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Answer: Peter had 48 quarters and 11 dimes.

Step-by-step explanation:

Let be "q" the number of quarters and "d" the number of dimes.

We know that $13.10 in cents is 1,310 cents. Then, we can set up the following system of equations:

[tex]\left \{ {{25q+10d=1,310} \atop {q=3d+15}} \right.[/tex]

Applying the Substitution method, we can substitute the second equation into the first one and solve for "d":

[tex]25(3d+15)+10d=1,310\\\\75d+375+10d=1,310\\\\85d=1,310-375\\\\d=\frac{935}{85}\\\\d=11[/tex]

Finally, we must substitute the value of "d" into the second equation to find the value of "q". Then:

[tex]q=3(11)+15\\\\q=33+15\\\\q=48[/tex]

Peter had 48 quarters and 11 dimes

Simultaneous Linear Equations could be solved by using several methods such as :

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

Let :

Number of quarters ( 25 cent coins ) = x

Number of dimes ( 10 cent coins ) = y

When he counted his quarters and dimes, he found they had a total value of $13.10.

The number of quarters was 15 more than 3 times the number of dimes.

If we would like to use the Substitution Method , then second equations above could be substituted into first equations.

0.25x + 0.10y = 13.10

0.25 (15 + 3y) + 0.10y = 13.10

3.75 + 0.75y + 0.10y = 13.10

0.85y = 13.10 - 3.75

0.85y = 9.35

y = 9.35 / 0.85

At last , we could find the value of x by substituting this y value into one of the two equations above :

x = 15 + 3y

x = 15 + 3(11)

x = 15 + 33

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations

For this case we must find the value of the variable "x" of the following equation:

[tex]5x (4-2) = 20[/tex]

We solve the operation within the parenthesis:

[tex]5x (2) = 20[/tex]

We multiply the left side:

[tex]10x = 20[/tex]

We divide both sides of the equation by 10:

[tex]x = \frac {20} {10}\\x = 2[/tex]

ANswer:

[tex]x = 2[/tex]

The solution of the expression given for x is 2.

Given is an expression 5x(4-2) = 20, we need to solve for x.

To solve the expression 5x(4-2) = 20 step by step, follow these steps:

Simplify the expression inside the parentheses:

5x(4 - 2) = 20

5x(2) = 20

Multiply 5x by 2:

10x = 20

Divide both sides of the equation by 10 to isolate x:

(10x)/10 = 20/10

x = 2

Therefore, the solution for x is 2.

Learn more about expression click;

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Answer:

[tex]10^{-6}=7[/tex]

Step-by-step explanation:

Remember that according to the laws of logarithms if [tex]log_ay=x[/tex], then [tex]a^x=y[/tex],

In other words to convert a logarithm to an exponential equation we just need to raise the base of the logarithm to the result and equate that to the argument of the logarithm.

Since our logarithm does not have a base, its base is 10; therefore [tex]a=10[/tex]. The argument of our logarithm is 7, so [tex]y=7[/tex]. The result of our logarithm is -6, so [tex]x=-6[/tex].

Replacing values

[tex]log_ay=x[/tex] ⇔ [tex]a^x=y[/tex]

[tex]log_{10}7=-6[/tex] ⇔ [tex]10^{-6}=7[/tex]

By the way [tex]log_{10}7=-6[/tex] is not a true equation since [tex]10^{-6}\neq 7[/tex].

An entrepreneur is a someone who organizes and conducts a business, and taking great financial risks.

Answer:

The correct answer would be option C, A person who takes a risk to create a new product or develop a better way to operate a business.

Step-by-step explanation:

An entrepreneur is a person who starts a new business alone. An Entrepreneur is responsible for all the profits and losses of the business. He takes risks in the hope of earning profits. He introduces new products in the market and develops better ways to operate a business. He is solely liable for all his decisions and the resulting profit or losses. Entrepreneurs are usually hard working, strong decision makers, risk takers, and highly innovative people.

To find the distance of objects sighted at angles of 29 degrees and 59 degrees, use the function d = 93 sec(theta). Substituting theta values, the distances are 106.87 feet and 166.39 feet, respectively.

To find the distance of an object sighted at angles of 29 degrees and 59 degrees, we can use the function given, d = 93 sec(theta). Substituting theta = 29 degrees, we get d = 93 sec(29) = 93*(1/cos(29)) = 93/0.8714 = 106.87 feet. Similarly, substituting theta = 59 degrees, we get d = 93 sec(59) = 93*(1/cos(59)) = 93/0.5588 = 166.39 feet.

Answer:

Last option: 4

Step-by-step explanation:

The quadratic equation simplified: [tex]x^2-4x=-\frac{7}{2}[/tex] has the form:

[tex]ax^2+bx=c[/tex]

In this case, you can identify that "a", "b" and "c" are:

[tex]a=1\\b=-4\\c=-\frac{7}{2}[/tex]

To solve this quadratic equation  by completing the square, Carlos should add [tex](\frac{b}{2})^2[/tex] to both sides of the equation. This is:

[tex](\frac{-4}{2})^2=(-2)^2=4[/tex]

Then:

[tex]x^2-4x+4=-\frac{7}{2}+4[/tex]

Therefore you can observe that the number he should add to both sides of the equation is: 4

2 as what he said above

Check the picture below.

so then, let's use the pythagorean theorem to find "x" and "y", and the distance is just x+y.

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{9}\\ b=\stackrel{opposite}{5}\\ \end{cases} \\\\\\ x=\sqrt{9^2+5^2}\implies x=\sqrt{81+25}\implies x=\sqrt{106} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{y}\\ a=\stackrel{adjacent}{17}\\ b=\stackrel{opposite}{5}\\ \end{cases} \\\\\\ y=\sqrt{17^2+5^2}\implies y=\sqrt{289+25}\implies y=\sqrt{314} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{total distance}}{x+y}\implies \sqrt{106}+\sqrt{314}\qquad \approx 10.296+17.72\qquad \approx 28.016[/tex]

Final answer:

To find the distance from Carson's house to Salemburg through Pueblo 'as the crow flies', we use the Pythagorean theorem. Adding together the two legs of a right triangle formed by the given distances and solving for the hypotenuse, we find it is approximately 26.48 miles.

Explanation:

To determine the distance from Carson's house to Salemburg through Pueblo 'as the crow flies', we need to create a diagram and use the Pythagorean theorem. First, we know that Salemburg is 17 miles south of Linbrooke, Linbrooke is 5 miles west of Pueblo, and Carson lives 9 miles north of Linbrooke. Therefore, the distance directly north from Carson's to Pueblo is 9 miles (since he is directly north of Linbrooke), and from Pueblo to Salemburg the direct line would consist of 5 miles west and 17 miles south, which forms a right triangle.

Using the Pythagorean theorem to find the length of the hypotenuse (direct line from Carson's past Pueblo to Salemburg), we have:

Calculate the total distance north-south by adding Carson's 9 miles north to Salemburg's 17 miles south, which gives us 26 miles.

Since we already have the west-east distance as 5 miles, we can set up the equation a^2 + b^2 = c^2, where 'a' is 5 miles, 'b' is 26 miles, and 'c' is the hypotenuse we are looking for.

Plugging in the values gives: 5^2 + 26^2 = c^2, or 25 + 676 = c^2, resulting in c^2 = 701.

Take the square root to find 'c': c ≈ 26.48 miles.

Therefore, the distance from Carson's house to Salemburg 'as the crow flies' passing through Pueblo is approximately 26.48 miles.

Answer:

Step-by-step explanation:

y2-y1/x2-x1= -3-(-3)/6-2= 0/4

Answer: The answer to your question is 4 ft

Step-by-step explanation: we know that the formula to find the area of a rectangle is

A=LW

In this problem, we have:

[tex]A= 30 ft^{2}[/tex]

[tex]L= 7.5ft[/tex]

Substitute the values and solve for W

30=7.5W

Divide by 7.5 on both sides

W= 30/ 7.5= 4ft

Answer:

The width of the tablecloth is 4 ft

Answer:I know that more than half of the students did not score more than 75 because the median (the middle number) is 68.

Step-by-step explanation:

Answer:

a)

The probability that an individual distance is greater than  210.00 cm is 0.1056

b)

The probability that the mean for  25  randomly selected distances is greater than  198.70 cm is 0.7917

c)

The normal distribution be used in part​ (b), even though the sample size does not exceed​ 30 since the parent population from which the sample has be obtained is Normal.

Step-by-step explanation:

a)

We let the random variable X denote the overhead reach distances of individual adult females. This implies that X is normally distributed with a mean of 200 cm and a standard deviation of 8 cm.

The probability that an individual distance is greater than 210 can be written as;

Pr(X>210)

We standardize the value to obtain the associated z-score;

[tex]P(X>210)=P(Z>\frac{210-200}{8})=P(Z>1.25)[/tex]

Using the standard normal tables, the area to the right of 1.25 is 0.1056. Therefore, the probability that an individual distance is greater than  

210.00 cm is 0.1056.

b)

The first step will be to determine the sampling distribution of the sample mean given that the variable overhead reach distance is normally distributed with a mean of  200 cm and a standard deviation of  8 cm.

In this case, the sample mean will also be normally distributed with a mean of 200 cm and a standard deviation of;

[tex]\frac{sigma}{\sqrt{n} }=\frac{8}{\sqrt{25} }=1.6[/tex]

The probability that the mean for  25  randomly selected distances is greater than  198.70 cm;

Pr(sample mean >198.70)

We standardize the value to obtain the associated z-score;

[tex]=P(Z>\frac{198.70-200}{1.6})=P(Z>-0.8125)[/tex]

Using the standard normal tables, the area to the right of -0.8125 is 0.7917. Therefore, the probability that the mean for  25  randomly selected distances is greater than  198.70 cm is 0.7917.

c)

The normal distribution be used in part​ (b), even though the sample size does not exceed​ 30 since the parent population from which the sample has be obtained is Normal.

Answer:

(1.5, 2.5) is the best approximate solution.

Step-by-step explanation:

According to the graph, at the point of intersection of these two lines, x is closest to 1.5 and y is simultaneously closest to 2.5.

(1.5, 2.5) is the best approximate solution.

Answer:

Step-by-step explanation:

1.5 AND 2.5

Answer:

(15 km/2 days)(5 days) = 37.5 km/week

(37.5 km/week)(4 weeks) = 150 km

The correct answer is A.

Answer: hey! sorry if very late :(

it's A).

Step-by-step explanation:

d

Answer:

Step-by-step explanation:

7. False.  Opposite angles of a rhombus are congruent, not necessarily supplementary unless it's a square.

8. False.  Parallelograms' consecutive angles must be supplementary.  168 and 22 do not add up to 180.

9. False.  Rhombuses are not the only quadrilateral with perpendicular diagonals.  Kites also have perpendicular diagonals.

10. Area of a regular polygon is:

A = 1/2 aP

where a is the apothem and P is the perimeter.

We're given a = 24.78, but we need to find the side length.

The interior angle of a regular polygon is:

θ = (n - 2) × 180° / n

So a hexagon with 6 sides has an interior angle of:

θ = (6 - 2) × 180° / 6

θ = 120°

If we draw lines from the bottom corner to the center, we get a 30-60-90 triangle.  Therefore:

(s/2) × √3 = 24.78

s/2 = 14.307

s = 28.61

So the perimeter is:

P = 6s

P = 171.68

And the area is:

A = 1/2 aP

A = 1/2 (24.78) (171.68)

A = 2127.13 cm²

11. Area of a regular polygon is:

A = 1/2 aP

where a is the apothem and P is the perimeter.

We're given s = 11, but we need to find the apothem.

The interior angle of a regular polygon is:

θ = (n - 2) × 180° / n

So a polygon with 11 sides has an interior angle of:

θ = (11 - 2) × 180° / 11

θ = 1620/11 °

If we draw lines from the bottom corner to the center, we get a right triangle with a base angle of θ/2.  Therefore:

tan (θ/2) = a / (s/2)

a = s/2 tan(θ/2)

a = 11/2 tan(810/11 °)

a = 18.73

The perimeter is:

P = 11s

P = 121

And the area is:

A = 1/2 aP

A = 1/2 (18.73) (121)

A = 1133.24 in²

Answer:

the answer would be 90

Step-by-step explanation:

100 giants fills 5/8 (100/160) of the theater leaving 3/8 of the theater for the elves.

3/8 times 240 elves is 90 elves.

If there were 150 elves that would also be 5/8 filled plus the original 5/8 filled with 100 giants! Some elves might suffer!!!

Answer: x=62

Step-by-step explanation:

A triangle is 180 degrees. When you add 71 and 47, it equals 118. Then subtract 118 from 180 and you are left with 62 degrees.

Hope this helps!

Answer: x = 62°

Remember: the interior angles of a triangle add up to 180°.

47 + 71 = 118

180 - 118 = 62

Answer:

[tex]\frac{dy}{dx} = \frac{cos(x+y)}{1-cos(x+y)}[/tex]

Step-by-step explanation:

We have the function [tex]y=sin(x+y)[/tex]

We need find the derivative of y with respect to x

Note that the function [tex]y = sin (x + y)[/tex] depends on the variable x and the variable y. Therefore the derivative of y with respect to x will be equal to the derivative of [tex]sin (x + y)[/tex] by the internal derivative of  [tex]sin (x + y)[/tex]

[tex]\frac{dy}{dx}= cos(x+y)*\frac{d}{dx}(x+y)[/tex]

[tex]\frac{dy}{dx}= cos(x+y)*(1+\frac{dy}{dx})\\\\\frac{dy}{dx}= cos(x+y)+\frac{dy}{dx}cos(x+y)\\\\\frac{dy}{dx} -\frac{dy}{dx}cos(x+y)=cos(x+y)\\\\\frac{dy}{dx}(1-cos(x+y))=cos(x+y)\\\\\frac{dy}{dx} = \frac{cos(x+y)}{1-cos(x+y)}[/tex]

Answer:

Step-by-step explanation:

Note that y=sin(x+y) is an implicit function; y appears on both sides of the equation, which makes it difficult or impossible to solve for y.

However, our job here is to find the derivative dy/dx.

We apply the derivative operator d/dx to both sides.  Here are the results:

dy

---- = cos(x + y)(dx/dx + dy/dx), or

dx                                                         Note:  dx/dx = 1

dy

---- = cos(x + y)(1 + dy/dx), or  = cos(x + y) + cos(x + y)(dy/dx)

dx

We move that cos(x + y)(dy/dx) term to the left side to consolidate dy/dx terms:

dy

----  -  cos(x + y)(dy/dx) = cos(x + y)

dx

or:

 dy

[ ---- ] [ 1 -  cos(x + y) ] = cos(x + y)

  dx

Finally, we divide both sides by [ 1 -  cos(x + y) ], obtaining the derivative:

 dy            cos(x + y)

[ ---- ]  -------------------------

  dx         1 -  cos(x + y)

Answer:

A. 1.2 yd

Step-by-step explanation:

We are informed that Mr.Reddrick has a 74 total yards of red and blue felt to distribute to students in his art class. Moreover, we also have the information that each of his 20 students gets 2.5 yards of blue felt for the project. This implies that the total blue felt distributed is;

20*2.5 = 50 yards

The remainder is the total red felt left for distribution;

74 - 50 = 24 yards

Since we have 20 students, each one of them receives;

24/20 = 1.2 yd

Answer:

A 1.2

Step-by-step explanation:

Answer:

Step-by-step explanation:

b) 1- scale factor from the first map to the second map:

[tex]\frac{8}{6}[/tex]  = 1.33

   2- landmark on the first map is a triangle with side lengths of 3 mm, 4 mm, and 5 mm.

Side lengths of the landmark on the second map

Divide the length by scale factor:

side lengths of 3 mm:  [tex]\frac{3}{1.33}[/tex] = 2.25 mm

side lengths of 4 mm:  [tex]\frac{4}{1.33}[/tex] = 3.007 mm

side lengths of 5 mm:  [tex]\frac{5}{1.33}[/tex] = 3.75 mm

Answer:

32 unit³

Step-by-step explanation:

Length of the crate has been given as 4 units

width of the crate = 2 units

Height of the crate = 4 units

Since the crate has been packed packed with the unit cubes.

Therefore, shape of the crate will be in the form of a rectangular prism.

Volume of the prism = Length × width × height

                     crate     = 4 × 2 × 4

                                   = 32 unit³

Volume of the shipping crate is 32 unit³.

Answer:

32 Units

Step-by-step explanation:

If u do 4x2x4=32 that is your answer all you got to do is x Lxwxh and U will find the volume

To solve the system of equations x − y = 5 and 2x − 3y = 4, we can use the method of substitution or elimination. By substituting the value of x from the first equation into the second equation, we can find the value of y. Then, substitute the value of y back into the first equation to find the value of x. The solution to the system of equations is (11, 6).

To solve the system of equations x − y = 5 and 2x − 3y = 4, we can use the method of substitution or elimination. Let's use the method of substitution:

From the first equation, we can rearrange it to x = y + 5. Now substitute this value of x into the second equation:

2(y + 5) − 3y = 4

Simplify and solve for y:

2y + 10 - 3y = 4

-y + 10 = 4

-y = -6

y = 6

Now substitute this value of y back into the first equation to find x:

x − 6 = 5

x = 11

Therefore, the solution to the system of equations is (11, 6). So, the correct answer is option D.

Answer:

Area of a pyramid = (1/3) x (base area) x (height)

Answer:

the building strong enough to withstand the denali quake

Step-by-step explanation:

denali quake 6.7  x 70 = 469

the building in denali should be strong enough to withstand an earthquake of that magnitude  

rat island quake 7.8 x 30 = 234

the building in the rat islands  should be strong enough to withstand an earthquake of that magnitude  

Answer:

1249.37

Step-by-step explanation:

7850 = 2 pi r

r = 7850/(2pi) = 1249.37

ANSWER

The radius is approximately 1249 units.

EXPLANATION

The relation between the radius of a circle and its circumference is expressed in the formula:

[tex]C = 2\pi \: r[/tex]

The circumference is given as 7,850 .

This implies that

[tex]7850 = 2\pi \: r[/tex]

[tex]r = \frac{7850}{2 \: \pi} [/tex]

[tex]r = 1249.4[/tex]

to the nearest tenth.

Answer:

Step-by-step explanation:

We have three pairs of rectangles:

4cm × 5cm

4cm × 7cm

5cm × 7cm

The formula of an area of a rectangle l × w:

A = l × w

l - length

w - width

Substitute:

A₁ = (4)(5) = 20 cm²

A₂ = (4)(7) = 28 cm²

A₃ = (5)(7) = 35 cm²

The Surface Area:

SA = 2A₁ + 2A₂ + 2A₃

Substitute:

SA = 2(20) + 2(28) + 2(35) = 40 + 56 + 70 = 166 cm²

Answer:

Option C. [tex]42\ yd^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the triangular prism is equal to

[tex]V=BH[/tex]

where

B is the area of the triangular base

H is the height of the prism

Convert 9 ft to yd

Remember that

1 ft=1/3 yd

9 ft=9*(1/3)=3 yd

Find the area of the base B

[tex]B=\frac{1}{2}(3)(4)=6\ yd^{2}[/tex]

we have

[tex]H=7\ yd[/tex]

substitute the values in the formula

[tex]V=BH[/tex]

[tex]V=(6)(7)=42\ yd^{3}[/tex]

Answer:

The answer is 42 yards! Sry im late. :(

This is the area of a triangle

Answer:

Use the formula Area=1/2bh

Step-by-step explanation:

Answer:

87380

Step-by-step explanation:

The sum to n terms of a geometric sequence is

[tex]S_{n}[/tex] = [tex]\frac{a(r^n-1)}{r-1}[/tex]

where a is the first term and r the common ratio

r = [tex]\frac{16}{4}[/tex] = 4 and a = 4, hence

[tex]S_{8}[/tex] = [tex]\frac{4(4^8-1)}{4-1}[/tex] = [tex]\frac{4(65535)}{4}[/tex] = 87380

Answer:

The height of the triangular pyramid is [tex]27\ cm[/tex]

Step-by-step explanation:

we know that

The volume of a triangular pyramid is equal to

[tex]V=\frac{1}{3}BH[/tex]

where

B is the area of the triangular base

H is the height of the pyramid

Find the area of the base B

[tex]B=\frac{1}{2}(15)(4)=30\ cm^{2}[/tex]

we have

[tex]V=270\ cm^{3}[/tex]

substitute and solve for H

[tex]270=\frac{1}{3}(30)H[/tex]

[tex]270=10H[/tex]

[tex]H=270/10=27\ cm[/tex]