How many solutions does this system of equations have?


exactly one

exactly two

infinitely many

none

Answer:

[tex]x \in \mathbb \: R[/tex]

Step-by-step explanation:

The given equation is:

[tex] - (2x + 2) - 1 = - x - (x + 3)[/tex]

We expand to get:

[tex] - 2x - 2 - 1 = - x - x - 3[/tex]

We group like terms to get:

[tex] - 2x + x + x = - 3 + 1 + 2[/tex]

We combine the like terms to obtain:

[tex] - 2x + 2x = - 3 + 3[/tex]

[tex] 0 = 0[/tex]

This is always true therefore the solution is infinite.

Answer:

The amount of numbers that have a G C F of 7 and a product of 490 is 2.

Step-by-step explanation:

On Prime Factorization 490   =   2   x   5   x   7   x   7

G CF = Greatest Common Factor

So, here the possible number who have products as 490 and G C F as 7 is

(a)  2 x 7 = 14  and   5 x 7  = 35

As, 14 and 35 on multiplication,gives 490 as a  product.

And, G C F  of 14 and 3 5 is also 7.

(b)  7  and   5 x 7 x  2  = 70

As, 7 and 70 on multiplication,gives 490 as a  product.

And, G C F  of 7  and 70 is also 7.

⇒ (14, 35) and (7,70) are the only such pairs.

Hence, the amount of numbers that have a G C F of 7 and a product of 490 is 2.

Final answer:

The question seeks the number of number pairs with a GCF of 7 and a product of 490. There are only two pairs that meet the criteria: (7, 70) and (10, 49). Each pair multiplies to 490 and has a GCF of 7.

Explanation:

The question asks for the number of pairs of numbers that have a Greatest Common Factor (GCF) of 7 and a product of 490. First, we must note that any pair of numbers with a GCF of 7 must be multiples of 7. So, we divide 490 by 7 to find another factor that is also a multiple of 7, which gives us 70. Now, we have two pairs of numbers that satisfy the condition: (7, 70) and (10, 49) because each pair when multiplied gives 490, and the GCF of each pair is 7. It's important to note that 490 is equal to 7^2 times 10, which means we won't find more than these two pairs without repeating the same factors in a different order.

The inequality which shows the number of weeks, w, you need to save to be able to go on a trip is 25w + 200 ≥ 535.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Total amount needed to go for a trip to California = $535

Already saved amount = $200

You decide to save an additional $25 per week.

Let w be the number of weeks needed to save $25 to get the amount needed to go for trip.

These saved amounts must be at least $535 to go for trip.

The amount saved after w weeks is 25w

Total saved amount = 200 + 25w

This saved amount must be ≥ 535.

So the inequality is 200 + 25w ≥ 535.

Hence the inequality which represents the amount need to save to go for trip is  200 + 25w ≥ 535.

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The required equation of line is:

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

Step-by-step explanation:

Given equation of line is:

y=-2x-3

The coefficient of x is the slope of line as the equation is in slope intercept form

Let m1 be the slope of given graph of line

So,

[tex]m_1=-2[/tex]

The product of slopes of perpendicular lines is -1

Let m2 be the slope of required line

Then

[tex]m_1.m_2 = -1\\-2 . m_2 = -1\\m_2 = \frac{-1}{-2}\\m_2 = \frac{1}{2}[/tex]

the slope-intercept form of line is:

[tex]y=m_2x+b[/tex]

Putting the value of slope

[tex]y=\frac{1}{2}x+b[/tex]

To find the value of b, putting the given point (-2,-1) in equation

[tex]-1=\frac{1}{2}(-2)+b\\-1 = -1 +b\\-1+1 = b\\b = 0[/tex]

Hence,

The required equation of line is:

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

Keywords: Equation of line, slope-intercept form

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Answer:

3x^3-18x^2+26x-8

Step-by-step explanation:

(x-4)(3x^2-6x+2)

3x^3-6x^2+2x-12x^2+24x-8

3x^3-18x^2+26x-8

Answer:

3x^3-18x^2+26x-8

Step-by-step explanation:

(x-4)(3x^2-6x+2)

3x^3-6x^2+2x-12x^2+24x-8

3x^3-18x^2+26x-8

Answer:

Because Alternate Interior angles are equal.

Step-by-step explanation:

STEP - I:

[tex]$ m \angle {5} = 3 . m \angle {\{3}\} $[/tex]

Reason:

This is the given data.

STEP - II:

It has multiplied and the reason is mentioned as well.

STEP - III:

[tex]$ m \angle{3} + m \angle{5} $[/tex] = 45° + 135° = 180°

Reason:

It has substituted the value of [tex]$ m\angle{5} $[/tex] from the previous step. The sum of [tex]$ m\angle{3} $[/tex] and [tex]$ m \angle{5} $[/tex] is 180°.

STEP - IV:

[tex]$ a \parallel b $[/tex]

Reason:

We calculated [tex]$ m\angle{5}[/tex] to be 135°.

Note that [tex]$ \angle {5} $[/tex] and [tex]$ \angle{6} $[/tex] are on the same line. That means their sum should be 180°.

i.e., [tex]$ m\angle{5} + m\angle{6} $[/tex] = 180°.

[tex]$ \implies $[/tex] 135° + [tex]$ m\angle{6} $[/tex] = 180°.

[tex]$ \implies m\angle{6} = $[/tex] 45°.

One of the ways to prove [tex]$ a \parallel b $[/tex] is to check if alternate interior angles are equal.

Here, [tex]$ m\angle{3} $[/tex] and [tex]$ m \angle {6} $[/tex] are alternate interior angles and they are equal.

[tex]$ \implies a \parallel b $[/tex].

Sigma notation of sequence −10, −13, −16, … is [tex]\sum_{n=1}^{6}-(3 n+7)[/tex]

Need to determine the sigma notation for the following sequence  

−10, −13, −16, …

Let's try to build a generic formula for given sequence  

The given sequence is in Arithmetic progression where first term = -10 and common difference = -3

The formula for arithmetic progression is given as:

[tex]a_n = a_1 + (n - 1)d[/tex]

Where,

[tex]a_n[/tex] is the nth term in the sequence

[tex]a_1[/tex] is the first term in the sequence

d is the common difference between the terms

Here in this sequence [tex]a_1[/tex] = -10 and d = -3

[tex]a_n = -10 + (n - 1)(-3)\\\\a_n = -10 - 3n + 3\\\\a_n = -3n - 7[/tex]

So generic formula for a term is – ( 3n + 7 )

[tex]\begin{array}{l}{\text { For } \mathrm{n}=1, \text { term is }-(3 \times 1+7)=-10} \\\\ {\text { For } \mathrm{n}=2, \text { term is }-(3 \times 2+7)=-13} \\\\ {\text { For } \mathrm{n}=3, \text { term is }-(3 \times 3+7)=-16}\end{array}[/tex]

And so on

Using sigma notation for arithmetic sequence:

[tex]\sum_{k=1}^{n} a_{k}[/tex]

So for first six terms value of n will vary from 1 to 6 and in sigma notation it can be represented as

[tex]\sum_{n=1}^{6}-(3 n+7)[/tex]

Answer:

D

Step-by-step explanation:

The line representing Bella has a steeper slope than Kofi's, so the slope of that line must be greater than 15.55.

Similarly, the line representing Elsie has a shallower slope than Kofi's, so the slope of that line must be less than 15.55.

The only option that fits is D.

Answer:

[tex]p (x) = x^{3} - 21x^{2}+ 147x - 343[/tex]

is the required polynomial with degree 3 and p ( 7 ) = 0

Step-by-step explanation:

Given:

p ( 7 ) = 0

To Find:

p ( x ) = ?

Solution:

Given p ( 7 ) = 0 that means substituting 7 in the polynomial function will get the value of the polynomial as 0.

Therefore zero's of the polynomial is seven i.e 7

Degree : Highest raise to power in the polynomial is the degree of the polynomial

We have the identity,

[tex](a -b)^{3} = a^{3}-3a^{2}b +3ab^{2} - b^{3}[/tex]

Take a = x

        b = 7

Substitute in the identity we get

[tex](x -7)^{3} = x^{3}-3x^{2}(7) +3x(7)^{2} - 7^{3}\\(x -7)^{3} = x^{3}-21x^{2} +147x - 343[/tex]

Which is the required Polynomial function in degree 3 and if we substitute 7 in the polynomial function will get the value of the polynomial function zero.

p ( 7 ) = 7³ - 21×7² + 147×7 - 7³

p ( 7 ) = 0

[tex]p (x) = x^{3} - 21x^{2}+ 147x - 343[/tex]

A polynomial function with degree 3 and P(7)=0 can be written as p(x) = a(x - 7)(x - r2)(x - r3), where r2 and r3 can be any real number and a is any non-zero real number.

The student has asked for a polynomial function with a degree of 3 such that P(7) equals 0. By definition, a polynomial function of degree n with given roots can be written as:

p(x) = a(x - r1)(x - r2)... (x - rn)

Since we have been given that P(7)=0 , we can choose 7 as one root, but the other roots can be chosen arbitrarily. So, we can create a polynomial function like below:

p(x) = a(x - 7)(x - r2)(x - r3)

Where r2 and r3 can be any real number and a is any non-zero real number. For example, if we choose r2=1, r3=2 and a=1. The function would be:

p(x) = 1*(x - 7)(x - 1)(x - 2) = ([tex]x^3 - 10x^2[/tex] + 29x - 14)

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Answer:

The quantity of lobster which are sold live each year in the United States and  Canada are 46 million pounds (approximately).

Step-by-step explanation:

Given:

Each year, 183 million pounds of lobster are caught in  the United States and Canada. Twenty-five percent of this amount is  sold live.

Now, to find how  many pounds of lobster are sold live each year in the United States and  Canada.

According to question:

25% of 183 million pounds.

[tex]\frac{25}{100}\times 183[/tex]

[tex]=0.25\times 183[/tex]

[tex]=45.75[/tex]

Each year 45.75 million pounds of lobster are sold live in the United States and Canada.

Therefore, the quantity of lobster which are sold live each year in the United States and  Canada are 46 million pounds (approximately).

Answer:

Range = {-2, 1, 4, 13}

Step-by-step explanation:

Domain is the set of x-values that are allowed for the function. The values for which the function is defined.

Range is the set of y-values that are allowed for the fucntion. The values for which the function is defined.

Since domain is given as:

Domain = {-1, 0, 1, 4}

We have to plug in each of the 4 values and find the corresponding 4 values for the range. Lets do this below:

y = 3x + 1

y = 3(-1) + 1

y = -2

y = 3x + 1

y = 3(0) + 1

y = 1

y = 3x + 1

y = 3(1) + 1

y = 4

y = 3x + 1

y = 3(4) + 1

y = 13

So, the range would be:

Range = {-2, 1, 4, 13}

Answer:

x^2-3x-3=0

Step-by-step explanation:

x^2=3x+3

x^2-3x-3=0

Answer:

A. packaging costs

Step-by-step explanation:

Packaging costs woupd change based on how many products are being shipped. The other payments are fixed because they are the same amount paid regularly. Packaging would be considered a variable cost.

Internet access fee is not an example of a fixed cost.

The fixed cost definition states that businesses incur a cost that does not change positively or negatively with the number of goods sold or services given.

A fixed cost is a cost that remains constant regardless of production or sales volume.

Examples of fixed costs include monthly rent, packaging costs, and weekly fixed electricity costs.

Internet access fee is not an example of a fixed cost since it fluctuates based on usage.

The cost of internet access fee will increase or decrease depending on the amount of data used or the duration of usage.

Hence, Internet access fee is not an example of a fixed cost.

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Answer:

yes

Step-by-step explanation:

Answer:

B. 10

Step-by-step explanation:

x + y = 21

xy = 110

Rewrite first equation. x + y = 21 becomes y = -x + 21

Now substitute this new equation in the second equation.

x(-x+21) = 110

-x^2 + 21x - 110

Divide by -1

x^2 - 21x + 110

(x - 10)(x - 11)

x = 10, 11

10 is less, so the youngest daughter is 10

Answer: this equation has no solutions ,I just got it correct

Step-by-step explanation:

Answer:

No solutions

Step-by-step explanation:

Khan Academy says its right

Answer:

10/18

Step-by-step explanation:

U only asked for what is equivalent

Answer:

10/18, 15/27, 20/36, 25/45, 30/54, 35/63, 40/72, 45/81, 50/90, 55/99, 60/108.

Step-by-step explanation:

Word problem - Jose played soccer for 5 hours every afternoon for 8 days. How many hours did Jose play soccer in all?

So this problem is about Jose and the amount of time he spends playing soccer.

Next, let's pick out what we know and what we want to find out.

We know that Jose played soccer for 5 hours every afternoon for 8 days. We want to find out how many hours of soccer he played in all so we need to multiply.

We multiply the amount of time he spent playing soccer each afternoon which is 5 hours by the number of days which is 8 days.

(8) (5) = 40

This means that Jose played 40 hours of soccer in all.

Answer: OPTION D.

Step-by-step explanation:

The rate of change of a linear function is also known as "Slope".

The slope can be calculated with the following formula:

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

Choose two points on the function "R" graphed:

[tex](1,0)\\(0,-3)[/tex]

You can say that:

 [tex]y_2=-3\\y_1=0\\\\x_2=0\\x_1=1[/tex]

Substituting values into the formula, you get:

[tex]m=\frac{-3-0}{0-1}=3[/tex]

Choose two point from the table that models the function "S":

[tex](4,21)\\(6,31)[/tex]

You can say that:

 [tex]y_2=31\\y_1=21\\\\x_2=6\\x_1=4[/tex]

Substituting values into the formula, you get:

[tex]m=\frac{31-21}{6-4}=5[/tex]

Therefore, you can conclude that the function "S" has a greater rate of change than Function "R".

Answer:

D: Function S has a greater rate of change than Function R.

Step-by-step explanation:

Function S has a greater rate of change than Function R.

Function R → m =

rise

run

=

6

2

= 3. Function S → m =

change in y

change in x

=

31 − 21

6 − 4

=

10

2

= 5

Since 5 > 3, function S has a greater rate of change.

Answer:

2 scoops

Step-by-step explanation:

Lester needs to add 2 scoops of flour of 1/3 cup measure.

We have Lester who needs to add 2/3 of a cup of flour but he only has a 1/3 cup measure.

We have to find out how many scoops of flour does Lester need to add.

Assume the number of scoops = x

Then -

10x = 100

x = 10

According to question, we have -

Amount of flour needed by Lester = 2/3

Size of Cup measure = 1/3

Assume that the the number of scoops of protein powder be y.

Then -

[tex]\frac{y}{3} = \frac{2}{3} \\\\y = \frac{2}{3} \times 3\\\\[/tex]

y = 2

Hence, Lester needs to add 2 scoops of flour 1/3 cup measure.

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Answer:

R = 8.31

Step-by-step explanation:

From the table choose a corresponding amount for Volume and pressure.  Plug it into the equation and solve for R.

Choosing the second row V = 16.62 and p = .5

p = R/V

.5=R/16.62

multiply both sides by 16.62 to isolate R

16.62(.5) = R

R = 8.31

Answer:8.31

Step-by-step explanation:

Answer:

there is an infinite amount of solutions

Step-by-step explanation:

negative 6t and positive 6t cancel each other out

plug in any number for t, and you will always get 0

The cost of the nylon rope is $0.8 per meter. For $1, you can purchase 1.25 meters of nylon rope.

The given equation is p=0.8L. Here, 'p' stands for the price in dollars and 'L' is the length of the nylon rope in meters.

A. To determine the cost per meter, we look at the coefficient in front of 'L' in our equation. Here, it is 0.8, signifying that the nylon rope costs $0.8 per meter.

B. To find out the length of rope that could be bought for $1, we use the equation by setting 'p' equal to 1 and solving for 'L'. Doing this gives us 'L' = 1 / 0.8 which equals to 1.25 meters.

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The value of a and b in given expression must be [tex]\frac{2}{5} \text { and } \frac{3}{5}[/tex] respectively so that given equality becomes identity.

Need to find the value of a and b in following expression so that following equality will become identity.

[tex]\frac{(x-1)}{(x+1)(x-4)}=\frac{a}{(x+1)}+\frac{b}{(x-4)}[/tex]   ------- eqn 1

Lets Simplify Right hand Side first,

[tex]\frac{a}{(x+1)}+\frac{b}{(x-4)}=\frac{a(x-4)+b(x+1)}{(x+1)(x-4)}[/tex]

[tex]\begin{array}{l}{=\frac{a x-4 a+b x+b}{(x+1)(x-4)}} \\\\ {=\frac{a x+b x-4 a+b}{(x+1)(x-4)}} \\\\ {=\frac{(a+b) x-4 a+b}{(x+1)(x-4)}}\end{array}[/tex]

[tex]=>\frac{a}{(x+1)}+\frac{b}{(x-4)}=\frac{(a+b) x-4 a+b}{(x+1)(x-4)}[/tex]

[tex]\text {On substituting } \frac{a}{(x+1)}+\frac{b}{(x-4)}=\frac{(a+b) x-4 a+b}{(x+1)(x-4)} \text { in equation } 1 \text { we get }[/tex]

[tex]\frac{(x-1)}{(x+1)(x-4)}=\frac{(a+b) x-4 a+b}{(x+1)(x-4)}[/tex]

On multiplying both sides by (x+1)(x-4) we get

[tex]\frac{(x-1)}{(x+1)(x-4)} \times(x+1)(x-4)=\frac{(a+b) x-4 a+b}{(x+1)(x-4)} \times(x+1)(x-4)[/tex]

[tex]\Rightarrow x-1=(a+b) x-(4 a-b)[/tex]

On comparing coefficient of x and constant term separately, we get

a + b = 1 and 4a - b = 1

On adding the two equations we get

a + b + 4a - b = 1 + 1

=> 5a = 2

=> [tex]a = \frac{2}{5}[/tex]

[tex]\text {Substituting } \mathrm{a}=\frac{2}{5} \text { in equation } a+b=1, \text { we get }[/tex]

[tex]\begin{array}{l}{\frac{2}{5}+b=1} \\\\ {\Rightarrow b=1-\frac{2}{5}=\frac{3}{5}}\end{array}[/tex]

So the value of a and b in given expression must be [tex]\frac{2}{5} \text { and } \frac{3}{5}[/tex] so that given equality becomes identity.

Answer:

18

Step-by-step explanation:

I'm 90% sure I'm right but I could be wrong

4 × 18 = 72

6 × 18 = 108

72 + 108 = 180 degrees

Which means the opposite angle diagonal from 6x would also equal 108 degrees

Same thing for 4x, 72 degrees

72° + 72 ° + 108° + 108° = 360 degrees

Answer:

She bought 3 large frames and 14 small frames

1 + 2 = 21 (reversing numbers)

2 + 3 = 32 (reversing numbers) + 4 = 36

3 + 4 = 43 (reversing numbers)

4 + 5 = 54 (reversing numbers) + 4 =58

Answer:

Step-by-step explanation:

This is a sequence using reversed numbers, and alternating a summing fixed amount.

In the first one you can see that it's only numbers being reversed.

The second one is also reversing numbers but adding 4 units, 32+4=36.

The third one has the same pattern in the first one, just numbers being reversed.

The fourth has the same pattern than the second one, reversed numbers and add 4 units. So, it would be 54+4=58.

Therefore, the answer is 58.

Answer:

1 and 7/8 chapter

Step-by-step explanation:

1 ÷ 1/5 = 5

3/8 x 5 = 15/8 or 1 7/8

Answer:

1 7/8 chapters

Step-by-step explanation: