Type the correct answer in the box. If necessary, use / for the fraction bar.
Both pyramids in the figure have the same base area as the prism. The ratio of the combined volume of the pyramids to the volume of the pris
expressed as a fraction in simplest form, is

Numerous other sorts of numbers exist, including natural, whole, rational, real, and integers. Positive and negative numbers, but not decimals or fractions, make up the category of integers.

Q      What are integers in mathematics?
ANS An integer is a whole number without any fraction or decimal part.

The traits of each group of numbers are as follows:

Answer:

A.

Step-by-step explanation:

The fractions of sixth graders that reached their goal after each day are given as follows:

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

In which the technical terms related to x and y are as follows:

The fraction can be represented by bars, in which:

As shown by the image at the end of the answer, the fractions are given as follows:

The image is given at the end of the answer.

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Answer:

first angle =35

second angle=63

third angle=82

Answer: [tex]x=7[/tex]

Step-by-step explanation:

[tex]3^x=2187\\\\x=\log_{3} (2187)\\\\x=7[/tex]

Step-by-step explanation:

you made a typo.

since we are using only the digits 1, 3, 6 and 9, the list has to start

1, 3, 6, 9, 11, 13, 16, 19, 31, 33

it has to continue with

36, 39

we can skip the 40s and 50s and have then

61, 63, 66, 69

we can skip the 70s and 80s and have then

91, 93, 96, 99

that means we have 20 (5×4) numbers for the first 100.

we would have the corresponding 20 numbers in the 100s. like 101, 103, ...

but we have to skip 101, 103, 106, 109, because they contain 0.

so, it is only 16 numbers in the 100s.

there are none in the 200s.

then again 16 in the 300s. and the 600s and 900s.

so, we have

20 + 4×16 = 84 numbers in the first 1000.

then we have

16 in each the 1100s, the 1300s, the 1600s and 1900s.

and we have none in the 2000s.

so, in total we have

84 + 4×16 = 84 + 64 = 148 numbers to write.

76263

Step-by-step explanation:

[tex] \: \: \: 20005[/tex]

[tex] + 56258[/tex]

___________

[tex] = 76263[/tex]

The scale factor in the simplest form of a fraction of the triangles will be 43/78.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

There is no effect of dilation on the angle.

The triangle on the right is a scaled duplicate of the triangle on the left.

The ratio of the side of a big triangle to the side of a small triangle. Then we have

Scale factor = 43 / 78

The scale factor in the simplest form of a fraction of the triangles will be 43/78.

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The statements that are a result of corresponding parts of congruent triangles being congruent are:

An isosceles triangle is a type of triangle with two equal sides and angles. The other types of triangle includes;

From the figure;

Sides EFGH are congruent, that is, equal

Since Sides EFGH are congruent, it can not be a rectangle, it is a square.

Triangle FGH and FEH are both isosceles triangle.

Diagonal FH bisects triangle FGH and FEH

So therefore, the isosceles triangle FGH and FEH are congruent and bisected by diagonal FH.

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Considering the expression of a line, the equation of the line that passes through the pair of points (-5,-4) and (0,4) is y=8/5x + 4.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, the value of the ordinate to the origin b can be obtained.

Being (x₁, y₁)= (-5, -4) and (x₂, y₂)= (0,4), the slope m can be calculated as:

m= (4 - (-4))÷ (0 - (-5))

m= (4 + 4)÷ (0 +5)

m= 8÷ 5

m= 8/5

Considering point 2 and the slope m, you obtain:

4= 8/5×0 + b

4= 0 +b

4= b

Finally, the equation of the line is y=8/5x + 4.

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Answer:

Step-by-step explanation: step 5
they have not proved the ASA postulate i.e. they the are missing a step to proove angle BEF = angle CED (Verticle angles)
so, correct answer is step number 5 and reason 'missing prior step'

The two values of x is x = 3 and x = 5/2 of the equation 2x²– 11x + 15 = 0 i.e, the option(a) and option(d)

What is a Quadratic equation ?

A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.

The given expression is ,

2x²– 11x + 15 = 0

Solve the equation and find roots

2x² - 6x - 5x + 15 = 0

Take common elements out

2x(x - 3) - 5(x - 3) = 0

we get the brackets same that means we're on right way,

(2x - 5) (x - 3) = 0

split the values into two and find values,

2x - 5 = 0            and        x - 3 = 0

2x = 5                               x = 3

x = 5 / 2

Hence, the  values of x is x = 3 and x = 5/2 of the equation 2x²– 11x + 15 = 0 i.e, the option(a) and option(d)

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Answer:

136-5x

Step-by-step explanation:

The first step Charlie should use to solve the equation will be to open the bracket on the left side of the equation.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

The equation Charlie wants to solve can be calculated as follows:

-1/4(x - 1) =2/3 x +2

The first step would be to open the parenthesis on the left side of the equation as follows:

-1/4(x - 1) =2/3 x +2

- 1 / 4 x + 1 / 4 = 2 / 3 x + 2

Let's subtract 1 / 4 from both sides of the equation

- 1 / 4 x + 1 / 4 = 2 / 3 x + 2

- 1 / 4 x + 1 / 4 - 1 / 4  = 2 / 3 x + 2 - 1 / 4

- 1 / 4 x = 2 / 3 x + 7  /4

subtract 2 / 3 x from both sides of the equation.

- 1 / 4 x = 2 / 3 x + 7  /4

- 1 / 4 x - 2 / 3 x = 2 / 3 x - 2 / 3 x + 7  /4

- 11 / 12 x = 7 / 4

cross multiply

-44x = 84

divide both sides by - 44

x = 84 / -44

x = - 21 / 11

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Answer:

6 pizzas

Step-by-step explanation:

12.99 times 3 which is the 3 pitchers of soda is 38.97

38.97 subtracted from 75 which is our total amount is 36.03

36.03 which is what we have left divided by 6 since each pizza is 6$ is 6.

If a₁ = 9 and aₙ = 4 + (aₙ - 1) in an arithmetic sequence, then the value of fifth term a₅ is equal to 25.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

From the information provided, we know that the common difference is equal to 4.

Substituting the given parameters into the formula, we have;

a₅ =  9 + (5 - 1)4

a₅ =  9 + 4(4)

a₅ =  9 + 16

a₅ =  25

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Complete Question:

If a₁ = 9 and aₙ = 4 + (aₙ - 1), then find the value of a₅.

Answer:

2+4K

Step-by-step explanation:

distribute the 2

2(1+2k)

2(1)+2(2k)

2+4K

Hopes this helps please mark brainliest

The record-holder ate 6.205 kilograms of hot dogs.

We are given that 73/10 hotdogs per minute is the record for the most hot dogs eaten and one hot dog and bun has a mass of 85 grams. Also, one kilogram is equal to 1,000 grams. Solving this problem would involve converting units.

In order to find out how many kilograms of hot dogs the record holder ate, we first need to convert 85 grams to kilograms. Since a kilogram is equal to 1,000 grams, 85 grams = 85 / 1,000 = 0.085 kilograms.

Then, we multiply 0.085 by 73 to get 6.205. We can conclude that the record-holder ate 6.205 kilograms of hot dogs.

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Answer: A

Step-by-step explanation:

Answer: Answer B: m angle 5 = 152 because m angle 2 = m angle 5

Step-by-step explanation: im in 8th grade math in 7th grade

Answer:

Vertex: (-2, 3) Axis of symmetry: x = -2 The parabola opens downward.

Step-by-step explanation:

The equation for the function of the ordered pair is y =10x+2.

What is equation for the function?

 An equation that has one solution for y for each value of x is referred to be a function. For each input of a particular type, a function assigns precisely one output. The names f(x) or g(x) are frequently used in place of y when naming functions. If our function's value is f(2), then we should calculate its value when x=2. Each functional equation contains some information about a function or several functions. An illustration of a functional equation is f (x) f (y) = x y, f(x) f(y) = x y.

Here in given order pair , let us take any two points,

[tex](x_1,y_1)=(0,2)\\(x_2,y_2)=(1,12)[/tex]

Now using slope formula,

=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m =10/1 = 10

Now using equation formula,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y-2 =10(x-0)

=> y-2 = 10x

=> y=10x+2.

Therefore equation of the following order pair is y = 10x+2.

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Answer:

Consider the right triangle below: State the Pythagorean Theorem as it relates to the above triangle. List the trig identities as they relate to the triangle above. Now suppose hypotenuse C represents a vector R, while sides B and A represent vector components Rx and Ry respectively. Redraw the triangle with the new labels below. Using Pythagorean Theorem, derive the equation for R.

The number of shares he buy is $615.

Given that Barney just bought stock in Purple Dinosaur Industries and he paid a total of $7,380 and the price of the stock is $12 for one share.

We want to find the number of shares Barney buys.

The total amount barney should pay is $7380.

The price of the stock for one share is $12.

The total number of shares barney buy is 7380/12=615.

Hence, the number of shares barney should buy when he paid a total $7380 and the price of stock for one share is $12 is $615.

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The probability that the number is a multiple of four is 0.25.

we know that if a number is multiple of four then its last 2 digits must be divisible by four.( i.e. ten's and one's places)

We are given only four numbers 1,2,3,4 , which can't be repeated.

So here , in this case , such numbers with last two digits divisible by four are 12,24 and 32 only

Having last two digits ‘12’ ;

the first two digits can be formed using 3 and 4 only . This can be done in (2!) = 2 ways.

Similar case will be happening with 24 and 32 as well.

So the total ways of getting a multiple of four will be = 2 + 2 + 2

                                                                                        = 6 ways

Now total numbers that can be made from given four digits = [tex]P_{4} ^{4}[/tex]

                                                                                                  = 24

So the probability of getting a multiple of four is = 6/ 24

                                                                                 = 0.25

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Answer:

H = 30 ft

Step-by-step explanation:

Since the triangle is 90 degrees and we have to find out how tall the streetlight is we have to subtract 90 and 40 degrees. Which we get 50 degrees, after we subtract 20 from the 50 degrees. So we get 30 ft or 30 degrees.

The correct statement is their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.

What is property of similar triangle?

If the corresponding sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are similar.

They have parallel corresponding sides, and they have angles with the same measure.

hence, the correct statement is their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.

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