The shadow of a building is 30m long when the angle of elevation of the sun is 56°. Calculate the:
(a) height of the building
(b) length of shadow when the sun is at an angle of 32°. ​

I THINK X IS 2) : -0.75

Answer:

X = 4

Step-by-step explanation:

Remove the fraction first by multiplying with 6 both sides.

Then leave the variable alone by diving with - 5

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Answer:  [tex]\textsf{x= 4}[/tex]

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Given: [tex]\textsf{-5/6x = -10/3}[/tex]

Find:  [tex]\textsf{The value of x}[/tex]

Solution: In order to get the value of x we must multiply both sides by -6/5 to help cancel the coefficient on the left side to leave x by itself.

Multiply both sides by -6/5

Simplify the expression

Therefore, the value of the unknown variable x is 4.

The ratio of Ali's score to Ben's score to Clare's score in its simplest form is  1 : 3.5 : 7

Given data:

Claire's score = 7 * Ali's score

Ben's score = 0.5 * Claire's score

let Ali's score = x

let Ben's score = y

let Claire's score = z

z = 7 * x = 7x

z = 7x

y = 0.5 * z = 1/2 * z = z / 2

plugging the value of z gives

y = 7x / 2

writing the ratios in terms of x gives

Ali : Ben : Claire

x : y : z

x : 7x/2 : 7x

reducing the terms by dividing through by x

1 : 7/2 : 7

OR

1 : 3.5 : 7

clearing the fraction gives

2 : 7 : 14

Therefore, the ratio of Ali's score to Ben's score to Clare's score in its simplest form is  1 : 3.5 : 7

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Answer: X = 2

Step-by-step explanation:

 2(2)+7 = 11 --> 9<11<15

Hope this helps you :)

The center of the circle is (3, -1) and the radius  of the circle is 4

The equation of the circle is given as

x^2 + y^2 - 6x + 2y = 6

The above equation is the standard equation of a circle

Start by converting the above standard equation of a circle to a form other than the standard equation

Using a graphing calculator, we have the following form

(x - 3)^2 + (y + 1)^2 = 4^2

The equation of a circle is represented as

(x - h)^2 + (y - k)^2 = r^2

Where the center is

Center = (h, k)

So, we have

(h, k) = (3, -1)

This means that

Center = (3, -1)

Hence, the center of the circle is (3, -1)

In (a), we have

Using a graphing calculator, we have the following form

(x - 3)^2 + (y + 1)^2 = 4^2

The equation of a circle is represented as

(x - h)^2 + (y - k)^2 = r^2

Where the radius is

Radius = r

So, we have

r = 4

This means that

Radius = 4

Hence, the radius  of the circle is 4

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Answer:

Step-by-step explanation:

sec(2a+6)cos (5a+3)=1

[tex]\frac{cos(5a+3)}{cos(2a+6)} =1\\[/tex]

cos(5a+3)=cos(2a+6)

cos(5a+3)-cos(2a+6)=0

[tex]-2sin(\frac{5a+3+2a+6)}{2} )sin(\frac{5a+3-2a-6)}{2} )=0\\-2sin(\frac{7a+9}{2} )sin(\frac{3a-3}{2} )=0\\either sin (\frac{7a+9}{2} )=0=sin ~n\pi \\\frac{7a+9}{2} =n~\pi \\7a+9=2n~\pi \\7a=2n~\pi -9\\a=\frac{2n\pi-9 }{7} \\where~n~is~an~integer.[/tex]

or

[tex]\sin\frac{3a-3}{2} =0=\sin ~n\pi \\3a-3=2n\pi \\3a=2n\pi+3\\a=\frac{2~n\pi+3 }{3}[/tex]

where n is an integer.

Answer:The answer is 2

no time for explonations

Answer:

x < - 9 or x > 1

Step-by-step explanation:

inequalities of the type | x | > a have a solution of the form

x < - a or x > a

| 2x + 8 | > 10 is of this type , then

2x + 8 < - 10 or 2x + 8 > 10 ( subtract 8 from both sides of each inequality) )

2x < - 18 or 2x > 2 ( divide both sides of each by 2 )

x < - 9 or x > 1

Answer:

The girls ran 8 laps in one hour, for the boys it is 48:6

Step-by-step explanation:

The girls ran 4 laps in 30 minutes so per hour is was be 8 laps because 4x2. So on the paper it would be 4x2=8

For the boys it would be 8x6 which is 48 dollars in one hour and 6 laps per hour so it would be 48:6 so just put 8x6=48 and it should work.

Answer:

horizontal line isywgwueve

Step-by-step explanation:

equivalent fractions are all fractions with different numbers in numerator and denominator, but after simplifying they have the same value.

like 1/2 and 3/6 are equivalent fractions to each other.

so, the equivalent fractions for 3/25 are

a/a × 3/25

for any "a".

e.g.

