The function f(x) is graphed on the coordinate plane.
What is f(−2) ?
Enter your answer in the box.
f(−2)=

The required unit rate is given as 23.9 mi per h.

Given that,
To determine the unit rate of the given 501.9 mi in 21 h,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Unit rate is given as,
Rate = 501.9/21 = 23.9 mi per h

Thus, the required unit rate is given as 23.9 mi per h.

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Consider right triangles BTZ and BUZ.

ZB = ZB (Common)

ZT = ZU (Given)

Therefore, ΔBTZ ≅ ΔBUZ (By RHS theorem)

Hence, by CPCTC,

∠BTZ = ∠BUZ

Answer:

(C)

Step-by-step explanation:

It is given that Point Z is equidistant from the vertices of ΔTUV, therefore ZT=ZU=ZV.

Now, from ΔBTZ and ΔBUZ, we have

ZT=ZU (Given)

BZ=ZB (common)

therefore, by RHS rule of congruency,

ΔBTZ≅ΔBUZ

Thus, by corresponding parts of congruent triangles, we have

∠BTZ=∠BUZ

Thus, option C is correct.

Also, it is not necessary that TA=TB and AZ=BZ because there is no information given regarding these equalities.

The number 3,868,000,000 in scientific notation is 3.868 x [tex]10^9[/tex].

We have,

Scientific notation is a way to express large or small numbers in a concise format. It consists of two parts:

a coefficient and a power of 10.

In the given number 3,868,000,000, we can express it in scientific notation by moving the decimal point to the left until there is only one non-zero digit to the left of the decimal point.

Count the number of places you moved the decimal point, and that becomes the exponent of 10.

Starting with 3,868,000,000, we can move the decimal point 9 places to the left to get 3.868.

The original number has been divided by [tex]10^9[/tex], so the exponent is 9.

Putting it all together,

We express 3,868,000,000 in scientific notation as

= 3.868 x [tex]10^9[/tex]

Where the coefficient is 3.868 and the exponent is 9.

Thus,

The number 3,868,000,000 in scientific notation is 3.868 x [tex]10^9[/tex].

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multiply price by amount bought for each then add them

roast beef: 2.00 * 1.25 = $2.50

turkey: 1.50 * 2.5 = $3.75

3.75 + 2.50 = $6.25 total cost

This is a mathematics problem about percentages. It tells us that 20% of the total number of sixth-grade students equals 22 students who are in the band. By setting up and solving a simple equation, we find that there are 110 sixth-grade students in the school.

The subject of your question is Mathematics. This problem is about percentages and can be solved by setting up an equation based on the given information.

It says that 20% which is (0.20 in decimal form) of the total number of sixth-grade students equals the 22 students who are in the band. Let's denote the total number of sixth-grade students by X.

Your equation will look like this: 0.20 × X = 22

To solve for X, divide both sides of the equation by 0.20:

X = 22 / 0.20

Therefore, X = 110.

So, there are 110 sixth-grade students in the school.

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To determine the weight of tack Cari can allow for each horse, use the inequality 6,240 + 5t ≤ 8,000, where 't' is the average weight of tack per horse. Solve for 't' to find that the maximum average weight of tack per horse is 352 pounds or less.

The inequality to determine the weight of tack per horse that Cari can allow would be based on the maximum weight the trailer can transport, which is 8,000 pounds, minus the combined weight of the horses. The combined weight of the horses is given as 6,240 pounds. Let t represent the average weight of tack per horse. Since Cari travels with 5 horses, the total weight of the tack for all horses would be 5t. The inequality would therefore be:

6,240 + 5t ≤ 8,000

To find the maximum average weight of tack per horse that Cari can allow, we should solve the inequality for t as follows:

5t ≤ 8,000 - 6,240

5t ≤ 1,760

t ≤ 1,760 / 5

t ≤ 352

So, the weight of tack per horse must be 352 pounds or less for Cari to safely transport the horses and the tack in the trailer.

The inequality that could be used to determine the weight of tack Cari can allow for each horse is: [tex]\[ 5t + 6,240 \leq 8,000 \][/tex]

Step 1

To determine the weight of tack Cari can allow for each horse, we can set up an inequality based on the total weight limit of the trailer. The total weight limit includes the weight of the horses and the weight of the tack.

Let [tex]\( t \)[/tex] represent the average weight of tack per horse.

The total weight of the horses and tack should not exceed the weight limit of the trailer, which is 8,000 pounds.

Step 2

The weight of the horses is given as 6,240 pounds.

Therefore, the weight of the tack can be represented as [tex]\( 5t \)[/tex] (5 horses each with an average weight of tack [tex]\( t \))[/tex].

Putting this all together, the inequality that represents this situation is:

[tex]\[ 5t + 6,240 \leq 8,000 \][/tex]

Complete correct question:

Cari owns a horse farm and a horse trailer that can transport up to 8,000 pounds of livestock and tack. She travels with 5 horses whose combined weight is 6,240 pounds. Let t represent the average weight of tack per horse. Which of the following inequalities could be used to determine the weight of tack Cari can allow for each horse?

6240+t≤ 8000

8000≥ 6240t

6240+5t≤ 8000

8000+6240≤ 5t

8000-6240≥ 5t

To solve the equation, assume the person's age is 'x', then translate the sentence into an equation: 300 - 3x = 114. Isolate the variable by subtracting 300 from both sides, then divide both sides by -3 to find 'x'. The person's age is 62.

The subject of this question is Mathematics. Specifically, it involves solving an equation to determine the age of the person mentioned in the quote.

To solve the equation, let's assume the person's age is 'x'. Then, we can translate the sentence '300 reduced by 3 times my age is 114' into the equation: 300 - 3x = 114.

To solve for 'x', we can isolate the variable by subtracting 300 from both sides of the equation, giving us -3x = -186. Finally, dividing both sides by -3, we find that x = 62. Therefore, the person's age is 62.

To find the cost of filling the gas tank, calculate the empty part of the tank, which is 5/8 of 25 gallons. Then multiply that by the cost of a gallon of gasoline, which gives you $46.25.

To solve this problem, we need to calculate how much gasoline is needed to fill up the car's tank considering that it's already 3/8 full and then multiply that by the cost of gasoline per gallon.

Firstly, we need to find out how much of the tank's capacity is empty. The tank has a total capacity of 25 gallons and 3/8 of it is already full. This means 5/8 of the tank is empty. The empty capacity is 5/8 * 25 = 15.625 gallons.

Given that a gallon of gasoline costs $2.96, we need to multiply the cost per gallon by the number of gallons needed. Therefore, the cost to fill the tank equals to 2.96 * 15.625 = $46.25.

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Answer:

Area of the new poster = 584.375 inch²

Step-by-step explanation:

Length of old poster = 8 1/2 inches = 8.5 inches

Breadth of old poster = 11 inches

Scale factor = 2 1/2 = 2.5

Length of new poster =  8.5 x 2.5 = 21.25 inch

Breadth of new poster =  11 x 2.5 = 27.5 inch

Area of new poster = 21.25 x 27.5 = 584.375 inch²

Area of the new poster = 584.375 inch²

Given that 3/4 of a track team are girls and 3/4 of these girls are in 8th grade, we can multiply the two fractions to find the fraction of the whole track team that are 8th-grade girls, which is 9/16.

The question involves two instances of finding 3/4 of a group. Initially, we are given a track team and we are told that 3/4 of the team are girls. If we let the total number of students in the team equal 1 (or 100%), then the fraction representing the girls is 3/4. Further, 3/4 of these girls are in 8th grade. Therefore, to find the fraction of 8th-grade girls out of the whole team, we multiply the two fractions together as follows: 3/4 * 3/4 = 9/16. This means that 9 out of 16 students are 8th-grade girls, assuming that the track team consists of 16 students. If the track team doesn't consist of 16 students, we can interpret the 9 out of 16 as a ratio.

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The fraction of the track team that are grade 8 girls is [tex]\(\frac{9}{16}\)[/tex].

To find the fraction of the track team that are grade 8 girls, we need to multiply the fraction of the team that are girls by the fraction of those girls who are in grade 8.

Let's denote the total number of students on the track team as [tex]\(T\)[/tex]. According to the information given:

- About[tex]\(\frac{3}{4}\)[/tex] of the students on the track team are girls. So the number of girls on the track team is [tex]\(\frac{3}{4}T\)[/tex].

- About [tex]\(\frac{3}{4}\)[/tex] of these girls are in grade 8. Therefore, the number of grade 8 girls is [tex]\(\frac{3}{4} \times \frac{3}{4}T = \frac{9}{16}T\)[/tex].

Thus, the fraction of the track team that are grade 8 girls is [tex]\(\frac{9}{16}\)[/tex]. This is found by dividing the number of grade 8 girls by the total number of students on the track team:

[tex]\[ \frac{\text{Number of grade 8 girls}}{\text{Total number of students on the track team}} = \frac{\frac{9}{16}T}{T} = \frac{9}{16} \][/tex]

Therefore, the fraction of the track team that consists of grade 8 girls is[tex]\(\frac{9}{16}\)[/tex].

Answer: - 51/4

Step-by-step explanation:

Final answer:

To calculate the total cost, find the individual costs of the pants and jeans, multiply them by the required quantity, and sum the resulting amounts. It costs $165.00 to buy 3 pairs of pants and 5 pairs of jeans.

Explanation:

To calculate the cost of buying 3 pairs of pants and 5 pairs of jeans, we first need to find the cost of one pair of pants and one pair of jeans. Given that 4 pairs of pants cost $90.00, the price per pair of pants is $90.00 ÷ 4 which equals $22.50. Similarly, 4 pairs of jeans cost $78.00, so the price per pair of jeans is $78.00 ÷ 4 which equals $19.50.

We then multiply the cost per pair of pants by the number of pants we want to buy, which is 3, and do the same for the jeans by multiplying the cost per pair by 5. Therefore, the total cost for the pants is 3 × $22.50 = $67.50, and the total cost for the jeans is 5 × $19.50 = $97.50.

Finally, we add these two amounts together to get the total cost: $67.50 + $97.50 = $165.00. So, it would cost $165.00 to buy 3 pairs of pants and 5 pairs of jeans.

race entry costs 55, they use 15 of it to cover costs so they get 55-15 = 40 per entry

 x = race entries

equation becomes 55000>= 40x +10000

45000>= 40x

x >= 45000/40 >= 1125

 they need at least 1125 race entries to make $55,000

When light energy meets the surface of sunglasses, some of it is transmitted, some are reflected, and some are absorbed.

Light energy is a form of electromagnetic radiation that is visible to the human eye.

It is a type of kinetic energy that travels in the form of waves at a speed of 299,792,458 meters per second in a vacuum.

We have,

The evidence that light has been transmitted through your sunglasses is that you can see through them.

The amount of light that is transmitted depends on the type of sunglasses and the properties of the lens material.

Sunglasses with darker lenses will transmit less light than those with lighter lenses.

The evidence that light has been reflected is that you can sometimes see reflections on the surface of your sunglasses.

This can be from the front surface of the lens or the back surface, depending on the design of the sunglasses.

Reflected light can also cause glare, which is why many sunglasses have anti-reflective coatings.

The evidence that light has been absorbed is that the lens of your sunglasses appears to be a different color.

The color of the lens is determined by the type of material used and the specific dyes or pigments added to the lens during manufacturing.

Different colors of lenses are designed to absorb different wavelengths of light, which can be useful for different activities such as driving or skiing.

Overall, the combination of transmission, reflection, and absorption of light in sunglasses helps to reduce the amount of light that reaches your eyes and can improve your visual comfort and clarity in bright environments.

Thus,

When light energy meets the surface of sunglasses, some of it is transmitted, some are reflected, and some are absorbed.

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