1. The sum of two angles is 85°, one angle is five more than the measure of the other angle. Write the equation that represents this scenario and find the measure of each angle. Be sure to show your
work.

Answer:

1/30 of a mile per minute.

Step-by-step explanation:

8/4 = 2 miles per hour.

2/60 = 1/30 of a mile per minute.

Square root functions are in the shape of a parabola, like a giant U, while cube root functions are more wide and swiggly, like a stretched out S.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

Here, given that,

we have to say that, How is the general shape of a cube root function different from the shape of a square root function.

Now, we get,

Square root functions are in the shape of a parabola, like a giant U, while cube root functions are more wide and swiggly, like a stretched out S.

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The equation that represent the gross pay is y = 0.12x + 1760. The commission was $10896 and gross pay was $12656

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Let y represent the gross pay for x total sales.

Donald Simmons a $1760 monthly salary plus a 12% commission on merchandise he sells each month, hence:

y = 1760 + 12% of x

y = 0.12x + 1760

Donald's sales were $90,800 for last month. Hence:

a) Commission = 0.12 * $90800 = $10896

b) Gross pay:

y = 10896 + 1760 = $12656

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The expression A' represents the statement for all of the elements which are not in set A.

A set is a collection of well defined objects.

Given that A students wants to write an expression for all of the elements which are not in set A.

The elements within set A are denoted by A.

We have to find  all of the elements which are not in set A.

U represents the universal set and A is the given set.

A'=U-A

Hence, the expression A' represents the statement for all of the elements which are not in set A.

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Rewriting the sum in the form a(b+c) such that the integers b and c have a common factor. 35+42 is 7(5 + 6).

The process of factorization simply has to do with the division of arithmetic algebraic expressions into the sum of their factors. in this case, multiplying the variables will yield the original expression. It means the writing of a number into smaller or simpler numbers that give the original number.

The common factor to both 35 and 42 is 7. This will be:

35 + 42 = 7(5 + 6)

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Complete question

How do i rewrite the sum in the form a(b+c) such that the integers b and c have a common factor. 35+42

Answer:

(a)  13.9 blocks (nearest tenth)

(b)  32.9 blocks (nearest tenth)

Step-by-step explanation:

The given scenario can be modeled as a right triangle.

If Amy walks south 7 blocks, one leg of the triangle is 7.

If Amy then walks west 12 blocks, the other leg of the triangle is 12.

To calculate the number of blocks Amy walks on her way home if she walks directly from school to her home, find the length of the hypotenuse of the right triangle.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

Substitute a = 7 and b = 12 into Pythagoras Theorem and solve for c (hypotenuse):

[tex]\implies 7^2+12^2=c^2[/tex]

[tex]\implies 49+144=c^2[/tex]

[tex]\implies 193=c^2[/tex]

[tex]\implies c=\sqrt{193}[/tex]

[tex]\implies c=13.8924439894...[/tex]

Therefore, Amy walks 13.9 blocks (nearest tenth) on her way home.

To calculate the number of blocks Amy walks in one day for her round trip to school and back home, sum the side lengths of the right triangle:

[tex]\implies 7 + 12 + 13.9 = 32.9[/tex]

Therefore, Amy walks 32.9 blocks (nearest tenth) in one day for her round trip to school and back home.

The right triangles are congruent by HL theorem.

The triangles having congruent corresponding parts are called congruent triangles.

Given are two right triangles, with equal hypotenuse and one of the bases.

The question is by which theorem do they are congruent,

HL theorem :-

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

Since, we know that, when two right triangles have congruent hypotenuse and one of their legs are also congruent, then both are congruent by HL theorem of congruence.

Here, both the right triangles are following the condition of the HL theorem.

Hence, the correct option is HL.

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The expression does not represent next year's population is 0.991. The correct option is A.

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 the population of a city decreases by 0.9% per year. The expression for the population depreciation is,

Population = ( 100% - 0.9%)P

Population = (1 - 0.009)P

Population = 0.991P

Hence, the expression not representing the depreciation is 0.991.

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The real property of 3 x (5 + 1) = (3 x 5) + (3x1) is the distributive property

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

3 x (5 + 1) = (3 x 5) + (3x1)

The distributive property of algebra states that

x * (a + b) = x * a + x * b

This means that

x = 3

a = 5 and b = 1

By comparison, we can conclude that the property is the distributive property

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Answer:

Ah and mc are parallel segments

The minimum is the smallest value in the data set. The maximum is the largest value in the data set.

We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.

A minimum or a maximum is called an extreme point. A local extreme point is the smallest or largest value in its neighborhood. If it is also the smallest or largest at the entire domain of the function, it is called a global extreme point. The local minima and maxima can be found by solving f'(x) = 0.

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Complete question is: What is the difference between Minimum or maximum value?

By taking a quotient, we will see that each cheetah has around 51 acres for itself.

