9. y + 7 = 2x
2y = 4x - 14

Solve each system of equations by substitution

Answer:

In our ordinary division, we are clear about the division of a number by the same number. The quotient is always 1 in such case.

For example:-

Divide 4 by 4.

Here,

[tex] \frac{4}{4} = 1[/tex]

Now let solve the above examples by using the laws of indices.

[tex] \frac{4}{4} = {4}^{1 - 1} = {4}^{0} = 1[/tex]

Similarly,

[tex] \frac{ {x}^{m} }{ {x}^{m} } = {x}^{m - m} = {x}^{0} = 1[/tex]

Thus,any base with zero index is equal to 1.

We need to tell the index of x for which x will be 1 , First of all , always remember that index of a number means power of the number or to which power it's raised to, like in 2³ , 2 is raised to 3 so 3 is the index. Also we knows an identity i.e

Let's put , m = n

[tex]{:\implies \quad \sf \dfrac{a^m}{a^m}=a^{m-m}}[/tex]

[tex]{:\implies \quad \boxed{\bf{a^{0}=1}}}[/tex]

Also , you should note that for a = 0 , the given expression becomes 0⁰ ,which is not defined , so the above expression is true only for [tex]{\bf{a\in (-\infty,0)\cup (0,\infty)}}[/tex]

Now , as we can replace variables , so , if we replace a by x , we get x⁰ = 1 .

Hence , the required index is 0

Answer:

openup 1 em We want to find the points on the curve y=2x^3-3x^2-12x+20y where the tangent line is parallel to the xx-axis, which means that the slope=0

Answer:

[tex](x + 3)(x + 7) \\ (x)(x) + (x)(7) + (3)(x) + (3)(7) \\ = {x}^{2} + 7x + 3x + 21 \\ = {x}^{2} + 10x + 21[/tex]

Answer:

you have to add the circumference of the circle C≈131.95 to the two 100m  sides of the rectangle

Step-by-step explanation:

Answer:

x=-1

Step-by-step explanation:

2x-5=-5x+2

7x=-7

x=-1

Answer:

r = 19

Step-by-step explanation:

calculate the slope using the slope formula and equate to 4

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 7, 3 ) and (x₂, y₂ ) = (- 3, r )

m = [tex]\frac{r-3}{-3-(-7)}[/tex] = [tex]\frac{r-3}{-3+7}[/tex] = [tex]\frac{r-3}{4}[/tex] , then

[tex]\frac{r-3}{4}[/tex] = 4 ( multiply both sides by 4 )

r - 3 = 16 ( add 3 to both sides )

r = 19

Answer:

Consider the given vectors.

a=3i+2j−6k

b=4i−3j+k

Now,

a⋅b=(3i+2j−6k)(4i−3j+k)

a⋅b=12−6−6=0

Therefore,

Two vectors a and b are perpendicular.

Thus, the angle between the vectors a and b =90

∘

Hence, this is the answer.

Answer:

3

Step-by-step explanation:

First, you can list all the factors of the numbers:

30 = 1, 2, 3, 5, 6, 30

21 = 1, 3, 7, 21

The greatest factor that is in both of the numbers is 3, so that is GCF.

Hope this helped somewhat!! :]

Answer:

Step-by-step explanation:

Here we report the identification and characterization of a new coronavirus ... M, membrane. c, Similarity plot based on the full-length genome

Answer:

False

Step-by-step explanation:

5:20 + 1:35 is 6:55, not 6:40/

Answer:

a) yes

b) yes

c) yes

d) no

e) no

The table that shows the amount of strawberry picked by Joslyn is a linear function

Rebecca's rate is greater than Joslyn's rate

From the table, we have the following values

(x,y) = (0,0) and (3,6)

The rate is then calculated as:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{6 - 0}{3 - 0}[/tex]

Evaluate

[tex]m = 2[/tex]

This means that:

Joslyn's rate is 2 cups per minute

From the question, we have:

Rebecca's rate is 2.5 cups per minute

2.5 is greater than 2

This means that:

Rebecca's rate is greater than Joslyn's rate

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Step-by-step explanation:

Use these equations.

Equation of a Hyperbola, centered at orgin

[tex] \frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

where a is the major axis

B is the minor axis.

Since a and X are first, the x axis is the major.

This also means the x axis contains the vertices and foci as well.

The equation of vertices when x is major axis is

[tex](x ±a)[/tex]

Since the vertices are (±1,0), and the orgin is (0,0). The length of a is 1.

So a=1.

The equation of foci is

[tex](x±c)[/tex]

Where c is formed by

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

We know that c is 2 since the distance from the foci and center is 2. A is 1, so let find b.

[tex] {2}^{2} = {1}^{2} + {b}^{2} [/tex]

[tex]4 = 1 + {b}^{2} [/tex]

[tex]3 = {b}^{2} [/tex]

[tex] \sqrt{3} = {b}[/tex]

So our equation is

[tex] \frac{ {x}^{2} }{1 {}^{2} } - \frac{ {y}^{2} }{ (\sqrt{3}) {}^{2} } = 1[/tex]

[tex] \frac{ {x}^{2} }{1} - \frac{ {y}^{2} }{3} = 1[/tex]

Answer:

39.864

Step-by-step explanation:

24*4=96

1827/96

=39.864

Answer: x = 0 and x = 7

Step-by-step explanation:

9x^2 - 63x = 0.

We can factor out 9x from both terms on the left side:

9x(x - 7) = 0.

To be equal to 0, one of the terms has to be 0.

Therefore, either 9x = 0 or x - 7 = 0.

First, we solve the case where 9x = 0.

Then, x = 0.

Second, we solve the case where x - 7 = 0.

We add 7 to both sides:

So, x = 7

Answer:

4x³+2x²+2x

Step-by-step explanation:

9x³-5x³+2x²-5x+7x+4-4

4x³+2x²+2x

The simplified expression for (9x³ + 2x² - 5x + 4)- (5x³ -7x + 4) is

2x( 2x² + x + 1).

We have the Expression,

(9x³ + 2x² - 5x + 4)- (5x³ -7x + 4)

Now, simplifying the expression we get

(9x³ + 2x² - 5x + 4)- (5x³ -7x + 4)

= 9x³- 5x³ +2x² -5x + 7x + 4 - 4

= 4x³ + 2x² + 2x

= 2x( 2x² + x + 1)

Thus, the simplified expression is 2x( 2x² + x + 1).

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Answer:  [tex]y = 650(0.907)^t[/tex]

This is the same as writing y = 650(0.907)^t

=====================================================

Explanation:

Exponential equations can be of the form y = a*b^t

In this case, we have

If we had exponential growth, then we'd compute 1 + 0.093 instead.

Based on those values, we go from y = a*b^t to y = 650(0.907)^t which is the same as writing [tex]y = 650(0.907)^t[/tex]

Other exponential forms are possible, but I think this form is the most intuitive. The 0.907 means that 90.7% of the sample remains after each year.

Answer:

is the ans 0.73

Step-by-step explanation:

is the ans 0.73 gram and time xa ra

The mass of the carton in grams if it were to be empty is 530 g

Two or more expressions with an Equal sign is called as Equation.

Let us find the weight of one bottle of water.

We have to  subtract the weight of the carton with 27 bottles from the weight of the carton with 24 bottles

11.53 kg - 10.33 kg = 1.20 kg

So, the weight of 3 bottles of water is 1.20 kg.

Divide 1.2 by 3 to find the weight of one bottle of water

1.20 kg / 3 = 0.4 kg

Now the weight of the empty carton

Subtract the weight of 27 bottles from the weight of the carton with 27 bottles:

11.53 kg - 27(0.4 kg) = 0.53 kg

Convert the weight of the empty carton from kilograms to grams:

0.53 kg × 1000 g/kg = 530 g

Therefore, the mass of the carton in grams if it were to be empty is 530 g

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Answer:

36

Step-by-step explanation:

2(4)^2 + 3(4) - 8

Use PEMDAS

2(16) + 3(4) - 8

32+12-8

=36

Answer:

False

Step-by-step explanation:

3x4=12

12 divided by 3=4

4x8=32

32=34

Hence, this equation is false.

Answer:

Hank uses 19/12 cans of beans.

Step-by-step explanation:

1. 2/3 X 4/4 = 8/12

2. 2/3 X 4/4 = 8/12

3. 1/4 X 3/3 = 3/12

4. 8/12 + 8/12 + 3/12=19/12

Answer:

Explanation:

5 books cost $21. That means you have to divide 21 by 5 to find the price of one book, which is $4.20. Then you multiply 4.2 by 7 to find the price of 7 books. 7 x $4.20= $29.40

Answer:

Mean: 60

Step-by-step explanation:

First of all, in order to find the mean, one must add all the numbers together (61,55,66,58,50,70), which would give a total of 360.

After that, divide that total by the quantity of numbers (in other words, the total number of numbers, which in this case is 6). So, you would have to divide 360 by 6 leading to an answer of 60(the mean, which in other words is like finding the average).

Answer: 0.02

Step-by-step explanation: hundreds is 0.0 and its 2 so it would be 0.02

Using place value chart value of [tex]2[/tex] in the [tex]304.72[/tex] is quals to [tex]0.02[/tex] (decimal form).

" Place value is defined as the value represented by each digit of a number on the basis of its position on a number."

According to the question,

Given number ,

[tex]304.72[/tex]

Place value of all digits in [tex]304.72[/tex]

Place value of [tex]4 = ones[/tex]

Place value of [tex]0 = tens[/tex]

Place value of [tex]3= hundreds[/tex]

Place value of [tex]7= tenth[/tex]

Place value of [tex]2 = hundredth[/tex]

                           [tex]= \frac{2}{100}[/tex]

                           [tex]=0.02[/tex] (decimal form)

Hence, value of [tex]2[/tex] in the [tex]304.72[/tex] is quals to [tex]0.02[/tex] (decimal form).

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The domain of the function is the amount of fuel in the airplane's tank,

The weight of the plane as a function of the amount of fuel is given as:

W=7F + 3000

The plane can take up to 200 gallons of fuel.

This means that, the domain of the function is the amount of fuel in the airplane's tank, and the set of values is all set of real numbers from 0 to 200

When F = 0, we have:

W = 7*0 + 3000

W = 3000

When F = 200, we have:

W = 7*200 + 3000

W = 4400

This means that, the range of the function is the weight of the airplane, and the set of values is all set of real numbers from 3000 to 4400

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Answer:

D. 25.7 sq.ft

Step-by-step explanation:

Area of the Figure = Area of Rectangle - Area of Semi Circle

Area of Rectangle = LW = 8*4 = 32 sq.ft

Area of Semicircle = 0.5*π*r² = 0.5*3.14*2² = 6.28 sq.ft

Area of the Figure = 32-6.28 = 25.72 ≈25.7

Check the picture below.

Make sure your calculator is in Degree mode.

The number of meters from that point on the ocean floor to the wreck is 319.83 meters.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

From the figure,

Tan 13.2° = 75 / x

x = 75/tan 13.2°
x = 75/0.2345                                      

x = 319.829 meters

x = 319.83 meters

Thus,

The distance from the point to the wreck is 319.83 meters.

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Answer:

x= 8

Its 8 because when you add 65 and 76 you get 141 and 180 - 141 is 39. 6x8-9 is 39.