Which of the following exponential expressions are equivalent to 64? (Select ALL correct answers for full credit).

Given,

ΔABC and ΔDEF are similar triangles.

AB = 6 feet, BC = 4 feet, AC = 7 feet

Let the shortest side of ΔDEF be  EF = 12 feet.

Let DE = x and DF = y

Since,  ΔABC and ΔDEF are similar,

[tex]\frac{BC}{EF}[/tex]  = [tex]\frac{AB}{DE} = \frac{AC}{DF}[/tex]

⇒ [tex]\frac{4}{12} = \frac{6}{x} =\frac{5}{y}[/tex]

On Solving,

x = 18 feet and y = 15 feet

We know,

Perimeter of a triangle = sum of all three sides

Hence, perimeter of ΔDEF = DE + EF + DF = 18 + 15 + 12 = 45 feet.

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If a tumor is injected with 0.2 grams of iodine-125, which has a decay rate of 1.15% per day. The  exponential model representing the number of grams f of iodine-125 remaining in the tumor after t days is: m = m0e^kt.

First is to use this formula to find the t day

t = - ln (2) / k

Where,

k = decay rate = 1.15% or 0.0115

Let plug in the formula

t = - In (2) / - 0.0115

t = 60.27

t = 60 (Approximately)

Now let make use of the exponential model to find the gram

m = m0e^kt

​where,

m0 =0.2 initial mass

t = 60 time in days

k = -1.15 / 100 = -0.0115 (continuous growth rate)

m0e^kt = 0.2×e^[-0.0115×60]

= 0.2×e^(-0.69)

= 0.100g

Therefore the exponential model is m = m0e^kt.

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In a case whereby Mrs. Lahti bought a pair of shoes for $50.80 and used a coupon for 20% off then  her discount will be  $12.7.

A discount can be described as as the decreases in price of a product which can be given to the consumer from the seller.

The given discount given in the question is  20%

Then the price she bought the pair of shoe is  $50.80

then the market price will be 100/80 * 50.80 = $63.5

Then the discount she got is ( $63.5 - $50.80) = $12.7

Therefore, discount she got is  $12.7

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Answer: C

Step-by-step explanation:

First, take the square root of both the numerator and denominator. The numerator would then be equal to 6 a^4 b^2 and the bottom would just be sqrt7c. Since you still have a sqrt in the denominator, rationalize the fraction by multiplying sqrt7c to both the numerator and denominator to get rid of the sqrt. This would leave you with answer choice C.

Answer:

[tex]\frac{6a^4b^2\sqrt{7c}}{7c}[/tex]

Step-by-step explanation:

You can distribute radicals across division such that: [tex]\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}[/tex]

So you get the expression: [tex]\frac{\sqrt{36a^8b^4}}{\sqrt{7c}}[/tex]

Similarly with division, you can distribute radicals across multiplication such that: [tex]\sqrt{ab}=\sqrt{a}*\sqrt{b}[/tex], and you can do this multiple times

So our expression on top becomes: [tex]\frac{\sqrt{36}*\sqrt{a^8}*\sqrt{b^4}}{\sqrt{7c}}[/tex]

Whenever we take the square root of a base to an exponent, we simply divide the exponent by two. In general if you take the "nth" root of any base to an exponent, you divide the exponent by n, since: [tex](x^a)^b=x^{a*b}[/tex] and radicals such as: [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex], so you're just multiplying the two, which results in a division of "n" which in this case is 2.

So the square root of a^8 simplifies to a^4 after dividing the exponent by 2, which makes since: [tex]a^4*a^4=a^{4+4}=a^8[/tex] which exemplifies the very definition of a square root.

Applying this same logic to b^4 and just simplifying sqrt(36) regularly we get the following expression:

[tex]\frac{6a^4b^2}{\sqrt{7c}}[/tex]

We generally don't want square roots in the denominator, so we rationalize it by multiplying by the sqrt(7c)/sqrt(7c) which just simplifies to one, so we're not actually changing the value but it removes the sqrt(7c) from the denominator

[tex]\frac{6a^4b^2}{\sqrt{7c}} *\frac{\sqrt{7c}}{\sqrt{7c}}\\\\\frac{6a^4b^2\sqrt{7c}}{7c}[/tex]

and this turns out to be our solution!

Answer:

-3/8

Step-by-step explanation:

Multiply the expression(PEMDAS).

Answer: -3/8

Step-by-step explanation: First you do 1/5 times 3/8 which is 3/40 and then you do 3/40 times -5 which would be -3/8.

Hope this helped!!!!

Answer:

285

Step-by-step explanation:

Answer:

d. 3.8 m

Step-by-step explanation:

The figure is omitted.

tan(70°) = h/1.4

h = 1.4 tan(70°) = 3.8

You can confirm this by drawing and labeling a right triangle.

Additionally, make sure your calculator is in degree mode.

Answer: y=32/x^2

Step-by-step explanation: Please mark brainilest. Since y and x^2 are inversely proportional, x^2(y)=k. K is some constant. Since they gave us an example of x and y, we can calculate k as 4*8=32. So our updated equation is y(x^2)=32. Dividing both sides by x^2 we get y=32/x^2, so we have y in terms of x

Answer:

y = 32x

Step-by-step explanation:

y = k/x^2

8 = k/2^2

8 = k/4

8×4 = 32

k = 32

y = 32x

Answer:

image has six circles

∴ A complete circle has 360°

360/6= 60 degrees

Plsss mark as brainliest

Answer:

90 degrees.

Step-by-step explanation:

90 degrees because if you take a right angle and add 90 more then you have half a circle then add 90 2 more times then you have a full circle since this is a circle is like right angles if you add 90 it is the same.

NO NEED TO MARK BRAINLEIST IT IS UP TO YOU.

RMSE =  (nΣt=1 (At-Ft)²/n is the formula .

What is Root Mean Square Error (RMSE)?

What makes a good RMSE?

Identify the formula used to calculate the root mean square error over a range of forecasted values, if the actual value of the time series at time t and the forecast value for time t are denoted by A t and F t respectively.

RMSE = [ (nΣt=1 (At-Ft)2) / n ]0.5

MSE = (nΣt=1 (At-Ft)²/n

RMSE = Root of MSE

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By solving a system of equations, we conclude that the cost of a senior citizen ticket is $10, and the cost of a student ticket is $14.

Let's define the variables:

x =  price of a senior citizen ticket.

y = price of a student ticket.

With the given information we can write a system of equations:

10*x + 3*y = 142

14*x + 6*y = 224

To solve if we subtract twice the first equation from the second equation, we get:

(14*x + 6*y) - 2*(10*x + 3*y) = 224 - 2*142

14x + 6y - 20x - 6y = -60

-6x = -60

x = -60/-6 = 10

So each senior citizen ticket costs 10 dollars.

Now that we know the value of x, we can find the value of y:

10*x + 3*y = 142

10*10 + 3*y = 142

3*y = 142 - 100 = 42

y = 42/3 = 14

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Answer:

x = -3

Step-by-step explanation:

6x + 4 = 4x - 2

-4x        -4x

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

2x + 4 = -2

      -4    -4

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

2x = -6

÷2     ÷2

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

x = -3

I hope this helps!

6x +  4 = 4x -2

2x = -6

x = -3

Answer:

01234

Step-by-step explanation:

Sequence is smallest to largest therefore the sequence is 01234

Answer:01234

Step-by-step explanation:

Hope this helps.

Answer:-60

Step-by-step explanation:

Answer:

Car B

Step-by-step explanation:

Car A 450/15 = 30 gallons per mile

Car B 651/21 = 31 gallons per mile

Car C 598/23 = 26 gallons per mile

Answer:

y-2=7(x+6)

Step-by-step explanation:

point slope form

Answer:

me + you = forevea

Step-by-step explanation:

you and me make sum good chemistry too bad were talkin ab math

Linear equations - each backpack costs $14 and 5 cents .

What are linear equations with one variable?

A linear equation is a one-variable equation of a straight line. The variable only has one power, which is 1. Simple algebraic operations are used to solve linear equations in one variable, which can have the form ax+b=0.

First, we categorise one-variable linear equations into one of three categories: identity, conditional, or inconsistent. The variable's identity equation holds true for all possible values.

let us assume that the backpack costs $x.
We are informed that each kit included a backpack and school supplies totaling $18.
there are 4 school supply kits in total,
according to the above conditions we have,

4(18+x)

we are also given that she spent a total of $130, thus,

4 (18+x) = 130

72 + 4x = 130

4x = 130 - 72

4x = 58

dividing both the sides with 4,

x = 58/4

thus, x = 14.5

therefore each backpack costs $14 and 5 cents

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The quotient is  Fraction 2 and 1 over 2.

A quotient is the value obtained by dividing one particular quantity by another. We can find the quotient when we are solving a division problem by multiplying the first term with the reciprocal of the second term. Reciprocal is the exchange between the numerator value and the denominator value.

(5/7) / (2/7)= (5/7) x (7/2)

= 35/14

14 will go into 35 twice = 28

35-28= 7

27/14 = 2 and 1/2

Therefore, we conclude that the quotient of  fraction 5 over 7 Division sign fraction 2 over 7 using a rectangle model is 2 and 1/2.

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Answer: $47,000 at 10% annually is ≈ $77,297.70 and $47,000 at 5% monthly is ≈ $569,611.01

Step-by-step explanation:

Use the compound interest formula. A=P(1+r/n)^nt

Multiplying the expression 9x² - (x² - 4)² . 4 + 3x - x² will give -4x⁴ + 40x² + 3x - 64

From the information given, we want to multiply the expression 9x² - (x² - 4)² . 4 + 3x - x². This will be illustrated thus:

Distribute

9x² - (x² - 4)² . 4 + 3x - x².

9x² - (x² - 4)(x² - 4) . 4 + 3x - x².

Now we can open the parentheses. This will be illustrated as:

9x² - 2(x⁴ - 4x² - 4(x² - 4) . 4 + 3x - x³

= -4x⁴ + 40x² + 3x - 64

The value of the expression is -4x⁴ + 40x² + 3x - 64.

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Multiply the expression 9x² - (x² - 4)² . 4 + 3x - x²

The total number of leaves that the science display have is 101 leaves.

As per the question, Thomas wants to display leaf specimens for a science fair.  Thomas has 98 leaves.

Total number of leaves Thomas have = 98

Thomas has 98 leaves, which is 3 fewer than the total needed. To calculate the total number of leaves Thomas need in the science display , we need to add 3 leaves in the total number of leaves Thomas have. So, we can write this mathematically as,

Total number of leaves that the science display have = Total number of leaves Thomas have + 3

Total number of leaves that the science display have = 98 + 3 = 101

So, the science display have a total of 101 leaves.

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Answer: 11x-27

Step-by-step explanation:

1- 3[2x-6+2] + 5(x-3)

2- 3[2x-4] + 5x-15

3- 6x-12+5x-15

4- 11x-27

Answer:

Step-by-step explanation: 10rh squared

To describe the transformation, dilation by a scale factor of 4 with center of dilation at origin the rule is (x,y)→(4x,4y) and , the coordinates of rectangle Q'R'S'T  will be Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .

In the question ,

the coordinates of the rectangle QRST are given as Q(-8,5), R(-8,7), S(-5,7), and T(-5,5)  .

we have to to dilate the rectangle by a scale factor of 4 with center of dilation at the origin.

So , to dilate the rectangle by a scale factor of 4 with center of dilation at the origin  we multiply coordinates of the original shape with the dilation factor .

So , the rule of transformation becomes

(x,y)→(4x,4y)

Using the above rule to find the coordinates of the rectangle Q'R'S'T' .

given Q = (-8,5)

So, Q' = (4*(-8),4*5)

Q' = (-32,20)

Given R = (-8,7)

So, R' = (4*(-8),4*7)

R' = (-32,28)

Given S = (-5,7)

So, S' = (4*(-5),4*7)

S' = (-20,28)

Given T= (-5,5)

So, T'  = (4*(-5),4*5)

T' = (-20,20)

hence , the rectangle Q'R'S'T' coordinates are  Q' = (-32,20) , R' = (-32,28) , S' = (-20,28) , T' = (-20,20) .

Therefore , to describe the transformation, dilation by a scale factor of 4 with center of dilation at  origin the rule is (x,y)→(4x,4y) and , the coordinates of rectangle Q'R'S'T will be Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .

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After estimation the area of the composite figure is equal to about           22 square units.

As given in the question,

For the given composite figure:

Let us estimate the area of 1 square = 1 square units

Total number of full squares = 12

Total number of more than half = 6

Consider area of more than half as 1 square units.

Total number of half squares = 8

Area of less than half is negligible.

Total estimated area of given composite figure

= 12 + 6 + [(1/2) ×8]

=12 + 6 +4

=22 square units

Therefore, after estimation the area of the composite figure is equal to about 22 square units.

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The rule that can also model the function is f(x)= 4 + 3x.

The initial population of fruit flies = 4 and the population of fruit flies triple every week

Let x represent number of weeks

Therefore function can be modelled as:

f(x)= 4 + 3x

Now assume population grows for two weeks, using the function:

f(x)= 4 + 3x

f(2)= 4+3×2

f(2)= 10

Therefore population grows to 10 fruit flies in 2 weeks based on our function

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Sarah is conducting a science experiment where she initially has a population of 4 fruit flies. Every week the population triples. She writes the function f(x)=4(3)x to predict the population growth. Which rule can also model the function?

Answer:

5 bottles of hand sanitizer
2 thermometers
4 packets of masks

Step-by-step explanation:

We start by factoring each of the numbers to find the common factor which will give us the number of bags used to distribute.

1155  = 5 x 231

462 =  2 x 231

924 =  4 x 231

We see that 231 is the common factor for all 3 numbers. It is also the greatest common factor.

Therefore the greatest number of bags that can be packed = 231

Each bag will contain:
5 bottles of hand sanitizer
2 thermometers
4 packets of masks

Answer: The answer 1/2(p+24)=21

Step-by-step explanation:
The answer could be found by solving each of the equations but that would have been time consuming so it is better to fine the answer through the word problem.

the sunglasses and flip flops were bought at a half-off sale, which means that each of their prices were reduced by 1/2. So the new price was 1/2 of the original price for each of the items. $21 was spent by adding the new price of both the items.
let, 1/2 of original price of sunglasses = p
therefore we get the equation,
new price for sunglasses = 1/2p

therefore
1/2p + 1/2(24) = 21
if we take 1/2 common,
1/2(p+24)=21