The measure of angle 5 is 80 degrees. The measure of angle 2 is one-eighth the measure of angle 5. What is the measure of angle 4

The domain of the given relation includes the set of all x-values in the relation, which is: {–4, −2, 3}.

The domain of a relation is the set of all possible x-values (input), while the y-values are the range.

Given the relation, {(−4, 3), (3, 6), (−2, 1), (3, 6)}:

Domain of the relation is: {–4, −2, 3}.

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Option A, with inequalities a + b ≥ 30 and b ≥ a + 10, correctly describes these conditions.

We are given that the sum of two positive integers, a and b, where b is greater, is at least 30, which can be represented as a + b ≥ 30.

The difference between the two integers is also at least 10, and since b is the greater integer, this relationship is given by b - a ≥ 10.

The correct system of inequalities that represents these conditions is Option A:
a + b ≥ 30
b ≥ a + 10

Option B is incorrect because it suggests b is less than or equal to a - 10, which doesn't make sense in this context since b is the greater integer.

Options C and D are incorrect because they suggest that the sum of a and b is less than or equal to 30, which contradicts the given that the sum is at least 30.

To show that the set of functions satisfying f' + 2f = 0 is a subspace of F(-∞,∞), we prove closure under addition and scalar multiplication.

Differentiable functions: To prove that the set of functions satisfying f' + 2f = 0 is a subspace of F(-∞,∞), we need to show that the set is closed under addition and scalar multiplication. This involves demonstrating that if two functions f1 and f2 satisfy the given differential equation, then any linear combination c1f1 + c2f2 also satisfies it.

Proof:

Let f1, f2 be solutions of f' + 2f = 0, then (c1f1 + c2f2)' + 2(c1f1 + c2f2) = c1(f1' + 2f1) + c2(f2' + 2f2) = c1(0) + c2(0) = 0. Therefore, any linear combination of solutions is also a solution.

Answer: the answer you will get is 4

Step-by-step explanation:

The volume of the prism is 927 cubic Inches.

This is defined as the measure of how much space there is within a three-dimensional object.

Area of Octagon A = 1/2 x apothem x perimeter

A= 1/2 x 4.83 x 4(8) = 77.28

Volume  = Area of the base × height

                = 77.28 x 12 = 927 cubic inches.

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erform a simple calculation to match the screen size of a standard TV to that of a widescreen TV. If you currently have a 4:3 TV and you want to continue watching 4:3 on a widescreen TV, multiply the diagonal length of the older TV model by 1.22. The result would be the diagonal screen size that the widescreen TV would have to be to match the old model.

Answer:

(2x-3) is the answer.

Step-by-step explanation:

The given expression is :

[tex]2xy+6x-3y-9[/tex]

Grouping these terms we get-

[tex]2x(y+3)-3(y+3)[/tex]

So, the factors are :

[tex](2x-3)(y+3)[/tex]

Hence, out of the given options (2x-3) is the answer.

And he other factor is (y+3) that is not mentioned in the options.

Final answer:

The factor of the expression 2xy + 6x - 3y - 9 is 2x - 3, which is found by factoring the expression by grouping.

Explanation:

The expression given is 2xy + 6x − 3y − 9. To determine which expression is a factor of it, we can attempt factoring by grouping. Grouping the terms as (2xy + 6x) and (− 3y − 9) and factoring out the common factors from each group gives us:

We can see that (y + 3) is a common factor between the two groups. Factoring this out, we get:

(2x − 3)(y + 3)

This shows that 2x − 3 is a factor of the given expression.

The value of 'm' in the equation y=mx represents the slope of the line. However, without specific 'x' or 'y' values or a complete equation like y=mx+b, it is impossible to determine the value of 'm'.

The formula y=mx is the slope-intercept form of a linear equation where y is the dependent variable, m is the slope, and x is the independent variable. However, in this particular case, the equation provided is not complete in this form because there is no specific 'x' or 'y' value provided, and so it's not possible to calculate 'm' directly from this equation. Instead, in a more complete example, like y = 3x, you could identify 'm' as 3 by simply looking at the coefficient of 'x'. In order to clarify your equation, please provide either specific values of 'x' and 'y', or a complete equation in the format y = mx + b, where b is the y-intercept.

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On Saturday, 285 hamburgers were sold.

A simultaneous equation is anyone or more equations that can have the same number of unknowns and be solved concurrently. And an equation system is a simultaneous equation.

Given, a local hamburger shop sold a combined total of 510 hamburgers and cheeseburgers on Saturday.

Let x represents the number of hamburgers sold and y represents the number of cheeseburgers sold.

So, x + y = 510     {equation 1}

According to the question,

there were 60 more cheeseburgers sold than hamburgers.

x = y+ 60

We have a system of equations,

Substituting the value of x to the equation 1,

y+60+ y = 510

2y = 510 - 60

y = 450 / 2

y = 225

Then, x = 285

Therefore, 285 hamburgers were sold on Saturday.

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The selling price for 10 hats, calculated by applying the cost function f(x) to find the cost and then the selling price function g(x), is $8.

The selling price of 10 hats can be found by first calculating the cost of materials to make those hats using the function f(x) = 0.5x + 1, and then applying the g(f(x)) function to find the selling price, where g(x) = x + 2.

First, we calculate the cost for making 10 hats:
f(10) = 0.5  imes 10 + 1 = 5 + 1 = 6.

Now, we use the selling price function g to calculate the selling price for 10 hats:
g(f(10)) = g(6) = 6 + 2 = 8.

Therefore, the selling price for 10 hats is $8.

Answer:

46

Step-by-step explanation:

Answer:

A: (-2,4)

Step-by-step explanation:

i did it on usatestprep

Answer:  Option 'D' is correct.

Step-by-step explanation:

Since we have given that

sin 48° cos 15° - cos 48° sin 15°

As we know that,

[tex]\sin A\cos B-\cos A\sin B=\sin(A-B)[/tex]

So, we get that

[tex]A=48\textdegree\\B=15\textdegree[/tex]

Now, put it in the above expression.

[tex]\sin (A-B)=\sin(48-15)=\sin 33\textdegree[/tex]

Hence, Option 'D' is correct.

What is the 12th term in the sequence?

an=−16+2n

n =term

n=12

Sub n=12

a(12)=-16+2(12)

a(12)=-16+24

a(12)=8

Answer:

A. in edge

Step-by-step explanation:

$75.69

Final answer:

After nine years, investing $2,600 in Raxin Accounting bonds will yield a greater return than investing $2,000 in their stocks, specifically $579.30 more due to the effect of compound interest.

Explanation:

If you invest $2,600 in Raxin Accounting bonds with a total yield of 11.4% annually and $2,000 in Raxin Accounting stocks with a total yield of 14.4% annually, we can calculate the future value of both investments after nine years using the formula for compound interest: Future Value = Principal × (1 + rate)^time.

For bonds: Future Value = $2,600 × (1 + 0.114)^9 = $2,600 × 2.7845 = $7,239.70

For stocks: Future Value = $2,000 × (1 + 0.144)^9 = $2,000 × 3.3302 = $6,660.40

Comparing the future values, the investment in Raxin Accounting bonds will yield a greater return after nine years, specifically $579.30 more than the investment in stocks.