-5x -4y = -15 and -x + 4y = -3

Answer:

The answer to your question is 365040000 lb or 3.65 x 10⁸ lb

Step-by-step explanation:

Data

Rectangular pyramid

base = 100 yd x 78 yd

height = 100 yd

weight of a stone = 468 lb/yd³

Process

1.- Calculate the volume of the pyramid

Volume = area of the base x height

-Substitution

Volume = 100 x 78 x 100

-Simplification

Volume = 780000 yd³

2.- Calculate the weight of the pyramid

                     468 lb ------------------------ 1 yd³

                         x      ------------------------780000 yd³

                         x = (780000 x 468) / 1

                         x = 365040000 lb or 3.65 x 10⁸ lb

Answer:

y=mx+b

Step-by-step explanation:

The formula to find the slope is y=mx+b

hope this helps

Answer:

you need to know what the pairs of numbers match to get a possible answer

Step-by-step explanation:

once u know that you can do the rest of the math and it depends how to multiply

Answer:

[tex]i_m=8.322\%\\\\624 \ compoundings\\\\A_{12}=\$1,304.88[/tex]

Step-by-step explanation:

#The equivalent interest rate per annum is equal to the effective interest rate.

-Given 8% compounded weekly( Take 1 yr=52 weeks) the effective interest rate is calculated as:

[tex]i_m=(1+i/m)^m-1\\\\\#where\\i=stated \ interest\ rate\\m=number \ of \ compoundings \ per \ year\\\\\therefore i_m=(1+0.08/52)^{52}-1\\\\=0.08322\approx 8.322\%[/tex]

Hence, the equivalent interest rate is 8.322%

-Assuming one year has 52 weeks,   the number of compoundings will be :

[tex]=compoundings \ per \ year \times \ no \ of \ years\\\\=52\times 12\\\\=624\ compoundings[/tex]

-The investment amount after 12 years is calculated as:

[tex]A=P(1+i_m)^n, n=number \ of \ years\\\\=500(1.08322)^{12}\\\\=1304.88[/tex]

Hence, the amount after 12 years is $1304.88

Answer:

8% annual interest rate when compounded weekly =

(1 + .08/ 52)^52 = 1.00153846153846154^52 = 1.08322047419671 =

8.322047419671% equivalent interest rate

In 12 years this will be compounded 624 times

12 year Total = 500 * (1.08322047419671)^12 =

1,304.8852611583 =

1,304.89 (rounded)

Answer:

l=8

Step-by-step explanation:

w=l-7

Area=l*(l-7)=8 u

l^2-7l-8=0

l^2- 8l+l-8=0

l(l-8)+l-8=0

(l-8)*(l+1)=0

l-8=0  ,   l=8  or

l+1=0,   l=-1 impossible

so l=8

To find the length of a rectangle when its width is the length minus 7 units and its area is 8 units, you can set up an equation and solve it. In this case, the length of the rectangle is 8 units.

To solve this problem, you need to set up an equation based on the given information. Let's assume the length of the rectangle is 'L'. According to the problem, the width of the rectangle is the length minus 7 units. So, the width can be represented as 'L-7'.

The area of a rectangle is given by the formula 'length x width'. In this case, the area of the rectangle is 8 units. So, the equation would be: L x (L-7) = 8.

To find the length of the rectangle, you need to solve the equation. Expand the equation: L^2 - 7L = 8. Rearrange it to form a quadratic equation: L^2 - 7L - 8 = 0. Factorize or use the quadratic formula to find the values of 'L'. It turns out that the length of the rectangle is 8 units.

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Answer:

in scientific notation​ the answer is 5.75x10^8

Answer: [tex]5.75[/tex] [tex]x[/tex] [tex]10^{8}[/tex]

Step-by-step explanation: To write a number in scientific notation, first write a decimal point in the number so that there is only one digit to the left of the decimal point.

So here, we have 5.75000000 and notice that there

is only one digit to the left of the decimal point.

Next, we count the number of places the decimal point would

need to move to get back to the original number, 575,000,000.

Since we would need to move the decimal point 8 places to the right,

we have an exponent of positive 8.

Now, scientific notation is always expressed as a number between 1 and 10 including 1 but not 10 and it is multiplied by 10 to a certain power that must be an integer.

So we have [tex]5.75000000[/tex] [tex]x[/tex] [tex]10^{8}[/tex].

Notice that the exponent is positive.

This is because we would need to move the decimal point to the right in order to get back to the original number.

So 575,000,000 can be written in scientific notation

as [tex]5.75000000[/tex] [tex]x[/tex] [tex]10^{8}[/tex] or just [tex]5.75[/tex] [tex]x[/tex] [tex]10^{8}[/tex].

Remember that we can drop zeroes at the end of a decimal.

So we have [tex]5.75[/tex] [tex]x[/tex] [tex]10^{8}[/tex].

Answer:

Blank 1: 40

Blank 2: 10

Step-by-step explanation:

You can start by representing the speed of the water as x and the speed of the dolphin as y, and writing an equation.

y+x=50

y-x=30

Adding these two equations together, you get:

2y=80

y=40 for the speed of the dolphin in still water. Now, you an use one of the previous equations to find the speed of the current.

40-x=30

x=10

Hope this helps!

Answer:

Proved down

Step-by-step explanation:

To prove that a triangle is isosceles use the distance formula to find the length of its side and check if there are two sides equal.

To prove that a triangle is right find the square of the longest side and then find the sum of the squares of the other two sides, if the two answers are equal, then the triangle is right (converse of Pythagoras Theorem).

The formula of the distance between two points is:

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

∵ x = (-1 , 5) and y = (4 , 4)

∴ [tex]x_{1}[/tex] = -1 and [tex]x_{2}[/tex] = 4

∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = 4

- Substitute them in the formula of the distance to find xy

∵ [tex]xy=\sqrt{(4--1)^{2}+(4-5)^{2}}=\sqrt{25+1}[/tex]

∴ [tex]xy=\sqrt{26}[/tex]



∵ x = (-1 , 5) and z = (-2 , 0)

∴ [tex]x_{1}[/tex] = -1 and [tex]x_{2}[/tex] = -2

∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = 0

- Substitute them in the formula of the distance to find xz

∵ [tex]xz=\sqrt{(-2--1)^{2}+(0-5)^{2}}=\sqrt{1+25}[/tex]

∴ [tex]xz=\sqrt{26}[/tex]

∵ xy = xz

- The isosceles triangle has two equal sides

∴ Δ xyz is an isosceles triangle

∵ y = (4 , 4) and z = (-2 , 0)

∴ [tex]x_{1}[/tex] = 4 and [tex]x_{2}[/tex] = -2

∴ [tex]y_{1}[/tex] = 4 and [tex]y_{2}[/tex] = 0

- Substitute them in the formula of the distance to find yz

∵ [tex]yz=\sqrt{(-2-4)^{2}+(0-4)^{2}}=\sqrt{36+16}[/tex]

∴ [tex]yz=\sqrt{52}[/tex]

yz is the longest side lets find its square

∵ (yz)² = ([tex]\sqrt{52}[/tex] )²

∴ (yz)² = 52

- Lets find the sum of the squares of the other two sides

∵ (xy)² + (xz)² =  ([tex]\sqrt{26}[/tex] )² +  ([tex]\sqrt{26}[/tex] )²

∴ (xy)² + (xz)² = 26 + 26 = 52

∴ (yz)² = (xy)² + (xz)²

- That means the angle opposite to yz is a right angle

∴ Δ xyz is a right isosceles triangle

List the numbers from least to greatest:

1, 3, 3, 4, 5, 6, 8, 9, 10

Mode: ( most number repeated in the list)

Mode: 3

The mode of the numbers 6, 4, 1, 9, 3, 8, 3, 5, 10 is 3, as it is the number that appears most frequently in the set.

The question asks to find the mode of the following numbers: 6, 4, 1, 9, 3, 8, 3, 5, 10. The mode is a measure of central tendency that represents the most frequently occurring number in a set of values. To find the mode, we need to count how many times each number occurs in our set.

Since the number 3 appears more frequently than any other number in the set, occurring twice, the mode of this set of numbers is 3.

Answer:

the answer is c

Step-by-step explanation:

Answer:

C. y + 8 = –5(x – 3)

second part is also C. y = –5x + 7

Step-by-step explanation:

Step-by-step explanation:

The combination of Wendell and Maggie’s ages is 33. Let Maggie's age is x. It is mentioned that Wendell’s age is 3 less than 3 times the age of Maggie. It means, Wendell’s age is (3x-3).

ATQ,

[tex]x+(3x-3)=33\\\\4x-3=33\\\\4x=36\\\\x=9[/tex]

The age of Maggie is x. So, Wendell's age is :

[tex]y=(3x-3)\\\\y=(3(9)-3)\\\\y=24[/tex]

So, Wendell age is 24 years.

Answer:

x = 51.1 degrees

Step-by-step explanation:

We notice that we can use the sine formula.

Why?

Well because Sin x =  (opposite side) /  hypotenuse

sin x = 7/9

x = arcsin 7/9 = 51.05755 degrees

rounded to the nearest tenth.

x = 51.1 degrees

Answer:(t-4)(4mn-1)

Step-by-step explanation:

Answer: The wheels turn about 3771 times in 5 miles.

Step-by-step explanation:

Given, Kelly rides on her bicycle such that the number of times wheels turn for every 140 feet = 20

Turns for every feet = [tex]\dfrac{20}{140}=\dfrac{1}{7}[/tex] ...(i)

To find : Number of times wheels turn in 5 miles.

Since , 1 mile = 5,280 feet

Then, 5 miles = 5 x (5,280 feet) = 26,400 feet

Now , Number of times the wheels turn in 26,400 feet = 26400 x (Turns for every feet)

[tex]26400\times\dfrac{1}{7}=3771.42857143\approx3771[/tex]   [From (i)

Hence, the wheels turn about 3771 times in 5 miles.

Answer:

105 sqrt(2) =x

Step-by-step explanation:

Since this is a right triangle we can use trig functions

so  sin theta = opposite side/hypotenuse

    sin 45 = x/210

Multiply each side by 210

210 sin 45 = x

We know sin 45 = sqrt(2)/2

210 * sqrt(2)/2 = x

105 sqrt(2) =x

Answer:

B

Step-by-step explanation:

Using trig ratios

sin(45) = opposite/hypotenuse

sin(45) = x/210

sqrt(2)/2 = x/210

x = 210sqrt(2)/2

x = 105sqrt(2)

Answer:

sin ( θ ) = 3√21 / 17

Step-by-step explanation:

Given:-

- The angle (θ) lies in the first quadrant. Where theta is defined as:

                               cos ( θ ) = 10 / 17

Find:-

- Find sin ( θ ) :

Solution:-

- We will draw a right angle triangle in the first quadrant. With base, B = 10 and hypotenuse H = 17. Since,

                               cos ( θ ) = B / H = 10 / 17

- Using pythagorean theorem determine the perpendicular side length:

                               H^2 - B^2 = P^2

                               17^2 - 10^2 = P^2

                               √189 = P

                              P = 3√21

- Now evaluate sin ( θ ):

                               sin ( θ ) = P / H

                               sin ( θ ) = 3√21 / 17

Answer:

√111 / 20

Step-by-step explanation:

The most vital factor for classifying two species into the same group is if they evolved from a shared ancestor, reflecting their place in the same clade and genetic similarities.

The most important factor for classifying two species into the same group is their evolutionary history, specifically whether they evolved from a shared ancestor. When scientists classify species, they adhere to the fundamental principle that all members of a group, or "clade," must have a recent common ancestor that is not shared with species from other groups. This is based on the idea that species within the same group will share more genetic similarities and phylogenetic traits than with those from different groups due to their more recent common ancestry.

Option A might seem plausible, as species in a group often share similar traits, but shared traits alone are not enough for classification without evolutionary context. Option C is incorrect because common names do not reflect scientific classification. Option D is also incorrect as geographic location is not a determinant for taxonomic classification. Thus, the correct answer to the original question is B, "The species have different common ancestors," as having a recent common ancestor is the most critical criterion for grouping species together.

Answer:

12y=$3

114 cans

Step-by-step explanation:

Let the cost of every can be represented by y. Therefore, for 12 cans, the cost will be the product of y cans and 12 hence cost is 12y

Since the cost incurred is $3 then we can represent these as

12y=$3

To solve for y, we divide both sides by 12 hence

Y=$3/12=$0.25

To find the number of cans that one will get with a buget of $28.5, we divide the budget by the cost of a can. This will be $28.5/$0.25=114 cans

Answer:

For the first cone: r = 7 cm, h = 21 cm

For the second cone: r = 8 cm, h = 24 cm

Step-by-step explanation:

The volume of the first cone is [tex]343\pi cm^3[/tex]

The volume of the second cone is [tex]512\pi cm^3[/tex]

We are told that the height of each cone is 3 times its radius, hence:

h = 3r

The volume of a cone is given as:

[tex]V = \frac{1}{3} \pi r^2h[/tex]

Substituting h = 3r:

[tex]V = \frac{1}{3} \pi r^2(3r)\\\\\\V = \frac{1}{3} \pi (3r^3)\\\\\\V = \pi r^3[/tex]

For the first cone, V = [tex]343\pi cm^3[/tex], radius, r, will be:

[tex]343\pi = \pi r^3\\\\\\=> r^3 = 343\\\\\\r = \sqrt[3]{343} \\\\\\r = 7 cm[/tex]

∴ Its height will be:

h = 3r = 3 * 7 = 21 cm

For the second cone, V = [tex]512\pi cm^3[/tex], radius, r, will be:

[tex]512\pi = \pi r^3\\\\\\=> r^3 = 512\\\\\\r = \sqrt[3]{512} \\\\\\r = 8 cm[/tex]

∴ Its height will be:

h = 3r = 3 * 8 = 24 cm

The radius and height of the first cone are 7 cm and 21 cm respectively while the radius and height of the second cone are 8 cm and 24 cm respectively.

Rectangle

Area = w × h

w = width

h = height

25ft × x=1125 ft²

=> x=1125 ft²/25 ft

x=45 ft

Answer:

x=1125÷25=45ft

Area=length × width therefore

length= area÷width

Answer:

Area of sector = 84.861

Step-by-step explanation:

Given

The radius of the circle = 9

central angle of sector = [tex]120^{o}[/tex]

value of pi π = 3.143

To find : the area of sector = ?

We know that the formula to calculate area of sector is given as:

area of sector = (π [tex]r^{2}[/tex]Θ)/ [tex]360^{o}[/tex]

where, r  is radius and Θ is the central angle of the sector

Substituting the known values in above formula, we get

area of sector = (3.143 x [tex]9^{2}[/tex] x [tex]120^{o}[/tex]) / [tex]360^{o}[/tex]

                        = 84.861

Hence area of sector is 84.861

Answer:

27 pi

Step-by-step explanation:

just did this one

The factored expression is 15(p - 2) . The discount per pair of shoe is $2

Using the expression given:

Factorize :

The greatest common factor of 15 and 30 is 15

Hence, the factored expression Using GCF is 15(p - 2)

b.)

The discount on the purchase is the constant value:

Number of shoes = 15

Discount per pair = Total discount/ Number of shoe pairs

Discount per pair of shoes = 30/15 = $2

Therefore, the discount on each pair of shoes is $2

Complete Question:

An online shoe store is having a sale. The original price of each pair of shoes is p dollars. The store sells 15 pairs of shoes and earns a total of (15p−30) dollars. a. Factor the expression using the GCF.

