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Answer:

X=36.4 or 36.37306696.... and Y=42

Step-by-step explanation:

So you have a 30-60-90 triangle!

Do Not Worry this is a hard subject to understand, but I will try to do my best with helping you. Right now you need to find x and y. All you have is 21.  Under your 60 angle, which is pointing downward, is the 21. And 21 is initially in the spot of x or 1. so 21 is the x(But not the x on the side of 90). I am sorry if this is a bit confusing.

You are then going to take your side which is x, the side that is directly in the path of 90, and it is going to be 21[tex]\sqrt{3[/tex]. Then on the side of your y, which is in the path of your 60, it will be 2 times your x.

The general layout of this is:

x is underneath the side of 90 degrees.

then on the side where 60 degrees and 30 degrees is, is going to be x[tex]\sqrt{3[/tex].

Then the last side, where 30 degrees and 90 degrees lay, will be 2(x).

So all you have to do is plug everything in.

x=36.4 in decimal

y=42(because all you had to do was plug 21 where the x is, because that is where x is in the general layout.)

The value of x = 42 units

The value of y = 21√3 units

The study of the correlation between a right-angled triangle's sides and angles is the focus of one of the most significant branches of mathematics in history: trigonometry. Hipparchus, a Greek mathematician, introduced this idea.

As per the given diagram:

The triangle is a right angle triangle.

Using trigonometric ratios to find x and y:

tan30° = (P/B)

tan30° = (21/y)

(1/√3) = (21/y)

y = 21√3 units

sin30° = (P/H)

(1/2) = (21/x)

x = 2 × 21

x = 42 units

The value of x and y is 42 units and 21√3 units, respectively.

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Answer:

1) [tex]\boxed{Option \ 3}[/tex]

2) [tex]\boxed{Option \ 2}[/tex]

Step-by-step explanation:

A) [tex]x^2-5x+6[/tex]

Using mid term break formula

[tex]x^2-6x+x-6\\x(x-6)+1(x-6)\\Taking \ (x+6) \ as \ common\\(x-6)(x+1)[/tex]

B) [tex]\frac{-20p^{-5}qr^6}{16p^{-2}q^{-3}r^4}[/tex]

Solving it using the two rules: => [tex]\frac{a^m}{a^n} = a^{m-n} \ and \ a^m * a^n = a^{m+n}[/tex]

=> [tex]\frac{-5p^{-3}q^4r^2}{4}[/tex]

We need to put p in the denominator to cancel its negative sign

=> [tex]\frac{-5q^4r^2}{4p^3}[/tex]

Answer:

C and b

Step-by-step explanation:

First question:

The polynomial expression we want to factor is x^2-5x-6

Let's calculate the discriminant to find the roots. The discrminant is b^2-4ac

● b= -5

● a = 1

● c = -6

b^2-4ac= (-5)^2-4*1*(-6) = 25+24 = 49>0

So this polynomial expression has two roots since the discriminant is positive

Let x" and x' be the roots:

● x'= (-b-7)/2a = (5-7)/2= -1

● x"= (-b+7)/2a = (5+7)/2 =6

7 is the root square of the discrminant

The factorization of this pulynomial is:

● a(x - x') (x-x")

● 1*(x-(-1)) (x-6)

● (x+1)(x-6)

So the right answer is c

■■■■■■■■■■■■■■■■■■■■■■■■

Second question:

The expression is: (-20*p^(-5)*q*r^(6))/(16*p^(-2)*q^(-3)*r^3)

To make it easier we will simplify the similar terms one by one.

● Constant terms

-20/16 = (-5*4)/(4*4) = -5/4

● terms containing p

-p^(-5)/p^(-2) = p^(-5-(-2)) = p^(-3) =1/p^3

● terms containg q

q/q^(-3)= q(1-(-3)) = q^4

● terms containg r

r^6/r^4 = r^(6-4) = r^2

Multiply all terms together:

● -5/4 *1/p^3 *q^4 *r^2

● (-5*q^4*r^2)/(4p^3)

The right answer is b

Answer:

y=2 or y-2=0

Step-by-step explanation:

to find the equation first find the slope m points (-1,2) and (5,2)

m=y2-y1/x2-x1 =2-2/5-(-1)=0/6=0

y=mx+b  the slope is zero then y=b=2

Answer: THE ANSWER IS A

Step-by-step explanation:

5-(3/2)^3

=13/8

im a math god

Answer:

3^6-4x=3^3x-3

Step-by-step explanation:

9^3-2x = 27^x-1  ( 9 is 3² and 27 is 3³)

(3²)^3-2x= (3³)^x-1    in case of exponential between brackets , multiply the exponents.

3^6-4x=3^3x-3

Answer:

x = 9/7

Step-by-step explanation:

9^3-2x = 27^x-1

(3^2)^3-2x = (3^3)^x-1

3^2(3-2x) = 3^3(x-1)

2(3-2x) = 3(x-1)

2(-2x+3) = 3x - 3

-4x + 6 = 3x - 3

-4x = 3x - 9

-7x = -9

x = -9/-7

x = 9/7

Explanation:

By definition, i = sqrt(-1)

Which means,

sqrt(-64) = sqrt(-1*64)

sqrt(-64) = sqrt(-1)*sqrt(64)

sqrt(-64) = i*sqrt(8^2)

sqrt(-64) = i*8

sqrt(-64) = 8i

On the second line, I used the rule sqrt(x*y) = sqrt(x)*sqrt(y). The fourth line used the rule sqrt(x^2) = x when x is nonnegative.

Answer:

Click 8i for Correct Answer

Step-by-step explanation:

P + 127 = 550        P = 423

Answer:

P = 423  

P + 127 = 550

Step-by-step explanation:

Answer: C: 60 ft

Step-by-step explanation:

Her pencil is 12 inches and its shadow is 4 inches. Her pencil is 3 times longer than its shadow, so using that logic we can conclude that the tower is 3 times longer than its shadow as well.

[tex]20*3=60[/tex]

The tower is 60 feet tall.

Answer: C. [tex]\sqrt{9} * \sqrt{4}[/tex]

Step-by-step explanation:

There is a square root rule that states [tex]\sqrt{x*y} = \sqrt{x} * \sqrt{y} \\[/tex]

We can apply this rule to this problem.

Given [tex]\sqrt{9*4}[/tex]

We can use the rule to make it equal to [tex]\sqrt{9} * \sqrt{4}[/tex]

This is answer choice C.

Answer: c

Step-by-step explanation: 9*4=36          36* 36 = 1296

9 * 9 = 81      4 * 4 = 16       81 * 16 =  1296    hope this helps

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:

a

Step-by-step explanation:

there are 4 quarts in a gallon.

4 times $0.79 =$3.16

Answer:

The correct option is;

With the compass point on G, construct an arc that intersect GD←→

Step-by-step explanation:

The steps for constructing a parallel line to a given point is as follows;

1) With the straightedge, a transversal is drawn intersecting the giving line and passing through point G

2) Copy the angle formed between the transversal and the given line and the to the point G starting by constructing an arc with the compass on point G to intersect GD←→ then with the compass opening still the same, place the compass on the point of intersection of the arc constructed from point G on GD and construct another arc to intersect the arc previous arc from G to GD

3) The line drawn from the intersection through is a parallel line to EF

Therefore, the correct option is that with the compass point on G, construct an arc that intersect GD←→.

Answer:

A.  With the compass on point D , construct an arc that intersects EF¯¯¯¯¯ and GD←→.

Step-by-step explanation:

I just took the test!

Answer:

3x√5 + 6√10x + 5√3x + 10√6

Step-by-step explanation:

(√3x + √5)(√15x + 2√30)

The above expression can be evaluated as follow:

(√3x + √5)(√15x + 2√30)

Expand

√3x (√15x + 2√30) + √5(√15x + 2√30)

x√45 + 2√90x + √75x + 2√150

Express in the best possible surd form.

x•3√5 + 2•3√10x + 5√3x + 2•5√6

3x√5 + 6√10x + 5√3x + 10√6

We can not simplify further.

Therefore,

(√3x + √5)(√15x + 2√30) =

3x√5 + 6√10x + 5√3x + 10√6

Answer:

a) Multiplica la variable independiente por -7 y luego resta 7

Step-by-step explanation:

Sea [tex]f(x) = -7\cdot x - 7[/tex], las acciones realizadas por la función sobre la variable independiente, esto es, [tex]x[/tex], son:

1) Multiplica la variable por 7.

2) Refleja el resultado anterior con eje de simetría en el eje x. (Multiplicación por -1).

3) Traslada vertical el resultado de 2) siete unidades en la dirección -y.

Por ende, la opción correcta es a).

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:

(C) 1809 in.2

Step-by-step explanation:

Took the test on edg :3

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°

Answer:

30

Step-by-step explanation:

4/5 (x-20)=8

4/5x-4/5*20=8

4/5x-16=8

4/5x=24

x=(24*5)/4

x=30

hope it helps..

Answer:

Slope = m = -5/2

Y-intercept = b = -3

Step-by-step explanation:

[tex]-5x-2y = -6[/tex]

Getting it in a slope - intercept form:

[tex]-2y = 5x+6\\Dividing \ both \ sides \ by \ -2\\y = \frac{-5x}{2} + (-3)\\y = \frac{-5x}{2} -3\\[/tex]

Comparing it wit the slope intercept equation [tex]y = mx+b[/tex] we get

Slope = m = -5/2

Y-intercept = b = -3

Answer:

-5 ≤ x≤ 3

Step-by-step explanation:

The domain is the values for x

x starts and -5 and includes -5 since the circle is closed

and goes to 3 and  includes 3 since the circle is closed

-5 ≤ x≤ 3

Answer:

first option

Step-by-step explanation:

The domain are the values from the x- axis that can be input into the function.

The closed circles at the ends of the graph indicate that x can equal these values.

left side value of x = - 5 and right hand value of x = 3, thus

domain is - 5 ≤ x ≤ 3

Answer:

23/30

Step-by-step explanation:

x/y

(3 5/6)/(3 3/4)

((3*6)+5/6)/((3*4)+ 3/4)

(18+5/6)/(12+3/4)

(23/6)/(15/4)

(23/6)*(4/15)

(23*3)/(6*15)

(69/90)

23/30

Answer:

1 1/45

Step-by-step explanation:

Answer:

cos C

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos C = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{12}{13}[/tex]

=======================================================

Explanation:

The distribution is perfectly symmetrical about the center 6. Notice how the left side is a mirror copy of the right side, due to the heights being the same. Because of this, the mean, median and mode are all the same value and that is 6. The mode is equal to 6 as this is the most frequent value.

The longer way to do this problem is to add up each value shown. We have four copies of '2', six copies of '3', and so on. The total sum you would get is 372. Divide this over 62 because there are 62 smaller green squares. The final result is the mean of 6.

The number closest to the mean of the given distribution is 6. Therefore, option A is the correct answer.

In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).

From the given histogram,

Number         Frequency

    2                      4

    3                      6

    4                      7

    5                      9

    6                     10

    7                      9

    8                      7

    9                      6

   10                      4

Here, the mean = [2(4)+3(6)+4(7)+5(9)+6(10)+7(9)+8(7)+9(6)+10(4)]/[4+6+7+9+10+9+7+6+4]

= [8+18+28+45+60+63+56+54+40]/62

= 372/62

= 6

Therefore, option A is the correct answer.

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Answer:

a

Step-by-step explanation:

The standard form of the equation of a circle is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (0, 0), thus

(x - 0)² + (y - 0)² = r², that is

x² + y² = r² → a

Answer:

72%

Step-by-step explanation:

First find the number of mangoes

200 -56 = 144

Take the number of mangoes over the total

144/200

.72

Change to percent by multiplying by 100

72%

Answer:

72%

Step-by-step explanation:

If 56 of the 200 fruits were durians, then [tex]200-56[/tex] of the fruits were mangoes. Therefore, 144 of the fruits were mangoes.

Now we can set up a percentage proportion to find what percent of 200 144 is.

[tex]\frac{144}{200} = \frac{x}{100}[/tex]

Multiply the cross values and divide by the value thats diagonal to the variable.

[tex]144\cdot100=14400\\14400\div200=72[/tex]

So, the answer is 72%

Hope this helped!

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:

(b) 0

Step-by-step explanation:

Assuming a typo in the last term:

5 (1728)^(1/3) + 100(81)^(1/4) - ( 6(10)^(1/2) )^2

=5(12) + 100(3) -36(10)

=60+300-360

=0

Answer:

[tex]\boxed{\sf (b) \ 0}[/tex]

Step-by-step explanation:

[tex]\sf 5\sqrt[3]{1728} +100\sqrt[4]{81} -(6\sqrt{10} )^2[/tex]

[tex]\sf Evaluate.[/tex]

[tex]\sf 5(12)+100(3) -((6)^2 (\sqrt{10})^2)[/tex]

[tex]\sf 60+300 -(36(10))[/tex]

[tex]\sf 360-360[/tex]

[tex]\sf 0[/tex]

Answer:

15 mL of the solution with 20% water will be needed.

Step-by-step explanation:

Use the inverse relationship

10 mL * (18-15)% = x mL * (20-18)%

x = 10 mL * (3/2) = 15 mL

Answer: 15mL

Step-by-step explanation:

Create a table. Multiply across and add down. The bottom row (Mixture) creates the equation.

                   Qty     ×     %             =      Total          

Solution A     10         15% → 0.15          10(0.15) = 1.5

Solution B      x          20% → 0.20        x(0.20) = 0.20x

Mixture      10 + x   ×    18% → 0.18   =    1.5 + 0.20x

                                  (10 + x)(0.18) = 1.5 + 0.20x

                                    1.8 + 0.18x  = 1.5 + 0.20x

                                    1.8               = 1.5 + 0.02x

                                    0.3              =          0.02x

                                                15  =  x

Answer:  A) 3.2 ft

Step-by-step explanation:

f(4) = -0.3(4)² + 2(4)

     = -4.8 + 8

     =  3.2

Answer:

3.2 feet

Step-by-step explanation:

Answer:

The divisor and dividend have the same signs.

Step-by-step explanation:

Let's look at all of the possible outcomes of dividing with different signs.

Positive / positive = positive

Positive / negative = negative

Negative / positive = negative

Negative / negative = positive

We can see that whenever the signs are the same, the quotient is positive.