Paula used these steps to solve an equation:
Step 1: -4(7 + 8) - 21 = 25
Step 2: -4r – 32 - 2x = 25
Step 3: -61 – 32 = 25
Step 4: -6x = 57
Step 5: x = -95
Between which two steps did Paula use the division property of equality?

Step-by-step explanation:

Paolo's expression 3(x+2)+3

Final answer:

To find how much light is transmitted through two screens that each transmit 18% of the light, multiply 18% by itself (0.18 x 0.18), which results in 3.24% of the original light being transmitted through both screens.

To determine how much light is transmitted through two light-blocking screens, we need to calculate the percentage of light that makes it through both screens. The first screen transmits 18% of the light. This means that only 18% of the initial light intensity will pass through the first screen.

When the light that has passed through the first screen encounters the second screen, again only 18% of that light will be transmitted. To find the total amount of light transmitted through two screens, we multiply the transmission rates of each screen:

Transmitted light through two screens = 18% of initial light * 18% = (0.18) * (0.18)

To get the final percentage, we multiply those two percentages:

Final transmission percentage = 0.18 * 0.18 = 0.0324 or 3.24%

Therefore, only 3.24% of the initial light is transmitted through two screens.

Answer:

Plz show the picture that goes long with the question!

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

90=30%x

x=30

200%x=2x=60

Answer:

600

Step-by-step explanation:

30%=0.3

0.3x=90

x=90/0.3=300

200%=2

2(300)=600

Answer:

37 : 46

Step-by-step explanation:

I nickel is equivalent to 0.05 dollars.

So, 37 nickels are equivalent to (0.05 × 37) = 1.85 dollars.

Again, we can write 1 dime is equal to 0.1 dollars.

So, 23 dimes are equivalent to (23 × 0.1) = 2.3 dollars.

Therefore, to compare 37 nickels to 23 dimes as a ratio reduced to lowest term will be 1.85 : 2.3 = 185 : 230 = 37 : 46 (Answer)

Final answer:

To write the comparison of 37 nickels to 23 dimes as a ratio in lowest terms, you convert the value of nickels and dimes to cents and simplify the ratio value-wise, resulting in a simplified ratio of 37:46.

Explanation:

The student is asking to express the comparison of 37 nickels to 23 dimes as a ratio reduced to lowest terms. Since both nickels and dimes are types of coins, it helps to understand that their value does not directly translate to a quantity ratio but rather a value ratio. A nickel is worth 5 cents, and a dime is worth 10 cents. Therefore, the value ratio of nickels to dimes is 5 cents per nickel to 10 cents per dime.

To find the simplified ratio, we can represent the comparison of the value of 37 nickels to 23 dimes as:

This ratio can be reduced by dividing both terms by the greatest common divisor of 185 and 230, which is 5:

So, the simplified ratio is 37:46.

The area of the room that is not covered by the rug is: [tex]21x^3+26x^2-24x+9[/tex]

Step-by-step explanation:

Let L be the length of the room

and

W be the width of the room

Then

L = 3x^2

W = 7x+14

Area of the bedroom:

[tex]A_r = L*W\\=3x^2(7x+14)\\=21x^3+42x^2[/tex]

Area of Rug:

Let S be the side of rug

S = 4x+3

[tex]A_{rug} =S^2\\=(4x+3)^2\\=(4x)^2+2(4x)(3)+(3)^2\\=16x^2+24x+9[/tex]

The area of the room that is not covered by the rug will be obtained by subtracting the area of the rug from the area of the room.

So,

[tex]Area\ of\ room\ not\ covered\ by\ rug =A_r - A_{rug}\\= 21x^3+42x^2-(16x^2+24x+9)\\=21x^3+42x^2-16x^2-24x-9\\=21x^3+26x^2-24x+9[/tex]

Hence,

The area of the room that is not covered by the rug is: [tex]21x^3+26x^2-24x+9[/tex]

Keywords: Rectangle, square

Learn more about area at:

#LearnwithBrainly

Answer:

It is not a right triangle.

Step-by-step explanation:

We can prove this by Pythagorean theorem because it represents to a right triangle.

Pythagorean theorem:

a² + b² = c²

Now substitute the values.

Note: the longest side will represent c

So,

a = 10 m

b = 16 m

c = 20 m

10² + 16² = 20²

The objective here is to make them equal.

100 + 256 = 400

356 ≠ 400

They are not equal so it is not considered a right triangle.

By applying the Pythagorean theorem to the triangle with side lengths of 10 metres,16 metres, and 20 metres, we can verify that it is a right-angled triangle due to the equality 10² + 16² = 20².

In Mathematics, specifically in Geometry, we can determine if a triangle is a right triangle using the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This formula is expressed as a² + b² = c² where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Applying the Pythagorean theorem to the triangle with side lengths of 10 metres,16 metres, and 20 metres, we set 20 metres (the largest measurement) as c (the hypotenuse) and the other two measurements as a and b. Thus, the equation becomes 10² + 16² = 20². After calculating, we find that 100 + 256 does indeed equal 400. Because these values are equal, the triangle is a right angled triangle.

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Answer:

1. Collinear

2. Parallel

3. Oblique

Step-by-step explanation:

1. The system of linear two variable equations are  

3x - 2y = 2 ........... (1) and  

6x - 4y = 4, ⇒ 3x - 2y = 2 ........... (2) {Dividing both sides with 2}

So, equations (1) and (2) are identical.  

Therefore, the lines are collinear. (Answer)

2. The system of linear two variable equations are  

4x - 3y = 12  

⇒ 3y = 4 x - 12

⇒ [tex]y = \frac{4}{3} x - 4[/tex] {In slope-intercept form} ......... (3)

And, - 12x + 9y = 10

⇒ 9y = 12x + 10

⇒ [tex]y = \frac{4}{3} x + \frac{10}{9}[/tex] {In slope-intercept form} .......... (4)

Since, equation (3) and (4) has the same slope, so, they are parallel. (Answer)

3. The system of linear two variable equations are  

3x + 2y = 19

⇒ [tex]y = - \frac{3}{2} x + \frac{19}{2}[/tex] ........... (5)

And, 4x - 5y = 10

⇒ [tex]y = \frac{4}{5}x - 2[/tex] ........ (6)

So, from the equations (5) and (6) we can say that the straight lines are oblique (intersecting). (Answer)

Answer:

you mean

[tex] - 7.2[/tex]

?

if so, then,

[tex] - 7.2 = - \frac{72}{10} [/tex]

[tex] - \frac{36}{5} [/tex]

...

Answer:

The final answer is 4∛7 cm.

Step-by-step explanation:

Given:

Volume of cube is 448 cm³.

Now, to find the length side(a) of cube.

Putting the formula of volume(v) of cube to get the side:

[tex]V = a^{3}[/tex]

[tex]448= a^{3}[/tex]

[tex]\sqrt[3]{448} = a[/tex]

[tex]4\times 4\times 4\times 7 = a[/tex]

[tex]4\sqrt[3]{7} = a[/tex]

The length side of a cube = 4∛7 cm.

Therefore, the final answer is 4∛7 cm.

Answer:

the numbers are 20 and 30

Answer:

-29/6

Step-by-step explanation:

1 1/6=7/6

-3 2/3=-11/3

-11/3-7/6

-22/6-7/6=-29/6

Answer:

x<8

Step-by-step explanation:

Open parenthesis first:

3x-6<18

Put all like terms on one side:

3x<18+6

3x<24

Simplify:

3x<24 -----> Divide both sides by 3 to cancel out the 3 in 3x.

x<8

~Stay golden~ :)

Answer: x<8

Step-by-step explanation:

3(x-2)<18

3x-6<18

+6 +6

3x<24

———-

3 3

x<8

Answer:

9 × 5= 45 .Frankie has 9 nickles.

Step-by-step explanation:

Because 5 divided by 45 equals to 9.

Answer:

19 dimes and 9 nickels

Step-by-step explanation:

Model the situation using two equations, then solve the system.

let n be number of nickels and d be number of dimes.

n + d = 28     <= This equation is about the number of coins.

0.05n + 0.10d =  2.35   <=This equation is about the worth in dollars.

Rearrange n + d = 28.

n = 28 - d

Now we can substitute this equation into the other one.

Sub n =28-d at the "d" variable for the equation 0.05n + 0.10d =  2.35

0.05n + 0.10d =  2.35

Now there is only one variable.

0.05(28 - d) + 0.10d =  2.35   <=distribute this

0.05(28 - d) + 0.10d =  2.35

1.4 - 0.05d + 0.10d = 2.35   <=combine like terms

1.4 + 0.05d = 2.35    <= begin to isolate d

0.05d = 2.35 - 1.4

0.05d = 0.95

d = 0.95/0.05

d = 19

Now that we know d=19, we can substitute it into any equation.

Choose the equation n + d = 28 because the numbers are easier.

n + d = 28

n + 19 = 28    <=isolate n

n = 28 - 19

n = 9

Since n=9 and d=19, Kay has 9 nickels and 19 dimes.

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Answer:

The measure of larger angle is 180°

Step-by-step explanation:

Given as :

For the pentagon

The measure of interior angles are

∠A = x ,

∠B = x ,

∠C = 2 x ,

∠D = 2 x ,

∠E = 3 x

We know, The sum of measure of all interior angles of pentagon = 540°

So, x + x + 2 x + 2 x + 3 x =   540°

or, 9 x =  540°

∴  x = [tex]\frac{540}{9}[/tex]

I.e x = 60°

So, The measure of angles are

∠A =  60°  ,

∠B =  60° ,

∠C = 2 ×  60° = 120° ,

∠D = 2 ×  60° = 120°,

∠E = 3  ×  60° = 180°

So, the measure of larger angle is 180°

Hence The measure of larger angle is 180° Answer

Answer:

We have to choose any one from option B and option C

Step-by-step explanation:

We have to perform a subtraction of two decimal numbers.

(9.43 - 4.286) = (9.430 - 4.286) = 5.144.

Hence, the answer is 5.144 which is given both options B and C.  

In case there are two options with the same value and the value is the answer, then you choose any one of them but not both.

Here in our case, we have to choose any one from option B and option C and we will be rewarded full marks. (Answer)

Answer:

x= -9.3

Step-by-step explanation:

assuming i have to calculate x from the given equation that is

[tex]\frac{5}{6} of x= -8[/tex]

⇒[tex]5x= -48[/tex]

⇒x= -48/5= -9.3

therefore x= -9.3

Answer:

5.898

Step-by-step explanation:

There are 365 days in a year.

There are 24 hours in a day.

There are 60 minutes in an hour.

In a day, there are 60 minutes each hour x 24 hours = 1440 minutes

In a year, there are 1440 minutes per day x 365 days = 525600 minutes

3.1 million = 3,100,000

3,100,000 / 525600 = 5.898 (rounded from 5.89802130898)

To calculate deaths per minute from an annual total of 3.1 million, we divide the total by days in a year, then by hours in a day, and finally by minutes in an hour, resulting in approximately 6 deaths per minute.

To find out how many deaths occur per minute from an annual total of approximately 3.1 million, we use a step-by-step mathematical calculation.

We start by dividing the total annual deaths by the number of days in a year, and then further dividing by the number of hours in a day, and finally by the number of minutes in an hour.

Therefore, on average, there are approximately 6 deaths per minute worldwide given an annual total of 3.1 million deaths.

Answer: y = 5x + 33

Step-by-step explanation:

y-2=5(x+7)

y-2 = 5*x + 35

y = 5x + 33

Answer: y = 5x + 33

Explanation:

First you must write the equation as you see it:

y-2=5(x+7)

Then do the math in side of the parentheses:

y-2 = 5*x + 35

Once you do the rest of the math, you shall have you answer:

y = 5x + 33

Hope this helps! :)

Answer:

$290.25

Step-by-step explanation:

32.25 x 9 = 290.25

Answer:

$290.25

Step-by-step explanation:

You just need to multiply the money and the days together to get your answer

$32.26 times 9 days

Answer: About 32% of the average adult female body is made out of water.

Step-by-step explanation:

According to the data given in the exercise [tex]\frac{8}{25}[/tex] of the body of an average adult female is made out of water.

Then, you need to convert from fraction to percent. The steps are:

1. Divide the numerator of the fraction (In this case the numerator is  8) by the denominator of the fraction (In this case the denominator is 25). Then:

[tex]\frac{8}{25}=0.32[/tex]

2. Multiply the result 0.32 by 100:

[tex]0.32*100=32\%[/tex]

Therefore,  about 32% of the average adult female body is made out of water.

The price of one adult ticket is $ 11 and the price of one student ticket is $ 11

Given that , Mofor’s school is selling tickets to the annual dance competition.  

Let the cost of one adult ticket be $m and the cost of one student tickets be $n.

On the first day of ticket sales the school sold 7 adult tickets and 6 tickets for a total of $143.  

[tex]\text { Then, } 7 \times \text { cost of one adult ticket }+6 \times \text { cost of one student ticket }=\$ 143[/tex]

7m + 6n = 143 ------- eqn (1)

The school took in $187 on the second day by selling 4 adult tickets and 13 student tickets.  

[tex]\text { Then, } 4 \times \text { cost of one adult ticket}+13 \times \text { cost of one student ticket}=\$ 187[/tex]

4m + 13n = 187  ------ eqn (2)

We have to find the price of an adult ticket and the price of a student ticket.

Now, let us solve the equations.

Multiply eqn 1 by 4

28m + 24n = 572  ----- eqn 3

Multiply eqn 2 by 7

28m + 91n = 1309  ---- eqn 4

Now subtract eqn 4 from eqn 3

28m + 24n = 572

28m + 91n = 1309

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

– 67n = - 737

67n = 737

n = 11

Plug in n = 11 in eqn 1

7m + 66 = 143

7m = 143 – 66

m = 11

Hence, the cost of one adult ticket is $ 11 and cost of one student ticket is $11

Answer:

height is 21cm and the base is 14cm

Step-by-step explanation:

Take a look at the equation for the area of a triangle [tex]A = \frac{bh}{2}[/tex]

Write "height of a triangle is 7 cm greater than the base" as an equation:

h = b + 7

Substitute h and the area of the triangle, 147 into the equation for area.

[tex]A = \frac{bh}{2}[/tex]

[tex]147 = \frac{b(b+7)}{2}[/tex] distribute over brackets

[tex]147 = \frac{b²+7b)}{2}[/tex]  get rid of fractions

[tex]147*2 = b²+7b[/tex]

[tex]294 = b²+7b[/tex]

Rearrange to standard for for quadratic equations

0 = b²+7b - 294

standard form is 0 = ax² + bx + c

In this base, the x variable is replaced by "b".

Use the quadratic formula to solve for b. Substitute the other three values.

[tex]x = \frac{-b ±\sqrt{b^{2}-4ac} }{2a}[/tex]

[tex]x = \frac{-(7) ±\sqrt{7^{2}-4(1)(-294)} }{2(1)}[/tex] Simplify

[tex]x = \frac{-7 ±\sqrt{1225} }{2}[/tex]

[tex]x = \frac{-7 ±35 }{2}[/tex]

Split the equation at ±

[tex]x = \frac{-7 +35 }{2}[/tex]

[tex]x = \frac{28}{2}[/tex]

[tex]x = 14[/tex]  <=base

[tex]x = \frac{-7 -35 }{2}[/tex]

[tex]x = \frac{-42}{2}[/tex]

[tex]x = -21[/tex]  <=We know this number is not possible, so its inadmissible.

The base is 14 cm.

Substitute base = 14 in h = b + 7

h = b + 7

h = 14 + 7

h = 21

The height is 21cm.

Therefore, the height is 21cm and the base is 14cm.

Answer:

53/3

Step-by-step explanation:

1 5/6=11/6

3 1/6=19/6

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

11/6+5(19/6)=11/6+95/6=106/6

simplify

53/3

Answer:

Step-by-step explanation:

I think that's it could be wrong

there we go ;)

Answer:

2400

Step-by-step explanation:

Plz do brainliess  answer

Answer: 2,400

Step-by-step explanation: You're rounding  2,500 to the nearest least whole hundred  number, so that would be 2,400 I hope I explained that right...

Answer: shown below

Step-by-step explanation:

It’s hard to explain but,

First you need to find the slope and y intercept of the equation and graph that. Graph y=3x-5. Graph y= -2x+3. Graph y=2. (In case you don’t know, f(x) is y.)

Then use the equation after the “if”. For example, to graph -1 < x < 4 for the equation y= -2x+3, find the numbers -1 and 4 located on the graph and find the points y=-2x+3 has on number -1 and 4. Both numbers are a open circle.

Do the same for the rest of the equations.

For the equation y= 2, the equation is x>4 (there’s a line under >, just can’t add it), Locate 4 on the graph. Find the point above 4. It is a closed circle pointing to the right because it is all numbers greater than or equal to 4.

Then for the equation y= 3x-5, the equation for it is x< -1. (Again, there’s a line under <) Find -1 on the graph. Look for the point y=3x-5 has under -1. It is a closed circle because all numbers are less than or equal to -1.

Answer:

21[tex]w^{10}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

Given

3[tex]w^{5}[/tex] × 7[tex]w^{5}[/tex]

= 3 × 7 × [tex]w^{(5+5)}[/tex]

= 21[tex]w^{10}[/tex]

The equation of line perpendicular to line containing points (-3, 4) and (1, 0) and passes through (-2, 6) in point slope form is y = x + 8

Given that line m contains points (-3, 4) and (1, 0)

We are asked to find the equation of line perpendicular to line containing points (-3, 4) and (1, 0) and passes through (-2, 6)

Let us first find slope of the line "m"

Given two points are (-3, 4) and (1, 0)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]\left(x_{1}, y_{1}\right)=(-3,4) \text { and }\left(x_{2}, y_{2}\right)=(1,0)[/tex]

[tex]m=\frac{0-4}{1-(-3)}=-1[/tex]

Thus slope of line m is -1

We know that product of slope of given line and perpendicular line are always -1

So, we get

[tex]\begin{array}{l}{\text { slope of line } m \times \text { slope of perpendicular line }=-1} \\\\ {-1 \times \text { slope of perpendicular line }=-1} \\\\ {\text { slope of perpendicular line }=1}\end{array}[/tex]

So we have got the slope of perpendicular line is 1 and it passes through (-2, 6)

Let us use the point slope form to find the required equation

The point slope form is given as:

[tex]y - y_1 = m(x - x_1)[/tex]

[tex](x_1, y_1) = (-2, 6)[/tex] and m = 1

y - 6 = 1(x - (-2))

y - 6 = x + 2

y = x + 8

Thus equation of required line in point slope form is y = x + 8