Find the equation for the horizontal line passing through the point (-6,-6).

\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}\)

\(\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4\)

Problem 2

The commutative property of addition is the idea of adding any two (or more) numbers in any order we want. In the example above, the 3 and 5 swap places. You can think of them commuting back and forth as if they are going from work to home (or vice versa).

A similar property is the commutative property of multiplication. An example would be 2*3 = 3*2 (shown in choice B).

========================================

Problem 3

The list of choices is not showing up, so I cannot answer this one. Please update.

Answer:

$144 interest

Step-by-step explanation:

SInce it is a simple interest you have to solve like this

Principal x Interest rate x term

so it will be

3,000 x 4.8% x 1

= 144$ interest in one year without any withdrawal.

According to the poster you have to invest $3000 or more, and 3,000 is the minimum principal amount so it will yield the minimum interest that you could get in a year.

I hope that this could help :)

Answer:

144 Dollars

Step-by-step explanation:

Apply the formula of simple interest:

total interest = Principal (3,000) . Interest rate in decimal ( 0,048) . Amout of time the rate was applied per year (1)

So, will be:

I = 3000 . 0,048 . 1

I = 144

3000 + 144 = 3144 is the total amount

The amout of interest is 144

Answer:

x = 45 degrees

Step-by-step explanation:

All angles in a triangle will add up to 180 degrees.  So far we have 57 degree of 180.  We also see a supplementary angle, with one side being 102 degrees, so the other is 78 degrees, because it must add up to 180.  We see that the arrows in the bases show that the corners are even, so now we know two corners: one with 57 degrees and the other with 78.  

Now, follow this equation to find x:

57 + 78 + x = 180

135 + x = 180

-135        -135

x = 45

Answer:

Formula for Geometric Mean is given by,. ⇒ Geometric ... Thanks!!!! 6 21 __ = __ х 31.5 a. X = 4 b. X = 9 C. X = 110.25.

Answer:

\( R_2 = \dfrac{R_1R_T}{R_1 - R_T} \)

Step-by-step explanation:

\( R_T = \dfrac{R_1R_2}{R_1 + R_2} \)

\( (R_1 + R_2)R_T = R_1R_2 \)

\( R_1R_T + R_2R_T = R_1R_2 \)

\( R_2R_T - R_1R_2 = -R_1R_T \)

\( R_2(R_T - R_1) = -R_1R_T \)

\( R_2 = \dfrac{-R_1R_T}{R_T - R_1} \)

\( R_2 = \dfrac{R_1R_T}{R_1 - R_T} \)

To find the area of the combined rectangles, we need the dimensions (length and width) of each rectangle. However, the provided text and numbers do not seem to correspond to a clear description of the rectangles or their dimensions. Could you please provide more specific information or clarify the question?

Answer:

48 miles

Step-by-step explanation:

i think thats it.

Answer: 4.

Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.

                                Hope this helps!

Step-by-step explanation:

7 cups of apple juice + 3 cups of pineapple juice = 11

40-11 =29

You need 29.

You need 10 cups of pineapple juice to make 40.

You need 6 cups of apple juice to make 40.

Answer:

B 49/3

Explanation:

I did the work, unlike your lazy ahh! :)

Answer:

x intercept: (-8,0)

y intercept: (0,2)

Answer:

Use calculation for the population  standard deviation

Step-by-step explanation:

We are given that the data data set represents the ages of all 6 of Nancy's grandchildren

11,8,5,6,3,9

We have to determine which standard deviation would used for calculation of  the given data set.

Sample standard deviation :If the data values represent the data collected from   subset of  population .Then the sample standard deviation should be used.

Population standard deviation:

If the data values represents the data collected from entire population, then population standard deviation should be used.

We can see that the given data collected from entire population.

Therefore, we would use  calculation for population standard deviation of given data set.

Answer:

d

Step-by-step explanation:

click d

Answer:

Its D

Step-by-step explanation:

its greater than OR less than you forgot but here you go

The answer is:

g(x + 1) = 6x + 1

g(4x) = 24x -5

Work/explanation:

To evaluate, I plug in x + 1 into the function:

\(\sf{g(x)=6x-5}\)

\(\sf{g(x+1)=6(x+1)-5}\)

Simplify

\(\sf{g(x+1)=6x+6-5}\)

\(\sf{g(x+1)=6x+1}\)

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

Do the same thing with g(4x)

\(\sf{g(4x)=6(4x)-5}\)

\(\sf{g(4x)=24x-5}\)

Hence, these are the answers.

Answer:

Lincoln Avenue is represented by the line \( x = 5 \), which is a VERTICAL LINE.

Step-by-step explanation:

The equation of the line of Washington Avenue, x = 3, suggests that the line is a vertical line, since a vertical line takes the form of x = k, where k is the value x would always take and also it is the x-intercept.

Given that Lincoln Avenue passes through the point (5, 2), and its line is parallel to that of Washington Avenue, it means that the line do not intercept each other, and Lincoln Avenue is also a vertical line.

Therefore, if Lincoln Avenue passes through (5, 2), its line can be represented also in the form, x = k. Where, k is the value that x would always take, and also, it is the x-intercept. x would always be 5 even when y changes.

Therefore, the equation of the line that represents Lincoln Avenue would be:

✅ \( x = 5 \)

✅This is also a Vertical line.

The composition of the functions are,

(f o g) (x) = \(\frac{5}{5-7x}\) and (g o f) (x) =  \(\frac{5x-35}{x}\)

Composition of two functions f and g can be defined as the operation of composition such that we get a third function h where h(x) = (f o g) (x).

Given two functions,

f(x) = \(\frac{x}{x-7}\) and g(x) = \(\frac{5}{x}\)

We have to find (f o g) (x) and (g o f) (x).

(f o g) (x) = f (g(x))

That is plug, g(x) instead of x into the equation of f(x).

(f o g) (x) = \(\frac{\frac{5}{x} }{\frac{5}{x} -7}\)

              = \(\frac{\frac{5}{x} }{\frac{5-7x}{x} }\)

              = \(\frac{5}{5-7x}\)

Now we have to find (g o f) (x).

(g o f) (x) = g (f(x))

That is, plug f(x) instead of x into the equation of g(x).

(g o f) (x) = \(\frac{5}{\frac{x}{x-7} }\)

              = \(\frac{5(x-7)}{x}\)

              = \(\frac{5x-35}{x}\)

Hence the composition of the given functions f and g are found.

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Answer:

The maintained speed while hiking= 3 miles per hour

Let t be the time which represent the independent variable.

Also we know that  Distance= Speed × Time

⇒ Distance traveled while hiking=3 ×t=3t

Let h represent the distance function in miles, and h(t) the dependent variable.

Then h(t)=3t

When we put t=4

Then h(4)=3×4 =12 miles.

Step-by-step explanation:

The equation in slope-intercept form of the line that passes through the point (3,4) and is parallel to the line represented by y=3x−2 is  y = 3x - 5.

The equation of a line can be represented in slope intercept form, point slope form, standard form and general form.

Linear equation in slope intercept form is as follows:

y = mx + b

where

Therefore, the line that passes through the point (3,4) and is parallel to the line represented by y = 3x −2.

parallel lines have the same slope.

Therefore, the slope of the line is 3.

The y-intercept can be found as follows:

using (3, 4)

y = 3x + b

4 = 3(3) + b

b = 4 - 9

b = -5

Therefore, the equation in slope intercept form is y = 3x - 5.

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Answer:

Solution given:

x+100=180°{linear pair}

x=180-100

x=80

Answer:

\(-2077\)

Step-by-step explanation:

\(i=1(-3-4)=-7(first)\)

\(i=2(-3-4*2)=-11\)

\(i=3(-3-4*3)=-15\)

\(i=31(-3-4*31)=-127(last)\)

Difference= -11-(-7)= -4

\(sum=\frac{n}{2}\)

\(= \frac{31}{2}[-7+(-127)]\)

\(=\frac{31}{2}*(-134)\)

\(=31*(-67)\)

\(= -2077\)

✧༝┉˚*❋ ❋ ❋┉༝✧

hope it helps..

have a great day!!

Answer

First one is A

Second one is B

Third one is D

Problem 1

Answer: Choice A

(30, 225); Rocket reaches max height of 225 ft after 30 seconds.

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

Explanation:

Distribute the 0.25 through to get

y = 0.25(60x-x^2)

y = 15x - 0.25x^2

y = -0.25x^2 + 15x

This is in standard form y = ax^2+bx+c with a = -0.25, b = 15 and c = 0.

The first two values mentioned lead to this x coordinate of the vertex.

h = -b/(2a)

h = -15/(2*(-0.25))

h = -15/(-0.5)

h = 30

This tells us the answer is between A and C.

If you were to plug x = 30 into the original equation, you'll get y = 225. It means that after x = 30 seconds, the rocket has reached its max height of 225 feet. Therefore, the answer must be choice A.

===========================================================

Problem 2

Answer:  Choice B

(x-3)^2 = -8(y-6)

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

Explanation:

vertex = base of the bulb = (3,6)

focus = top of the bulb = (3,4)

This flashlight is pointed downward, which forms a downward opening parabola.

The distance from the vertex to the focus is p = 2 units. This is known as the focal distance.

We'll plug that in along with the vertex (h,k) = (3,6) in the formula below

4p(y-k) = (x-h)^2

4*2(y-6) = (x-3)^2

8(y-6) = (x-3)^2

Unfortunately that equation above produces a parabola that opens upward. To fix things, we stick a negative out front on either side, which will reflect the parabola over the x axis to make the parabola open downward. That leads us to choice B.

===========================================================

Problem 3

Answer:  D) square

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

Explanation:

We can form a point by intersecting the plane through the point where the two cones meet. The plane needs to be parallel to the base of each cone.

We can also form a line. To do so, we intersect the plane at exactly  along the edge of the cone. Make the plane tangent to the cone.

Lastly, we can form a circle by intersecting any plane parallel to the cone's base. This plane cannot pass through the meeting point of the two cones. Rather, the plane passes through one of the cones.

Those three previous paragraphs mean that we can rule out choices A,B,C. The only thing we can't form is a square. We can form straight lines, but we cannot form perpendicular lines needed to get a square. Nice work on selecting the correct answer.

Using the Pythagorean Theorem, the distance between Pole X and Pole Z is of 15.3 m.

The Pythagorean Theorem relates the length of the legs \(l_1\) and \(l_2\) of a right triangle with the length of the hypotenuse h, according to the following equation:

\(h^2 = l_1^2 + l_2^2\)

The first part of the distance is the hypotenuse of a right triangle of sides 0.5 and 2.5, tracing a right triangle at the top of pole X and tracing it to segment Y, hence:

df² = 0.5² + 2.5²

df = sqrt(0.5² + 2.5²)

df = 2.55m.

For the second part, we apply equivalent triangles, as we can also trace a right triangle at the top of segment Y to segment Z, hence:

0.5/2.5 = df/ds

1/5 = 2.55/ds

ds = 2.55 x 5 = 12.75m

Then the total distance is:

2.55 + 12.75 = 15.3 m.

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Equation:

\(tan(x) = \frac{opp}{adj}\)

Answer:

Step-by-step explanation:

The two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let \($&\overline{A B} \cong \overline{D E} \\\) and \($&\overline{A C} \cong \overline{D F}\)

Angle between \($\overline{A B}$\) and \($\overline{A C}$\) exists \($\angle A$\).

Angle between \($\overline{D E}$\) and \($\overline{D F}$\) exists \($\angle D$\).

Therefore, \($\triangle A B C \cong \triangle D E F$\) by SAS, if \($\angle A \cong \angle D$$\).

Given:

\($&\overline{A B} \cong \overline{D E} \\\) and

\($&\overline{A C} \cong \overline{D F}\)

According to the SAS congruence property, two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let \($&\overline{A B} \cong \overline{D E} \\\) and \($&\overline{A C} \cong \overline{D F}\)

Angle between \($\overline{A B}$\) and \($\overline{A C}$\) exists \($\angle A$\).

Angle between \($\overline{D E}$\) and \($\overline{D F}$\) exists \($\angle D$\).

Therefore, \($\triangle A B C \cong \triangle D E F$\) by SAS, if \($\angle A \cong \angle D$$\).

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Answer:

Step-by-step explanation:

Large sheet:

 Length = 9 inches

 Width of large sheet = area ÷ length = 5 inches

 ratio of length to width = 9:5

Small sheet:

 Length = 4 inches

 Width = 3 inches

 ratio of length to width = 4:3

9:5 ≠ 4:3

The sheets are not similar

The large sheet and small sheet are not similar because they have different dimensions.

What is the area of a rectangle ?

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.

It is given that large sheet has a length of 9 inches and an area of 45 square inches whereas the small sheet has length of 4 inches and a width of 3 inches.

Let's find out the area of small sheet which will be :

A = L × B

A = 4 × 3

A = 12 inches²

Whereas , in case of large sheet the area is 45 inches². So , the area of both sheets are not similar.

Let's check if dimensions are same.

Width of large sheet will be :

A = L × B

45 = 9 × B

or

B = 5 inches

So , dimensions are also not equal.

Therefore , the large sheet and small sheet are not similar because they have different dimensions.

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The value of m + n is given as follows:

A. 18.

The exponential expression for this problem is defined as follows:

\((x^5y^6)^{\frac{1}{5}}(x^3y^4}^{\frac{1}{4}}\)

Applying the power of power rule, we have that the exponents are given as follows:

Then the values of m and n are given as follows:

m = 7, n = 11.

Thus the sum is given as follows:

m + n = 7 + 11 = 18.

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Answer:

$6.47

Step-by-step explanation:

set up a ratio

\(\frac{1.99}{1} =\frac{x}{3.25}\)

cross multiply

6.47=x

Answer:

The system of equation that models the projectile of the two balls is option;

C. y = -16·x² + 12·x + 3

y = -16·x² + 9·x + 3.25

Step-by-step explanation:

The general equation for vertical (upward) motion under gravity is presented as follows;

h - h₀ = u·t + 1/2·g·t²

Where;

h = The final height reached

h₀ = The initial height

u = The initial velocity

g = The acceleration due to gravity ≈ -32 feet/second

t = The time taken

We can rewrite the above equation with different letters for the variables as follows;

h = y,

h₀ = y₀, and

t = x

Therefore, we have;

y - y₀ = u·x - 1/2 × 32 × x²

y = u·x - 1/2 × 32 × x² + y₀ = u·x - 16· x² + y₀

y = u·x - 16· x² + y₀ = -16·x² + u·x + y₀

y = -16·x² + u·x + y₀

For Tara, we have;

u = 12 feet/second

y₀ = 3 feet

Therefore, we get;

y = -16·x² + 12·x + 3

For Mallory, we have;

u = 9 feet/second

y₀ = 3.25 feet

Therefore, we get;

y = -16·x² + 9·x + 3.25

The correct option is therefore;

y = -16·x² + 12·x + 3

y = -16·x² + 9·x + 3.25