6/50, 15/125, 300/2500, ...

Based on the number of pounds of egg salad to the price of dollars, the unit price of the salad can be found to be A. $5 / 1 lb

The unit price of the pounds of egg salad can be found as:

= Price of egg salad / Weight of egg salad

When the weight is 1, the unit price from the graph is:
=  $5 / 1 lb

When the weight is 2, the unit price is:

= 10 / 2

= 5 / 1 in simpler terms

When the weight is 3, the unit price is:

= 15 / 3

= 5 / 1 in simpler terms

In conclusion, the unit price of salad is $5 / 1 lb

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The required measure of the line DE segment is 29.

What does a line in mathematics mean?

(9) Given ,

               DF = 42

Here,

DF = DE + EF

From the given put the values of  DF = 42, DE = 7x +1 and EF = 4x - 3

42 = 7x + 1 + 4x - 3

42 = 11x - 2

11x = 44

x = 4

DE = 7x + 1

Put the value of x in above equation,

DE = 7 * 4  + 1

DE = 28 + 1

DE = 29

Thus, the required measure of the DE segment is 29.

( 10 )  JL = JK + KL

10x - 2 = ( 5x - 8 ) + ( 7x - 12 )

    2x = 18

  x = 9

∴KL = 7x - 12 = 7 * 9 - 12   ⇒63 - 12 = 51

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66.00 divided by 4 equals 16.5

[tex]cos(62) = \frac{ab}{cb} \\ ab = cb.cos(62) \\ ab = 12.cos(62) \approx5.6[/tex]

Answer:

p =12/7

Step-by-step explanation:

Answer:

p = 12/7

Step-by-step explanation:

7p - 4 = 8

    +4   +4

7p = 12

/        /

7       7

p = 12/7

If a random sample of 100 individuals finds a sample mean value of 22 and sample standard deviation of 3. The 99% confidence interval for the population mean is: A. [21.23 , 22.77].

Using this formula

Confidence interval=Sample means± (z-score× Standard deviation/√Sample size)

Let plug in the formula

The corresponding z-scores for 99% confidence interval is ± 2.575

Hence:

Confidence interval=22± (2.575×3÷√100)

Confidence interval=22± (2.575×3÷10)

Confidence interval=22± (2.575×0.3)

Confidence interval=22± 0.7725

Confidence interval=(22-0.7725); (22+ 0.7725)

Confidence interval=21.23, 22.77

Therefore If a random sample of 100 individuals finds a sample mean value of 22 and sample standard deviation of 3. The 99% confidence interval for the population mean is: A. [21.23 , 22.77].

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Answer:

5:2

Step-by-step explanation:

A ratio is basically a fraction but horizontally for eg. this: 5:8! This question is asking us to find the ratio of the emails that Jamie received to the emails that she answered.

According to the question, Jamie got 20 emails and responds to 8 of them. The ratio would look like this: 20:8 (because a ratio is just a fraction but horizontal, doesn't mean that there will be mixed numbers!) but not this 8:20. Ratios have a specific order that they have to be in and that will vary depending on the question. If the question says to find the ratio of emails that Jamie responded to to the emails that she received, then in this case 8:20 would be correct.

For now, the answer is 20:8. However, we still need to simplify it by finding its lowest common factor (unless the question asks you to not simplify it, it's better to simplify the answer like a fraction). The lowest common factor would be 4 for 20 and 8. 4 goes in 20 5 times sand 4 goes into 8 2 times.

Your final answer should be: 5:2

If you have any further questions please ask!

Answer:

Step-by-step explanation:

Given square TUVW, you want the perimeter and area of square T'U'V'W' after it has been dilated by a factor of 5/2 and translated by (0, -8).

Counting grid squares, or reading coordinates, we find the length of a side of square TUVW to be 8 units. Then the perimeter is ...

  P = 4s = 4·8 = 32 . . . . units

After dilation, the perimeter of the square is the preimage value multiplied by the dilation factor.

 perimeter of T'U'V'W' = (5/2)(perimeter of TUVW) = (5/2)(32 units)

  perimeter of T'U'V'W' = 80 units.

The area is the square of the side length. The side length of T'U'V'W' is ...

  s' = (5/2)(8) = 20 . . . . units

Then the area is

  A' = (s')² = (20 units)² = 400 units²

area of T'U'V'W' is 400 units².

__

Additional comment

Translation is a rigid transformation. It does not change the dimensions, so does not change the perimeter or area of the dilated square.

Keri's total score in her last gymnastics which had three different types of acts is 17.25.

A decimal separates the whole part and the integer part of a given number. Decimal can also be written as fractions.

Keri in her last gymnastics competition scored a 5.65 on the floor exercise, 5.85 on the vault, and 5.57 on balance.

∴ Her total score will be the sum of all the scores she obtained in all those three performances which are,

= ( 5.65 + 5.85 + 5.75).

= 17.25.

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The amount of the check with 6 percent of the amount invested was (2) $27.00.

So, 6% of $450:
Then,

Therefore, the amount of the check with 6 percent of the amount invested was (2) $27.00.

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Width of the box is 8 inches and length is 11 inches.

Height of the box is 9 inches given

Length of the box is 3 inches more than the width.

Let the width be x then length = x+3

Volume of the box is = 792 (given)

Volume is the amount of space occupied by the any three dimensional figure. To find the volume of a box we simply multiply length width and height

Volume = length * width * height

792 = (x+3)*x*9

[tex](x^2+3x)*9=792\\9x^2+27x=792\\9x^2+27x-792=0[/tex]

Divide the above equation by 9 as 9 is the common factor

we get

[tex]x^2+3x-88=0[/tex]

now solve this equation by splitting the middle term we get,

[tex]x^2+11x-8x-88=0\\x(x+11)-8(x+11)=0\\(x+11)(x-8)=0\\x=-11,8[/tex]

width is always positive so we consider x = 8

Length = x+3 = 8+3 =11

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The numbers of ways can this be done, if the order of the choices is relevant is 181,440 ways and the numbers of  ways can this be done, if the order of the choices is not relevant is 36 ways.

a. N permutations

N permutations = nPr  = n!/ (n-r)!

N permutations = 9P7 = 9!/(9-7)!

N permutations = 9×8×7×6×5×4×3

N permutations= 181,440

b. N combinations :

N combinations = nCr = n!/((n-r)!r!)

N combinations = 9C7 = 9!/((9-7)!7!)

N combinations =9×8×7×6×5×4×3 ×2!/7!×2!

N combinations = 9×8×7×6×5×4×3 /7!

N combinations =181,440/7!

N combinations =36

Therefore the numbers of ways can this be done, if the order of the choices is relevant is 181,440 ways and the numbers of  ways can this be done, if the order of the choices is not relevant is 36 ways.

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Answer:

5 Servings

Step-by-step explanation:

The smallest interior angle of a triangle, produces largest exterior angle. Hence, measurement of the exterior largest angle is 359.47°

An angle is the figure formed by the two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by the two rays lie in the plane that contains the rays. Angles are also formed by the intersection of the two planes. These are called the dihedral angles. Two intersecting curves may also define an angle, which is the angle of rays lying tangent to the respective curves at their point of intersection.

Angle is also used to designate the measure of an angle or of rotation. This measure is the ratio of length of a circular arc to its radius. In the case of a geometric angle, arc is centered at the vertex and delimited by the sides. In case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation.

We know that sum of all the angles of a triangle is equal to 180°

s°+(1/7s+3)°+(1/7s+30)°= 180°

[tex]s+\frac{22}{7}s+\frac{22}{7}s[/tex]= 180°

[tex]\frac{51}{7} s[/tex]=180°

s= 24.7°

both the similar angles =0.53°

Therefore, the largest external angle is:

360°-0.53° = 359.47°

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Answer:

2/3s of 30

Step-by-step explanation:

2/3s of 30 is 10 and 1/5 of 25 is 5 and 10 is in fact larger than 5

The equation 4y = -4x + 2³​ is a linear function

A linear function can be explained as an algebraic equation, whose every  term is either a constant or the product of a constant and a variable (raised to the first power only).

The equation 4y = -4x + 2³​ is a linear function since both variables x and y meet the criteria, and both constants a and b do comply with rules as well

The exponent of x is 1, that is, it is raised to the first power only and the equation follows the definition of a function: for each input (x) there is only one output (y). The graph of any linear function in one variable  is always  a straight line.

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The percentage of students at the college have a GPA between 2.3 and 3.3 is C. 68.26%.

How far is 2.3 from 2.8. This will be:

= (2.3-2.8) = -0.5

That means 2.3 is one standard deviation to the left of the mean.

How far is 3.3 from 2.8? This is (3.3-2.8) = 0.5

That means 3.3 is one standard deviation to the right of the mean.

According to the empirical rule 68% of normally distributed data is within 1 standard deviation of the mean.

Therefore, the correct option is C.

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At one college GPA's are normally distributed with a mean of 2.8 and a standard deviation of .5. What percentage of students at the college have a GPA between 2.3 and 3.3?

a)84.13% b)99.74% c) 68.26% d) 95.44%

Cindy's age is 40 years and Madison's age is 17 years.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that Madison and Cindy have a combined age of 65 Cindy is 20 less than four times Madison's age. The age will be calculated by using the information.

C + M = 65

C = 4M - 20

4M - 20 + M = 65

5M = 65 + 20

5M = 85

M = 85 / 5

M = 17 years

Therefore, Cindy's age is 40 years and Madison's age is 17 years.

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Answer:

Step-by-step explanation: