Find the sum

(-14.2b - 97.35) + (6.76d - 118.7 – 3.4d)

Answer:

x = 36°

y = 66°

z = 78°

Step-by-step explanation:

Setup equations:

Allowing the first angle to be x, the second to be y, and the third to be z, the three sentences describing the relationships between angle measures are given below:

Substituting equation 3, into equations 1 and 2

Eq1:  x + y + z = 180°

x + y + (y+12°) = 180°

x + 2y + 12° = 180°

x + 2y = 168°

x = 168° - 2y

Eq2:  y + z = 4x

substituting the result from equation 1, and Equation 3...

y + (y+12°) = 4*(168° - 2y)

2y + 12° = 672° - 8y

10y = 660°

y = 66°

Substituting back into Equation 3...

Eq3:  z = y + 12°

z = (66°) + 12°

z = 78°

Substituting both y, and z into Equation 1...

x + y + z = 180°

x + (66°) + (78°) = 180°

x + 144° = 180°

x = 36°

So, the three angle measures are:

x = 36°

y = 66°

z = 78°

"The sum of the measures of the angles of a triangle is 180."

x + y + z = 180°

36° + 66° + 78° = 180°

True

"The sum of the measures of the second and third angles is four times the measure of the first angle"

y + z = 4x

66° + 78° = 4*(36°)

144° = 144°

True

"The third angle is 12 more than the second"

z = y + 12°

78° = 66° + 12°

True

Yes, there is an analogous ratio between 2:1 and 20:10.

We just cancel by a common factor. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Also, since each pair of numbers has the same relationship to one another, the ratios are equivalent.

By dividing the terms of each ratio by their greatest common factor, we may simplify both ratios to explain why.

As the greatest common factor for the ratio 2:1 is 1, additional simplification is not necessary.

The greatest common factor for the ratio 20:10 is 10. When we multiply both terms by 10, we get:

20 ÷ 10 : 10 ÷ 10

= 2 : 1

As a result, both ratios have the same reduced form, 2:1, making them equal.

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Answer:

P= 4a would be the answer

Answer:

Step-by-step explanation:

\(\frac{15}{7} or \frac{26}{9}\)

The real solutions of the equation of X² + 12X - 64 = 0 are 4 and (-16)

To find the real solutions for a quadratic equation, we need to understand this concept:

(x - a).(x - b) = x² - (a+b)x +ab

We can also use the ABC formula where:

ax² + bx + c = 0

Then:

x = -b ±√(b² - 4ac)

              2a

Using the given equation, we know that:

a = 1

b = 12

c = -64

Then, we will use the ABC formula to find the real solutions for the equation:

x = -(12) ± √(12² - 4(1)(-64))

                       2(1)

x = -(12) ± √(144 - 256)

               2

x = -12 ± √400

           2

x = -12 ± 20

           2

x1 = (-12 + 20) / 2

x1 = 8/2 = 4

x2 = (-12 - 20)/2

x2 = (-32)/2 = -16

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Complete Question:

find all real solutions of the equation by completing the square. (enter your answers as a comma-separated list. if there is no real solution, enter no real solution.) X² + 12X - 64 = 0

The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.

To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.

Add the square of half of the coefficient of x to both sides of the equation:

x² + 2x + (2/2)² = 319 + (2/2)²

x² + 2x + 1 = 320

The left-hand side of the equation can now be factored as a perfect square:

(x+1)² = 320

This is the equation in the form (x+a)²=b, where a=1 and b=320.

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The complete question is as follows:

What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?

x² + 2x = 319

Answer:

  4.5 kWh

Step-by-step explanation:

You want an estimate of the mean of the solar panel output represented by the given histogram.

The mean of the output values can be estimated as the weighted average of the middle of each interval, weighted by the area of the histogram in that interval.

The computation looks like ...

  \(\dfrac{.5\times1+1.5\times1+2.5\times1+3.5\times4+4.5\times4+5.5\times3+6.5\times 2+7.5\times2}{1+1+1+4+4+3+2+2}\\\\\\=\dfrac{81}{18}=4.5\)

The mean daily energy output of the solar panel is about 4.5 kWh.

<95141404393>

The diameter of the tin in the picture is  \(3d/5\) where 'd' is the diameter of the tin in reality.

Determining the diameter of tin:

Since there is no indication of dimensions, represent the diameter with a variable 'd' and find the diameter of the tin according to the given condition in the problem.

Here we have assumed that the diameter of the tin is 'd' in reality and the diameter of the tin picture can be calculated as given below.  

Here we have

A ricoffy tin container with no dimensions indicated

Let d and h be the diameter and height of the tin

Given that the container is 2/5 times smaller than d

then the diameter of the tin in the picture \(= d - 2/5(d)\)

\(= [5d - 2d]/5 = 3d/5\)

Therefore, The diameter of the tin in the picture is  \(3d/5\) where 'd' is the diameter of the tin in reality.

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Answer:

the answer is number 4 h(x) = 1/4 x

Answer:

the  answer is 4 h(x) = 1/4 x.

Step-by-step explanation:

Hello!

∠AED and ∠BEC are opposite angles

so ∠AED = ∠BEC = 36°.

Answer:

w=36

f=12

k=13

Step-by-step explanation:

Answer:

Answer:

7 + 2 = 9, so AC = 7/9 and CD = 2/9

1 + 2 = 3, so AB = 1/3 = 3/9 and

BD = 2/3 = 6/9

AB + BC = AC

3/9 + BC = 7/9, so BC = 4/9

AB:BC:CD = (3/9):(4/9):(2/9) = 3:4:2

Answer:

there is no image

Step-by-step explanation:

1)

The axis of symmetry is x = -6.

2)

Vertex is (-6, 26).

3)

f(x) has a maximum value.

4)

f(x) is concave down.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

f(x) = -x² - 12x - 10

This is in the form of ax² + bx + c.

a = -1, b = -12, c = -10

The axis of symmetry is x = -b/2a

x = 12/(-2)

x = -6

Now,

f(x) = -x² - 12x - 10

f(x) = -(x² + 12x + 10)

f(x) = - { (x² + 12x + 36) - 36 + 10}

f(x) = -(x + 6)² + 26

This is in the form of f(x) = a (x - h)² + k

a = -1, h = -6, k = 26

Vertex = (h, k) = (-6, 26)

Now,

f(x) = -x² - 12x - 10

f'(x) = -2x - 12

f''(x) = -2

It is a negative value.

This means f(x) has a maximum value.

Now,

From the graph, we see that f(x) is concave down.

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Answer:

there is 175 adults and 125 children

Step-by-step explanation:

The minimum profit occurs at L = 0, where Q = 0.

To find the value of L that maximizes the profit Q = L²\(e^{(0.01L)\).

We need to differentiate Q with respect to L and find the critical points where the derivative equals zero.

Then we can determine whether each critical point is a maximum or a minimum by examining the second derivative.

Testing for critical points:Q = L²\(e^{(0.01L)\)

Q' = \(2Le^{(0.01L)\) + \(0.01 L^2e^{(0.01L)\)

= 0(2L + 0.01L²) \(e^{(0.01L)\)

= 0L (critical point) or 200 \(e^{(0.01L)\)

= 0 (extraneous, ignore)

2L + 0.01L² = 0L(2 + 0.01L) = 0L = 0 or L = -200 (extraneous, ignore)

The only critical point is at L = 0.

Testing for maximum or minimum:Q'' = \(2e^{(0.01L)\) + 0.02Le^(0.01L) + 0.0001L²\(e^{(0.01L)Q''(0)\)

= \(2e^{(0)\) = 2Since Q''(0) > 0,

The critical point at L = 0 is a minimum.

Therefore, there is no value of L that maximizes the profit.

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The values of L that will maximize the profit are 0 and -200

From the question, we have the following parameters that can be used in our computation:

\(Q = L\²e^{0.01L\)

Differentiate the function

So, we have

\(Q' = \frac{L \cdot (L + 200) \cdot e^{0.01L}}{100}\)

Set the equation to 0

\(\frac{L \cdot (L + 200) \cdot e^{0.01L}}{100} = 0\)

Cross multiply

\(L \cdot (L + 200) \cdot e^{0.01L} =0\)

When expanded, we have

L = 0, L + 200 = 0 and \(e^{0.01L} =0\)

When solved for L, we have

L = 0 and L = -200

Hence, the values of L are 0 and -200

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the total number of laptops ar lightning school at the end of 2020 is 1134

Explanation

Step 1

Let

x represents the year after 2015=2020-2015=

x=5

In 2015, there were 759 laptop, Starting in 2016, the school bought 75 more laptops at the end of each year,it is

let's check

in 2015

Step 2

now, we need the total for 2020

Hence, the total number of laptops ar lightning school at the end of 2020 is 1134

Haha ITS MATHXL

Anyways, constant rate of +90 and currently has 1560.

Say y will be the amount of students, and x is how many years later.

y=90x+1560

So for a), the answer is y=90x+1560

For b), plug in 3 for x, since 2017 is 3 years after 2014.

y=90(3)+1560
y=270+1560
y=1830

Amount of students in 2017: 1830

For c), plug in 2010 for y.

2010=90x+1560
Subtract 1560 both sides
450=90x

Divide both sides by 90
x=5

Answers

a) y=90x+1560
b) 1830
c) 5 Years Later, or 2019

Hope this helps!

Answer:

D. A pair of intersecting lines

Step-by-step explanation:

A conic section is a fancy name for a curve that you get when you slice a double cone with a plane. Imagine you have two ice cream cones stuck together at the tips, and you cut them with a knife. Depending on how you cut them, you can get different shapes. These shapes are called conic sections, and they include circles, ellipses, parabolas and hyperbolas. If you cut them right at the tip, you get a point. If you cut them slightly above the tip, you get a line. If you cut them at an angle, you get two lines that cross each other. That's what happened in your question. The plane cut the cone at an angle, so the curve is two intersecting lines. That means the correct answer is D. A pair of intersecting lines.

