What is the exponential form of log5 15,625 = 6?

Answer:

Decrease

Step-by-step explanation:

The area of the smaller rectangle (KLMN) is 16.

Since rectangles ABCD and KLMN are similar, their corresponding sides are proportional.

Let's assume the length of side AB in rectangle ABCD is x, and the length of side KL in rectangle KLMN is y.

We can set up the proportion:

(x/y) = (20/16)

To find the area of the smaller rectangle, we need to determine the ratio of their areas.

Since the area of a rectangle is given by the product of its length and width, the ratio of the areas will be equal to the square of the ratio of their sides:

(Area of ABCD)/(Area of KLMN) = (x²)/(y²)

We are given that the area of ABCD is 25, so we have:

25/(Area of KLMN) = (x²)/(y²)

To find the area of KLMN, we need to substitute the values of x and y from the proportion:

25/(Area of KLMN) = (20/16)²

Simplifying the right side:

25/(Area of KLMN) = (5/4)²

25/(Area of KLMN) = 25/16

Cross-multiplying:

25 × 16 = 25 × (Area of KLMN)

400 = 25 × (Area of KLMN)

Dividing both sides by 25:

16 = Area of KLMN

Therefore, the area of the smaller rectangle (KLMN) is 16.

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Answer:

Step-by-step explanation:

it think it 23 becasue u add

1 divide it by 2

Answer:

the number is 7

Step-by-step explanation:

I am not sure what you mean by "translate" but here is my solution to the problem.

first write the question as a equation: 3x - 5 = 16

then add 5 to both sides: 3x = 21

divide both sides by 3: x = 7

double check

3*7 - 5 = 16

the number is 7

Answer:

Step-by-step explanation:

Translation: 3x - 5 = 16

Hence, the translation is 3x - 5 = 16 and the missing value is 7.

Hoped this helped.

\(BrainiacUser1357\)

Answer:

Pretty sure it's 47°

9514 1404 393

Answer:

  13.3 m

Step-by-step explanation:

Let d represent the length of the diagonal. Then the length of the rectangle is (d-2) and the width is (d-6). The area is the product of length and width, so is ...

  A = LW

  83 = (d -2)(d -6) = d² -8d +12

  71 = d² -8d . . . . . . . . subtract 12 to get the constant out of the way

  d² -8d +16 = 87 . . . . add (-8/2)² = 16 to both sides to complete the square

  (d -4)² = 87 . . . . . . . write as a square

  d -4 = √87 . . . . . . . positive square root

  d = 4 +√87 ≈ 13.3 . . . . add 4

The diagonal is about 13.3 meters long.

_____

Additional comment

If you check to see if the side lengths actually correspond to those of a rectangle, you find that they do not. The geometry described here is impossible. The rectangle with the proposed relations between sides and diagonal would have a diagonal of about 12.899 m and an area of about 75.19 m².

(A) The required down payment is $48,000.

(B) The amount of the mortgage is $192,000.

(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

(a) To find the required down payment, we need to calculate 20% of the house price.

Down payment = 20% of $240,000

Down payment = 0.2 * $240,000

Down payment = $48,000

The required down payment is $48,000.

(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.

Mortgage amount = Total cost of the house - Down payment

Mortgage amount = $240,000 - $48,000

Mortgage amount = $192,000

The amount of the mortgage is $192,000.

(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal amount (mortgage amount)

r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)

n = Total number of monthly payments (30 years multiplied by 12 months)

Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

Using this formula and performing the calculation will give you the monthly payment amount.

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The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.

To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.

Since the owner wants the total cost to be under $2000, we can set up the inequality:

43H + 750 < 2000

Now, let's solve this inequality for H, the number of hours:

43H < 2000 - 750

43H < 1250

Dividing both sides of the inequality by 43:

H < 1250/43

To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.

Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:

H < 29

Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.

By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.

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We have that by answering the following question Therefore, the width inequality of the coal tray must be at least 5.30 inches.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many basic inequalities may be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are split or added on both sides. Exchange left and right.

We are given the formula:

\(P = 1 / (I + Fd^2)\)

Let's assume that the limits on the variables are as follows:

0 < P < 100 (since P can be converted to a percentage)

0 < I < infinity

0 < F < infinity

0 < d < infinity

\(0.53 = 1 / (I + F(16/d)^2)\\0.53(I + F(16/d)^2) = 1\\I + F(16/d)^2 = 1/0.53\\I + F(256/d^2) = 1.8868\\\)

Since d > 0, we know that:

\(256/d^2 < infinity\)

Therefore, we can say:

\(I + F(256/d^2) < I + infinity\\I + F(256/d^2) < infinity\\1/0.53 < infinity\\1 < 0.53 infinity\\F(256/d^2) < 1/0.53 - I\\d^2 > 256F / (1/0.53 - I)\\d > \sqrt(256F / (1/0.53 - I))\\d > \sqrt(256(0.01) / (1/0.53)) = 5.30\\d > 5.30\\\)

Therefore, the width of the coal tray must be at least 5.30 inches.

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We have the following two points that belong to a line:

And also the slope of the line:

And we have to find the missing coordinate r.

To find that, we can proceed as follows:

1. We can label both points as follows:

• (6, r) ---> x1 = 6, y1 = r

• (-22, 15) ---> x2 = -22, y2 = 15

2. Now, we can use the formula for the slope of a line - since the slope of the line was given. Then we have:

3. Then we can substitute the corresponding values into the above equation as follows:

4. And now, we have to solve the equation for r as follows:

5. Finally, we can subtract 15 from both sides of the equation:

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

6

Step-by-step explanation:

Plato

Answer:

2x

Step-by-step explanation:

Answer:

11325

Step-by-step explanation:

\(\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[a+l]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $l$ is the last term.\\\phantom{ww}$\bullet$ $n$ is the number of terms.\\\end{minipage}}\)

A positive integer is a whole number that is greater than zero.

Therefore:

Substitute the values into the formula to find the sum of the first 150 positive integers:

\(\implies S_{150}=\dfrac{1}{2}(150)\left[1+150\right]\)

\(\implies S_{150}=75 \cdot 151\)

\(\implies S_{150}=11325\)

Answer:

simple interest=$97.50.

compound interest= $100.668

Step-by-step explanation:

Given:

Principal (P) = $750

Rate (R) = 6.5% (in decimal form, 0.065)

Time (T) = 2 years

Simple Interest = Principal*Rate*Time

Using the formula, the simple interest is calculated as follows:

Simple Interest = $750*0.065*2 = $97.50

Therefore, the simple interest for $750 with a 6.5% interest rate over 2 years is $97.50.

Again:

Compound Interest = Principal*(1 + Rate)^(Time)-Principal

Using the same values as above, the compound interest can be calculated as follows:

Compound Interest = $750*(1+0.065)^(2)-$750

= $750*1.065^2 -$750

= $750 × 1.134225 - $750

= $850.66875-$750

= $100.668

Therefore, the compound interest for $750 with a 6.5% interest rate over 2 years is $100.668

The truck driver would deliver 105 packages in a 7 hours day

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:

y - 15 = [(60-15)/(4-1)](x - 1)

y = 15x

For a 7 hour day (x = 7):

y = 15(7) = 105

The driver would deliver 105 packages in 7 hours

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Answer:

x=3

Y=−4

Step-by-step explanation:

Y=−7/3x+3

Y=−1/3x−3

​

Consider the first equation. Add  

3

7

​

x to both sides.

Y+

3

7

​

x=3

Consider the second equation. Add  

3

1

​

x to both sides.

Y+

3

1

​

x=−3

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

Y+

3

7

​

x=3,Y+

3

1

​

x=−3

Choose one of the equations and solve it for Y by isolating Y on the left hand side of the equal sign.

Y+

3

7

​

x=3

Subtract  

3

7x

​

 from both sides of the equation.

Y=−

3

7

​

x+3

Substitute −

3

7x

​

+3 for Y in the other equation, Y+

3

1

​

x=−3.

−

3

7

​

x+3+

3

1

​

x=−3

Add −

3

7x

​

 to  

3

x

​

.

−2x+3=−3

Subtract 3 from both sides of the equation.

−2x=−6

Divide both sides by −2.

x=3

Substitute 3 for x in Y=−

3

7

​

x+3. Because the resulting equation contains only one variable, you can solve for Y directly.

Y=−

3

7

​

×3+3

Multiply −

3

7

​

 times 3.

Y=−7+3

Add 3 to −7.

Y=−4

The system is now solved.

Y=−4,x=3

We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{19 \: inches}}}}}\)

Step-by-step explanation:

Let the width be 'w'.

Length of a rectangle ( l ) = 5 + w

Perimeter of a rectangle = 66 inches

First, finding the width of a rectangle

\( \boxed{ \sf{perimeter \: of \: rectangle = 2(l + w)}}\)

\( \dashrightarrow{ \sf{66 = 2(5 + w + w)}}\)

\( \dashrightarrow{ \sf{66 = 2(5 + 2w)}}\)

\( \dashrightarrow{ \sf{66 = 10 + 4w}}\)

\( \dashrightarrow{ \sf{10 + 4w = 66}}\)

\( \dashrightarrow{ \sf{4w = 66 - 10}}\)

\( \dashrightarrow{ \sf{4w = 56}}\)

\( \dashrightarrow{ \sf{ \frac{4w}{4} = \frac{56}{4} }}\)

\( \dashrightarrow{ \sf{w = 14 \: inches}}\)

Width of a rectangle ( w ) = 14 inches

Now, Substituting / Replacing the value of w in order to find the length of rectangle

\( \sf{length = 5 + w}\)

\( \dashrightarrow{ \sf{length = 5 + 14}}\)

\( \dashrightarrow{ \sf{19 \: inches}}\)

Length of a rectangle = 19 inches

Hope I helped!!

Best regards! :D

Answer:

C. 5 × 3

Step-by-step explanation:

The order of a matrix is the number of rows and columns that a matrix has. Rows are listed first and columns are listed second. The matrix has 5 rows going across horizontally and 3 columns going down vertically.

So, the order of the matrix is 5 × 3.

Hope that helps.

Answer:

C

Step-by-step explanation:

i just guessed but it was correct

Answer:

.048

Step-by-step explanation:

6 thousandths = 0.006

So, 0.006 times 8 would be...

.006

x    8

.048

Hope this helps you out! I'm not exactly sure how to explain how to multiply, but if you're confused, you can always ask someone for help...have a great day :)

Answer:

105 cm³

Step-by-step explanation:
i think lol

The graph of the function y = (1/3)ˣ+4 is vertically shifted graph of the function y = (1/3)ˣ

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given is a function y = (1/3)ˣ+4, we need to compare the graph of this function to the graph of the function y = (1/3)ˣ

We know that,

In vertical shifting, adding a constant to a function will shift its graph vertically, adding a positive constant c will shift the graph upward c units, while adding a negative constant c will shift it downward c units.

Here, we can see, in y = (1/3)ˣ+4, constant 4 is added, that mean the graph of the function y = (1/3)ˣ is vertically shifted upward 4 units.

Hence, the graph of the function y = (1/3)ˣ+4 is vertically shifted graph of the function y = (1/3)ˣ

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Step-by-step explanation:

It is not clear from the given information which angles and sides are being referred to as "107⁰", "-x-8", "-42-7", and "3y-1". However, we can use some properties of rhombuses to solve for x, y, and z.

Opposite angles in a rhombus are equal. Therefore, if one angle is 107⁰, then the opposite angle is also 107⁰.

The diagonals of a rhombus are perpendicular bisectors of each other. This means that they intersect at a right angle and divide each other into two equal parts.

The diagonals of a rhombus bisect each other's angles. This means that the angles formed by each diagonal with the sides of the rhombus are equal.

Using these properties, we can set up some equations to solve for x, y, and z:

Let's assume that "-x-8" and "-42-7" are the lengths of the diagonals of the rhombus, and that "3y-1" is the length of one of the sides.

Since the diagonals bisect each other's angles, we know that the angles formed by each diagonal with the side of the rhombus are equal. Let's call each of these angles "z":

-z + 107⁰ + z = 180⁰ (sum of angles in a triangle)

107⁰ = 180⁰ - 2z

2z = 73⁰

z = 36.5⁰

Now let's use the fact that the diagonals are perpendicular bisectors of each other:

(-x-8)/2 = (-42-7)/2

-x-8 = -49

-x = -41

x = 41

Finally, let's use the fact that the sides of a rhombus are equal:

-x-8 = 3y-1

41-8 = 3y-1

33 = 3y

y = 11

Therefore, the values of x, y, and z in the rhombus are:

x = 41

y = 11

z = 36.5⁰

Answer:

170.6

Step-by-step explanation:

170.55

The tenths place is where the left 5 is.

1. Drop everything to its right.

170.5

2. Look at the first digit that was dropped. It is a 5. That means the last digit that remains goes up by 1 to 6.

Answer: 170.6

Answer:

170.6

Step-by-step explanation:

170.55 ≈ 170.6

When you are rounding numbers, you have to look at the digit after the digit you are rounding to. So if you are rounding to the nearest tenth, you need to look at the digit next to it which is the hundredth. If the hundredth is 1-4, then you round down. If the hundredth is 5-9, then you round up. Since the hundredth is 5, you round the 5 in the tenth place up to 6.

Option D

if any confusion leave a comment

Answer:

1) 5cm

2) 15cm

3) 7.4cm

4) 12.5cm

5) 3.9cm

6) 10cm

Step-by-step explanation:

Square both values, then add the 2 values. After, with the answer, root it. This method applies for all the questions given.

For example:

For your first question:

4^2 + 3^2 = 25

√25 = 5cm

Hope this helps!