The vehicle's fuel efficiency is no less than 35 miles per gallon

Answer:

y = 2x + 5

Step-by-step explanation:

The slope is

[tex]\frac{-1-7}{-3-1}=2[/tex]

Substituting into point-slope form, we get the equation to be

[tex]y-7=2(x-1)[/tex]

which rearranges into slope-intercept form as:

[tex]y-7=2x-2 \\ \\ y=2x+5[/tex]

Answer:   y = 11-x

This is the same as y = -x+11

To get either result, we subtract x from both sides of the original equation. This is to undo the plus x.

Answer:

10.

Step-by-step explanation:

1) formula of the required slope is:

[tex]slpoe=\frac{y_2-y_1}{x_2-x_1};[/tex]

2) according to the formula above:

[tex]slope=\frac{2+8}{5-4}=10.[/tex]

P.S. x₁=2; x₂=-8; y₁=5; y₂=4.

The slope of the line, m = 8/9.

The y-intercept of the line, b = 4/9.

An equation that represents a line can be expressed in slope-intercept form as, y = mx + b, where we have the following:

Slope = m

Y-intercept = b.

Given that a line is represented by the equation, 8x - 9y = -4, rewrite the equation in slope-intercept form:

8x - 9y = -4

8x - 9y - 8x = -8x - 4 [subtraction property of equality]

-9y = -8x - 4

-9y/-9 = -8x/-9 - 4/-9 [division property of equality]

y = 8/9x + 4/9

Therefore:

The slope of the line, m = 8/9.

The y-intercept of the line, b = 4/9.

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Using linear functions and the given table, it is found that:

A linear function is modeled by:

y = mx + b

In which:

From the table, we have that:

For the supply equation, we have two points:

(9.8, 190), (10, 220).

Hence the slope is given by:

m = (220 - 190)/(10 - 9.8) = 150.

Hence:

y = 150x + b.

When x = 9.8, y = 190, hence:

190 = 150(9.8) + b

b = -1280.

Hence:

y = 150x - 1280.

We want to find x when y = 200, hence:

200 = 150x - 1280

x = 1480/150

x = $9.87.

The quantity supplied will be equal to 200,000 at a price of $9.87.

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The value of C3 will increase with a factor of 4 because the value of B2 increased with a factor of 2 and C3 is multiplying B2 by 2.

Given data

B2 is changed from 7 to 9

C3 contains the formula =B2*2

Finding the increment in B2

= 9 - 7

= 2

The effect on C3

C3 = B2 * 2

C3 = 2 * 2

C3 = 4

We can therefore say that The value of C3 will increase with a factor of 4 because the value of B2 increased with a factor of 2 and C3 is multiplying B2 by 2.

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The statement that describes the combined functions V(x) and S(x) is B. The sum function is linear but the volume function is not.

It should be noted that we are given that f(x) and g(x) are linear. Due to this, the sum function S(x) is linear.

And we know the shape of our figure, so we just need to multiply the dimensions for V(x) but the product of three linear functions results in a cubic function, and we conclude V(x) is not linear.

Therefore, the statement that describes the combined functions V(x) and S(x) is that the sum function is linear but the volume function is not.

In conclusion, the correct option is B.

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The ordered pair which is a solution to the given inequality is: C. (2, 1).

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:

Next, we would test the ordered pair with the given inequality to determine a solution as follows:

For ordered pair (4, 4), we have:

3x + 2y < 15

3(4) + 2(4) < 15

12 + 8 < 15

20 < 15 (False).

For ordered pair (3, 3), we have:

3x + 2y < 15

3(3) + 2(3) < 15

9 + 6 < 15

15 < 15 (False).

7x - 4y > 9

7(3) - 4(3) > 9

21 - 12 > 9

9 > 9 (False)

For ordered pair (2, 1), we have:

3x + 2y < 15

3(2) + 2(1) < 15

6 + 2 < 15

8 < 15 (True).

7x - 4y > 9

7(2) - 4(1) > 9

14 - 4 > 9

10 > 9 (True)

For ordered pair (1, 0), we have:

3x + 2y < 15

3(1) + 2(0) < 15

3 + 0 < 15

3 < 15 (True).

7x - 4y > 9

7(1) - 4(0) > 9

7 - 4 > 9

3 > 9 (False)

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Answer:

56 yd²

Step-by-step explanation:

You cut up the figure into 2 distinctive rectangles where it looks like one small rectangle is intersecting a larger one.

So you would do

4(4 + 4 + 4) = 4(12) = 48 yd²

2(4) = 8 yd²

Add

8 + 48 = 56

56 yd²

Hope this helps! :)

Answer:

2,835

Step-by-step explanation:

63 x 5 = 315

63 x 4 = 252

    315

+2520

2835

34 = -2x

Divide through by -2

x = -17

The polynomials that match with other equivalent expressions are :

(a) → (iii), (b) → (ii), (c) → (iv), (d) → (i)

Consider the polynomials,

(a) 4x² + 18x                                (i) 2x(2x + 1)

(b) 4x² + 2x + 18x +9                   (ii) (2x + 1)(2x +9)

(c) (2x + 3)(2x + 3)                       (iii) 2x(2x + 9)    

(d) 4x² + 2x                                   (iv) 4x² + 12x + 9

Now,

Consider the polynomial 2x(2x + 1),

2x(2x + 1) = 2x(2x) + 2x(1)

2x(2x + 1) = 4x² + 2

Therefore, (d) is equal to (i).

Consider the polynomial 2x(2x + 9),

2x(2x + 9) = 2x(2x) + 2x(9)

2x(2x + 9) = 4x² + 18x

Therefore, (a) is equal to (iii).

Consider the polynomial (2x + 1)(2x +9) ,

(2x + 1)(2x +9)  = (2x)(2x) + (2x)(9) + (2x)(1) + 9

(2x + 1)(2x +9) = 4x² + 18x + 2x + 9

Therefore, (b) is equal to (ii).

Consider the polynomial (2x + 3)(2x + 3),

(2x + 3)(2x + 3) = (2x)(2x) + (2x)(3) + (3)(2x) + 9

(2x + 3)(2x + 3) = 4x² + 12x + 9

Therefore, (c) is equal to (iv).

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The complete question is mentioned below:

Match the polynomial on the left with the appropriately factored expression on the right.

(a) 4x² + 18x                                (i) 2x(2x + 1)

(b) 4x² + 2x + 18x +9                   (ii) (2x + 1)(2x +9)

(c) (2x + 3)(2x + 3)                       (iii) 2x(2x + 9)    

(d) 4x² + 2x                                   (iv) 4x² + 12x + 9

Using translation concepts, it is found that:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up. Other types of transformations are rotations or dilation.

For the first question, the rule for a reflection over the x-axis is given by:

(x,y) -> (x,-y).

Then:

P': (-5,-3) -> (-5,3).

The coordinates of P' are (-5,3).

For the second question, the rule for a 180º clockwise rotation about the origin is given by:

(x,y) -> (-x,-y).

Hence:

Hence:

The coordinates of the new triangle are P'(5,3),  K'(3,1) and Y'(1,4).

For a dilation by a scale factor of 2, every coordinate is multiplied by 2, hence:

The new coordinates of the dilated triangle are: A'(2,2), B'(10,4) and C'(6,10).

The rule for a translation 5 units down is:

(x,y) -> (x, y - 5).

Hence:

(-1,4) -> (-1,-5).

The new coordinates of C' are (-1,-5).

For the final question, a translation is when just the position of the image changes up/down, having no changes in size or orientation, hence:

The bottom-right image(the one that is already marked) represents a translation.

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Answer:

A) -1

Step-by-step explanation:

Sandra has 4³ jars of honey and each one sells for 42 dollars, then if she sells total money = 2.688 * 10³ dollars.

Y = 42x is Sandra's equation.

To find her hourly rate, we need to find how much she earns in "1" hour. Since x is hours, we plug in x = 1 and find y (which is her pay).

Y = 42x

Y = 42(1)

Y = 42

Therefore, $42 is Sandra's hourly rate.

Based on the condition,

Sandra has 4³ jars of honey and each one sells for 42 dollars.

= 4³ * 42$

The expression to exponent expression model is equal to = 4³ * 42

Simplify the expression,

= 4³ * 42$

4³ means 4*4*4 = 64

We can write 64 is in this equation,

= 64 * 42$

= 2688$

= $2.688 * 10³

Hence,

The expression to model the situation is equal to = $2.688 * 10³

Therefore,

Sandra has 4³ jars of honey and each one sells for 42 dollars, then if she sells total money = 2.688 * 10³ dollars.

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Answer:

1 and -8

Step-by-step explanation:

g(1) = 3*1-2

     = 3-2

     = 1

g(-2) = 3*-2-2

       = -6-2

       = -8

The required value of the function at g(1) and g(-2) are 1 and -8 respectively.

Given that,
g(a) = 3a - 2
To determine the value function at a = 1 and a = -2

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given function is,
g(a) = 3a-2

at a = 1
g(1) = 3 * 1 - 2
g(1) = 3 - 2
g(1) = 1

Now,
at  = -2
G(-2) = 3 * -2 - 2
G(-2) = -6 - 2
g(-2) = -8

Thus, the required value of the function at g(1) and g(-2) are 1 and -8 respectively.

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the logarithm of x ells us the value of the exponent y of 10 such that 10^y is equal to x.

First, let's define the natural logarithm.

We know that the natural logarithm is the inverse of the exponential function, then:

[tex]e^{ln(x)} = x\\ln(e^x) = x[/tex]

So the natural logarithm of x tells us the value of the exponent y of e such that e^y is equal to x.

And the logarithmic function is a logarithm on base 10, which is written as:

log(x) = log₁₀(x) = ln(x)/ln(10)

If we say that this is equal to e^y for some value of y, we get:

ln(x) = ln(10)*y

If now we apply the exponential function in both sides, we get:

expo(ln(x)) = exp(ln(10)*y) = 10^y

x = 10^y

So, the logarithm of x ells us the value of the exponent y of 10 such that 10^y is equal to x.

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Answer: h(-7)=70

Step-by-step explanation:

h(x)=x^2-3x

h(-7)=(-7)^2-3(-7)

h(-7)=49-(-21)

h(-7)=49+21

h(-7)=70

Answer: alright, here we go

Step-by-step explanation:

best way to represent this is linear equations, so:

y=-0.5x+12
y=-2x+18

-2x+18=-0.5+12
+0.5x    +0.5x
-1.5x+18=12
      -18    -18
-1.5x=-6
-x=-4
x=4

y=-2(4)+18
y=-8+18
y=10

answer: (4,10)
answer: h=4

bonus: the candles will each be ten inches tall after four hours

The equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1) is y - 1 = 3/2(x+3)

One of the most popular ways to represent a linear equation is in point-slope form, which has the following structure:

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

where (x1, y1) is a point on the line, m is the slope, and x and y are variables that denote further points along the line. When one point on the line and the slope are known, the point-slope form can be employed. Given that at least one point and the slope of the line are known, it is helpful for locating further points on a line.

According to the given values;

Equation of a line in point-slope form

The equation of a line in point-slope form is expressed as:

y-y0 = m(x-x0)

where:

m is the slope

(x0,y0) is the point on the line

The slope of the given line is as shown:

Slope = 2-(-4)/2-(-2)

Slope = 2+4/2+2

Slope = 6/4 = 3/2

Substitute the slope and the point

y - 1 = 3/2(x-(-3))

y - 1 = 3/2(x+3)

Hence the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1) is y - 1 = 3/2(x+3)

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The set A’ using the roster method is A' = {5, 6, 8}

The sets are given as

Universal set, U = {5, 6, 7, 8, 9, 10, 11}

Set A, A = {7, 9, 10, 11}

The elements of the set A’ are the elements that are in the universal set but not in set A

Using the above as a guide, we have the following values

A' = {5, 6, 8}

The above is in roster method or form

Hence, the set A’ using the roster method is A' = {5, 6, 8}

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Answer:

a = -3

(-3)² = -9

Answer: -9

Step-by-step explanation:

-3 x -3 = -9

(I think)

Answer:

the answer is 0.888

Which is 8÷9

Answer: The answer is B: 0.88888888888

Step-by-step explanation:

The correct answer is 1x+7y=-15.

Finding an equation in standard form for a line with the points (-8, -1) and (-1, -2) is what we're after.

Since a, b, and c are integer coefficients in standard form, a and b CANNOT equal 0 or be negative.

It is helpful to first put the line in a different form, such as slope-intercept form, which is represented by the equation y=mx+b, where m is the slope and b is the y intercept.

Let's start by calculating the slope using the equation, which can be done from two points.

(y_2-y_1)/(x_2-x_1)

x1 = -8

y1 = -1

x2 = -1

y2 = -2

Substituting the value = (-2-(-1 ))/((-1-(-8))

= -2+1/-1+8

= -1/7

Thus the slope is -1/7

y=mx+b

y=(-1/7)x+b

-1=(-1/7)(-8)+b

-1=8/7+b

-1-8/7=b

-7-8/7=b

-15/7 = b

substituting the value in equation,

y = (-1/7)x-15/7

7y=-1x-15

Thus the equation is,

1x+7y=-15

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Answer: y = 2x - 3

Step-by-step explanation:

y = mx + b

y + 2x - 3

you need to add 3.43 liters of pure alcohol to reach a concentration of 30%.

Let's define the variable x as the number of liters of the 30% that you need to use.

The concentration of the mixture then will be:

1*x +  0.1*12

Where the concentration for the x liters is 100%, because this is pure alcohol, and for the 12 liters we use a concentration of 10%.

Now, that must be equal to a mixture with a concentration of the 30%, then we can write:

x + 0.1*12 = (x + 12)*0.3

Now we just need to solve this linear equation for x.

x + 1.2 = x*0.3 + 12*0.3

x - x*0.3 = 12*0.3 - 1.2

x*0.7 = 12*0.3 - 1.2

x = (12*0.3 - 1.2)/0.7 = 3.43

This means that you need to add 3.43 liters of pure alcohol to reach a concentration of 30%.

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The quadratic function to represent the given situation is                         y=-(1/312)x²+x+3

A quadratic function is of the form y=g(x) where g(x) is a polynomial in x with degree 2.

The baseball is hit at a initial height of 3 feet. The baseball follows a path of a parabola.

Maximum height=81 feet

Distance from home plate =156 feet

So, (156,81) is the vertex of the parabolic path.

We know that when vertex is at (h,k) then the vertex form of the parabola is  y=a(x-h)²+k

So the quadratic equation is of the form

y=a(x-156)²+81

Now the initial height is given as 3 feet.

So at x=0, y=3

Putting the values in the equation we get:

3=a(0-156)²+81

or, -78=a×156²

or, a=-(78÷156²)

or, a=-(1/312)

So the quadratic equation can be written as

y=-(1/312)(x-156)²+81

Simplifying we get : y=-(1/312)x²+x+3

The quadratic function to represent the path of the baseball is given by y=-(1/312)x²+x+3

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Scale Factor: A measure for similar figures.

Similar Figures: Two figures which are same in shape. these shapes do not have the same size as shapes with the same shape and size are congruent.

Finding the scale Factor: The scale factor can be found by dividing the dimension of the new shape by the dimension of the old shape.

21 ÷ 6 = 3.5

The scale factor would be 3.5

Now we can use this scale factor to find the dimension of the smaller rectangle.

52.5 cm ÷ 3.5 = 15 cm

The dimension of the smaller rectangle is 15 cm

We can check the answer by multiplying the new found dimension by the scale factor:

15 cm x 3.5 = 52.5 cm  

∴ The scale factor is 3.5

∴ The dimension of the smaller rectangle is 15 cm