If we assume that the cheetahs are evenly distributed along the whole area, then the number of acres that each cheetah has to itself is equal to the quotient between the total area, and the total number of cheetahs.

There are 969 acres and 19 cheetahs, then the quotient is:

969/19 = 51

That is the number of acres that each cheetah has for itself.

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Answer:

−12r+32−2r 2

Step-by-step explanation:

(−8−r)(2r−4)

Apply the distributive property by multiplying each term of −8−r by each term of 2r−4.

−16r+32−2r

2

+4r

Combine −16r and 4r to get −12r.

Answer:

R-12

Step-by-step explanation:

Open the parenthesis, then solve

-8-r + 2r-4

-r+2r-8-4

r-12

Your answer will be R-12

Answer:

27:-3×9

51:-3×17

In 27 and 51 the common one is 3 and hence it is the greatest common factor.✓✓

if you want smallest or lowest common factor then you have to take the common 3 as one and multiply like this:-3×9×17=459 is the Lowest common factor.

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Answer:

  see below

Step-by-step explanation:

You want the ingredient quantities for several different multiples of the basic recipe.

To fill the table, consider what the column heading is as a multiple of the recipe for 12 people. Use that multiplier for the rest of the numbers in the column.

  [tex]\begin{array}{ccccc}\text{12 people}&\times2&\times3&\times\dfrac{1}{3}&\times\dfrac{1}{2\vphantom{g_g}}\\\cline{1-5}1\text{ cup}&2&3&\dfrac{1\vphantom{b^b}}{3\vphantom{g_g}}&\dfrac{1}{2}\\3\text{ cups}&6&9&1&1\dfrac{1}{2}\\2\text{ cups}&4&6&\dfrac{2}{3\vphantom{_g}}&1\\\dfrac{1}{2}\text{ cup}&1&1\dfrac{1}{2}&\dfrac{1}{6}&\dfrac{1\vphantom{^b}}{4\vphantom{_g}}\\1\dfrac{\vphantom{^b}1}{3}&2\dfrac{2}{3}&4&\dfrac{4}{9}&\dfrac{2}{3}\end{array}[/tex]

The angle of elevation of the fly's flight path is approximately 57.74 degrees.

In a right triangle, the hypotenuse is the side opposite the right angle. It is always the longest side of the triangle and is the side opposite to the 90 degrees angle. It is also the side that forms the "hypotenuse" of the right triangle.

The Pythagorean theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as c^2 = a^2 + b^2, where a and b are the legs of the triangle and c is the hypotenuse. This theorem can be used to find the length of the hypotenuse of a right triangle when the lengths of the other two sides are known.

Let's call the angle we're trying to find "theta". The horizontal distance is 30 feet, the vertical distance is 32 feet and the height is 9 feet.

Using pythagorean theorem:

$c^2 = a^2 + b^2$

$c = \sqrt{30^2 + 32^2}$ = $\sqrt{900 + 1024}$ = $\sqrt{1924}$

Now we can use the tangent function:

$\tan(\theta) = \frac{opposite}{adjacent} = \frac{32}{30}$

Now we can find the angle, theta, by using the inverse tangent function:

$\theta = \tan^{-1}(\frac{32}{30})$

The angle of elevation of the fly's flight path is approximately 57.74 degrees.

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The total number of students in the student body is 110.

Percentage is the ratio of an amount expressed as a number out of 100. The sign that is used to represent percentage is %.

In order to convert a number to percentage, multiply the number by 100. Percentage is a measure of frequency.

In order to determine the total number of students in the student body, divide the number of students that watch TV everyday by the given percentage.

Number of students in the student body = number of students that watch TV everyday / percentage

88 / 80%

= 88 / 0.8 = 110

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Answer:

look below!

Step-by-step explanation:

To get the vertex for an equation your best bet is to convert the form into vertex form,which is y=a(x−h)+k . In vertex form (h,k) is the vertex

The conditions of the line to be intersecting, parallel, and coincident are explained below.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The types of lines are as follows:

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Answer:

Shop B

Step-by-step explanation:

First, find the number of scarves that Shop A sold: 15% of 120 scarves is 15/100 * 120 scarves = 18 scarves.

Then, find the number of scarves that Shop B sold: an eighth of 152 scarves is 152/8 = 152/8 = 19 scarves.

Since 18 scarves is less than 19 scarves, Shop B sold more scarves.

Using the addition operation, the number of cups of flour Sasha needs to make both a batch of muffins and a loaf of bread is 2⁵/₁₂ cups.

We can use the addition operation to determine the quantity of flour that Sasha needs.

We add the cups of flour needed for both items to determine the total quantity.

The quantity of flour for making a batch of muffins = 3/4 cups

The quantity of flour for making a loaf of bread = 1²/₃ cups

The total quantity of flour needed for making a batch of muffins and a loaf of bread = 2⁵/₁₂ cups (³/₄ + 1²/₃)

(³/₄ + 1²/₃)

= ³/₄ + ⁵/₃

= (9 + 20)/12

= 29/12

= 2⁵/₁₂

Thus, to make a batch of muffins and a loaf of bread, Sasha needs 2⁵/₁₂ cups of flour.

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Part A

Reason:

Divide the side lengths of B over A to get B/A = 3/5. The order is important. The fraction 3/5 is smaller than 1 to indicate a size reduction. There are no units involved with the scale factor.

=========================================

Part B

Reason:

The linear scale factor is 3/5. The area scale factor is (3/5)^2 = 9/25. It means if figure A had area 25, then figure B would have area 9.

Let's use that idea to set up the following:

(area of figure B)/(area of figure A) = 9/25

B/A = 9/25

x/15 = 9/25

25x = 15*9

25x = 135

x = 135/25

x = 5.4 represents the area of figure B

Answer:

7 cars

11 bikes

Step-by-step explanation:

18 cars would have 72 tires. This is 22 more tires than necessary. If we add a bike, we lose four tires (from the car) and add two (from the bike). This means we lose two tires. 22/2 is 11 so it would be 11 bikes and 7 cars.

11 bikes = 22 tires

7 cars = 28 tires

22+28=50 tires

Answer: 8

Step-by-step explanation:

Im guessing this is your question

Noah's family bought some fruit bars to put in the gift bags. They bought one box each of four flavors: apple, strawberry, blueberry, and peach. The boxes all had the same number of bars. Noah wanted to taste the flavors and ate one bar from each box. There were 28 bars left for the gift bags. Use the tape diagrams to determine how many fruit bars were originally in each box.

Answer:

Step-by-step explanation:

x-5

me bye u see okay later

An equation which has one (1) solution include the following: D. |W| = 0.

In Mathematics, an absolute value function can be defined as a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0) of a cartesian coordinate (graph).

Mathematically, an absolute value function can be represented by this mathematical expression:

|x| = x, x ≥ 0.

|x| = x, x < 0.

Generally speaking, an equation or absolute value function would have exactly one (1) solution when there is only one (1) value for the variable (W) that makes the equation to be true as shown below:

|W| = 0

W = ±0

W = 0

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The volume of the given solid. Bounded by the cylinder y^2+z^2=4 and the planes x=2y, x=0, z=0 in the first octant is 16/3 unit cute

V = ∫ dV

= ∫0→2 ∫ 0→π/2 ∫ 0→ 2·r·sin(φ) [ r ] dzdφdr

Factorize to have

= ∫0→2 ∫ 0→π/2 [ r·2·r·sin(φ) - r·0 ] dφdr

= ∫0→2 ∫ 0→π/2 [ 2·r²·sin(φ) ] dφdr

= ∫0→2 [ -2·r²·cos(π/2) + 2·r²·cos(0) ] dr

= ∫0→2 [ 2·r² ] dr

= (2/3)·2³ - (2/3)·0³

Conclusively, this implies that the volume is = 16/3

In conclusion, the volume of the given solid is 16/3. cubic units

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Each nested cart add to the length of the row is 1.5 feet long.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, the store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long.

Each row has a starting cart that is 4 feet long, and the nested carts are next to it.  

It is measured that a row of 13 nested carts has a length of 23.5 feet.

Therefore, the original length of 13 nested carts is (23.5 - 4) = 19.5 feet.

So, each nested cart add to the length of the row 19.5/13 =1.5 feet

Again, a row of 18 nested carts to be 31 feet long.

Therefore, the actual added length of 18 nested carts is (31 - 4) = 27 feet.

So, each nested cart add to the length of the row 27/18 =1.5 feet

Therefore, each nested cart add to the length of the row is 1.5 feet long.

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"Your question is incomplete, probably the complete question/missing part is:"

A store is designing the space for rows of nested shopping carts. Each row has a starting cart that is 4 feet long, followed by the nested carts (so 0 nested carts means there's just the starting cart). The store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long.

How much does each nested cart add to the length of the row?

The given statement “if the slope of a line is 3, then the slope of a parallel line is 4” is false because parallel lines have equal slopes

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

Slope of a line = 3

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 3

This means that the slope is 3

The slopes of parallel lines are equal

This means that the slope of the other line is 3

Hence, the statement is false

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Answer:

sq root of 21=7

Step-by-step explanation:

we need to use Pythagoras theorem

so distance(isa-jul)^2 +distance(ele-jul)^2= distance(isa-ele)^2

now just do the square root and there you go.

A number between 47 and 53 such that the prime factors are not repeated is:

3*17 = 51

Remember that any number can be written as a product of prime factors.

If we want to find a number between 47 and 53, such that there are no repeated factors, we just need to take different primes and multiply them.

For example:

2*3*5*7 = 210

There are no repeated factors, but the number is not in the desired range.

2*5*7 = 70

Still not in the range.

You can try some times until you get for example:

3*17 = 51

This a number in the desired range, such that their prime factors are not repeated.

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