Solve 3c − 5f = 55 for f. Show your work.

The equation is 4x + 12 = 180. Then the value of the smallest integer will be 42.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The sum of four consecutive even integers is 180.

Let x be the smallest integer. Then the other three consecutive even integers will be x + 2, x + 4, and x + 6. Then the equation is given as,

x + x + 2 + x + 4 + x + 6 = 180

4x + 12 = 180

4x = 168

x = 42

The value of the smallest integer will be 42.

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Answer:  36 cm

Step-by-step explanation:

Given : The expression 2l+2w is used to find the perimeter of a rectangle with length l and width w.

To find :  The perimeter of a rectangle with length 14cm and width 4cm.

Substitute l=14 and w=4 in the given expression , we get

Perimeter= [tex]2(14)+2(4) =28+8=36\ cm[/tex]

Hence, the perimeter of a rectangle with length 14cm and width 4cm= 36 cm

Answer:

Hello!

Great question!

The correct answer would be "Common Factor."

Step-by-step explanation:

It is a common factor when it is a factor of two (or more) numbers.

The number which can be divided out of each term in an expression is called the GCF or greatest common factor of that number.

GCF or greatest common factor is the common number which all the term has in a group of terms. It is the number which can divide each number of the group.

For example, let a group of number as,

[tex]\{1,2,4,8,16\}[/tex]

The number which can be divided out of each term in this data is 16 which is the greater common factor of this data set.

Thus, the number which can be divided out of each term in an expression is called the GCF or greatest common factor of that number.

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The value of x in the figure given is E. √70.

The answer is E. √70.

The two triangles are similar by the AAA Similarity Theorem, since they have two pairs of congruent angles, namely ∠ABD and ∠CAD, and ∠BAD and ∠CDA.

Since the triangles are similar, the ratio of corresponding sides is constant. In particular, the ratio of AD to CD is the same as the ratio of BD to AD.

We are given that AD = 14 and CD = 20, so the ratio of AD to CD is 14/20. We are also given that BD = x, so the ratio of BD to AD is x/14.

Setting these two ratios equal to each other, we get x/14 = 14/20, which simplifies to x = √70.

Here is a proof that shows why the two triangles are similar:

AAA Similarity: Triangles ABD and CAD have two pairs of congruent angles, namely <ADB> and <CAD>, because they are both right angles.

SSS Similarity: Triangles ABD and CAD have three pairs of corresponding sides that are proportional, namely AD/CD = 14/20, BD/AD = x/14, and AB/CD = √70/20. Therefore, the two triangles are similar by the SSS Similarity Theorem.

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To find the dimensions of the shipping box, calculate the volume in cubic inches, then set up and solve the volume equation x(x + 5)(3x - 1), substituting the given volume after conversion from cubic feet. Solve for x, then use it to find and round the box's dimensions.

To find the dimensions of the shipping box, we need to calculate the volume using the given dimensions in inches and compare it to the provided volume in cubic feet. Recall that the conversion factor between cubic feet and cubic inches is 1 cubic foot equals 1,728 cubic inches. Firstly, convert the volume of the box from cubic feet to cubic inches: 7.6 cubic feet are 7.6 x 1,728 cubic inches.

Next, we can set up the volume equation for the box using the given dimensional expressions: volume = width x length x height, which for this box is x x (x + 5) x (3x - 1). Now we solve the equation for x given that the volume in cubic inches is equal to 7.6 x 1,728 inches.

Once x is found, we can determine the width, length, and height by plugging x back into the expressions x, x + 5, and 3x - 1, respectively, and rounding each to the nearest inch.

To find the dimensions of the rectangular patio, use the equations for perimeter and area and solve for length and width.

To find the dimensions of the rectangular patio, we can use the given information about its perimeter and area. Let's assume the length of the patio is L and the width is W.

The perimeter is given as 34 meters, which is equal to 2L + 2W. So, we have the equation 2L + 2W = 34.

The area is given as 70 square meters, which is equal to L * W. So, we have the equation L * W = 70.

We can use these equations to solve for L and W using substitution or elimination method.

The coming head in the fourth time is independent of the coming head in the first three times thus the probability of coming head in the fourth time is 1/2.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

In our daily time, there are several instances in the everyday world where we may need to draw conclusions about how everything will turn out.

As per the given,

In the first three attempts coming head in the first three times.

In the fourth attempt, the probability will be independent of the first three events.

Thus, the probability of coming ahead in the fourth time will be as,

Number of desire output/number of total output

=> 1 / 2

Hence "The coming head in the fourth time is independent of the coming head in the first three times thus the probability of coming head in the fourth time is 1/2".

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Answer:

The probability of the event below of rolling a 5 is 0.0625.

Step-by-step explanation:

Given is : A probability experiment consists of rolling a fair 16​-sided die. Find the probability of the event below of rolling a 5.

Total number of faces = 16

So, there is only one way for rolling a 5 on a die

And the probability of rolling a 5 on a die = [tex]\frac{1}{16}[/tex]

= 0.0625

The provided math problem involves writing a program that helps to calculate the number of cookie boxes and containers required to ship a specific number of cookies considering the capacity of each item. If there are leftover cookies that do not fill a box or if there are leftover boxes that do not fill a container, these are also calculated.

This is a programming problem which requires logic to calculate the number of boxes and containers needed to ship a given number of cookies. Assume that 'total_cookies', 'cookies_per_box', and 'boxes_per_container' are user inputs. Initially, you should calculate the total boxes by 'total_boxes = total_cookies / cookies_per_box'. The floored division operator is applied to discard the last box if it contains less than the specified number of cookies. Then, calculate the total containers with 'total_containers = total_boxes / boxes_per_container'. Again, you use the floored division operator to discard the last container if it contains less than the specified number of boxes. Lastly, calculate the leftover cookies and boxes, which is done by applying the modulus operator. 'leftover_cookies = total_cookies % cookies_per_box' and 'leftover_boxes = total_boxes % boxes_per_container'.

The logic of the given program focuses on the calculation of boxes and containers needed to ship the given number of cookies keeping in consideration the capacity of each box and container. Also, the algorithm calculates the leftover cookies and boxes, if not enough to fill a box or container fully.

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Answer:

too tenes

This is the correct answer because it is a play on words comparing tents which describes the native american home structure of a wigwam and a teepee and tense, will which describes a physiological response to high anxiety6.

In this exercise we have to use the knowledge of finance to calculate the monthly amount of insurance, so the best alternative that represents this amount is:

Option C

In this exercise we want to calculate the monthly insurance payment amount, so from the given values ​​we find:

[tex]Payment= (Bodily Injury)+ (Property Damage)+ (Collision)+(Comprehensive)[/tex]

Substituting the values ​​in the formula given above we find that:

[tex]Payment= 22.5 + 120.5 + 415.25 + 100 \\= 658.25\\658.25/12 = 54.854[/tex]

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The rate of change of the quadratic function over the interval −4≤x≤−2 is 2.

To find the rate of change of the quadratic function [tex]$f(x)=x^2+4 x+5$[/tex] , over the interval −4≤x≤−2, we need to find the average rate of change over that interval.

The average rate of change of a function f(x) over an interval [a,b] is given by:

[tex]Average Rate of Change =\frac{f(b)-f(a)}{b-a}$[/tex]

So, in this case:

a=−4

b=−2

We calculate f(−4) and f(−2):

[tex]$\begin{aligned} & f(-4)=(-4)^2+4(-4)+5=16-16+5=5 \\ & f(-2)=(-2)^2+4(-2)+5=4-8+5=1\end{aligned}$[/tex]

Now we can find the rate of change:

Rate of Change = [tex]$\frac{1-5}{-2-(-4)}=\frac{-4}{-2}=2$[/tex]

The average rate of change of the function f(x)=x² + 4x + 5 over the interval from x = -4 to x = -2 is -2.

The rate of change for the quadratic function f(x)=x² + 4x + 5 over the interval from x = -4 to x = -2 can be calculated using the average rate of change formula. This formula is given by:

Rate of Change = [f(x2) - f(x1)] / (x2 - x1)

Where x1 = -4 and x2 = -2. We first calculate f(-4) and f(-2) by plugging these values into the function:

f(-4) = (-4)² + 4(-4) + 5 = 16 - 16 + 5 = 5

f(-2) = (-2)² + 4(-2) + 5 = 4 - 8 + 5 = 1

Now we use these results in our rate of change formula:

Rate of Change = (1 - 5) / (-2 + 4) = -4 / 2 = -2

The average rate of change of the function f(x) over the interval from x = -4 to x = -2 is -2.

If two vectors are represented both in magnitude and direction by the two adjacent sides of a triangle taken in an order, then their resultant is given by the third side taken in the reverse order.

Resultant vector :

                          R = sqrt of A^2 + B^2 + 2ABcosθ

given :

           A = 200 units

           B = 300 units

           θ = 30 degrees

∴ R = sqrt of 200^2 + 300^2 + 2(200)(300)cos35

the answer is 477.805656

If two vectors are represented both in magnitude and direction by the two adjacent sides of a triangle taken in an order, then their resultant is given by the third side taken in the reverse order.

Resultant vector :

                         R = sqrt of A^2 + B^2 + 2ABcosθ

given :

          A = 200 units

          B = 300 units

          θ = 30 degrees

∴ R = sqrt of 200^2 + 300^2 + 2(200)(300)cos35

the answer is 477.805656

Area of triangle is given as:

A = (1/2) b * h

where b is base and h is height

So given that:

A = 1768 inches^2

b = 52 inches

Rearranging the equation to find for h:

h = 2 A / b

h = 2 * 1768 inches^2 / 52 inches

h = 68 inches

Answer:

The statement is true. Supplementary angles have measures that add up to 180°. Each right angle has a measure of 90°. 90°+ 90° = 180°.

Step-by-step explanation: