Which exponential equation is equivalent to the logarithmic equation below 4^c=256

Answer:

f (-5) = -81

Step-by-step explanation:

f (-5) = - (-5)² + 10.(-5) - 6 = -81

Answer:

A.) The function is increasing for all real values of x where x < -4

Step-by-step explanation:

On the interval x < -4, all of the x values are increasing. Before x = -4, the line assumes a positive slope because it is heading upwards. After this interval, the function is decreasing because the slope is heading downwards.

On the interval -6 < x < -2, all of the x values are positive because they lie above the x-axis. This does not necessarily mean that all of the values are increasing.

On the interval x < -6 and x > -2, all of the x values are negative because they lie below the x-axis.

Using a linear function, we have that:

A linear function is modeled by:

y = mx + b

In which:

Since there are currently 368 glasses(y-intercept), and each set on sale comes with 10 glasses(slope), the number of glasses after x sales is given by:

y = 368 + 10x.

She needs at least 673 glasses, hence the inequality is:

[tex]y \geq 673[/tex]

[tex]368 + 10x \geq 673[/tex].

Now we solve the inequality to find the number of sets needed:

[tex]10x \geq 305[/tex]

[tex]x \geq 30.5[/tex]

As the number of sets is an integer number, the solution is:

[tex]x \geq 31[/tex].

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Answer:

3rd graph from the top.

Step-by-step explanation:

It can't be the top one because the kids shoulder doesn't start at the ground.

It can't be the second or fourth because it shows him not waiting in line.

Therefore it must be the 3rd!

Answer: 3rd option

Step-by-step explanation:

Because the description says that it starts not at 0(from the kid's shoulder), the 1st and 4th options are out.

2nd option is incorrect because the kid had to stand in line so the shoulder height doesn't change(unless he was picking stuff up or something)

That leaves the 3rd option.

Answer:

Therefore, we can say that the exponent will be negative if the number is less than 1 and vice versa.

Step-by-step explanation:

We are asked to explain that when we convert a decimal number to scientific notation how will we know whether the exponent is negative.

If the given number is greater than 1 then the exponent is positive and if less than 1 the exponent is negative.

Answer:

Answer is 544

Hope it helps you

Answer:

- HOW TO FIND VOLUME OF PRISM -

1st step - Write the formula for finding the volume of a regular pentagonal prism. The formula is V = [1/2 x 5 x side x apothem] x height of the prism.

2nd step - Find the area of the pentagonal base face. Let's say the length of a side is 6 cm and the length of the apothem is 7 cm.

3rd step - Find the height. Let's say the height of the shape is 10 cm.

4th step - Multiply the area of the pentagonal base face times the height. ...

and last step - State your answer in cubic units.

Step-by-step explanation:

:):):)

a) If μ₁ is the average learning rate of the 6th graders without background noise level and μ₂  is the average learning rate of the 6th graders with the background noise level

The Null Hypothesis is that the learning rate of the 6th graders is not affected by the background noise level.

The null hypothesis, H₀:  μ₁ = μ₂

b) The Alternative Hypothesis is that the learning rate of the 6th graders is affected by the background noise level.

An alternative hypothesis, Hа:  μ₁ ≠ μ₂

c) Assumptions that must be met about the data before she can correctly use an independent t-test

There must be a random selection of the 6th graders

That the two groups are normally similar in their learning abilities

The division of students into the two groups should be at random

d) She has to make these assumptions to prevent bias and inaccuracy of results. If these assumptions are not made, the outcome of the experiment may not reflect the true effect of background noise on the learning of the 6th graders.

She can still get accurate results if she includes some bias in the selection to prove a particular result.

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The numbering system we commonly use is called the decimal numbering system because it uses 10 symbols to represent all possible numbers.

A way of writing numbers is known as a number system.

There are the following number systems:

Hence, we can say that the numbering system we commonly use is called the decimal numbering system because it uses 10 symbols to represent all possible numbers.

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The cost to cover the garden with mulch will be $12.00, as the area of the rectangular garden is 12 ft.².

The cost of one bag of mulch is given as $5.00.

The area covered by one bag of mulch is 5 ft.².

Therefore, the cost to cover 1 ft.² of the garden with mulch is $(5/5) = $1.00.

To find the area of the rectangular plot representing the garden, we do the follows:

The distance formula between two points (x₁, y₁) and (x₂, y₂) is,

d = √((x₂ - x₁)² + (y₂ - y₁)²).

The length of the rectangular plot between points (3, 9) and (5, 9):

Length = √((5 - 3)² + (9 - 9)²) = √(2² + 0²) = √(4) = 2.

The width of the rectangular plot between the points (3, 3) and (3, 9):

Width = √((3 - 3)² + (9 - 3)²) = √(0² + 6²) = √(36) = 6.

Therefore, the area of the rectangular plot = Length*Width = 2*6 = 12 ft.².

Therefore, the cost to cover the rectangular plot with mulch, at the cost of $1.00 per 1 ft.² = $1*12 = $12.00.

Therefore, the cost to cover the garden with mulch will be $12.00, as the area of the rectangular garden is 12 ft.².

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Janice estimate is under by approximately 0. 6 units. Option B

The longest part is called the hypotenuse

The formula for finding the hypotenuse, we use the Pythagorean theorem

Hypotenuse = square root of both opposite square and adjacent square

We have that,

Hypotenuse = [tex]\sqrt{16^2 + 20^2}[/tex]

Hypotenuse = [tex]\sqrt{256+ 400}[/tex]

Hypotenuse = [tex]\sqrt{656}[/tex]

Find the square root

Hypotenuse = 25. 6

The length of the longest part = 25. 6

Janice estimated it to be 25

Comparing her estimate with the actual length = Actual length - estimate

⇒ 25. 6 - 25

⇒ 0. 6

Therefore, Janice estimate is under by approximately 0. 6 units. Option B

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Answer: B. It is under by approximately 0.6 units.

Step-by-step explanation: Just did it on edge 2023

In the given diagram, the measure of ∠3 will be 105°.

In the given diagram, ∠3 and ∠6 are consecutive interior angles.

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary.

That is,

∠3 + ∠6 = 180°

From the given information,

∠6 = 75°

Then,

∠3 + 75° = 180°

∠3 = 180° - 75°

∠3 = 105°

Hence, the measure of ∠3 will be 105°.

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Answer:

9/19

Step-by-step explanation:

To write the probability as a fraction, put the total number on the bottom and put the number of ways the event can happen, put that on top.

They said there are 38 slots. That's the total, it goes on the bottom.

Landing on an Odd Number is the event we're looking at. There are 18 ways that can happen: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35

That number 18 (bc 18 ways to get an odd number) goes on top.

P(Odd) = 18/38

Always simplify when possible.

18/38

= 9/19

Answer:

[tex]\frac{11}{15} =0.733333333333[/tex]

Step-by-step explanation:

• Here The sample space S is the set of possible outcomes (ordered pairs of marbles) that we can draw at random (without replacement) from the bag.

Then

[tex]\text{cardS} =P^{2}_{10}=10\times 9=90[/tex]

……………………………………………

Drawing two marbles where the marbles are different colors

means

drawing (1green ,1 yellow) or (1green ,1 red) or (1yellow ,1 red)

Remark: the order intervene

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

•• Let E be the event “Drawing two marbles where the marbles are different colors”.

CardE = 2×3×3 + 2×3×4 + 2×3×4 = 66  (2 is for the order)

Conclusion:

[tex]p\left( E\right) =\frac{66}{90} =\frac{11}{15} =0.733333333333[/tex]

Method 2 :

[tex]p\left( E\right) =2\times \frac{3}{10} \times \frac{3}{9} +2\times \frac{3}{10} \times \frac{4}{9} +2\times \frac{3}{10} \times \frac{4}{9} =0.733333333333[/tex]

Answer:

[tex]\sf \dfrac{11}{15}[/tex]

Step-by-step explanation:

The bag of marbles contains:

⇒ Total marbles = 3 + 3 + 4 = 10

Probability Formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

First draw

[tex]\implies \sf P(green)=\dfrac{3}{10}[/tex]

[tex]\implies \sf P(yellow)=\dfrac{3}{10}[/tex]

[tex]\implies \sf P(red)=\dfrac{4}{10}[/tex]

Second draw

As the first marble is not replaced there are now 9 marbles in the bag.

If the first marble was green, the probability of drawing a yellow is now 3/9 and the probability of drawing a red is now 4/9.

If the first marble was yellow, the probability of drawing a green is now 3/9 and the probability of drawing a red is now 4/9.

If the first marble was red, the probability of drawing a green is now 3/9 and the probability of drawing a yellow is now 3/9.

To find the individual probabilities of picking 2 different colors, multiply the probability of the first draw by the probability of the second draw:

[tex]\implies \sf P(green)\:and\:P(red)=\dfrac{3}{10} \times \dfrac{4}{9}=\dfrac{12}{90}[/tex]

[tex]\implies \sf P(green)\:and\:P(yellow)=\dfrac{3}{10} \times \dfrac{3}{9}=\dfrac{9}{90}[/tex]

[tex]\implies \sf P(yellow)\:and\:P(green)=\dfrac{3}{10} \times \dfrac{3}{9}=\dfrac{9}{90}[/tex]

[tex]\implies \sf P(yellow)\:and\:P(red)=\dfrac{3}{10} \times \dfrac{4}{9}=\dfrac{12}{90}[/tex]

[tex]\implies \sf P(red)\:and\:P(green)=\dfrac{4}{10} \times \dfrac{3}{9}=\dfrac{12}{90}[/tex]

[tex]\implies \sf P(red)\:and\:P(yellow)=\dfrac{4}{10} \times \dfrac{3}{9}=\dfrac{12}{90}[/tex]

To find the probability of drawing two marbles at random and the marbles being different colors, add the individual probabilities listed above:

[tex]\begin{aligned}\implies \sf P(2\:different\:color\:marbles) &=\sf \dfrac{12}{90}+\dfrac{9}{90}+\dfrac{9}{90}+\dfrac{12}{90}+\dfrac{12}{90}+\dfrac{12}{90}\\\\ & = \sf \dfrac{66}{90}\\\\ & =\sf \dfrac{11}{15}\end{aligned}[/tex]

Answer:

Step-by-step explanation:

So for the 1st one you're going to use your protractor and line it up so that BC is at 0 degrees, that way you can look at the point A to determine the angle. Now that you have the angle you're going to take your protractor and draw one point which will be where the two lines meet, line this up in the middle and then draw a point at 0 degrees and a point at the angle you found. Now draw another point at half the angle (like in the previous answer I answered). Draw a line from the middle point and connect it to all these three points (4 in total but one of them is going connected to all of them, like the point B in the image you sent).

For the second question you're going to take the angle you found in the first answer and multiply it by 2. Now start off by drawing a middle point which will connect the two other lines. Line up your protractor so that point is at bottom but in the middle (Check my photo for clarification). Now go to the value that is twice the angle and draw a point there, and also draw a point at 0 degrees) and then connect the two points to the middle point.

For question 3 you don't really need the hint, all you need is to multiply the angle by 1.5 but I'll send another image explaining what it's trying to explain.

The domain of g(x) is [4, 7)

The function is given as:

g(x) = f(x + 3)

Since f(x) is a function, then g(x) is also a function

The domain of f(x) is given as:

[1, 4)

The equivalent of these values in g(x) are

x = 1 + 3 = 4

x = 4 + 3 = 7

Hence, the domain of g(x) is [4, 7)

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Answer:

Pete's average speed is 12.5 miles per hour

Step-by-step explanation:

Miles per hour means how many miles were driven in 1 hour so :

50 miles in 4 hours = ? miles in 1 hour
4 ÷ x = 1

4/x = 1

x = 4

50÷4 = ?

50/4 = ?

? = 12.5

Pete's average speed is 12.5 miles per hour

Hope this helped and have a good day

Answer:

b.) 2

Explanation:

Parallel slopes have same slope.

Perpendicular slopes have negatively inverse slope.

[tex]\sf Here \ given \ equation: y = -\dfrac{1}{2} x - 6[/tex]

Comparing it with slope intercept form, "y = mx + b" where m is slope.

Here parallel slope: -1/2

Perpendicular slope: -(-1/2)⁻¹ = 2

Two common tangents occur when two circles intersect each other at two points.

It should be noted that two common tangents are also referred to as transverse common tangents.

In this case, two common tangents occur when two circles intersect each other at two points.

The diagram is attached.

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Answer:

a) i) -0.5

   ii) -0.28125

b)  -0.254102 (6 d.p.)

Step-by-step explanation:

Given iteration formula:

[tex]x_{n+1}=\dfrac{\left(x_n\right)^3-1}{4} \quad \textsf{and} \quad x_1=-1[/tex]

Part (a)(i)

Substitute the value of x₁ into the formula and solve for x₂ :

[tex]\begin{aligned}\implies x_2 & =\dfrac{\left(x_1\right)^3-1}{4}\\\\& =\dfrac{\left(-1\right)^3-1}{4}\\\\ & = \dfrac{-1-1}{4}\\\\ & = \dfrac{-2}{4}\\\\ & = -0.5\end{aligned}[/tex]

Part (a)(ii)

Substitute the value of x₂ into the formula and solve for x₃ :

[tex]\begin{aligned}\implies x_3 & =\dfrac{\left(x_2\right)^3-1}{4}\\\\& =\dfrac{\left(-0.5\right)^3-1}{4}\\\\ & = \dfrac{-0.125-1}{4}\\\\ & = \dfrac{-1.125}{4}\\\\ & = -0.28125\end{aligned}[/tex]

Part (b)

To find the solution to 6 decimal places, keep substituting each new value into the iteration formula until the answers are the same when rounded to the required level of accuracy.

[tex]\implies x_4=-0.2555618286...[/tex]

[tex]\implies x_5=-0.2541728038...[/tex]

[tex]\implies x_6=-0.2541051331...[/tex]

[tex]\implies x_7=-0.2541018552...=-0.254102\:\: \sf (6 \:d.p.)[/tex]

[tex]\implies x_8=-0.2541016964...=-0.254102\:\: \sf (6 \:d.p.)[/tex]

[tex]\implies x_9=-0.2541016888...=-0.254102\:\: \sf (6 \:d.p.)[/tex]

Therefore, the solution is -0.254102 (6 d.p.).

[tex]not \: penny \: or \: dime = quarter \: or \: nickle[/tex]

[tex]p(x) = \frac{13 + 18}{86} = \frac{31}{86} = 0.36[/tex]

[tex]gallons \: for \: car \: 1 = \frac{450}{18} = 25 \: gal[/tex]

[tex]gallons \: for \: car \: 2 = \frac{450}{25} = 18 \: gal[/tex]

[tex]we \: need \: 25 + 18 = 43 \: gallons[/tex]

[tex]43 \times 2.49 = 107.07 \: dollars[/tex]

Answer:

Copying a line segment or angle is an illustration of transformation. Both are similar, because they are both rigid transformation.

When an angle is copied to a new angle, the new angle and the old angle will have the same measure

Similarly;

When a line segment is copied to a new segment, the new line segment and the old line segment will have the same measure

This type of transformation is referred to as a rigid transformation.

Hence, copying a line segment is similar to copying an angle, because they are both rigid transformations

Step-by-step explanation:

Answer:

1. The volumes are equal.

2. The base areas are equal.

3. The prisms have the same height.

Step-by-step explanation:

I don't see no answered to check all that apply but here is the answers about properties and two prisms

Answer:

Circumference = 18.84 ft

Area = 28.26 ft squared

Step-by-step explanation:

C(circumference) = 2 x [tex]\pi[/tex] x r(radius)

radius = 1/2 circumference

1. divide circumference by two to get the radius, which would be three ft.

2. multiply the radius by pie (3.14) and then multiply that by two and you have your circumference, which is 18.84 ft

area = [tex]\pi[/tex] x r(radius)^2

1. find the radius squared, which would be 9 because 3^2 = 3 x 3 which = 9

2. multiply 9 by pie (3.14) and you get the area which =  28.26

The reflection of a point over the x axis is given by the equation (x, y) ⇒ (x, -y).

If the point (-8,2) is reflected over the y-axis, the new point would be (8, 2)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

The reflection of a point over the x axis is given by the equation (x, y) ⇒ (x, -y).

If the point (-8,2) is reflected over the y-axis, the new point would be (8, 2)

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Answer:

Step-by-step explanation:

Answer:  [tex]\frac{-70a^3-195^2-20a-78}{60}[/tex]  or  [tex]-\frac{7}{6} a^3-\frac{13}{4} a^2-\frac{1}{3} a-\frac{13}{10}[/tex]  

When we say subtract this from that, the value or word after from is the one which is ahead of the equation. For example, subtract 9 from 10, then the expression will be 10-9 .  [Answer is 1]

The expression that can be formed from the picture is and the solution is shown in the steps below.

[tex](\frac{a^3}{3} -\frac{3a^2}{4} -\frac{5}{2}) - (\frac{5a^2}{2} +\frac{3a^3}{2} +\frac{a}{3} -\frac{6}{5} )[/tex]           [Formed the expression]
[tex]\frac{a^3}{3} -\frac{3a^2}{4} -\frac{5}{2} - \frac{5a^2}{2} -\frac{3a^3}{2} -\frac{a}{3} +\frac{6}{5}[/tex]                 [Removed the brackets]
[tex]\frac{a^3-a}{3} +\frac{6}{5} -\frac{3a^2}{4} +\frac{-5a^2-3a^3-5}{2}[/tex]       [Brought common denominators together]
[tex]\frac{20(a^3-a)}{60} +\frac{6*12}{60} -\frac{15(3a^2)}{60} +\frac{30(-5a^2-3a^3-5)}{60}[/tex]       [LCM of 3,5,4 and 2]
[tex]\frac{20a^3-20a+72-45a^2-150a^2-90a^3-150}{60}[/tex]                  [Multiplied the numerators]
[tex]\frac{-70a^3-195^2-20a-78}{60}[/tex]                                                    [simplified]
[tex]-\frac{7}{6} a^3-\frac{13}{4} a^2-\frac{1}{3} a-\frac{13}{10}[/tex]                                        [More simplified]

I tried my best to show my steps and solve it. Thank you.

 ∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
    hope it helped
┗━━━━━━━┛

Step-by-step explanation:

z = 12 = k × 3 × -1

12 = k×-3

-4 = k

z = k× -5×6 = k×-30 = -4 × -30 = 120

Answer: undefined

Step-by-step explanation:

[tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{-13-12}{5-5}[/tex]

[tex]\frac{-25}{0}[/tex]

= undefined

The congruency statement is true TS ≅ HG. so option C is correct.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Given information;

Triangle G H J is rotated 90 degrees about point X to form triangle S T R.

Triangle GHJ is rotated 90° about point X, resulting in triangle STR.

Now, if any triangle is rotated 90 degrees about a point the two sides will be ≅ to each other.

So, ST = GH

RT= HJ

SR= GJ

<S= <G

<T = <H

<R=<J

The side TS ≅ HG.

Hence, option (c) is correct.

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Answer:

C

Step-by-step explanation:

Trust me bro