What is the area of the rectangle, in square centimeters?

A rectangle with length 12 centimeters and width 5 centimeters.
17
34
30
60

Answer:

[tex]d=5t+20[/tex]

Step-by-step explanation:

The equation that will model this situation will be of the form

[tex]d=mt+b[/tex]

where [tex]t[/tex] is the time in hours john has traveled since the gas station, and  [tex]d[/tex] is the distance.

Now we know that John has already traveled 20 miles when he is at the gas station, this means at [tex]t=0[/tex], [tex]d=20[/tex]; or

[tex]20=m(0)+b[/tex]

[tex]\boxed{b=20}[/tex]

Thus we have

[tex]d=mt+20[/tex].

Now we need to figure out [tex]m.[/tex]

When John reaches home 2 hours later he notes that he has traveled 30 miles, which means he has traveled 30 - 20 = 10 miles; thus we have

[tex]m= \frac{\Delta d}{\Delta t} =\frac{10 miles}{2hours} =5[/tex]

[tex]\boxed{m=5}[/tex]

Now we have the full equation:

[tex]\boxed{d=5t+20}[/tex]

Answer:

False

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b

where m is the slope and c the y- intercept

Answer:

The equivalent expression can be given as:

⇒  [tex]2t-3q[/tex]

Step-by-step explanation:

Given expression:

[tex]-3t+4q+5t-7q[/tex]

To write an equivalent expression:

Solution:

In order to write an equivalent expression, we will combine the like terms. By like terms, we mean the terms with the same variable constant.

For example : [tex]5x[/tex] and [tex]-3x[/tex]  are like terms.

We have:

[tex]-3t+4q+5t-7q[/tex]

Combining like terms :

⇒ [tex]-3t+5t+4q-7q[/tex]

⇒  [tex]2t-3q[/tex]

Thus, the equivalent expression can be given as:

⇒  [tex]2t-3q[/tex]

Answer:

y equals 45, because you substitute the x in the bigger equation with -2, and then solve for y

Answer:

Yes

Step-by-step explanation: 2/8 is eq equivalent to 1/4 when reduced to the lowest term(i.e form)

Yes, this is because 2/8 is equivalent to one fourth, this is because eighths are fourths cut in half, so, you only need two of them to make a one right.

Hope this helps, if not, comment below please!!!

Answer:

20+4x

Step-by-step explanation:

Distributive property is quite easy to learn... its just multiplication in an easier form to visualize once you're used to using it.

To first start this problem you want to use the number 4 in the expression 4(5+x). You then want to multiply 4 by both terms inside of the parentheses. So you would do both 4*5 and 4*x. You would then get 20+4x because 4*5=20 and 4*x is just put together as 4x.

Answer:

[tex]4(5+x)=20+4.x[/tex]

Step-by-step explanation:

Distributive property:-

The distributive property is one of the most frequently used properties in mathematics.

Distributive property

a(b+c) = a.b+a.c ((using multiplication of distributive law)

given

[tex]4(5+x) = 4.5+4.x[/tex]

[tex]4(5+x)=20+4.x[/tex]

Answer:

5 multiple choice questions

Step-by-step explanation:

Write equations to represent the situation.

let "x" be the number of multiple choice questions

let "y" be the number of short answer questions

Equation for the total number of questions:

x + y = 20        # of multiple choice questions + # of short answer questions

Equation for the total points: (Multiply the type of question with how many points you get.)

x + 3y = 50     You don't need to write '1' beside 'x' for multiplying by 1.

The system of equations we need to solve is:

x + y = 20 and x + 3y = 50

We can solve using the substitution method.

Rearrange x + y = 20 to isolate one variable.

Isolate 'y'.

x + y = 20

x - x + y = 20 - x     Subtract 'x' from both sides

y = 20 - x

Take the other equation x + 3y = 50. You can replace 'y' with the equation that equals 'y' that we got when rearranging.

Substitute y for 20 - x

x + 3y = 50

x + 3(20 - x) = 50    Use distributive property. Multiply the 3 outside the bracket by each number inside the bracket.

x + 60 - 3x = 50     Combine like terms. 'x' and '-3x' are alike because they both have 'x'.

60 - 2x = 50          Start isolating 'x'.

60 - 60 - 2x = 50 - 60     Subtract 60 from both sides.

-2x = 50 - 60     60-60 cancels out on the left side.

-2x = -10

-2x/-2 = -10/-2       Divide both sides by -2 to isolate 'x'.

x = -10/-2           -2x/-2 becomes 'x'. -2/-2 cancels out.

x = 5          Number of multiple choice questions

Therefore there are 5 multiple choice questions.

If you needed the number of short answer questions too, you would substitute x for 5 in any of the other equations.

Answer:

720$

Step-by-step explanation:

(1000+(230*24))-5800=720

Answer:

Subtracting Polynomials is very similar to adding polynomials. In fact, we will be changing the subtraction problem to an addition problem. In the Pre-Algebra section of the website, we started out by reviewing integers. We said, " When you subtract integers, you must add the opposite. We also talked about the Keep - Change- Change Rule.

Step-by-step explanation:

The explanation regarding the adding or subtracting polynomials compare to adding or subtracting integers is explained below:

The following information should be considered:

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Answer:

-4

Step-by-step explanation:

-1(p+2)/2=-3-p

Multiplying both sides by 2

-p-2=2(-3-p)

-p-2=-6-2p

Combining similar terms

-p+2p=-6+2

p=-4

Answer:

111

Step-by-step explanation:

So firstly, you have two t-shirts, so you do 15.22*2=30.44. Then you use 67.94, and subtract 30.44, which is 37.5

Simple as that!!

Answer:

He have 0.96 acres of early corn.

Step-by-step explanation:

Given:

Toms garden is 8 acres. Two fifths is corn.

Of that, three tenths is early corn and one tenth is late corn.

Now, to find the acres of early corn.

Total garden = 8 acres.

Total Corn in garden = [tex]\frac{2}{5}\ of\ 8=\frac{2}{5} \times 8=\frac{16}{5}[/tex] acres.

As, given of the total corn in garden, three tenths is early corn.

Now, to get the early corn he have:

= [tex]\frac{3}{10} of \frac{16}{5}[/tex]

= [tex]\frac{3}{10} \times \frac{16}{5}[/tex]

= [tex]\frac{48}{50}[/tex]

= [tex]0.96\ acres.[/tex]

Therefore, he have 0.96 acres of early corn.

Final answer:

To solve these physics problems, we used vector mathematics to find the speed of the ball, its position after a certain time, the time it aligns with a certain point, and the speed of a player to intercept it. Additionally, we considered gravity as a factor for a more realistic model of the ball's motion.

Explanation:

Speed of the ball: To find the speed of the ball, we calculate the magnitude of the velocity vector (5i + 8j) m/s using the Pythagorean theorem, which results in \(\sqrt{5^2 + 8^2} = \sqrt{89}\) m/s.

Position vector after t seconds: We calculate the position vector at time t by using the initial position vector (2i + j) m and adding the product of the velocity vector and time t. This yields the formula (2i + j) + t(5i + 8j).

Time when the ball is due north of B: For the ball to be due north of B, their i-components must be equal. Given B's position vector is (10i + 7j), we set the i-component equal to 10 and solve for t, getting t = (10 - 2)/5 = 1.6 seconds.

Value of v for the running player: Since the player intercepts the ball after 1.6 seconds, and the ball's j-component of the velocity is 8 m/s, the player's velocity v must be the distance covered in the j direction divided by time, which is (8j - 7j)/1.6 = 0.625 m/s.

Physical factor for a more realistic model: One physical factor to make the model more realistic could be the effect of gravity on the ball's trajectory, which would cause the ball to follow a parabolic path rather than a straight line.

Answer:

3/4

Step-by-step explanation:

im a big brain so yea

Answer:

Step-by-step explanation:

15/45 = 1/3  {giving by 15th table}

        = 0.33

Answer:

16 lamps

Step-by-step explanation:

we know that

96 lamps represent the 100%

so

using proportion

Find out how many lamps represent 16 2/3%

but first convert to an improper fraction

[tex]16\frac{2}{3}\%=\frac{16*3+2}{3}=\frac{50}{3}\%[/tex]

Apply proportion

[tex]\frac{96}{100\%}=\frac{x}{\frac{50}{3}\%} \\\\x= (\frac{50}{3})(96)/100\\\\x=16[/tex]

Answer:

16 lamps

Step-by-step explanation:

Answer:

a is 7/25

b is 14/25

c is 24

Step-by-step explanation:

a) because there are 25 possible outcomes and 7 of them are 3 it is 7/25

b) using the same logic 14 possible outcomes are even

c) because the probability of it being 2 is 3/25, which can be made into ?/200 by multiplying the 25 by 8, which means we have to do the same to the 3, making it 24

Answer:

x = 12

Step-by-step explanation:

1. Set up a proportion:

32             (32 + x)

------   =      ------------

24             (24 + 9)

2. Cross-multiply & solve for x:

32*(24 + 9)    =     24*(32 + x)

1056     =     768 + 24x

288      =      24x

    12     =       x

    x     =   12

She had 100 points then lost 12-0 points.

Subtract 120 from 100.

100 - 120 = -20

Answer:20

Step-by-step explanation:

Answer:

153

Step-by-step explanation:

The figure shows a right triangle with acute angle of 27°,  this angle is the angle between the water level and the ski ramp.

It is also shown the suplementary angle 27° marked as X°, which is the angle that you must determine.

In the figure is clear that x is the exterior angle of the corner with the angle of 27° and that X° + 27° = 180°.

Then you can solve for X.

X = 180° - 27° = 153°.

Answer: 153°  

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Answer:

9

Step-by-step explanation:

The way to find the answer is by finding the point we're the two circles intersect and adding the number in that space to the number in the middle as the people in the middle are shown to be capable of both things as well

Answer:

Krutika get 21

Alex get 21

Gordon get 7

Step-by-step explanation:

Given: Total amount= 49

           Ratio= 3:3:1

Now, finding the amount received by Krutika, Alex and Gordon.

First, lets find the sum of ratio

Sum of ratio= [tex]3+3+1= 7[/tex]

We know now that amount will be distributed in the following fraction:

Krutika= [tex]\frac{3}{7}[/tex]

Alex= [tex]\frac{3}{7}[/tex]

Gordon= [tex]\frac{1}{7}[/tex]

∴ Amount received by Krutika= [tex]\frac{3}{7}\times 49= 21[/tex]

Alex,

Amount received by Alex= [tex]\frac{3}{7}\times 49= 21[/tex]

Gordon,

Amount received by Gordon= [tex]\frac{1}{7}\times 49= 7[/tex]

Hence, they get 21,21 and 7 respectively out of 49.

KKrutika and Alex each get £21, and Gordon gets £7.

To find out how much money each person gets, you need to divide the total amount of money (£49) in the ratio of 3:3:1.

First, add up the parts of the ratio to find the total number of parts: 3 + 3 + 1 = 7.  

Next, divide the total amount of money (£49) by the total number of parts (7) to find the value of one part: £49 ÷ 7 = £7.  

Finally, multiply the value of one part (£7) by each part of the ratio to find out how much money each person gets: KKrutika and Alex each get £7 × 3 = £21, and Gordon gets £7 × 1 = £7.

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Answer:

???

Step-by-step explanation:

Where's the problem/question?

We can multiply first equation x + 3y = -14 by 2 to get rid of varibale "x"

Solution:

Given that, the system of equations are:

x + 3y = -14 ----- eqn 1

2x + y = -3 --------- eqn 2

We can solve by elimination method

For doing elimination, we have to make the any one of coefficient of variable same

Here, in eqn 1 we have 1 as coefficient for "x"

In eqn 2, we have 2 as coeficient for "x"

So, we can multiply eqn 1 by 2, to get rid of "x"

2(x + 3y = -14)

2x + 6y = -28 ------- eqn 3

If we subtract eqn 2 from eqn 3, we will get the solution

2x + 6y = -28

2x + y = -3

( - ) ----------------

5y = -25

Substitute y = -5 in eqn 1

x + 3(-5) = -14

x -15 = -14

Thus the solution is x = 1 and y = -5. So we have multiplied equation 1 by 2 to get of varibale "x" and solved the equations

Answer:875 feet

350÷2=175

350+350+175=875

Step-by-step explanation:

Answer:

The flower garden width would be 6 ft

Step-by-step explanation:

A = 12 ft^2 = x(x + 4) becomes:

x^2 + 4x - 12 = 0, or (by completing the square) x^2 + 4x + 4 - 4 - 12 = 0

Thus, we have (x + 2)^2 - 16 = 0, or (x + 2)^2 = 16

Taking the square root of both sides yields x + 2 = ±4.

In this context only a positive x value makes sense:  x = 2 + 4  =>  x = 6.

The flower garden width would be 6 ft.  The other dimension would be 6 - 4, or 2, ft.

To find the width of the flower garden when the area is 12 square feet, the equation A = x(x-4) is used. Solving for x, the width of the flower garden is 6 feet.

To find the width of the flower garden when the area is 12 square feet:

Plug in A=12 into the equation: 12 = x(x-4)

Solve the equation for x by factoring or using the quadratic formula

The possible values for x are 6 and -2, but since width can't be negative, the width of the flower garden is 6 feet (B)

Answer:

Data;

1) Line P to Q can be represented as

[tex]--\\PQ[/tex]

2)

The Line P, Q and R will be represented as

[tex]PQ + QR = PR[/tex]

3)

The point P and Q will be represented as

[tex]< \to \\PQ[/tex]

With the sign above it's head

4)

point P will be represented as

[tex].P[/tex]

5)

The point PQ moving towards in the right hand side can be represented as

[tex]\to\\PQ[/tex]

Learn more on lines and points here;

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