Solve each of the following exponential equations using common bases:

1.) 4^(3x+5)=8^(4x-3)

2.) 9^(2x+3)=〖(1/27)〗^(3x+1)

3.) 4^(x+6)∙8^(x-9)=64

Answers

Answer 1

Answer:

x=19/6, x=-9/13, x=33/4

Step-by-step explanation:

1) 2^(6x+10)=2^(12x-9), 6x+10=12x-9, x=19/6

2) 3^(4x+6)=3^(-9x-3), 4x+6=-9x-3, x=-9/13

3) 2^(x+6)*2^(3x-27)=2^(6), 4x-27=6, x=33/4


Related Questions

given the preimage and image, find the dilation scale factor​

Answers

Given:

The preimage and image of a triangle in the given figure.

To find:

The dilation scale factor.

Solution:

From the given figure it is clear that the vertices of the triangle ABC are A(-2,-2), B(-1,2) and C(2,1).

The vertices of the triangle A'B'C' are A'(-4,-4), B'(-2,4) and C'(4,2).

If a figure is dilated by factor K with (0,0) as the center of dilation, then

[tex](x,y)\to (kx,ky)[/tex]

Let the scale factor be K, then the image of point A is:

[tex]A(-2,-2)\to A'(k(-2),k(-2))[/tex]

[tex]A(-2,-2)\to A'(-2k,-2k)[/tex]

From the given figure it is clear that the image of point A is A'(-4,-4).

[tex]A'(-2k,-2k)=A'(-4,-4)[/tex]

On comparing both sides, we get

[tex]-2k=-4[/tex]

[tex]k=\dfrac{-4}{-2}[/tex]

[tex]k=2[/tex]

Therefore, the dilation scale factor is 2.

need help with part b of the attached screenshot please

Answers

9514 1404 393

Answer:

  (b) 82.9253

Step-by-step explanation:

The first attachment shows the rectangles. The second shows the sum of their areas.

Celine goes to the book fair where paperback books are $2 and hardback books are $4.50. Celine buys three
paperback and 5 hardback books. How much change will Celine receive if she has $35?

7. Equation:

8. Solve:

Answers

Answer:

7. 35-(2*3+5*4.5)

8. 6.5

please help me with this

Answers

L=p*r*t = 1000*0.05*3 = 150

Which of the
following shows the graph of y = 2e*?

Answers

you didn’t add any pictures so how could i help you with this?

please help i will give brainliest

Answers

The answer is probability of getting 2 red is 25/8
I think it is 3/12 because 3 reds

Is it possible to relate cyclones to mathematics?
If yes, explain your thinking with the help of drawings (no need to use
downloaded images) What are the mathematical concepts, theorems and
shapes related to cyclones.

Answers

Answer:

Yes

Step-by-step explanation:

Statistics can perdict cyclones for example lets say that somewhere a cyclone happens almost every February then its statistically likely to happen this February too.

Stacy spent £18 on ingredients for bread.
She made 12 loaves and sold them for £1.80 each.
Calculate her percentage profit.

Answers

12 x 1.80 = $21.6 —> total money earned by selling the bread
21.6 - 18 = $3.6 —> total profit

what is a = with a ~ thing on top?​

Answers

greater than or equal to

I need help what’s the answer?

Answers

Answer:

30 words per minute

Step-by-step explanation:

Take the number of words and divide by the number of minutes

150/5 = 30

300/10 =30

450/15 = 30

600/20 = 30

30 words per minute

Answer:

janae types 30 words each minutes.

Step-by-step explanation:

if 5minutes = 150 words

[tex]1 \: minute = \frac{150words}{5minutes} [/tex]

[tex] = \: 30words[/tex]

Gabriela was given a 15% increase in wages. If she earned $36,000 last year, what can she expect to earn this year?

Answers

She should expect to earn around £41,100

The increase in the amount of wages of Gabriela is $ 41,400

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount after increase in wages be = A

Now , the initial amount of Gabriela be = $ 36,000

And , the percentage increase in the wages = 15 %

So , the equation will be

Total amount after increase in wages A = initial amount + ( percentage increase x initial amount )

Total amount after increase in wages A = 36,000 + ( 15/100 x 36,000 )

Total amount after increase in wages A = 36000 + ( 15 x 360 )

Total amount after increase in wages A = 36000 + 5400

Total amount after increase in wages A = $ 41,400

Therefore , the value of A is $ 41,400

Hence , The increase in the amount of wages of Gabriela is $ 41,400

To learn more about equations click :

https://brainly.com/question/10413253

#SPJ2

qrx + prx + pqx > pqr . Find x

Answers

Answer:

[tex]x(qr + pr + pq) > pqr \: \: \: by \: dividing \: both \: sides \: by \: (qr + pr + pq)[/tex]

we get that

Step-by-step explanation:

[tex]x > \frac{qr + pr + pq}{pqr} [/tex]

please help me out asap
(geometry)

Answers

Answer:

x = 30

Step-by-step explanation:

If A and B were parallel, then 2x + 50 and 5x - 80 are same- side interior angles and sum to 180° , then

2x + 50 + 5x - 80 = 180

7x - 30 = 180 ( add 30 to both sides )

7x = 210 ( divide both sides by 7 )

x = 30

Instructions: Find the measure of the missing angles in the kite

Answers

Answer:

m∠1 = 103

m∠2 = 103

Step-by-step explanation:

by definition, the opposite angles of a kite are congruent.

we know that a quadrilateral's angles add up to 360.

