L
9) Consider the following equations:
x= 10-t
t + 50 = x2 + 50
What equation would result from
combining the given equations?

Answer:

Step-by-step explanation:

y=-3x-1

Applying the cosine ratio of trigonometry, the exact value of cos(-60°) which equals cos (π/3) is: C. 1/2.

In trigonometry, the vaue of the cosine ratio is the cosine of the reference angle which equals the ratio of the adjcent side over the hypotenuse.

To get the exact value of cos(-60°), convert 60 to radians.

π radian = 180

60° = (π/3) radians

Note: cos (-θ) = cos θ

Therefore, cos (-π/3) = cos (π/3)

cos (π/3) = 1/2

The exact value of cos(-60°) = 1/2 (option C).

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Answer:

b = 25 degrees

c = 81 degrees

d = 64 degrees

Recall: SOHCAHTOA

Sin M = Opp/Hyp

Reference angle = M

Opp = 3√/21

Hyp = 15

Sin M = (3-√21)/15

Sin M = √21/5

Cos M = Adj/Hyp

Reference angle = M

Adj = 6

Hyp = 15

Cos M = 6/15

Cos M = 2/5

Tan M = Opp/Adj

Reference angle = M

Opp = 3√21

Adj = 6

Tan M = (3√21)/6

Tan M = √21/2

:Therefore: Sin M = √21/5

Cos M = 2/5

Tan M = √21/2

Answer:

[tex]\sf \sin M=\boxed{\dfrac{\sqrt{21}}{5}}[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

[tex]\sf \sin M=\dfrac{3\sqrt{21}}{15}\quad\cos M=\dfrac{6}{15}\quad\tan M=\dfrac{3\sqrt{21}}{6}[/tex]

[tex]\implies \sf \sin M=\dfrac{3\sqrt{21}}{15}=\dfrac{\sqrt{21}}{5}[/tex]

Answer:

20 x 12=240  

Step-by-step explanation:

Answer:

lw + [tex]\frac{1}{2}[/tex] × π × [tex](\frac{l}{2} )^{2}[/tex] ⇒ Answer D is correct

Step-by-step explanation:

First, let us find the area of the semi-circle.

Area = [tex]\frac{1}{2}[/tex] × π × r²

Given that,

diameter of the semi-circle is ⇒ l

∴ radius ⇒ l / 2

Let us find it now.

Area = [tex]\frac{1}{2}[/tex] × π × r²

Area =  [tex]\frac{1}{2}[/tex] × π × [tex](\frac{l}{2} )^{2}[/tex]

Secondly, let us find the area of the rectangle.

Area = length × width

Given that,

length ⇒ l

width ⇒ w

Let us find it now.

Area = length × width

Area = l ×w

Area = lw

And now let us find the total area.

Total area =  Area of the rectangle + Area of the semi - circle

Tota area = lw + [tex]\frac{1}{2}[/tex] × π × [tex](\frac{l}{2} )^{2}[/tex]

Answer:

Step-by-step explanation:

The general standard form of an equation is written in expressed as shown;

(x-a)²+(y-b)² = r²

(a,b) is the centre of the circle and r is the radius

Given the equation of the circle x^2 + y^2 - 4x + 14y +28 =0, we need to find the centre of the circle and its radius.

comparing the equation given with x²+y²+2gx+2fy+c =0

(-g, -f) is the centre

radius = √g²+f²-c

On comparison,

2gx = - 4x

g = -4/2

g = -2

2fy =  14y

f = 14/2

f = 7

c = 28

r = √(-2)²+7²-28

r = √4+49-28

r = √25

r = 5

comparing centre (a,b) to (-g, -f)

a = -g = -(-2)

a = 2

b = -f = -7

b = -7

substituting the centre (a, b) and the radius r into the equation

(x-a)²+(y-b)² = r²

The required equation will be (x-2)²+(y+7)² = 5²

(x-2)²+(y+7)² = 25

Answer:

X=40°

Step-by-step explanation:

40+30=70

40+30=70

70+70=140

140+40=180

The angles will builder has to cut to make the window fit is 40°, 70° and 70°.

Given that, the measures of the three angles of a triangle are x°, (x+30)° and (x+30)°.

The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.

Now, x°+(x+30)°+(x+30)°= 180°

⇒3x+60°=180°

⇒3x=180°-60°

⇒3x=120°

⇒x=40°

So, x°=40°,  (x+30)°= 70°

Therefore, the angles will builder has to cut to make the window fit is 40°, 70° and 70°.

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Answer: C. (4, 0)

Step-by-step explanation:

    We can graph the equation given to solve. See attached.

   The answer to this question is C. (4, 0)

Step-by-step explanation:

-y is the same as writing -1y. if we forget about the y’s, -1 + 2 = 1. so -1y + 2y = 1y, or just y to be simpler :)

i hope this helps :)

[tex]-y+2y=2y-y=(2-1)y=y[/tex]

It is positive because the coefficient is positive.

Answer:

450

Step-by-step explanation:

1. Based on the given conditions, formulate:

1350 x 5 ÷ (5 + 4 + 6)

2. Calculate

[tex]\frac{1350x5}{5 + 4 + 6}[/tex]  The numerator is 1350 multiply by 5

[tex]\frac{6750}{5 + 4 + 6}[/tex]

[tex]\frac{6750}{15}[/tex]

Answer: 450

Answer:

15

Step-by-step explanation:

to get from 10 to 25 you time by 2½

so then times 6 by 2½ and the answer is 15

Answer:

4) 97%

6) 13%

Step-by-step explanation:

4) We are given that 3% for 250 million are diesel.

100% - 3% = 97% NON DIESEL cars

97% of 250 million is 242.45 million.

______________________________

6) We know that 17% (buses) and 70% (cars) are part of that total.

We also know that the total needs to be 100%

So, we simply do this:

100 - (17+70) = 13 (%)

So, 13% of the survey participants had bikes

Answer:

22 ounces is more

Step-by-step explanation:

1 pound is equal to 16 ounces

Answer:

1 pound

Step-by-step explanation:

1pound=16oz 22oz= 1.375pound

Answer:

Step-by-step explanation:

The solution is Option A.

The value of x is given from proportion and x = 10 1/2 or x = 10.5

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the first rectangle be A

The dimensions of the rectangle A = 4 by 3

Let the second rectangle be B

The dimensions of the rectangle B = 14 by x

The two rectangles A and B are similar , so

Now , the proportion equation will be

3 / 4 = x / 14

Multiply by 14 on both sides of the equation , we get

x = ( 14 × 3 ) / 4

x = 42/4

x = 10.5

The value of x = 10 1/2

Therefore , the value of x is 10 1/2

Hence , the value of x of the rectangle is 10 1/2

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Answer:

34

Step-by-step explanation:

Usually when finding the perimeter all you have to do is add the sides.

Answer:

B  at least 103 flights are on time. :)

Step-by-step explanation:

First we need to turn the percentage into a decimal :)

131 x 0.80 = 104.8

The answer should be B  at least 103 flights are on time.

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Answer:

[tex] \frac{7}{8} - \frac{1}{2} = \frac{7 - 4}{8} = \frac{3}{8} [/tex]

Step-by-step explanation:

I hope I helped you! :)

Answer:

\sqrt{45}

Step-by-step explanation:

A^2+B^2=C^2

36+?=81

81-36=45

[tex]\sqrt{45}[/tex]=

Answer:

Step-by-step explanation:

Pythagorean Theorem

Here, we are missing one of the altitudes, so we can arrange the equation to form :

Solving

Answer:

1/3

Step-by-step explanation:

Answer:

1/6  

Step-by-step explanation:

2/3-1/2 =     find the denominator 3×2=6

4/6-3/6 =     rewrite with a denominator of 6

(4-3)/6 = 1/6     subtract numerators

Check the picture below.

so notice the top part of the picture

if we move the "4" and "17" sides  close to each other, till one is on top of the other, the side in red, can never be less than 17 - 4, or 13, it cannot be 13 either, because then both lines will be on on top and we wouldn't have a triangle just a flat-line, so whatever the red line is, it must be more than 13.

notice the bottom part of the picture

if we separate the "4" and "17" sides, and lay them flat, the most the red side can be is 4 + 17 or 21, it can never be greater than 21, it can't be 21 either because if we lay "4" and "17" flat, we lose the triangle and all we'd have is a flat-line.  So whatever the red side is, must be less than 21.

Answer:

280 m³

Step-by-step explanation:

Volume of a Triangular Prism

Solving

Answer:

280

Step-by-step explanation:

So first lets establish the formula for a Triangular Prism :

1/2 * b * h * l

now lets use the mesurements given to substitute into the formula :

1/2 * 7 * 8 * 10

now lets solve it by first multiplying all the whole numbers together!

7 * 8 = 56

56 * 10 = 560

Finally lets multiply 560 by 1/2 or in other words, divide 560 by 2 :

560/2 = 280

Answer:

540

Step-by-step explanation:

Answer:

533.3mph

Step-by-step explanation:

Answer:

length times width equals area LxW=Area

Step-by-step explanation:

so,

4 times 4= 26 yards

1=4 square yards

then 26X4 = 104 square yards

Answer:

Step-by-step explanation:

Answer:

a) [tex]7x-15=20[/tex]

b)     [tex]\frac{20+15}{7}[/tex]

c)  [tex]5[/tex]

Step-by-step explanation: