Which of the following has a graph that is a straight line?

Equation 1: y = 4x^3 + 6
Equation 2: y = 5x − 4.5
Equation 3: y^2 = x − 1
Equation 4: y = 2x^2 + 6

Answer:

The correct option is 2.

Step-by-step explanation:

It is given that triangle ABC is similar to triangle PQR.

In triangle ABC, AB=c, BC=a, and AC=b.

In triangle PQR, PQ=r, QR=p, PR=q.

The corresponding sides of similar triangles are proportional.

Since [tex]\triangle ABC\sim \triangle PQR[/tex], therefore their corresponding sides are proportional.

[tex]\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}[/tex]

[tex]\frac{c}{r}=\frac{a}{p}=\frac{b}{q}[/tex]

It meas the ratio c:r = a:p = b:q.

Therefore the correct option is 2.

Answer:

Step-by-step explanation:

To find the right answer we have to solve the system of equation:

[tex]\left \{ {{12a+16c=176} \atop {10a+8c=120}} \right.[/tex]

If we multiply the second equation by -2, we could eliminate the c-variable and solve for a-variable:

[tex]\left \{ {{12a+16c=176} \atop {-20a-16c=-240}} \right.\\-8a=-64\\a=\frac{-64}{-8}=8[/tex]

Now, we replace this value in one equation to obtain the other value:

[tex]10a + 8c =120\\10(8)+8c=120\\80+8c=120\\8c=120-80\\c=\frac{40}{8}=5[/tex]

So, the solution of the system is [tex](8,5)[/tex], which means that there are 8 adults and 5 children.

Also, according to the linear expressions The Bryants spend $12 per adult and $16 per child, and a total amount of $176. The Jordan family spend $10 per adult and $8 per child, and a total amount of $120. Both families together spent $296.

Therefore, the right answers are D and G

Answer:

B. be solved

Step-by-step explanation:

the real answer is 5.79, the other person had had miscalculation

To find out which is bigger, we calculate 40% of 210 and 1/4 of 320. 40% of 210 is greater than 1/4 of 320.

To find out which is bigger, 40% of 210 or 1/4 of 320, we need to calculate both values.

First, 40% of 210 can be calculated by multiplying 210 by 0.4. This gives us 84.

Next, 1/4 of 320 can be calculated by dividing 320 by 4. This gives us 80.

Therefore, 40% of 210 is greater than 1/4 of 320.

Answer:

Since, a 45°-45°-90° triangle is a special type of isosceles right triangle, where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.

In 45°−45°−90° triangle

Sides are in the proportion [tex]1:1:\sqrt{2}[/tex]

then,

the measures of the sides are [tex]x , x ,\sqrt{2}x[/tex]

The length of hypotenuse= [tex]\sqrt{2}[/tex] times the length of the leg.   ....[1]

Given: length of hypotenuse = 128 cm.

then,

from [1] we have;

128 = [tex]\sqrt{2}\cdot x[/tex]

or

[tex]x=\frac{128}{\sqrt{2}}[/tex] = [tex]\frac{128}{\sqrt{2} } \times  \frac{\sqrt{2}}{\sqrt{2}}  = \frac{128\sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}[/tex]

Simplify:

[tex]x =\frac{128 \cdot \sqrt{2}}{2} =64\sqrt{2}[/tex] cm.

Therefore, the length of one leg of the triangle is; [tex]64\sqrt{2}[/tex] cm.

To find the average number of vehicles waiting at a traffic intensity of 0.92, we substitute 0.92 into the function w(x) = x² / (2(1-x)) to arrive at the answer 5.29.

The average number of vehicles waiting in line is modeled by the function w(x) = x^2 / (2(1-x)) where x represents traffic intensity. The question is asking us to calculate the average number of vehicles waiting when the traffic intensity is 0.92. By plugging this value into the function, we get w(0.92) = 0.92^2 / (2(1-0.92)), which simplifies to w(0.92) = 0.8464 / 0.16. The result is 5.29, so the average number of vehicles waiting would be 5.29 when the traffic intensity is 0.92. To find the average number of vehicles waiting when the traffic intensity is 0.92, we substitute the value of x into the given function w(x)=x^2/2(1-x). In this case, x=0.92. So, the average number of vehicles waiting can be found by evaluating w(0.92).

w(0.92) = (0.92)^2 / 2(1 - 0.92)

w(0.92) = 0.8464 / (2 * 0.08)

w(0.92) = 10.58

Therefore, when the traffic intensity is 0.92, the average number of vehicles waiting is approximately 10.58.

Using the simple interest formula, an investment of $480 at a 7% annual interest rate will earn $67.20 in simple interest after 2 years.

Finding Simple Interest on an Investment

To calculate the simple interest earned after 2 years on a $480 investment at a 7% annual interest rate, you can use the simple interest formula: Interest = Principal times Rate times Time.

The principal (P) is the initial amount of money, which in this case is $480. The rate (R) is the annual interest rate expressed as a decimal, so 7% becomes 0.07. The time (T) is the number of years the money is invested or borrowed, which is 2 years in this scenario.

Using the simple interest formula:

Interest = 480 times 0.07 times 2

Interest = 33.6 times 2

Interest = $67.20

Therefore, an investment of $480 at a 7% annual interest rate will earn $67.20 in simple interest after 2 years.

To find the youngest age for a lawyer to have an average income of $450,000, you solve the income function equation and round to the nearest year.

The youngest age for which the average income of a lawyer is $450,000 can be found by solving the given function:

I(x) = 10000 + 2000x

Given I(x) = $450,000, the equation becomes:

Rounded to the nearest year, the youngest age would be 220 years old.

The theorem that proves x is parallel to y is the Converse of the Alternate Interior Angles Theorem, which states that if alternate interior angles are congruent, the lines are parallel. The correct answer to the question of which postulate or theorem proves that x is parallel to y is B. Converse of the Alternate Interior Angles Theorem.

According to this theorem, if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. The other options, such as the converse of the corresponding angles postulate or the converse of the consecutive interior angles theorem, are related but specifically address different sets of angles formed when two lines are cut by a transversal.

In geometry, it is crucial to apply the correct postulates or theorems to prove specific properties, like parallel lines. The reliability of these mathematical proofs, like those in trigonometry or physics, comes from the logical sequence of applying these fundamental principles accurately.

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Answer:

yea, most likely it´s 3/4 y + 1/5 ≥ 7/8

Step-by-step explanation:

Answer:

a) The answer is: (x + a, y + b)

b) The answer is: (-1, -2)

The initial coordinates are:

(x, y) = (-2, -5)

should be the answer.

Let's find a and b.

a is a distance in x direction: a = 1

b is a distance in y direction: b = 3

The final position is:

(x + a, y + b) = (-2 + 1, -5 + 3) = (-1, -2)

Step-by-step explanation:

Answer:

870 calories Option D.

Step-by-step explanation:

A bag of chips contains calories per serving = 145

If each bag contains servings = 3

so total calories per bag = 3 × 145

                                         = 435

Now we have to calculate the total servings in 2 bags.

Number of calories in 1 bag = 435

Therefore, number of calories in 2 bags = 435 × 2

                                                                   = 870 calories

Option D. 870 calories is the answer.

Answer:

The population of foxville is 12000.

Step-by-step explanation:

It is given that the population of foxville is about 12 times 10 to the power of 3.

Population of foxville = [tex]12\times 10^3[/tex]

[tex]12\times 10^3[/tex] is a scientific notation of a number.

We need to write this number in another way.

[tex]12\times 10^3=12\times 1000[/tex]

[tex]12\times 10^3=12000[/tex]

Therefore, the population of foxville is 12000.

Answer:

In FLVS it is the third option

Step-by-step explanation:

Hope this helps :)

To predict the number of votes for Nuncio for class president, multiply 3/4 (or 0.75) by the total number of students (340), resulting in a prediction that 255 students would vote for Nuncio.

To predict how many of the 340 students in the school would vote for Nuncio for class president, we need to understand the proportion that we got from the survey. Since 3 out of 4 students said they would vote for Nuncio, this is the same as 75% or 0.75 when expressed as a decimal.

We then apply this proportion to the total number of students in the school:

Convert the fraction 3/4 to a decimal: 3 ÷ 4 = 0.75.

Multiply the total number of students by the decimal: 340 students × 0.75 = 255 students.

Therefore, we predict that 255 of the 340 students would vote for Nuncio for class president.

To calculate the probability of getting a blackjack from a single well-shuffled deck, you must consider the probability of drawing an Ace and then a 10-value card or vice versa, and add those probabilities together. The same process applies to two decks with adjusted numbers. You will then round the final probabilities to four decimal places.

To answer the question of the probability of getting a blackjack in a single deck, consider that there are 4 aces in a deck and 16 cards that are either a face card or a 10 (each suit has 4 such cards - Jacks, Queens, Kings, and 10s). When one card is drawn, the remaining cards are one fewer, so we need to adjust our probability for the second card.

For the probability of a blackjack from two decks, follow the same steps, but adjust the numbers for a 104-card deck.

After doing the calculations, we round the probabilities to four decimal places as instructed.

PEMDAS- [Parenthese, Exponents, Multiplication, Division, Addition, Subtraction.]

Since there is no Parentheses, nor Exponents, you have to go straight to multiplication. Then to addition

30+30×0+1

30×0=0

30+0+1=31.

I hope my answer has come to your help. God bless and have a nice day ahead!