Which negative angle is equivalent to an 85° angle?
A. An angle measuring -95°
B. An angle measuring -275°
C. An angle measuring -85°
D. An angle measuring -265°

Answer:

g(x) is shifted 4 units left and 6 units down from f(x).

Step-by-step explanation:

The parent function is:

f(x).

The child function is:

[tex]g(x) = f(x+4) - 6[/tex]

Transformation 1:

[tex]g(x) = f(x+4)[/tex]

Shifting a function f(x) a units to the left is finding f(x + a). So g(x) = f(x + 4) is f(x) shifted 4 units to the left.

Transformation 2:

[tex]g(x) = f(x+4) - 6[/tex]

Subtracting a function f(x) by a constant a is the same as shifting the function a units down. So subtracting by 6 is shifting the function 6 units down. Thus, the correct answer is:

g(x) is shifted 4 units left and 6 units down from f(x).

Answer:

17.46 ft

Step-by-step explanation:

The inclined plane is in the shape of a right triangle, therefore we can use the Pythagorean theorem to find the length of the inclined plane. The formula for this theorem is the following

[tex]a^{2} + b^{2} = c^{2}[/tex]

Where a and b are the two sides and c is the hypotenuse/inclined side. Therefore, we can simply plug in the lengths of the two sides into the formula and solve for c.

[tex]a^{2} + b^{2} = c^{2}[/tex]

[tex]7^{2} + 16^{2} = c^{2}[/tex]

[tex]49 + 256 = c^{2}[/tex]

[tex]305 = c^{2}[/tex]   ... square root both sides

17.46 = c

Answer:

x = 10

Step-by-step explanation:

The true statement over the interval [-3, 0] is: B. average rate of change of function f is less than that of function g.

Over a given interval, the average rate of change of a function is found using the formula: change in y / change in x = f(b) - f(a) / b - a.

Average rate of change of function g over [-3, 0]:

a = -3, f(a) = 5

b = 0, f(b) = 14

Average rate of change = (14 - 5)/(0 - (-3)) = 3

Average rate of change of function f over [-3, 0]:

a = -3, f(a) = -4.5

b = 0, f(b) = 0

Average rate of change = (0 - (-4.5))/(0 - (-3)) = 1.5

Therefore, the correct answer is: B. average rate of change of function f is less than that of function g.

Learn more about average rate of change on:

https://brainly.com/question/11627203

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Answer:

[tex]Volume = \frac{3}{128}ft^3[/tex]

Step-by-step explanation:

Given

[tex]Length = 1\ cube[/tex]

[tex]Width = 3\ cubes[/tex]

[tex]Height = 4\ cubes[/tex]

[tex]1\ cube = \frac{1}{8}ft[/tex]

Required

The volume of the cube

Start by calculating the dimension in ft

[tex]Length = 1\ cube[/tex]

[tex]Length = 1 * \frac{1}{8}ft[/tex]

[tex]Length = \frac{1}{8}ft[/tex]

[tex]Width = 3\ cubes[/tex]

[tex]Width = 3 * \frac{1}{8}ft[/tex]

[tex]Width = \frac{3}{8}ft[/tex]

[tex]Height = 4\ cubes[/tex]

[tex]Height = 4 * \frac{1}{8}ft[/tex]

[tex]Height = \frac{1}{2}ft[/tex]

So, the volume is:

[tex]Volume = Length * Width * Height[/tex]

[tex]Volume = \frac{1}{8}ft * \frac{3}{8}ft * \frac{1}{2}ft[/tex]

[tex]Volume = \frac{1}{8} * \frac{3}{8} * \frac{1}{2}ft^3[/tex]

Using a calculator, we have:

[tex]Volume = \frac{3}{128}ft^3[/tex]

Answer:

[tex]x=15[/tex]

Step-by-step explanation:

Pythagorean theorem: [tex]c^2 = a^2 + b^2[/tex], where c is the longest side (hypotenuse), a and b are the other sides of the right angled triangle.

In this question, c is labelled as [tex]x[/tex].

Therefore, we can use the theorem to find [tex]x[/tex].

[tex]x^2 = a^2+b^2[/tex]

So, substitute in the other sides and solve for [tex]x[/tex].

[tex]x^2 = (9)^2 + (12)^2\\x^2 = 81 + 144\\x^2 = 225\\x = 15[/tex]

We can see the answer is correct because it is meant to be the largest side and [tex]15> 12>9[/tex].

Answer:

71

Step-by-step explanation:

cumulative means all together

Explanation:

The period of a function measures how long a cycle takes. Think of tides on a beach. There's a regular pattern that can be predicted whether its high tide or low tide. Time is often the critical component with the period. Since choice D mentions time and the key term "repeat", this is why it's the answer.

The other values, while useful elsewhere, aren't going to tell us anything about the period. The initial value being 5 doesn't tell us when y = 5 shows up again, and if the function is repeating itself at this point or not. So info about choice A is not sufficient to determine the period. The same goes for choices B and C as well.

Answer:

Step-by-step explanation:

Given quadratic equation is,

-32 = 2(x² + 10x)

-32 + 50 = 2(x² + 10x + 25)

18 = 2(x + 5)²

9 = (x + 5)²

± 3 = (x + 5)

x = -2 or x = -8

Answer:

6(3x - 4)

Step-by-step explanation:

From the question, we can deduce the following points;

- 6 is multiplied by 3x minus 4

Translating the word problem into an algebraic expression, we have;

6 * (3x - 4)

Answer:

E

Step-by-step explanation:

well, yes we know what coins there are and that they’re in jars right? but to find which jar is worth the most, we need to know how many coins are in each. she could have 300 pennies, 2 quarters, 4 dimes, and 7 nickels. we need more information to answer this question so E is the only correct option!

Step-by-step explanation:

Its Undefined.

Reason

Slope (m) = y2 - y1/(x2-x1)

= 3-(-6)/(12-12)

=9/0

Undefined

You can clearly see this from the points. The x value has 2 different values for y... Which Makes the points not that of a function.

Answer:

[tex]\implies f(x) = ( x + 2)^2[/tex]

Step-by-step explanation:

Given :-

And we need to rewrite the function by completing the square. The function is ,

[tex]\implies f(x) = x^2+8x + 4[/tex]

[tex]\implies ( a + b)^2= a^2+b^2+2ab [/tex]

Rewriting the function :-

[tex]\implies f(x) = x^2+8x + 4\\\\\implies f(x) = x^2 + 2.2.2x + 2^2[/tex]

[tex]\implies f(x) = ( x + 2)^2[/tex]

Hence the function in whole square form is (x + 2)² .

Answer:

7

Step-by-step explanation:

-3 + 3 = 0

0 + 4 = 4

4 + 3 = 7

Answer:

[tex]7^\circ\text{C}[/tex]

Step-by-step explanation:

Calculate second temperature minus the first one.

4 - (-3) = 4 + 3 = 7

Answer:

56.55

Step-by-step explanation:

Solution

V=

π

r

2

h

=

π

3

2

2

≈

56.54867

Answer:

25 people were surveyed.

Step-by-step explanation:

Add up the frequency.

Answer:

24

Step-by-step explanation:

Answer: 25 units^2

Step-by-step explanation:

This is the correct answer

Answer:

A

Step-by-step explanation:

Answer:

Your answer would be 4^-3.

Step-by-step explanation:

So, a negative exponent by definition, is writing out 1/x^y. Where x is the number and y is the negative exponent.

In this case, 4 would be the number and -3 would be the negative exponent.

So we're going from 1/x^y to x^-y in order to solve this. Therefore, this is something where the numbers can just be plugged in.

1/x^y ---> x^-y

1/4^3 ---> 4^-3

Your answer would be 4^-3.

Answer:

Option D is correct

Step-by-step explanation:

Hope it is helpful....

Answer:

yea

Step-by-step explanation:

x=13 so 13-9=4

Answer:

(4,5)

Step-by-step explanation:

Use the midpoint formula

(( x1 + x2)/2, (y1 + y2)/2 )

Answer:

0.0623 ± ( 2.056 )( 0.0224 ) can be used to compute a 95% confidence interval for the slope of the population regression line of y on x

Step-by-step explanation:

Given the data in the question;

sample size n = 28

slope of the least squares regression line of y on x or sample estimate = 0.0623

standard error = 0.0224

95% confidence interval

level of significance ∝ = 1 - 95% = 1 - 0.95 = 0.05

degree of freedom df = n - 2 = 28 - 2 = 26

∴ the equation will be;

⇒ sample estimate ± ( t-test) ( standard error )

⇒ sample estimate ± ( [tex]t_{\alpha /2, df[/tex]) ( standard error )

⇒ sample estimate ± ( [tex]t_{0.05 /2, 26[/tex]) ( standard error )

⇒ sample estimate ± ( [tex]t_{0.025, 26[/tex]) ( standard error )

{ from t table; ( [tex]t_{0.025, 26[/tex]) = 2.055529 = 2.056

so we substitute

⇒ 0.0623 ± ( 2.056 )( 0.0224 )

Therefore, 0.0623 ± ( 2.056 )( 0.0224 ) can be used to compute a 95% confidence interval for the slope of the population regression line of y on x

Answer:

(a) 160 Naira

(b) Undefined

Step-by-step explanation:

Given

Let:

[tex]y \to[/tex] cost of bag of rice

[tex]x \to[/tex] people demanding the bag

So, we have:

[tex]y\ = \frac{k}{\sqrt x} + c[/tex] ---- The variation

[tex]y = 100; x = 36[/tex]

[tex]y = 150; x = 144[/tex]

We have:

[tex]y\ = \frac{k}{\sqrt x} + c[/tex]

When: [tex]y = 100; x = 36[/tex]

[tex]100 = \frac{k}{\sqrt {36}} + c[/tex]

[tex]100 = \frac{k}{6} + c[/tex] -- (1)

When: [tex]y = 150; x = 144[/tex]

[tex]150 = \frac{k}{\sqrt {144}} + c[/tex]

[tex]150 = \frac{k}{12} + c[/tex]--- (2)

Subtract (1) from (2)

[tex]150 - 100 = \frac{k}{12} - \frac{k}{6} + c - c[/tex]

[tex]50 = \frac{k}{12} - \frac{k}{6}[/tex]

Multiply through by 12

[tex]600 = k - 2k[/tex]

[tex]600 = -k[/tex]

[tex]k = -600[/tex]

To solve for x, we have:

[tex]100 = \frac{k}{6} + c[/tex] -- (1)

This gives:

[tex]100 = \frac{-600}{6} + c[/tex]

[tex]100 = -100 + c[/tex]

[tex]c = 100 + 100[/tex]

[tex]c = 200[/tex]

So, the equation is:

[tex]y\ = \frac{k}{\sqrt x} + c[/tex]

[tex]y = -\frac{600}{\sqrt x} + 200[/tex]

Solving (1): y; when x = 225

We have:

[tex]y = -\frac{600}{\sqrt x} + 200[/tex]

[tex]y = -\frac{600}{\sqrt {225}} + 200[/tex]

[tex]y = -\frac{600}{15} + 200[/tex]

[tex]y = -40 + 200[/tex]

[tex]y = 160[/tex]

Solving (2): x; when x = 200

We have:

[tex]y = -\frac{600}{\sqrt x} + 200[/tex]

[tex]200 = -\frac{600}{\sqrt x} + 200[/tex]

Collect like terms

[tex]\frac{600}{\sqrt x} = 200 - 200[/tex]

[tex]\frac{600}{\sqrt x} =0[/tex]

Cross multiply

[tex]600 =0 * \sqrt x[/tex]

[tex]600 =0[/tex]

x is undefined

Answer:

Option 4

Step-by-step explanation:

Let any two real number a and b (no matter +ve, -ve or 0). a ≥ b

The average of them will always lie in between them or be equal(if 0).

Let's prove : According to the statement,

a ≥ (a + b)/2 ≥ b

2a ≥ a + b ≥ 2b

2a ≥ a + b and a + b ≥ 2b

a ≥ b and a ≥ b, as we assumed.

Moreover, as the average exists in between a and b, we have the average (a + b)/2. Similarly, there exists one more average of (a + b)/2 and a or b, which definitely lie between a and b as (a + b)/2 lies there and smaller than a and b.

In the same order, we can have many average and the process would stop. This leads to infinite number between a and b.

Notice that we talked about all the numbers moreover there are many irrational(non-terminating like 9.898989.... etc numbers as well.

Option (4), infinite solutions.

Note: we solved for all the number (not specifically odd, even, natural, whole, integer, etc).

Answer:

For a general function f(x), the domain is the set of the possible values of x that we can input in the function.

The trick to find the domain is first to assume that the domain is the set of all real numbers, and then let's try to find the values of x that cause a problem in the function. (If the graph is cut in some value of x, such that it ends with an open or a closed point, then these values define the domain).

Such that one of these problems can be like x = 1 in the function:

g(x) = 1/(x - 1)

Because that value causes the denominator to be equal to zero, then the domain of that function will be the set of all real numbers except the value x = 1.

In this case, we have:

f(x) = x^2 - 4

There is no value of x that causes a problem for this function, then the domain is the sett of all real numbers.

Correct option D.

Answer:

[tex] (x-1.3) ^2 + (y+3.5) ^2= 37 [/tex]

Step-by-step explanation:

Radius of the circle [tex] r = \sqrt {37}\: units [/tex]

Center of the circle (h, k) = (1.3, - 3.5)

Equation of the circle in center radius form is given as:

[tex] (x-h) ^2 + (y-k) ^2= r^2 [/tex]

Plugging the values of h, k and r in the above equation, we find:

[tex] (x-1.3) ^2 + (y+3.5) ^2= (\sqrt {37})^2 [/tex]

[tex] (x-1.3) ^2 + (y+3.5) ^2= 37 [/tex]

This is the required equation of the circle.

Answer:

1

Step-by-step explanation:

First, we can find the equation of the parabola. The standard form of a parabola is ax^2 + bx + c,

where c is the y-intercept. The y-intercept on the graph is -5, and every option starts with x^2, so the equation must be x^2 - 5. This rules out options 3 and 4.

Next, we can find the equation of the line. The options are all given in slope-intercept form: y = mx + b, where b is the y-intercept. The y-intercept on the graph is 1, and option 1 has 1 in the place of b. Therefore, option 1 is the answer.