The polygons in each pair are similar. Find the
missing side length.
40
Type your answer...
20
?
4

Answer:

A. 145 degree

Step-by-step explanation:

A triangle has 180 degree

109 + 36 = 145 degree

180 - 145 = 35 degree

35 degrees is the missing angle of the triangle. This angle must add with angle 1 equal to 180 degrees.

180 - 35 = 145 degree

So, the answer is A

Answer:

ANGLE 1 = 145°

Step-by-step explanation:

Angle 1 is right next to the EMPTY interior angle of the triangle and they are on a straight line!

This means, these two angles (angle 1 and the empty angle next to it) are supplementary angles!

Supplementary angles are angles on a straight line and they always add up to 180°

To find it, we need to find the degrees of the empty angle.
To find it, we need to look at the whole triangle.

Remember, all triangles equal 180°

Let's find this empty angle

180° - 109 - 36 = 35°

The empty angle = 35°

BUT WE ARE NOT DONE!

We are looking for angle 1, not the empty angle.

To find angle 1, we must remember that the empty angle (which we found was 35°) and angle 1 make a supplementary angle (which totals up to 180°)

Let's find angle 1, using subtraction.

180° - 35 = 145°

ANGLE 1 = 145°

Answer:

Step-by-step explanation:

You have a triangle with its midline length given as x+5 and its parallel base line length given as 3x-1. We presume you want to know the value of x and the lengths of the segments.

The midline is half the length of the parallel base line, so you have ...

  x +5 = 1/2(3x -1)

  2x +10 = 3x -1 . . . . . . . multiply by 2

  11 = x  . . . . . . . . . . . . . add 1-2x

The midline length is x+5 = 11+5 = 16.

The base line length is 3x-1 = 33 -1 = 32, twice the length of the midline.

The solution to the triangle is ...

Answer: No, it works out to a different number. The 1st will end up with 605 bison.

Step-by-step explanation:

1st Herd: (550 x 10%) = 55 Bison

550 + 55 = 605   Thus 550 with a 10% increase is 605 Bison.

2nd herd: if you take 10% of 605 bison that number of (60.5) will give you a greater loss when taken away from 605.

605 - 60.5 = 544.5 bison remaining if 605 has a 10% loss.

Herd 2 started with approximately 611 bison. Check your math by multiplying 611 by 10% = 61.1

then subtract (611 - 61.1) = 549.9

So Herd 1 Does Not Equal Herd 2.

The integer that makes the inequality 3(n − 6) < 2(n + 12) false is

The integer that makes the inequality false is solved by substituting the values and solving the inequality

3(n − 6) < 2(n + 12)

for n = -5

substituting the value of n

3(-5 − 6) < 2(-5 + 12)

= -33 < 14

3(n − 6) < 2(n + 12)

for n = 3

substituting the value of n

3(3 − 6) < 2(3 + 12)

= -9 < 30

3(n − 6) < 2(n + 12)

for n = 12

substituting the value of n

3(12 − 6) < 2(12 + 12)

= 18 < 48

3(n − 6) < 2(n + 12)

for n = 42

substituting the value of n

3(42 − 6) < 2(42 + 12)

= 108 < 108 wrong

This is the only wrong solution since 108 = 108

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Answer: B

Step-by-step explanation:

Answer:

it's point B

Step-by-step explanation:

The difference between -4 and -2 is -2 . And there are 8 steps from -2 and to -4.This means each step represents -2/8 which equals to -1/4. Then divide that number by -1/4

[tex] -2 \frac{6}{8} \div \frac{1}{4} \\ = 11[/tex]

Then count 11 steps from 0

ok.

Answer:

thus: x = 5, y = -3

Step-by-step explanation:

Solve the following system:

{y + x = 2 | (equation 1)

-4 y + 3 x = 27 | (equation 2)

Swap equation 1 with equation 2:

{3 x - 4 y = 27 | (equation 1)

x + y = 2 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{3 x - 4 y = 27 | (equation 1)

0 x + (7 y)/3 = -7 | (equation 2)

Multiply equation 2 by 3/7:

{3 x - 4 y = 27 | (equation 1)

0 x + y = -3 | (equation 2)

Add 4 × (equation 2) to equation 1:

{3 x + 0 y = 15 | (equation 1)

0 x + y = -3 | (equation 2)

Divide equation 1 by 3:

{x + 0 y = 5 | (equation 1)

0 x + y = -3 | (equation 2)

Collect results:

Answer: {x = 5, y = -3

The values of X ∩ Y are 1, 3, 5, and 7.

A set is a collection of items where there are operations such as:

Union of sets, the intersection of sets, complements of sets.

We have,

X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }

Y = {-3, -1, 1, 3, 5, 7, 20}

Now,

X ∩ Y

= The values common to both sets.

= {1, 3, 5, 7 }

Thus,

X ∩ Y = {1, 3, 5, 7 }

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Answer:

  10 pounds

Step-by-step explanation:

You want to know the number of pounds of peanuts in a mix of $5/lb peanuts and $6/lb almonds that gives 14 pounds of nuts for $74.

Let p represent the number of pounds of peanuts in the mix. The (14-p) is weight of almonds, and the total cost is ...

  5p +6(14 -p) = 74

Simplifying the equation gives ...

  -p +84 = 74

  10 = p . . . . . . . . add p-74

You should buy 10 pounds of peanuts to make the 14 lb bag cost $74.

__

Additional comment

You notice that simplifying the equation gives p a negative coefficient. If you choose the variable to represent the more expensive contributor, then the coefficient of that comes out positive. (We like positive coefficients, as they tend to reduce errors.)

Here, the problem is requesting the amount of the lower cost contributor, so we used the variable to represent that.

Often, you are asked to solve mixture problems using a system of equations. Those would use a variable for each of the quantities, and the equations would be ...

You notice that substituting for 'a' gives the equation we used above.

Jumping directly to this step saves a bit of written work, though the mental work is the same.

The linear equality for the given graph is x > 0.

Option (B) is correct.

What is linear equality?

In mathematics, a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

The hollow circle in the linear equality shows that the point should be excluded and the line is going towards the positive x-axis.

So we can prepare the linear equality as

                       x > 0

Hence, the linear equality for the given graph is x > 0.

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The costs for the given candy are $7 for strawberry taffy and $6 for banana taffy. By writing equations and simplifying them, we get the requiredd values.

To solve two equations,

It is given that, two friends visited a taffy shop.

Winton bought - 2 kg of strawberry taffy and 1 kg of banana taffy for $20.

Audrey bought - 4 kg of strawberry taffy and 4 kg of banana taffy for $52.

Then, we can write the above information into equations as

2S + B = 20 ...(1)

4S + 4B = 52 ...(2)

Where S represents strawberry taffy and B represents banana taffy.

From (1), we can write

B = 20 - 2S

Then, on substituting in (2), we get

4S + 4(20 - 2S) = 52

⇒ 4S + 80 - 8S = 52

⇒ -4S = 52 - 80 = -28

⇒ 4S = 28

∴ S = 7

Thus, the cost of strawberry taffy is $7.

On substituting S = 7 in (1), we get

2(7) + B = 20

⇒ 14 + B = 20

⇒ B = 20 - 14

∴ B = 6

Thus, the cost of banana taffy is $6.

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the work to prove that the series is convergent using one of the convergence series tests.the series a is convergent and series b is divergent.

a. The alternating series test can be used to prove that the series is convergent. The alternating series test states that if a series is of the form [tex]$a_1-a_2+a_3-a_4+\cdots$[/tex] and satisfies the conditions:

1. [tex]$a_n \geq 0$[/tex] for all n

2. [tex]$a_{n+1} \leq a_n$[/tex] for all n

3. [tex]$\lim_{n\to \infty} a_n = 0$[/tex]

Then the series is convergent.

In this case, the series is of the form [tex]$2-\frac{2}{2}+\frac{2}{3}-\frac{2}{4}+\cdots$[/tex] which satisfies all the conditions of the alternating series test.

Therefore, the series is convergent.

b. The divergence test states that if the limit of the sequence of partial sums is not finite, then the series is divergent. However, in this case, the limit of the sequence of partial sums is finite and thus the divergence test fails to prove that the series is divergent.

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Answer: 167/30

Step-by-step explanation:

1/6 + 5.4

5.4 = 54/10

So we have 1/6 + 54/10

The common factor is 60

10/60 + 324/60

334/60

167/30

Answer:

1/6 + 5.4 = 167/30 = 5  17/30

Step-by-step explanation:

Conversion of a decimal number to a fraction: 5.4 = 54/

10

= 27/5

a) Write down the decimal 5.4 divided by 1: 5.4 = 5.4/

b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

5.4/1

= 54/10

Note: 54/10

is called a decimal fraction.

c) Simplify and reduce the fraction

54/10

= 27 * 2/5 * 2

= 27 * 2/5 * 2 = 27/5

Add: 1/6 + 5.4 = 1/6 + 27/5 = 1 · 5/

6 · 5 + 27 · 6/

5 · 6

= 5/30 + 162/30 = 5 + 162/30

= 167/30

The largest right circular cone that can fit within a cube has a volume of 718.67 cm3.

When a cone's axis is the line from the vertex to the circular base's midpoint, the cone is said to be right circular. In other words, a right angle is formed when the center of the circular base joins the cone's peak.

A three-dimensional form called an inverted frustum that resembles a conical cylinder. When the vertex of a cone is inverted after being sliced by a plane parallel to the shape's base, it is said to have this shape.

The formula r2+rl, where r is the radius of the circular base, h is the height of the cone, l is the slant height, and is an approximation, is used to determine the surface area of a cone as 3.14

Side of cube: 14 cm

Cube's radius is 14/2 cm, or 7 cm.

h=14cm for height

Volume'=1/3piR x 2hM =1/3 x 22 x 7 x 7 x7

= 718.67 cm3.

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Answer:

D) $3,264.00

Step-by-step explanation:

I = Prt

I = $1600 × 0.0325 × 32 = $1664

total = $1600 + $1664 = $3264

The result of the logarithmic functions by logarithm tables are listed below:

This question can be resolved by means of logarithm properties and logarithm tables or numerical methods. Now we proceed to evaluate each logarithmic functions:

Case 1:

㏒₁₀ 0.1

By using rational numbers:

㏒₁₀ (1 / 100)

By logarithm properties:

㏒₁₀ 1 - ㏒₁₀ 100

By logarithm tables:

0 - 2

- 2

Case 2:

㏒₅ 125

By logarithm tables:

3

Case 3:

㏒₈ 64

By logarithm tables:

2

Case 4:

[tex]\log_{\frac{1}{3} } 9[/tex]

By logarithm tables:

- 2

Case 5:

[tex]\log_{\frac{1}{2}} \frac{1}{2}[/tex]

By logarithm tables:

1

Case 6:

㏒₄₉ 7

By logarithm tables:

1 / 2

Case 7:

㏒₉ 3

By logarithm tables:

1 / 2

Case 8:

㏒₃ 81

By logarithm tables:

4

Case 9:

㏒₄ 8

By logarithm tables:

3 / 2

Case 10:

㏒₁₀₀ 10,000

By logarithm tables:

2

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The partial derivative of function f(x, y) = xy/cos(x) is  ∂/∂y [xy/cos(x)] = x sec(x)

In this question we have been given a function y′ = f(x,y) = xy/cos(x)

We need to find the partial derivative of function f(x, y) with respect to y, ∂f/∂y

Consider the partial derivative of function

∂f/∂y = ∂/∂y [xy/cos(x)]

∂f/∂y = ∂/∂y [xy * 1/cos(x)]

we know that 1/cos(x) = sec(x)

∂f/∂y = ∂/∂y [xy * sec(x)]

∂f/∂y = x sec(x)  ∂/∂y (y)

∂f/∂y = x sec(x) * 1

∂f/∂y = x sec(x)

Therefore,  ∂/∂y [xy/cos(x)] = x sec(x)

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Answer:

-191

Step-by-step explanation:

Answer:

[tex] \sf \: c) - 191[/tex]

Step-by-step explanation:

Given problem,

→ (-135) - 72 - (-16)

Let's solve the problem,

→ (-135) - 72 - (-16)

→ (-135) - 72 + 16

→ (-135 - 72) + 16

→ -(135 + 72) + 16

→ -207 + 16

→ -191

Hence, answer is -191.

Answer:

1,5,7 = 145 degrees

2,3,6,8 = 35 degrees

Step-by-step explanation:

1,5, and 7 are interior angles:

Interior angles are those that lie inside a polygon. For example, a triangle has 3 interior angles. The other way to define interior angles is "angles enclosed in the interior region of two parallel lines when intersected by a transversal are known as interior angles".

2,3,6, and 8 are exterior angles:

An Exterior Angle is the angle formed by one side of a polygon and the extension of the adjacent side. In all polygons, there are two sets of exterior angles, one that goes around clockwise and the other goes around counterclockwise.

Hope this helps :))

Answer: The answer would be 9.125.

Step-by-step explanation:

I can't really find an explanation for it.  Sorry.

The remaining angles are 80 and 30

The sum of angles of a triangle = 180

One angle is given as                 = 70

The sum of the remaining angles= 110

Now we apply the theory of ratios

The ratio between the angles are given as 3:8

So one angle will be 3 parts of 110 and other eight parts of 110

Total number of parts = 3+8 = 11

Angle 1                         = (3*110)/11

                                     =  30

Angle 2                        = (8*110)/11

                                     = 80

So the other two angles are 30 and 70.

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Answer: 3a

Step-by-step explanation:

(4a*6a)/8a

24a^2/8a

3a

[tex]4a\times6a[/tex]

[tex]4\times6=24\\4a\times6a=24a[/tex]

[tex]\dfrac{24a}{8a}[/tex]

[tex]=\fbox{3a}[/tex]

The effect of the medicine is only left for the interval of 0 ≤ t ≤ 6.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that  Let's look at an example of a common medication, called ibuprofen. When a patient takes a 400 mg dose of ibuprofen, it releases into the bloodstream at a certain rate and then decreases over time. The function that models this concentration of medicine over time is complex and looks like this:

P(t) = 0.5t + 3.45t³ - 96.65t² + 347.7t, when 0 ≤t≤6.

The graph is repeating after the value of t as 6.

Hence, the interval will be 0 ≤t≤6.

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Answer:

The median is 25

Step-by-step explanation:

I counted the numbers and it was 30 I divided it to 2

Answer:

The expression represents a cubic polynomial with 3 terms. The constant term is -1, the leading term is x^3, and the leading coefficient is 1.

Step-by-step explanation:

The length, L, of a teel rod i 7. 36, correct to 2 decimal place then The error interval for L is [7.355,7.365)

we know that

In this problem

The least significant digit is in the hundredths place.

The error can be as much  0.005 m

Determine the lower bound

To find out the lower bound subtract the error from the value

so 7.355

Determine the upper bound

To find out the upper bound adds the error to the value

7.365

so

Since 7.365 is rounded up to 7.37, the maximum value of L must be less than that.

therefore

7.355 < L < 7.365

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Answer:

11.25

Step-by-step explanation:

(1.35 × 10^7) / (1.2 × 10^6) =

= 135/12

= 11.25

Answer: 11.25 is the answer

Answer:

5.083

Step-by-step explanation:

[tex]V=\frac{1}{3}Bh=(1/3)(1/2)(1.7)(3.9)(4.6)=5.083[/tex]

Answer:

8 < f

Step-by-step explanation:

Because it says the cooler could hold less than eight large fish

Less than mean <

So the equation is 8<f

Answer: b  8 < f

Step-by-step explanation:

when a person's test performance can be compared with that of a representative and pretested sample of people, the test is said to be norm-referenced.

Norm-referenced tests are assessments that measure an individual's performance against a predetermined group, or norm. A norm-referenced test is designed to evaluate how a person performs in comparison to a representative and pretested sample of people. This type of testing is especially common with achievement tests, such as the SAT or IQ tests, where the scores are meant to represent how the individual compares to others of the same age or in the same educational setting. The results of norm-referenced tests can be used to rank individuals according to their performance on the test, allowing for an easy comparison between individuals. Norm-referenced tests are designed to provide a comprehensive view of an individual’s strengths and weaknesses in comparison to a predetermined group.

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The unit rate of change of flour (y) with respect to sugar (x) will be 2.25.

        r = Δy/Δx

        [tex]\lim_{x \to \;0} (r) = \lim_{x \to \;0}[/tex] (Δy/Δx) = dy/dx

Given is that Melissa made three batches of oatmeal cookies. Her recipe calls for amounts of sugar (in cups) and flour (in cups) in the following ratios as shown in the question.

We can write the rate of change as -

r = Δy/Δx

r = (y₂ - y₁)/(x₂ - x₁)

y₂ = [tex]$6\frac{3}{4}[/tex] = 27/4

y₁ = [tex]$4\frac{1}{2}[/tex] = 9/2

x₂ = 3

x₁ = 2

Using the values -

r = (27/4 - 9/2)/(3 - 2)

r = (27 - 18)/4

r = 9/4

r = 2.25

Therefore, the unit rate of change will be 2.25.

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The equation of a line parallel to -3x - y= -4  and passing through a point  (1,4) is y = -3x + 7.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the line is parallel to  -3x - y = -4 and it passes through (1, 4).

Parallel lines have the same slope.

Hence,

-3x - y = -4

y = -3x + 4

The slope of the line is -3.

Let's find y-intercept using (1, 4)

y = -3x + b

4 = -3(1) + b

4 + 3 = b

b = 7

Therefore, the equation of the line is y = -3x + 7.

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