find the missing side. round your answer to the nearest tenth​

Answer:

x=-2

Step-by-step explanation:

(2/3)^x-1=27/8

Rewriting the right hand side

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

We know that a^-b = 1/a^b  Hint: { 1/(3/2) = 2/3}

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

The bases are the same, so the exponents are the same

x-1 = -3

x -1+1 = -3+1

x = -2

Let's start with proving that side AB is parallel to side CD

First off, let's find the slope of line AB. So we'll use the slope formula.

[tex]A = (x_1,y_1) = (2,-1)\\\\B = (x_2,y_2) = (1,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - (-1)}{1 - 2}\\\\m = \frac{3 + 1}{1 - 2}\\\\m = \frac{4}{-1}\\\\m = -4\\\\[/tex]

The slope of AB is -4.

Now let's find the slope of line CD.

[tex]C = (x_1,y_1) = (6,5)\\\\D = (x_2,y_2) = (7,1)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{1 - 5}{7 - 6}\\\\m = \frac{-4}{1}\\\\m = -4\\\\[/tex]

The slope of CD is also -4.

Recall that parallel lines always have equal slope (but different y intercepts).

This proves that AB is parallel to CD.

--------------------------

We'll follow the same steps to show that AD is parallel to BC.

Find the slope of AD

[tex]A = (x_1,y_1) = (2,-1)\\\\D = (x_2,y_2) = (7,1)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{1 - (-1)}{7 - 2}\\\\m = \frac{1 + 1}{7 - 2}\\\\m = \frac{2}{5}\\\\[/tex]

Now find the slope of BC

[tex]B = (x_1,y_1) = (1,3)\\\\C = (x_2,y_2) = (6,5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{5 - 3}{6 - 1}\\\\m = \frac{2}{5}\\\\[/tex]

We get 2/5 each time, so these lines are parallel as well.

--------------------------

In short, the first section shows that AB is parallel to CD. The second section proved that AD is parallel to BC.

Because we have two pairs of parallel opposite sides, we can say that ABCD is a parallelogram.

Edit: I have attached the diagram below.

9514 1404 393

Answer:

  see below

Step-by-step explanation:

The cost for purchase of 0 tokens is $60. This "initial value" is the y-intercept of the function.

The cost for each token is $1.00/10 = 1/10 (dollar), so the slope of the function is 1/10.

The slope-intercept form of the function can be written ...

  y = mx + b . . . . . for slope m and y-intercept b

  y = 1/10x + 60

__

The minimum value of this function is 60, so the range is y ≥ 60.

The function is defined for all real numbers, but only makes sense for all non-negative integers. So, we cannot claim the domain is all real numbers.

Answer:

(B, C, E)

Step-by-step explanation:

Let's evaluate each answer choice:

"The slope of the function is $1.00"

Wrong. The slope is how much one game token costs. It costs $1 per 10 tokens, not 1 token. To find the cost of 1 game token, you would divide 1 by 10, giving you a value of 1/10.

"The y-intercept of the function is $60"

Correct. The initial fee is $60, and this initial fee doesn't change, so it's the y-intercept.

"The function can be represented by the equation y = 1/10x + 60"

Correct. We just mentioned before that the slope is 1/10 and the y-intercept is 60.

"The domain is all real numbers"

Wrong. "All real numbers" also includes negative numbers. However, x represents the number of tokens bought, and you can't buy a negative amount of tokens.

"The range is {y| y >= 60}"

Correct. The range represents the total cost of a yearly membership. When you get the membership, you're ALWAYS going to have to pay $60, no matter how many tokens you buy after that.

Hope this helps (●'◡'●)

The cost of the tomato sauce for one potion given the cost per ounce is $1.30.

Multiplication is the process of determining the production of more than one number. It is an example of a mathematical operation.

In order to determine the answer, multiply the cost per ounce by the total ounces needed for one portion.

$0.37 x 3.5 = $1.30

To learn more about multiplication, please check: https://brainly.com/question/13814687

Answer:

x = 14

Step-by-step explanation:

x - 42 = 98 – 9x

Add 9x to each side

x - 42+9x = 98 – 9x+9x

10x-42 = 98

Add 42 to each sid

10x-42+42 = 98+42

10x = 140

Divide by 10

10x/10 =140/10

x = 14

Answer:

5•782×10^-5

Step-by-step explanation:

(5•9×10^4((9•8×10^5)

(59×10^-1×10^4)×(98×10^-1×10^5)

(59×98) (10^-1×10×4×10-1×10^5)

5782×10^-1+^4+^-1+^5

578×10^7

5•782×10^7-^2

5•782×10^-5

Thanks Hope It Help

The average rate of change is the same as the slope. Even though this graph is a parabola, we still use the slope formula with the corresponding points. Had the question asked for the instantaneous rate of change, we would have needed to find a derivative.

Slope formula: (y2 - y1) / (x2 - x1)

Point 1: (0,4)

Point 2: (2,8)

(8 - 4) / (2 - 0)

4 / 2

2

The average rate of change from x = 0 to x = 2 is 2.

Hope this helps!

Answer:

5

Step-by-step explanation:

because line PF DIVIDED LINE BPA INTO TWO EQUAL HALF THEREFORE LINE BP IS EQUAL TO LINE AB WHICH IS EQUAL TO 5

The required value of the PV is 12 in the triangle DEF where p is the incenter.

Given; Point P is the incenter of ΔDEF. Point P is the point of concurrency of the angle bisector. PV to be determined.

The incenter of a triangle is the intersection point of the internal angle bisectors of the triangle.

In expressions, it can be clarified as the point where the internal angle bisectors of the triangle and perpendicular distance from this point to any of the sides of triangle is the same.

Since in the triangle FGH, P is the incenter and PW, PV,PX is perpendicular distance to the sides HF, GF and GH respectively.

From image given,

PW = 12

So by the property of the incenter, perpendicular distance from this point to any of the sides of triangle is the same.

PW = PV

PV = 12

Therefore, the required value of the PV is 12 in triangle DEF where p is the incenter.

Learn more about incenter here:

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as according to law if a number is multiplied at one side then it will be divide to other side

so

Step-by-step explanation:

plz mark me asbrain liest

Answer:

The answer is B because it's all real numbers since it won't stop

Step-by-step explanation:

The domain of the function shown is -∞ ≤ x ≤ +∞

The domain and range are the main characters of a function. The domain of a function is the inputs of the given function on the other hand the range signifies the possible outputs we can have.

Given is a graph we need to determine its domain,

We know,

The domain of a function represents the set of coordinates in the x-axis that belongs to the curve of the function itself. After a brief inspection, we see that function has an horizontal asymptote at y = 1, and no vertical asymptotes. Therefore, the domain of the function shown is -∞ ≤ x ≤ +∞.

Hence, the domain of the function shown is -∞ ≤ x ≤ +∞

Learn more about domain click;

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Answer:

A model is an estimate of a data set.

A useful model can be used to make predictions.

Step-by-step explanation:

There are various models used in mathematics which are used to predict variables. The regression model is used to predict the relation between two variables. There are various other models which help to predict the future events and outcome of these events.

Answer:

Step-by-step explanation:

The answer is D 28 degrees

Answer:

36

Step-by-step explanation:

Number of points Fran won = points Fran had - points Calvin had

14 - (-22)

= 14 + 22

= 36

Answer:

The answer to this would be B.) 4.7 cm

Step-by-step explanation:

Arch = (Angle/360)(2[tex]\pi[/tex]r)

= (45/360)(2[tex]\pi[/tex]6)

= (0.125)(12[tex]\pi[/tex])

=1.5[tex]\pi[/tex]

≈4.71cm (assuming [tex]\pi[/tex] = 3.14)

Since an arch of a circle is just part of the circumference, you just need to multiply the circumference by the measure of the arch's angle divided by 360 (the angle measure of a circle).

Answer:

b,c

Step-by-step explanation:

The axis of symmetry is along the vertex

a has a vertex at x=1

b has a vertex at x = -1

c has a vertex at x=-1

d has a vertex at x =2

Explanation:

Notice how the vertical line through the center of these parabolas is at x = -1. In other words, the vertical line cuts through -1 on the x axis. Reflecting one half of the parabola over this line will result in the other half.

The value of x is 40°

Answer:

Solution given:

In triangle BCE

<C+<B+<E=180°[sum of interior angle of a triangle]

<C+60°+x°=180°

<C=180°-60°-x°

<C=120°-x°

again

<A=<C[exterior angle of a cyclic quadrilateral is equal to the opposite interior angle]

2x=120-x

2x+x=120°

3x°=120°

x°=120°/3°

x°=40°

Now we have to,

find the required value of x.

Then in ∆ BCE,

By sum of interior angle of a triangle.

→ <C+<B+<E = 180°

→ <C+60°+x = 180°

→ <C = 180-60-x

→ <C = 120-x

Now by the exterior angle of,

A cyclic quadrilateral is equal to the opposite interior angle.

→ <A = <C

→ 2x = 120-x

→ 2x+x = 120

→ 3x = 120

→ x = 120/3

→ x = 40°

Hence, 40° is the value of x.

Answer:

Perform a horizontal line test

Step-by-step explanation:

sin X = 37/64

sin X = .578

X = sin ^-1 (.578)

X = 35.3°

hope it's correct

Answer:

the real answer is

2X/19

Explanation:

The x coordinates are -4 and 14. They add up to -4+14 = 10. Then this cuts in half to get 10/2 = 5. This is the x coordinate of the midpoint.

We'll follow this same idea for the y coordinates as well.

10+0 = 10 which cuts in half to 10/2 = 5, and this is the y coordinate of the midpoint.

Therefore, the midpoint is (5,5).

Coincidentally, the x and y coordinates are the same for the midpoint (both are 5). This won't always happen.

Answer: b and d

Step-by-step explanation:

edge21/22

Answer:

2. given

5. substitution

Step-by-step explanation:

that the perimeter is 12 is simply a given fact. in the same way as the shape of the object is defined as square.

nothing was calculated, this information is simply there at the beginning, is "given" to us.

step 5 simply takes step 3 and substitutes all sides by the same side, as (per definition) all sides in a square are equal. so, every side can stand in for every other side.

Answer:

5.1

Step-by-step explanation:

[tex]tan \ 25 = \frac{opposite \ side}{adjacen \ side}\\\\tan \ 25 =\frac{x}{11}\\\\0.4663 =\frac{x}{11}[/tex]

0.4663 * 11 = x

x = 5.1293

x = 5.1

Answer:

12m²n

Step-by-step explanation:

→ Collect the m and n terms together

12m²n

[tex] - \frac{2}{5} [/tex]

Answer:

676,131

Step-by-step explanation:

L.C.M of 75,125 and 225,

=>676,125

Leaves a remainder 6 means,

=>676,125 + 6

=>676,131

That means,

When you divide 676,131 by 75,125 or 225,

You get remainder 6 .

That is why we add 6 to the L.C.M

Answer:

D

Step-by-step explanation:

the slope of a line is simply the gradient given by the equation

y2-y1/x2-x1

x1 is 5, x2 is-5,y1 is 11 and y2 is -1

m=-1-11/-5-5

=-12/-10

=6/5

Answer:

(1,-5)

Step-by-step explanation:

4x + 2y = -6

-3x -2y = 7

in this case you can just add the two items together

x = 1

4(1) + 2y = -6

2 y = -10

y = -5