Solving a two-step equation for y

5y + 12 = 32

a
y=5
b
y=6
c
y=8.8
d
y=4

Answer:

£754.4

Step-by-step explanation:

explanation shown in image provided

Answer:

25 and 31, respectively

Step-by-step explanation:

1. Divide the number of miles (77 1/2) by the number of gallons (3 1/10).

2. Whatever number you get is where you place your dot

Tip: Converting fractions to decimals can make the work easier (in this case [77 1/2=77.5], [3 1/10=3.1], [99 1/5=99.2], and [3 1/5=3.2]

To find the answer to this question the first step is to solve both equations for y, the first is already solved, so we only need to do this with the second one.

According to this, both equations have the same slope, it means that they are parallel lines.

Answer:

33

Step-by-step explanation:

Let's call their ages m and b.

We have:

m = b + 12

m - 17 = 4(b - 17) → m = 4b - 51

b + 12 = 4b - 51

3b = 63

b = 21

m = 21 + 12 = 33

Answer:

33.

Step-by-step explanation:

If Michael's age is x years now then Brandon's age is  x - 12.

17 years ago  Michael was x - 17 years old and this was 4 times  Brandon's age so:

x - 17 = 4(x - 12 - 17)

x - 17 = 4x - 48 - 68

4x - x =  -17 + 48 + 68

3x = 99

x = 33.

So Michael is now 33 years old.

Answer: Circle = 5    Triangle = 2     Square = 6

Step-by-step explanation:  5 + 2 = 7          2 + 6 = 8              6+2 =8, 8 + 5 =13

The amount that Carl will receive after 3 years is $ 27,146.49 when he invested $ 1220 at 9 % compound interest monthly.

We are given that:

Principal amount = P = $ 1,220

Compound interest rate = r = 9 % monthly

Time = 3 years = 3 × 12 months = 36 months.

The amount after 3 years will be given by:

Amount = 1,220 ( 1 + 0.09)³⁶

Amount = 1,220 ( 1.09 )³⁶

Amount = 1220 ( 22.25 )

Amount = $ 27,146.49

Therefore, we get that, the amount that Carl will receive after 3 years is $ 27,146.49 when he invested $ 1220 at 9 % compound interest monthly.

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Answer:14.

Step-by-step explanation:

14.2 is closer to 14 than 15

Answer:

14

Step-by-step explanation:

The nearest whole number in 14.2 is 4.

Since 2 is less than 5, the 4 stays the same.

We get left with 14.

Answer:

W = 81

Step-by-step explanation:

We'll be using the Exterior Angles Theorem for this question

The theorem states that the sum of any two angles of a triangle is equal to the exterior angle of the other angle.

Therefore

(3x-24) + (2x) = 4x + 11

It's just simple algerbra from there

(3x-24) + (2x) = 4x + 11/

5x - 24 = 4x + 11

x-24 = 11

x = 35

BUT WAIT! The question asks for the angle W, not x.

So just plug in x

3(35) - 24

105 - 24

81

Answer:

OPTION C

Step-by-step explanation:

\( \frac{1}{2} (x - \frac{3}{4} ) = \frac{5}{12} \)

\((x - \frac{3}{4} ) = \frac{5}{6} \)

\(x = \frac{3}{4} + \frac{5}{6} \)

\(x = \frac{9 + 10}{12} \)

\(x = \frac{19}{12}

\frac{3}{4} y - \frac{3}{2} = \frac{5}{2} \)

\( \frac{3}{4} y = 4\)

\(y = \frac{16}{3} \)

The maximum speed a 60 g kitten can expect to travel at is 6 mph.

The speed of the car is determined by the mass of the mouse inside it. This is because a 20 g mouse can travel at 3 mph, and the mass of the kitten is three times greater.

Therefore, the car has to be able to provide three times more force to the kitten than the mouse in order for the kitten to travel at the same speed as the mouse. According to Newton's Second Law, the force exerted by the car is equal to the mass of the mouse multiplied by the acceleration of the mouse.

Therefore, the force exerted by the car on the 60 g kitten must be three times greater than the force exerted by the car on the 20 g mouse. This means that the car must be able to accelerate the kitten at three times the acceleration of the mouse, which is 6 mph.

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the latest toy for pet mice is a car that they can drive. the design allows the motor to carry a 20 g mouse at speeds of up to 3 miles per hour. a 60 g kitten could expect to travel at what maximum speed?

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 128 and 144 is 16Divide both the numerator and denominator by the GCD

128 ÷ 16144 ÷ 16Reduced fraction: 89

Therefore, 128/144 simplified to lowest terms is 8/9.

The linear equation that defines the dependent variable, t, in terms of the independent variable, a is t = 4/3a - 1.

Linear equation:

Linear equation is an algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.

The general form of the linear equation is

y = mx + c

where

y = dependent variable

m = slope

x = independent variable

c = y - intercept

Given,

Here we have the table with the values of t and the value of a.

Now, we need to find the linear equation for this table.

In order to find the linear equation, we need the values of slope and the y intercept values.

To find the value of slope we have to take two point from the given table.

They are (4,5) and (12, 11).

Now, apply the value on the slope formula, then we get,

m = (12 - 4) / (11 - 5)

m = 8/6

When we simplify it, then we get,

m = 4/3

Now, we have to use the slope m and the point (4,5), to find the value of y intercept,

Then we get the value of c as,

5 = 4/3 (4) + c

15 = 16 + c

c = -1

Therefore, the linear equation of the table is, t = 4/3a - 1

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If a 20. 0 kg double coconut oscillates on a spring 42. 7 times each minute, then the spring constant of the spring is 689 N/m.

The spring constant, also known as the force constant or stiffness, is a measure of the elasticity of a spring or any other elastic object. It is defined as the force required to stretch or compress a spring by a unit distance.

The period of oscillation of the coconut can be calculated as:

\(T = \frac{60}{42.7} = 1.405\) seconds

The mass of the coconut is 20.0 kg, so we can use the formula for the period of oscillation of a mass on a spring:

\(T=2\pi \sqrt{\frac{m}{k}}\)

where m is the mass of the coconut and k is the spring constant.

Rearranging this formula gives:

\(k = (2\pi)^2 *(\frac{m}{T})^2\)

Substituting the values we have:

\(k = (2\pi)^2 *(\frac{20.0}{1.405})^2\)

k = 689 N/m (to three significant figures)

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Answer:

True

Step-by-step explanation:

(a) The probability of having all six children be girls is (1/2)^6, or 1/64.
(b) The probability of having all six children be the same sex (either all boys or all girls) is (1/2)^6 + (1/2)^6, or 2/64, or 1/32.
(c) The probability of having at least one boy is 1 - 1/64, or 63/64

The probability of having a child of a particular sex is 50%. Given a family with six children, we can calculate the probability of each event as follows:
(a) All the children being girls: the probability is (1/2)^6, or 1/64.
(b) All the children being the same sex (either all boys or all girls): the probability is (1/2)^6 + (1/2)^6, or 2/64, or 1/32.
(c) At least one boy being in the family: the probability is 1 - (1/2)^6, or 63/64. This can be calculated by finding the probability of having no boys (all girls) and then subtracting it from 1.
In summary, the probability of having a particular outcome in a family with six children depends on the number of children of each sex and can be calculated using the formula (1/2)^n, where n is the number of children of a particular sex.


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Complete question:

Assume that the probability of the birth of a child of a particular sex is 50%. In a family with six children, find the probability of each event.

(a) All the children are girls.

(b) All the children are the same sex.

(c) There is at least one boy.

Answer:

PS = 82.8 ; XT = 46.1

Step-by-step explanation:

PZ = \(\sqrt{TP^2 - TZ^2}\) = √(82.8² - 76.5²) = √1003.59

TZ = SZ = 76.5

PS = \(\sqrt{PZ^2 +SZ^2}\) = √(1003.59 + 5852.25) = 82.8 units

XT = RX = 46.1 units

Answer:

x = 16

Step-by-step explanation:

x +  3*x = 64

x + 3x = 64

4x = 64

/4    /4

x = 16

Check:

x +  3*x = 64

16 + 3(16) = 64

16 + 48 = 64

64 = 64

Hope this helps!

Answer:

16 + 48 = 64

Step-by-step explanation:

Answer: An equation could be x = 3y.

Step-by-step explanation:

If Jose has done 100 more science experiments than Gabby and the number of science experiments done by Gabby is x, an expression representing Jose's experiments is 100 + x.

Mathematically, an expression is the combination of variables, constants, values, and numbers using mathematical operands but without an equal symbol (=).

The basic mathematical operands include addition (+), subtraction (-), division (÷), and multiplication (×).

Let the number of science experiments performed by Gabby = x

The number of science experiments performed by Jose = x + 100

x + 100

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Answer:

Yes

Step-by-step explanation:

It is a function because the x value doesnt repeat itself. The x value is the input

The equation is

Haul-n-Save: y= 0.79 x+ 30

Rent It Trucking: y= 0.55 x+ 75.

Given that,

Based on the above information, the equation is as follows:

Haul-n-Save: y= 0.79 x+ 30

Rent It Trucking: y= 0.55 x+ 75.

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Answer:

commutative property

Step-by-step explanation:

it is

He works for 55 hours in order to receive grossly $1,144

From the question, the given parameters are

Hourly rate = $20.80 per hour

Total earnings = $1,144

The number of hours he works for is the quotient of the total earning and the hourly rate

This is represented as

Number of hours =  Total amount /Hourly rate

Substitute the known values in the above equation

So, we have the following equation

Number of hours =  1144/20.8

Evaluate

Number of hours = 55

Hence, the number of hours is 55 hours

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The percentage of 5 7 inches should be very less because on average the height is 65 and that is what it means by mean of the data and the standard deviation is 2.5 that means on average the height goes up or down by 2.5 inches from the mean so what it means is that there can be (65+2.5) Inches or (65-2.5) Inches. now let us sort of do a mathematical guess of this percentage.

We have done a guess that is very close to the actual guess.

Solving for $b$, we get $b² = 144$, so $b = 12$. Therefore, the specific positive number $b$ is $12$.

How to solve the question?

To rewrite the quadratic x² + bx + 44 in the form (x+m)²+ 8, we need to complete the square. To do this, we want to find a value m such that when we expand x+m)², we get x² + bx (the first two terms of the original quadratic).

Expanding (x+m)², we get x² + 2mx + m². To get x² + bx, we need 2mto be equal to bx Thus, m = b².

Now we can substitute this value of m into x+m² and simplify:

(x+m)² + 8 = x+{b}2² + 8 = x²+ bx +b²}{4} + 8(x+m)

2 +8=(x+ 2b ) 2 +8=x 2 +bx+ 4b 2 +8

We want this expression to be equivalent to x² + bx + 44, so we set the coefficients of x² and x equal:

1 = 11=1

b = bb=b

\frac{b^2}{4} + 8 = 44

4b2 +8=44

Solving for b, we get b²= 144, so b = 12. Therefore, the specific positive number b is 12

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Expanding $(x+m)²+8$ gives $x²+2mx+m²+8$. We see that $b$ must be $\boxed{12}$.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation.

Expanding $(x+m)²+8$ gives $x²+2mx+m²+8$.

Notice that $m²+8=44$, so $m=\pm6$. Thus, we have two possible quadratics: $(x+6)²+8$ and $(x-6)²+8$.

Either way, expanding the quadratic gives $x²+12x+44$ or $x²-12x+44$, respectively. Comparing coefficients, we see that $b$ must be $\boxed{12}$.

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The formula for finding the total surface area of ​​the faces of a cylindrical container is 2r(h + r), where r is the radius of the circular base of the cylinder and h is its height.

The cylindrical container has two rounded bottoms and a curved surface. We need to take these two things into account to get the total surface area of ​​the cylindrical container.

The equation for the all-out region of a barrel-shaped compartment is 2r(h + r), where r is the span of the round base and h is the level of the chamber.

The region (2πrh) of a bent surface of a chamber can be gotten by adding the regions (2πr²) of the upper and lower roundabout surfaces. The area of ​​each cylindrical face is taken into account in the resulting formula.

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The question is -

What is the formula for calculating the total surface area of the faces of the cylindrical container?

Answer:

Option (C)

Step-by-step explanation:

Domain of any graph is defined by the x-values or the input values of a function.

Similarly, y-values on the graph of a function define the Range.

In the graph attached, x-values varies from (-∞) to (+∞).

Therefore, Domain of the graphed function will be (-∞, ∞)

Or -∞ < x < ∞

Similarly, y-values of the graph varies from (-∞) to (1)

Therefore, range of the graphed function will be (-∞, 1).

Or -∞ < y < 1

Option (C) will be the answer.

Answer:

569.7

Step-by-step explanation:

30/100×1899=569.7

Answer:

569.7

Step-by-step explanation:

Because 30% is equal to .3, then,

1899*.3 = 569.5

Answer:

d = st, d = 100 x 3

Step-by-step explanation:

distance = speed x time

distance = 100 x 3, therefore, distance = 300, but if you just want the equation, it is d = 100 x 3 or d = st

Step-by-step explanation:

d = 100 x 3.

d= 100n

where n = time the journey took.