halp pls ok

x =x=x, equals
^\circ
∘

Answer:

Θ ≈ 58°

Step-by-step explanation:

using the Cosine Rule in the triangle

cosΘ = [tex]\frac{80^2+60^2-70^2}{2(80)(60)}[/tex] = [tex]\frac{64000+3600-4900}{9600}[/tex] = [tex]\frac{5100}{9600}[/tex] = [tex]\frac{51}{96}[/tex] , then

Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{51}{96}[/tex] ) ≈ 58° ( to the nearest degree )

Answer:

22

Step-by-step explanation:

Dion (d) is 4 years older than Agustina (a)

d=a+4

In 3 years the sum of their ages will be 46

d+3+a+3=46

d+a+6=46

d+a=40

d=40-a

d=a+4

a+4=40-a

2a=36

a=18

Plug a back in

18+4=d

22=d

d=22

Sorry if this was a little long.

The value of 6 to the power of 5/6to the power of 2 is 6 to the power of 3

The expression is given as:

6 to the power of 5/6to the power of 2.

Rewrite properly as:

6^5/6^2

Apply the law of indices

6^(5-2)

Evaluate the difference

6^3

Hence, the value of 6 to the power of 5/6to the power of 2 is 6 to the power of 3

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The expression cos⁴ θ in terms of the first power of cosine is [ 3 + 2cos 2θ + cos 4θ]/8.

The power-reducing formula, for cosine, is,

cos² θ = (1/2)[1 + cos 2θ].

In the question, we are asked to use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos⁴ θ.

We can do it as follows:

cos⁴ θ

= (cos² θ)²

= {(1/2)[1 + cos 2θ]}²

= (1/4)[1 + cos 2θ]²

= (1/4)(1 + 2cos 2θ + cos² 2θ] {Using (a + b)² = a² + 2ab + b²}

= 1/4 + (1/2)cos 2θ + (1/4)(cos ² 2θ)

= 1/4 + (1/2)cos 2θ + (1/4)(1/2)[1 + cos 4θ]

= 1/4 + cos 2θ/4 + 1/8 + cos 4θ/8

= 3/8 + cos 2θ/4 + cos 4θ/8

= [ 3 + 2cos 2θ + cos 4θ]/8.

Thus, the expression cos⁴ θ in terms of the first power of cosine is [ 3 + 2cos 2θ + cos 4θ]/8.

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Answer:

x = 3

Step-by-step explanation:

Here ,

4x + 9 =7x

--> 4x - 7x = -9

--> -3x = -9

--> ≠ x = -9/3

--> x = 3

The area of the shaded face of the cylinder is 1,520 mm².

We can see that the shaded area of the cylinder is circular in shape.

This means that we can find the area of the shaded area by finding the area of the circle.

The radius of the circle is given as 22 mm.

The formula for finding the area of a circle is given as:

Area = πr²

= 3.14 × 22 × 22

= 1,519.76

≈ 1520 mm²

Therefore, we have found the area of the shaded face of the cylinder to be 1,520 mm².

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Disclaimer: The question was incomplete, the complete question is attached below.

Using a system of equations, it is found that she earns $5.5 for each hat and $7 for each scarf sold.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

One week she earns $114.00 by selling eight hats and 10 scarves, hence:

8x + 10y = 114.

The following week she sold 12 hats and six scarves and earned $108.00, hence:

12x + 6y = 108

Simplifying by 6:

2x + y = 18

y = 18 - 2x.

Replacing in the first equation:

8x + 10y = 114.

8x + 10(18 - 2x) = 114

12x = 66

x = 66/12

x = 5.5

y = 18 - 2x = 18 - 2 x 5.5 = 7.

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The correct option is D. the number of sweatshirts for which cost and income are equal.

Any equation that contains only one element which squares the variable and none that raises it to a higher power.

The general form form of quadratic equation is-

ax² + bx + c = 0

According to the question;

Use the substitute method to get the quantity of sweatshirts in which cost and earnings are equal.

Step 1: Write the following system of equations as the first step.

[tex]\begin{aligned}&y=35 x \\&y=-0.05(x-400)^{2}+9492\end{aligned}[/tex]

Step 2: Replace the value of "y" in the equation (2).

[tex]35 x=-0.05(x-400)^{2}+9492[/tex]

Step 3: Make the equation above simpler.

[tex]35 x=-0.05 x^{2}-8000+40 x+9492[/tex]

Step 4: Write the preceding equation in generalised quadratic form.

[tex]0.05 x^{2}-5 x-1492=0[/tex]

The processes above lead to the conclusion that option D provides the proper statement.

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The complete question is-

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league. What does the solution of the system represent in this context?

y=35x

y=-0.05(x-400)^2+9,492

A. the number of sweatshirts that generate the maximum income

B. the number of sweatshirts that generate the minimum cost

C. the number of sweatshirts for which the difference between cost and income is greatest.

D. the number of sweatshirts for which cost and income are equal

Answer:

D

Step-by-step explanation:

He said so

From statement equation, the number of correct answers will result in a passing grade is 9.3

Given that each question on the quiz is worth 8 points.

Also given a score of 75 is a passing grade.

Let the number of correct answered questions be x

Thus the total score of the correct answers is 8x

The statement equation is -

⇒ 8x = 75

⇒ x = 75/8 = 9.3

∴  x ≈ 9

Therefore, from statement equation, the number of correct answers will result in a passing grade is 9.3

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Step-by-step explanation:

Let S be the set of all the stores in the sample, A be the set of stores dealing with Asian companies and E but the set of stores dealing with European companies

i. The set of stores that deal with European or Asian companies is A ∪ E. The inclusion-exclusion principle states that |A ∪ E| = |A| + |E| - |A ∩ E| = 266 + 308 - 103 = 471. So P(A ∪ E) = 471/500 = 0.942

ii. E' = S - E. |S-E| = 500 - 308 = 192. So P(E') = 192/500 = 0.384

iii. |A - E| = |A| - |A ∩ E| = 266 - 103 = 163. So P(A - E) = 163/500 = 0.326

iv. Stores that do not deal with only one type of company, must deal with both Asian and European companies. We are given that |A ∩ E| = 103. So P(A ∩ E) = 103/500 = 0.206

Easy, right?

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The minimum volume of molten metal which should be added to mold It into a cube exists [tex]$24 cm^3[/tex].

Volume exists as a scalar quantity representing the amount of three-dimensional space encircled by a closed surface.

The minimum volume of a shape with measured dimensions exists provided by the lowest values of the dimensions when accounting for measurement error. Maximum Volume: The maximum volume of a shape with measured dimensions exists provided by the highest values of the measurements when accounting for measurement error.

The volume of the cube [tex]= 8*6*4[/tex]

[tex]= 192 cm^3[/tex]

To create the X as the sides of the cube we should add material.

The nearest cube number to 192 exists at 216

The amount of material to be added exists

= 216 -192

[tex]= 24 cm^3[/tex]

The minimum volume of molten metal which should be added to mold It into a cube exists [tex]$24 cm^3[/tex].

Therefore, the correct answer is an option (4) 24.

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Answer:

y = 6x + 8

Step-by-step explanation:

y = mx + b

20 = 6(2) + b

b = 8

y = 6x + 8

[tex]t \geqslant 35[/tex]

From Longman Dictionary of Contemporary English opens an account to start an account at a bank or other financial organization by putting money into it Mary was in the bank to ask about opening a current account.

Step 1: Visit the official website of the bank in which you wish to open an account. Step 2: Fill in the application form online along with a digital copy of address proof, identity proof, age proof, income/employment proof, and photographs.

You need to be at least 18 years old to open an account. However, you can open a joint account as a minor with a parent or legal guardian as an account co-owner. Some banks do offer accounts tailored for minors.

Please check the attached file for a complete answer.

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The difference of the expression is as follows:

(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5) = - 6y⁴ + 4y² - 12

3(x - 5) - (2x + 4) = x - 19

The difference of the expression can be found when we combine the like terms.

Therefore,

(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5)

6y⁴ + 3y² - 7  - 12y⁴ + y² - 5

6y⁴ - 12y⁴ + 3y² + y² - 7 - 5

- 6y⁴ + 4y² - 12

3(x - 5) - (2x + 4)

3x - 15 - 2x - 4

3x - 2x - 15 - 4

x - 19

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The computation shows that the amount that will be charged will be $5.00 and $9.00 respectively.

When the customer has a 6 pound Chihuahua, the amount that will be charged will be $5.00.

When a customer has a 65 pound Labrador, the amount that will be charged is $9.00.

This is illustrated as the cost is based on the weights given.

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The explanation about the graph is illustrated below.

The graph shows 0 to 30 on the x-axis at increments of 5 and 0 to 12 on the y-axis at increments of 1. The label on the x-axis is Temperature in degrees C, and the label on the y axis is the Number of Sweaters Sold.

If you will draw lines through, (12.5,6) and (15,4), it will best represent a line of best fit, because most of the points on the same and opposite sides of line are equidistant from each other.

Equation of line passing through (12.5,6) and (15,4) A line of best is the line that passes through all or some points or only through a single point, which describes the relationship between x and y values of data set

4x + 5y = 80

5y = -4x + 80.

y = -4x/5 + 16

Slope = -4/5 and y intercept is 16.

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Answer:

1st quartile is 136

The second quartile is also the median 142

The third quartile is 162

The interquartile range is the difference between the 3rd and first quartile or 26

Step-by-step explanation:

An action that would not interfere with the airflow patterns at the front opening of the biosafety cabinet is a researcher discarding waste within the biosafety cabinet to prevent the movement of their arms in and out of the front opening.

It should be noted that biosafety simply means the use of safety equipment as specifically designs tools to ensure that people are protected from hazards.

In this case, when a researcher discards waste within the biosafety cabinet to prevent the movement of their arms in and out of the front opening, it won't interfere with the airflow pattern.

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16-4(3x-2)²

=16-4(3x-2)(3x-2)

=16+−36x²+48x+−16

=(−36x²)+(48x)+(16+−16)

=−36x²+48x

Answer:

[tex] \red{- 12x(3x - 4)}[/tex]

Step-by-step explanation:

We know that,

[tex](a - b)^{2} = {a}^{2} - 2ab + {b}^{2} \\ [/tex]

Accordingly, let us solve the sum now.

[tex]16 - 4(3x - 2)^{2} \\ 16 - 4(9 {x}^{2} - 12x + 4) \\ 16 - 36 {x}^{2} + 48x - 16 \\ - 36 {x}^{2} + 48x \\ - 12x(3x - 4)[/tex]

The area of the given figure is 38 square units

The area of the given trapezoid is expressed as:

A = 0.5(a+b)h

where

a and b are the sides

h is the height

Substitute

A = 0.5(9+10) * 4

A = 19 * 2

A = 38 square units

Hence the area of the given figure is 38 square units

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The values of x and y are 19 and 14 respectively.

Given the hypotenuse = 24

Opposite = x

Adjacent = y

Let's use the sine ratio to find the opposite side

sin of angle = opposite/hypotenuse

sin 54 = x/24

Cross multiplysin 54 × 24 ,= x

x = 19.42

x = 19

To find the adjacent side, we use cosine ratio

cos = adjacent/hypotenuse

cos 54 = y/25

Cross multiply

cos 54 × 24 = y

y = 14

Thus, the values of x and y are 19 and 14 respectively.

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Dave is 18 years old.

A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3. Word illustration: The product of 8 and 3 is 11

Given

Let x be Dave’s age today. Then:

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

x=3x+9–3x+9

x=18

Dave is 18 years old.

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Answer:

[tex]y-1=5(x-8)[/tex]

More than 93 percent of all blank coupons are distributed as freestanding inserts in newspapers.

What is percent?

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Solving the given equation, the value of v that makes the statement true is:

A. v = 8.

The equation is:

[tex]12 = 12 + \frac{v - 8}{2}[/tex]

Hence:

[tex]\frac{v - 8}{2} = 0[/tex]

Applying cross multiplication:

v - 8 = 0

v = 8.

Hence option A is correct.

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Answer:

15.7 square feet

Step-by-step explanation:

To find the area of the garden we find the area of the rectangle and the area of the semicircle.

The area of the rectangle:

A=bh

A=(29)(20)

A=580ft^2

As shown in the picture, the width of the rectangle is 20 ft wide, which means that the diameter of the semicircle is also 20ft wide. The diameter is two times the radius, which means the radius of the semicircle is 10ft.

The area of a circle is represented by the equation: [tex]A=\pi r^{2}[/tex]

A semicircle is half of a circle, therefore the equation to find the area of a semicircle is: [tex]A=\frac{1}{2}\pi r^{2}[/tex]

Plugging our radius of 10ft in we get:

[tex]A=\frac{1}{2}\pi (10)\\ A=5\pi[/tex]

We use 3.14 for our value of [tex]\pi[/tex] to get:

[tex]A=5(3.14)\\A=15.7ft^{2}[/tex]

Therefore, the area of the rose garden is 15.7 square feet.

Equation of the parabola is [tex]y=\frac{1}{8} (x-7)^2[/tex] with a focus at [tex](7,2)[/tex] and a directrix at [tex]y=-2[/tex]

How to find the equation of parabola with focus and directrix ?

We know that focus of the parabola [tex](h,k+p)=(7,2)[/tex]

So [tex]k+p=2[/tex]......(a)

And directrix of the parabola

[tex]y=k-p\\=-2[/tex]

[tex]k-p=-2[/tex]........(b)

So add the equation (a) AND (b)

[tex]k+p=2\\k-p=-2\\------------\\2k=0\\k=0\\p=2[/tex]

Equation of the parabola with directrix and focus

[tex]y-k=\frac{1}{4p} (x-h)^2[/tex]

Substitute all the values

[tex]y-0=\frac{1}{4(2)} (x-7)^2\\y=\frac{1}{8} (x-7)^2[/tex]

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