I hope this helps you ace your math question.

1. Length of side DE = 9

Length of side DF = 15

2. Length of side DE = 5.625

Length of side EF = 4.96

3. Length of side DF = 10

Length of side EF = 6.61

Given,

Two triangles

Triangle ABC and Triangle DEF ; These are similar triangles

That is,

AB = DE, BC = EF, AC = DF

Here,

AB = 3

BC = 4

1. EF = 12

AB/BC = DE/EF

3/4 = x/12

x = (12 x 3) / 4

x = 3 x 3 = 9

Length of side DE = 9

DF = \(\sqrt{9^{2} +12^{2} }\) = \(\sqrt{81 + 144}\) = √225 = 15

Now,

2. DF = 7.5

AB/BC = DE/DF

3/4 = x/7.5

x = (7.5 x 3) / 4

x = 5.625

Length of side DE = 5.625

EF =  \(\sqrt{7.5^{2}-5.625^{2} }\) = \(\sqrt{56.25-31.64}\) = √24.61 = 4.96

Next,

3. DE = 7.5

AB/BC = DE/DF

3/4 = 7.5/x

x = (7.5 × 4) / 3 = 30/3

x = 10

Length of side DF = 10

EF =  \(\sqrt{10^{2}-7.5^{2} }\) = \(\sqrt{100-56.25}\) = √43.75 = 6.61

That is,

1. Length of side DE = 9

Length of side DF = 15

2. Length of side DE = 5.625

Length of side EF = 4.96

3. Length of side DF = 10

Length of side EF = 6.61

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Answer:

37

Step-by-step explanation:

x=-4

=2(5-(-4)2+1

=2(5+4)2+1

=2(9)2+1

=18(2)+1

=36+1

=37

Answer:

  94.3

Step-by-step explanation:

You want to know how to fill in the proportion associated with the question, "What is 115% of 82?"

The diagram is intended to help you match parts of the question to parts of the proportion. The attachment shows the intended relation.

The solution is found by multiplying both sides by 82:

  (x/82)·82 = (115/100)·82

  x = 94.3

The question can also be written as a statement:

  "what" is 115% of 82

When written as an equation, "is" means "equals", and "of" means "times":

  what = 115% × 82

Of course, you can use any variable name of your choosing in place of "what". In your diagram, that is "x". And, you know how to write a percentage as a fraction or decimal, so this becomes ...

  x = 115/100 × 82 = 1.15 × 82

All that remains is to evaluate this expression.

  x = 1.15 × 82 = 94.3

So, the answer to the question is ...

  94.3 is 115% of 82.

Trigonometric ratios are ratios between any two sides of a right triangle that can then be used to determine the measure of an angle between those two sides. Primary trigonometric ratios (in a right triangle trigonometry) are: sin (x), cos (x) and tan (x)

On the basis of any two side lengths, we may even determine the acute angle measurements in a right triangle. We may get the ratios of the lengths of the triangle's sides to an acute angle in a right triangle by knowing the acute angle's measurement.

In a triangle, the longest side is located across from the largest angle, while the shortest side is located across from the smallest angle.

Triangle Unfairness: The lengths of any two sides added together in a triangle always exceed the length of the third side.

Pythagoras Theorem, a²+b²=c² in a right triangle with hypotenuse c.

A triangle is a right triangle if its sides conform to the relationship a²+b²=c²

The right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The other two inner angles add up to 90 degrees.

Remember that the Pythagorean theorem only holds true for right triangles, in which case the converse of the theorem also holds true. In other words, if a triangle's sides satisfy the connection, then it must be a right triangle.

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Answer:

A. negative sixteen

Answer:

9 squirrels and 36 birds

Step-by-step explanation:

4x+x=45

5x=45

x=9

4*9=36

A compound interest formula is a type of exponential equation. That is option C

Exponential equations are those equations that has their variables as exponents. A typical example of this type of equation is the compound interest formula.

The compound interest formula is an exponential equation because the little sum invested as capital, once the interest is added, the balance will earn more capital during the next compounding period.

Therefore, a compound interest formula is a type of exponential equation.

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if you are using a simple-moving average and you want your forecast to ignore occasional noise in the data, Only A & C are of the following is true .

What is the meaning of the simple moving average?

The average of a range of prices is determined by the number of periods that fall within the range using simple moving averages.

                             A technical indicator called a simple moving average can help forecast whether a price trend—be it bullish or bearish—will continue or reverse.

What is not necessary for simpler forecasting techniques?

various types and amounts of data are needed for various forecasting methodologies. Less information is necessary for simpler techniques, such as the time series techniques outlined below.

                                       Complex models require a lot of data. It might be expensive to create precise forecasts.

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