Use triangle XYZ to answer questions 3-5.

1) Use special right triangles to help find the length of segment XY. What is the exact height of triangle XYZ?
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2)What is the exact area of triangle XYZ? Leave your answer in radical terms.
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3)What is the area of triangle XYZ to the nearest tenth of a square in?

Answer:

Option 4

Step-by-step explanation:

                h = x units

   diameter = x units

                 r = (x/2) units

    [tex]\sf \boxed{\text{ \bf Volume of cone = $\dfrac{1}{3} \pi r^2h$}}[/tex]

                                   [tex]\sf =\dfrac{1}{3}*\pi * (\dfrac{x}{2})^2*x\\\\=\dfrac{1}{3}*\pi*\dfrac{x^2}{4}*x\\\\=\dfrac{1}{12}\pi x^3[/tex]

Answer:

19i

Step-by-step explanation:

note that [tex]\sqrt{-1}[/tex] = i

[tex]\sqrt{-361}[/tex]

= [tex]\sqrt{361(-1)}[/tex]

= [tex]\sqrt{361}[/tex] × [tex]\sqrt{-1}[/tex]

= 19 × i

= 19i

Answer:

See below

Step-by-step explanation:

If the whole rectangle were shaded (all 25 parts) that would be 100%

So, we can set up a proportion.

25 = 100%

11 = x

Then, cross-multiply to get,

25x = 1100

Divide both sides by 25 to solve for x

x = 44.

The x value represents the percentage shaded.

44%

Answer:

B

Step-by-step explanation:

I got it right on the test

Answer:

B

Step-by-step explanation:

Radhika attempted 8 questions incorrectly, while Mohini attempted 13 questions incorrectly.

The given parameters are:

Correct = +3

Wrong = -2

Let the correct attempt be x and the incorrect attempt be y.

The equation that represents the total score is:

Total = 3x - 2y

She scored a total of 20.

So, we have:

3x - 2y = 20

She got 12 correctly.

So, we have:

3 * 12 - 2y = 20

Evaluate the product

36 - 2y = 20

Subtract 36 from both sides

-2y = -16

Divide by -2

y = 8

Hence, Radhika attempted 8 questions incorrectly.

In (a), we have the equation that represents the total score is:

Total = 3x - 2y

She scored a total of -5

So, we have:

3x - 2y = -5

She got 7 correctly.

So, we have:

3 * 7 - 2y = -5

Evaluate the product

21 - 2y = -5

Subtract 21 from both sides

-2y = -26

Divide by -2

y = 13

Hence, Mohini attempted 13 questions incorrectly.

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Fish fed during night  is equal to  1/6 tons

Let the weight of the fish fed at night = X tons

In the morning, the weight of the fish fed Wm = 2/15 tons.

In the afternoon, 1/15 ton more fish fed during the morning.

∴ Weight of fish fed in afternoon Wa

= 2/15 + 1/15

= 3/15 tons

Given that,

Wm + Wa + Wn = 1/2 tons

∴ 2/15 + 3/15 + Wn = 1/2

∴Wn = 1/2 - 5/15

∴ Wn = 3/6 - 2/6

∴ Wn = 1/6 tons

Fish fed during night = 1/6 tons.

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Answer:

a = 4

b = 7

c = 0

4n² + 7n = 0

4/4n² + 7n/4 = 0/4

= n² + 7/4n = 0

a = 1

b = 7/4

c = 0

b = 7/4

(b/2)² = (7/4 ÷ 2)²

Use fraction rule.

7/4 ÷ 2² = 7/4² / 2²

square the numbers

7/4² / 2² = 49/16 ÷ 4

49/16 ÷ 4 = 49/16 × 1/4

49/16 × 1/4 = 49/64

Add to both sides of the equation using 49/64

b = 7/4

b/2 = 7/4 ÷ 2

simplify

b/2 = 7 ÷ (4 × 2)

simplify(arithmetic)

b/2 = 7/8

n² + 7/4n + 49/64 = 49/64

(n + 7/8)² = 49/64

[tex](n+\frac{7}{8})^2=\frac{49}{64}\\\sqrt{(n+\frac{7}{8})^2}=\sqrt{\frac{49}{64}}\\[/tex]

Next, cancel out the square on the left side.

[tex]n+\frac{7}{8}=+/-\sqrt{\frac{49}{64}}[/tex]

Subtract 7/8 from both of the sides.

[tex]n+\frac{7}{8}-\frac{7}{8}=-\frac{7}{8}+/-\sqrt{\frac{49}{64}}[/tex]

Simplify the left side.

[tex]n=-\frac{7}{8}+/-\sqrt{\frac{49}{64}}\\n=-\frac{7}{8}+/-\frac{\sqrt{49}}{\sqrt{64}}\\n=-\frac{7}{8}+/-\frac{7}{8}\\n_1=0\\n_2=-\frac{7}{4}[/tex]

That wraps it up for this equation. Hope it helped!

Answer:

The answer is A

Step-by-step explanation: if 4 is the radius you take 4 and square it

(4 times 4= 16)

16 times pie

(in this case 3.14)

equals: 50.24

The point that is not included in the solution set for the inequality in the graph is (-1, 3).

In the information given, (h, k) is the vertex point. In the graph, the vertex point will be (1, 2). The equation will be:

y = a(x + 1)² + 2

By the point of the graph(0, 3) the value of a will be:

3 = a(0 - 1)² + 2

3 = a + 2

a = 3 - 2

a = 1

The equation this becomes:

y = 1(x - 1)² + 2.

y = x² - 2x + 1 + 2

y = x² - 2x + 3

Therefore, the point that is not included in the solution set for the inequality is (-1, 3).

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Deena is 420 miles from home in 12 hours.

The graph is shown below. The graph is linear

From the question, we are to determine how far Deena is from home in 12 hours

From the given linear equation,

y = 35x

We are to determine how far Deena is from home in 12 hours

That is,

x = 12 hours

Put x = 12 into the equation,

∴y = 35(12)
y = 420 miles

Hence, Deena is 420 miles from home in 12 hours.

The graph is shown below. The graph is linear

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A coterminal angle of θ such that 0 ≤ θ ≤ 2π is equal to 7π/4 and the exact value of Sin(θ) = -1/√2.

A coterminal angle can be defined as an angle that share the terminal side of an angle which occupies the standard position i.e it has the same initial side.

In this scenario, all angles that are multiples of 2π and added to the given angle (-9π/4) would be coterminal. For the range [0, 2π], 8π should be added to the given angle as follows:

Coterminal angle = -9π/4 + 4π

Coterminal angle = -9π/4 + 16π/4

Coterminal angle = 7π/4.

The reference angle is given by:

7π/4 -π = 3π/4.

Therefore, the exact values of all six (6) trigonometric functions evaluated at θ are:

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The sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa are shown in the picture by the Venn diagram.

It is defined as the diagram that shows a logical relation between sets.

The Venn diagram consists of circles to show the logical relation.

We have:

From a sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa, 30 took all the three beverages, 70 took coffee and cocoa, 110 took coffee only, and 185 took cocoon only.

We can represent the above data by the Venn diagram as shown in the picture.

From the Venn diagram:

The number of customers who took none of the beverages

= 800 - 580 = 220

The number of customers who took tea only = 95

The number of customers who took tea and cocoa only = 70

The number of customers who took tea and coffee only = 50

The number of customers who took none of the beverages = 220

Thus, in the sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa are shown in the picture by the Venn diagram.

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The line of the best fit is shown in the picture which is approximate near the dots.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

The slope and y-intercept can be found using the formula below:

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

We have a given a scatter plot shows the data for NCAA quarterbacks comparing their attempted passes to completed passes.

We can draw a line of best fit y = mx + c

Thus, the line of the best fit is shown in the picture which is approximate near the dots.

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Answer: The equation of a linear relationship is y = mx + b, where m is the rate of change, or slope, and b is the y-intercept (The value of y when x is 0).

Step-by-step explanation:

Answer:

Step-by-step explanation:

Harry buys a ream of computer paper priced at $9.99 before a 6.0%

sales tax. He uses a coupon at checkout for a 10% discount. After the

purchase he mails in a form

Answer:

The answer should be D.

The functions that are one to one are the set of ordered pairs.

It should be noted that the set of ordered pairs simply means an object that the pairs are significant.

On the other hand, a mapping diagram simply consists of two parallel columns that represents the domain and the range.

In this case, the functions that are one to one are the set of ordered pairs.

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Answer: 2,111 soccer balls

Step-by-step explanation:

         We will divide the total amount of money by the price per ball to find how many balls the league can buy.

        $6,333 / $3 = 2,111

        The league can buy 2,111 soccer balls.

Notice that the left side of the third equation is 2 times the left side of the first equation:

6x - 8y + 2z = 2 (3x - 4y + z)

The first equation says

3x - 4y + z = -5

while the third equation would reduce to

2 (3x - 4y + z) = 10   ⇒   3x - 4y + z = 5

but -5 ≠ 5, so there is no solution to the system.

The correct number line which represents the solution set for the inequality is shown in option 2.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

Inequality is,

⇒ 2x - 6 ≥ 6 (x - 2) + 8

Now, We cam simplify as;

⇒ 2x - 6 ≥ 6 (x - 2) + 8

⇒ 2x - 6 ≥ 6x - 12 + 8

⇒ 2x - 6x ≥ - 12 + 8 + 6

⇒ - 4x ≥ 2

⇒ 4x ≤ - 2

⇒ x ≤ - 1/2

⇒ x ≤ - 0.5

Hence, The correct number line which represents the solution set for the inequality is shown in option 2.

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Answer:

0.75gal.

Step-by-step explanation:

(4gal.) (2qt) - (3gal.) (3qt) =

the easiest way to solve this would be get everything in the same units,

lets make the qt to gallons

2qt = 0.5gal                          divide the volume value by 4

3qt = 0.75gal

 (4gal.) + (0.5gal.) - (3gal.) + (0.75gal.)

= (4.5gal.) - (3.75gal.)

= 0.75gal.

Answer:

m = 50h, where m is the distance traveled in miles

Step-by-step explanation:

we can see that this is an absolute value function. we know that for the graph to be shifted to the left the value of the constant inside the absolute value should be positive. and the fact that it is shifted down means that there is a negative constant outside the absolute value. the equation is:

| X + 5 | - 1

Answer:

−5(x+2)=−4x−12−x+2

Step-by-step explanation:

1) −5(x+2)=−4x−12−x+2

−5x−10=−4−10−x

-5x= -5x

0=0

so, it is true for all values

Answer:

[tex]x = \dfrac{21}8[/tex]

Step-by-step explanation:

[tex]~~~~~~~~\dfrac 1 2 -x + \dfrac 34 = x-4\\\\\\\implies \dfrac 24 + \dfrac 34 - x =x-4\\\\\\\implies \dfrac 54+4=x+x\\\\\\\implies 2x = \dfrac{21}{4}\\\\\\\implies x = \dfrac{21}{4 \cdot 2}\\\\\\\implies x = \dfrac{21}8[/tex]

Answer:

If using a calculator, you can calculate one number as a percentage of another by dividing the numbers and multiplying by 100.

Step-by-step explanation:

Answer:

I think it's 35x^2 +16x-24 listen I'm not sure yet I could be wrong

Step-by-step explanation:

the missing side is given by sqrt(16² - 8²)

hence,

the number that belongs in the green box is 192