Find the missing side of the triangle using the Pythagorean Theorem.​

Answer:

3 games

Step-by-step explanation:

Answer:5 units!

Step-by-step explanation:

.

The value of x will be  5 units  for the sphere that has the volume of (500/3)π cubic units.

From the formula of the volume of sphere,

volume of sphere = 4/3 πr³

where, r is the radius

in our case,

volume = (500/3)π

radius = x

substituting the given values

(500/3)π = (4/3)π *x³

x³ = 125

x= 5 units

Therefore, the value of x will be 5 units.

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Complete question:

The volume of the sphere is 500/3 π cubic units.

What is the value of x?

4 units

5 units

8 units

10 units

Answer:

A

Step-by-step explanation:

Thanks to the given angle, we can say that the triangle formed by tracing another height has two congruent legs

So

x = 9 + 7 = 16

y = √2 * 9^2 = 9√2

Answer:

A

Step-by-step explanation:

Completing the rectangle formed by legs 9 and 7 , gives us a right triangle on the left.

Using the sine ratio and the exact value sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{9}{y}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

y = 9[tex]\sqrt{2}[/tex]

Using the tan ratio in the right triangle and the value tan45° = 1 , then

tan45° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{9}{adj}[/tex] = 1

adj = 9

Then

x = 9 + 7 = 16

B = 7x - 6 is the correct answer.

Answer:

475 students, 125 adults

Step-by-step explanation:

x + y= 600......equation 1

5x +9y= 3500.......equation 2

From equation 1

x +y = 600

x= 600-y

Substitute 600-y for x in equation 2

5(600-y) +9y= 3500

3000-5y+9y= 3500

3000+4y= 3500

4y= 3500-3000

4y= 500

y= 500/4

y= 125

Substitute 125 for y in equation 1

x + y= 600

x + 125= 600

x = 600-125

x= 475

Hence there are 475 students and 125 adults

Answer:

35 ounces

Step-by-step explanation:

If Roger drinks 30% of the water, that means there will be 70% of it left. We can turn percentages into decimals by dividing them by 100. If we multiply 50 by 0.7, we get 35 ounces.

Answer:

Step-by-step explanation:

The equation of the growth is:

Since the target number is 76 we get:

Answer: 46 months

Step-by-step explanation:

Answer:

15 mm

Step-by-step explanation:

Since both pyramids are joined together, this means that the base of the pyramid which is a square have the same dimensions.

Let the length and width of the base be x, hence the dimension of the base is x mm by x mm.

For the first pyramid, the volume is:

V₁ = a²h₁/3; where a is the length of the square base, h₁ is the height.

Since the pyramid has a height of 16 mm, hence:

V₁ = 16x²/3

the second pyramid, the volume is:

V₂ = a²h₂/3; where a is the length of the square base, h₂ is the height.

Since the pyramid has a height of 20 mm, hence:

V₂ = 20x²/3

Since the total volume (V) of the pyramid is 2700 mm³, hence:

V = V₁ + V₂

V = 16x²/3 + 20x²/3

2700 = 16x²/3 + 20x²/3

2700 = 36x²/3

36x² = 8100

x² = 225

x = 15 mm

Answer:

Step-by-step explanation:

The range is the set of y-values.

The graphed function has its range between 0 and 7, both inclusive.

So the range is:

Answer:

y < 5/3

Step-by-step explanation:

3y + 5 < 10

Let's subtract 5.

3y < 5

Okay. We have something manageable. Let's divide by 3.

y < 5/3

That's our answer.

Answer:

x = 3.6

Step-by-step explanation:

[tex]Cos \theta = \frac{adjacent}{hypotenuse} \\\\ \ where \ \theta = 69^\circ , \ adjacent = TS = x ,\ Hypotenuse = SU = 10[/tex]

[tex]cos \ 69 = \frac{x}{10}\\\\x = 10 \times cos \ 69\\\\x = 10 \times 0.3584\\\\x= 3.584 \\\\x = 3.6[/tex]

Answer:

x= -33

Step-by-step explanation:

expand the equation : 2/3x +4 =-18

Then simplify to 2/3x=-22

multiply both sides by 3/2x to get x=-33

Answer:

x = -33

Step-by-step explanation:

2/3(x+6) = -18

x + 6 = (3/2)(-18)

x + 6 = -27

x = -33

The number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.

A system of equations is a set or collection of equations that you deal with all together at once. For a system to have a unique solution, the number of equations must equal the number of unknowns.

For the given situation,

Peter sold a cup of lemon juice = $1.25

Peter sold a cup of apple juice =  $2.50

Total number of cups sold = 155 cups

Total amount = $256

Let number of cup of lemon juice be x and

let number of cup of apple juice be y

The equations for the above statements are

[tex]x + y = 155 ------- (1)\\1.25x +2.50y = 256 ------- (2)[/tex]

From equation 1,

⇒ [tex]x=155-y[/tex]

Now substitute x in equation 2,

⇒ [tex]1.25(155-y)+2.50y=256[/tex]

⇒ [tex]193.75-1.25y+2.50y=256[/tex]

⇒ [tex]1.25y=256-193.75[/tex]

⇒ [tex]1.25y=62.25\\[/tex]

⇒ [tex]y=\frac{62.25}{1.25}[/tex]

⇒ [tex]y=49.8[/tex] ≈ [tex]50[/tex]

Now substitute y in equation 1,

⇒ [tex]x=155-50[/tex]

⇒ [tex]x=105[/tex]

Hence we can conclude that the number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.

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Answer:

I believe the last answer is correct

Step-by-step explanation:

Both runners are gaining money

9514 1404 393

Answer:

  B.  log_b(a) - log_b(d)

Step-by-step explanation:

The applicable rule of logarithms is ...

  log(a/b) = log(a) -log(b)

All the logs need to have the same base.

__

Here, the base is 'b', but the rule still applies:

  [tex]\log_b{\dfrac{a}{d}}=\log_b{(a)}-\log_b{(d)}[/tex]

Answer:

92.99

Step-by-step explanation:

The value of area of sector ABC is,

Area = 93.05 square units.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

In circle B;

⇒ m ∠ABC = 74° and AB = 12 units

Hence, We can formulate;

The value of area of sector ABC is,

Area = (angle / 360)  π r²

Area = (74/360) × 3.14 × 12²

Area = 93.05 square units.

Thus, The value of area of sector ABC is,

Area = 93.05 square units.

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Answer:

x = 67/x^4

Step-by-step explanation:

I did step by step on the whiteboard. I hope it helps!

Step-by-step explanation:

their mean is....

6+3+2+1+3+2+1+3+0+1/10=2.1

3+2+1+1+4+0+1+2+0/10=1.4

1+1+2+2+2+4+3+1+1+1/10=1.8

2+3+3+1+2+2+2+1+7+1/10=2.4

the means are 2.1,1.4,1.8,2.4

the average mean is

21+14+18+24/40

32+45/40

77/40=1.925

the average mean is 1.925

Answer:

[tex]\frac{5\sqrt{2} }{2}[/tex]

Step-by-step explanation:

Divide 5 by [tex]\sqrt{2}[/tex] , then rationalize denominator

Answer:

Solution given:

Since the given triangle is isosceles and right angled triangle

perpendicular [p]=base[b]=x

hypotenuse [h]=5

we have

by using Pythagoras law

p²+b²=h²

x²+x²=5²

2x²=25

x²=25/2

x²=18

x=[tex]\sqrt{\frac{25}{2}}[/tex]

x=[tex]\bold{\frac{5\sqrt{2}}{2}}[/tex]

Answer:

that he lines are not going strait

Step-by-step explanation:

Answer:

894

Step-by-step explanation:

this can be "split" into 3 rectangles.

their areas can be easily calculated. and then we simply sum them all up for the answer.

rectangle 1 on the top

R1 = 5×9 = 45

rectangle 2 in the middle

R2 = (19+5)×(35-9-15) = 24×11 = 264

rectangle 3 at the bottom

R3 = 39×15 = 585

and all together

45+264+585 = 894

Answer:

x = 3

Step-by-step explanation:

Step-by-step explanation:

3(8x-8)/2=64

3(8x-8)=64×2

24x-24=128

24x=128+24

24x=152

24x/24=152/24

x=6.3

Answer:

247.18

Step-by-step explanation:

please watch the diagram carefully to see marked areas

According to given situation cosine law in trigonometry identities used

[tex]c^{2}=b^{2} +a^{2} -2abcosx[/tex] to find the bearing angle of P from R is 67 degree.

If the identities or equations are applicable for all the triangles and not just for right triangles, then they are the triangle identities. These identities will include:

Sine law

Cosine law

Tangent law

According to question,

The angle between RP & RQ.

Using the cosine law

[tex]PQ^{2} = RP^{2} + QR^{2} - 2PR*RQ*cosx\\12^{2}=8^2+10^2-2*8*10cosx\\cosx = \frac{164-144}{160} \\cosx = \frac{20}{160} \\cosx =\frac{1}{8}[/tex]

[tex]x=83[/tex] degree

[tex]150-83=67[/tex]

Hence, the bearing of P from R​ is 67 degree

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Answer:

A. 4, 8, 12

Step-by-step explanation:

there is a scale factor f=2 to "go" from one triangle to the other.

that means all sides of the target triangle are created out of their corresponding side of the source triangle by multiplying them by the scale factor.

so,

2×f = 2×2 = 4

4×f = 4×2 = 8

6×f = 6×2 = 12

The lengths of DE, EF, and DF are 4, 8 and 12 respectively, (option 1)

Two triangles are said to be similar if their corresponding sides are in equal ratio and corresponding angles are congruent.

Given that, Δ ABC~ Δ DEF and the scale factor from Δ ABC to Δ DEF is 2

Since, the scale factor is 2, therefore each side of Δ ABC is increased by 2 in Δ DEF

Therefore,

DE = 2AB

EF = 2BC

DF = 2AC

Therefore,

DE = 4

EF = 8

DF = 12

Hence, the lengths of DE, EF, and DF are 4, 8 and 12 respectively, (option 1)\

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Answer: (-1, 2)

Step-by-step explanation:

Let's start by solving for x in

[tex]-5x+2y=9\\-5x+2y+-2y=9+-2y\\-5x=9+-2y\\\frac{-5x}{-5} =\frac{9+-2y}{-5} \\x=\frac{2}{5} y+\frac{-9}{5}[/tex]

We can now sub this value of x in 3x+5y=7 and solve

[tex]3x+5y=7\\3(\frac{2}{5} y+\frac{-9}{5})+5y=7\\(3)(\frac{2}{5} y)+(3)(\frac{-9}{5})+5y=7\\\frac{6}{5} y+\frac{-27}{5}+5y=7\\\frac{6}{5} y+\frac{25}{5}y +\frac{-27}{5}=7\\\frac{31}{5} y+\frac{-27}{5}=7\\\frac{31}{5} y+\frac{-27}{5}+\frac{27}{5}=7+\frac{27}{5}\\\frac{31}{5} y=\frac{62}{5} \\\frac{\frac{31}{5} y}{\frac{31}{5}} =\frac{\frac{62}{5} }{\frac{31}{5}} \\y=2[/tex]

Now we can sub in 2 for y in one of the equations

[tex]3x+5(2)=7\\3x+10=7\\3x+10-10=7-10\\3x=-3\\\frac{3x}{3} =\frac{-3}{3} \\x=-1[/tex]

x=-1 and y=2 giving us the point (-1, 2)

Answer:

Step-by-step explanation:

Answer:

y = -x - 6

Step-by-step explanation:

Parallel lines have same slope

y = -x + 9   {y = mx  + c}

m = -1  

(x₁, y₁) = (7 , -13)

Equation: y - y₁ = m(x -x₁)

y - [-13] = -1(x -7)

y+ 13 = -x + 7

    y = - x + 7 - 13

y = -x - 6