Solve problems involving proportions


Question 20.

If the speed of a boat in still water is 13 mph,

a.) what is its speed going against a current with a rate of x mph?

b.) what is its speed going with a current with a rate of x mph?

Answer: To find how long it takes Kyle to reach school, we can use the formula:

Time = Distance / Speed

Given that Kyle's parents travel at a constant speed of 40 km/h and the distance from their house to school is 60 km, we can substitute these values into the formula:

Time = Distance / Speed = 60 km / 40 km/h

To convert the answer from hours to minutes we have to multiply the result by 60.

Time = (60 km / 40 km/h) * 60 = 1.5 * 60 = 90 minutes

So it takes Kyle 90 minutes to reach school from their house if their speed is constant at 40 km/h and the distance they are traveling is 60 km.

Step-by-step explanation:

Answer:

You can buy 17 oranges for rupee 24.

Step-by-step explanation:

3 dozen = 3 x 12 = 39 oranges

54 ÷ 39 = 1.38461538462

1 orange = rupee 1.38

1.38461538462 x 17 = 23.5384615385

17 oranges = rupee 23.54

If you add the cost of 1 more orange it would cost more than rupee 24 so you can only buy 17 oranges for rupee 24.

Hope this helps :)

Answer:

5/12

Step-by-step explanation:

Use associative property of addition:

2/5 + 5/12 + (-2/5) = (2/5 + (-2/5)) + 5/12  ==> switch 5/12 and -2/5

(2/5 + (-2/5)) + 5/12 =    ==> simplify

(2/5 - 2/5) + 5/12 =

0 + 5/12 = 5/12

Answer:

5

Step-by-step explanation:

We will use the Pythagorean theorem to solve this problem. We know [tex]a^{2} + b^{2} = c^{2}[/tex]. (a, in this case, will be c) Now, we can substitute in our numbers, giving us:

[tex]a^{2} + 12^{2} = 13^{2}[/tex]

Simplifying:

[tex]a^{2} + 144 = 169[/tex]

Subtract 144 from both sides gives us:

[tex]a^{2} = 25[/tex]

Square rooting both sides gives us:

[tex]a = 5[/tex]

So, the missing measurement (c) is 5.

Hope this helped!

Answer: 80

Step-by-step explanation:

280-47=233 people who like cats or dogs

153+138=291 people who like cats, dogs, or both

291-233=58 people who like both

People who like cats = 138-58=80

Answer:

30cm

Step-by-step explanation:

it will be the root of 900cm²

=30cm

Answer:

x = 4

Step-by-step explanation:

We can look at the hypotenuse of both the triangles to find the factor that we multiply by. (In similar triangles, corresponding sides are always in the same ratio)

Big triangle:little triangle

25:5

5:1

So, we have to multiply the corresponding side of the little triangle by 5 to get an equivalent value.

Solve for x:

3x+8 = 4(5) [ratio!!]

3x+8 = 20

(subtract 8 from both sides)

3x = 12

(divide both sides by 3)

x = 4

Thus, we have our answer!

After evaluating the expression 58 + (4x12-40) to the power of 2, we get 4356 or 4.356 ×10³ in scientific notation.

An expression or mathematical expression is a finite combination of symbols that are well-formed in accordance with context-dependent rules. To help define the logical syntax and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping.

Authors frequently distinguish between a formula and an expression, with the former referring to a mathematical object and the latter to a statement about such an object.

We have been asked to evaluate the Expression

​58 + (4x12-40) to the power of 2

⇒ (​58 + (4x12-40))²

Use (a + b)² = a² + b² + 2ab

= 58² + (4x12-40)² + 2(​58)(4x12-40)

= 3364 + (4x12-40)² + 116(4x12-40)

= 3364 + (48-40)² + 116(48-40)

= 3364 + (8)² + 116(8)

= 3364 + 64 + 928

= 4356

= 4.356 ×10³

Thus, After evaluating the expression 58 + (4x12-40) to the power of 2, we get 4356 or 4.356 ×10³ in scientific notation.

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The equation that represents the linear function is y =32x

What is a linear equation explain?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                            The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

A linear function is represented as

                    y = mx + c

The slope is calculated as

          m = y₂ - y₁/x₂ - x₁

        m = 576 - 64/18 - 2

        m = 512/16

         m = 32

The linear equation is then calculated as

        y = 32( x - 2 ) + 64

         y = 32x - 64 + 64

          y =  32x

Hence, the equation that represents the linear function is y =32x

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The complete question is -

A linear function has the table of values shown. The information in the table shows the number of tickets sold on opening night of a movie as a function of the number of hours since the tickets have been on sale. Number of Hours (x) 2 6 18

Number of Tickets Sold (y) 64 192 576

1.Write the equation that gives the number of tickets sold, y, as a linear function of the number of hours, x, since the tickets have been on sale.

Answer:

[tex]\frac{2}{9}[/tex]

Step-by-step explanation:

[tex]A=lw=\frac{1}{3} \cdot \frac{2}{3}=\frac{2}{9}[/tex]

statement CBA ≅ TWR is true.

The theorem that states that two triangle is congruent when there three corresponding sides are equal and all three corresponding angles are also equal.

given, triangle ABC and Triangle RWT both are right-angled.

we examined that three corresponding sides of ABC is equal to the corresponding sides of RWT and same for the three corresponding angles.

we measured, right angle A = right angle R

base length AB = base length RW

hypotenuse BC = hypotenuse WT

Side length AC = side length RT

angle C = angle T

angle B = angle W

as per the properties of congruence theorem ABC and RWT are congruent.

hence the statement CBA ≅ TWR is true.

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5 raised to the fourth power (written as 5^4) is equal to 5 multiplied by itself 4 times. Mathematically, it can be written as:

5^4 = 5 * 5 * 5 * 5 = 625

So, the value of 5 to the fourth power is 625.

I hope this helps :)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5^4}[/tex]

[tex]\mathsf{= 5 \times 5 \times 5 \times 5}[/tex]

[tex]\mathsf{= 25 \times 25}[/tex]

[tex]\mathsf{= 625}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{625}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

yes b is a right answer hope it will help you and please make me brainlist

The percentage of  mass of Cs in the sample is 25%

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. A percentage, indicates hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

To calculate the percentage of  Cs in the sample

100/400 x 100

=25%

To calculate the percentage of cesium (Cs) in the sample

300/400 x 100

=75%

Hence, 25% is the percentage of  Cs in the sample

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Adrian must multiply his money by 1.03 to find his total balance in a year in one step.

The following calculation must be done in order to determine what Adrian should multiply his current balance by in order to find his total balance in a year in one step, assuming that no money will be added to or subtracted from the investment. Adrian invests money in an account that offers simple interest of 3% per year.

Current balance = X

Interest = 3% = 3/100 = 0.03

Interest + principal = 1.03

1.03X = Total balance in a year

Therefore, Adrian must multiply his money by 1.03 to find his total balance in a year in one step.

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Answer:

6x

Step-by-step explanation:

Combine like terms

Answer:

You will need 3 [tex]\frac{11}{15}[/tex] cups of sugar.

Step-by-step explanation:

1 1/3 x 2 4/5

another name for 1 is 3/3

3/3 + 1/3 = 4/3

Another name for 1 is 5/5

5/5 + 5/5 + 4/5 = 14/5

[tex]\frac{4}{3 }[/tex] x [tex]\frac{14}{5}[/tex] = [tex]\frac{56}{15}[/tex]

I can break 56 into 15 + 15 + 15 + 11

[tex]\frac{15}{15}[/tex] + [tex]\frac{15}{15}[/tex] + [tex]\frac{15}{15}[/tex] + [tex]\frac{11}{15}[/tex]  another name for [tex]\frac{15}{15}[/tex] is 1

1 + 1 + 1 + [tex]\frac{11}{15}[/tex]

3 [tex]\frac{11}{15}[/tex]

The required dilated coordinates of the quadrilateral is given as,
D'  {-4, 2}, E' (-8/3, -2), F' (10/3, -4/3), and G'  (-2, 2).

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
Initial corrdiantes

D = (-6, 3)
G = (-3, 3)
E = (-4, -3)
F = (5, -2)

Dilated coordinates of a quadrilateral with by scale factor of 2/3 is given as,
D' = (-6 × 2 / 3, 3 × 2 / 3)

D' = {-4, 2}

Similarly,

G = (-2, 2)
E = (-8/3, -2)
F = (10/3, -4/3)

Thus, the required dilated coordinates of the quadrilateral is given as,
D'  {-4, 2}, E' (-8/3, -2), F' (10/3, -4/3), and G'  (-2, 2).

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Answer:

The answer is, 5² + 12² = AC²

This is the Pythagorean theorem which states that sum of the squares of the two sides of a right angled triangle is equal to the square of the hypotenuse.

base² + height² = hypotenuse² or in this case, 5² + 12² = AC²

Pls mark as brainliest. I really need for no apparent reason. Cheers

Staff at the learning center can teach whole groups of students who need extra help or focus on working one-on-one with a specific child. They work on improving knowledge of academic subjects like biology as well as skills like reading comprehension.

Learning centre instructors work in programmes that assist at-risk students in strengthening their academic skills. Learning centre instructors can work for a private or public learning centre. Learning centre instructors work with students to teach them valuable skills and academic subjects no matter where they work.

Learning centre instructors can teach large groups of students who require extra assistance or work one-on-one with a specific child. They work on improving academic knowledge, such as biology, as well as skills, such as reading comprehension.

They are in charge of creating the overall curriculum and training programme. Learning centre instructors must also have excellent classroom management skills as well as patience in order to work with students who are experiencing difficulties.

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Answer:

11 days

Step-by-step explanation:

It will last: 10/1 : 9/10 = 10/1 x 10/9 = 100/9 = 11,111... days

Answer: 11.1 days

Step-by-step explanation:

Everyday, Sandy uses 9/10 of a bag of cups.

Use unitary method.

9/10 bag - 1 day

10 bag - 10/(9/10) = 100/9 ≈ 11.1 days

Pls mark as brainliest. I really need for no apparent reason. Cheers

Answer:

3.981071706 × 105

Answer:

3.981071706 x 10^5

Step-by-step explanation:

In standard form, a number is written as a decimal multiplied by a power of 10. To convert 398107.1706 to standard form, we can move the decimal point until we have a number between 1 and 10 and a power of 10 that will make the original number.

398107.1706 = 3.981071706 x 10^5

The total number of oranges that the trader bought is 31

A trader bought some oranges at the price of #50 each

He finds that Six of these oranges are rotten

He sells the remaining at #80

He makes a profit of #450

Therefore the number of oranges that the trader bought is

Let y represent the number of oranges that the trader bought

At a price of #50= 50x

6 oranges were rotten= x-6

Profit = 450

450= 80(x-6)-50x

450= 80x-480-50x

450= 80x-50x-480

450= 30x-480

450+480= 30x

930= 30x

x= 930/30

x= 31

Hence the trader bought 31 oranges

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Answer:

y = 5/4x - 8

Step-by-step explanation:

first you convert the equation to y = mx + b

then you add the the -8 into the x and the 2 into the y and solve for b

b = -8 and since it is parallel same slope.

hope this helps :)

The side length of the triangle AC and BC will be 72 and 31. Then the correct option is A.

The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.

The sine law in the triangle ΔABC is given as,

AB / sin C = BC / sin A = AC / sin B

In triangle ABC, ∠A = 25°, ∠C = 55° and AB = 60. Then the third angle is given as,

∠A + ∠B + ∠C = 180°

25° + ∠B + 55° = 180°

∠B = 100°

Then the length of BC is given as,

60 / sin 55° = BC / sin 25°

BC = 30.955

BC ≈ 31

Then the length of AC is given as,

60 / sin 55° = AC / sin 100°

AC = 72.134

AC ≈ 72

The side length of the triangle AC and BC will be 72 and 31. Then the correct option is A.

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Answer: 1/2 PI actually ez not gonna lie

Step-by-step explanation: We know that pi times radius squared times 45/360 equals 1/2 pi. PI*radius^2*0.125 = 1/2PI. Solve algebra to get r^2 = 4 or radius = 2. We need the diameter to find circumference. D = 2*r or D = 4. D * PI * 45/360 = answer. We get 4 * PI * 0.125 = 1/2 PI

The value of x, if x is a real number and the expression, [tex]\frac{x + 2\cdot \mathbf{i}}{1 + \mathbf{i}}[/tex] is a purely imaginary number is x = -2. The correct option is option b.

b. -2

An imaginary number is a number which is obtained by finding the square root of a negative number.

The specified expression is; [tex]\frac{x+2\cdot \mathbf{i}}{1 + \mathbf{i}}[/tex]

Multiplying the numerator and the denominator by the complex conjugate of the denominator, (1 - i), we get;

[tex]\frac{x+2\cdot \mathbf{i}}{1 + \mathbf{i}}\times \frac{1 - \mathbf{i}}{1 - \mathbf{i}} =\frac{x - x \cdot \mathbf{i}+2 \cdot \mathbf{i}-2\cdot \mathbf{i}^2}{1 - \mathbf{i}^2}[/tex]

[tex]\frac{x - x \cdot \mathbf{i}+2 \cdot \mathbf{i}-2\cdot \mathbf{i}^2}{1 - \mathbf{i}^2} = \frac{x + (2 - x)\cdot \mathbf{i} + 2}{1 - (-1)} =\frac{x + (2 - x)\cdot \mathbf{i} + 2}{2}[/tex]

Where x is real, for the number to be purely an imaginary number, we get;

[tex]\dfrac{x + (2 - x)\cdot \mathbf{i} + 2}{2} = \dfrac{x +2+ (2 - x)\cdot \mathbf{i} }{2} = \dfrac{0+ (2 - x)\cdot \mathbf{i} }{2}[/tex]

[tex]\frac{0+ (2 - x)\cdot \mathbf{i} }{2} = \frac{(2 - x)\cdot \mathbf{i} }{2} = \frac{(2-x)}{2} \cdot \mathbf{i}[/tex]

Therefore, for the number to be a purely imaginary number, then; x + 2 in the numerator following the multiplication of the numerator and the denominator by the complex conjugate of 1 + i, which is 1 - i, should be 0, and we get;

x + 2 = 0

x = 0 - 2 = -2

x = -2

The value of x such that the expression (x + 2·i)/(1 + i) is a purely imaginary number is; x = -2

The correct option is; b. -2

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Answer:

The amount of money in the account at the end of 5 years is $9,841.63.

Step-by-step explanation:

The compound interest formula is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = 8000, r = 0.04, n = 4 (because interest is compounded quarterly), and t = 5 (because we are trying to find the balance after 5 years).

So the formula becomes:

A = 8000(1 + 0.04/4)^(4*5)

By plugging the number into the formula we can find the final amount after 5 years

A = $9,841.63

The amount of money in the account at the end of 5 years is $10,404.69, and the interest earned is $2404.69.

To calculate the amount of money in the account at the end of 5 years, we need to use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

To calculate the amount of interest earned, we subtract the initial deposit from the final amount: interest = A - P.

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Answer:

8

Step-by-step explanation:

8 x 5 = 40