Solve the quadratic equation below by completing the square. What are the
solutions?
x2 + 10x + 22 = 31

Answer:

A

Step-by-step explanation:

equivalent because each are 1:2

Final answer:

After simplifying each pair of ratios, only 12: 24, and 50:100 (Pair A) are equivalent ratios, as both simplify to 1:2. The other pairs are not equivalent since their simplified forms are different.

Explanation:

To determine which of the pairs of ratios are equivalent, we can simplify each ratio or convert them to fractions and simplify to see if they have the same value. Let's look at each pair:

From the above, only the pair A) 12: 24, 50:100 are equivalent ratios.

Answer:

x=2

Step-by-step explanation:

Vertical lines have the same x value all the time.  It is of the form x=

Their slope is undefined

The line passes through the point (2,4) and the x value is 2

x=2

Answer:

48

Let me know if this was right :)                                                

Answer:

They must mix

37 pounds of the House Blend

3 pounds of the Kenya Blend.

Step-by-step explanation:

Let 'x' be House coffe and 'y' be Kenya Coffee. Then:

10.50x + 12.80y = 10.67(40)

Also, we knw that:

x + y = 40

Solving the system of equations above, we have that:

x ≈37.0435 ≈ 37 pounds

y ≈2.95652 ≈ 3 pounds

They must mix

37 pounds of the House Blend

3 pounds of the Kenya Blend.

The key  property of the absolute value parent function is:

        C. It’s vertex is at the origin.

The absolute value parent function is given by:

                  [tex]f(x)=|x|[/tex]

i.e. the graph of the function lie in the first and second quadrant.

[tex]xy=\log_{5\sqrt5}{125}\cdot\log_{2\sqrt2}64\\\\xy=\dfrac{\log_5125}{\log_5 5\sqrt5}\cdot\dfrac{\log_264}{\log_22\sqrt2}\\\\xy=\dfrac{3}{\log_55^{\tfrac{3}{2}}}\cdot\dfrac{6}{\log_22^{\tfrac{3}{2}}}\\\\xy=\dfrac{3}{\dfrac{3}{2}}\cdot\dfrac{6}{\dfrac{3}{2}}\\\\xy=3\cdot\dfrac{2}{3}\cdot6\cdot\dfrac{3}{2}\\\\xy=18[/tex]

Answer:

The product of x and y is 8.

Step-by-step explanation:

It is given that

[tex]x=\log_{5\sqrt{5}}\left(125\right)[/tex]

[tex]y=\log_{2\sqrt{2}}\left(64\right)[/tex]

We need to find the product of x and y.

[tex]x\cdot y=\log_{5\sqrt{5}}\left(125\right)\cdot\log_{2\sqrt{2}}\left(64\right)[/tex]

It can be written as

[tex]xy=\log_{5\sqrt{5}}\left(5\sqrt{5}\right)^2\cdot\log_{2\sqrt{2}}\left(2\sqrt{2}\right)^4[/tex]

Using the properties of logarithm, we get

[tex]xy=2\cdot 4[/tex]                    [tex][\because log_aa^x=x][/tex]

[tex]xy=8[/tex]

Therefore the product of x and y is 8.

Answer:

0.025 $/in.

Step-by-step explanation:

The store bought 300 ft of rope.

1 ft = 12 in.

300 ft * 12 in./ft = 3600 in.

The store bought 3600 inches of rope.

The store sells 40 inches of rope for $1.60. We can find the selling unit price of rope in dollars per inch.

($1.60)/(40 in.) = $0.04/in.

The store sells the rope at a price of $0.04 per inch.

The store sold all the rope at $0.04/in.

3600 in. * $0.04/in. = $144

The store sold all the rope for $144.

The profit was $54 for selling ll the rope.

$144 - $54 = $90

The bought the rope for $90.

The cost is dollars per inch is

($90)/(3600 in.) = 0.025 $/in.

Answer:

You will need  220 mL of the 60% solution  and  80 mL of pure alcohol.

Step-by-step explanation:

Let 'x' be the amount of 50% alcohol solution and y the amount of pure alcohol.

Therefore:  

(0.5x + y)/300 = 0.65 ⇒ 0.5x + y = 190

x + y = 300

Solving the sistem of equations:

x = 220 and y = 080

Therefore, You will need

220 mL of the 60% solution

and  80 mL of pure alcohol.

Answer:

Step-by-step explanation:

-3*j = -3j

(-3)(-1) = 3

Answer

-3j + 3 Notice the sign change. Be careful about that when signs are used with the distributive property.

Answer: B.97

Step-by-step explanation:

When two parallel lines are intersected by a transversal line then the sum of adjacent angles is 180°.

From the given figure , BD is parallel to XY and a transversal intersecting it making a pair of adjacent angles 83° and y°.

[tex]83^{\circ}+y^{\circ}=180^{\circ}\\\\\Rightarrow\ y^{\circ}=180^{\circ}-83^{\circ}=97^{\circ}[/tex]

Hence, the value of y= 97.

Answer:it is 83

Step-by-step explanation:

Answer:

[tex]\3.11\ ounces[/tex]

Step-by-step explanation:

we know that

To find the number of ounces of food each turtle will receive, divide the total ounces of food by the total number of turtles

so

[tex]\frac{84}{27}=3.11\ ounces[/tex]

Answer: 3.1

Step-by-step explanation: which is 3.1 with the line on top!

Answer:

f || m

Step-by-step explanation:

If f is parallel to k and k is parallel to m

then f must be parallel to m

To prove that two functions are inverse, we need to show that applying one function and then the other will result in the original input. By evaluating f(g(x)) and g(f(x)), we can confirm that f(x) = x + 3/2 and g(x) = 2x - 3 are inverse functions.

To prove that two functions f(x) and g(x) are inverse, we need to show that applying one function and then the other will result in the original input. In other words, f(g(x)) = x and g(f(x)) = x. Let's check if this holds true for the functions given:

Since f(g(x)) = x and g(f(x)) = x, we can conclude that f(x) = x + \frac {3}{2} and g(x) = 2x - 3 are indeed inverses of each other.

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f(x) and g(x) are inverse functions.

To prove that f(x) = x + 3/2 and g(x) = 2x - 3 are inverses, find their compositions and show they equal x, establishing them as inverse functions.

To prove that f(x) = x + 3/2 and g(x) = 2x - 3 are inverses:

Answer:

Step-by-step explanation:

Look at the picture.

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=12ft,\ leg=H,\ hypotenuse=20ft[/tex]

Substitute:

[tex]12^2+H^2=20^2[/tex]

[tex]144+H^2=400[/tex]             subtract 144 from both sides

[tex]H^2=256\to H=\sqrt{156}\\\\H=16\ ft[/tex]

Answer:

16 feet

Step-by-step explanation:

for edg

Answer:

C

Step-by-step explanation:

The center of inscribed circle into triangle is point of intersection of all interior angles of triangle.

The center of circumscribed circle over triabgle is point of intersection of perpendicular bisectors to the sides.

Circumscribed circle always passes through the vertices of the triangle.

Inscribed circle is always tangent to the triangle's sides.

In your case angles' bisectors and perpendicular bisectors intesect at one point, so point A is the center of inscribed circle and the center of corcumsribed circle. Thus, these circles pass through the points X, Y, Z and G, E, F, respectively.

Answer:

10.4

Step-by-step explanation:

The way to find percentage is by multiplying the number you want to find the percentage of by the percentage and divide it by 100

So, in the case of 16% of 65

we multiply 65 by 16 =1040

then we divide by 100

Hence 1040/100=10.40

which is same as 10.4

HOPE IT HELPS....

The solution of the expression 16 percent of 65 is 10.4.

A percentage is a ratio that may be written as a fraction of 100.

A fraction is a ratio between two quantities. The upper part is called numerator and the lower part is called denominator.

A collection of constants, variables connected using one or more arithmetic operator is called an expression.

This can be simplified as:

[tex]\dfrac{16}{100} \times65 = 10.4[/tex]  in decimal form.

Thus, 16 percent of 65 is 10.4

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Answer:

C

Step-by-step explanation:

MEAN:4+7+11+11+16+17=66÷6=11

MEDIAN:11+11=22÷2=11

MODE=11

Answer:

The correct answer is option C

4,7,11,11,16,17

mean = mode = median = 11

Step-by-step explanation:

Check option A

10,10,12,12,13,13

Mean = 12, mode = 12,13 , 14 and median = 12

Check option B

2,3,4,4,5,7

Mean = 4.15, mode = 4 and median = 4

Check option C

4,7,11,11,16,17

Mean = 11, mode = 11 and median = 11

Check option D

1,2,3,3,5,6

Mean = 3.33, mode =3 and median = 3

The correct answer is option C

4,7,11,11,16,17

mean = median = mode = 11

42 ounces

In this question, it is asking how many ounces of fiber did the Koala eat that day.

In order to solve this question, we would need to gather some important information from the question.

Important Information:

With the information above, we can solve the question.

We know that koalas only absorb 25% of fiber. We also know that a koala absorbed 10.5 ounces of fiber.

This means that the 10.5 ounces is 25% of fiber. This is 1/4 of the fiber it ate.

Now, we just need to find the other 3/4.

We could just multiply 10.5 by 4 to find how much fiber it ate that day.

[tex]10.5*4=42[/tex]

When you multiply, you should get 42.

This means that the Koala ate 42 ounces of fiber that day.

Answer:

42

Step-by-step explanation:

We seek the answer to the question "10.5 ounces is 25% of what number?" If we call the unknown number of ounces x, we have the equation 10.5=0.25x. Dividing both sides by 0.25, we have x=10.5/0.25=42 ounces of fiber.

Answer:

Increasing

Step-by-step explanation:

Let's see what happens if we choose a value for b greater than 1.

Let's try b=2.

[tex]f(x)=2^x[/tex].

I'm going to keep increasing x. If y increases, the the function is increasing. If y decreases, the function is decreasing.

Let's start with x=1.

[tex]y=2^1=2[/tex]

Now x=2.

[tex]y=2^2=4[/tex]

The y's got higher as you increased x so the function is increasing.

The function keep increasing for the varying value of x, hence the exponential function is increasing

Given the exponential function f(x) = [tex]b^x[/tex]

We are to check if the function is increasing or decreasing if b is greater than 1

Let b = 2 and x = 1

[tex]f(1) = 2^1\\f(1) = 2[/tex]

Let b = 2 when x = 2

[tex]f(2)=2^2\\f(2)=4[/tex]

Let b = 2 when x = 3

[tex]f(3)=2^3\\f(3)=8[/tex]

You can see that the function keep increasing for the varying value of x, hence the exponential function is increasing

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20% of 50 is found by multiplying the base (50) by the decimal equivalent of the percent (0.2). The calculation yields an amount of 10, which indicates that 20% of 50 is 10.

Calculating percents involves using the basic equation that relates the percent, the base (also called 'whole' or 'total'), and the amount (or 'part'). The equation can be represented as percent = (amount/base)  imes 100. To find what is 20% of 50, we use this equation, where the percent is known (20%) and the base is known (50), but the amount is what we are looking for.

First, let's convert the percent to a decimal to make the calculation easier: 20% = 20/100 = 0.2. Then, we multiply the base (50) by the decimal form of the percent (0.2): 50 x 0.2 = 10. So, 20% of 50 is 10.

Therefore, the correct representation relating the Percent, Amount, and Base in this problem is option A) Percent=20%, Amount=50, Base=unknown, since we're calculating the amount based on the known percent and base.

Answer:

C.) percent= 20%, Amount=unknown, Base =50

Step-by-step explanation:

20% is the percent

50 is the amount

20% of 50 is the unknown. This is the amount.

20% of 50 = 0.2 × 50 = 10

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

[tex]\huge\text{Note}\rightarrow[/tex] [tex]\leq \& \geq \ = \huge\text{closed circle}\\ < \& > = \huge\text{(o)(p)(e)(n)(e)(d) circle}[/tex]

[tex]\huge\text{So, we know that A or C could be our answer}.[/tex]

[tex]\huge\text{Eliminate option B and D}[/tex]

→ [tex]\huge\text{Find the absolute value of the problem}[/tex]

→ [tex]\huge\text{You can now know that  it could be:}[/tex]  

[tex]\huge\text{x}\large\huge{\ >}\huge\text{ 10 or x }< \huge\text{ -10}[/tex]

→ [tex]\huge\text{Possible answer \#1: x }>\huge\text{10}\\\\\huge\text{Possible answer \#2: x}<\huge\text{ -10}[/tex]

→ [tex]\boxed{\boxed{\huge\text{Answer: C}}}[/tex]  

[tex]\huge\text{Option A. would be too small}[/tex] [tex]\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

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

Answer:

b

Step-by-step explanation:

Answer:

B. 4.030

Step-by-step explanation:

We need to compare 4.026 with the numbers int he four choices.

All number have the same whole number part, 4.

To compare them, all you need to do is compare the decimal part.

All numbers have 3 places after the decimal point, so the decimal parts are all in thousandths.

A. 4 and 20 thousandths

B. 4 and 30 thousandths

C. 4 and 21 thousandths

D. 4 and 6 thousandths.

The number you are given is 4 and 26 thousandths.

Of all the thousandths in the choices, only 30 thousandths is greater than 26 thousandths, so 4.030 is the only number greater than 4.026.

Answer:

Step-by-step explanation:

Factorial is used to multiply any natural number with all the numbers smaller than it. It is denoted by n! (n is the natural number)

where n! = n*(n-1)*(n-2)*(n-3)*(n-4) so on....

For example if we take factorial of 5.

Then,

5!= 5*(5-1)*(5-2)*(5-3)*(5-4)

= 5*4*3*2*1

= 120

It is used for the questions which asks us to order a number of things or in how many ways you can arrange something....

Factorial is a key function in mathematics used to calculate permutations and arrangements. It represents the number of ways objects can be arranged within a set number. Factorial is essential in combinatorics and probability theory.

Factorial is a mathematical function denoted as n! and calculated as the product of all positive integers up to n.

The purpose of factorial is to represent the number of ways in which a set of objects can be arranged or permutations can be made within a set number of objects.

Factorial is extensively used in mathematics, especially in combinatorics and probability theory.

1

Answer:

15/56

Step-by-step explanation:

You just multiply 3/7 by 5/8 to get 15/56. Since you cannot simplify it more, that is the fraction of boys in mrs.jones class compared to the whole sixth grade class

Answer:

15/56

Step-by-step explanation:

Let the total number of students be x

Number of boys=[tex]\frac{3}{7}[/tex] of x

Number of boys in Mrs jones' class= [tex]\frac{3}{7}[/tex]of[tex]\frac{5}{8}[/tex]

Fraction of number of boys of Mrs jones' class to total class strength=[tex]\frac{15x/56}{x}[/tex]

Hence, the fraction is[tex]\frac{15}{56}[/tex]

Answer:

lol i need help with the same question

Step-by-step explanation:

Roger, with a batting average of 0.250, recorded 60 successful hits from a total of 240 attempts. Therefore, he failed to get a hit 180 times.

In this question, we are dealing with Roger's batting average and his performance. A batting average of 0.250 means that for every 4 at-bats, Roger gets a hit on average 1 time. So, if he has been at bat a total of 240 times, we can expect that he got hits 0.250 times out of these at-bats. So to calculate the number of successful hits, we multiple 240 by 0.250 which equals 60. Therefore, Roger has hit the ball 60 times. To find out how many times he failed to get hits, we subtract his hits from his total tries. So, 240 - 60 = 180. Therefore, Roger failed to get a hit 180 times.

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Answer:

D. 15/17

Step-by-step explanation:

Sine is opposite/hypotenuse and the opposite side to 62 degrees is 15 while the hypotenuse is 17

The value of sin 62° will be equal to 15/17.

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

The formula for sin angle is given as:-

SinФ = Perpendicular /  Hypotenuse

From the figure, Perpendicular is 15 and the hypotenuse is 17 so the value will be:-

Sin62°  =  15  /  17

Therefore the value of sin 62° will be equal to 15/17.

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Answer:

Polygon ABCDE = 50 units

Polygon FGHIJ = 23.4 units

Polygon KLMNO = 19.24 units

Polygon UVWXY = 38 units

Step-by-step explanation:

In order to find the perimeter, we have to find lengths of all sides of given points

The distance formula will be used to find the lengths

[tex]d = \sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }[/tex]

where (x_1,y_1) are coordinates of first point and (x_2,y_2) are coordinates of second point)

So,

For A(1,1), B(6,13), C(8,13), D(16,-2) and E(1, -2)

AB = 13 units

BC = 2 units

CD = 17 units

DE = 15 units

EA = 3 units

Perimeter of polygon ABCDE = 13+2+17+15+3 = 50 units

For F(14,-10), G(16,-10), H(19,-6), I(14,-2) and J(11,-6)

FG = 2 units

GH = 5 units

HI = 6.40 units

IJ = 5 units

JF = 5 units

Perimeter of polygon FGHIJ = 2+5+6.40+5+5 = 23.4 units

For K(4,2), L(8,2), M(12,5), N(6,5) and O(4,4)

KL = 4 units

LM = 5 units

MN = 6 units

NO = 2.24 units

OK = 2 units

Perimeter of polygon KLMNO = 4+5+6+2.24+2 = 19.24 units

For P(7,2), Q(12,2), R(12,6), S(7,10) and T(4,6)

PQ= 5 units

QR= 4 units

RS=6.40 units

ST= 5 units

TP = 5 units

Perimeter of polygon PQRST = 5+4+6.40+5+5 = 25.40 units

For U(4,-1), V(12, -1), W(20,-7), X(8, -7) and Y(4,-4)

UV = 8 units

VW = 10 units

WX = 12 units

XY = 5 units

YU = 3 units

Perimeter of polygon UVWXY = 8+10+12+5+3 = 38 units

Answer: A) 1.7 Years

Step-by-step explanation:

Answer:

A. 1.7 years

Step-by-step explanation:

Let [tex]P_1[/tex] be the original value of first car,

Since, the car depreciates at an annual rate of  10%,

Let after [tex]t_1[/tex] years the value of car is depreciated to 60%,

That is,

[tex]P_1(1-\frac{10}{100})^{t_1}=60\%\text{ of }P_1[/tex]

[tex]P_1(1-0.1)^{t_1}=0.6P_1[/tex]

[tex]0.9^{t_1}=0.6[/tex]

Taking ln on both sides,

[tex]t_1ln(0.9) = ln(0.6)[/tex]

[tex]\implies t_1=\frac{ln(0.6)}{ln(0.9)}[/tex]

Now, let [tex]P_2[/tex] is the original value of second car,

Since, the car depreciates at an annual rate of 15%

Suppose after [tex]t_2[/tex] years it is depreciated to 60%,

[tex]P_2(1-\frac{15}{100})^{t_2}=60\%\text{ of }P_2[/tex]

[tex]P_2(1-0.15)^{t_2}=0.6P_2[/tex]

[tex]0.85^{t_2}=0.6[/tex]

Taking ln on both sides,

[tex]t_2ln(0.85) = ln(0.6)[/tex]

[tex]\implies t_2=\frac{ln(0.6)}{ln(0.85)}[/tex]

[tex]\because t_1-t_2=\frac{ln(0.6)}{ln(0.90)}-\frac{ln(0.6)}{ln(0.85)}[/tex]

[tex]=1.70518303046[/tex]

[tex]\approx 1.7[/tex]

Hence, the approximate difference in the ages of the two cars is 1.7 years,

Option 'A' is correct.

Answer:

A(5,3)  ->A'(5,-3)

B(2,1)   ->B'(2,-1)

C(-2,4)  ->C'(-2,-4)

Step-by-step explanation:

If a point is reflected over the x-axis, it ends up on the opposite side of the x-axis with the same distance from the x-axis.

So what that means is the x-coordinate will stay the same and the y-coordinate will be opposite of what it was.

So if we reflect each of your points through the x-axis you will get:

A(5,3)  ->A'(5,-3)

B(2,1)   ->B'(2,-1)

C(-2,4)  ->C'(-2,-4)

Answer:

(5,-3) (2,-1) (-2,-4)

Step-by-step explanation:

When reflection over the x-axis the rule is (x,y) becomes (x, -y)

so your x will stay the same but your y will change

Answer:

The total  number of votes was [tex]7,007[/tex]

Step-by-step explanation:

Let

x -----> the number of yes votes

y -----> the number of no votes

we know that

[tex]\frac{x}{y} =\frac{6}{5}[/tex]

isolate variable y

[tex]y=\frac{5}{6}x[/tex] -----> equation A

[tex]x=3,822[/tex] -----> equation B

Substitute equation B in equation A and solve for y

[tex]y=\frac{5}{6}(3,822)=3,185[/tex]

therefore

To find out the total number of votes sum the number of yes votes plus the number of no votes

[tex]3,822+3,185=7,007[/tex]

Answer: 7,007 votes :)

Step-by-step explanation:

Hope that helps