RACTICL
n set
1. How much interest is earned in 9 months on a deposit of
$7000 at 8 percent simple interest?

Answer:

[tex]y=-3x+14[/tex]  or  [tex]3x+y=14[/tex]

Step-by-step explanation:

we have

[tex]y+1=-3(x-5)[/tex] ----> equation of the line into point-slope form

step 1

Convert to slope intercept form

The equation of the line into slope intercept form is equal to

[tex]y=mx+b[/tex]

so

[tex]y+1=-3(x-5)[/tex]

[tex]y+1=-3x+15[/tex]

[tex]y=-3x+15-1[/tex]

[tex]y=-3x+14[/tex] ----> equation of the line into slope intercept form

step 2

Convert to standard form

The equation of the line into standard form is equal to

[tex]Ax+By=C[/tex]

so

we have

[tex]y=-3x+14[/tex]

Adds 3x both sides

[tex]3x+y=14[/tex] ----> equation of the line in standard form

Answer:

y^3 + 27

Step-by-step explanation:

(y+3)(y2 – 3y+9)

distribute y

y^3 - 3y^2 + 9y

distribute 3

3y^2 - 9y + 27

add/combine like terms and order correctly

y^3 + (3y^2 - 3y^2) + (9y - 9y) + 27

answer

y^3 + 27

Answer:

Rational Numbers

Step-by-step explanation:

According to the definition of rational numbers, the numbers which can be written in the form of p/q where p and q belong to the set of integers and q is not equals to zero are called rational numbers i.e 8/9, 9/6, -3/4

So, the answer to given question is:

Rational Number ..

Answer:

[tex]\large\boxed{D)\ x^2(3x^2+2x-9)-5x(3x^2+2x-9)}[/tex]

Step-by-step explanation:

[tex]\text{Use the distributive property}\ a(b+c)=ab+ac.\\\\(x^2-5x)(3x^2+2x-9)=(x^2)(3x^2+2x-9)+(-5x)(3x^2+2x-9)[/tex]

Answer:

x^2(3x^2 + 2x - 9) - 5x(3x^2+2x-9)

the answer is B) 128

if the diameter of the cylinder's base is 8, then its radius is half that, or 4.

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=8 \end{cases}\implies V=\pi (4)^2(8)\implies V=128\pi[/tex]

Answer:

y+3=-6(x +9)

Step-by-step explanation:

equation represents a line that passes through (-9, -3) and has a slope of -6is:

y+3=-6(x +9)

because : The equation of a linear function in point-slope form is:                    y – y1 = m(x – x1) ....m : the slope

The point is A (x1 , y1)

you have m = - 6      x1 = -9      y1 = -3

The equation represents a line that passes through (-9, -3) and has a slope of -6 is y+3 = -6(x+9).

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a line is passing through the point (-9, -3) and the slope of -6,

We need to determine the equation of the line,

The general formula of a line passing through a point (x', y') and have slope m is given by,

y-y' = m(x-x')

Here, (x', y') = (-9, -3), m = -6,

Therefore, the equation of the asked will be =

y-(-3) = -6(x-(-9))

y+3 = -6(x+9)

Hence, the equation represents a line that passes through (-9, -3) and has a slope of -6 is y+3 = -6(x+9)

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Answer:

240 melons

Step-by-step explanation:

First, multiply the # of boxes and # of bags

(30 * 4 = 120)

Then, multiply that with 2

(120*2=240)

x^2 + 2 = 38

Subtract 2 from each side:

x^2 = 36

Take the square root of both sides:

x = √36

x = 6

Answer:

-1/5

Step-by-step explanation:

Check the picture below.

since the larger cube has a volume of 6 cubic units, let's see what is the volume of one of the small cubes, and check how many times does that volume go into the other.

[tex]\bf \stackrel{\textit{volume of a cube}}{V=s^3}~~ \begin{cases} s=side's~ length\\ \cline{1-1} s=\frac{1}{2} \end{cases}\implies V=\left( \cfrac{1}{2} \right)^3\implies V=\cfrac{1}{8} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{how many times does }\frac{1}{8}\textit{ go into 6?}}{6\div \cfrac{1}{8}\implies \cfrac{6}{1}\div \cfrac{1}{8}\implies \cfrac{6}{1}\cdot \cfrac{8}{1}}\implies 48[/tex]

Answer:

Step-by-step explanation:

Answer:

Third option

Step-by-step explanation:

Given expression is:

[tex]\sqrt[3]{32x^8y^{10}}[/tex]

Making the exponents multiples of 3

[tex]=\sqrt[3]{8*4*x^6*x^2*y^{9}*y}\\=\sqrt[3]{2^3*4*x^6*x^2*y^{9}*y}\\Applying\ radical\\=2^{(3*\frac{1}{3})} *4^{\frac{1}{3} }*x^{(6*\frac{1}{3})}*x^{(2*\frac{1}{3})}*y^{(9*\frac{1}{3})}*y^{\frac{1}{3}}\\=2x^2y^3\sqrt[3]{4x^2y}[/tex]

Hence,

Option No 3 is correct ..

Answer:

Step-by-step explanation:

Nice work with the latex. It is a hard language to use.

Numerator:

take out x(x^2 + 7x + 10)

Factor the contents of the brackets: (x + 2)(x + 5)

Combine x * (x + 2) * (x + 5)

Denominator: Leave at is it is.

Combine

[tex]\dfrac{(x)(x + 2)(x + 5)}{x^4*(x + 2)}[/tex]

Be very careful with this next step. Cancel the x and the (x + 2) in the top and bottom. You are left with

[tex]\dfrac{(x +5)}{x^3}[/tex]

The reason you have to be so careful is that you have to (or you should) mention that these cancellations can take place only if x ≠ 0 or that (x + 2)≠ 0

Answer:

B

Step-by-step explanation:

A) a ≥ 3 + 2j; j ≥ 14, a ≤ 35

B) a ≤ 3 + 2j; j ≥ 14, a ≤ 35

C) a ≥ 3 + 2j; j ≤ 14, a ≤ 35

D) a ≤ 3 + 2j; j ≤ 14, a ≤ 35

All the system of linear inequalities which can be used to find the possible ages of Anna, a, and Jamie, j are,

a < 3 + 3j

j ≥ 14

a ≤ 35

We have to given that,

Anna is no more than 3 years older than 2 times Jamie’s age.

Jamie is at least 14 and Anna is at most 35.

Let us assume that,

Age of Anna = a

Age of Jamie's = j

Hence, system of linear inequalities which can be used to find the possible ages of Anna, a, and Jamie, j are,

For Anna is no more than 3 years older than 2 times Jamie’s age.

a < 3 + 3j

And, Jamie is at least 14 and Anna is at most 35.

j ≥ 14

a ≤ 35

Thus, All the system of linear inequalities which can be used to find the possible ages of Anna, a, and Jamie, j are,

a < 3 + 3j

j ≥ 14

a ≤ 35

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Answer:

-1

Step-by-step explanation:

To find the slope, we use the formula

m = (y2-y1)/(x2-x1)

   = (5-7)/(-3--5)

   = (5-7)/(-3+5)

   = -2/2

  =-1

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept

We have the equation y = 75x + 50.

Therefore

slope: m = 75

y-intercept: b = 50

Answer:

it should be (based on the instructions we don't have) [tex]\frac{-3}{2}[/tex]

Step-by-step explanation:

because the "D" in the parenthesis has 2 negative signs, it inverts itself making it just what D equals, which on the number line is [tex]\frac{-3}{2}[/tex]

Answer:

A

Step-by-step explanation:

You can write any equation that is adding or subtracting like n+(-x)=y

Answer:-1

Step-by-step explanation:

Answer:

Letter (D), or y = -3x - 4

Step-by-step explanation:

A slope of -3 should be self explanatory, and y intercept is determined by the b value in the form y = mx + b. Since b is negative, we are looking for -4. Therefore, your answer is (D).

Hope this helps!

Answer:

Step-by-step explanation:

Look at the picture.

ΔABC and ΔACD are similar. Therefore corresponding sides are in proportion:

[tex]\dfrac{AB}{AC}=\dfrac{AC}{AD}[/tex]

We have

[tex]AB=2+6=8,\ AC=x,\ AD=2[/tex]

Substitute:

[tex]\dfrac{8}{x}=\dfrac{x}{2}[/tex]          cross multiply

[tex]x^2=(8)(2)\\\\x^2=16\to x=\sqrt{16}\\\\x=8[/tex]

Answer:

1. 13.98

2. 14.47

Step-by-step explanation:

The question is on sample standard deviation and population standard deviation

Arrange the data in increasing order

12,14, 16,16,17,19,21,26,35,37,42,43,45,46,56

n=15

Find the mean of the data set

[tex]mean = (12+14+ 16+16+17+19+21+26+35+37+42+43+45+46+56)/15[/tex]

mean= 29.67 ⇒30

Find the deviations

You subtract the value of mean from each of  the data set given

Deviations= -18, -16, -14, -14, -13,-11, -9,-4,5,7,12,13,15,16,26

Find squares of deviations

= 324, 256, 196, 196, 169, 121, 81, 16, 25, 49, 144, 196, 225, 256, 676

Find sum of squares of deviations

[tex]324+ 256+ 196+ 196+ 169+ 121+ 81+ 16+ 25+ 49+ 144+ 196+ 225+ 256+ 676 = 2930[/tex]

1. Treating the data set to represent an entire population then;

Variance= sum of squares of deviation/number of data set

Variance= 2930/15 = 195.33

Population standard deviation = √195.33 = 13.98

2. Treating the data set as a sample , the number of data set is reduced by one.i.e n= 15-1= 14

Sample Variance=2930/14 =209.29

sample standard deviation= √209.29 = 14.47

Answer:

x:2x:√3x.

Step-by-step explanation:

I would write it as x:2x:√3x.

The hypotenuse is twice the length of the shorter leg and the longer leg is the square root of 3 times the shorter leg.

Answer:

The correct option is A) x : 2x : x√3

Step-by-step explanation:

Consider the provided information.

For a 30-60-90 triangle.

The side opposite to the 30° angle is x.

The side opposite the 60° angle is √3 x.

The side opposite the 90° angle is 2 x.

Side opposite to the 30° angle is the smallest side as 30° is the smallest angle among 30-60-90. Similarly the side opposite of 60° is the second largest side as 60° is the second largest angle and for the side opposite of 90° is the largest side as 90° is the largest angle.

Hence, the correct option is A) x : 2x : x√3

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Using the rules of exponents

•  [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]

• [tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]

Hence

[tex]16^{-\frac{3}{4} }[/tex] = [tex]\frac{1}{16^{\frac{3}{4} } }[/tex]

= [tex]\frac{1}{\sqrt[4]{16^{3} } }[/tex] = [tex]\frac{1}{2^{3} }[/tex] = [tex]\frac{1}{8}[/tex]

Answer:

Choice B), [tex]f(x) = -3|x|[/tex].

Step-by-step explanation:

Each point on the graph of [tex]g(x)[/tex] can be represented as [tex](x, g(x))[/tex].

When the graph of [tex]g(x)[/tex] is reflected over the x-axis, each point on the graph is also reflected over the x-axis. The x-coordinate of each point will not change but the sign in front of the y-coordinate will flip. For example, [tex]1[/tex] (same as [tex]+1[/tex]) will become [tex]-1[/tex], and vice versa. In general, [tex](x, g(x))[/tex] will become [tex](x, -g(x))[/tex].

On the other hand, points on the graph of [tex]f(x)[/tex] can be represented as [tex](x, f(x))[/tex]. [tex]f(x)[/tex] is the reflection of [tex]g(x)[/tex], so [tex](x, -g(x))[/tex] and [tex](x, f(x))[/tex] shall be equivalent. In other words,

[tex]f(x) = -g(x) = - 3|x|[/tex].

How many minutes are in 9 hrs

1 hr = 60 min

You must apply dimensional analysis (aka setting up fractions where the units you want will cancel out and the ones you want stay)

[tex]\frac{9 hr}{1} *\frac{60 min}{1hr}[/tex]

9 hrs is 540 min

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

so since there is 60 minutes in 1 hour and 60 is divisible by 10 all you have to do is multiply 6 by 9 and you get 54 but since it's 60 than that changes the answer to 540 since it's divisible by 10

Answer:

Option B is correct.

Step-by-step explanation:

Solving using synthetic division

-8 | 2 14 9

The synthetic division is shown in image attached.

The remainder is: 25

The quotient is : 2x-2

So, Option B is correct.

Answer:

Because he could only cover 50% of the price 25 by the coupon and 25 which he had.

Answer:

The answer is c

The simplest basic geometric object is a point. It is named with a capital letter and symbolized by a dot. The correct option is C.

The simplest basic geometric object is a point. It is named with a capital letter and symbolized by a dot. A point has no size and solely represents the position (that is, zero length, zero width, and zero height).

Since a plane is a flat, endlessly long two-dimensional surface. A plane is a two-dimensional analog that can incorporate three dimensions of space, a line, and a point.

Now, the statement that will be true about the three points given is that only one plane can be drawn so it contains all three points.

Hence, the correct option is C.

The complete question is mentioned in the image below.

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Answer:

3v+5+8u is written as a product of three factors is incorrect because factors are associated with multiplication and multiplication is only used twice within the problem and also they are all be add

3v+5+8u is written as a sum of three terms is correct because sum is associated with addition and three terms are being added together

8 is a coefficient is correct because a coefficient is a number being multiplied by a variable in this case and its still a variable in both ways of looking at it because terms are also single numbers

8u and 5 are like terms is incorrect because you cannot add them together

5 is a constant is correct because a constant is a single number

none of these are true is incorrect because there are correct answers

Answer:

it would be the 1st one

Step-by-step explanation:

Answer:

(-4,-10)

Step-by-step explanation:

Given that ;

y=1x-6 -----------------------(a)

x= -4--------------------------(b)

Substitute value of x (b) in (a) above

y= 1(-4) -6

y= -4-6 = -10

Solutions

x=-4   and y= -10    ⇒    ( -4, -10)

Graphically we observe that x =  -4  and y = -10 at point m where the two graphs intersect

Answer:

-4,-8

Step-by-step explanation: