Select the correct answer. which exponential equation is equivalent to this logarithmic equation?

The relationship between d and t.

d = 49t

The correct equation is C.

How quickly something or someone is moving is determined by their speed. If you know how far an object has traveled and how long it has taken, you can calculate its average speed. Speed equals distance times time, according to the speed formula. Knowing the units for distance and time will help you determine what the units are for speed.

speed = 49 miles/hour

Distance

Time

as we know :

Speed = Distance  /  Time .

Then:

49 = Distance/Time

Distance = 49*Time .

the relationship between d and t ( d = 49t).

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I understand that the question you are looking for is :

A cheetah runs at a speed of 49 miles for every hour. If the distance traveled, in miles, is d and time, in hours, is t, which equation shows the relationship between d and t?

A. d = 49 + t

B. t = 49 + d

C. d = 49t

D. t = 49d

The roots of the given polynomials exist  [tex]$x=8+\sqrt{10}$[/tex], and [tex]$x=8-\sqrt{10}$[/tex].

For a quadratic equation of the form [tex]$a x^{2}+b x+c=0$[/tex] the solutions are

[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$[/tex]

Therefore by using the formula we have

[tex]$x^{2}-16 x+54=0$$[/tex]

Let, a = 1, b = -16 and c = 54

Substitute the values in the above equation, and we get

[tex]$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$$[/tex]

simplifying the equation, we get

[tex]$&x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1} \\[/tex]

[tex]$&x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1} \\[/tex]

[tex]$&x=8+\sqrt{10}, x=8-\sqrt{10}[/tex]

Therefore, the roots of the given polynomials are [tex]$x=8+\sqrt{10}$[/tex], and

[tex]$x=8-\sqrt{10}$[/tex].

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Answer:

x=8-[tex]\sqrt{10}[/tex] and x=8+[tex]\sqrt{10}[/tex]

Step-by-step explanation:

It was right for me

The answer is [tex]\boxed {\frac{3b - 8}{4b}}[/tex].

The inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3 is f⁻¹(x) = 4x² - 3, for x ≤ - 1/2.

In the question, we are asked to find the inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3.

The domain for the given function is x ≥ -3.

Thus, its range is x ≤ - 1/2.

To find the inverse, we equate f(x) = y, to get:

(-1/2)√(x + 3) = y,

or, √(x + 3) = -2y.

Squaring both sides, we get:

x + 3 = (-2y)²,

or, x + 3 = 4y²,

or, x = 4y² - 3.

Thus, the inverse of the function f(x) = (-1/2)√(x + 3), is, f⁻¹(x) = 4x² - 3.

The inverse will have the domain equal to the range of the original function, that is, x ≤ - 1/2.

Thus, the inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3 is f⁻¹(x) = 4x² - 3, for x ≤ - 1/2.

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The provided question is incomplete. The complete question is:

"Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Find the inverse of the given function.

f(x) = (-1/2)√(x + 3), x ≥ -3

f⁻¹(x) =   x² -   , for x ≤    ."

The required percentage increase is 36%. So, a number increased by 36% is the same as the number multiplied by 1.36.

The formula for calculating the percentage increase of a number is

%increase = 100 × (Final - initial)/initial

Consider the number as 'x'

The result when the number is multiplied by 1.36 is 1.36x

So, the percentage increase is calculated as follows:

%increase = 100 × (Final - initial)/initial

Where Initial = x and Final - 1.36x

⇒ %increase = 100 × (1.36x - x)/x

⇒ %increase = 100 × x(1.36 - 1)/x

⇒ %increase = 100 × 0.36

⇒ %increase = 100 × 36/100

∴ %increase = 36

Thus, when a number is multiplied by 1.36, the result obtained is equal to the 36% increase in the number.

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The correct option of this expression is (B) 2(x-3)(x-4)

What is expression?

Given, expression is ;  2x²-14x+24 = 0

Now take common 2 from  this expression  both side.

        2(  x² - 7x + 12) = 0

          2(x² - (4 +3)x + 12) = 0

        2 (  x² - 4x - 3x + 12) = 0

        2 ( x( x - 4 ) -3 ( x - 4 )) = 0

        2  ( x - 3 ) ( x - 4 ) = 0

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The complete question is -

Select the correct answer. Which expression is equivalent to the given expression? 2x²-14x+24

A.(2x-12)(x-2)

B.2(x-3)(x-4)

C.2(x-8)(x+3)

D.2(x-5)(x-2)

This real-world problem has the limitations 75< x <110 and 0< y[tex]\leq[/tex] 50, hence:

option (C) is the best choice.

The term "inequality" refers to a mathematical expression in which both sides have mathematical signs that are either less than or greater than one another, and the expression is one where the two sides are not on equal footing.

We have:

Your senior vacation is scheduled to include a class trip to a beach. Only when it's between 75 and 110 degrees do guests at the resort get access to the pool. 50 passengers can go with you.

Let y be the number of passengers and x be the temperature

75 to 110 degrees are the range of the temperature.

75 < x < 110

50 passengers can go with you.

0 < y ≤ 50

In order to illustrate this real-world issue, the limitations are 75 <x <110 and 0< y [tex]\leq[/tex]50.

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The box and whisker plot is a 71 and 53 and 89 which represent the

median, upper value and lower value.

According to the statement

we have given that the some data of the marks of 18 students and we have to make the plot of that data.

So, For this purpose, we have given that the

A box and whisker plot is a visual tool that is used to graphically display the median, lower and upper quartiles, and lower and upper extremes of a set of data.

And it is used to find the median and the lower value and the maximum value.

So, The median become:

median = n /2

median = 18/2

median = 9th term and

median value is 71.

And then the lower value of the data is a 53.

And the upper value of the data is a 89.

So, overall we can say that the combination of median, upper value and lower value is called the box and whisker plot.

So, The box and whisker plot is a 71 and 53 and 89 which represent the

median, upper value and lower value.

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I believe that its easier to understand the multiplication of a radical than that of a polynomial.

In mathematics, a radical is the opposite of an exponent that is represented with a symbol '√' also known as root.

A polynomial is an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division.

When multiplying radicals with the same index, multiply under the radical, and then multiply in front of the radical. An example is:

= 3✓2 × 4✓2

= 12✓4

= 12 × 2

= 24

The multiplication of a radical is easier.

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The function can be solved as follows:

(h - g)(2.1) = 3.51

g(x) = 2x² + 3x - 9

h(x) = x² + 2x - 6

(h - g)(x) = h(x) - g(x)

(h - g)(x) = 2x² + 3x - 9 - ( x² + 2x - 6)

(h - g)(x) =  2x² + 3x - 9 - x² - 2x + 6

(h - g)(x) = 2x² - x² + 3x - 2x - 9 + 6

(h - g)(x) = x² + x - 3

Therefore,

(h - g)(2.1) = (2.1)² + (2.1) - 3

(h - g)(2.1) = 4.41 + 2.1 - 3

(h - g)(2.1) = 6.51 - 3

(h - g)(2.1) = 3.51

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Step-by-step explanation:

Area of rectangle= length × breadth

A= a²+6a+8

= a²+4a+2a+8

= a(a+4) + 2(a+4)

= (a+4)(a+2)

length= a+4

breadth= a+2

Answer: 3

Step-by-step explanation:

We can solve this problem by recognizing that z is the geometric mean of 9 and 9+4. This property is outlined in the following formula:

[tex]\frac{hypotenuse}{leg}=\frac{leg}{part}[/tex]

where hypotenuse is the longest side of the triangle, leg is the side of the triangle we are calculating for, and part is the part of the hypotenuse on the side of the leg.

Here, the hypotenuse is 13, or 4 + 9. The leg is z, as it is the side of the triangle we are trying to find. Finally, the part is 9. It is the part of the hypotenuse that is on the side of the leg.

Let's plug in these values:

[tex]\frac{13}{z}=\frac{z}{9}\\117=z^2\\z=\sqrt{117}[/tex]

117 is the product of 9 and 13. Since 9 is a perfect square, we can take it out from the square root.

[tex]z=\sqrt{9*13}\\z=\sqrt{9}*\sqrt{13}\\z=3\sqrt{13}[/tex]

The "?" must be a 3.

Step-by-step explanation:

so ,

Question 6 :-

5 × (3+4) - 4

first solve the Bracket ......

5 × (7) - 4

after multiplication ......

35 - 4

= 31

so , Answer is 1st one ....

Question 7 :-

8 + 1/2 × (6-2) -1

so , here also solve the Bracket first .....

8 + 1/2 × (4) - 1

after multiplication .....

8 + 2 - 1

after + and - .......

10 - 1

= 9 .......

so , Answer is 2nd one .....

Answer:

Q6: 5 times the sum of 3 and 4, then subtract 4.

Q7: Add 8 to half the difference of 6 and 2, then subtract 1.

Step-by-step explanation:

[tex]5 \times (3 + 4) -4[/tex]

• First of all, we can see that 5 is being multiplied by something, so we can say "5 times...".

• Next we see that the 5 was being multiplied by the sum of 3 and 4, so we can combinedly say "5 times the sum of 3 and 4...".

• And finally, we see that 4 is taken away from the result. Therefore we can say " 5 times the sum of 3 and 4, then subtract 4".

[tex]8 + \frac{1}{2} \times (6-2) -1[/tex]

• Firstly, we can see that 8 is being added to something, so we can say "Add 8...".

• Next, we see that 8 was being added to [tex]\bf \frac{1}{2}[/tex] of something, so we can combinedly say "Add 8 to half of...".

• Then we see that the difference (i.e., result of subtraction) of 6 and 2 was being halved. Therefore we say "Add 8 to half of the difference of 6 and 2...".

• Finally, we can see that 1 is subtracted from the result. Therefore, we can say "Add 8 to half of the difference of 6 and 2, then subtract 1".

The height of the ground from the base of the window is 144 inches.

One angle of a right angle triangle is equals to 90 degrees.

Therefore, the sides and angles of the right triangle can be found using trigonometric ratios.

tan x = WY / XY

tan x  = opposite / adjacent

tan x = 24 / 8

x = tan⁻¹ 3

x = tan⁻¹ 3

x = 71.5650511771

x = 71.60°

tan 71.60 = h / 48

cross multiply

h = 48 tan 71.60

h = 48 × 3

h = 144 inches

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

Area of shaded region is equal to :

Area of rectangle - Area of two triangles ~

1. Area of rectangle :

[tex]\qquad \sf  \dashrightarrow \: length \times width[/tex]

[tex]\qquad \sf  \dashrightarrow \: 20 \times 15[/tex]

[tex]\qquad \sf  \dashrightarrow \: 300 \: \: cm {}^{2} [/tex]

2. Area of first triangle :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (base) \times (height)[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (20 - 18) \times (15)[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (2) \times (15)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 15 \: \: cm {}^{2} [/tex]

3. Area of second triangle :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (base) \times (height)[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (6) \times(20)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 \times 20[/tex]

[tex]\qquad \sf  \dashrightarrow \: 60 \: \: cm {}^{2} [/tex]

Area of shaded region is :

[tex]\qquad \sf  \dashrightarrow \: 300 - (15 + 60)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 300 - 75[/tex]

[tex]\qquad \sf  \dashrightarrow \: 225 \: \: cm {}^{2} [/tex]

The sentence "If this is the last chance you have to speak to him, what do you want to tell him" will be the best response from the leader.

This refers to the act of imitating the character and behaviour of someone who is different from yourself which an example is a training exercise which involves imitating of another people.

Sometimes, during the role play, the member of the group can run out of words while presenting a role, hence, as the member states, "i don’t know what to say to my father", the sentence "If this is the last chance you have to speak to him, what do you want to tell him" will be the best response from the leader to induce the member to talk.

Therefore, the Option C is correct.

Missing word "a. What or whom do you want to get away from? b. What made you come if you didn't want to be here today? c. If this is the last chance you have to speak to him, what do you want to tell him? d. What do you imagine will happen if you don't talk about it?"

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The logarithmic equation f(x) = log₈(x + 1) + 4 is shifted left by 1 unit and up by 4 units

The logarithmic equation is given as:

f(x) = log₈(x + 1) + 4

The parent function of the logarithmic equation is

y = log₈(x)

When the logarithmic equation is translated 1 unit left, we have:

y = log₈(x + 1)

When the logarithmic equation is translated 4 units up, we have:

y = log₈(x + 1) + 4

This means that the logarithmic equation f(x) = log₈(x + 1) + 4 is shifted left by 1 unit and up by 4 units

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The building is 151 meters tall

From the question, we have the following parameters about the building and the man

Man's height = 138 cm

Man's shadow = 149 cm

Building's shadow = 163 m

Based on the above parameters, we have the following equivalent ratio:

Ratio = Height : Shadow

So, we have:

Man's height : Man's shadow = Building's height : Building's shadow

Substitute the known values in the above equation

138 cm : 149 cm = Building's height : 163 m

Remove the units

138 : 149 = Building's height : 163

Express as fraction

138 /149 = Building's height/163

Multiply both sides by 163

Building's height = 163 * 138 /149

Evaluate the product

Building's height = 151 m

Hence, the building is 151 meters tall

So, the complete parameters are:

Man's height = 138 cm

Man's shadow = 149 cm

Building's shadow = 163 m

Building's height = 151 m

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Two regular octagons and eight congruent rectangles are perfect for the creation of 3-D figures.

According to the statement

we have to tell and explain about the types of shapes which are required for the creations of 3-D figure.

For this purpose, Firstly we have to know about the 3-D figures.

So,

A shape is a graphical representation of an object or its external boundary and outline, as opposed to other properties such as color, texture, or material type.

A plane shape is constrained to lie on a plane, in contrast to solid 3-D shapes.

After that we know that the

When the all dimensions of a given shape can be observed at the same time, then its is said to be in a 3-D. However, polygons are shapes which has 3 or mores sides. Examples are: trigon, hexagon, octagon etc.

Thus, since the in the 3-D figure have 8 sides connected which is greater than their width.

This confirms that the sides of the figure made up of eight congruent rectangles, because the 3-D figure has eight regular sides. Then, the height of the figure would be the length of the rectangles.

After that all this condition, Two regular octagons and eight congruent rectangles are perfect for the creation of 3-D figures.

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Correct option is A. The value of f(3) is -11

The value of x = 3 corresponds to the following function on the piece wise

[tex]f(x) = -3x -2[/tex]

Substitute 3 for x

[tex]f(3) = -3(3) -2[/tex]

Expand

[tex]f(3) = -9 -2[/tex]

Evaluate -9 -2

[tex]f(3) = -11[/tex]

Hence, the value of f(3) is (a) -11

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Answer: A.) -11

Step-by-step explanation: i hope this helps :)

Answer:

13. x^2 + y^2 = 3

14. B

Step-by-step explanation:

13. Since it's centered at the origin, (0, 0), the values of h and k in (x - h)^2 + (y - k)^2 =  r^2 are equal to zero. So we simply have x^2 + y^2, and since the radius is the square root of 3, squaring the radius gives us 3.

14. B is the only circle with both a radius of 3 that's also shifted to the right 1 and down 2, since it's centered at (h, k), which is (1, -2).

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The possible length of the unit in centimeters given a perimeter of 29 meters is 725 centimeters

convert to centimeters

Perimeter of a square = 4a

where,

Perimeter of a square = 4a

2900 = 4a

divide both sides by 4

a = 2900/4

a = 725 centimeters

Therefore, the possible length of the unit in centimeters given a perimeter of 29 meters is 725 centimeters

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Answer:

(a) 22cm^2

Step-by-step explanation:

(a) 6*3=18

2*2=4

4+18=22

See below for the description of the figure

The equation is given as:

36 + 27 = 9 * (4 + 3)

Open the bracket

36 + 27 = 9 * 4 + 9 * 3

The above when represented on a figure is represented by the given figure.

From the figure, we have the following highlights:

This means that the figure has 7 columns and 9 rows where the partitions on the figure are the product of the rows and column in each partition

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The answers are :

Proof 1

2. Vertically Opposing Angles (V.O.A) (vertically opposite angles are equal)

Proof 2

3. Alternate angles (alternate angles of a transversal are equal)

4. ASA congruence (2 angles and 1 side, where the side is between the angles)

Answer:

5) 3(2+3x)+4(y+2x)-6

Step-by-step explanation: its gone be -6 either way

Answer:

12 square in

Step-by-step explanation:

In the diagram, the diameter is 4 in. Radius is half the length of diameter, so the radius of the yellow circle is 2 in. Using the given formula, A = pi*r*r, we can calculate the approximate area of the circle.

A = pi*r*r = 3*2*2 = 12 square in

Answer:

12 in^2

Step-by-step explanation:

Since the formula to find the area of a circle is already up, we can use that to solve the question.

In the image, we can see that the diameter of the circle is 4inches. Since two radii equal one diameter, one radius is 2 inches.

--> The reason why we found the radius is because the 'r' in the formula means radius. We need the value of the radius to find the area of the circle.

Now, we can just replace r with 2.

--> A = 4[tex]\pi[/tex]

Since the question told us to replace [tex]\pi[/tex] with 3, we can do that.

--> A = 4 x 3

--> A = 12

We can conclude that the area of the circle is 12 in^2.