If c – a = b, which of the following statements is true?
A. a + b = c
B. c + b = a
C. a – c = b
D. b – c = a

Answer:

BC = 6.8

Step-by-step explanation:

The distance from A to B, then from B to C, is the same distance as from A to C.

Thus,

AB + BC = AC

AB = 8x + 8

BC = 4x + 2

AC = 22

AB + BC = AC

(8x + 8) + (4x + 2) = 22

Expanding the parenthesis:

8x + 8 + 4x + 2 = 22

8x + 4x + 8 + 2 = 22

12x + 12 = 22

Subtracting 12 from both sides:

12x = 10

Dividing both sides by 12:

x = 10/12 = 1.2

x = 1.2

We're looking for BC. As we know,

BC = 4x + 2

Let's now put in x = 1.2 into this equation:

BC = 4x + 2

BC = 4 * 1.2 + 2

Since 4 * 1.2 is 4.8:

BC = 4.8 + 2

BC = 6.8

Answer: BC = 6.8

Answer:

90 -4.75x = 75 -3.25x

90-75= 4.75x-3.25x

x= 10

Step-by-step explanation:

Answer:

10 drinks

Step-by-step explanation:

We can set up an equation to find the amount of drinks needed, x.

[tex]90-4.75x = 75-3.25x[/tex]

Now let’s solve for x by isolating it on one side of the equation.

Subtract 75 from both sides:

[tex]15 - 4.75x = -3.25x[/tex]

Add 3.25x to both sides:

[tex]15-1.5x=0[/tex]

Add 1.5x to both sides:

[tex]15 = 1.5x[/tex]

Divide both sides by 1.5:

[tex]x = 10[/tex]

Hope this helped!

Answer:

4,978 because after 3 digits you have to put a coma

Answer:

4,978

Step-by-step explanation:

Answer:

60000

Step-by-step explanation:

Answer:

60,000

Step-by-step explanation:

2 times 30,000 is 60,000

Answer:

Step-by-step explanation:

Let the height (the dependent variable) be h.

Let the independent variable (x) be y

h = 8y + 10

So at birth, these creatures are 10 cm long. At each birthday, they are another 8 cm.

Take the fifth year which is where the table begins.

y= 8*5 + 10

y = 40 + 10

y = 50 cm which is exactly what you got.

Answer:

false

Step-by-step explanation:

Answer:

Alvin: 49

Elga: 40

Step-by-step explanation:

Hey there!☺

[tex]Answer:\boxed{40}[/tex]

[tex]Explanation:[/tex]

Elga's age can be represented as "x". If Elga is x years old, then Alvin's age would be represented as "x+9", since Alvin is 9 years older than Elga.

Their combined age is 89. If you were to write that as an equation in terms of "x", you would have the following equation.

[tex]x+x+9=89[/tex]

Since the question is asking for Elga's age, which is x, you're going to be solving the equation for the value of x.

First add like terms: [tex]x+x+9=89 \rightarrow 2x+9=89[/tex]

Subtract both sides by 9 to leave x alone: [tex]2x+9-9=89-9 \rightarrow 2x=80[/tex]

Divide both sides by 2 to find x: [tex]\frac{2x}{2} = \frac{80}{2} \rightarrow x=40[/tex]

Since x is equal to 40, Elga is 40 years old, and Alvin would be 49 years old.

You can also check if the answer is correct by adding their ages.

[tex]40+49=89\ \br \checkmark[/tex]

Elga is 40 years old.

Hope this helps!

[tex]\text{-TestedHyperr}[/tex]

Answer:

On the y axis (the vertical line titled y) graph a point at 3, then from there rise 3 and walk 1 and plot a point. keep doing this until you can graph a line.

Step-by-step explanation:

hope this helps :)

Answer:

[tex]MP= (4.5,2)[/tex] another way of writing [tex]MP= (\frac{9}{2}, 2)[/tex]

Step-by-step explanation:

[tex]MP= (\frac{x_1+x_2}{2})(\frac{y_1+y_2}{2})[/tex]

[tex]MP= (\frac{7+2}{2})(\frac{0+4}{2})[/tex] 7+2=9 0+1=1

[tex]MP= (\frac{9}{2})(\frac{2}{2})[/tex]  MP= (4.5,2)

The coordinates of the mid - point of XY will be -  M(4.5, 2)

We have two coordinate points - X(7, 0) and  Y(2, 4).

We have to find the coordinates of the mid - point of the line segment XY.

It states that a line with endpoint coordinates as - [x(1), y(1)] and

[x(2), y(2)] has its mid - point at the coordinates -

[tex]$x(m) =\frac{x(1)+x(2)}{2}[/tex]

[tex]$y(m) = \frac{y(1)+y(2)}{2}[/tex]

According to question, we have -

Assume that the coordinates of Mid - Point = M(h, k)

Coordinates of X= (7, 0)

Coordinates of Y= (2, 4)

Using the Mid - Point formula -

h = [tex]\frac{7+2}{2}[/tex] = 4.5

and

k = [tex]\frac{0+4}{2}[/tex] = 2

Hence, the coordinates of the mid - point of XY will be -  M(4.5, 2)

To solve more questions on Mid - points, visit the link below -

brainly.com/question/25377004

#SPJ2

Answer:

Simplify the expression.

−16x

Step-by-step explanation:

Answer:

42 cm^2

Step-by-step explanation:

Base = 21 cm

Height = 4 cm

Area = [tex]\frac{base\times height}{2}[/tex]

Substitute values into the given equation

[tex]A = \frac{21\times 4}{2} \\\\A = \frac{84}{2} \\\\A = 42cm^2[/tex]

This is an isosceles triangle. The two angles opposite the two equal sides are equal. With this knowledge, we now know that the angles are 61, 61, x.

We also know that the sum of all the angles of a triangle is equal to 180 degrees.

61 + 61 + x = 180.

Combine like terms.

122 + x = 180

Subtract 122 from both sides.

x = 58 degrees

Answer:-32

Step-by-step explanation:

You times the two numbers and add a negative sign in front of it

8 would be a negative in this situation and 4 would be a positive. So the problem would look like this:

-8 x 4 = ?

For this particular problem, we would do 8 x 4 which would equal 32. Then we would try to find which one has the greater absolute value.

Absolute Value:

4 = 4

-8 = |8|

Since -8 has the greater absolute value, the answer would be negative.

The Answer: -32

Answer:

x>-2

Step-by-step explanation:

-3x+2<8

Subtract 2 from each side

-3x+2-2<8 -2

-3x < 6

Divide each side by -3. remembering to flip the inequality

-3x/-3 >6/-3

x>-2

Answer:

1049.682 is 75.3% of 1394 or as a fraction is 1049 341/500

Step-by-step explanation:

1394/x=100/75.3

(1394/x)*x=(100/75.3)*x       - we multiply both sides of the equation by x

1394=1.32802124834*x       - we divide both sides of the equation by (1.32802124834) to get x

1394/1.32802124834=x

1049.682=x

x=1049.682

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{1049.682}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{75.3\% \: of \: 1394}[/tex]

Convert 75.3 percent into fraction

To convert a percentage to a fraction, divide it by 100

[tex] \dashrightarrow{ \sf{ \frac{75.3}{100} \times 1394}}[/tex]

Calculate

[tex] \dashrightarrow{ \boxed{ \sf{1049.682}}}[/tex]

Hope I helped!

Best regards! :D

One revolution is completed when a fixed point on the wheel travels a distance equal to the circumference of the wheel, which is 2π (13 cm) = 26π cm.

So we have

1 rev = 26π cm

1 rev = 2π rad

1 min = 60 s

(a) The angular velocity of the wheel is

(35 rev/min) * (2π rad/rev) * (1/60 min/s) = 7π/6 rad/s

or approximately 3.665 rad/s.

(b) The linear velocity is

(35 rev/min) * (26π cm/rev) * (1/60 min/s) = 91π/6 cm/s

or roughly 47.648 cm/s.

The angular velocity of the wheel is 3.665 radians/sec.

The linear velocity is the hamster running is 47.648 cm/sec.

A hamster running in a wheel of radius 13 cm spins the wheel at 35 revolutions per minute.

Angular Velocity It is defined as the rate of change in angular displacement of a particle in a circular motion.

The angular velocity of the wheel is given by;

[tex]\rm 1 \revolution = 2\pi \ radians\\\\Angular \ velocity = 35 \times 2\pi \ radians \ per \ minute\\\\Angular\ velocity = 70\pi \ radians \ per\ minute\\\\1 \ min = 60\ second\\\\Angular \ velocity = 70\pi \times \dfrac{1}{60} \\\rm \\Angular \ velocity = \dfrac{7}{6} \times 3.14 \ radians \ per \ second\\\\Angular \ velocity = 3.65\ radians \ per \ second\\\\[/tex]

The angular velocity of the wheel is 3.665 radians/sec.

Linear velocity definition deals with the measurement of an object’s velocity when it moves along a specific direction.

The linear velocity is the hamster running is given by;

[tex]\rm Linear \ velocity = 35 \times 26\pi \times \dfrac{1}{60}\\\\Linear \ velocity = 35 \times 26 \times 3.14 \times \dfrac{1}{60}\\\\ Linear \ velocity =47.648 \ cm \ per \ second[/tex]

The linear velocity is the hamster running is 47.648 cm/sec.

To know more about Angular velocity click the link given below.

https://brainly.com/question/88155

Answer:

There are 15 friends

Step-by-step explanation:

The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. That is, what is intended with it is to find the fourth term of a proportion knowing the other three.

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) in the same proportion, the rule of three applies as follows:

a ⇒ b

c ⇒ x

Then: [tex]x=\frac{c*b}{a}[/tex]

where a, b and c are known values ​​and x is the value to be calculated.

In this case, the rule of three applies as follows: if 1/20 of a ton is the weight of 1 person, 3/4 of a ton is the weight of how many people?

[tex]number of people =\frac{\frac{3}{4} of a ton*1 person }{\frac{1}{20} of a ton}[/tex]

or, what is the same,

number of people* [tex]\frac{1}{20}[/tex] = [tex]\frac{3}{4}[/tex]

Solving:

number of people= 15

There are 15 friends

Answer:

(4,2)

Step-by-step explanation:

[tex]Midpoint =\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(8,\:5\right),\:\\\left(x_2,\:y_2\right)=\left(0,\:-1\right)\\\\=\left(\frac{0+8}{2},\:\frac{-1+5}{2}\right)\\\\= (\frac{8}{2} , \frac{4}{2} )\\\\Simplify\\=\left(4,\:2\right)[/tex]

Answer:

(4,2)

Step-by-step explanation:

you know why

Answer:

[tex]I=\frac{p-2w}{2}[/tex]

Step-by-step explanation:

[tex]p=2I+2w\\\\p-2w=2I+2w-2w\\\\p-2w=2I\\\\\frac{p-2w}{2}= I[/tex]

Answer:

m = 1

Step-by-step explanation:

4 x 1 + 3 = 7

Answer:  Addition property

Step-by-step explanation:

In the equation 4m + n = 7  , it indicates that n is 3, which means 3 has been added to it to get 4m + 3 = 7   so 3 has been added on each side.

Answer:

Point A reamains unchanged.

Step-by-step explanation:

Let

A(1, -1)

B(1, 1)

C(-4, -1)

D (-4, 1)

REFLECTED OVER Y-AXIS:

When we reflected over Y-AXIS we have to change the sign of X-Coordinates of all vertices so, above given vertices becomes

A(-1, -1)

B(-1, 1)

C(4, -1)

D (4, 1)

REFLECTED OVER X-AXIS:

When we reflected over X-AXIS we have to change the sign of Y-Coordinates of all vertices so, above given vertices becomes

A(-1, 1)

B(-1, -1)

C(4, 1)

D (4,-1)

When we rotated over 180 degree than we have to change the signs of both coordinates of all vertices

A(1, -1)

B(1, 1)

C(-4, -1)

D (-4,1)

we can see that after the opertion of all three processes i.e  reflected over the y-axis, reflected over the x-axis, and rotated 180ºrespectively vertices are same as original vertices so, Rectangle remain unchanged. and point A is also unchanged

Answer:

119.2

Step-by-step explanation:

Given the following :

Mean (m) = 100 years

Standard deviation (sd) = 15 years

closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of the

distribution?

Obtain the Zscore for 90th percentile (0.90) on the z table = 1.28

Zscore = (X - mean) / standard deviation

1.28 = (X - 100) / 15

1.28 × 15 = X - 100

19.2 = X - 100

19.2 + 100 = X

X = 119.2

Using the normal distribution, it is found that an age of 119 years is closest to the 90th percentile.

-------------------

Normal Probability Distribution

The z-score formula is used, which, in a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], is given by:  

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

-------------------

Thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 100}{15}[/tex]

[tex]X - 100 = 15(1.28)[/tex]

[tex]X = 119.2[/tex]

An age of 119 years is closest to the 90th percentile.

A similar problem is given at https://brainly.com/question/15686085

Answer:

(x-7)(x+5) for the first one. ( 3 x − 1 ) ( x + 5 ) = 0 for the second.

Step-by-step explanation:

Answer:

Please see the attached pictures for full solution.