117 º+ 37º + 2xº = 360º

2xº = 206º

xº=103º

Amy needs to use a combination of the 12-cup and 36-cup baking pans to fill the order. With only eighteen 12-cup baking pans in her shop, how many of the 36-cup baking pans does she need to complete the order? ​

Answers

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the total orders is not given.

To solve this question, I will assume a value for the total number of order.

Let

[tex]x \to 12-cup[/tex]

[tex]n_x = 18[/tex] ---- number of 12-cup

[tex]y \to 36-cup[/tex]

[tex]n_y = ??[/tex] ---- number of 36-cup

[tex]n \to[/tex] Total order

Required

Calculate [tex]n_y[/tex]

To do this, we make use of the following equation:

[tex]n_x * x + n_y * y = n[/tex]

Substitute known values

[tex]18 * 12 + n_y * 36 = n[/tex]

[tex]216 + 36n_y= n[/tex]

Collect like terms

[tex]36n_y= n - 216[/tex]

Divide both sides by 36

[tex]n_y= \frac{n - 216}{36}[/tex]

Assume the number of orders is: 540 cups

The equation becomes

[tex]n_y= \frac{540 - 216}{36}[/tex]

[tex]n_y= \frac{324}{36}[/tex]

[tex]n_y= 9[/tex]

which point is on the line that passes through point H and is perpendicular to line FG?

Answers

Answer:

The correct answer is (-6, 10).

Step-by-step explanation:

You can find the equation of the blue line and then find out which point is on the perpendicular line to that blue line but you also can figure this out visually by looking at where the points are.

Feel free to message me if you still have questions :)

Answer:

(–6, 10)

Step-by-step explanation:

Find NM
--------------------------------

Answers

Answer:

[tex] MN= \boxed{15}[/tex]

Step-by-step explanation:

refer the attachment

therefore Let,

[tex]a = x - 3 + 16 = x + 13[/tex][tex]b = x - 3[/tex][tex]c = x + 3[/tex]

according to the question

[tex] \displaystyle (x - 3 ) (x + 13) =( x + 3 {)}^{2} [/tex]

simplify square and Multiplication:

[tex] \displaystyle {x}^{2} + 10x - 39 = {x}^{2} + 6x + 9[/tex]

cancel x² from both sides:

[tex] \displaystyle 10x - 39 = 6x + 9[/tex]

cancel 6x from both sides:

[tex] \displaystyle 4x - 39 = 9[/tex]

add 39 to both sides:

[tex] \displaystyle 4x = 48[/tex]

divide both sides by 4:

[tex] \displaystyle \boxed{x = 12}[/tex]

given that,

[tex] MN= x + 3[/tex]

substitute the got value of x:

[tex] MN= 12 + 3[/tex]

simplify addition hence,

[tex] MN= \boxed{15}[/tex]

Classify the triangle.
obtuse
equiangular
right
acute

Answers

Answer:

acute triangle

Step-by-step explanation:

We have 3 angles that are not equal to each other

They are all smaller than 90 degrees which means they are acute angles

Answer:

Acute

Step-by-step explanation:

Acute=less than 90 degrees

Obtuse=more than 90 degrees

Right=1 side has 90 degrees

Equiangular=every side has the same degree

Therefore, it would be Acute

9. Calculate the angle of elevation of the line of sight of a person 27.5 m away from a tree, whose
eye is 1.8 m above the ground, and is looking at the top of a 19.4 tree. (draw a diagram and
answer to the nearest degree)

Answers

Answer:

32.61° is the answer

Step-by-step explanation:

Tanx=17.6/27.5

For which distributions is the median the best measure of center?



Select each correct answer.

Answers

Answer:

it will be the correct answer..

because

The median is the most informative measure of central tendency for skewed distributions or distributions with outliers. For example, the median is often used as a measure of central tendency for income distributions, which are generally highly skewed.

Use a calculator to determine the unknown angle, to the nearest degree, in each of the following expressions.

tan A = 5/4

cos G = 0.88

Answers

Answer:

Using a calculator;

A is approximately 51.34°

G is approximately 28.36°

Step-by-step explanation:

Part 1

The given trigonometric ratio is presented as follows;

tan A = 5/4

Therefore, the angle, A = arctan(5/4)

Using a calculator,  the value of A is found as follows;

1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)

2. Entering 5/4 into the calculator, using the keypad

3 . Selecting the arctan button to give, A ≈ 51.34°

Part 2

The given trigonometric ratio is cos G = 0.88

Therefore, G = arccos(0.88)

1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)

2. Enter 0.88 into the calculator by typing

3. Select arccos from the function menu, to give

arcos(0.88) = G ≈ 28.36°.

Step by step explanation of finding the value of x and y

Answers

Answer:

[tex]x=4\sqrt{2}\\y=7[/tex]

Step-by-step explanation:

In order to solve this problem, the easiest approach is to draw a line connecting the vertex between the side with a measure of (y) and (3) to the side with the length (x). This side should be parallel to the side with a length of (4).

Since the new side constructed (call this side (b)), is parallel to the side with a length of (4) and is intersected by segments that are perpendicular to the side with a length of (4), the side (b) and (4) must have the same measure. Therefore (b = 4).

The triangle formed with sides (x) and (b) is a (45 - 45 - 90) triangle. Meaning that its angles have the following measure, (45 - 45- 90). This means that its sides follow the following ratio:

angle : side opposite

[tex]45:x\\45:x\\90:x\sqrt{2}[/tex]

Apply this logic to the given situation.

[tex]x=b*\sqrt{2}\\x = 4\sqrt{2}[/tex]

The side (b) divides the side (y) into two parts. Call the part that is a side of the triangle ([tex]y_1[/tex]) the side that is a part of the rectangle is called ([tex]y_2[/tex]). As per the logic used to find the lengths of side (b), one can use similar logic to find the length of side ([tex]y_2[/tex]). The sides ([tex]y_2[/tex]) and (3) are parallel and are intersected by the sides with a measure of (4) and (b), therefore  ([tex]y_2[/tex]) and (3) are cognrunet. Thus ([tex]y_2[/tex] = 3).

The base angles converse theorem states that when two angles in a triangle are congruent, the triangle is isosceles, and the sides opposite the congruent angles are also congruent. Thus, one can state the following:

[tex]y_1=b\\y_1=4[/tex]

Now add up the measurement of ([tex]y_2[/tex]) and ([tex]y_1[/tex]) to find the measure of (y):

[tex]y_2+y_1=y\\4+3=y\\7=y[/tex]

Find Point P is the incenter of DEF . point p of concurrency of the angle bisectors . find PT

Answers

PT is 8 because since P is the incenter it's equidistant from all sides.

Calculate expression value : G = 2x^3 + 35x^2 + 15x + 1 with x = -17

Answers

I got G= -20195

Not sure if this is correct the question was a little confusing
Answer:

G = -20195

Step-by-step explanation:

G = 2x^3 + 35x^2 + 15x + 1 where x = -17

Substitute all the x’s for -17!

G = 2(-17)^3 + 35(-17)^2 + 15(-17) + 1

Solve for the exponents first!

G = 2(-4913) + 35(-289) + 15(-17) + 1

Multiply

G = -9826 + -10115 + -255 + 1

Add -9826 + -10115

G = -19941 + -255 + 1

Add -19941 + -255

G = -20196 + 1

Add -20196 + 1

G = -20195

A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $57,077 , and the variable costs will be $11.75 per book. With the other method, the one-time fixed costs will total $22,459, and the variable costs will be $21.25 per book. For how many books produced will the costs from the two methods be the same?

Answers

Answer:

for 3644 produced books the costs will be the same.

Step-by-step explanation:

x = number of books

f(x) = production method 1 costs

g(x) = production method 2 costs

f(x) = 11.75x + 57077

g(x) = 21.25x + 22459

for what number of books (x) will that be the same ?

11.75x + 57077 = 21.25x + 22459

34618 = 9.5x

x = 34618 / 9.5 = 3644

Find θ. Round to the nearest degree.

hypotenuse = 14
adjacent = 5

5.1.3: Right Triangle Trigonometry

Answers

Answer:

the answer is c

Step-by-step explanation:

when solving for theta, we are given the side length adjacent to it (5) and the length of the hypotenuse ( 14).

the trigonometric function that deals with adjacent and hypotenuse values is cosine.

you can use SOH CAH TOA

stands for :

sin = opposite/hypotenuse

cos = adjacent/ hypotenuse

tan = opposite/adjacent

we dont know theta so :

cos(theta) = 5/14

cos = about 69

check :

cos(69) = 5/14

                   cos(69) = 0.35836794954

                   5/14 = 0.35714285714

What is 13/3.5 and could you give a step by step

Answers

Answer:

[tex]3\frac{5}{7}[/tex]

Step-by-step explanation:

13 ÷ 3.5

[tex]3.5=3\frac{5}{10}[/tex]

Vicky makes jewelry.she uses 42 beads for each necklace that she makes,and she has 500 beads.how many necklaces can she make explain with work?

Answers

Answer:

11

Step-by-step explanation:

Vicky used 462 beads to make 11 necklaces, she would have left 38 beads.

Answer:

He make seven necklaces

Solve for x. round to the nearest tenth, if necessary.​

Answers

Answer:

50.7

Step-by-step explanation:

38+1.3+90 from the right angle=129.3

180-129.3=50.7

Which recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1?

6, 1, –4, –9, –14

Answers

Answer:

f(n) = f(n - 1) - 5

Step-by-step explanation:

The recursive formula allows a term in the sequence to be found by adding the constant difference to the previous term.

Here d = 1 - 6 = - 4 - 1 = - 9 - (- 4) = - 14 - (- 9) = - 5 , then

f(n) = f(n - 1) - 5 with n ≥ 1 and f(1) = 6

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