Which graph represents y = Two-thirdsx + 3?
On a coordinate plane, a line goes through points (negative 2, 0) and (0, 3).
On a coordinate plane, a line goes through points (0, negative 3) and (4, 0).
On a coordinate plane, a line goes through points (negative 3, 1) and (0, 3).
On a coordinate plane, a line goes through points (0, 3) and (3, 1).

The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is, 3 / 5

We have to given that;

the terminal side of theta in standard position contains the point (6,-8)

Hence, For given condition we get;

The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,

Here, x = 6, y = - 8

Hence, We get;

r = √x² + y²

r  = √6² + 8²

r = √36 + 64

r = √100

r = 10

So, The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,

cos θ = x / r

cos θ = 6 / 10

cos θ =  3 / 5

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₋2.3 < ₋8/3 is the correct answer.

Given, we need to compare the terms.

₋8/3 = ₋2.67

therefore, 2.3 is less than 2.667

hence we form it as ₋2.3 < ₋2.67

we form: ₋2.3 < ₋8/3

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Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

The area of the blue-shaded region is 19.95 m²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a rectangle with length 14 m, and diagonal 15.5 m, a parallelogram has been cut out of it, we need to find the area remaining,

Using the Pythagoras theorem,

15.5² = 14²+w² [width]

w² = 240.25-196

w² = 44.25

w = 6.65

Therefore, the width of the rectangle is 6.65 m

That mean, the height of the parallelogram is 6.65 m,

The area of the blue-shaded region, is calculated by subtracting the area of the parallelogram by the area of the rectangle,

Area of the remaining region = 14×6.65-11×6.65

= 6.65(14-11) = 6.65×3

= 19.95 m²

Hence, the area of the blue-shaded region is 19.95 m²

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Answer:

d. y = 3x + 5

Step-by-step explanation:

plug x = 2 in the equation y = 3x +5

y = 3*2 + 5

y = 11

so x = 2, y = 11

we know d is the correct statement

Answer:

your question and is d option

Answer:

box 2 and 3

Step-by-step explanation:

the rays are the only two that form the angle of 1

Answer:

[1.3,∞)

Step-by-step explanation: The instructions on this weren't really clear, so I converted it to interval notation

Answer:

(4,0)

Step-by-step explanation:

You basically are plotting a point on the positive number 4 on the x line. Since they're only asking for an X and not a Y, you'd leave it as (4,0). Hope this helps!

Answer:

x+14.

Step-by-step explanation:

Sum of a number and 14 is x+14.

Answer:

The answer is 6

Step-by-step explanation:

Since you have to divvied 40 to 8 witch gives you 6

Answer:

Step-by-step explanation:

Given:

a₁ = 3

an+1 = (an)² + 1To find:

a₃Solution:

We can use the recursive formula given to find the value of a₃.a₂ = a₁ + 1² = 3 + 1 = 4

a₃ = a₂² + 1 = 4² + 1 = 17Therefore, the value of a₃ is 17.Answer: a₃ = 17

Answer:

The length of the third side is approximately ≈ 14.79 inches

Step-by-step explanation:

A piece of wire is bent into the shape of a triangle. Two sides have lengths of 16 inches and 23 inches. The angle between these two sides is 40°. What is the length of the third side to the nearest hundredth of an inch?

Use the law of cosines to find the length of the missing side.

Let C be the third side.

A = 18

B = 23

Angle C = 40^∘

c^2  =  a^2  +  b^2 - 2ab  cos C

c =  √a^2 + b^2 - 2ab cos C

c =  √18^2 + 23 ^2 - 2 (18) (23) cos 40^∘

c = √583 - 828 cos40^∘

≈ 14.79

Thus, The length of the third side is approximately  14.79 inches.

Hope this helps!

Answer:

•  Mean = 30.4

•  Median = 30

•  Mode = None

•  Range = 5

Step-by-step explanation:

To find the mean, we add all the numbers together and divide by the total number of numbers. In this case, we have 5 numbers: 28, 32, 29, 30, and 33. Adding them together gives us 152. Dividing by 5 gives us a mean of 30.4.

To find the median, we need to order the numbers from smallest to largest: 28, 29, 30, 32, and 33. The median is the middle number which is 30.

To find the mode, we look for the number that appears most frequently in the list. In this case, there is no number that appears more than once so there is no mode.

To find the range, we subtract the smallest number from the largest number. In this case, the smallest number is 28 and the largest number is 33 so the range is 5.

Therefore:

•  Mean = 30.4

•  Median = 30

•  Mode = None

•  Range = 5

I hope that helps!

Answer:

b

Step-by-step explanation:

to prove if NP is tangent to MN

we could prove if NPM is a right triangle

By pythagorean theorem

a^2+b^2=c^2

where a=MN=33

b=NP=180

c=MP=MQ+QP=152+33=185

so

33^2+180^2=185^2

but

1089+32400 is not equal to 34225

33489 is different from 34225

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer:

B. 2 + (3^2 * 5) - 3

Step-by-step explanation:

Hey! Sorry for the long wait, I'm still in school and can't really be here 24/7 but I'm proud to announce that I have your answer!

So we have 4 expressions and we need to get our answer to 44. This question already includes the notion that parenthesis placements make a huge difference, so let's review them.

2 + 3^2 * (5 - 3)

Use PEMDAS

2 + 3^2 * 2

2 + 9 * 2

2 + 18

20

2 + (3^2 * 5) - 3

2 + (9 * 5) - 3

2 + 45 - 3

47 - 3

44

(2 + 3^2) * 5 - 3

(2 + 9) * 5 - 3

11 * 5 - 3

55 - 3

52

(2 + 3)^2 * 5 - 3

(5)^2 * 5 - 3

25 * 5 - 3

125 - 3

122

As we can see, B. is our answer due to its equivlance to 44.

Answer:

Area = 49π

Step-by-step explanation:

circle Area = π x (radius)²

Assuming d = 14 is the diameter (which the problem really should state explicitly, not leave you to assume), then the radius is half of that.

So r = 7, where 'r' is the radius.

Area = π x r² = π(7)² = π(49)

Area = 49π is the exact answer, so it is the one I prefer.

Area = 153.86 is the decimal you get if you multiply 49 x 3.14

Hope this helps.

Answer:

ANSWER

Step-by-step explanation:

Without knowing the specific function w(x), it is impossible to determine the domain of the inverse function w^-1(x). However, in general, the domain of an inverse function is the range of the original function, and vice versa.

If we assume that w(x) is a one-to-one function (which is necessary for it to have an inverse function), we can determine the range of w(x) and use it to find the domain of w^-1(x).

For example, if we know that w(x) is a function that takes all real numbers except x=2, then the range of w(x) is (-∞,2) U (2,∞). The domain of w^-1(x) is then the same as the range of w(x), which is (-∞,2) U (2,∞). Therefore, the domain of w^-1(x) is x ≠ 2.

Without more information about w(x), we cannot determine the domain of w^-1(x) more precisely.

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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Answer:60

Step-by-step explanation:

Answer:

\(4^2=5^2+7^2-2(5)(7) cos A\\\\\)

\(A=34.0^o\)

-----------------

\(\frac{4}{Sin34^o} =\frac{5}{SinB} \\\\\)

\(B=44.4^o\)

--------------

\(7^2=4^2+5^2-2(4)(5)CosC\)

\(C= 101.5^o\)

\(---------\)

hope it helps...

have a great day!!

All the missing elements of the triangle by the Cosine rule are A = 40°, B = 45°, and C = 102°.

Given that,

Three sides on a triangle are,

a = 4

b = 5

c = 7

Used the formula of the Cosine rule which states that,

a² = b² + c² - 2bc cos A

b² = a² + c² - 2ac cos B

c² = a² + b² - 2ab cos C

Where, a, b, and c are three sides and A, B, and C are angles of a triangle.

Now, apply the Cosine rule to find the all angles of a given triangle,

a² = b² + c² - 2bc cos A

Substitute a = 4, b = 5 and c = 7,

4² = 5² + 7² - 2 × 5 × 7 cos A

16 = 25 + 49 - 70 cos A

70 cos A = 74 - 16

70 cos A = 58

Divide both sides by 58,

cos A = 58/70

cos A = 0.83

A = cos ⁻¹ (0.83)

A = 33.9°

Round to the whole number,

A = 40°

b² = a² + c² - 2ac cos B

Substitute a = 4, b = 5 and c = 7,

5² = 4² + 7² - 2 × 4 × 7 cos B

25 = 16 + 49 - 56 cos B

25 = 65 - 56 cos B

56 cos B = 65 - 25

56 cos B = 40

cos B = 40/56

cos B = 0.71

B = cos ⁻¹ (0.71)

B = 44.7°

Round to the whole number,

B = 45°

c² = a² + b² - 2ab cos C

Substitute a = 4, b = 5 and c = 7,

7² = 4² + 5² - 2 × 4 × 5 cos C

49 = 16 + 25 - 40 cos C

49 = 41 - 40 cos C

40 cos C = 41 - 49

40 cos C = - 8

cos C = - 8/40

cos C = - 1/5

cos C = - 0.2

C = cos ⁻¹ (0.2)

C = 101.5°

Round to the whole number,

C = 102°

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Answer: 4(x+2)

Step-by-step explanation:

1. Take the GCF from both terms and put it on the outside of the parentheses

2. Factor each term inside of the parentheses, in this case, 4

Answer: x=4.7

Step-by-step explanation: 1. Subtract 3.9 to both sides to get 0.4x=1.88

2. Divide by 0.4 to both sides to get that x=4.7

Answer:9

Step-by-step explanation:

Answer:

To see if multiple ratios are proportional, you could write them as fractions, reduce them, and compare them. If the reduced fractions are all the same, then you have proportional ratios.

Step-by-step explanation:

Answer:

they are proportional

Step-by-step explanation:

to find if they are proportional, we will take x/y ratios and compare several of them, it will tell us if they are proportional or not and give us the constant of proportionality

x1/y1 = 21/3 = 7/1

x2 / y2 = 70 / 10 = 7 / 1

x3 / y3 = 49 /7 = 7 / 1

Since the x/y ration does not change, they are proportional, which means that whatever the value of y, the value of x will be y multiplied by the constant of proportionality

and the constant of proportionality is 7

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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