[tex] \sqrt[3]{y} = a(c + \frac{1}{x})[/tex]
​

Answer:

See my explanation

Step-by-step explanation:

-2x + (x - 4) = 18

-x - 4 = 18

-x = 22          <- this is wrong in question writing as x = 22

so, x = -22

Answer:

x-intercept → (-5, 0)

Step-by-step explanation:

Let the equation of the line having pairs given in the table is,

y - y' = m(x - x')

m = slope of the line

(x', y') is a point lying on the line.

From the given table,

Two points (33, -22) and (52, -33) lie on the line.

Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                        m = [tex]\frac{-33+22}{52-33}[/tex]

                        m = [tex]-\frac{11}{19}[/tex]

Equation of the line passing through (33, -22) and slope = [tex]-\frac{11}{19}[/tex] will be,

y + 22 = [tex]-\frac{11}{19}(x - 33)[/tex]

For x-intercept y = 0,

0 + 22 = [tex]-\frac{11}{19}(x-33)[/tex]

-38 = x - 33

x = -38 + 33

x = -5

Therefore, x-intercept of the line is (-5, 0).

Answer:

-5,0

Step-by-step explanation:

khan academy

Answer:

O B. 17 units

Step-by-step explanation:

The chord is AC and the radius of the circle is perpendicular to the chord at B. AB = 8.5 units. According to the perpendicular bisector theorem, if the radius of a circle is perpendicular to a chord then the radius bisects the chord. This means that chord AC is bisected by the radius of the circle at point B. The length of the circle is calculated using:

[tex]AB=\frac{AC}{2}\\ AC=2*AB\\cross multiplying:\\AC = 2*8.5\ units\\AC = 17 \ units[/tex]

The length of the chord is 17 units.

Answer:

The answer is 17 units :D

Step-by-step explanation:

Answer:

140 toy cars

Step-by-step explanation:

The ratio of Ed's toy car to Pete's toy car is initially given as 5:2

Ed gave Pete a total number of 30 cars

Let x represent the greatest common factor that exists between both number

Number of Ed's car is represented as 5x

Number of Pete car is represented as 2x

Since they each have an equal number of cars which is 30 then we can solve for x as follows

5x-30=2x+30

Collect the like terms

5x-2x= 30+30

3x= 60

Divide both sides by the coefficient of x which is 3

3x/3=60/3

x=20

Ed's car is 5x, we substitute 20 for x

5(20)

= 100 cars

Pete car is 2x,we substitute 20 for x

2(20)

= 40 cars

Therefore, the total number of cars can be calculated as follows

= 100+40

= 140 toy cars

Hence they have 140 toy cars altogether

Answer:

140

Step-by-step explanation:

Answer:

x = 8

or

x = -4

Step-by-step explanation:

3x² - 12x = 96

Divide both sides by 3

x² - 4x = 32

Add 4 to both sides

x² - 4x + 4 = 32 + 4

(x - 2)² = 6²

Find the square root of both sides

√(x - 2)² = √6²

x - 2 = +/- 6

x - 2 = +6 or -6

x - 2=+6

x=6+2

x=8

x - 2=-6

x=-6+2

x=-4

x = 8

or

x = -4

Answer:

divide the number by 8 and write the remainder like this 10 r 5.Then you get your answer by going through the remainders in an upward direction. So the answer is 125

Answer:

130

Step-by-step explanation:

just did test on plato/edmentum..it was correct

84 (the answer above) is incorrect

Answer:

Hi sorry for late respond but the answer in 130!!

Step-by-step explanation:

Answer:

Devi's present age = 15 years

Devi's Mother's present age = 45 years

Step-by-step explanation:

Let the present age of Devi be x years.

Therefore, mother's present age = 3x

Five years ago:

Devi's age = (x - 5) years

Mother's age =( 3x - 5) years

According to the given condition:

Five years ago:

Devi's mother's age = 4 times Devi's age

3x - 5 = 4( x - 5)

3x - 5 = 4x - 20

20 - 5 = 4x - 3x

15 = x

x = 15 years

3x = 3* 15 = 45 years

Hence,

Devi's present age = 15 years

Devi's Mother's present age = 45 years

Answer:

k= l/3 - 14/3j

Step-by-step explanation:

l = 14j + 3k

Solve for k

l = 14j + 3k

Subtract 14j from both sides

l - 14j =14j + 3k - 14j

l - 14j = 3k

Divide both sides by 3

l - 14j / 3=3k / 3

k= l/3 - 14/3j

Or

1/3(l - 14j) = k

Answer:

Which expression is equivalent to ‐10

k

‐

10

?

Step-by-step explanation:

Answer:

y>9x+6

Step-by-step explanation:

y-9x+(9x)>6+(9x)

y>9x+6

Answer:

x = 4 or x = - [tex]\frac{5}{7}[/tex]

Step-by-step explanation:

Given

(2x - 8)(7x + 5) = 0

Equate each factor to zero and solve for x

2x - 8 = 0 ⇒ 2x = 8 ⇒ x = 4

7x + 5 = 0 ⇒ 7x = - 5 ⇒ x = - [tex]\frac{5}{7}[/tex]

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:

1. True

2. False.

3. True.

Step-by-step explanation:

1. The total area within any continuous probability distribution is equal to 1.00: it is true because the maximum probability (value) is one (1), therefore, the total (maximum) area is also one (1).

Hence, for continuous probability distribution: probability = area.

2. For any continuous probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: False because it has an infinite number of possible values, which can not be counted or uncountable.

Hence, it cannot be computed.

3. For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: True because it has a finite number of possible values, which are countable or can be counted.

Hence, it can be computed.

Answer:

B

Step-by-step explanation:

C is too little and D is too much

Answer:

(B), in which the first two values are 2 and 10.

Step-by-step explanation:

We can tell that this is a proportional relationship because we can examine the numbers in there.

(2,10)

(4,20)

and (6,30).

If you notice, the x value times 5 gets us the y value for every single point there.

Therefore, B is proportional and it's equation is y = 5x.

Hope this helped!

Answer:

B.

Step-by-step explanation:

B. Is the only one that proportional because,

(2,10)

(4,20)

(6,30)

All these x values multiply by 5 to get the y value.

So the equation is y = 5x meaning it is linear and it goes through the origin which makes it proportional.

Thus,

answer choice B is correct.

Hope this helps :)

Answer:

  60°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between sides of a right triangle and angles.

  Tan = Opposite/Adjacent

  tan(T) = SU/ST

  tan(T) = (5√51)/(5√17) = √3

Now, the arctangent function is used to find the angle whose tangent is √3.

 T = arctan(√3) = 60°

Step-by-step explanation:

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Answer:

(5, 11) and (2, 2)

Step-by-step explanation:

y = (x-2)² + 2

y + 4 = 3x

(x-2)² + 2 + 4 = 3x

x² - 4x + 4 + 6 = 3x

x² - 7x + 10 = 0

(x - 5)(x - 2) = 0

x - 5 = 0, x = 5

x - 2 = 0, x = 2

y = (5-2)² + 2 = 11

(5, 11)

y = (2-2)² + 2 = 2

(2, 2)

Answer:

[tex]\large \boxed{\sf \bf \ \text{ The solutions are } x=2, y=2 \text{ and } x=5, y=11.} \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We want to solve this system of equations.

[tex]\begin{cases}&y=(x-2)^2+2\\&y+4=3x\end{cases}[/tex]

This is equivalent to (subtract 4 from the second equation).

[tex]\begin{cases}&y=(x-2)^2+2\\&y=3x-4\end{cases}[/tex]

Then, we can write y = y, meaning:

[tex](x-2)^2+2=3x-4\\\\\text{*** We develop the left side. ***}\\\\x^2-4x+4+2=3x-4 \\\\\text{*** We simplify. *** }\\\\x^2-4x+6=3x-4\\\\\text{*** We subtract 3x-4 from both sides. ***}\\\\x^2-4x+6-3x+4=0\\\\\text{*** We simplify. *** }\\\\x^2-7x+10=0[/tex]

[tex]\text{*** The sum of the zeroes is 7 and the product 10 = 5 x 2 ***}\\\\\text{*** We can factorise. ***}\\\\x^2-5x-2x+10=x(x-5)-2(x-5)=(x-2)(x-5)=0\\\\x-2 = 0 \ \ or \ \ x-5 = 0\\\\x= 2 \ \ or \ \ x=5[/tex]

For x = 2, y =0+2=2 (from the first equation) and for x = 5 y=3*5-4=15-4=11 (from the second equation)

So the solutions are (2,2) and (5,11)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

$24 will be the cost of tennis racquet with weight 25 oz.

Step-by-step explanation:

Given that Price of racquet is inversely proportional to its weight.

i.e.

[tex]Price \propto \dfrac{1}{Weight}[/tex]

We can replace the proportional sign with a constant of proportionality.

[tex]Price = \dfrac{C}{Weight}[/tex]

Where C is a constant named as constant of proportionality.

Given that cost of 20 oz. racquet is $30.00

Putting both the values :

[tex]30 = \dfrac{C}{20}\\\Rightarrow C = 600[/tex]

So, the equation becomes:

[tex]Price = \dfrac{600}{Weight}[/tex]

Now, we have to find the price of 25 oz. racquet.

Putting Weight = 25 oz and finding Price:

[tex]Price = \dfrac{600}{25}\\\Rightarrow Price = \$24[/tex]

So, $24 will be the cost of tennis racquet with weight 25 oz.

Answer:

(C) 1809 in.2

Step-by-step explanation:

Took the test on edg :3

Answer:

(10, 17)

Step-by-step explanation:

It might be easier to explain with a picture or drawing, but I am new to this, so I would try using words.

Assuming the fruit market is on that straight line from Tia's home to Lei's, So we look at both address (coordinates)

From Tia to Lei, x coordinate is from 4 to 12, that's increased by 8, divide by 4, one step is 2.

y coordinate is from 8 to 20, an increase of 12, divide by 4 again, one step is 3.

The fruit market is at 3/4 distance, so 3 steps, on both x and y coordinates.

x: 4+6 = 10

y: 8+9=17

The fruit market is at point (10,17)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The point (x,y) which divides the segment AB with endpoints at A(x₁,y₁) and B(x₂,y₂) in ratio m:n has cordinates

[tex]x= \dfrac{nx_1+nx_2}{m+n}[/tex]

[tex]y= \dfrac{ny_1+ny_2}{m+n}[/tex]

Tia is at P(4, 8) and Lei is at Q(12, 20).

The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then PM : PQ = 3:4 or PM : MQ = 3:1

So,

[tex]x= \dfrac{1.4+3.12}{3+1} = \dfrac{4+36}{4} = \dfrac{40}{4} = 10 \\y= \dfrac{1.8+3.20}{3+1} = \dfrac{8+60}{4} = \dfrac{68}{4} = 17[/tex]

Hence, the fruit market is at point (10,17) which means it is placed at the corner of 10th Street and 17th Avenue.

Learn more about graph here:

brainly.com/question/16608196

#SPJ5

Answer:

We could rewrite 7/2 as 7a + 2

Step-by-step explanation:

Complex numbers is when real numbers [i.e: 1, 1/2, 200, 5/7, etc..) and an imaginary numbers [numbers that give a negative result when squared] are combine together.

Answer:

A

Step-by-step explanation:

Using ZPP we get x = 0, 2x + 4 = 0, x + 5 = 0. Solving these, we get x = 0, x = -2, x = -5.

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:

45°

Step-by-step explanation:

[tex]tan^{-1}(1)[/tex] = 45°

Answer:

[tex]\huge\boxed{\theta=45^o\ \vee\ \theta=225^o}[/tex]

Step-by-step explanation:

[tex]\tan\theta=1[/tex]

[tex]\bold{METHOD\ 1}\\\\\text{Use the table in the attachment}\\\\\tan45^o=1\to\theta=45^o\ \vee\ \theta=45^o+180^o=225^o\\\\\bold{METHOD\ 2}\\\\\tan\theta=1\to\tan^{-1}1=\theta\to\theta=45^o\ \vee\ \theta=225^o[/tex]

Area of a triangle is 1/2 x base x height.

The graphed triangle has height of 2 and base of 2.

Area = /2 x 2 x 2 = 2 square units.

The triangle gets enlarged by a scale factor of 2, so the new height would be 2 x 2 = 4 and the new base would be 2 x 2 = 4

Area of enlarged triangle = 1/2 x 4 x 4 = 8 square units.

The answer is C) 8

Answer:

[tex]\frac{9}{4}/\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]-2\frac{1}{4}[/tex] is equilavalent to [tex]-\frac{9}{4\\}[/tex].

[tex]-\frac{2}{3}[/tex] can stay put.

The equation is division so neither answers #2 and #3 are the correct ones because when dividing fractions the second fraction has to be flipped in order to continue multiplying instead.

In addition, when two negatives are put together the answer must always be positive.  

Hence the answer is [tex]\frac{9}{4}/\frac{3}{2}[/tex].

Answer:

[tex]\frac{7}{12}[/tex] of the cake

Step-by-step explanation:

add [tex]\frac{1}{8}[/tex] and [tex]\frac{1}{6}[/tex] to see the total amount of cake eaten.

a. find the common denominator: 8 x 3 = 24 and 6 x 4 = 24

b. multiply accordingly to get the correct numerator: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex]

c. add: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex] = [tex]\frac{7}{24}[/tex]

subtract found value from total to find left over cake.

a. 24 - 7 = 14

simplify.

a. [tex]\frac{14}{24}[/tex] = [tex]\frac{7}{12}[/tex]

You are left with [tex]\frac{7}{12}[/tex] of the cake.

Answer:

x=15

angle b=7*15=105

angle a=180-105=75

angle c=2x=30

Step-by-step explanation:

b=7x

sum of straight angle :=180

isoceles traingle = 2 sides are equal, and two angles are equal

b+a=180

7x+a=180

sum of traingle =180

2a+c=180

2a+2x=180  first equation

7x+a=180    second equation

solve by elimination ( multiply second equation by 2)

2a+2x=180

2a+14x=360 ( subtract)

2a+2x-2a-14x=180-360

-12x=-180

x=-180/12=

x=15

angle b=7*15=105

angle a=180-105=75

angle c=2x=30

Answer:

[tex]\approx[/tex] 11 litres of water will fit inside the container.

Step-by-step explanation:

As per the given figure, we have a container formed with combination of a right angled cone placed at the top of a right cylinder.

Given:

Height of cylinder, [tex]h_1[/tex] = 15 cm

Diameter of cylinder/ cone, D = 26 cm

Slant height of cone, l = 20 cm

Here, we need to find the volume of container.[tex]\\Volume_{Container} = Volume_{Cylinder}+Volume_{Cone}\\\Rightarrow Volume_{Container} = \pi r_1^2 h_1+\dfrac{1}{3}\pi r_2^2 h_2[/tex]

Here,

[tex]r_1=r_2 = \dfrac{Diameter}{2} = \dfrac{26}{2} =13\ cm[/tex]

To find the Height of Cylinder, we can use the following formula:

[tex]l^2 = r_2^2+h_2^2\\\Rightarrow h_2^2 = 20^2-13^2\\\Rightarrow h_2^2 = 400-169\\\Rightarrow h_2^2 = 231\\\Rightarrow h_2=15.2\ cm \approx 15\ cm[/tex]

Now, putting the values to find the volume of container:

[tex]Volume_{Container} = \pi \times 13^2 \times 15+\dfrac{1}{3}\pi \times 13^2 \times 15\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 15+\pi \times 13^2 \times 5\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 20\\\Rightarrow Volume_{Container} = 10613.2 \approx 10613\ cm^3[/tex]

Converting [tex]cm^{3 }[/tex] to litres:

[tex]10613 cm^3 = 10.613\ litres \approx 11\ litres[/tex]

[tex]\approx[/tex] 11 litres of water will fit inside the container.