = 1.533 square meters

Area of the scale model = Length * Width

Area of the scale model = 1.533 * 1

Now, we can calculate, the measurements of the house to calculate its volume:

Height of the actual house = 6.24 meters

Length of the actual house = 1.533 * 11.77 = 18.04 meters

Width of the actual house = 1 * 11.77 = 11.77 meters

Volume of the actual house = 6.24 * 18.04 * 11.77

Volume of the actual house = 1,324.94 cubic meters

Ans 11ft

Step-by-step explanation:

Sq Area= length * length

Length=√area=√121=11

Answer:

it is B. -11 and 47

Step-by-step explanation:

you have to take away 47 and 11 and it equals 36.

Answer:

n>12

Step-by-step explanation:

n/6>2

n>2*6

n>12

The Graph of the inequality is shown below.

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have the inequality,

n÷6>2

Multiply both side by 6 we get

(n ÷ 6 ) 6 > 2 x 6

n > 12.

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Answer:

  E.  19

Step-by-step explanation:

  z = (5)(11)(2·2·7)(2·19)

  z = 2³·5·7·11·19

The greatest prime factor is 19.

Answer:15

Step-by-step explanation:9+6=15

Answer: 15

Step-by-step explanation:

9+6

Answer:

The volume of the plastic pipe  is 141 cubic centimetre

Step-by-step explanation:

Given:

The Length of the plastic water pipe = 12 cm

The inner Diameter of the  plastic water pipe = 12 cm

The outer Diameter of the  plastic water pipe = 15 cm

To Find:

the volume of the plastic pipe not the hollow interior to the nearest hundredth = ?

Solution:

The volume of the plastic water pipe can be found by using the volume of the cylinder formula

The Volume of the cylinder  = [tex]\pi r^2 h[/tex]

Where

r is the radius

h is the height

Radius r  [tex]= \frac{diameter}{2} = \frac{15}{2} = 7.5 cm[/tex]

On substituting the values

The Volume of the cylinder  

= [tex]\pi (7.5) (6)[/tex]

= [tex]45 \pi[/tex]

=  141.37   cubic centimetre

= 141  cubic centimetre

Answer:

A grand total of 50 dimes

Step-by-step explanation: