Simplify this problem. |3r−15| if r<5

Step-by-step explanation:

1. Yes  addition, subtraction, multiplication, and division can be performed on polynomials. like our everyday arithmetic dealings with mathematical operators, polynomials are no exception when it comes to math operators, the four   basic operations addition, subtraction, multiplication, and division can be performed on polynomials as well.

2. It can be less handy plus the operation can get messy if you do not have a good sense/understanding/hold of what you are doing things can get messy.

3. I personally know that the simplest is the addition of polynomials

4. I cant say which is difficult, but the operation that can get things messy  for me most time is the division operation

Answer:

2,666.67 L of water

Step-by-step explanation:

Solve for W:

1) 3200 = 2400 + 0.3w

2) 800 = 0.3w

Divide both sides by 0.3 to get the variable alone

3) (800)/0.3 = (0.3w)/0.3

4) w = 2,666.67 L

Answer:

D. 1.3

Step-by-step explanation:

Perimeter (square) = 4*side

4 = 4*side

side = 1

We have triangle QVR. QV is a hypotenuse.

If we look at the triangle QTR, QT is a hypotenuse.

QV should be less than QT.

Let's find QT using Pythagorean theorem.

c² = a² + b²

QT² = QR² + RT² = 1² + 1² = 2

QT = √2 ≈ 1.4

QV < QT

QV < 1.4

We have 1.3 and 1 that are less than 1.4, but 1 is a length of a leg of the triangle, so 1 is impossible.

Answer D. 1.3

Answer:

45.

Step-by-step explanation:

100% of a number is the number itself. So, 100% of 45 is 45.

Hope this helps!

Answer:it’s 45

Step-by-step explanation:It’s just the whole number nothing less:)

Answer:

L = length of the ladder;

K = distance between wall and the foot of the ladder;  

a = angle between ladder and the ground

cos(a) = K/L,

L=K/cos(a),

L=K/cos(35°),

L=5/cos(35°),

L=6.1 m

Answer: 6.1

Step-by-step explanation:

Answer:

Part 1: 359,007 ft³

Part 2: 216 times smaller

Part 3: 21600%

Step-by-step explanation:

Part 1:

The parameters for the tank are;

The radius of the tank = 70 feet

The volume of a sphere = 4/3·π·r³

Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere

The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3

Plugging in the value for the radius gives

Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.

Part 2:

The dimension of the scale model  = 1/6 × Actual dimension

Therefore, we have the radius of the sphere of the scale model = 1/6 × 70

Which gives;

The radius of the sphere of the scale model = 35/3 = 11.67 feet

The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³

The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times

The number of times smaller the scale model is than the actual volume =  216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.

Part 3:

The percentage of the mock-up, x, to the volume of the actual tank is given as follows

x/100 ×  1662  = 359,007

∴ x = 216 × 100 = 21600%

The percentage of the mock-up, to the volume of the actual tank is 21600%.

Answer:

Part 1: 359,007 ft³

Part 2: 216 times smaller

Part 3: 21600%

Step-by-step explanation:

Part 1:

The parameters for the tank are;

The radius of the tank = 70 feet

The volume of a sphere = 4/3·π·r³

Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere

The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3

Plugging in the value for the radius gives

Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.

Part 2:

The dimension of the scale model  = 1/6 × Actual dimension

Therefore, we have the radius of the sphere of the scale model = 1/6 × 70

Which gives;

The radius of the sphere of the scale model = 35/3 = 11.67 feet

The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³

The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times

The number of times smaller the scale model is than the actual volume =  216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.

Part 3:

The percentage of the mock-up, x, to the volume of the actual tank is given as follows

x/100 ×  1662  = 359,007

∴ x = 216 × 100 = 21600%

The percentage of the mock-up, to the volume of the actual tank is 21600%.

Answer:

here is your answer

Answer:hey guys just saying its 1/52

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

1 to the tenth power is also 1 multiplied by 1 10 times.

1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 = 1

1 to any power will always have the answer of 1.

Answer:

  80°

Step-by-step explanation:

The sum of the measures of the acute angles in a right triangle is 90°. The sum of ratio measures in the ratio 8 : 1 is (8+1) = 9. Thus, each of those measures stands for 90°/9 = 10°. Then the angle ratio is ...

  80° : 10° = 8 : 1

The measure of the largest acute angle in the triangle is ...

  10° × 8 = 80°

Answer: None of them

I think your teacher made a typo. See explanation below for details

=================================================

Explanation:

With math problems like this one, it is often very tricky to find integer solutions. Luckily, we're given a list of choices. Let's plug them in one at a time and see what happens.

If y = 5, then

y^2 - 7x^2 = 11

5^2 - 7x^2 = 11

25 - 7x^2 = 11

-7x^2 = 11-25

-7x^2 = -14

x^2 = -14/(-7)

x^2 = 2

But x^2 = 2 does not have any integer solutions. The two solutions are irrational. So we can rule out choice F.

Repeat for y = 4 and you should find that x^2 = 5/7, which also does not have any integer solutions. Choice G can be ruled out.

Choices H through K are even worse. Not only are there no integer solutions, but there aren't any real number solutions either (there are complex or imaginary solutions though). Plugging in y = 3 leads to x^2 = -2/7 which has imaginary solutions due to applying the square root to a negative radicand. Similar situations happen with J and K as well.

In summary, none of these answer choices are valid. We need to have two integers x and y that satisfy the equation. I think your teacher made a typo somewhere.

Answer:

             [tex]\bold{A_{_{\Delta XYZ}}=927.5\ cm^2}[/tex]

Step-by-step explanation:

m∠Z = 180° - 118° - 28° = 34°

[tex]\sin(28^o)\approx0.4695\\\\\sin(118^o)=\sin(180^o-62^o)=\sin62^o\approx0.8829 \\\\\sin(34^o)\approx0.5592\\\\[/tex]

[tex]\dfrac{\overline{XY}}{\sin Z}=\dfrac{\overline{YZ}}{\sin X}\\\\\\\overline{XY}=\dfrac{\overline{YZ}}{\sin X}\cdot\sin Z\\\\\\\overline{XY}=\dfrac{42}{0.4695}\cdot0.5592\\\\\overline{XZ}=50.024281...\\\\\\A_{_{\Delta XYZ}}=\frac12\cdot\overline{XY}\cdot\overline{YZ}\cdot\sin(\angle Z)\\\\\\A_{_{\Delta XYZ}}\approx\frac12\cdot50.0243\cdot42\cdot0.8829=927.4955...\approx927.5[/tex]

Answer:

(2, 2), (5, 3), (9, 4), and (13, 5).

Step-by-step explanation:

The inverse of a function makes it so that the x-values become y-values, and y-values become x-values.

The current coordinates are (2, 2), (3, 5), (4, 9), and (5, 13).

If the function were inversed, the coordinates would be (2, 2), (5, 3), (9, 4), and (13, 5).

Hope this helps!

Answer:

a) 20 students

b) 20 students

Step-by-step explanation:

a) From the given frequency table, we have to check the number of students that scored above 73.5 and add them up.

Therefore, the number of students that have grades above 73.5 are:

14 + 4 + 2 = 20 students

b) 75 falls in between 74 - 76 and we do not have the individual frequencies of the grades (74, 75, 76).

However, we can use the data we have from the table to make an assumption.

The number of students that have grades below 75 will be:

13 + 5 + 2 = 20 students

Answer:

Given,

Volume of a cone = 1540 cm[tex] {}^{3} [/tex]

Radius ( r ) = 7 cm

π ( pi ) = [tex] \frac{22}{7} [/tex]

Height of cone ( h ) = ?

Now, let's find the height of cone:

Volume of cone = [tex]\pi \: {r}^{2} \frac{h}{3} [/tex]

plug the values

[tex]1540 = \frac{22}{7} \times {(7)}^{2} \times \frac{h}{3} [/tex]

Evaluate

[tex]1540 = \frac{22}{7} \times 49 \times \frac{h}{3} [/tex]

Calculate

[tex]1540 = \frac{154 \: h}{3} [/tex]

Apply cross product property

[tex]154 \: h = 1540 \times 3[/tex]

Calculate the product

[tex]154 \: h = 4620[/tex]

Divide both sides of the equation by 154

[tex] \frac{154 \: h}{154} = \frac{4620}{154} [/tex]

Calculate

[tex]h \: = 30 \: cm[/tex]

Hope this helps...

Best regards!!

Answer:

A. Volume = 462 cm³; Surface Area = 458 cm²

B. Volume

C. Surface area

Step-by-step explanation:

A. Given a rectangular box:

[tex] Width (w) = 3 cm [/tex]

[tex] Height (h) = 14 cm [/tex]

[tex] length (l) = 11 cm [/tex]

=>Volume of the juice box

[tex] Volume (V) = whl [/tex]

[tex] Volume (V) = 3*14*11 [/tex]

[tex] = 3*14*11 = 462 [/tex]

Volume of juice box = 462 cm³

=>Surface area (S.A) of juice box:

[tex] S.A = 2(wl + hl + hw) [/tex]

[tex] S.A = 2(3*11 + 14*11 + 14*3) [/tex]

[tex] S.A = 2(33 + 154 + 42) [/tex]

[tex] S.A = 2(229) [/tex]

[tex] S.A = 458 cm^2 [/tex]

Surface area of juice box = 458 cm²

B. Volume would be used to find the amount of juice the box can hold

C. Surface area would be used to know how much wax to buy to use in coating the box.

Answer:

3

Step-by-step explanation:

We are adding 2 each time

-3 +2 = -1

-1 +2 = 1

To get the next term add 2

1 +2 = 3

Answer: 3

Step-by-step explanation:

Answer:

arc KL=minor arc

arc LJK=major arc

Step-by-step explanation:

so minor arc is a arc which is larger than a semicircle .

a major arc is a circle having measure less than radians.

Answer:

i need help this too

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,

x = 5

Now, let's find the value of C

[tex]c = 3x - 2[/tex]

plug the value of x

[tex] = 3 \times 5 - 2[/tex]

Multiply the numbers

[tex] = 15 - 2[/tex]

Calculate the difference

[tex] = 13[/tex]

Hope this helps..

Best regards!!

Answer:

it is C.

Step-by-step explanation:

The common difference is -7

-27 -(-20)= -27 + 20 = -7

-34 -(-27)= -34 + 27 = -7

-41 -(-34)= -41 + 34 = -7

-48 -(-41)= -48 + 41 = -7

Answer:

Step-by-step explanation:

When we talk about the transformation of functions, we can mention stretching, rotating, dilating, shifting. However, when we want to transform linear functions, there are only two transformations that are worthy in that case, those are vertical stretch or compression and vertical shift.

Now, you may ask, why only vertical transformation? the reason behind that is because horizontal transformation would give the exact same result because it's only a straight line which we are transforming.

Another common question would be, why only two transformations? it's because with these two you can get all the results because it's a straight line.

The image attached shows examples of this.

Answer:

m ∠DBC=80−10=70

m ∠ABC=80+30=110

Step-by-step explanation:

m ∠DBC+m ∠ABC=180

( x−10)+(x+30.)=180

2x+20=180

2x=180-20

2x=160

x=80

>>m ∠DBC=80−10=70

>>m ∠ABC=80+30=110

Answer:

[tex]\boxed{<DBC = 70 degrees}\\\boxed{<ABC = 110 degrees}[/tex]

Step-by-step explanation:

∠ABC and ∠DBC are supplementary which means that the sum of these two angles is equal to 180.

∠ABC + ∠DBC = 180

Given that: ∠ABC = x+30 and ∠DBC = x - 10

So,

=> x+30+x-10 = 180

=> 2x+20 = 180

=> 2x = 180-20

=> 2x = 160

Dividing both sides by 2

=> x = 80

Now, Finding measures of the angles.

=> ∠DBC = x-10 = 80-10 = 70 degrees

=> ∠ABC = x+30 =80+30 = 110 degrees

Answer:

$24.

Step-by-step explanation:

Let's say Carlos has $c of money, and Mariame has $m of money.

c = 2.75m

c + m = 90

2.75m + m = 90

3.75m = 90

m = 24

c + 24 = 90

c = 66

So, Mariame has $24 and Carlos has $66.

Hope this helps!

Answer:

[tex]\boxed{x=1}[/tex]

Step-by-step explanation:

[tex]mean=\frac{sum \: of \: terms}{number \: of \: terms}[/tex]

[tex]2=\frac{2+4+1+1+x+3+2}{7}[/tex]

[tex]2=\frac{13+x}{7}[/tex]

[tex]14=13+x[/tex]

[tex]x=1[/tex]

Answer:

Option B is the correct option.

Step-by-step explanation:

[tex] {(4 - 2)}^{3} - 3 \times 4[/tex]

Subtract the numbers

[tex] = {(2)}^{3 } - 3 \times 4[/tex]

Multiply the numbers

[tex] = {(2)}^{3} - 12[/tex]

Evaluate the power

[tex] = 8 - 12[/tex]

Calculate the difference

[tex] = - 4[/tex]

Hope this helps..

Best regards!!

Answer:

[tex]\boxed{-4}[/tex]

Step-by-step explanation:

[tex](4-2)^3-3 \times 4[/tex]

Brackets or parenthesis are to be evaluated first. Subtract the numbers in the brackets.

[tex](2)^3-3 \times 4[/tex]

Evaluate the power or exponent.

[tex]8-3 \times 4[/tex]

Multiply the numbers.

[tex]8-12[/tex]

Finally, subtract the numbers.

[tex]=-4[/tex]

Answer:

12

Step-by-step explanation:

If you add the ratio you will get 8 and 1 in the ratio number represents

6 people so 5-3=2

Therefore, the no. of girls minus boys= 6×2=12

so you need 12 more boys to make it to be a ratio of 1:1

Answer:

a   1 : 5

Step-by-step explanation:

Blue mables: 3

green and red marbles: 8 + 7 = 15

then, the radio blue:(green+red) is:

3 : 15

simplified unit rate is:

3/3 = 1

15/3 = 5

then:

3:15

is equal to:

1:5

Answer:

a   1 : 5

Answer:

y = 2x+4

Step-by-step explanation:

The y intercept ( where it crosses the y axis ) is 4

The slope is positive because the line goes up from the bottom left to top right

We pick two point ( -2,0) and ( 0,4)

The slope is found by

m= (y2-y1)/(x2-x1)

 = ( 4-0)/(0- -2)

  = 4/ (0+2)

  = 4/2

   = 2

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 2x+4

Answer:

The equation to this line is y=-4x+4

Step-by-step explanation:

If you look at the graph you can see that the y intercept is 4.

To find the slope take two points on the graph and plug it into be y2-y1/x2-x1

I chose (0,-2) and (-1,2) So  2+2=4  and -1-0= -1 so  4/-1= -4