Match each equation to the situation it represents.

Answer: [tex]x= \frac{-1+\sqrt{97} }{8} , \frac{-1-\sqrt{97} }{8}[/tex]

Step-by-step explanation:

Use the Quadratic Formula .. if you use Completing the Square it'll take longer!!

In general, given [tex]ax^{2} +bx+c=0[/tex] , there exists two solutions where:

[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex] , [tex]\frac{-b-\sqrt{b^{2} }-4ac}{2a}[/tex]

In this case, a=4 , b=1 and c= -6

[tex]x= \frac{-1+\sqrt{1-4*4*-6} }{2*4}[/tex] , [tex]\frac{-1-\sqrt{1-4*4*-6} }{2*4}[/tex]

Simplify.

[tex]x=\frac{-1+\sqrt{97} }{8}[/tex] , [tex]\frac{-1-\sqrt{97} }{8}[/tex]

Answer:

6

Step-by-step explanation:

3x2

Answer:

4.5 + pi (3.14) is a  rational because it is a terminating decimal.  irrational because it is a non-terminating and non-repeating decimal.

hope this helped!

Answer:

5^15

Step-by-step explanation:

When the bases are the same, we add the exponents when multiplying

5^10 * 5^5

5^(10+5)

5^15

Answer:

5 to the power of 15

Step-by-step explanation:

Answer: it would be 1.25 since 1/4 is a fraction

1st 1/4 x 5/1

2nd 1+4 =5  keep the denominator

so the final product would be 5/4 or 1.25

Solution of expression 1/4 × 5 is 1.25

Division is an operation that represents the basic idea of repeated subtraction of the same number. It is inverse of multiplication operation.

Given expression

1/4 × 5

= 5/4

= 1.25

Hence, 1.25 is solution of given expression.

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Answer:

The item that would be represented by the independent variable in this situation is:

Step-by-step explanation:

To identify if a variable is dependent or independent, you must think about what variable needs from other to accomplish the exercise, for example, the distance traveled and the time, suppose you want to see how much distance you travel in a determined time, in this case, the distance is a dependent variable and the time an independent variable, this is because the distance you travel depends on the time you use in this activity, but the time will continue advancing no matter if the distance is advancing or not, in the case given, the jars of jam depends on the number of strawberries that Candice has (more jars of jam needs more strawberries) but the strawberries don't depend on the jars of jam, so, the jars of jam are the dependent variable and the strawberries the independent variable.

Answer:

B

Step-by-step explanation:

Answer:

3 b 11 6

Step-by-step explanation:

3 b 1 2 ⋅ b 4 3

Move  

b 4 3 . 3 ( b 4 3 b 1 2 )

Use the power rule  

a m a n = a m + n

to combine exponents.

3 b 4 3 + 1 2

To write  

4 3

as a fraction with a common denominator, multiply by  

2 2 . 3 b 4 3 ⋅ 2 2 + 12

To write  1 2

as a fraction with a common denominator, multiply by  

3 3 . 3 b4 3 ⋅ 2 2 + 1 2 ⋅ 3 3

Write each expression with a common denominator of  

6

, by multiplying each by an appropriate factor of  

1 .

Tap for more steps...

3 b 4 ⋅ 2 6 +3 6

Combine the numerators over the common denominator.

3 b 4 ⋅ 2 + 3 6

Simplify the numerator.

Answer:

y=1/2x - 1/2

Step-by-step explanation:

Slope intercept form is y=mx+b

The m is the slope of the line and the b is the y-intercept.

You must first the slope. The formula of a slope is (y1-y2)/(x1-x2). In this example it is (-2-3)/(-9-1) which equals 1/2. By order of elimanation we can see that y=1/2x-1/2 is correct.

Answer:

A approximation of 34 minutes and 30 seconds each day .

Step-by-step explanation:

First you would need to convert 4 hours to minutes , so 1 hour equals 60 minutes - 60 min = 1 hour, 60 min times 4 = 240 minutes in total. There are 7 days in total of the week, 240 minutes - 7 days of the week : 240 divided by 7 , equals a approaximation of 34 minutes and 30 seconds each day.

Answer:

All true

Step-by-step explanation:

By definition, an asymptote is a line at which the values of the function approach but never reach as one or both of the x or y coordinates tends to positive or negative infinity. Therefore, the graph of a rational function R never intersects any of its asymptotes.

The mode is the most frequent or most occurring value. The value 17 shows up the most times, at two times, so this is the mode. The value 19 is not even part of the given set of values, so you can immediately cross of choice A.

Side note: it is possible for a set to have more than one mode, and it's also possible to not have a mode at all.

Answer:

17

Step-by-step explanation:

It's the only number that repeats and I also took the test :)

The points (2, -5) when reflected across the origin becomes (-2, 5)

Reflection is a mathematical transformation of a shape by moving the vertices of the shape a distance equal to the distance between the line of reflection and the original point.

Other types of transformational processes are: Rotation and translation.

Analysis:

In transformation in the origin, the line of reflection is x = 0 and y = 0.

Which means both coordinates of the point would be changed.

At x = 2, 2 is 2 units from the origin. The only point which is 2 units away from the origin in the opposite side is -2.

Also at x = -5, that is 5 units away from the origin. The only point 5 units away from the origin is 5. so the new coordinate is 5.

In conclusion, the new point after reflection would be (-2, 5)

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Answer:

number 4 is D

Answer:

#4 is D

annnnnnnddddddddddddd............. I dont see the answers for number 5 ;(

Answer:

Step-by-step explanation:

its basically the success you expect after the work you put in. success is not guarenteed here. thats all i got to say.

Answer: It is something you put a lot of time in to do something. Success is not Guarenteed here in this world. And that is a fact. I just started middle school and I barly past 6th grade. Life can be very hard for lot's of people. Don't give up because of one thing keep going. (And no I am not an old lady I am only 12 years old.)   Have a very nice life. =D

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Answer:

3

Step-by-step explanation:

2a+6=12

Step 1: Subtract 6 from both sides.

2a+6=12

-6 -6

2a=6

Step 2: Divide both sides by 2.

2a/2=6/2

a=3

Answer:

a= 3

Step-by-step explanation:

2a+6=12

2a=12-6

2a=6

a=6/2

a=3 #

Answer:

C     f(x) = 0.5(2x)

Step-by-step explanation: I got a 96 on the the test so you can trust, unlessssss this is the one question I got wrong!!! .... It's not though so don't worry.

f(x) = 2(0.5)ˣ is the exponential function which has a growth factor of One-half.

A relation is a function if it has only One y-value for each x-value.

An exponential function with a growth factor of 1/2 would have 1.5^x as part of it

y=a(1+0.5)ˣ is the general term of the exponential function.

In the given functions

f(x) = 2(0.5)ˣ On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0.

It goes through (negative 1, 2) and crosses the y-axis at (0, 0.5).

Hence, f(x) = 2(0.5)ˣ is the exponential function which has a growth factor of One-half.

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Answer:

5

Step-by-step explanation:

Let's call the length AD y.

[tex]\dfrac{x+2}{y}=\dfrac{8x-14}{2y} \\\\\\2(x+2)=8x-14 \\\\\\2x+4=8x-14 \\\\\\4=6x-14 \\\\\\6x=18 \\\\\\x=3 \\\\\\DE=x+2=3+2=5[/tex]

Hope this helps!

Answer:

n = - 5

Step-by-step explanation:

Using the rules of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex]

Consider the left side

[tex]\frac{y^4.y^{n} }{y^2}[/tex]

= [tex]\frac{y^{4+n} }{y^2}[/tex]

= [tex]y^{4+n-2}[/tex]

= [tex]y^{2+n}[/tex], then

[tex]y^{2+n}[/tex] = [tex]y^{-3}[/tex]

Since the bases on both sides are the same, equate the exponents

2 + n = - 3 ( subtract 2 from both sides )

n = - 5

Answer:6.3 in.

Step-by-step explanation:

Given

Radius of sphere [tex]r=4\ cm[/tex]

When ball is immersed in beaker, it causes the water to flowout of beaker which is collected in the conical vessel

Such that amount of water equivalent to sphere volume is collected in it.

volume of ball

[tex]V_s=\frac{4\pi }{3}r^3[/tex]

[tex]V_s=\frac{4\pi }{3}\times 4^3[/tex]

[tex]V_s=\frac{256\pi }{3}\ cm^3[/tex]

Now volume of water collected is in shape of cone then volume of cone

[tex]V_c=\frac{\pi }{3}r^2h[/tex]

and [tex]V_s=V_c[/tex]

[tex]\frac{256\pi }{3}=\frac{\pi }{3}(4)^2\times h\ quad [\text{h=height of cone formed}][/tex]

[tex]h=4^2=16\ cm\approx 6.29\approx 6.3\ in.[/tex]

Answer:

[tex]9[/tex]

Step-by-step explanation:

The prime factorization of [tex]192[/tex] is [tex]2^6 \cdot 3[/tex], and since [tex]2^6[/tex] is already a perfect cube of [tex]4[/tex], we just have to deal with the [tex]3[/tex]. To make it a perfect cube, we have to multiply [tex]3[/tex] three times, and so we have to make it [tex]3 \cdot 3 \cdot 3[/tex], and we already have one three so we just add the other two threes, which equal [tex]3^2=9[/tex].

Answer:

2/15

Step-by-step explanation:

75u = 12 - 2

75u = 10

u = 10 / 75 = 2/15

Answer:

75u=12-2

75u=10

u=10/75

Answer:

15.94490514

Step-by-step explanation:

First, work out the average, or arithmetic mean, of the numbers:

Count: 5(How many numbers)

Sum: 357(All the numbers added up)

Mean: 71.4(Arithmetic mean = Sum / Count)

Then, take each number, subtract the mean and square the result:

Differences:

4.6, -26.4, -7.4, 8.6, 20.6

(Every Number minus Mean)

Differences^2:

21.16, 696.96, 54.76, 73.96, 424.36

(Square of each difference)

Now calculate the Variance:

Sum of Differences2:1271.2(Add up the Squared Differences)

Variance:254.24(Sum of Differences2 / Count)

Lastly, take the square root of the Variance:

Standard Deviation:15.94490514 (The square root of the Variance)

Answer:

6 units

Step-by-step explanation:

Since the x coordinate is the same, we only have to look at the difference of the y coordinates

2 - -4

2+4

6

The distance is 6 units

Answer:

the answer is 6 units

Step-by-step explanation:

Answer:

7p-3

Step-by-step explanation:

We are given the expression:

8p - 3 + 9p + 6p + 2p - 6p - 3p - 9p

To simplify, we can combine like terms. Add all the terms with a variable, then add the terms without a variable.

(8p + 9p + 6p + 2p - 6p - 3p - 9p)+ -3

(25p -18p) -3

7p-3

Steps:

Group like terms:

8p - 3 + 9p + 6p + 2p - 6p - 3p - 9p-3

Add similar elements:

8p - 3 + 9p + 6p + 2p - 6p - 3p - 9p = 7p

=7p−3

Answer: =7p−3

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Hope this helps.

Answer:32/3

Step-by-step explanation:

1/3(2)4^2

1/3(2)(4^2)

2/3(16)

32/2

Answer:

f(2)=16/3

Step-by-step explanation:

f(2)=1/3 (4^2)

f(2)=1/3(16)

f(2)=16/3

Answer:

-3x

Step-by-step explanation:

The term that goes in the box is

x * -3

-3x

Answer:

9.622 x 10^6

Step-by-step explanation:

Answer:

9,622*10 to the power of 3

Step-by-step explanation:

when using scientific notations you use ''10 to the power of ''

So in this case you have 3 zeroes which makes it 10 to the power of 3

[tex]9622000=9622*10^{3}[/tex]

Answer:

Both are correct.

Step-by-step explanation:

A square is a rhombus because it has 4 equal sides but it also has two pairs of parallel side which therefore makes it a parallelogram as well.

Answer:

∠A is 118 degrees

Step-by-step explanation:

every triangle is 180 degrees

(3x+13) + (x-8) +(x) = 180

simplify

5x + 5 = 180

-5        = -5

5x = 175

175 divided by 5 is 35

so x= 35

∠A= 3(35) + 13

3 times 35 is 105

105 + 13 = 118

so ∠A is 118 degrees

hope this helps!