Math homework help 2.0

Answer:

-3x + 10

Step-by-step explanation:

you add like terms of 20 and negative 10 to simplify to -3x +10

The initial expression is:

We need to use the addition of fractions rule, and we obtain:

The answer is 13/12

Angle x =  90°, y = 5 and angle z =  75°.

Here, we are given two figures as shown in the figure above.

Figure 1 is a kite. The diagonals of a kite bisect each other at right angles.

Thus, here, the angle made by the intersection point of diagonals BD and AC will be 90°.

Thus, angle x =  90°.

Now, figure 2 is an isosceles trapezoid. In an isosceles trapezoid the two non-parallel sides are equal and the angles opposite to them are also equal.

Thus, here the two non-parallel sides- FE and GH will be equal.

⇒ y = 5

Further, the angle opposite to GH is 75° and that opposite to FE is z.

Thus, z =  75°

Hence, we find that angle x =  90°, y = 5 and angle z =  75°.

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Answer:

j = [tex]\frac{4}{20}[/tex]

Step-by-step explanation:

[tex]\frac{13}{20}[/tex] = j + [tex]\frac{9}{20}[/tex] ( subtract [tex]\frac{9}{20}[/tex] from both sides )

[tex]\frac{13}{20}[/tex] - [tex]\frac{9}{20}[/tex] = j , that is

j = [tex]\frac{4}{20}[/tex]

Answer: its 22over40

Step-by-step explanation:

The steps for using a compass and straightedge to construct the bisector will be:

1. Place the point of the compass on point G and draw an arc that intersects the sides of ∠G.

2.Label the points of intersection as points H and J.

3. Place the point of the compass on point H and draw an arc in the interior of the angle.

4. Without changing the opening of the compass, place the point of the compass on point J and draw another arc in the interior of the angle.

5.Label the intersection of the arcs in the interior of the angle as point K.

6. Use the straightedge to draw GK.

Bisection in geometry is the division of something into two equal or congruent portions, usually by a line, which is then known as a bisector. The segment bisector and the angle bisector are the most commonly used forms of bisectors.

To bisect anything implies to divide it into two equal sections. A bisector is a line that divides anything into two equal pieces. Bisectors include segment bisectors, angle bisectors, and shape bisectors. A segment bisector is a line that runs across the center of a particular segment.

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Let's cut the given solid into two parts to easily get its total volume:

Let's determine the volume of figure A:

Let's determine the volume of figure B:

Let's add the volume of the A and B to get the total volume of the given figure.

We get,

Therefore, the volume of the figure is 1,536 cm³.

The area of Rachel's bedroom is 72 square feet. The bedroom area that is eight times of Rachel's closet. The length of the closet if it is 3 feet wide is 3.

Given that,

The area of Rachel's bedroom is 72 square feet. The bedroom has an area that is eight times that of Rachel's closet.

We have to find what is the length of the closet if it is 3 feet wide.

First we divide the area of Rachel's bedroom is 72 square feet and eight times that of Rachel's closet.

72/8=9

Now, we multiply 3 and the length as l is equal to 9 feet wide

3×l=9

l=9/3

l=3

Therefore, The length of the closet if it is 3 feet wide is 3.

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Answer:

Step-by-step explanation:

The bottom right box.

The sigma notation of the series is  [tex]\sum_{n=3}^9(2n)[/tex]

How to write the sigma notation?

                          2n = 6

                          n   = 3

                        2n = 18

                           n = 9

              The limits are [3,9]

                     [tex]\sum_{n=3}^9(2n)[/tex]  = 84

What is a sigma notation?

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The probability of passing one test or the other is given by:

0.63 = 63%.

In a Venn probability, two non-independent events are related with each other, as are their probabilities.

The "or probability" between these two events is given by the rule presented as follows:

P(A or B) = P(A) + P(B) - P(A and B)

In the context of this problem, these events are given as follows:

The probabilities of each event and the and probability are listed as follows:

P(A) = 0.58, P(B) = 0.24, P(A and B) = 0.19.

Hence the probability of passing one test or the other is calculated as follows:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.58 + 0.24 - 0.19 = 0.63 = 63%.

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Step-by-step explanation:

If Cora uses the 15% off coupon first then the new total is $92.65. After using the $10 off coupon, the total is $82.65.

If Cora uses the $10 off coupon first, the total goes to $99. Taking 15% off of $99 leaves her with a total of $84.15.

Thus, it would be better for Cora to use the 15% off coupon before using the $10 off coupon.

The values of x that will give a range of 55 include 42 and -13.

A range simply means the difference between the highest number that is given and the lowest number that is given.

In this case, the chose numbers include:.

Larger number = 42

Smaller number = -13

Range = Larger number - Small number

= 42 - (-13)

= 42 + 13

= 55

The range of 55 is gotten.

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The two possible values of x given the range are -13 and 58.

Range is used to measure the variation of a dataset. Range is the difference between the highest number in the dataset and the lowest number in the dataset.

Range = highest number - lowest number

x can either be the largest number in the dataset or the smallest number in the dataset.

Value of x if it is the smallest value in the dataset.

42 - x = 55

x = 42 - 55

x = -13

Value of x if it is the largest value in the dataset.

x - 3 = 55

x = 55 + 3

x = 58

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Answer: 1.001 x 10^3

Step-by-step explanation:

The food is available for all snow geese for 11.5 days before the research and rescue center runs out.

According to the question,

We have the following details:

Number of snow geese in the research and rescue center = 9

Number of ounces of seeds eaten by each goose = 16 ounces

So, number of ounces of seeds eaten by 9 snow geese = (16*9) ounces

Number of ounces of seeds eaten by 9 snow geese = 144 ounces

Now, there are 1,656 ounces of seeds.

So, the number of days before the center runs out of the food = Total number of ounces of seeds/Number of ounces of seeds eaten by 9 snow geese

Number of days before the center runs out of the food = 1656/144

Number of days before the center runs out of the food = 11.5 days

Hence, the number of days for which food is available for all snow geese before the center runs out is 11.5 days.

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Answer:

The food is available for all snow geese for 11.5 days before the research and rescue center runs out.

Step-by-step explanation:

The sum identities in trigonometry are cos^2(x)+sin^2(x)=1

                                                                 sec^2-tan^2(x)=1

                                                                 cosec^2(x)-cot^2(x)=1

Trigonometry: Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. Trigonometry is found all throughout geometry, as every straight-sided shape may be broken into as a collection of triangles

Let's prove using the angle addition formula for cosine:

cos(α+β)=cos(α)cos(β)-sin(α)sin(β)

we know that sin(-x)= -sin x and

                       cos(-x)=cos x

we need to proceed to the proof ,

let α=x and β=-x

cos(x+(-x))=cos(x)cos(-x)-sin(x)sin(-x)

cos(0)  = cos(x)cos(x)+sin(x)sin(x)

cos^2(x)+sin^2(x)=1

Hence, it is proved

to prove another identity i.e., sec^2-tan^2(x)=1

start from cos^2(x)+sin^2(x)=1

divide both the sides by cos^2(x)

cos^2(x)/cos^2(x)+sin^2(x)/cos^2(x)=1/cos^2(x)

1+tan^2(x)=sec^2(x)

sec^2-tan^2(x)=1

Hence, it is proved

to prove another identity i.e., cosec^2(x)-cot^2(x)=1

start from cos^2(x)+sin^2(x)=1

divide both sides by sin^2(x)

cos^2(x)/sin^2(x)+sin^2(x)/sin^2(x)=1/sin^2(x)

cot^2(x)+1=cosec^2(x)

cosec^2(x)-cot^2(x)=1

Hence, it is proved

The sum identities in trigonometry are proved

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Answer:400

Step-by-step explanation: 12/3= 4 4x100= 400

The linear inequality leads us to the conclusion that the silver pass will be more advantageous if a visitor stays at the theme park for more than three days.

Let the number of days be x.

So, cost of single pass for one day is 50 +10 = $60

cost of single pass for x days is 60x.

cost of silver pass for one day is 120 +20 = $140

cost of silver pass for x days is 120+20x.

Now, for silver pass to be worth to buy instead of single pass will be when it costs lesser than that of the single pass.

So,

Cost of silver pass < cost of single pass

120 + 20x < 60x

120 < 40x

x>3,

So, we can say conclude from the linear inequality that the silver pass will be more beneficial if someone is staying at amusement park for more than 3 days.

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Answer:

-16/35

Step-by-step explanation:

4/7 ÷ -5/4

=> 4/7 × -4/5

=> -16/35

Answer:

Having 1 angle being 90 degrees

The system of inequalities are

x + y = 12,

25x + 10y ≤ 150

x ≥ 9,

y ≥ 4 and the graph of the inequality is attached below.

Inequality:

Inequality refers the relationship between two values that are not equal is defined by inequalities. Inequality means not equal.

Given,

No. of summer job Owen working = 2 (tutoring and clearing tables)

Cost per hour (tutoring) = $25

Cost per hour (clearing tables) = $10

In a week,

Total working hour = 12

Minimum Amount earned = $150

Maximum hours (tutoring) = 9

Maximum hours (clearing tables) = 4

Here we need to find the system of inequalities and we have to plot the graph for it.

Then we need to find one possible solution for it.

Let us consider x be the number of hours for tutoring and y be the number of clearing table.

So, the total number of working hours,

x + y = 12

And the amount earned in the week,

25x + 10y ≤ 150

And we also know that,

x ≥ 9 and y ≥ 4.

The graph of the equation is attached below.

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Answer:

m = 1/7

Step-by-step explanation:

Given:

(x1 = 7, y1 = 0) and (x2 = 0, y2= -1)

We know:

slope m = vertical change in y / horizontal change in x

m= (y2-y1)/(x2-x1)

Calculate slope:

m= (y2-y1)/(x2-x1) = (-1-0)/(0-7) = -1/ -7 = 1/7

Answer: M x X

P x E

YW x RK

Step-by-step explanation:

When the value of y varies directly with x and x = 5, y = 12 then, the value of x when y = 1 is 5/12.

What is direct variation?

The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a. (where k is a constant). When two variables are coupled in a way that ensures the ratio of their values never changes, this relationship is referred to as being in direct variation. Different mathematical structures are used to express direct variation. Since the ratio of y to x never changes, y and x fluctuate directly in equation form.

As given in the question,

when x = 5, y = 12,

x and y varies directly, it means they are directly proportional:

y ∝ x

y = kx {here, k is a constant}

Putting the value of x and y, and finding the value of k:

k = 12/5

Now, we need to find x when y = 1. so,

y = kx

putting the values,

1 = (12/5)x

x = 5/12

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The length of the ramp is 10.7 feet high.

What is ratio of triangle ?

 The definition of the tangent (tan) of the angle is the ratio of the opposing to the neighbouring in any right triangle. The tangent's value for the red triangle is given by: tan(c) = 1 / 2 =.5. We maintain the same angle c for the blue triangle, but we have doubled the sizes of the adjacent and opposite sides.

It always helps to draw a diagram and find the right triangle.  

In this case, the triangle has the loading dock as one leg, the ramp as the hypotenuse, and the distance of the ramp from the loading dock as the other leg.

Call that distance x.  Use the tangent of 25° to find x.

=> tan(25°) = [tex]\frac{opposite }{adjacent}[/tex]

=> tan(25°) = [tex]\frac{5}{x}[/tex]

=> x = 5/ tan(25°)≈ 10.7 feet.

Hence the length of ramp is 10.7 ft.

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Based on the information provided about this map, we have the following answers:

A scale factor can be defined as the ratio of two (2) corresponding length of sides or diameter in two similar geometric figures such as equilateral triangles, river, planets in our solar system, etc.

Mathematically, the scale factor of a figure such as a map can be calculated by using this formula:

Scale factor = Dimension of image/Dimension of original figure

In Mathematics, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion of units.

Conversion:

1 = 5000000

6.5 = X

Cross-multiplying, we have:

X = 6.5 × 5000000

X = 32,500,000 cm

X = 325 km.

The amount of centimeters that can be used to represent a distance of 650 km on a map with a scale of 1:1500000 is given by:

Conversion:

1 = 1500000

X = 6.5

Therefore, we have:

X = 650/15

X = 43.333 cm.

We would determine the scale of the map as follows;

Conversion:

7 cm ⇒ 63,000,000 cm = 630 km

Therefore, the scale of the map is given by:

Scale = 7:63,000,000 = 7/63,000,000

Scale = 1/9,000,000

Scale = 1:9,000,000

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Answer:

- 36x + 9

Step-by-step explanation:

- 12(3x - [tex]\frac{3}{4}[/tex] ) ← multiply each term in the parenthesis by - 12

= - 36x + 9

Answer:

-36x + 9

Step-by-step explanation:

Given expression:

[tex]-12\left(3x-\dfrac{3}{4}\right)[/tex]

Apply the distributive rule:

[tex]\implies -12 \cdot 3x -12 \cdot -\dfrac{3}{4}[/tex]

Multiply -12 and 3x:

[tex]\implies -36x -12 \cdot -\dfrac{3}{4}[/tex]

Apply the rule  -a(-b) = ab:

[tex]\implies -36x +12 \cdot \dfrac{3}{4}[/tex]

Convert 12 into a fraction:

[tex]\implies -36x +\dfrac{12}{1} \cdot \dfrac{3}{4}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{ac}{db}}:[/tex]

[tex]\implies -36x +\dfrac{36}{4}[/tex]

Divide the numbers:

[tex]\implies -36x +9[/tex]

Therefore, the equivalent expression to the given expression is:

Answer:down below

Step-by-step explanation:A square gives the greatest area. If the river were not there, you would divide 1700 by 4 to get a square 425 feet by 425 feet. Because of the river, add 425 feet to the side opposite the river to get a rectangle 425 feet by 850 feet.

Now for the algebra that you need.

P=2l+2w but there is only one length.

P=l+2w

1700=l+2w

1700-2w=l

A=lw

A=(1700-2w)w

A=1700w-2w2

This is a parabola that opens downward so there is a maximum point, the vertex, which is (h,k).

h=-b/2a is the "maximizing point" and k is the maximum area

-b/2a=-1700/(-4)

-b/2a=425 feet

One width will be 425 feet, the length will be (425+425)=850 feet, and the second width will also be 425 feet.

A=lw

The maximum area will be A=850*425=361,250 square feet.

Notice that if you substitute 425 into the equation A=1700w-2w2 you will get the same answer.

1700*425-2*4252

722,500-2*180,625

722,500-361,250

The equation of a line that is perpendicular to y = 4x + 8 and passes through (−8, 4) is y = - 1 / 4 x + 2 (y equals negative one-fourth times x plus 2)

The equation of the line is perpendicular to y = 4x + 8 and passes through (-8, 4).

Therefore, the equation of a line can be represented as follows;

y = mx + b

where

Therefore, perpendicular lines follows the rule below:

m₁ m₂ = -1

4m₂ = -1

m₂ = - 1 / 4

Hence, let's find the y -intercept using (-8, 4)

y = - 1 / 4 x + b

4 = - 1 / 4 (-8) + b

4 = 2 + b

b = 4 - 2

b = 2

Therefore, the equation is y = - 1 / 4 x + 2

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Answer: D.) y = 4x + 4

Step-by-step explanation:

just did the assignment