Step by step on how to do this plz

Answer:

The answer is option 2.

Step-by-step explanation:

First, you have to find the height of the triangle using Cosine Rule, cosθ = adjacent/hypotenuse :

[tex]cos(θ) = \frac{adj.}{hypo.} [/tex]

[tex]θ = 30,adj. = h,hypo = 18[/tex]

[tex] \cos(30) = \frac{h}{18} [/tex]

[tex]18 \cos(30) = h[/tex]

[tex]h = 9 \sqrt{3} \: m[/tex]

Next, you have to find the area of triangle using Sin Rule, Area = 1/2×a×b×sinC where a, b represent the side length of the angle and C is the angle :

[tex]area = \frac{1}{2} \times a \times b \times sin(C)[/tex]

[tex]let \: a = 9 \sqrt{3} ,b = 18,C = 30[/tex]

[tex]area = \frac{1}{2} \times 9 \sqrt{3} \times 18 \times \sin(30) [/tex]

[tex]area = 70.1 \: {m}^{2} \: (near.tenth)[/tex]

Answer:

70.1

Step-by-step explanation:

This is a 30-60-90 right triangle.

The ratio of side lengths is as follows:

short leg   :   long leg   : hypotenuse

    1            :    sqrt(3)     :       2

The short leg is 1/2 the hypotenuse.

The long leg is sqrt(3) times the short leg.

A = bh/2

A = (18/2)(18/2 * sqrt(3))/2

A = 70.1

Answer:

[tex]5\frac{3}{5}[/tex]

Step-by-step explanation:

[tex]4*1\frac{2}{5} = 4 * \frac{7}{5} = \frac{28}{5} = 5\frac{3}{5}[/tex]

Answer:

[tex]\boxed{ 5\frac{3}{5}}[/tex]

Step-by-step explanation:

[tex]\displaystyle 4 \times 1\frac{2}{5}[/tex]

[tex]\sf Convert \ mixed \ fraction \ into \ improper \ fraction.[/tex]

[tex]\displaystyle 4 \times \frac{7}{5}[/tex]

[tex]\sf Multiply.[/tex]

[tex]\displaystyle \frac{28}{5}[/tex]

[tex]\sf Convert \ improper \ fraction \ into \ mixed \ fraction.[/tex]

[tex]\displaystyle 5\frac{3}{5}[/tex]

Answer:

Width: 4

Length: 6

Step-by-step explanation:

We can create a systems of equations for this problem, assuming W is width and L is length.

W = 3L-14

WL = 24

We can substitute W into the equation.

(3L-14)L = 24

3L²-14L = 24

3L² - 14L - 24 = 0

(3L+4)(L-6)=0

L = 6

Now we can find W by substituting L into the equation.

[tex]6\cdotw=24\\w = 4[/tex]

Hope this helped!

-1/7 belongs to B. Rational numbers and F. Real numbers.

A set is a collecting of well defined objects one form of writing a set is in roaster method where we write the elements with commas and close them with second brackets.

According to the given question we have to select all the sets in which the number - 1/7 is an element.

-1/7 is a rational number as it can be written in p/q form where q ≠ 0.

This also contain in the set of real numbers as in -1/7 there is no imaginary part.

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Answer:

1/3

Step-by-step explanation:

We are going to a small shape from a big shape, so the scale factor must be less than 1.

3 (which is a side on the blue figure) and 9 (a side on the green figure)

3 and 9 are easy numbers (for me...) so 3:9 is smaller than 1.

3:9 simplified is 1:3 = 1/3

so 1/3 is the scale factor.

Let's make sure it's right....

9 * 1/3 (green figure to blue figure) is = 3.

3.6 * 1/3 = 1.2

you can check it yourself on a calculator if you don't believe me

I hope this helps have a great day!!!!

Root 16=4 and root 49=7

Therefore,4 and 7 are rational as they have terminating decimal expansion.

Therefore,4+7=11 (rational)

[tex] \sqrt{16} + \sqrt{49} = \boxed{11}[/tex]

Answer:

The probability that a 57-year-old was involved in an accident is 0.0656.

Step-by-step explanation:

We are given the data for the drivers involved in an accident of different age groups.

And we have to find the probability that a 57-year-old was involved in an accident.

From the table given to us, it clear that a 57-year-old driver will lie in the age group of 55 - 64.

Now, the number of licensed drivers in the age group of 55 - 64 are 30,355 (in thousands).

The point to be noted here is that the data given of drivers in accidents (thousands) will include the data of drivers in fatal accidents.

So, the number of 57-year-old drivers involved in accidents are 1990 (in thousands).

The probability that a 57-year-old was involved in an accident is given by;

                        = [tex]\frac{1990}{30,355}[/tex]

                        = [tex]\frac{398}{6071}[/tex] = 0.0656 or 6.56%

Answer:

1/6 < x

Step-by-step explanation:

–2(8x – 4) < 2x + 5

Distribute

-16x +8 < 2x+5

Add 16x to each side

-16x+8+16x < 2x+16x+5

8<18x+5

Subtract 5 from each side

8-5 < 18x+5-5

3 <18x

Divide each side by 18

3/18 <18x/18

1/6 < x

Answer:

(-37, 3)

Step-by-step explanation:

Answer:

Hey there!

For this question, we write a proportion.

[tex]\frac{40}{0.6}=\frac{250}{x}[/tex]

[tex]40x=150[/tex]

[tex]x=3.75[/tex]

Thus, the nurse to give the patient exactly 3.75 ml of the solution.

Let me know if this helps :)

The volume of the simethicone solution given by a nurse is 3.75 milliliters.

Given:

To find:

The milliliters of a solution to be given to the patient by a nurse.

Solution:

Mass of simethicone drug to be given = 250 mg

Let the volume of the solution with 250 mg of simethicone be x.

The concentration of simethicone in solution = 40 mg/0.6 mL

Mass of simethicone in 1 mL of solution:

[tex]40 mg/0.6 mL=\frac{40 mg}{0.6 mL}\\\\=\frac{400 mg}{6 mL}[/tex]

The mass of simethicone in 'x' mL of solution:

[tex]250 mg=x\times \frac{400 mg}{6 mL}\\\\x=\frac{250 mg\times 6 mL}{400 mg}\\\\x=3.75 mL[/tex]

The volume of the simethicone solution given by a nurse is 3.75 milliliters.

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Answer:

6

Step-by-step explanation:

18 silly bands / 6 children = 3 silly bands per child.

2 children * 3 bands each = 6 bands total

Answer:

6 silly bands

Step-by-step explanation:

18 divided by 6 = 3  , so each child gets 3 so 3 + 3 is 6 which means 6 silly bands are in the drawer

Answer:

A function normally tells you what y is if you know what x is.

Answer:

The answer is 7

Length of all the the three segments is equal to the length of the line segment AD

Cathy worked a total of 160 + 4 + 2 = 166 hours in a fortnight.

So the answer is 166

Here is the calculation:

Cathy's basic pay for the fortnight is 7.2 × 70 = $504.

Her overtime pay for the week is (1.5 × 7.2) × 9 = $97.2.

Her weekend pay is (2 × 7.2) × 6 = $86.4.

Her total pay for the fortnight is 504 + 97.2 + 86.4 = $687.6.

Therefore, Cathy worked a total of 160 + 4 + 2 = 166 hours in a fortnight.

So the answer is 166

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Answer:

17/7

Step-by-step explanation:

the ratio would be 51/21 then to simplify divide both numbers by 3 to get 17/7

Hi there! :)

Answer:

[tex]\huge\boxed{\frac{17}{7} }[/tex]

Given ratio of 51 boys to 21 girls:

Write as a ratio:

[tex]51 : 21[/tex]

Divide both terms by GCF, or 3:

[tex]\frac{51}{3} : \frac{21}{3}[/tex]

[tex]17 : 7[/tex] or [tex]\frac{17}{7}[/tex]

Therefore, the ratio is 17 boys to 7 girls, or   [tex]\boxed {\frac{17}{7}}[/tex]

Answer:

64 cm^2

Step-by-step explanation:

I assume the side of the base measures 4 cm, and the height of each triangular side (the slant height) is 6 cm.

SA = s^2 + 4 * bh/2

SA = (4 cm)^2 + 2(4 cm)(6 cm)

SA = 16 cm^2 + 48 cm^2

SA = 64 cm^2

Answer:

-7 is a Negative Number, which is also an integer.

Step-by-step explanation:

Negative numbers are any number less than 0. The greater a negative number is, is the smaller its value.

Answer: x^2 + (x+2)(x-2)

Step-by-step explanation:

The caret ^ before the 2 indicates that the 2 is an exponent. It means "x squared"

If the keyboard doesn't allow exponents the caret is the thing to use.

The expression for the square of Lara’s age and the product of ages of Lara’s best friends is x² + (x-2)(x+2)

The first thing to do is to calculate the square of Lara's age and this will be:

= x × x = x²

The product of the ages of Lara’s best friends will be (x-2)(x+2).

Therefore, the expression that can be used to calculate the square of Lara’s age and the product of ages of Lara’s best friends is x² + (x-2)(x+2)

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A equation representing the area Bruce covered, y, in terms of the number of tiles he used x is y = 4x

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation

According to the question

The area Bruce covered  shows by y axis

The number of tiles he used is x axis .

The tiles Bruce used is 1/4 of a square foot in area .

Therefore,

Area of tiles in square foot = 4 number of titles

                                             = 4x

now,

Equation will be :

y = 4x

Hence, A equation representing the area Bruce covered, y, in terms of the number of tiles he used x is y = 4x

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Answer:

[tex]\huge\boxed{B) x = 20}[/tex]

Step-by-step explanation:

50 * 5x = 5000

Dividing both sides by 50

=> 5x = 5000/50

=> 5x = 100

Dividing both sides by 5

=> x = 20

Answer:

the answer is B

Step-by-step explanation:

X: (x)50=20

Answer:

No qualitative graph shown here.

Step-by-step explanation:

No qualititative graph is shown here.  The given graph is quantitative, as it involves numerical measures.

Answer:

qualitative graph are graph that are used to represent situation that do not necessarily have numerial value it repressent the essential elements of a situation in a graphical form

Answer:

[tex]Average\ Rate = 10[/tex]

Step-by-step explanation:

Given

[tex]g(x) = -x^2[/tex]

[tex](-8,-2)[/tex]

Required

Determine the average rate of change;

Average rate of change is calculated as thus;

[tex]Average\ Rate = \frac{g(b) - g(a)}{b - a}[/tex]

Where

[tex](a,b) = (-8,-2)[/tex]

i.e. a = -8 and b = -2

[tex]Average\ Rate = \frac{g(b) - g(a)}{b - a}[/tex] becomes

[tex]Average\ Rate = \frac{g(-2) - g(-8)}{-2 - (-8)}[/tex]

[tex]Average\ Rate = \frac{g(-2) - g(-8)}{-2 + 8}[/tex]

[tex]Average\ Rate = \frac{g(-2) - g(-8)}{6}[/tex]

Calculating g(-2)

Substitute -2 for x in [tex]g(x) = -x^2[/tex]

[tex]g(-2) = -(-2)^2[/tex]

[tex]g(-2) = -4[/tex]

Calculating g(-8)

Substitute -8 for x in [tex]g(x) = -x^2[/tex]

[tex]g(-8) = -(-8)^2[/tex]

[tex]g(-8) = -64[/tex]

Substitute values for g(-2) and g(-8)

[tex]Average\ Rate = \frac{g(-2) - g(-8)}{6}[/tex]

[tex]Average\ Rate = \frac{-4 - (-64)}{6}[/tex]

[tex]Average\ Rate = \frac{-4 + 64}{6}[/tex]

[tex]Average\ Rate = \frac{60}{6}[/tex]

[tex]Average\ Rate = 10[/tex]

Hence, the average rate of change is 10

Answer:

D. g(x) is a reflection of f(x) over the x-axis.

Step-by-step explanation:

Given

f(x) = 2x²

g(x) = -2x²

Required

Determine the difference between f(x) and g(x)

Start by expanding g(x)

g(x) = -2x²

g(x) = -1 * 2x²

Substitute 2x² for f(x)

g(x) = -1 * f(x)

g(x) = -f(x)

Using the format (x,y):

Take for instance x = 2

f(x) = 2x² = 2 * 2² = 2 * 4 = 8

This means (x,y) = (2,8)

g(x) = -f(x)= -8

This means that (2,-8)

Notice that only the y value changed in both cases from 8 to -8

From the above expression, g(x) = -f(x) and illustration of when x = 2

This implies that g(x) is a reflection of f(x) along the x axis..

From the list of given options, the correct answer is D.

Let's think about the square root of 33 here for a second.

What two perfect squares surround 33?

The answer is 25 and 36.

Then, let's take the square root of both 25 and 36, which are 5 and 6. Therefore, since the square root of 25 and 36 are both nearest to the square root of 33, then the square root of 3 must be between 5 and 6.

The correct answer is A (or option 1): 5 < root 33 < 6

Hope this helps! :)

Answer:

a (the first choice)

Step-by-step explanation:

To start, you should think of square root values near 33 that you know the answer to. For example, the square root of 25 is 5, and the square root of 36 is 6. Therefore, you know that the square root of 33 is 5.something because it is in between 25 and 36.

Answer: All options are in slope-intercept form

i hope this helps .

Step-by-step explanation:

1.

[tex]\mathrm{For\:a\:line\:in\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is}\:\\\mathbf{m}\:\mathrm{and}\:\mathbf{y}\:\mathrm{intercept\:is}\:\mathbf{b}\\y=-\frac{8}{7}x-\frac{3}{2}\\[/tex]

2.

[tex]\mathrm{For\:a\:line\:in\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is}\:\\\mathbf{m}\:\mathrm{and}\:\mathbf{y}\:\mathrm{intercept\:is}\:\mathbf{b}\\\\y=\frac{7}{8}x-\frac{3}{2}[/tex]

3.

[tex]\mathrm{For\:a\:line\:in\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is}\:\\\mathbf{m}\:\mathrm{and}\:\mathbf{y}\:\mathrm{intercept\:is}\:\mathbf{b}\\\\y=-\frac{7}{8}x-\frac{3}{2}[/tex]

4.

[tex]\mathrm{For\:a\:line\:in\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is}\:\\\mathbf{m}\:\mathrm{and}\:\mathbf{y}\:\mathrm{intercept\:is}\:\mathbf{b}\\\\y=-\frac{3}{2}x+\frac{7}{8}\\[/tex]

Answer:

2/12 is not a reasonable answer for the fraction of his book Min has read. The fraction should be closer to 1/2.

Step-by-step explanation:

First, find common denominators. Note that what you do to the denominator, you must do to the numerator:

1/8

1/4 x (2/2) = 2/8

1/8 + 2/8 = 3/8

Find common denominators between the amount he read as well as the amount he thinks he read:

(3/8)(3/3) = 9/24

(2/12)(2/2) = 4/24

Min has read 9/24 of his book, while he states that he read 4/24 of his book.

2/12 is not a reasonable answer for the fraction of his book Min has read. The fraction should be closer to 1/2.

Note: 9 is only 3 parts away from 12 (12/24), while 9 is 5 parts away from 4 (4/24).

~

Answer: i think its b

Step-by-step explanation:

Answer:

its

1/7

step by step

Answer:

The answer is H because there are 7 balls in total and two of which is red so the possiblity of getting the red ball is 2/7

Answer:

Of course the answer is 2.

It says 'Double'!

The required scale factor is 2 in a manner to double the volume of the fish tanks. Option A is correct.

The figure is shown of the fish tank, a scale factor to be determined that is applied to the dimensions so the volume becomes twice the former volume.

Volume is defined as the ratio of the mass of an object to its density.

The volume of the fish tank = v
Now new the volume of the new fish tank = 2v
Scale factor = New volume/old volume
                  =  2v/v
                  = 2

Since the scale factor is 2 the dimension of new fish tank should be doubled to get twice the volume of the old fish tank.

The required scale factor is 2 in a manner to double the volume of the fish tanks. Option A is correct.

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