Each member of the school chess team receives a chess set and clock. The total cost of these items for 5 members is $125. Jenna knows that a chess set costs $10, but she does not know how much a clock costs. She sets up the equation below to solve for the cost of a clock, represented in her equation by x.

Answer: 108

Step-by-step explanation:

Answer with Step-by-step explanation:

We are given  that

COAL is a rhombus .

CA and LO are the diagonals of rhombus COAL.

CA=27 m

OL=19 m

We know that

Diagonals of rhombus are bisect to each other.

Let P(0,0) be the intersecting point of diagonals

Therefore, CP=PA

LP=PO

Length PO=[tex]\frac{1}{2}LO=\frac{19}{2}=9.5 m[/tex]

Length of CP=[tex]\frac{1}{2}PA=\farc{1}{2}(27)=13.5 m[/tex]

Let C([tex]0,y_2),O(x_1,0),A(0,y_1) \;and\;L(x_2,0)[/tex].

Distance formula:[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using the formula

[tex]CP=\sqrt{(0-0)^2+(0-y_2)^2}=13.5[/tex]

[tex]\sqrt{y^2_2}=13.5[/tex]

[tex]y_2=\pm 13.5[/tex]

C(0,13.5) or (0,-13.5)

[tex]\sqrt{(y_2-y_1)^2}=27[/tex]

Substitute the value [tex]y_2=13.5[/tex]

[tex]\sqrt{13.5-y_1}=27[/tex]

[tex]13.5-y_1=\pm 27[/tex]

[tex]y_1=13.5-27=-13.5[/tex]

A(0,-13.5)

[tex]13.5-y_1=-27[/tex]

[tex]y_1=13.5+27=40.5[/tex]

A(0,40.5)

Substitute [tex]y_2=-13.5[/tex]

[tex]\sqrt{(-13.5-y_1)^2}=27[/tex]

[tex]-13.5-y_1=\pm 27[/tex]

[tex]-13.5-y_1=27[/tex]

[tex]y_1=-13.5-27=-40.5[/tex]

A(0,-40.5)

[tex]-13.5-y_1=-27[/tex]

[tex]y_1=-13.5+27=13.5[/tex]

A(0,13.5)

[tex]LP=\sqrt{(x_2-0)^2}=9.5[/tex]

[tex]\sqrt{x^2_2}=9.5[/tex]

[tex]x_2=\pm 9.5[/tex]

L(9.5,0) or L(-9.5,0)

[tex]\sqrt{x_2-x_1)^2}=19[/tex]

[tex](9.5-x_1)^2}=19[/tex]

[tex]9.5-x_1=\pm 19[/tex]

[tex]9.5-x_1=19[/tex]

[tex]x_1=9.5-19=-9.5[/tex]

[tex]9.5-x_1=-19[/tex]

[tex]x_1=9.5+19=28.5[/tex]

[tex](-9.5-x_1)=19[/tex]

[tex]-9.5-x_1=\pm 19[/tex]

[tex]-9.5-x_1=19[/tex]

[tex]x_1=-9.5-19=-28.5[/tex]

[tex]-9.5-x_1=-19[/tex]

[tex]-9.5+19=x_1[/tex]

[tex]x_1=9.5[/tex]

O(-9.5,0) or O(28.5,0) or (-28.5,0) or (9.5,0)

1. Let us first find the missing interior angle.

m<C+53+61=180

m<C=66 degrees

law of sines: [tex]\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}[/tex]

a,b, and c represents the lengths of the triangles and A,B, and C represents the measures of the interior angles opposite to the sides.

For the purposes of this problem let us use a shorthand version for the law of sines.

[tex]\frac{sin(B)}{b} =\frac{sin(C)}{c}\\\frac{sin(61degrees)}{b} =\frac{sin(66degrees)}{142}\\b=142sin(61degrees)/sin(66degrees)\\[/tex]

b=134.95 meters approx.

AC is equal to length b in this case so AC=134.95 meters approx.

2. law of cosines: a²=b²+c²-2bccos(A)

Let us rearrange this formula so that we can solve for cos(C) in terms of a, b, and c (the sides lengths of the triangle).

a²=b²+c²-2bccos(A)

a²-b²-c²=-2bccos(A)

[tex]\frac{a^{2}-b^{2}-c^{2}}{-2bc}[/tex]=cos(A)

cos(A)=[tex]\frac{a^{2}-b^{2}-c^{2}}{-2bc}[/tex]

Now, because we want to find measure of angle A...

cos(A)=[tex]\frac{13.7^{2}-12.2^{2}-22.1^{2}}{-2(12.2)(22.1)}[/tex]

cos(A)=0.83 approx.

A=33.52 degrees approx.

3. Solving with law of cosines.

law of cosines: a²=b²+c²-2bccos(A)

a²=16²+18²-2(16)(18)cos(52 degrees)

a²=256+324-576cos(52 degrees)

a²=580-576cos(52 degrees)

a²=225.38 approx.

a=15.01 units approx.

Solving with law of sines.

law of sines: [tex]\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}[/tex]

For the purposes of this problem let us use a shorthand version for the law of sines.

[tex]\frac{sin(71 degrees)}{18} =\frac{sin(52 degrees)}{x}\\xsin(71 degrees)=18sin(52degrees)\\x=\frac{18sin(52degrees)}{sin(71 degrees)} \\[/tex]

x=15.00 un approx.

Answer:

3 8/35 is the answer your welcome

Answer:

[tex]\displaystyle x = 8[/tex]

Step-by-step explanation:

Anything set to equal x is considered an undefined rate of change [slope], which is a vertical line. This is not a function, since it flunks the vertical line test.

I am joyous to assist you anytime.

Answer:

True

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

20 squared+21 sqaured= 29 squared

This seems confusing, like part of the question was cut off, but I'll try my best!

Answer: (For Part A)

I'm gonna assume that the $25.30 is the sum of all food and beverages.

So, if that's the case, the bill should be $27.32

Step-by-step explanation:

The meals tax is 8%, so all you have to do is multiply 25.30 (or 25.3) with 0.08 (8%) to get 2.024. Then you add 2.024 to the original number;

25.30 + 2.024 = 27.324

Finally you round to the nearest cent. So you get $27.32

However this might be incorrect because it looks like a  part of the question is missing.

Step-by-step explanation:

If you're asking for an equation, the equation would be: [tex]y=-4x-3[/tex]

(probably what you're looking for) if you're looking for what y equals, the answer is: 9

for equation:

1. write an equation with the information you have

[tex]y=-4x+b[/tex]

2. Plug in the values for x and y

[tex]-7=-4(1)+b[/tex] where b equals -3

so your equation would be [tex]y=-4x-3[/tex]

for what y equals:

1. since you've figured out the equation, plug in the value for x and solve for y

[tex]y=-4(-3)-3[/tex] which then gives you [tex]y=9[/tex]

Answer:

Amy spent $11 for lunch.

Step-by-step explanation:

x+y=25

x+(x+3)=25

2x+3=25

2x=25-3

2x=22

x=22/2

x=11

Answer:amy spent 11 dollars.

Step-by-step explanation:I did math

Answer:

(2.5, 2 )

Step-by-step explanation:

Given the 2 equations

2x + 2y = 9 → (1)

2x - y = 3 → (2)

Rearrange (2) expressing y in terms of x

y = 2x - 3 → (3)

Substitute y = 2x - 3 into (1)

2x + 2(2x - 3) = 9 ← distribute left side and simplify

2x + 4x - 6 = 9

6x - 6 = 9 ( add 6 to both sides )

6x = 15 ( divide both sides by 6 )

x = 2.5

Substitute x = 2.5 into (3) for corresponding value of y

y = 2(2.5) - 3 = 5 - 3 = 2

Solution is (2.5, 2 )

Solve this using the elimination process.

They're already lined up so just solve!

2x + 2x = 4x

2y+ (-y) = 3y

9 + 3 = 12

4x + (-1y) = 12

Now solve.

4x + -1 x y = 12

4x - y = 12

4x = 12 + y

x = 12 + y / 4

First, when a problem is lined up with the same vales/terms, you can use the elimination process while doing math.

Then, make your equation by adding and subtracting the same terms.

Therefore, you finally get your answer.

Keep in mind not all answers will be a full number.

Answer:

Step-by-step explanation:

16) 4 * y/5

The value of y should be greater than 5

For example if y = 6, then 4* 6/5 = 24/5 = 4.8

If y= 10, then 4* 10/5 = 4 * 2 = 8

y > 5

17) 1 pound = 16 ounce

3020 pounds =3020 * 16 = 48320 ounces

Answer:

3 pounds and 3/4th of a pound

Step-by-step explanation:

2000 x 3 is 6000 and you have 1500 left

you can divide 2000 equally by 4 and get 500.

Multiply 500x3 and get 1500

(the 3 and the 4 is how i got the fraction)

6000+1500 = 7500

boom big brain answer good luck

In this question, we know that 1 ton = 2000

We're trying to find how many tons is 7500 tons.

In order to find your answer, you would divide 7500 by 2000 in order to know how many tons there are.

Divide:

7500 ÷ 2000 = 3.75

This means that there are 3.75 tons in 7500 pounds

Answer:

3.75 tons

Answer:

There is 1.587 ounces of sodium chloride that he will need.

Since we have given that

Quantity of sodium chloride in grams = 45 grams

We need to find the number of ounces of sodium chloride.

As we know that

1 ounce = 28.35 gram

So, 1 gram =

So, 45 grams =

Hence, there is 1.587 ounces of sodium chloride that he will need.

Step-by-step explanation: Since we have given that

Quantity of sodium chloride in grams = 45 grams

We need to find the number of ounces of sodium chloride.

As we know that

1 ounce = 28.35 gram

So, 1 gram =

So, 45 grams =

Hence, there is 1.587 ounces of sodium chloride that he will need.

We have 1 square with side length 8 inches, and 4 triangles with a base length of 8 inches and a height of 15.

Surface area = (8 × 8) + 4(0.5 × 8 × 15)

The first part of this equation is the area of the square

The second part is the area of a triangle, multiplied by 4 (because there are 4 triangles)

= 64 + 4(60)

= 64 + 240

= 304 in²

The total surface area is 304 square inches.

Let me know if you need any clarifications, thanks!

Good evening ,

Answer:

domain: ]−∞,+∞[

range: ]−∞,4]

Step-by-step explanation:

Look at the photo below for more info.

:)

The domain of the function f(x) = -3(x-5)² +4 is all real numbers, written as (-∞, ∞). The range, or possible values of f(x), is (-∞, 4] since the parabola opens downwards and the maximum value is 4.

The function f(x) = -3(x-5)² +4 is a parabola that opens downwards. The domain of a function is the set of all values that x can take. For any parabolic function, the domain is always all real numbers, which we could write as (-∞, ∞).

The range of a function refers to the possible values of f(x). In this case, since the parabola opens downwards, the maximum value of f(x) is at the vertex of the function. This parabola's vertex is at (5,4), so its maximum, and thus the upper boundary of the range, is 4. The parabola continues downwards to negative infinity, so the range is (-∞, 4].

Therefore, the domain is (-∞, ∞), and the range is (-∞, 4].

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Answer:

C. [tex]x=20^{\circ}[/tex]

Step-by-step explanation:

Angle 6 and angle with measure 45° are vertical angles (opposite angles whan two lines intersect). By Vertical Angles Theorem, vertical angles are congruent, so

[tex]m\angle 6=45^{\circ}[/tex]

Angle 6 and angle with measure [tex]5x+35^{\circ}[/tex] are the same side interior angles when two parallel lines are cut by transversal. The same side interior angles add up to 180°, then

[tex]m\angle 6+5x+35^{\circ}=180^{\circ}\\ \\45^{\circ}+5x+35^{\circ}=180^{\circ}\\ \\5x=180^{\circ}-45^{\circ}-35^{\circ}\\ \\5x=100^{\circ}\\ \\x=20^{\circ}[/tex]  

Trevon have 692 paper clips after buying 500 more clips.

Step-by-step explanation:

Let,

Paper clips Caroline have = x

Paper clips Trevon have = y

According to given statement;

x = 5y   Eqn 1

After Trevon buys another 500 paper clips, he has 268 paper clips fewer than Caroline.

y + 500 = x - 268

y + 500 +268 = x

y + 768 = x     Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex]y+768 = 5y\\768=5y-y\\768 = 4y\\4y=768[/tex]

Dividing both sides by 4

[tex]\frac{4y}{4}=\frac{768}{4}\\y=192[/tex]

Number of paper clips Trevon has now = y+500 = 192+500 = 692

Trevon have 692 paper clips after buying 500 more clips.

Keywords: linear equation, substitution method

Learn more about substitution method at:

#LearnwithBrainly

To find out how many paper clips Trevon has now, we set up an algebraic equation and solve it to determine that Trevon originally had 192 paper clips. After buying an additional 500, he now has a total of 692 paper clips.

The student's question involves solving a basic algebra word problem where Caroline has 5 times as many paper clips as Trevon. When Trevon buys another 500 paper clips, he has 268 paper clips fewer than Caroline. To solve this, we can set up the equation to find the original number of paper clips Trevon had:

So, Trevon originally had 192 paper clips. After buying another 500, Trevon now has 192 + 500 = 692 paper clips.

The equation for the height, h, in terms of the base, b, and area, A is [tex]h = \frac{2A}{b}[/tex]

Solution:

Given that area of a triangle is given by the formula:

[tex]A = \frac{1}{2}bh[/tex]

Where,

A is the area of triangle

b is the base of triangle

h is the height of triangle

We have to find the equation for height in terms of base and area

So we have to arrange the equation in such a way that height can be found by using area and base

Given formula is:

[tex]A = \frac{1}{2}bh[/tex]

Keep "h" alone in L.H.S and move the other terms to other side of formula

[tex]A = \frac{bh}{2}\\\\2A = bh\\\\h = \frac{2A}{b}[/tex]

Thus height is expressed in terms of base and area

Answer:

The Probability of Alicia picking a red shirt is [tex]\frac{2}{9}[/tex].

Step-by-step explanation:

Given,

Number of White shirts = 4

Number of Red shirts = 2

Number of Blue shirts = 3

Solution,

Total number of shirts = Number of White shirts + Number of Red shirts + Number of Blue shirts = [tex]4+2+3=9[/tex]

[tex]P(E)=\frac{Total\ number\ of\ possible\ outcomes}{Total\ number\ of\ outcomes}[/tex]

Therefore,

[tex]P(of\ red\ shirts)=\frac{2}{9}[/tex]

Hence The Probability of Alicia picking a red shirt is [tex]\frac{2}{9}[/tex].

Answer:

[insert name here] drove his scooter around. When he started, his speed increased constantly to 10 mph (O-A). He cruised at 10mph for a few seconds. (A-B) Then he slowed down (B-C) and stopped for a few seconds (C-D). He then started speeding up (D-E) and cruised for a few more seconds. (E-F)

Step-by-step explanation:

Picture############

Answer:

weight * (4 / 5) = 30

weight * .8 = 30

weight = 30 / .8

weight = 37.5 pounds

Step-by-step explanation:

Answer:

Step-by-step explanation:

Is called a letter that stands for the number

Answer:

Step-by-step explanation:

√10x - 1 = 7

Square both sides,

10x - 1 = 7²

10x - 1 =  49

10x = 49 + 1

10x = 50

x = 50/10

x=5

Answer:

Approx. 2

Step-by-step explanation:

round 3.8 to the nearest whole number, which is 4.

Divide 4 by 2.

3.8/2 is approx. 2.

(the exact answer would be 1.9)

To estimate the result of 3.8 divided by 2, you can round 3.8 to 4 which, when divided by 2, gives an estimate of 2. This method provides a result that is close to the actual answer of 1.9.

The question '3.8 divided by 2 estimated' is asking for an approximate result of dividing 3.8 by 2. To estimate this, you can round 3.8 to 4 because it is close to this even number which makes mental math easier. Now, divide 4 by 2 to get 2. Although this is an estimate, the actual calculation of 3.8 / 2 yields 1.9. So, our estimated answer is close to the actual result.

When performing division, estimation can be a useful tool, especially when dealing with decimals. Estimating can also help in checking the reasonableness of answers obtained via calculators, which can sometimes provide more precision than necessary. For example, when using significant figures in calculations, a calculator does not limit the precision of the result, but estimating can help a user decide how many decimal places to report.

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Answer:

k=2

Step-by-step explanation:

We are given that two function f(x) and g(x)

[tex]g(x)=f(kx)[/tex]

From given graph

[tex]g(-2)=0[/tex]

[tex]f(-4)=0[/tex]

[tex]g(-2)=f(-4)[/tex]

By comparing we get

x=-2 and

[tex]kx=-4[/tex]

[tex]k(-2)=-4[/tex]

[tex]k=\frac{-4}{-2}=2[/tex]

Hence, the value of k=2

Based on information provided, the value of k is 2.

Here's why:

1. Understanding the problem: We are given two functions, f(x) and g(x), where g(x) is defined as f(k * x). The graph shows both functions, and we are asked to find the value of k.

2. Analyzing the graph: The graph shows two lines:

  - The red line represents f(x).

  - The blue line represents g(x).

3. Key observation: We are given that g(-2) = 0. This means the blue line intersects the x-axis at x = -2.

4. Relating g(x) to f(x): Since g(x) = f(k * x), we know that the blue line is obtained by horizontally stretching or compressing the red line by a factor of k.

5. Finding k: To make the blue line intersect the x-axis at x = -2, we need to stretch the red line to the left by a factor of 2. This means k = 2.

Therefore, based on the given information and the analysis of the graph, the value of k is 2.

Answer:

18 feet

Step-by-step explanation:

1 inch = 6 feet

3 * 6 = 18

Answer: Lucy sews [tex]\frac{16}{21}[/tex] of a dress in one hour.

Step-by-step explanation:

The complete question is:

"Lucy is a dress maker. She sew [tex]\frac{4}{7}[/tex] of a dress in [tex]\frac{3}{4}[/tex] hour. At this rate, how many dresses does Lucy sew in one hour?"

Let "x" represents the number of dresses that Lucy sews in one hour.

You need to analize the information given in the exercise.

According to the exercise, you know that, in [tex]\frac{3}{4}[/tex] hour, Lucy sews [tex]\frac{4}{7}[/tex] of a dress.

Then, knowing this data, you can set up the following proportion:

[tex]\frac{\frac{4}{7}}{\frac{3}{4}}=\frac{x}{1}[/tex]

Therefore, you must solve for "x" in order to find the he number of dresses that Lucy sew in one hour.

You get this result:

[tex](1)(\frac{4*4}{7*4})=x\\\\x=(1)(\frac{16}{21})\\\\x=\frac{16}{21}[/tex]

Then, Lucy sews [tex]\frac{16}{21}[/tex] of a dress in one hour.

Answer:3/8 as a fraction and 3/8%

Step-by-step explanation: