Find the domain of the following graph:


−7 < x ≤9


−7 < y ≤ 9


−7 < x ≤5


−7 < y ≤ 5

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:

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:

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.

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:

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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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

  [tex]y = -3x^2-4x+3[/tex]

Explanation

The standard form of a parabola is

  [tex]y = ax^2 + bx + c,[/tex]

where [tex]a \ne 0[/tex], and [tex]a,b,c[/tex] are real numbers.

If it passes through (0,3) then when x = 0, y = 3 so this means that

  [tex]3 = a(0)^2 + b(0) + c \implies c = 3[/tex]

so [tex]y = ax^2 + bx + 3[/tex].

If it passes through (1,-4), then when x = 1, y = -4 so

  [tex]\begin{aligned}-4 &= a(1)^2 + b(1) + 3 \\a+b+3 &= -4 \\a+b &= -7 && \text{(I).}\end{aligned}[/tex]

If it passes through (-1,4) then when x = -1, y = 4 so

  [tex]\begin{aligned}4 &= a(-1)^2 + b(-1) + 3 \\a-b+3 &= 4 \\a-b &= 1 && \text{(II).}\end{aligned}[/tex]

Because both (I) and (II) need to be satisfied, we have the system of equations,

  [tex]\begin{cases}a+b &= -7\qquad\text{(I)}\\a-b &= 1\qquad\text{(II)}\end{cases}[/tex]

which we can easily solve by adding the two equations up to get

  [tex]\begin{aligned}(a+a) + (b-b) &= -7 + 1 \\ 2a&= -6 \\a &= -3.\end{aligned}[/tex]

Then we take any of the previous equations to solve for b:

  [tex]\begin{aligned}a+b &= -7\\-3 + b &= -7 \\ b &= -4\end{aligned}[/tex]

Thus the parabola in standard form is

  [tex]y = -3x^2-4x+3.[/tex]

So with the three points that are given to us, we will plug them into the standard form formula that I had mentioned earlier. Firstly, plug (0,3) into the equation since the 0 will cancel out the a and b variable:

[tex]3=a*0^2+b*0+c\\3=c[/tex]

Now we know that the value of c is 3.

Next, plug (1,-4) into the standard form formula and simplify (Remember to plug 3 into the c variable):

[tex]-4=a*1^2+1*b+3\\-4=a+b+3\\-7=a+b[/tex]

Next, plug (-1,4) into the standard form formula and simplify:

[tex]4=a*(-1)^2+b*(-1)+3\\4=a-b+3\\1=a-b[/tex]

With the last two simplified equations, we will create a system of equations:

[tex]-7=a+b\\1=a-b[/tex]

With this, I will be using the elimination method. Add the two equations together, and the following equation is the result:

[tex]-6=2a[/tex]

From here we can solve for a. For this, just divide both sides by 2:

[tex]-3=a[/tex]

Now that we have the value of a, plug it into either equation to solve for b:

[tex]-7=-3+b\\-4=b\\\\1=-3-b\\4=-b\\-4=b[/tex]

Now, plug the obtained values in our standard form equation and your final answer will be:

[tex]y=-3x^2-4x+3[/tex]

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.

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:

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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Answer:

          7 sqrt(3) =x

Step-by-step explanation:

We know that sin 60 = opposite / hypotenuse

                       sin 60 = x/14

Multiply both sides by 14

                          14 sin 60 = x

                        14 * (sqrt(3)/2) =x

                      7 sqrt(3) =x

Answer:

A

B

Q

D

Step-by-step explanation:

Answer:

The answer is 5

The total cost of painting and tiling a community hall shaped as a cuboid with the given dimensions is £972. This is based on calculating the surface area for paint and the floor area for tiles, then multiplying by the respective costs per m².

To solve this problem, we first need to figure out the total surface area of the cuboid, which will include the floor area for the tiles, and all sides for the paint.
Surface area of the cuboid involves calculating area for all six sides, which totals to 2*(lb + bh + hl), where l is length, b is breadth, and h is height.
Substituting the values given, the total surface area of the cuboid is 2*(40*15 + 15*3 + 3*40) = 2*(600 + 45 + 120) = 2*765 = 1530m2.
The floor area is length * breadth i.e., 40m * 3m = 120 m2.

Next, we calculate the cost of painting and tiling. We know 10 liters of paint covers 25 m2 and costs £10.
So, 1 litre covers 25/10 = 2.5m2 and similarly costs £10/10 = £1.
Therefore, the paint costs for 1530 m2 are 1530/2.5 = 612 litres * £1/litre = £612.

For tiling, the cost for 1m2 is £3, so for a 120 m2 floor, the cost will be 120m2*£3/m2 = £360.
Therefore, the total cost for paint and tiles is £612 + £360 = £972.

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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:

4

Step-by-step explanation:

40-24=16

16/4=4

4 tanks

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:

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:

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:

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.

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

Step-by-step explanation:

56 x 3 = 168

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:

[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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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.

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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