The answer for study guide

Answer:

[tex]\cos x=15\div 17[/tex]

Step-by-step explanation:

Recall the mnemonics SOH-CAH-TOA.

The CAH means the cosine ratio is the ratio of the adjacent side to the hypotenuse.

From the given triangle;

[tex]\cos x=\frac{Adjacent}{Hypotenuse}[/tex]

The side adjacent to the [tex]x\degree[/tex] is 15cm and the hypotenuse is 17cm.

We substitute the values to get;

[tex]\cos x=\frac{15}{17}[/tex] or [tex]\cos x=15\div 17[/tex].

Answer:

LN=64 units

Step-by-step explanation:

step 1

Find the value of x

we know that

LN=LM+MN -----> equation A

see the attached figure to better understand the problem

we have

LN=12x+16

LM=10x+8

MN=5x-4

substitute the values in the equation A

12x+16=(10x+8)+(5x-4)

Solve for x

12x+16=15x+4

15x-12x=16-4

3x=12

x=4

step 2

Find the value of LN

LN=12x+16

LN=12(4)+16=64 units

Answer:

they can both take 7 lessons each

Answer:

Each one can take 7 lessons.

Step-by-step explanation:

Dylan and Dusty plan to take weekly surfing lessons together.

They want to spend $100 each on new surfboards = $100 × 2

                                                                                     = $200

They want to spent total amount for lessons and surfboards is at most $480.

After spending on two new surfboards the money left with

= 480 - 200

= $280

The charges for 2-hours classes for surfing lessons = $20 per person

The charges for 1 hour classes for them = $20.00

With $280  they will be able to take maximum number of lessons

= [tex]\frac{280}{20}[/tex]

= 14 lessons

Each one can take 14/2 = 7  lessons.

Answer:

That can be factored:

(x +6) * (x -2)

Therefore, x = -6 and x =2

Step-by-step explanation:

For this case we have the following quadratic equation:

[tex]x ^ 2 + 4x-12 = 0[/tex]

We can factor the equation, for it, we must find two numbers that when multiplied give as result -12 and when summed give as result +4. These numbers are: +6 and -2.

Then, the factorization is given by:

[tex](x + 6) (x-2) = 0[/tex]

Thus, the solutions are:

[tex]x_ {1} = - 6\\x_ {2} = 2[/tex]

Answer:

[tex]x_ {1} = - 6\\x_ {2} = 2[/tex]

Answer:

A clockwise rotation 90° about the origin followed by a translation

2 units to the right and 6 units down produces Δ X'Y'Z' from Δ XYZ

Step-by-step explanation:

* Lets revise the rotation and translation

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 180° anti-clock wise

∴ Its image is (-x , -y)

- If point (x , y) rotated about the origin by angle 270° anti-clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 90° clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180° clock wise

∴ Its image is (-x , -y)

- If point (x , y) rotated about the origin by angle 270° clock wise

∴ Its image is (-y , x)

- If the point (x , y) translated horizontally to the right by h units

∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

∴ Its image is = (x , y - k)

* Now lets solve the problem

- Δ XYZ has vertices X = (-5 , 3) , Y = (-2 , 3) , Z = (-2 , 1)

∵ Δ XYZ rotate 90° clockwise about the origin the image will be (y , -x)

∴ The image of X is (3 , 5)

∴ The image of Y is (3 , 2)

∴ The image of Z is (1 , 2)

- From the graph

∵ X' = (5 , -1)

∵ Y' = (5 , -4)

∵ Z' = (3 , -4)

- Every x-coordinate add by 2

∴ There is a translation 2 units to the right

- Every y-coordinate subtracted by 6

∴ There is a translation 6 units down

- From all above

* A clockwise rotation 90° about the origin followed by a translation

 2 units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ

Answer:

A clockwise rotation 90° about the origin followed by a translation

2 units to the right and 6 units down produces Δ X'Y'Z' from Δ XYZ

Step-by-step explanation:

The linear function that models the puppy's growth is A. y = 3x+3.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given Shayla is tracking the weight of the smallest dog in a litter.

Week 0 weight in ounces 3, week 1 weight in ounces 6, week 2 weight in ounces 9, and, week 3 weight in ounces 12.

From this, we can conclude that every week weight of the dog is increasing by 3 ounces.

This can be numerically expressed as y = 3x+3.

Where y is the total weight and x represents the no. of weeks.

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Answer:

100000

Step-by-step explanation:

Since we have the natural base of the log, the base is 10.

Now think of it this way, since we are solving for the value that is being "logged" we can say 10 to the power of 5 equals what?

And since 10^5 is 100000, x is 100000.

The value of x is 100000.

A logarithm helps us know by what power a number must be raised to get the desired number.

A natural log is a log with base 10.

For example,

We want to know by what power must 10 be raised so we get 1000 as an output,

therefore, we can write it as,

[tex]\bold{log_{10} 1000 = 3}[/tex]

[tex]\bold{10^3 = 1000}[/tex]

where, 10 is the base meaning number to which power is to be raised,

1000 is the desired number,

And 3 is the answer.

Now, looking at our question,

[tex]\bold{log\ x= 5}[/tex]

can be written as

[tex]\bold{log_{10} x= 5}[/tex]

[tex]\bold{10^5 = x}[/tex]

[tex]\bold{10^5 = 100000}[/tex]

Therefore, 10 is been raised to the power of 5 giving the desired result which is 100,000.

Hence, the value of x is 100000.

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Answer:

D

Step-by-step explanation:

you cannot take the root of a negative number so that eliminates B and C. you can take the root of 0 to be 0 so D is valid.

The correct inequality will be x≥0

Inequality a statement of an order relationship which are greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

So, here the values of x will be all the numbers greater or equal to 0

So the correct inequality will be x≥0

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Answer:

This is four term polynomial.

Step-by-step explanation:

Polynomial comes from poly(meaning “many”) and nomial (in this case meaning “term”). So it says “many terms”  A  polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

In this expression, we are to determine  the polynomials depending on the number of terms present in the expression. The prefixes of the classification suggest the number of terms present.

a^2 - b + c - d^3  

This is an example of a four-term polynomial. The first term is  a^2, second one is -b, the third one is c, and the fourth one is -d^3.

Answer:

[tex]\large\boxed{\dfrac{V_{cone}}{V_{prism}}=\dfrac{1}{3}}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a cone:}\ V_{cone}=\dfrac{1}{3}B_cH_c\\\\B_c-base\ area\ of\ a\ cone\\H_c-height\ of\ a\ cone\\\\\text{The formula of a volume of a prism:}\ V_{prism}=B_pH_p\\\\B_p-base\ area\ of\ a\ prism\\H_p-height\ of\ a\ prism\\\\\text{The cone and the prism have the same base area and height.}\\\text{Therefore}\\\\V_{cone}=\dfrac{1}{3}BH\ \text{and}\ V_{prism}=BH\\\\\text{The ratio of the volume of the cone to the volume of the prism:}[/tex]

[tex]\dfrac{V_{cone}}{V_{prism}}=\dfrac{\frac{1}{3}BH}{BH}=\dfrac{1}{3}[/tex]

The solution is, 1:3 the ratio of the volume of the come to the volume of the prism.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

The cone in the diagram has the same height and base area as the prism.

now, we know that,

The formula of volume of a cone:

if 'B' is the base of the cone,

and 'h' is the height of the cone,  

its volume is V = (1/3) (Bh) cubic units.

The formula of volume of a prism:

if 'B' is the base of the prism,

and 'h' is the height of the prism,  

its volume is V = (Bh) cubic units.

The cone in the diagram has the same height and base area as the prism.

so, the ratio of the volume of the come to the volume of the prism:

The formula of volume of a cone: The formula of volume of a prism

= 1/3 *BH : BH

=1/3

=1:3

Hence, The solution is, 1:3 the ratio of the volume of the come to the volume of the prism.

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Answer:

13x - 4

Step-by-step explanation:

f(x) + g(x) = 10x + 4 + 3x - 8.

First, we must rearrange it so we can add like terms.

10x + 3x + 4 - 8.

Add together 10x and 3x.

13x + 4 - 8.

Subtract 4 - 8.

13x - 4.

Therefore, the answer is 13x - 4.

Answer:

The answer has to be 13x-4

Step-by-step explanation:

10x+4 + 3x-8

13x+4-8 (Combine like terms)

13x-4

Answer:

C. -26

Step-by-step explanation:

First, subtract by 4 both sides of equation.

4+m/8-4=3/4-4

Then, simplify.

4+m/8-4=m/8

3/4-4=-13/4

m/8=-13/4

Multiply by 8 both sides of equation.

8m/8=8(-13/4)

Simplify to find the answer.

8(-13/4)

-8*13/4

13*8/4=-104/4

104/4=-26

X=-26 is the correct answer.

C. -26 is the correct answer.

For this case we must solve the following equation:

[tex]4+ \frac {m} {8} = \frac {3} {4}[/tex]

We subtract 4 on both sides of the equation:

[tex]\frac {m} {8} = \frac {3} {4} -4\\\frac {m} {8} = \frac {3-16} {4}\\\frac {m} {8} = \frac {-13} {4}[/tex]

We multiply by 8 on both sides of the equation:

[tex]m = \frac {-13 * 8} {4}[/tex]

[tex]m = -26[/tex]

Answer:

Option C

Answer:

-2

Step-by-step explanation:

y = -2x + 2; your y-intercept is [0, 2] and your x-intercept is [1, 0] (not all the time your x-intercept will be an endpoint). Simply do rise\run until you hit another endpoint, starting from your y-intercept. As you can see, you go two blocks south, then one block over east. Do you understand?

Answer:

The slope is -2

Step-by-step explanation:

Slope = Rise/Run = -2/1 = -2

Answer:

[tex]12[/tex]

Step-by-step explanation:

[tex]3 \times (5 + 4) \times 2 - 42 \\ \\ 1. \: 3 \times 9 \times 2 - 42 \\ 2. \: 54 - 42 \\ 12[/tex]

Answer:Y = 16

Step-by-step explanation:

Y=6 and x = 3

If Y varies directly as x, then

Y = kx

Substitute the value of Y and x

6 = k * 3

Make k the subject of the formula

K = 6/3

k = 2

:. The equation connecting Y and x is

Y=2x

When x = 8

Y = 2*8

Y= 16

Yes, that is correct.

I even searched it, and saw that the answer was 16.

Nice Job!! :)

Answer:

No

Step-by-step explanation:

A function has only one y value for each x value.  Here, we have two points that have the same x value but different y values: (-8, -6) and (-8, 1).  So this is not a function.

Answer:

$96.25

Step-by-step explanation:

Find the unit rate of pay:

$52.50

------------- = $8.75/hr

 6 hours

Now multiply this rate by 11 hours:

($8.75/hr)(11 hrs) = $96.25

Answer: $ 96. 25

Step-by-step explanation:

It is said that two variables x and z vary directly if they meet the following relationship:

[tex]z = kx[/tex]

Where k is the constant of variation.

In this case z represents the gains and x represents the hours of work.

Now we must find the value of the constant k.

We know that for 6 hours of work the earnings are $ 52.50

So

[tex]x = 6[/tex]

[tex]z = \$\ 52.50[/tex]

[tex]52.50 = 6k[/tex]

[tex]k= \frac{52.50}{6}[/tex]

[tex]k= 8.75[/tex]

Then the equation is:

[tex]z = 8.75x[/tex]

Finally when x = 11, then:

[tex]z = 8.75*11\\\\z =\$\ 96.25[/tex]

Answer:

a. 21/4, 11/2, 49/10, 5/1

b. James 5.5, Olivia 5 1/4, Feng 5, Carmela 4.9

Step-by-step explanation:

Answer with Step-by-step explanation:

Olivia:   [tex]5\dfrac{1}{4}[/tex]

             = [tex]\frac{21}{4}[/tex]    (21/4=5.25)

James: 5.5

           = [tex]\dfrac{55}{10}[/tex]

           = [tex]\dfrac{11}{2}[/tex]

Carmela: 4.9

             =  [tex]\dfrac{49}{10}[/tex]

Feng: 5

         =   [tex]\dfrac{5}{1}[/tex]

b. Heights from greatest to least is:

James 5.5

Olivia 5.25

Feng 5

Carmela 4.9

Answer:

B) 30

Step-by-step explanation:

Bill saves 60 dollars a month so first you have to find out how much he saves in a year

To find that you multiply 60 by 12 since there are 12 months in a year

60*12 = 720

Tom saves 750 in a year so you have to subtract 750 by 720 to know how much more tom saves

750 - 720 = 30

Tom saves Option(B) $30 more than Bill in a year.

It is given that Tom saves $750 a year where as Bill saves $60 a month.

Thus savings for Bill in a month is $60 .

For 1 year, Bill saves -

(12 * $60) = $720 .

Now definitely Tom saves more than Bill,

Savings made by Tom more than Bill is -

= ($750 - $720) = $30 .

Therefore, Tom saves Option(B) $30 more than Bill in a year.

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Answer:

A

Step-by-step explanation:

Connect the top of the tower (assuming the person's height can be ignored), the bottom of the tower, and the tree to form a right triangle.

Since the person is looking down at a 45 degree, it means the triangle is a equilateral triangle, so the length from the base of the tower to the base of the tree is also 300ft.

Answer:

4

Step-by-step explanation:

We are given that a PE class has 12 boys and 8 girls. The teacher needs to divide in maximum number of teams so that each team has an equal number of boys and girls.

For this, we will factors of 12 and 8 and their greatest common factor.

12 = 4 × 3 = 2 × 2 × 3

8 = 4 × 2 = 2 × 2 × 2

The greatest common factor is 4, therefore the maximum number of teams with equal number of boys and girls is 4.

Answer:

C.  

x + 0.05x = 3.15, which has one solution

Step-by-step explanation:

Let x = the price Joshua pays for the pack of pens

He add 5% (=.05 in decimal form)

That is x* .05

The new cost is 3.15

x+.05x = 3.15

This will have one solution

Answer:

The correct option is C.

Step-by-step explanation:

It is given that Joshua sells a pack of pens for $3.15, which is 5 percent more than he pays for them.

Selling price of a pack of pens = $3.15

Let x be the amount he pays for a pack of pens.

x + 5% of x = 3.15

It can be written as

[tex]x+\frac{5}{100}x=3.15[/tex]

[tex]x+0.05x=3.15[/tex]

[tex]1.05x=3.15[/tex]

Divide both sides by 1.05.

[tex]x=\frac{3.15}{1.05}[/tex]

[tex]x=3[/tex]

The required equation is x+0.05x=3.15 and this equation has one solution.

Therefore, the correct option is C.

Statistical questions are questions that are answered by collecting variable data, which can be given as an average/range/percentage. This question has a single answer, and therefore it is not a statistical question. A statistical question would be, for example, What is the average amount of time students in this class spend playing musical instruments?

Answer:

X=- 12

Step-by-step explanation:

Answer:

x = -12

Step-by-step explanation:

—10x + 1 + 7х = 37

Combine like terms

-3x +1 = 37

Subtract 1 from each side

-3x+1-1 = 37-1

-3x = 36

Divide each side by -3

-3x/-3 = 36/-3

x = -12

ANSWER

[tex]\frac{dy}{dx} = x{(3x)}^{ {x}^{2} } (ln(9 {x}^{2} ) + 1)[/tex]

EXPLANATION

The given equation is;

[tex]y = {(3x)}^{ {x}^{2} } [/tex]

Take natural log of both sides:

[tex] ln(y) = ln({(3x)}^{ {x}^{2} } )[/tex]

This implies that,

[tex]ln(y) = {x}^{2} ln({(3x)})[/tex]

We differentiate to get,

[tex] \frac{1}{y} \frac{dy}{dx} = ln(3x) (2x) + {x}^{2} ( \frac{1}{x} )[/tex]

This simplifies to

[tex] \frac{dy}{dx} =y (2x ln(3x) + x)[/tex]We substitute for y to get:

[tex]\frac{dy}{dx} = {(3x)}^{ {x}^{2} } (2x ln(3x) + x)[/tex]

Or

[tex]\frac{dy}{dx} = x{(3x)}^{ {x}^{2} } (2ln(3x) + 1)[/tex]

[tex]\frac{dy}{dx} = x{(3x)}^{ {x}^{2} } (ln(9 {x}^{2} ) + 1)[/tex]

Answer:

2 + r = 7

Step-by-step explanation:

To write an equation for the image, simply look on both sides and add everything together. On the left side we have seven 1's, which adds up to 7. On the right side, we have 2 1's, which add up to 2, and a variable r. Now, we do not know the value of the variable r, so we simply leave it be. Therefore, the right side is equal to 2 + r. Since the image represents a balanced equation, the left side must equal the right side.

Left side = 7

Right side = 2 + r

Left side = Right side

7 = 2 + r

2 + r = 7

Answer:

[tex]\large\boxed{1.\ the\ slope\ is\ \dfrac{1}{4}}\\\boxed{2.\ y=3x-5}\\\boxed{3.\ (3, 6)}[/tex]

Step-by-step explanation:

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_2}\\\\l\ \parallel\ k\iff m_1=m_2\\\\m-slope\\b-y-intercept\to(0,\ b)\\\\1.\\\\y=-4x+1\to m_1=-4\\\\m_2=-\dfrac{1}{-4}=\dfrac{1}{4}[/tex]

[tex]2.\\y=3x+2\to m_1=3\\\\m_2=3,\ b=-5\\\\y=3x-5[/tex]

[tex]\text{Calculate}\ a\ \text{and}\ b:\\\\a=\dfrac{6-(-9)}{5}=\dfrac{15}{5}=3\\\\b=\dfrac{8-(-2)}{5}=\dfrac{10}{5}=2\\\\\text{Calculate the coordinates of a point:}\\\\x=-9+4a\to x=-9+4(3)=-9+12=3\\\\y=-2+4b\to y=-2+4(2)=-2+8=6[/tex]

Answer:

Step-by-step explanation:

Use a table with trigonometric functions (look at the photo) or use the calculator knowing that:

[tex]\cot\theta=\dfrac{1}{\tan\theta}=\left(\tan\theta\right)^{-1}[/tex]

Answer:

50 is the answer

Step-by-step explanation: