Find the value of x and y in the diagram below.
30°
X
y
7
= 7V5, y = 14
B. X= 14, y = 2V3
A. =
C. X=
73
-3.y=14.3
D. x= 14./2,8-73
3

Answer:

y = (1/2)x + 2

Step-by-step explanation:

it is a straight line so it will be in the form of y = mx + c

m = gradient, c = y intercept

Reading from graph it cuts the y-axis at 2,

so c = 2

to find gradient we can pick any 2 points on the line,

e.g (0,2) and (10,7)

gradient = (y1 - y2) / (x1 - x2) = (7 - 2) / (10 - 0)

= 1/2

so the equation is y = (1/2)x + 2

Using slope intercept formula, the equation of the blue line

y = (1/2)x + 2.

The slope intercept form is one of the form to represent" equation of the straight iine".

According to the question,

The graph intercept the y-axis at 2.

Slope intercept formula, y = mx + c where m = slope of the line, c = y- intercept of the line,  x, y as variable.

From given, y-intercept, c = 2.

To find slope of the line take any two points on the line (0,2) and (10,7).

Formula to find slope of the line m = (y₁ -y₂)/(x₁ - x₂).

m = (2-7)/(0-10)=  [tex]\frac{1}{2}[/tex]

Hence, the equation of the blue line  y = (1/2)x + 2.

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Given:

Consider the given expression is

[tex]\log_59+\log_521-\log_57[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]\log_59+\log_521-\log_57[/tex]

It can be written as

[tex]=\log_5(9\times 21)-\log_57[/tex]       [tex][\because \log_ax+\log_ay=log_a(xy)][/tex]

[tex]=\log_5\dfrac{9\times 21}{7}[/tex]       [tex][\because \log_ax-\log_ay=log_a\dfrac{x}{y}][/tex]

[tex]=\log_5(9\times 3)[/tex]

[tex]=\log_527[/tex]

Therefore, the simplified form of the given expression is [tex]\log_527[/tex].

Answer:

8.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

Multiply -6 to the first bracket so it would be

-6+6y-6x This is the answer

Answer:

Vc = (π/3)✓17 ≈ 4.12 ft³

Step-by-step explanation:

h = ✓(4²+1²)

h = ✓17

V = πr²h/3

V = π(1)²✓17/3

V = (π/3)✓17 ≈ 4.12

Answer:

uh the area is 45 for the first one because 15*9 is 135 and 15*6 is 90 because you get 6 from 15-9 to get the length for the triangle. Then 135-90 is 45.

Step-by-step explanation:

The area for the second shape is 114 because you will take 14 multiplied by 12 and you get 168, then you will take 6*9 which is 54 and subtract that from 168, and you should get 114.

The area for the third shape is i dont even know because it doesnt give numbers unless your trying to find it with the letters but at least you got the first two

Answer:

45

Step-by-step explanation:

Answer:

The exponent of the variable of this equation is 2.

And here's the solution to the equation:

[tex]x^{2} +8=5[/tex]

[tex]x^{2} = 5 - 8[/tex]

[tex]x^{2} = -3[/tex]

[tex]x[/tex] ∉ R

Answer:

1504

Step-by-step explanation:

3472-1968=1504

CHECK

1968+1504=3472

Answer:

7. A

8. C

Step-by-step explanation:

7. 2(-2)^2 - 3(-2) + 4 = 18 (A.)

8. 2(3a)^2 - 3(3a) + 4 = C

Answer:

-1/2x + 4.5

Step-by-step explanation:

Find out the slope by substituting the values in the formulas.

y2 - y1 / x2 - x1      6 - 2 / -3 - 5

-1/2

Now find the y-intercept.

y = mx + b

6 = -1/2 (-3) + b

6 = 3/2 + b

9/2 = b

Answer:

angle 6 is equal to 70° vertically opposite angle on the same side of transeversal.

Answer:

draw the picture then put a box around it and label the body parts and that fun stuff

Answer: (9,1)

Step-by-step explanation: This is because x (7) moves left and right, and y (0) moves up and down. the formula would be (x, y) --->(x+2, y+1)

Answer:

14

Step-by-step explanation:

Answer:14.5% of 19 is 13.05, so the value of n would actually be 13.05

Answer:

256

Step-by-step explanation:

Answer:

16 is the answer because 64/4 is 16 so 16*4 is 64 meaning that there are 16 books on each shelf

Step-by-step explanation:

hope this helped

Answer:

See below, please!

Step-by-step explanation:

[tex]\frac{11(8+14)}{5}[/tex]. Use PEMDAS. Sum of 8 and 14 is 22, multiply that by 11, and then divide by 5. Your answer is 48.4.

Hope this helped!

Answer:

Step-by-step explanation:

This means the area of each hexagon inside out starting from the one with unit area is 4/3 of the previous one.

The original hexagon has the area of:

Answer:

(4/3)^98units.

Step-by-step explanation:

By hexagonal property in which cut off the triangles obtained be the joining of m.p of adjacent sides which left 3/4 of total area.

Answer:

[tex]Volume = x^3y^4[/tex]

Step-by-step explanation:

Given

[tex]Length = xy^2[/tex]

[tex]Height = y^2[/tex]

[tex]Width = x^2[/tex]

Required

Determine the volume

The volume is calculated as:

[tex]Volume = Length * Width * Height[/tex]

[tex]Volume = xy^2 * x^2 * y^2[/tex]

This gives:

[tex]Volume = x^3y^4[/tex]

Answer:

14

Step-by-step explanation:

Add all values in "Times spun".

9 + 11 + 7 + 9 + 7 + 7

= 50

The spinner was spun a total of 50 times in the table.

We are looking for information if the spinner is spun 100 times, which is double of 50.

To predict information for spinning 100 times, double the data given in the table.

# of times "5" was spun for 50 spins (in table): 7

Double 7:

7 * 2 = 14

# of times "5" will likely be spun for 100 spins: 14

Or, solve using proportions:

The proportions are given in: (times "5" was spun)/(total spins)

[tex]\frac{7}{50} = \frac{?}{100}[/tex]

Since you double 50 to make 100, double 7 to solve for "?"

[tex]\frac{7}{50} = \frac{14}{100}[/tex]

∴ if you spin the spinner 100 times, you will spin "5" 14 times.

Answer:

14

Step-by-step explanation:

7 * 2 = 14

Answer:

radius r = 3 cm

height h = 10 cm

volume V = 282.743339 cm^3

lateral surface area L = 188.495559 cm^2

top surface area T = 28.2743339 cm^2

base surface area B = 28.2743339 cm^2

total surface area A = 245.044227 cm^2

In Terms of Pi π

volume V = 90 π cm3

lateral surface area L = 60 π cm^2

top surface area T = 9 π cm^2

base surface area B = 9 π cm^2

total surface area A = 78 π cm^2

Step-by-step explanation:

Cylinder Formulas in terms of r and h:

Calculate volume of a cylinder:

V = πr2h

Calculate the lateral surface area of a cylinder (just the curved outside)**:

L = 2πrh

Calculate the top and bottom surface area of a cylinder (2 circles):

T = B = πr2

Total surface area of a closed cylinder is:

A = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)

Agenda: r = radius

h = height

V = volume

L = lateral surface area

T = top surface area

B = base surface area

A = total surface area

π = pi = 3.1415926535898

√ = square root

The value of Surface Area of the cylinder is 245.04 cm².

Surface area is the amount of space covering the outside of a three-dimensional shape.

It is given that the cylinder has

radius r = 3 cm

height h = 10 cm

volume V of the cylinder = πr²h = 282.74 cm³

the lateral surface area of a cylinder

L = 2πrh

lateral surface area L = 188.495559 cm²

the top and bottom surface area of a cylinder (2 circles):

T = B = πr²

top surface area T = 28.2743339 cm²

base surface area B = 28.2743339 cm²

Total surface area of a closed cylinder is:

A = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)

total surface area A = 245.044227 cm²

total surface area A = 78 π cm²

Therefore the value of Surface Area of the cylinder is 245.04 cm².

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Answer:

23.5

Step-by-step explanation:

30.2-6.7=23.5

23.5+6.7=30.2

Answer:

(20×20)+(2×20×30)

400+1200

1600inches^2

Answer:

1600 in^2

Step-by-step explanation:

We only have to add the areas of one square in the centre and 4 surrounding triangles.

area of the square=20×20=400 in^2

area of one triangle=1/2×20×30=300 in^2

area of four triangles=4×300=1200 in^2

So, total surface area of the square pyramid=400+1200=1600 in^2

*The units given should be in^2.

Answer:

a

Step-by-step explanation:

Answer:a and b

Step-by-step explanation:

Answer:

Sofia will be 19 years old

Step-by-step explanation:

First:

What know that David is 30 right now.

David=30

We also know that David is 7 years older than Mark, meaning that David-7=Mark

30-7=23        -Mark

And last we know that Mark is 4 years older than Sofia So we would do 23-4 to get Sofia age,

23-4=19        -Sofia

So in conclusion...

SOFIA: 19  

MARK: 23

DAVID: 30