How many pints are equivalent to 2 1/4 gallons.

Answer:

x = -7

Step-by-step explanation:

Solve for x:

4 (1 - x) + 2 x = -3 (x + 1)

4 (1 - x) = 4 - 4 x:

2 x + 4 - 4 x = -3 (x + 1)

2 x - 4 x = -2 x:

-2 x + 4 = -3 (x + 1)

Expand out terms of the right hand side:

4 - 2 x = -3 x - 3

Add 3 x to both sides:

3 x - 2 x + 4 = (3 x - 3 x) - 3

3 x - 3 x = 0:

3 x - 2 x + 4 = -3

3 x - 2 x = x:

x + 4 = -3

Subtract 4 from both sides:

x + (4 - 4) = -4 - 3

4 - 4 = 0:

x = -4 - 3

-4 - 3 = -7:

Answer:  x = -7

Answer:

X=-7

Step-by-step explanation:

Step-by-step explanation:

Empirical Probability is the experimental probability.

The probability formula is

the number of times an event occured/total times all events happen.

We know we rolled the dice 60 times so that will be in the numerator.

We roll 2, 9 times

We roll 4, 12 times

We roll 6, 8 times so

we roll even numbers a total of 29 times, so our experimentally Probability is

\( \frac{29}{50} = 0.58\)

to solve for m

distribute into parentheses

176 = -16 - 24m

get m on one side

176 + 16 = -24m

192 = -24m

divide by -24

-8 = m

m = -8

Answer:

Infinite, any number

Step-by-step explanation:

Simplify

30 - 3x = 30 - 3x

Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.

Answer:

$1680

Step-by-step explanation:

I = 5%

P = $1600

period = 1 year

$1600 + 15% = $1680

Answer:

$1680.

Step-by-step explanation:

The interest for 1 year = 1600 * 5%

= 1600 * 0.05

= $80.

So the new balance = old balance + interest

= 1600 + 80

= $1680.

Answer: c

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

4x9=36

5x9=45

6x9=54

7x9=63

(:

Answer:

9

Step-by-step explanation:

divide the y (revenue) by the x (books)

Answer:

B. 28.27

Step-by-step explanation:

Answer:

please look at detailed answers below

Step-by-step explanation:

example 1 is correct.

example 2:

x = (12 sin 15) / sin 75 = 3.22.

example 3:

x/sin 90 = 19/sin (180 - 90 -36)

x = (19 sin 90) / sin 54

= 23.5

example 4:

x/sin 53 = 7/sin (180 -90 - 53)

x = (7 sin 53)/ sin

= 9.29

Answer:

Step-by-step explanation:

4x + 10

C.

4-7(x+5)

4-7x+5

-7x+9

B. 2+5(x-7)

7(x-7)

7x-49

D. 7-3(x - 5)

7-3x-15

-3x-8

its 1,002

Let f(x) = lnx and g(x) = log₂x. for all 0 < x < 1, f(x) < g(x): True.

In this scenario and exercise, we would determine the corresponding output value for the functions f(x) and g(x) under the given mathematical operation and independent variables.

When x = 1, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(1) = ln(1).

f(1) = 0.

When x = 2, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(2) = ln(2).

f(2) = 0.69314718

When x = 1, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(1) = log₂(1)

g(1) = 0.

When x = 2, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(2) = log₂(2)

g(2) = 1.

In this context, we can logically deduce that the function f(x) is less than function g(x) for all 0 < x < 1.

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Answer:

62/3

Step-by-step explanation:

The Fraction Part would be reduce 35/3 and then you add 9+35/3 and that equals 62/3

Using PEMDAS and substituting 6 for x, the results of the mathematical operations are as follows:

PEMDAS is the order of mathematical operations that explains the correct sequential steps for evaluating mathematical expressions.

PEMDAS means that mathematical operations must follow the following order:

1) 9. x - 6 ( if x = 6)

= 9 x 6 - 6

= 54 - 6

= 48

2) 10. 7 + x ( if x = 6)

= 10 x 7 + 6

= 70 + 6

= 76

3) 11. 3x - 9 ( if x = 6)

= 11 x 3(6) - 9

= 11 x 18 - 9

= 198 - 9

= 189

4) 12. 63/x ( if x = 6)

= 12 x 63/6

= 126

5) 13. 5 + 5x + 10 ( if x = 6)

= 13 x 5 + 5(6) + 10

= 65 + 30 + 10

= 105

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Answer:

x = - 5, x = 15

Step-by-step explanation:

Assuming you require to find the values of x

Calculate the distance PQ using the distance formula and equate to 20

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-x_{1})^2 }\)

with (x₁, y₁ ) = P (15, x ) and (x₂, y₂ ) = Q (x, - 5 )

PQ = \(\sqrt{(-5-x)^2+(x-15)^2}\) = 20 ( square both sides )

(- 5 - x)² + (x - 15)² = 20² ← expand factors on left side using FOIL

25 + 10x + x² + x² - 30x + 225 = 400

2x² - 20x + 250 = 400 ( subtract 400 from both sides )

2x² - 20x - 150 = 0 ( divide through by 2 )

x² - 10x - 75 = 0

consider the factors of the constant term (- 75) which sum to give the coefficient of the x- term (- 10)

the factors are - 15 and + 5 , since

- 15 × 5 = - 75 and - 15 + 5 = - 10 , then

(x - 15)(x + 5) = 0

equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 15 = 0 ⇒ x = 15

Answer:

C

Step-by-step explanation:

I hope this helps!!!!

The best estimate of the fraction 29/40 would be; 0.7

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

We need to find the decimal that best best estimate of the fraction 29/40

A negative divided by a negative is positive, then;

29/40 = 0.72

Therefore, The best estimate of the fraction 29/40 would be; 0.7

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\(\bf Step-by-step~explanation:\)

Kareem's statement: 4:1 is equal to 12:9. Let's see if this is correct.

\(\bf Step ~1:\)

We have to simplify the ratios. Since 4:1 is already simplified, we do not have to do anything with it. 12:9 could be simplified. To do so, we need to find the greatest common factor (GCF) of both numbers. The GCF of 12 and 9 is 3. Since 3 is the GCF for both numbers, we divide them by 3.

\(\bf 12 /3=4\\9/3=3\)

First number: 4

Second number: 3

Ratio: 4:3

\(\bf Step~2:\)

We compare the ratio 4:3 to 4:1. Since they have different values, they are not equivalent to each other.

\(\large\boxed{\bf Our~final~answer: ~Kareem~is~wrong.}\)

\(\bf {Explanation~in~Step~1}\)

4 : 1 and 12 : 9 are not equivalent

Kareem is wrong

Correct question:

Kareem says that the ratio 4:1 is equivalent to the ratio 12:9 because

4 + 8 = 12 and 1 + 8 = 9. Is Kareem correct? Explain how you know

4 : 1 is in its simplest form already

12 : 9

= 12/9

= 4/3

= 4 : 3

Therefore,

4 : 1 and 12 : 9 are not equivalent

Kareem is wrong based on his assumption that 4 + 8 = 12 and 1 + 8 = 9

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Answer:

101

Step-by-step explanation:

The cost of the games is 3 * 49

147

Subtract this from the starting amount

248-147

101

Answer:

\(\frac{1}{96}\)

Step-by-step explanation:

Spinning a 5 is \(\frac{1}{12}\)

Spinning even is \(\frac{1}{2}\)

Spinning multiple of 4 is \(\frac{1}{4}\)

\(\frac{1}{12} *\frac{1}{2} *\frac{1}{4}\)\(=\frac{1}{96}\)

Answer:

43/52

Step-by-step explanation:

The total number of male is 52 according to the table, 43 are righthanded also according to the table so there you go.

Answer:

43/100

Step-by-step explanation:

the total number of people is 100. the number people will be right handed given that they are a male is 43 the probability 43/100

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Given:

The triangle VUW is the right-angled triangle.

Required:

Explanation:

The adjacent side of the angle V is VU=2.

The hypotenuse of the triangle is VW=5.

Use the cosine formula.

Substitute the adjacent side =2, and the hypotenuse = VW=5 in the formula.

Final answer:

∠G+∠H+∠J=180 and ∠K+∠L+∠M=180 from the angle sum property of triangle, ∠H=∠L (3rd Angle Theorem) and ∆GHJ≅∆KLM from ASA congruency theorem.

In the given question we have to prove ∆GHJ congrurnce ∆KLM.

Given that: ∠G≅∠K, ∠J≅∠M, \(\over{HJ}\) ≅ \(\over{LM}\).

As given that;

∠G≅∠K

∠J≅∠M

\(\over{HJ}\) ≅ \(\over{LM}\)

So from the angle sum property of triangle

∠G+∠H+∠J=180................(1)

∠K+∠L+∠M=180.................(2)

Now equation equation 1 and 2

∠G+∠H+∠J=∠K+∠L+∠M

As we know that ∠G=∠K, ∠J=∠M

So now the expression is

∠G+∠H+∠J=∠G+∠L+∠J

After solving ∠H=∠L (3rd Angle Theorem)

Since, ∠H=∠L, HJ=LM and ∠G=∠K, so from the theorem Angle Side Angle(ASA) congruency,

∆GHJ≅∆KLM

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Answer:

≈5.099

Step-by-step explanation:

1) the rule is:

\(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2};\)

2) according to the rule above, the required distance is:

\(d=\sqrt{(-2-3)^2+(-2+3)^2}=\sqrt{26}\)

d≈5.099

The linear and exponential equations for the amount of money in the banks indicates;

TCF Bank Equation

y = 100·x + 1000

Well Fargo Bank Equation

y = (1.06)ˣ

The number of years it will take for both accounts to have the same amount of money is about 17 years

An exponential equation is an equation of the form; y = a·bˣ, where the input variable, x is an exponent.

The equation for calculating the amount in each bank, based on the details are;

TCF Bank;

Amount invested = $1,000

Amount added each year = 100·x

Well Fargo Bank Equation

The percentage of the amount earned as interest each year = 6% = 0.06

The exponential equation for compound interest amount is; y = 1000·(1 + 0.06)ˣ

Therefore; y = 1000·(1.06)ˣ

When the amount in the two accounts have the same amount of money, we get;

1000·(1.06)ˣ = 100·x + 1000

Therefore; (1.06)ˣ = (100·x + 1000)/1000 = 0.1·x + 1

(1.06)ˣ = 0.1·x + 1

Solving the above equation using the substitution method and graphing indicates that we get;

x = 0, and x ≈ 17.125732

Therefore, it takes about 17 years for the two accounts to have the same amount of money

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Speed is the time rate at which an object is moving along a path. Then 0.6×10-8 years will the spaceship take to reach the extrasolar planet.

Speed is the time rate at which an object is moving along a path.

The formula for speed is distance/time

Given that

An extrasolar planet is observed at a distance of 4.2 x 10° kilometers away.

Distance= 4.2 x 10°

A group of scientists has designed a spaceship that can travel at the speed of 7 x 10⁸ kilometers per year

Speed = 7 x 10⁸

Time we need to calculate

Time =Distance/speed

Time = 4.2 x 10°/7 x 10⁸

=0.6×10⁻⁸

Hence 0.6×10-8 years will the spaceship take to reach the extrasolar planet.

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The value of m that satisfies the equation -3 + m = 9 is m = 12.

To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.

-3 + m = 9

To move -3 to the other side, we can add 3 to both sides of the equation:

-3 + 3 + m = 9 + 3

Simplifying, we have:

m = 12

Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.

None of the provided answer options (A, B, C, D) match the correct solution.

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Parallel lines don't have any solutions since they never intersect

Answer:

When the lines are parallel, there are no solutions, and sometimes the two equations will graph as the same line, in which case we have an infinite number of solutions.

Answer:

add up to 90 degree

Step-by-step explanation:

Step-by-step explanation:

The body reverses direction whenever we go from Positve velocity to negative velocity or vice versa.

So here it is (2,7) exclusive then (7,10) exclusive.

A constant speed means a slope of 0. Here it is (3,6).

c. Since speed is non negative, we would reflect any part of the velocity function that is below the time.axis about the time axis

So we would get

Above is the function, don't worry bout the math part.

D. Knowing that acceleration is the derivative of velocity with respect to time, the derivative of any linear function is the slope of that linear function. So if we find the slope of different paths, we will get a constant and then we can graph it

We must use the original graph because acceleration is a vector meaning it can be negative.

We would get

the second graph is acceleration vs time