The average speed for a family trip is 62 miles per hour. Which equation models the distance traveled d and time in hours t?

Answer:

$8.33

Step-by-step explanation:

$14.69                                                                  50.00

+ $20.99                                                            -  41.67

=35.68                                                                =   $8.33

+5.99

=$41.67

Answer:

[tex]\sqrt{x^2+y^2}-x[/tex]

Step-by-step explanation:

[tex]\textsf{Mulitply by}\quad\dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}:[/tex]

[tex]\implies \dfrac{y^2}{\sqrt{x^2+y^2}+x} \times \dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2}+x)(\sqrt{x^2+y^2}-x)}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2})^2-x^2}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{x^2+y^2-x^2}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{y^2}[/tex]

[tex]\textsf{Cancel the common factor}\:y^2:[/tex]

[tex]\implies \sqrt{x^2+y^2}-x[/tex]

Rationalising the denominator of the given fraction means we need to multiply both the numerator and the denominator of the fraction by the conjugate of the expression in the denominator. For example:

[tex]\;\longrightarrow\dfrac{1}{a+b}[/tex]

Here the conjugate of denominator of the expression is a - b. So we need to multiply both the numerator and denominator with the fraction.

[tex]\;\longrightarrow \dfrac{1}{a+b} \times \dfrac{a-b}{a-b}[/tex]

Hence, this is what the rationalization means.

We have been given and equation and we have been asked to rationalise the equation.

The conjugate of the denominator of the given equation is √(x² + y²) - x. Therefore;

[tex]\implies \dfrac{y^2}{\sqrt{x^2+y^2}+x} \times \dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2}+x)(\sqrt{x^2+y^2}-x)}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2})^2-x^2}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{x^2+y^2-x^2}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{y^2}[/tex]

[tex]\implies \boxed{\sqrt{x^2+y^2}}[/tex]

Hence, this is our required solution for this question.

Answer: -124 - 2,194= -2408

(I think this is right, but if not i'm sorry!)

Answer: 2318

Step-by-step explanation: 2194- (-124)=

2318

Answer:

[tex]\huge\boxed{\sf Slope = m = 5}[/tex]

Step-by-step explanation:

Given slope equation:

y = 5x + 4

Comparing it with the standard form of slope equation

y = mx + b

Where m is slope and b is y-intercept

Hence,

by comparing both equation, we get:

Slope = m = 5

[tex]\rule[225]{225}{2}[/tex]

Answer:

The contestant needs to answer the next 26 consecutive questions correctly.

Step-by-step explanation:

[tex] \frac{37 + x}{44 + x} = \frac{9}{10} [/tex]

[tex]9(44 + x) = 10(37 + x)[/tex]

[tex]396 + 9x = 370 + 10x[/tex]

[tex]x = 26[/tex]

The contestant needs to answer the next 26 consecutive questions correctly.

Proportion is an equation that defines that the two given ratios are equivalent to each other.

In other words, the proportion states the equality of the two fractions or the ratios.

In proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

Given that, a game show contestant has answered 37 out of 44 trivia questions correctly so far.

We need to solve an equation given to find the number of consecutive questions the contestant needs to answer correctly,

So, the equation is,

37+x / 44 + x = 90/100

37+x / 44 + x = 9/10

10(37+x) = 9(44+x)

370+10x = 396+9x

x = 26

Hence, the contestant needs to answer the next 26 consecutive questions correctly.

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Answer:

A 233.3 or 233 1/3

Step-by-step explanation:

X =1/4

Y =25

1/4 X 100= 25

2 1/3 X 100= 233.3

Answer:

Step-by-step explanation:

Given:

Isolate the term of x from one side of the equation.

Use the distributive property.

DISTRIBUTIVE PROPERTY:

[tex]\Longrightarrow: \sf{A(B+C)=AB+AC}[/tex]

Each term within the parentheses can be multiplied by a factor outside the parentheses.

3(x+1)

3*x=3x

3*1=3

Rewrite the expression down.

3x+3

3x+3+2(3x+4)

Multiply expand.

2(3x+4)

2*3x=6x

2*4=8

6x+8

3x+3+6x+8

Combine like terms.

3x+6x+3+8

Add the numbers from left to right.

3+8=11

3x+6x+11

Add.

Solutions:

3x+6x=9x

[tex]\Longrightarrow: \boxed{\sf{9x+11}}[/tex]

I hope this helps. Let me know if you have any questions.

Answer:

[tex]P=\left(\dfrac{13}{3},-\dfrac{1}{3}\right)[/tex]

[tex]|\overrightarrow{MN}|=4\sqrt{5}[/tex]

Step-by-step explanation:

Part (a)

[tex]x_P=\dfrac13(x_N-x_M)+x_M=\dfrac13(7-3)+3=\dfrac{13}{3}[/tex]

[tex]y_P=\dfrac13(y_N-y_M)+y_M=\dfrac13(5-(-3))+(-3)=-\dfrac13[/tex]

[tex]\implies P=\left(\dfrac{13}{3},-\dfrac{1}{3}\right)[/tex]

Part (b)

The magnitude of MN is the distance between points M and N.

Using the distance between two points formula, where

[tex](x_1,y_1)=(3,-3)[/tex]  and  [tex](x_2,y_2)=(7,5)[/tex]

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\implies |\overrightarrow{MN}|=\sqrt{(7-3)^2+(5-(-3))^2}[/tex]

[tex]\implies |\overrightarrow{MN}|=4\sqrt{5}[/tex]

Answer:

11² = 121

Step-by-step explanation:

When you divide powers with the same base, subtract the exponents.

[tex] \dfrac{11^6}{11^4} = 11^{6 - 4} = 11^2 = 121 [/tex]

Answer:

121

Step-by-step explanation:

11 to the 6 power = 1771561

11 to the 4 power = 14641

1771561/14641 = 121

Answer:

3 1/3 yd^3

Step-by-step explanation:

Volume of a rectangular prism: L*W*H

ft. = 1/3 yd.

3/3 = 1 yd.

6/3 = 2 yd.

5/3 = 1 2/3 yd.

1*2*1 2/3

=2* 1 2/3

=2 4/3

= 3 1/3 yd.^3

Answer: 10.6

Step-by-step explanation: it has a .3% increase each time, therefore it would be D. 10.6

Answer: 17160 feet

Step-by-step explanation: Convert 3.25miles to feet. Multiply by 5280

The options that are true about the system of linear equations are;

A) The solution is (4,0).

C) The solution is (0,−1).

D) There are infinitely many solutions.

From the given linear equation graph, we see that the linear equation that is graphed is given by;

y = ¹/₄x - 1

Now, the solution to the given equation will be the value of x that corresponds with the value of y when traced on the graph.

Let us access (4, 0)

At x = 4, we have;

y = ¹/₄(4) - 1

y = 0

Thus, (4, 0) is a solution of the graph.

Let us access (0, -1)

At x = 0, we have;

y = ¹/₄(0) - 1

y = -1

Thus, there are many solutions to the graph

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For the given arithmetic sequence we have:

We know that we have 20 seats on the front row, and then we add 3 more on each row, so the formula will be:

[tex]A_n = 20 + (n - 1)*3[/tex]

This gives the number of seats on the n-th row.

B) The last row has 83 seats, then we need to solve:

[tex]A_n = 20 + (n - 1)*3 = 83\\\\(n - 1)*3 = 83 - 20 = 63\\\\n - 1 = 63/3 = 21\\\\n = 21 + 1 = 22[/tex]

So we conclude that there are 22 rows.

C) The total number of seats will be:

[tex]\sum_{n = 1\ to\ 22} (20 + (n - 1)*3)[/tex]

D) Instead of using the sum above (we should add 22 terms) we use the general formula for the sum of N terms in an arithmetic sequence:

[tex]S_N = (N/2)*(2A_1 + (N - 1)*d)[/tex]

In this case, we replace N by 22, and d is the common difference of the sequence, which we know is equal to 3, so we wil have:

[tex]S_{22} = (22/2)*(2*20+ (22 - 1)*3) = 11*(40 + 21*3) = 1,133[/tex]

There are 1,133 seats in total.

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Answer:

7

Step-by-step explanation

2x = 14

divide by 2

Answer:

b

Step-by-step explanation:

Answer:

25.2% of the boys want to play inside

Step-by-step explanation:

Answer:

1/125 probability for each student so, a 0.8 percent probably of winning per student.

Step-by-step explanation:

you should try to keep it under 5 minutes.

since there will be easier ones and harder ones, its ok to take up to 10 minutes on a test as long a you try to get the easy ones done first. if you can skip questions then go back to them later, do the hardest ones first thengo back and do the easier ones afterwards.

Try to take your time when you need to. if you get stuck, think about what it says. Try to think of it another way. You also want to get as much done as you can, this is because if you miss 5-10 questions, the grade could be seriously decreased, as you might have gotten a few other questions wrong.

Make sure to do a "QC" as I call it; or a "Quick Check." If it looks good and it's reasonable then you are fine to move on. it it doesnt look right, retrace your steps. Then rewrite it if you got something else on your next try for the QC.

I hope you do good!

May luck be with you!

Answer: Move terms to the left side−52+3=−9−5x2+3x=−9−52+3−(−9)=0−

Common factor−52+3+9=0−5x2+3x+9=0−(52−3−9)=0

Divide both sides by the same factor−(52−3−9)=0−(5x2−3x−9)=052−3−9=0

Solution=3±321 over 10

Step-by-step explanation:

Answer: 1/3 as an equation

Step-by-step explanation: file attached

Answer:

Step-by-step explanation:

When you square a number, whether it's positive or negative, the square is always positive.  That is, a2 is positive whether a is positive or negative.  Examples:

12 = 1 x 1 = 1

(-1)2 = (-1) x (-1) = 1

52 = 5 x 5 = 25

(-5)2 = (-5) x (-5) = 25

Since the answer is always positive, you don't need the absolute value signs: |a2| = a2.

hope this helps can i get brainly pls

Answer:

V = 56.52

Step-by-step explanation:

Formiula

V = (1/3) * pi * r^2 * h

Givens

pi = 3.14

r = 3 yard

h = 6 yards

Solution

V = (1/3) * 3.14 * 3^2 * 6          Multiply 1/3 * 6

V = 2 * 3.14 * 9

V = 56.52

Distance formula: sqrt((x2-x1)^2 + (y2-y1)^2)

distance = sqrt((-1 -2)^2 + (-5-5)^2)
distance = sqrt(109)

Distance = 10.44

Answer:

Step-by-step explanation:

I did this before. I'm 14 :D

E-

y=20x

Eli ironed 2 more hours and got 400 shirts.

S-

y=35x

Let x be the number of shirts ironed.

400/20x = 20.

20-2=18.

That means she ironed 360 shirts prior.

If both of them were at the same speed of 18 by (let x represent). Then Samantha ironed 630 shirts while Eli ironed 360 shirts, but ironed 2 more hours which got him to get 400 shirts.

Answer:

10

Step-by-step explanation:

Add all the numbers : 3+2+26+9 = 40

Divide the total with the number of data you have which is 4 so 40÷4= 10

A fraction is equavalent to the top number divided by the bottom number.

5/8 is equivalent to 5 ÷ 8

Answer: C.  5 ÷ 8

The number of video games in Matthew’s collection is 12

To solve the problem, we need to know what simultaneous equations are

These are a pair of equations which contain two variables.

Now, let

Given that the number of video games in Anthony’s collection is 5 times the number in Matthew’s collection, we have that y = 5x (1)

Also, the total number of video games in both collections is 72.

So, x + y = 72 (2)

Substituting equation (1) into (2), we have

x + 5x = 72

6x = 72

x = 72/6

x = 12

So,  the number of video games in Matthew’s collection is 12

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If 140 people were surveyed, from the given table, the number of people that preferred crab is; 42

We are given;

Total sample size; n = 140

Now, from the table we see the percentages that preffered each seafood.

Percentage that preferred Shrimp = 24%

Percentage that preferred Crab = 30%

Percentage that preferred Fish = 36%

Percentage that preferred Neither = 10%

Thus;

Number that preferred Crab = 30% * 140

Number that preferred Crab = 42 people

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Answer:18

Step-by-step explanation:

Its is 18 caycausecause the arrow is pointing next to it

1

Relative frequency is frequency relative to some quantity, usually the marginal or total frequency. The needed relative frequencies are: 14/50, 15/50, and 44/50 respectively.

Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency).

The two way table given is:

                           Alaska                  Not Alaska               Total

Hawaiii                    6                            15                            21

Not Hawaii              8                            21                            29

Total                       14                            36                           50

Calculating the needed relative frequencies one by one:

Case 1: The relative frequency for students who have been to Alaska

Thus, the relative frequency for students who have been to Alaska (relative to total count) is 14/50

Case 2: The relative frequency for students who have been to Hawaii but not Alaska

Thus, the relative frequency for students who have been to Alaska (relative to total count) is 15/50

Case 3: The relative frequency for students who have not been to Alaska or Hawaii

Thus, the relative frequency for students who have been to Alaska (relative to total count) is 44/50

Thus, the needed relative frequencies are: 14/50, 15/50, and 44/50 respectively.

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[tex]f(x) = 3 \sqrt[3]{x} [/tex]

[tex]lim f(x) = 3 \sqrt[3]{ - \infty } = - \infty \\ x = > - \infty [/tex]

[tex]limf(x) = 3 \sqrt[3]{ \infty } = \infty \\ x = > \infty [/tex]

Answer:

As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.

Step-by-step explanation:

I got it right on the test.