Use the substitution method to solve the system of equations

Answer:

4

Step-by-step explanation:

40-24=16

16/4=4

4 tanks

Answer:

[tex]\frac{5}{18}[/tex] square feet.

Step-by-step explanation:

We have been given that the length of a rectangular piece of wood is 5/12 foot and width is 2/3 foot.

Since area of a rectangle is width times length, so to find the area of piece of wood we will multiply 5/12 by 2/3.

[tex]\text{Area of wood}=\frac{5}{12}\times \frac{2}{3}[/tex]

[tex]\text{Area of wood}=\frac{5}{6}\times \frac{1}{3}[/tex]

[tex]\text{Area of wood}=\frac{5}{6\times 3}[/tex]

[tex]\text{Area of wood}=\frac{5}{18}[/tex]

Therefore, area of piece of wood will be [tex]\frac{5}{18}[/tex] square feet.

Answer:

8*5^n-1 / 2^n-1 = n

This is the function for your sequence

8*5^n-1 / 2^n-1 = n

The Sequence Calculator finds a equation of the sequence or also allows you to view the next terms in a sequence. Arithmetic Sequence Formula: an = a1 +d(n −1) a n = a 1 + d (n - 1) Geometric Sequence Formula: an = a1rn−1 a n = a 1 r n - 1

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Answer:

10 goody bags.

Step-by-step explanation:

We are asked to find the largest number of identical goody bags that can be using 50 bouncy balls and 110 pokemon cards.

In order to solve our problem we will use GCF (Greatest common factor). Let us find out GCF of 50 and 110.

The factors of 50 are: 1, 2, 5, 10, 25, 50.

The factors of 110 are:  1, 2, 5, 10, 11, 22, 55, 110.

We can see that GCF of 50 and 110 is 10 as 10*11=110 and 10*5=50.

Therefore, the largest number of identical goody bags is 10 with 5 bouncy balls and 11 pokemon cards in each goody bag.

Answer:

40% of the pieces of fruit in the Bowl are apples.    

Step-by-step explanation:

Given the statement:- There are 15 pieces of fruit in a bowl and six of them are apples.

⇒ Total number of pieces of fruit  in a bowl = 15 pieces

and  

Number of pieces of apple in a bowl = 6 pieces.

To find the percentage of the pieces of fruit in the Bowl are apples.

[tex]Percentage = \frac{Number of pieces of apple in bowl}{Total number of pieces of fruit in Bowl} \times 100[/tex]

                           = [tex]\frac{6}{15} \times 100 = 40\%[/tex]

Therefore, 40% of the pieces of fruit in the Bowl are apples.

The percentage of apples present in the bowl is [tex]40\%[/tex].

According to the question, there are 15 pieces of fruit in a bowl and 6 of them are apples.

So, the percentage of apples present in the bowl is evaluated as-

[tex]Percentage\;of\;apples=\dfrac{Apples}{Total\;number\;of\;fruits}\times 100\%\\Percentage\;of\;apples=\dfrac{6}{15}\times 100\%\\Percentage\;of\;apples=40\%[/tex]

Hence, the percentage of apples present in the bowl is [tex]40\%[/tex].

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First, let's ignore the answer choices and solve for a value of x ourselves.

2(8 - x) < 4

Distributive property.

16 - 2x < 4

Subtract 16 from both sides.

-2x < -12

Divide both sides by -2 (and flip the inequality sign)

x > 6

The value of x is going to be greater than 6, and so, we can observe the answer choices, and whichever value is greater than 6, is the correct answer.

Answer:

d x=10

Step-by-step explanation:

Answer:

The answer is 5

Answer:

i just did the quiz and its  FALSE  i got it wrong so i thought you should have a right answer

Step-by-step explanation:

The order of operations in mathematics ensures that the result of a numerical expression is the same regardless of the order in which the operations are performed. - True

In mathematics, the order of operations is a set of rules that dictate the order in which mathematical operations should be performed in an expression. Following these rules ensures that you always get the same result, regardless of the order in which the operations are performed.

The order of operations, also known as PEMDAS, stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). For example, in the expression 4 + 5 × 2, according to the order of operations, you would perform the multiplication first and then the addition. So, the correct way to evaluate this expression would be 4 + (5 × 2) = 4 + 10 = 14.

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Complete Question:

You will always get the same result in a numerical expression no matter the order in which you perform the operations. True/False ?

Answer:

[tex]3m^2+5n^2+8mn[/tex]

[tex]x^2-11x+17[/tex];0

Step-by-step explanation:

We have been given [tex]m^2+3mn−n^2 [/tex] and [tex]4m^2+5mn+6n^2[/tex]

for (1) we will subtract [tex]4m^2+5mn+6n^2[/tex]  from [tex]m^2+3mn−n^2 [/tex]  that is:

[tex]4m^2+5mn+6n^2-m^2+3mn-n^2[/tex]

Now, simplify the like terms we get:

[tex]4m^2-m^2+6n^2-n^2+5mn+3mn[/tex]

After simplification we get:

[tex]3m^2+5n^2+8mn[/tex]

Hence, [tex]3m^2+5n^2+8mn[/tex] is the required result.

(2) Now, we need to find how much less than [tex]3x^2-7x+9[/tex] is [tex]2x^2+4x-8[/tex]

Subtract [tex]3x^2-7x+9[/tex] from [tex]2x^2+4x-8[/tex] we get:

[tex]3x^2-7x+9-2x^2-4x+8[/tex]

After simplifying like terms

[tex]x^2-11x+17[/tex]

When x=2 the the above  expression becomes:

[tex](2)^2-11(2)+17[/tex]

[tex]4-22+17=0[/tex]

For the first question, 4m^2+5mn+6n^2 is 3m^2+2mn+7n^2 greater than m^2+3mn-n^2. For the second question, 3x^2-7x+9 is x^2 -11x + 17 less than 2x^2+4x−8 and the value of the result when x=2 is 12.

For the first question, begin by subtracting the given expressions (m^2 + 3mn - n^2) from (4m^2+5mn+6n^2). This equates to:

(4m^2 + 5mn + 6n^2) - (m^2 + 3mn - n^2) = 3m^2 + 2mn + 7n^2

For the second question, we subtract (2x^2+4x−8) from (3x^2−7x+9). This is equal to:

(3x^2−7x+9) - (2x^2+4x−8) = x^2 -11x + 17

To find the value of the result when x=2, simple plug in '2' wherever x is in the equation, giving the result 17 - 22 + 17 = 12

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Find the volume of the rectangle:

8 x 2 x 4 = 64 cubic inches.

This means the square can have a volume of 64 cubic inches.

The formula for the volume of a square is V = S^# where S is the length of the side.

Replace V with 64 to solve for S:

64 = S^3

To find S, take the cubic root of 64:

S = ∛64

S = 4

The length of a side is 4 inches.

Answer:

Minimum 15 bracelets to be sold to meet the break even.

Step-by-step explanation:

The cost price of bracelets is represented by C(x) =180+8x

The revenue earned (selling price) is represented by R(x) =20x

In these two functions x represents number of bracelets.

If P represents the profit then P = 20x-(180+8x)

P = 20x-180-8x = (12x-180)

For break even profit P = 0

12x-180 =0

12x = 180

x = 180÷12

x = 15

So minimum quantity of bracelets to be sold is 15 for the break even.

Answer:

512

Step-by-step explanation:

64 / 2 = 32

32 * 16 = 512

64 / 2 * 16 = 512

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[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{62 \div 2 \times 16}\\\\\mathsf{= \dfrac{62}{2} \times 16}\\\\\mathsf{= \bold{32}\times16}\\\\\mathsf{= \bf 512}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak{512}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

(-3, -1)

Step-by-step explanation:

As its reflected across the y-axis  the y coordinate remains the same but the new x-coordinate is the opposite value.

Answer:

3.5

Step-by-step explanation:

The speed difference is 40 mph

then divide the distance by the speed difference and you get 3.5

Answer:

they will be 140 miles apart in 2 hours

Step-by-step explanation:

in one hour they will be 70 miles apart since 15 + 55 = 70 and then they get 70 more miles apart in the second hour and 70 + 70 = 140 so 2 hours

Answer:

ABCD must be a paralellogram

Step-by-step explanation:

In parallelogram, rectangle, square and rhombus the diagonals bisect each other. Since angle ABC=91°, then this quadrilateral cannot be rectangle and cannot be square, because rectangle and square have all right angles (90°).

If diagonals of a quadrilateral bisect each other, then quadrilateral is parallelogram. A rhombus is a parallelogram with all congruent sides.

You know nothing about any lengths in the diagram, then you can state that this quadrilateral is parallelogram (always) and can be rhombus (sometimes).

By rearranging the formula for the volume of a cylinder to solve for height, and substituting the given values for volume and radius, we find that the height of the can is 5 inches.

To solve for the height h of the cylinder, we need to rearrange the formula for the volume of a cylinder, V =
2h, to solve for h. This is done by dividing both sides of the equation by
2, thus isolating h on one side of the equation.

The rearranged formula becomes:

h = V / (2)

Using the given volume of the can, 62.8 cubic inches, and the given radius of 2 inches, we plug these values into our formula:

h = 62.8 / (3.14 × 2²)

h = 62.8 / (3.14 × 4)

h = 62.8 / 12.56

h = 5 inches

Therefore, the height of the can is 5 inches.

Answer:

the information is in the theorem itself and to prove it set up an equation in the same format the theorem uses and test it.

Step-by-step explanation:

Step 1.

Calculate measure of angle α:

[tex]47^o-38^o=9^o[/tex]

Step 2.

Calculate what fraction of the angle 360° ​​is the angle α:

[tex]\dfrac{9^o}{360^o}=\dfrac{1}{40}[/tex]

Step 3.

Calculate the circumference of the Earth (circle):

[tex]C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi[/tex]

Step 4.

The length of arc is equal 1/40 of the circumference:

[tex]\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi[/tex]

[tex]\pi\approx3.14\to\dfrac{1}{40}C\approx200\cdot3.14=628\ mi[/tex]

The distance between San Francisco, CA, and Seattle, WA, along the longitudinal line is approximately 628 miles, calculated using the formula for arc length of a sphere, considering the Earth's radius and the difference in degrees of latitude.

The question revolves around the concept of calculating the arc length in degrees, which is a topic in mathematics, specifically trigonometry.  

The formula for calculating the arc length of a sphere is arc length = radius x angle (in radians).

We already know the radius of the earth (4000 miles) and the difference in latitude between Seattle and San Francisco (47°-38°=9°).

However, in the formula, we need the angle to be in radians. To convert degrees to radians, we use the formula 1 degree = π/180 radians.

So, 9° equals 9*(π/180) = 0.157 radians.

Now, we substitute the values into the formula: arc length = 4000 miles * 0.157 radians. This gives an answer of approximately 628 miles.

Therefore, the distance between San Francisco, CA, and Seattle, WA, along the longitudinal line is about 628 miles.

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Answer: choice C) 60 degrees

smaller angle = 3*x; larger angle = 6*x

The two angles are supplementary, so they add to 180

6x+3x = 180

9x = 180

x = 180/9

x = 20

If x = 20, then,

smaller angle = 3*x = 3*20 = 60 degrees

(the other angle being 6*x = 6*20 = 120; note how 60+120 = 180)

Answer:

try going with C

Step-by-step explanation:

Answer:

79

Step-by-step explanation:

Since the triangles are similar, the sides that are the same length have angles that are the same size at the top.

There might be a simpler way to do this, if there is, sorry.

If you look at the graph, x is greater than 3 but less than 5.

So: x > 3 and x < 5

I would simplify each solution set and get "x" by itself (until I get the right answer):

A.) 2x - 4 > 6 or 3x < 9

2x - 4 > 6    Add 4 on both sides

2x > 10      Divide 2 on both sides

x > 5        (you could stop here and go to the next choice since you know this does not match the graph)

3x < 9     Divide 3 on both sides

x < 3

x > 5 and x < 3

B.)   2x - 4 < 6 and 3x > 9

x < 5   and    x > 3

Your answer is B or the 2nd option

[C and D would have given a negative number]

The compound sentence that has its solution set shown on the graph is 3x + 8 > -7 and -4x < 12.

The solution set for the given compound inequalities is represented by the graph where the shaded region includes the points -1, 0, 1, 2, 3, 4, and 5. The compound sentence that has this solution set is:

3x + 8 > -7 and -4x < 12

Let's break down the compound sentence step by step:

Solve the first inequality: 3x + 8 > -7. Subtract 8 from both sides to get 3x > -15. Divide both sides by 3 to get x > -5.

Solve the second inequality: -4x < 12. Divide both sides by -4 and flip the inequality sign to get x > -3.

Combine the two inequalities by using the word 'and': x > -5 and x > -3.

The solution to this compound sentence is the values of x that satisfy both inequalities, which is x > -3.

Therefore, the compound sentence 3x + 8 > -7 and -4x < 12 has its solution set shown on the given graph.

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Answer:

168 = x

Step-by-step explanation:

mean  = u=132

standard deviation =sigma = 20

z score =z=1.8

The formula is

z = (x-u)/ sigma

Substituting what we know

1.8 = (x-132)/20

Multiply by 20

1.8*20 = (x-132)/20 *20

36 = x-132

Add 132 to each side

36+132 = x-132+132

168 = x

Multiply the standard deviation by the z-score and add that to the mean:

Value = 132 + (20*1.8) = 132 + 36 = 168

The value would be 168.

Answer:

a is less than or equal to -5

Step-by-step explanation:

Answer:

a ≤-5

Step-by-step explanation:

a-3 ≤-8

Add 3 to each side

a-3 +3≤-8+3

a ≤-5

Answer:

69.75

Step-by-step explanation:

6.5%  = 0.065

So the cost of the textbook = 65.49 + 0.065*65.49

=  69.75  to nearest hundredth

Answer:

A

B

Q

D

Step-by-step explanation:

Answer:168

Step-by-step explanation:

56 x 3 = 168