What is the solution to the system of equations?

y = 2/3x + 3
x =-2

[-2, -15/2 ]
[-2, 5/3]
(-2, 11/6
(-2, 13/3)

=========================================================

Explanation:

The floor is a 7 meter by 5 meter rectangle. The perimeter is

P = 2(L+W)

P = 2(7+5)

P = 2(12)

P = 24

The perimeter of the floor is 24 meters.

Multiply this perimeter by the unknown height h to get 24h

This expression represents the lateral surface area. This is the combined wall area. Set this equal to 120 and solve for h.

24h = 120

h = 120/24

h = 5

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

Check:

One pair of walls is 7 meters by 5 meters, giving an area of 7*5 = 35 square meters each. So far that's 2*35 = 70 square meters for these two walls combined.

The other pair of walls is 5 by 5. Each has an area of 5*5 = 25 which doubles to 2*25 = 50

The total wall area is 70+50 = 120 to confirm the answer.

Answer:

Step-by-step explanation:

So sin is defined as [tex]\frac{opposite}{hypotenuse}[/tex]. and cosine is defined as [tex]\frac{adjacent}{hypoteunse}[/tex]. So we need the adjacent side. Since we already have the opposite, and hypotenuse, you can use the Pythagorean identity to solve for the missing side: [tex]a^2+b^2 = c^2[/tex]

[tex]15^2 + b^2 = 19^2[/tex]

[tex]225 + b^2 = 361[/tex]

[tex]b^2 = 136[/tex]

[tex]b = \sqrt{136}[/tex]

[tex]b = \sqrt{4} * \sqrt{34}[/tex]

[tex]b = 2\sqrt{34}[/tex]

This is the adjacent side, so now plug this into the cosine equation and you get: [tex]\frac{2\sqrt{34}}{19}[/tex]

Answer:

11.0 cm

P=38 cm

38/3=12.67cm length of one side

Base of triangle = 12.67/2 =6.34 cm

Use formula [tex]a^2+b^2=c^2[/tex]

[tex]6.34^2+x^2=12.67^2\\\\=11.0 cm[/tex]

x = altitude of triangle

In the given diagram, the value of x is 15

From the question, we are to determine the value of x

From one of the circle theorems, we have that

Opposite angles of a cyclic quadrilateral are supplementary.

Thus, in the diagram

5x + 7x = 180°

12x = 180°

x = 180°/12

x = 15

Hence, the value of x is 15

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The equivalent expression without parenthesis that can be used to determine the total number of flowers the florist used is 4c + 36

The equivalent expression without parenthesis that can be used to determine the total number of flowers the florist used.

total number of flower the florist used for the bouquet = 4(c + 9)

Therefore,

total number of flower the florist used for the bouquet = 4c + 36

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Answer:

Step-by-step explanation:

Answer:

The answer is

5/2x^2+11/30x+2

[tex] \frac{5}{2}x ^{2} + \frac{11}{30} x + 2[/tex]

Answer:

25

Step-by-step explanation:

un carro tiene 4 ruedas, entonces divide 100 por 4

100÷4=25

The volume of the rectangular box is 12 cubic inches

The formula for measuring the volume of a rectangular box is expressed as:

V = lwh

l is the length

w is the width

h is the height

Given the following

l = 2in

w = 3in

h = 2in

Substitute

V = 2* 3 * 2

V = 12 cubic inches

Hence the volume of the rectangular box is 12 cubic inches

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Answer:

You divide 360 by 5 which is 72 & Then muiltiply that by 2.
Your answer would be 144 tho.

Answer: 28.78

Step-by-step explanation:

[tex]\frac{\sin A}{a}=\frac{\sin B}{b}\\\\ \sin A=\frac{a \sin B}{b}\\\\\sin A=\frac{12 \sin 37^{\circ}}{15}\\\\\sin A=0.481452...\\\\A \approx 28.78^{\circ}, 151.21^{\circ}[/tex]

However, we disregard the second case, giving 28.78 degrees.

Step-by-step explanation:

Let assume that

Cost of 1 burger = $ x

Cost of 1 doughnuts = $ y

According to statement, 9 burgers and 1 doughnut cost $ 31.30

[tex]\begin{gathered}\sf \: 9x + y = 31.3 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf\implies \sf \: y = 31.3 - 9x - - - (1) \\ \\ \end{gathered}[/tex]

According to statement again, 3 doughnuts and 6 burgers cost $ 26.70

[tex]\begin{gathered}\sf \: 6x + 3y = 26.7 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: 3(2x + y) = 26.7 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: 2x + y = 8.9 \\ \\ \end{gathered}[/tex]

On substituting the value of y from equation (1), we get

[tex]\begin{gathered}\sf \: 2x + 31.3 - 9x = 8.9 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: 31.3 - 7x = 8.9 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: - 7x = 8.9 - 31.3 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: - 7x = - 22.4 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\bf\implies \: x = 3.2 \\ \\ \end{gathered}[/tex]

So,

Cost of 2 burgers = 3.2 × 2 = $ 6.4

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

We need to make linear equations, to solve this problem.

let the cost of each burger be x, and that of each doughnut be y.

[tex] \qquad❖ \: \sf \:9x + y = 31 .30[/tex]

[tex] \qquad❖ \: \sf \:y = (31 . 30 - 9x)[/tex]

put value of y in other equation.

[tex] \qquad❖ \: \sf \:6x + 3y = 26.70[/tex]

[tex] \qquad❖ \: \sf \:6x + 3(31.3 - 9x) = 26.70[/tex]

[tex] \qquad❖ \: \sf \:6x + 93.90 - 27x = 26.70[/tex]

[tex] \qquad❖ \: \sf \:6x - 27x = 26.70 - 93.90[/tex]

[tex] \qquad❖ \: \sf \:27x - 6x = 93.90 - 26.70[/tex]

[tex] \qquad❖ \: \sf \:21x =67 .20[/tex]

[tex] \qquad❖ \: \sf \:x = 67.20 \div 21[/tex]

[tex] \qquad❖ \: \sf \:x = 3.20[/tex]

So, cost of each burger is x = $ 3.20

[tex] \qquad \large \sf {Conclusion} : [/tex]

Therefore, cost of two burgers is :

Answer:

f is sometimes positive and sometimes negative on the interval

Step-by-step explanation:

So if you were to expand out the x's you would have x^2 * x * x * x which will result in x^5. and because the leading coefficient is positive, it will be going towards positive infinity as x goes towards positive infinity, and because the degree is odd the end behaviors will be opposite, so as x goes towards negative infinity the value of f(x) will be going towards negative infinity. One other thing to note is that because x^2 technically is two zeroes, with the same value, the zero at x=0 has a multiplicity of 2, meaning that it will not cross the x-axis, but rather have a turning point, once it intersects the x-axis, because the zero has an even multiplicity. Given this information we can draw a graph. So as you can see in the graph, it will sometimes be negative and sometimes positive

Answer:

The answer is C: 3/4

Step-by-step explanation:

Your equation is equal to (3/2)/(4/2) due to absolute value (all numbers are positive even if negative symbol is infront of it) which is equal to 3/4.

Step-by-step explanation:

what is the real problem definition ?

is there now an absolute value around the top "-2", or not ?

in any case, remember, when we divide 2 rational numbers like this :

a/b / c/d

the result is

"outer multiplication" over "inner multiplication" :

a×d / b×c

as alternative you can always also say

a/b / c/d = a/b × d/c = a×d / b×c

so,

if the problem is

3/-2 / |-4/-2|

the result is

3×2 / 4×-2 = 6/-8 = - 3/4

if the problem is

3/|-2| / |-4/-2|

the result is

3×2 / 4×2 = 6/8 = 3/4

please pick the solution based on the actual problem.

Answer:

2u^5+5

Step-by-step explanation:

Drop parenthesis and add like terms.

[tex]7u^{5}-5u^{5}+5=2u^{5}+5[/tex]

Hope this helps!

If not, I am sorry.

The range of a function are the dependent variables for which the function exists. The range of the function will be y ≥ 5

The range of a function are the dependent variables for which the function exists

Given the function below;

f(x) = √x+7 + 5

The function can only exist for values less than or equal to -7 that is x ≤ -7.

Substitute

f(-7) =  √-7+7 + 5

f(-7) = 5

The range of the function will be y ≥ 5

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A function assigns the value of each element of one set to the other specific element of another set. The correct option is A.

Suppose that the given function is

[tex]f:X\rightarrow Y[/tex]

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

[tex]f^{-1}: Y \rightarrow X[/tex]

such that:

[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]

(and vice versa).

It simply means that the inverse of 'f' is an undone operator, that takes back the effect of 'f'

The graph that represents the inverse of the given function is option A because graph A is showing more rapid growth as compared to the given graph.

Hence, the correct option is A.

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(-∞,8) is interval is the solution to set 0.35x – 4.8 < 5.2 – 0.9x.

0.35x - 4.8 < 5.2 - 0.9x

Adding 0.9x to both sides of equation.

0.35x - 4.8 + 0.9x < 5.2 - 0.9x + 0.9x

1.25x - 4.8 < 5.2

Adding 4.8 to both sides of equation.

1.25x - 4.8 + 4.8< 5.2 + 4.8

1.25x < 10

Dividing both sides of equation by 1.25

x < [tex]\frac{10}{1.25}[/tex]

Hence x < 8

Thus, (-∞,8) interval is the solution to given set 0.35x – 4.8 < 5.2 – 0.9x.

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Answer : I think 3rd is the answer

The [tex]n[/tex]-th term [tex](n\ge1)[/tex] in the series is evidently

[tex]\dfrac{2n-1}{(2n-1)!} = \dfrac{2n-1}{(2n-1)(2n-2)!} = \dfrac1{(2n-2)!}[/tex]

By the ratio test, the infinite series converges, since

[tex]\displaystyle \lim_{n\to\infty} \left| \frac{\frac1{(2(n+1)-2)!}}{\frac1{(2n-2)!}}\right| = \lim_{n\to\infty} \frac{(2n-2)!}{(2n)!} = \lim_{n\to\infty} \frac1{2n(2n-1)} = 0 < 1[/tex]

The time when movie finished was 21 : 38.

It is given that Theodore started watching movie at 19:30 and length of movie was 1 hour and 56 minutes.

We have to find the time when the movie finished if there was a break of 12 minutes also between movie.

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations and the symbols are called variables.

As per the question ;

Theodore started watching movie at 19:30.

The length of movie = 1 hour and 56 minutes

Break = 12 minutes

So ;

Total length of running of movie = 2 hours and 8 minutes

The time when movie finished will be ;

= 19 :30 + 2:08

= 21 : 38

Thus , the time when movie finished was 21 : 38.

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The equation of the line passing through the coordinates but with its coordinates interchanged i.e (5, 7) and (9, 11)

Given a linear function that contains the coordinate point on its line (5, 7) and (9, 11)

The equation of its reciprocal can be determine by finding the equation of the line passing through the coordinates but with its coordinates interchanged i.e (5, 7) and (9, 11)

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A pair of points which is perpendicular to line L is: D. (3, -5),(-6, 3).

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

For points A, we have:

[tex]Slope = \frac{3\;-\;(-6)}{3\;-\;(-9)}\\\\Slope = \frac{9}{12}[/tex]

Slope = 9/12.

For points B, we have:

[tex]Slope = \frac{6\;-\;(-2)}{-6\;-\;(-9)}\\\\Slope = \frac{8}{-3}[/tex]

Slope = -8/3.

For points C, we have:

[tex]Slope = \frac{3\;-\;(-6)}{3\;-\;(-5)}\\\\Slope = \frac{9}{8}[/tex]

Slope = 9/8.

For points D, we have:

[tex]Slope = \frac{3\;-\;(-5)}{-6\;-\;3}\\\\Slope = \frac{-8}{9}[/tex]

Slope = -8/9.

In Mathematics, the condition for perpendicularity of two lines is:

m₁ × m₂ = -1

9/8 × 8/9 = -1

Thus, points (3,−5) and (−6,3) are perpendicular to line L.

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Complete Question:

Line L has a slope of 9/8. The line through which of the following pair of points is perpendicular to L?

A. (−9,−6),(3,3)

B. (9,−2),(−6,6)

C. (−5,−6),(3,3)

D. (3,−5),(−6,3)

The probability of getting tails and rolling an odd number is P = 0.25

The probability of getting tails on the coin is 0.5

On the dice, there are 6 numbers and 3 are odd, so the probability of rolling an odd number is:

p = 3/6 = 0.5

The joint probability (of getting tails and rolling an odd number) is equal to the product between the individual probabilities:

P(odd and T) = 0.5*0.5 = 0.25

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By evaluating the linear function f(x) = x - 3 at x = 5 and discarding the another function in the table given, we conclude that f(5) = 2 belongs to that linear equation.

In this problem we must check if the given relationship between the independent variable (x) and the dependent variable (y) exists in any of the two functions: (i) a table, (ii) an expression.

After a quick analysis, we conclude that f(5) = 2 is a point of the linear function f(x) = x - 3. Here is the proof:

f(5) = 5 - 3

f(5) = 2

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Answer:A which is x-3

Step-by-step explanation:

The surface area of the composite shape is: 315 in.².

Surface area = surface area of square pyramid + surface area of square prism - 2(base area)

Surface area of square pyramid = Area of base + 1/2(perimeter of base × slant height) = 9² + 1/2[4(9) × 7] = 207 in.²

Surface area of square prism = 2a² + 4ah = 2(9²) + 4(9)(3)

Surface area of square prism = 2(9²) + 4(9)(3) = 270 in.².

Base area = 9² = 81 in.².

Surface area of the composite shape = 207 + 270 - 2(81) = 315 in.².

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Answer:

315 in.²

Step-by-step explanation:

Recall:

area of rectangle = length × width

area of triangle = base × height / 2

Base of prism: 9 in. × 9 in. = 81 in.²

4 sides of prism: 4 × 9 in. × 3 in. = 108 in.²

Lateral area of pyramid: 4 × 9 in. × 7 in. / 2 = 126 in.²

Total area = 81 in.² + 108 in.² + 126 in.² = 315 in.²

Anna should use the following equation,

[tex]a_{15} = 4(3)^{15}[/tex]

Equation for Determining the Number of Bacterial Cells

Initially, the count of bacterial cells = 4

It is given that the bacterial cell triples every month.

Hence, the equation for the count of bacterial cells after first month is,

a₁ = 4(3)

This count of 4(3) triples again in the second month.

So, after the second month, the equation for the count of bacterial cells is given by,

a₂ = 4(3)(3) = 4(3)²

Calculating the Count of Bacterial Cells For Each Month

Again, this count triples in the third month.

Therefore, the  equation for the count of bacterial cells after the third month becomes,

a₃ = 4(3)(3)(3) = 4(3)³

This count triples again in the fourth month and this process continues till 15 months.

Hence, the equation for determining the number of bacterial cells comes out to be as follows,

a₁₅ = 4(3)¹⁵

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Answer:

Step-by-step explanation:

Amy = x years

Ben = x + 2  (years)

Alice = x - 6 (years)

Answer:

a)

Amy's age is x.

• Ben's age is 2 more than Amy's age.

∴ Ben's age = x + 2

• Alice's age is 6 less than Amy's age.

∴ Alice's age = x - 6

The information given about the probability shows that the cardinality of D is 18.

From the complete information, the number of red-colored cards is 26.

Also, the number of red-colored number cards will be 18.

The cardinality of a set is a measure of a set's size, meaning the number of elements in the set.

Here, the cardinality of set D is 18.

Here is the complete question:

Take a deck of playing cards. Form following sets out of those:

A = Set of Face Cards

B = Set of Red Coloured Face cards

C = Set of Black Coloured Face Cards

D = Set of Red Coloured Number Cards

Find the Cardinality of set D

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