15p−30=

b. The discount per pair of shoes is $

Answer:

75

Step-by-step explanation:

9x5=45

15x5=75

Answer:

75

Step-by-step explanation:

9:15=45: _

very similar to cross multiplying

9/15  =  (45/ something)

something =  45 / (9/15)  =   45 * (15/9) = 5*15 = 75

Answer:

3

Step-by-step explanation:

to convert the centimeters to inches, divide 137. 16 by 2.54

you should get 54

then divide by 18

you get three

You can make 3 necklaces from 137.16 centimeters of silver chain, given that each necklace is 18 inches long. We first converted the necklace length to centimeters, and then divided the total length of silver chain by the length of each necklace.

To find out how many necklaces can be made from 137.16 centimeters of silver chain, we first need to convert the units because the length of the necklace chain is given in inches, while the total amount of silver chain is given in centimeters.

We know that 1 inch is equal to 2.54 centimeters. Therefore, if each necklace is 18 inches long, the length of each necklace in centimeters is 18 inches * 2.54 cm/inch = 45.72 cm.

Now, to find the number of necklaces that can be made, we divide the total length of silver chain by the length of each necklace. That is 137.16 cm / 45.72 cm/necklace = 3 necklaces (rounded down to the nearest whole necklace, because we cannot make a fraction of a necklace).

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Answer:

Step-by-step explanation:

If two quantities are inversely proportional, it means that an increase in the value of one variable would cause a corresponding decrease in the other variable and vice versa.

Given that M varies inversely as the square of P, if we introduce a constant of proportionality, k, the expression becomes

M = k/P²

If M = 9 when P = 2, then

9 = k/2² = k/4

k = 9 × 4 = 36

Therefore, the inverse variation equation is

M = 36/P²

When P = 3,

M = 36/3² = 36/9

M = 4

Jerry will spend $355.7988 on molding.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

we have,

Scale: 1 foot = 14 inches

As, the measurement of walls is 2372 inches.

The, using Scale the wall measured

= 2372/14

= 169.428 foot

Now, the molding costs $2.10 per foot then the cost of 169.428 foot is

= 169.428 x 2.10

= $355.7988

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Answer:

I would say c

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

10 times 4 equals 40

4 will be the value of n for the given expression.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, an expression 10n = 40

Simplifying the equation for n

=> 10n = 40

divide by 10 into both sides

=> 10n/10 = 40/10

=> n = 4

Therefore, the value of n for the given expression will be 4.

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Answer:

1438.52544

Step-by-step explanation:

Given:

Given that AGN is a triangle with circle inscribed in it.

The circle touch the triangle at the point R, T and E.

The length of AR is 35 units.

The length of RG is 21 units.

The length of NE is 19 units.

We need to determine the perimeter of the triangle AGN.

Length of GE:

Since, we know the property that, "if two segments from a exterior point are tangent to the circle, then they are congruent".

Since, RG and EG from an exterior point G are tangents to the circle, then RG and EG are congruent.

Thus, we have;

[tex]RG=EG[/tex]

 [tex]21=EG[/tex]

Thus, the length of GE is 21 units.

Length of TN:

Since, we know the property that, "if two segments from a exterior point are tangent to the circle, then they are congruent".

Since, TN and NE from an exterior point N are tangents to the circle, then TN and NE are congruent.

Thus, we have;

[tex]TN=NE[/tex]

[tex]TN=19[/tex]

Thus, the length of TN is 19 units.

Length of AT:

Since, we know the property that, "if two segments from a exterior point are tangent to the circle, then they are congruent".

Since, AT and AR from an exterior point A are tangents to the circle, then AT and AR are congruent.

Thus, we have;

[tex]AT=AR[/tex]

[tex]AT=35[/tex]

Thus, the length of AT is 35 units.

Perimeter of AGN:

The perimeter of AGN is given by

[tex]\triangle AGN=AR+RG+GE+EN+TN+AT[/tex]

Substituting the values, we get;

[tex]\triangle AGN=35+21+21+19+19+35[/tex]

[tex]\triangle AGN=150[/tex]

Thus, the perimeter of the triangle AGN is 150 units.

Answer:

150

Step-by-step explanation:

Segment AE divides the triangle into two congruent right angle triangles

AG = AN = 35 + 21 = 56

NG = 2(19) = 38

Perimeter = 56 + 56 + 38

150