Fill In the proportion No explanation just need answer got disconnected from last tutor

EF =21

4) Let's find out the measure of the line segment EF, using the Trapezoid Midsegment Formula:

4.1) We can plug into that the lengths of AD and BC:

Note that the Midsegment is the average of the bases of a trapezoid.

4.3) Hence, the answer is 21

We will have the following:

a)

b)

Given:

Quadratic equation

To find:

Values of x satisfying given equation.

Explanation:

Roots of equation of type

roots will be (x-a)(x-b) and x = a,b.

Solution:

We will factorize equation as:

Hence, 3 and 7 are values of x.

Answer:

[tex](y - 9) = (-8/3)\, (x - 7)[/tex].

Step-by-step explanation:

If a line in a cartesian plane has slope [tex]m[/tex], and the point [tex](x_{0},\, y_{0})[/tex] is on this line, then the point-slope equation of this line will be [tex](y - y_{0}) = m\, (x - x_{0})[/tex].

The slope of a line measures the rate of change in [tex]y[/tex]-coordinates relative to the change in the [tex]x[/tex]-coordinates. If a line goes through two points [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex], the slope of that line will be:

[tex]\begin{aligned}m &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}}\end{aligned}[/tex].

In this question, the two points on this line are [tex](7,\, 9)[/tex] and [tex](10,\, 1)[/tex], such that [tex]x_{0} = 7[/tex], [tex]y_{0} = 9[/tex], [tex]x_{1} = 10[/tex], and [tex]y_{1} = 1[/tex]. Substitute these values into the equation to find the slope of this line:

[tex]\begin{aligned}m &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}} \\ &= \frac{1 - 9}{10 - 7} \\ &= \left(-\frac{8}{3}\right)\end{aligned}[/tex].

With the point [tex](7,\, 9)[/tex] as the specific point [tex](x_{0},\, y_{0})[/tex] (such that [tex]x_{0} = 7[/tex] and [tex]y_{0} = 1[/tex]) as well as a slope of [tex]m = (-8 / 3)[/tex], the point-slope equation of this line will be:

[tex]y - y_{0} = m\, (x - x_{0})[/tex].

[tex]\displaystyle y - 9 = \left(-\frac{8}{3}\right)\, (x - 7)[/tex].

Answer:

he ran 96 miles farther in the second week.

Explanation:

Given that A long distance runner runs 2⁵ miles one week;

And 2⁷ miles the next week;

The amount of miles farther he run in the second week than the first week is;

Therefore, he ran 96 miles farther in the second week.

To create the table of values, we need to find the coordinates of the given points.

The coordinatesare given by (x,y), where x ican be found by drawing an imaginary vertical line passing through the point, and the x-value is the value of the x-axis where the line intercepts the x-axis.

The y-coordinate is given by the point of interception on the y-axis of a horizontal line passing through the point, so, for the fir tpoint the coordinates are:

If we apply the same procedure to the next points, we can find the following coordinates:

Thus, th table of values will be:

x y

-2 5

-1 4

0 3

1 2

2 1

You have that 3/16 of the animals are dogs and 5/24 of the animals are cat.

To determine the fraction of animals that are neither dogs nor cat, consider the following:

If 3/16 are dogs, then 13/16 are other animals, but from this fraction, 5/24 are cats. Then, the subtraction 13/16 - 5/24 results in the fraction of animals that are neither dogs nor cat:

simplify the last fraction:

Hence, 29/48 of the animal are neither dogs nor cats

Given:

To evaluate the function at x=1, we simplify the given relation first:

We let:

y=f(x)

We plug in x=1 into the above function:

Therefore,

Let:

x = Number of sodas purchased

y = Number of hamburgers purchased

The food truck charges $3 for sodas, so the total cost for sodas will be:

3*x=3x

also, it charges $8 for each hamburger, hence, the total cost for hamburgers will be:

8*y = 8y

Since Jack wants to spend no more than $30, the total cost must be less or equal than $30:

Algebra / Graphs and Functions / Equations of Parallel and Perpendicular Lines

We have the line:

We must find the equation:

0. of the perpendicular line,

1. and the parallel line,

to the given line that passes through the point (-2, 3).

1) Perpendicular line

The equation of the perpendicular line has the form:

Where mₚ is the slope, and (x₀, y₀) = (-2, 3).

From the equation of the given line, we see that its slope is m = 7. The slope of the perpendicular line mₚ is given by the equation:

Replacing mₚ = -1/7 and (x₀, y₀) = (-2, 3) in the equation of the perpendicular line, we get:

2) Parallel line

The equation of the perpendicular line has the form:

Where mₚ is the slope, and (x₀, y₀) = (-2, 3).

From the equation of the given line, we see that its slope is m = 7. The parallel line has the same slope as the given line, so we have:

Replacing mₚ = 7 and (x₀, y₀) = (-2, 3) in the equation of the parallel line, we get:

3) Graph

Plotting the equations obtained, we get the following graph:

1) Equation of the perpendicular line:

2) Equation of the parallel line:

In the number 44,244, we can see two pairs of 4's.

The first pair (to the left) has a higher value than the second pair to the right, but the 4's have something in common: The leftmost 4 is ten times as high as the rightmost 4.

For this reason, we start the number as forty-four thousand and end up with forty-four.

a) We have a number X that is twice the difference of a number c and 40.

We can write this as:

b) Four times the sum of a number f and fifty.

Then, X is:

Answer:

option 3

Step-by-step explanation:

As long as both lines are rotated the same direction and the same angle, then the angle between the two lines will not change.

In rectangle , 38.5 sq units  is the area of the blue shape.

What is rectangle?

We can split the shape into two rectangles.

The small rectangle at the top has an area of 14 sq units (2 * 7).

The middle rectangle has an area of 49 sq units ( 7*7).

Since the blue part in the middle rectangle is half of the whole rectangle, the area of the blue part there is 24.5 sq units.

Adding that to 14 sq units will give us 38.5 sq units.

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The given polynomial is expressed as

P(x) = - 3x^2 + 9x

The domain values are the x values. To find P(-5), it means that we would substitute x = - 5 into the polynomial. It becomes

P(- 5) = - 3(- 5)^2 + 9(- 5)

P(- 5) = - 3 * 25 - 45

P(- 5) = - 75 - 45

P(- 5) = - 120

System 2x2

Find slopes of k1 and k2

k1 slope = (10--2)/(4-0) = 12/4 = 3

k2 slope= (-9 -9)/ (8-0) = 8/-18 = -4/9

Now find k1, and k2 interceptions with y

k1 , interception= -2

k2 ,interception = 4

Then now, form the 2 equations

y = 3x - 2

and

y = (-4/9)x + 4

Now rewrite equations

3x - y = 2

and

9y + 4x = 36

Then now looking at options ,we find that

ANSWER IS

OPTION A)

3x - y = 2

the perimeter of a cuadrilateral is 2L+2W=68 where L is the length of the room

since L= 18 feet

we will have that

2(18)+2W=68

then

W=(68-36)/2= 32/2=16

The amount that was invested at 9% is $10303 , and at 6% is $1032  .

In the question ,

it is given that

total amount invested is $11335 .

let the amount invested at 9% be "x" .

so , the interest earned from 9% part is 0.09x

and let the amount invested at 6% be "y" .

the interest earned from 6% part is 0.06y

So , the equation is x + y = 11335   .

x = 11335 - y

Also given that interest earned from 9% amount exceeds the interest earned from 6%  by $865.35   .

So , according to the question

0.09x = 0.06y + 865.35

On substituting  x = 11335 - y in the above equation , we get

0.09(11335 - y) = 0.06y + 865.35

1020.15 - 0.09y = 0.06y + 865.35

0.09y + 0.06y = 1020.15 - 865.35

0.15y = 154.8

y = 154.8/0.15

y = 1032

and x = 11335 - 1032

x = 10303

Therefore , The amount that was invested at 9% is $10303 , and at 6% is $1032  .

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ANSWER:

a. 9.9, 1.8

b. 9.9, 0.2882

c. 0.5239

d. 0.6368

e. No

f.

Q1 = 9.7069

Q3 = 10.0931

IQR = 0.3862

STEP-BY-STEP EXPLANATION:

a.

X ~ N (9.9, 1.8)

b.

x ~ N (9.9, 1.8/√39)

x ~ N (9.9, 0.2882)

c.

P(X > 9.8)

We calculate the probability as follows:

d.

p (x > 9.8)

We calculate the probability as follows:

e.

No, you don't need to make the assumption

f.

Q1 = 0.25

In this case the value of z = 0.25, so we look for the closest value in the normal table, like this:

Thanks to this, we make the following equation:

Q3 = 0.75

In this case the value of z = 0.75, so we look for the closest value in the normal table, like this:

Therefore:

Therefore, the interquartile range would be:

The simple interest is given by:

where P is the principal (the amount we invest in the account), r is the interest rate and t is the time of investment.

Let P be the interest Larry made in the 2% account, the simple interest in this case is given by:

Now for the second account we would have an envestment of (17000-P), then the simple interest have to be:

and we know that both investments have to be equal to 610, then we have:

Therefore Larry invested $8000 in the 2% account and $9000 in the 5% account.

Part A

The dimensions of the shape shown are given as

length, l = 12 in

breadth (b) = width, w = 4 in

The area of the shape is given as;

Therefore, the area of the shape is 48 square inches.

Part B

The perimeter of a shape is the sum of all the outer sides enclosing the shape

From the above shape, we add all four sides together

Consequently, we can get the perimeter using formula method as well

Therefore, the perimeter of the shape is 32 inches.

Part C

From the dimension given in the question, since the shape has a length and width, and the length and width are not equal, then the shape is a rectangle.

The shape, therefore, is a rectangle.

Solution

The slope is given by

Hence, the slope is 3

The y-intercept is the point where the graph cuts the y-axis. The y-axis is the line x = 0, therefore, to find the y-coordinate of this point we just need to evaluate x = 0 in our function.

Any nonzero real number raised to the power of zero is one, therefore

The y-intercept is (0, -1).

A line of the form x = a, where "a" is a number is a VERTICAL LINE. The graph of the line x = - 4 is shown below:

The line that is parallel to this will also be a vertical line of the form x = a.

The line parallel passes through (-3, -5). So, this will have equation

x = - 3

[tex]\frac{1 }{8*a^{9}*b^{12}}[/tex].

[tex](\frac{a^{-3} }{2b^{4} } )^{3}[/tex]

[tex]\frac{a^{(-3*3)} }{2^{(3)} b^{(4*3)} } \\ \\\frac{a^{(-9)} }{8b^{(12)} }\\ \\\frac{a^{-9} }{8b^{12} }[/tex]

[tex]\frac{1 }{8b^{12} *a^{9}}\\ \\\frac{1 }{8*a^{9}*b^{12}}[/tex]

[tex](\frac{a^{-3} }{2b^{4} } )^{3}=\frac{1 }{8*a^{9}*b^{12}}[/tex].

You have the following rotation:

The result of the previous rotation, by taking into account the rules for the exponents for the transformations is:

The rotation R⁰ means a rotation of 0 degrees of a specific point.

Then, the given rotation appiled to point B does not move the point B from its place. The transformation makes B to go to B

answer: B

Answer:

We know that RT=36 and that RS=2x+3 and ST=7x+6. We notice that

Then, plugging the corresponding values and expressions we have

Solving this equation for x,

Then te value of x is 3.

Once we have the value of x we are able to find the value of RS and ST, we just have to substitute said value in the expressions. Then

Therefore RS=9 and ST=27.

If we have the expression:

This is the same to write:

So the answer is 1.2x.