Define coefficiend, base and index of an algebraic term with an example​

The solution to the system of equations is: (1, -8).

The solution is the coordinate of the point where both lines of the equations meet.

Second equation: 3y + 30 = 6x, rewrote in slope-intercept form:

3y = 6x - 30

y = 6x/3 - 30/3

y = 2x - 10 --> eqn. 1

Find the slope (m) and y-intercept (b) of the first graphed equation:

Slope (m) = change in y/change in x = rise/run = -4/2 = -2

The line intersects the y-axis at y = -6, so, the y-intercept, b = -6.

The first equation would be: y = -2x - 6 ---> eqn. 2

Subtract eqn. 2 from eqn. 1 to eliminate x

y = 2x - 10 --> eqn. 1

y = -2x - 6 ---> eqn. 2

2y = 0 - 16

2y = -16

y = -16/2

y = -8

Substitute y = -8 into eqn. 1 to find x:

-8 = 2x - 10

-8 + 10 = 2x

2 = 2x

2/2 = x

1 = x

x = 1

The solution is therefore: (1, -8).

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Answer:

[tex]9^{28}[/tex]

Step-by-step explanation:

using the rule of exponents

[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex](9^7)^{4}[/tex] = [tex]9^{7(4)}[/tex] = [tex]9^{28}[/tex]

Final answer:

The value of the expression is 31.

Step-by-step explanation:

Substitution is a process of putting the values of variable in the expression.

Given: p=17 and q=3

To find: value of 2p-q

We will substitute the values and simplify.

Putting the values of variables in the expression as

2p-q = 2x17-3 =34-3 = 31

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

[tex]\large\textbf{What does your current question look like?}[/tex]

[tex]\mathsf{2p - q}[/tex]

[tex]\large\textbf{How will we make the question easier to solve?}[/tex]

[tex]\mathsf{2p - q}[/tex]

[tex]\mathsf{= 2(17) - 3}[/tex]

[tex]\mathsf{= 34 - 3}[/tex]

[tex]\mathsf{= 31}[/tex]

[tex]\large\textbf{What is the \boxed{overall} answer?}[/tex]

[tex]\large\boxed{\mathsf{17}}\large\checkmark[/tex]

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

Answer:

It's A 48,736

Step-by-step explanation:

Answer:

48,856.11

Step-by-step explanation:

Compound interest is generally written as: [tex]A=P(1+\frac{r}{n})^{nt}[/tex] where P = principle amount, r = interest rate, n=compound periods, t = time. This is compounded continuously which can be defined as: [tex]A=Pe^{rt}[/tex]. If you're confused what e is, one of the definitions, is [tex]\lim_{x\to\infty}{(1+\frac{1}{x})^x[/tex]. This is essentially the very definition of continuous compound. It's when the amount of compounds (n in the equation) goes towards infinity. So using the previous defined equation simply plug the values into the equation.

[tex]A=(40000)e^{0.025*8}[/tex]

Multiply inside the exponent

[tex]A=(40000)*e^{0.2}[/tex]

raise e to the power of 0.2

[tex]A\approx40000*1.221[/tex]

Multiply

[tex]A=48,856.11[/tex]

There are 4 elements in the set A and 8 elements in set B that is n(A) = 4 and n(B) = 8

This is the total number of elements in a set. Given the following sets;

A = {c, d, e, f}

B = {odd numbers greater than 5 and less than 23}

B = {7,9,11,13, 15, 17, 19, 21}

Since there are 4 elements in the set A and 8 elements in set B hence n(A) = 4 and n(B) = 8

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Answer:

Formulae is Future value, see in picture I've done example 1 for u.

The domain of the function g(x)=l2xl +2 is all real numbers and the range is from (0,∞).

Given g(x)= l2xl +2

First of all we know that modulas gives two values for x<0 and x>=0.

The function g(x) if opened gives two values.

for x>=0 g(x)=2x+2

for x<0 g(x)=-2x+2

because we have not told about the description about x so we can put any value in the function.

So the domain is all real numbers.

Now when we take g(x)=2x+2 for x>=0

putting x=0 we get 2 and rest are positive values so the value of g(x) keeps increasing as we increase the value of x. So here range is [2,∞).

Now take g(x)=-2x+2 for x<0

putting smallest number starting from zero but not 0 we will get a number near to 0 but not zero and because when a negative number multiplies with -2 it becomes positive and increase the value of g(x) so here the range becomes (0,∞).

When we talk about overall range it will be [2,∞) ∪(0,∞)

it will be (0,∞).

Hence the domain of the function g(x) is all real numbers and range is from 0 to infinity.

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Answer: 1.9 inches

Step-by-step explanation:

- the equation to find the volume of a cylinder is V = π r^2 h

- so we can just change this equation around to H = V / π r^2

- so H = 384/ π 8^2 = 1.91 or 1.9

hope this helps :)

The greatest common factor will be (x² – xy + y²).

This is a value or expression that can divide the given expressions without leaving a remainder.

Given the following expressions

x^3+^3 and x^2 - xy + y^2

Expand x^3+y^3

x^3+y^3 =(x + y)(x² – xy + y²).

Since (x² – xy + y²) is common to both expression, hence the greatest common factor will be (x² – xy + y²).

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The equation of the quadratic function shown in the graph y - 8 = -2(x + 1)².

The vertex of this parabola is (-1, 8).  It opens downward, so the x² term has a negative coefficient.  The zeros are (-3, 0) and (1, 0), and the y-intercept is (0, 7).

Through the vertex form of the equation of a parabola we get:

y - (8) = a(x - (-1)) + 7, or.y - 8 = a(x + 1)².

Find coefficient a by substituting the coordinates (-3, 0) in this equation:

0 - 8 = a(-3 + 1)^2, or

-8 = a(-2)² or a = -2

The desired equation is y - 8 = -2(x + 1)^2

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Answer:

60(5) = 300 :D

Step-by-step explanation:

First lets make the equation :)

Orders 60 roses

This week will order 5x as many as last week

60 x 5 OR 60(5)

60(5) = 300 :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

AB = 11 units

Step-by-step explanation:

a given ratio also tells us how many equally sized units there are in the whole (in this case the line).

the ratio 4:7 tells us therefore, that from the whole line 7 ratii units (of 7+4 = 11 ratio units) are on the side of CB.

4 ratio units (of the 11 ratio units) are on the side of AC.

AC is the distance between A and C.

that is

0.6 - -3.4 = 0.6 + 3.4 = 4 line units

aha ! the distance is 4 units on the number line, and the ratio tells us that AC is 4 ratio units.

so, line unit and ratio units are 1:1 the same.

that means that CB with 7 ratio units is then also 7 line units long.

so, the whole line AB is then 4 + 7 = 11 line units long.

Answer:

11 units

Step-by-step explanation:

correct on plato

Answer:

3.2 km

Step-by-step explanation:

4cm÷5km=0.8 per cm to km

4km×0.8 km=3.2 km represents

Answer:

3.2 km

Step-by-step explanation:

[tex]\frac{4}{5} =\frac{x}{4}[/tex]

[tex]x=\frac{(4)(4)}{5} =\frac{16}{5} =3.2[/tex]

Hope this helps

Answer:

n = 4

Step-by-step explanation:

[tex]\frac{n}{6} =\frac{24}{36}[/tex]

cross multiply

24*6 = 144

n * 36 = 36n

144 = 36n

divide both sides by 36

n = 4

answer is D

n=4

simplify the fraction on the right to get 4/6

n/6 = 4/6

since denominators are same, you can cancel those

therefore, your answer will be n=4

The value of the given complex number is -1

Given the polar form of a complex number expressed as:

[tex](cos\theta + isin\theta)^n\\[/tex]

This can also be expressed according to the de moivre's theorem as;

[tex]=(cos\theta + isin\theta)^n\\\\=(cosn\theta+isinn\theta)[/tex]

Given the expression below;

[tex](cos\frac{\pi}{6} + isin\frac{\pi}{6} )^{18}\\(cos18\cdot\frac{\pi}{6} + isin18\cdot\frac{\pi}{6} )\\(cos3\pi + isin3\pi)\\=-1[/tex]

Hence the value of the given complex number is -1

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Step-by-step explanation:

in such a case the easiest approach might be using the point-slope form of a line equation :

y - y1 = m(x - x1)

with m being the slope, and (x1, y1) being a point on the line.

so, in our case that would be

y - 8 = 8(x - 4)

simplified this would be

y - 8 = 8x - 32

y = 8x - 24

FYI - this would be then the slope-intercept form (-24 would be the intercept point on the y-axis).

Answer:

Step-by-step explanation:

x intercept equals pi

Answer:

x intercept= 6

Step-by-step explanation:

Answer:

9.00,9.20,9.30

Step-by-step explanation:

Answer:

i think this is the answers

Step-by-step explanation:

-13.78xy

Answer: All real numbers

Step-by-step explanation:

I assume you meant [tex]y=5.3^x[/tex].

In this case, the domain is the set of real numbers, as is with most standard exponential functions.

Answer:

The length of the shortest side of the pentagon would be:

40.2

Answer:

If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

Step-by-step explanation:

The category in the pie chart that was chosen by 1/8 of those that were surveyed is documentary.

From the pie chart, it can be seen that comedy and drama have the highest fraction as they have 1/4 each.

Therefore, the percentage of those who choose comedy or drama will be:

= (1/4 + 1/4) × 100

= 2/4 × 100

= 50%

Lastly, if 24% chose news, the others that choose others will be:

= 1/3 × 24

= 8%

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Answer:

Step-by-step explanation:

C=(10,-1)

D=(-6,3)

[tex]mid~point~x=\frac{10+(-6)}{2} =\frac{10-6}{2} =\frac{4}{2} =2\\y=\frac{-1+3}{2} =\frac{2}{2} =1[/tex]

mid point=(2,1)

The midpoint of line segment CD is M = (2, 1).

We have,

To find the midpoint of the line segment CD, we can use the midpoint formula:

M = ((X₁ + X₂)/2, (Y₁ + Y₂)/2)

Given C = (10, -1) and D = (-6, 3), we can substitute the values into the formula:

M = ((10 + (-6))/2, (-1 + 3)/2)

= (4/2, 2/2)

= (2, 1)

Therefore,

The midpoint of line segment CD is M = (2, 1).

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The given graph is a function.

The correct option is (B).

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.

As we draw the vertical line then for one input x there is one output.

Hence, the given graph is function.

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Answer:

24

Step-by-step explanation:

[tex]8 * \frac{x}{8}=3 * 8[/tex]

x = 24

Answer:

24

Step-by-step explanation:

Let the number we are looking for = [tex]x[/tex].

∴ According to the question:

[tex]x[/tex] ÷ 8 = 3

• Multiply both sides by 8:
[tex]x[/tex] = 8 x 3

[tex]x[/tex] = 24

The age of the man whose normal pressure measures 128 mmHg is approximately 38 years.

The quadratic formula can be used to determine the age of a man whose normal blood pressure measures 128 mmHg. This can be expressed mathematically as:

[tex]\mathbf{ \dfrac{-b \pm\sqrt{b^2 - 4ac}}{2a}}[/tex]

From the given equation:

P = 0.006A² - 0.02A + 120

where;

128 =  0.006A² - 0.02A + 120

= 0.006A² - 0.02A + 120 - 128

= 0.006A² - 0.02A - 8

where:

[tex]\mathbf{ \dfrac{-(-0.02) \pm\sqrt{(-0.02)^2 - 4(0.006)(-8)}}{2(0.006)}}[/tex]

[tex]\mathbf{ = \dfrac{(0.02) \pm 0.43863}{0.012}}[/tex]

= 38.2195 or -34.8862

Taking the positive integer value, the age of the man whose normal pressure measures 128 mmHg is approximately 38 years.

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It's the water

The salt would be the solute that dissolves in the solvent.

Temp - is a factor

(affecting rate at which salt dissolves)

grams - unit of measure

Hope this helps!

The equation which accurately solves for the integers is; 5n = 2(2n +3) +1.

It follows from the task content that the first number is represented by n.

On this note, it follows that the second, and third numbers are; (n+1) and (n+2) respectively.

On this note, since five times the first number is equal to one more than twice the sum of the second and third numbers; we have;

5n = 2(n+1+n+2) +1

5n = 2(2n+3)+1.

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