find the missing lenghts of the sides

1.50

Let h and f represent the cost of 1 hamburger and 1 order of fries, respectively. Then you can write two equations for the cost of the orders.

... 5h +3f = 9.90

... 3h +5f = 8.50

Using Cramer's rule, the cost of a hamburger can be found to be ...

... h = (3·8.50 -5·9.90)/(3·3 -5·5) = (25.50 -49.50)/(9 -25)

... = -24/-16

... h = 1.50

The cost of one hamburger is 1.50.

_____

Formulation of Cramer's Rule

For equations ...

... ax +by = c

... dx +ey = f

The rule tells you ...

... x = (bf -ec)/(bd -ea)

... y = (cd -fa)/(bd -ea)

_____

Note that we have chosen this method of solution because we only needed the value of one of the variables. It is effectively the same as substitution (or elimination), but does all the steps in one formula.

Using the matrix solution methods on a calculator is another fast way to solve a pair of equations like this.

$392.16 in interest saved

The payoff in 1 year costs a total of 12 × $366.72 = $4400.64.

The payoff in 2 years costs a total of 24 × $199.70 = $4792.80.

Paying off the balance in 1 year saves interest charges of ...

... 4792.80 -4400.64 = $392.16

The area of the label for a cylindrical coffee can with a height of 14 cm and a radius of 5 cm is approximately 440 square centimeters.

The subject in this case is Mathematics, and the question pertains to the use of geometry to determine the area of a label on a cylindrical coffee can. Specifically, the question asks to calculate the area of the cylindrical surface (lateral surface), which will be used as the label area. To calculate this, one needs to use the formula for the lateral surface area of a cylinder, which is 2πrh, where r is the radius and h is the height of the cylinder.

Given a cylinder with a height of 14 centimeters and a radius of 5 centimeters, the area of the label can be calculated as follows:

Area = 2π(5 cm)(14 cm) = 2π×5 cm×14 cm = 2×3.1416×5 cm×14 cm ≈ 440 cm².

Substituting the given expressions for bore and stroke and 8 cylinders, you have ...

... D = π((k/2)/2)^2 · h · 8

... D = (π/2)hk^2 . . . . simplified expression for 8 cylinders

_____

For bore = 4 in, stroke = 3.4 in, n = 4, the displacement is ...

... D = π(4 in/2)^2 · (3.4 in) · 4 = 54.4π in^3

... D ≈ 170.9 in^3

Answer:

[tex]85.4[/tex] cubic inch

Step-by-step explanation:

Given-

Displacement = [tex]\pi (\frac{bore}{2} )^2 * stroke * n[/tex]

Now,

bore is represented as [tex]\frac{k}{2}[/tex]

and stroke is represented as [tex]h[/tex]

and number of cylindres "n"[tex]= 8[/tex]

Substituting these values in above equation, we get -

Displacement [tex]= \pi (\frac{\frac{k}{2} }{2})^2*h*8\\= \pi \frac{k^2}{16} * h* 8\\= \frac{\pi* k^2*h}{2}[/tex]

Now substituting the given values, in above equation we get -

Displacement [tex]= \frac{\pi* 4^2*3.4 }{2}\\= \frac{\3.14* 16*3.4 }{2} \\ = 85.408\\= 85.41= 85.4[/tex]cubic inch

(a) To make use of the forms of the equation for a line this problem requires, we must first calculate the slope (m) of the line between the two given points. That is computed by ...

... m = (change in y)/(change in x)

... m = (8 -3)/(2 -0) = 5/2

The second given point tells us the y-intercept (b) is 3, so the equation for the line is ...

... y = mx + b

... y = 5/2x + 3

(b) As in part (a), we must calculate the slope of the line. That is ...

... m = (change in y)/(change in x)

... m = (4 -3)/(1 -3) = 1/(-2) = -1/2

Using the first point (h, k) in the point-slope form of the equation of a line, we have ...

... y -k = m(x -h)

... y -4 = -1/2(x -1) . . . . . point-slope equation

Simplifying this, we get

... y = -1/2x +1/2 +4

... y = -1/2x +9/2 . . . . . slope-intercept equation

(c) The slopes of the two equations are different, so they must intersect at exactly one point. The equations are consistent.

(d) We can substitute the "y" from one equation into the other to give ...

... 5/2x +3 = -1/2x +9/2

... 3x = 3/2 . . . . . . . add 1/2x -6/2

... x = 1/2 . . . . . . . . divide by 3

Using the first equation to find y:

... y = (5/2)·(1/2) +3 = 5/4 +12/4

... y = 17/4

The point of intersection is (x, y) = (1/2, 17/4).

Answer:

1: The diver is 8 feet below sea level.

2: -20

3: -20 + 20 = 0

Step-by-step explanation:

1: This is determined by adding 4 to negative 12. -12 +4 = -8

2: You get this by subtracting 12 from negative 8. -8 - 12 = -20

3: This is done by adding 20 to negative 20. -20 + 20 = 0

The diver's depth in relation to sea level is determined by subtracting the ascent from the initial descent and subsequent descents are added or subtracted accordingly. To reach sea level from a negative depth, the diver needs to ascend by swimming.

The depth of the diver in terms of sea level is -8 feet. This was determined by subtracting the ascent of 4 feet from the initial descent of 12 feet below sea level, resulting in -8 feet.

The new depth of the diver in terms of sea level is -20 feet. This was determined by adding the additional descent of 12 feet to the previous depth of -8 feet below sea level, resulting in -20 feet.

The diver will reach sea level from the position found in part B by swimming up 20 feet. This will bring the depth of the diver to 0 feet below sea level, which is equivalent to sea level.

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[tex]\bf \textit{Logarithm of exponentials} \\\\ log_a\left( x^b \right)\implies b\cdot log_a(x) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf 5\cdot 21^{5x}=16\implies 21^{5x}=\cfrac{16}{5}\implies \stackrel{\textit{taking \underline{log } to both sides}}{\log\left( 21^{5x} \right)=\log\left( \cfrac{16}{5} \right)} \\\\\\ 5x\log(21)=\log\left( \cfrac{16}{5} \right)\implies 5x=\cfrac{~~\log\left( \frac{16}{5}\right)~~}{\log(21)}\implies x=\cfrac{~~\log\left( \frac{16}{5}\right)~~}{5\log(21)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill x\approx 0.0764094095937~\hfill[/tex]

Answer:

X=log 3.2/5 log 21

Step-by-step explanation:

X=0.0764094

Answer:

Step-by-step explanation:

First put the point slope form equation into slope intercept form.

y−2=0.5(x+3)

y - 2 = .5x + 1.5

y - 2 + 2 = .5x + 1.5 + 2

y = .5x + 3.5

With it in the slope intercept form we can see that the y intercept is at (0,3.5)

Find a graph that has this as the y intercept. Next we can graph it like the picture I have attached. You graph the equation by inserting numbers for x.

Answer:

Step-by-step explanation:

The given equation is y - 2 = 0.5(x + 3)

Since the equation is of a straight line so we further rewrite the equation in the form of intercept form.

y - 2 = 0.5x + 1.5

y = 0.5x + 1.5 + 2

y = 0.5x + 3.5

Now plot the graph for the points suitable for the equation

x     0       2        -2         4        -4

y     3.5    4.5     2.5      5.5     1.5

Now the graph which matches the graph plotted will be the graph of the equation.

Answer:Temperature of 10 degrees

Step-by-step explanation:

The others involve a decrease of 10 units, justifying use of a megative number.

The situation would not be represented by the integer -10 is Temperature of 10 degrees.

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

Integers come in three types:

Given:

The representation of integer -10.

first, You owe $10

Owning is taken which can be represented as -10.

Temperature of 10 degrees have no clear idea of above or below 0 degree.

and, hole 10 feet deep can be represented as -10.

if we take ground at 0 then the above will positive integer and depth will be negative integer.

Lastly, 10 yard penalty can be represented as -10.

Penalty means deduction which can be shown as negative integer.

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96,767,921

5 - 7 + 2 - 6 ÷ 2 + 24^3 * 7000 - 76 = 96,767,921

Exponentiation is performed first, followed by multiplication and division in their order of appearance.

= 5 - 7 + 2 - 6 ÷ 2 + 13,824 · 7000 -76

= 5 - 7 + 2 - 3 + 96,768,000 -76

Then addition and subtraction are peformed in the order of appearance. (The commutative and associative laws apply.)

= (5 -7 +2) +96,768,000 -3 -76

= 96,767,921

_____

A Google or Bing search box will evaluate an arithmetic expression strictly according to the order of operations. Your result is attached. The preferred symbols are * (asterisk) for "times" and / (slash) for "divided by". The usual ^ (caret) is used for "to the power of." If you intend grouping, parentheses are required.

There are 7 work stations.

This is because:

7/8 divided by 1/6 divided by 2 =

7/8 times 16/1 times 1/2 = 7

Hope this helps :)

Workstations the teacher set up in each of the classrooms is is mathematically given as,

⇒ x = 7

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

An art teacher has a total of 7/8 pound of clay.

And, The teacher puts 1/16 pound of clay at each workstation.

Since, The teacher sets up an equal number of workstations in each of 2 classrooms

Generally the equation for the workstations is mathematically given as,

1/16(x) = 7/8

x = 16 × 7/(8×2)

x = 7

Therefore, The workstations the teacher set up in each of the classrooms is, ⇒ x = 7

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Answer:

The height of the Mantis is 145 feet

Step-by-step explanation:

There is a table with the roller coasters' heights at Cedar Point amusement park in the assignment that is missing from the post.

Looking up the info online, the Millennium Force is 310 feet tall.

The Mantis is 165 feet shorter than the Millennium Force.

So the height of the Mantis is 310 - 165 = 145 feet

To find the height of the Mantis roller coaster, subtract 165 feet from the height of the Millennium Force roller coaster.

The problem states that the Mantis is 165 feet shorter than the Millennium Force. To find the height of the Mantis, we need to subtract 165 feet from the height of the Millennium Force.

If we let x represent the height of the Millennium Force, then the height of the Mantis would be x - 165 feet.

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y = (1/2)x - 5

Try the answers:

... -4 ≠ (1/2)·2 + 5

... -4 ≠ (1/2)·2 - 3

... -4 = (1/2)·2 - 5 . . . . . the third choice works

... -4 ≠ (1/2)·2 + 3

___

You can write the point-slope form equation and simplify.

... y -k = m(x -h) . . . . . . equation for line of slope m through point (h, k)

... y -(-4) = (1/2)(x -2) . . . filled in with your values, m=1/2, (h, k) = (2, -4)

... y = (1/2)x -1 -4 . . . . subtract 4, eliminate parentheses

... y = (1/2)x - 5 . . . . . simplified. (Matches the 3rd selection.)

Answer: y = one half x − 5

Step-by-step explanation:

We know that , the equation of line that passes through point (a,b) and has slope m is given by :-

[tex](y-b)=m(x-a)[/tex]

Given : Point = (a,b)=(2, -4)

Slope = [tex]\dfrac{1}{2}[/tex]

Then, the equation of the line will be (substitute all the values in the above formula) :-

[tex](y-(-4))=\dfrac{1}{2}(x-2)[/tex]

[tex]\Rightarrow\ y+4=\dfrac{1}{2}(x-2)[/tex]

[tex]\Rightarrow\ y+4=\dfrac{1}{2}x-1[/tex]

Subtract 4 from both sides , we get

[tex]y=\dfrac{1}{2}x-1-4[/tex]

[tex]y=\dfrac{1}{2}x-5[/tex]

Hence, the correct answer is y = one half x − 5

Answer:

16

Step-by-step explanation:

We need to evaluate the expression 3x-2

Plugging in x=6, we get

3(6)-2

=18-2

=16

Answer:

16

Step-by-step explanation:

3x – 2 if x = 6

To solve this we substitute the x with 6.

3x – 2 = 3(6) - 2

           = (3×6) - 2

           = 18 - 2

            = 16

The absolute value function that represents the parent function f(x) = |x| reflected over the x-axis and translated 1 unit to the right is g(x) = -|x-1|.

The absolute value function that represents the parent function f(x) = |x|, reflected over the x-axis and translated 1 unit to the right is g(x) = -|x-1|.

Reflecting over the x-axis involves multiplying the function by -1 to get -|x|. Translating 1 unit to the right involves substituting (x-1) for x within the absolute value to get -|x-1|.

Therefore, the transformation involves two steps:

Answer:

It is irrational and equal to 4 + 5 square root of 2.

Step-by-step explanation:

[tex]\sqrt{2}(5+\sqrt{8})=5\sqrt{2}+\sqrt{2\cdot 8}=5\sqrt{2}+\sqrt{16}\\\\=4+5\sqrt{2}[/tex]

The square root of 2 in the result makes the result irrational.

Answer:

It is irrational since the square root sign in the answer is present.

Step-by-step explanation:

We are given with two factors: square root of 2 and 5 + square root of 8. We use a scientific calculator that displays irrational answers. The product of the two factors is 4 + 5 square root of 2. The answer is irrational since the square root sign in the answer is present.

Answer:

at least 43 1/4 minutes (or 44 rounded)

Step-by-step explanation:

I set up an equation:

175+6x=10x

Isolate x:

175=4x

x=43.25

is this a college question? (just curious)

Answer:

an = 65 + 5[tex]_{n - 1}[/tex]

a1 = 65

Step-by-step explanation:

If the begining value is 65, then a1 has to be itL

a1 = 65

Then, if this amount increased every minute then 5 has to be added to this value each time:

an = 65 + 5

But this means that 5 is added to 65 every time with no increase, so the five must me multiplied by the n value:

an = 65 + 5[tex]_{n}[/tex]

a2 = 65 + 10 = 75

But this value should be 70 because it is the first point after 65 so it should be +5 not +10

To do this we can simply subtract one from the n value that is being multiplied by 5:

an = 65 + 5[tex]_{n - 1}[/tex]

Which is the recursive rule!

Answer:

To see if a table of values represents a linear function, check to see if there's a constant rate of change. If there is, you're looking at a linear function!

Step-by-step explanation:

Answer:

Step-by-step explanation:

If it has an exponent, it's non-linear. (There are other ways it can be non-linear, too, but this is the one applicable here.)

Answer:

D. 98:112

Step-by-step explanation:

We want to find Annette:Joaquin

49:56

Both of these numbers are divisible by 7. so we need to divide both of them by 7.

7: 8

Now multiply by each side by 14

7*14 : 8*14

98: 112

Answer:

y=14x+75 where y is equal to 14x+75. Hope this helps.

Step-by-step explanation:

Answer:

y=14x+75

Step-by-step explanation:

y=mx+b is the slope intercept form which you will use for equations like these.

the M represents what it recurring, and in this case it is 14 dollars per month

The b represents your initial value and in this case it is 75 dollars

The 14x represents that it is 14 per, and the 75 represents the initial cost.

Answer:

t = 3

Step-by-step explanation:

The ball thrown vertically upward reaches its maximum height after 3 seconds, as calculated by setting the derivative of the position function, which represents the velocity, to zero.

The question is about determining how many seconds it will take for a ball thrown vertically upward to reach its maximum height. The ball's position as a function of time is given by 30t - 5t2 meters. To find when the ball reaches its maximum height, we need to find the time at which the velocity is zero. The velocity function is the derivative of the position function, which is 30 - 10t. Setting the velocity equal to zero gives us the time when the ball reaches its maximum height:

0 = 30 - 10t

t = 3 seconds

The ball will reach its maximum distance from the ground after 3 seconds.

Answer:

36 cm²

Step-by-step explanation:

1. ΔBEF & ΔADF are similar; 2. the height of ΔABE is 3height of ΔBEF; 3. area of ΔABE is 3 area of ΔBEF; 4. area of ΔABE= area of ΔACE; 5. area of ΔABC = 2 area of ΔACE; 6. Area of ABCD = 2 area of ΔABC = 12 area of BEF.

36 cm²

Step-by-step explanation:

1. ΔBEF & ΔADF are similar; 2. the height of ΔABE is 3height of ΔBEF; 3. area of ΔABE is 3 area of ΔBEF; 4. area of ΔABE= area of ΔACE; 5. area of ΔABC = 2 area of ΔACE; 6. Area of ABCD = 2 area of ΔABC = 12 area of BEF.

2x^2 -5x -2

See the attached for the polynomial long division.

Answer:

8x10^-7

Step-by-step explanation:

First one you have correct however the second one you were close lets figure it out:

0.0000008

In order to move the decimal in front of the eight we have to "jump" 7 times to the right.  Furthermore since we have to move the decimal to the right our exponent will be negative.  That means that we have:

[tex]0.0000008=8 \times 10^{-7}[/tex]

~~~Brainliest Appreciated~~~

To express in scientific notation, move the decimal so it is after the first non-zero digit, and count the number of steps as the power of 10. 42,670,000 becomes 4.267 * 10^7 and 0.0000008 becomes 8 * 10^-7.

To convert a value to scientific notation, you need to express it as a product of a number between 1 and 10 and a power of 10.

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Answer:

y=1/2x+15

y=x/2+15

Step-by-step explanation:

Every y-value is the sum of one-half of x and 15.

y = 1/2 x+15

We can rewrite this as

x/2 +15

Answer:

negative $1.60 was the "interest" added to Vito's account

Step-by-step explanation:

new balance = old balance + deposits - withdrawals + interest

$9669.26 = $6955.01 + 2815.85 - 100.00 + interest . . . . fill in givens

$9669.26 = $9670.86 + interest . . . . . simplify

$9669.26 - 9670.86 = interest = -$1.60 . . . . . subtract 9670.86

_____

Comment on the problem

This result is "unexpected." Usually an interest amount will be positive. Please have your teacher work this problem for you and explain the result.

Vito Melvin started with $6,955.01 in his account, deposited $2,815.85, and withdrew $100. The expected balance was $9,670.86, but the actual balance was $9,669.26, meaning Vito earned $1.60 in interest.

This problem is about calculating interest earned on a bank account. Let's start by looking at Vito Melvin's actions with his bank account.

He began with a previous balance of $6,955.01. He then made a deposit of $2,815.85 and then withdrew $100. This means his new balance should be his previous balance plus his deposit minus his withdrawal. In calculation, (($6,955.01 + $2,815.85) - $100) = $9,670.86.

However, Vito's actual balance is $9,669.26. The difference between the expected balance ($9,670.86) and the actual balance ($9,669.26) is the interest he earned. So, subtract the actual balance from the expected balance to find the interest: $9,670.86 - $9,669.26 = $1.60.

Therefore, Vito Melvin earned $1.60 in interest.

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Answer:

r(b) = 4b +3

Step-by-step explanation:

There are only two variables and the one that is not b is r. So, this amounts to solving for r. Divide the given equation by the coefficient of r:

... 4b = r -3

Add the constant:

... 4b +3 = r

Express in function notation.

... r(b) = 4b +3

Answer:

2b³ +2a -2c . . . . degree 3 polynomial

Step-by-step explanation:

The monomials are ...

... 4a . . . . degree 1 in a

... -5b·b² = -5b³ . . . . degree 3 in b

... -3c . . . . degree 1 in c

... 7b³ . . . . degee 3 in b (like term with -5b³)

... +c . . . . degree 1 in c (like term with -3c)

... -2a . . . . degree 1 in a (like term with 4a)

So, we have 3 pairs of like terms. The like terms can be combined by summing their coefficients.

The degree of the polynomial is that of the highest-degree term. (Here, the b³ term makes it a polynomial of degree 3.)

... 4a -2a = (4-2)a = 2a . . . . combining the "a" terms

... -5b³ +7b³ = (-5+7)b³ = 2b³ . . . . combining the b³ terms

... -3c +c = (-3 +1)c = -2c . . . . combining the "c" terms

In standard form, we write the highest-degree term first. Follwing terms are in order by decreasing degree. It is convenient, but perhaps not required, to then write the terms of the same degree in alphabetical order.

... = 2b³ +2a -2c . . . . a 3rd degree polynomial

Answer:

1/2 of his book

Step-by-step explanation:

1/3 of an hour = 1/6 of the book

3/3 of an hour = 3/6 or 1/2 of the book read