y = 5x + 4
Write two ordered pairs (x, y) that are solutions
Write two ordered pairs (x, y) that are NOT solutions

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:

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:

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:

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:

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:

[tex]\dfrac{10}{4} \ hour[/tex]

Step-by-step explanation:

Given that :

Jack had 4 hours of school.

He spent 45 minutes in the library

1/2 hour on a science lecture  and;

had a lunch break of 25 minutes

The objective is to determine how much time is left for the school to get over and we are to write the answer as a fraction.

In order to do that, we will have to convert the minutes into hours,

we all know that; 60 minutes = 1 hour.

Then,

45 minutes = (45/60)hour = 3/4 hour

25/60 minutes = 1/4 hour

Therefore, the amount of time left  for the school to get over is:

= [tex]4 - (\dfrac{3}{4}+\dfrac{1}{2}+ \dfrac{1}{4})[/tex]

=  [tex]\dfrac{16-(3+2+1)}{4}[/tex]

= [tex]\dfrac{16-6}{4}[/tex]

= [tex]\dfrac{10}{4} \ hour[/tex]

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:

Hey there!

The solution is where the lines intersect, and here we see that would be (-4,3)

Hope this helps :)

Answer:

it is c because i took test review

Step-by-step explanation:

Answer:

C The solution should be 6, and the cyclists will need to ride 6 laps before the sprint to the finish.

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:

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:

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:

Check the answer below.

Step-by-step explanation:

This is a very trivial but professional question. Note that all of millimetre, centimetre and metres are acceptable metric units but the millimetre is more preferable by builders and architects because:

1. It is easier to work with integer values on building and architectural plans, an advantage given by measuring and recording in millimetre.

2. working in millimetre allows for precision. The builder will record values that are very close to the true value

3. The measurement will be easily readable by anybody that sees it.

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:

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:

[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:

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:

  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:

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:

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:

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:

             [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:

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:

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

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:

(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:

$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!