Let $x$ be a value such that $8x^2 + 7x - 1 = 0$ and $24x^2+53x-7 = 0.$ What is the value of $x$? Express your answer as a simplified common fraction.

The formula of a slope:

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

We have the points (6, 2) and (9, r), the slope m = -1. Substitute:

[tex]-1=\dfrac{r-2}{9-6}\\\\-1=\dfrac{r-2}{3}\qquad\text{multiply both sides by 3}\\\\-3=r-2\qquad\text{add 2 to both sides}\\\\\boxed{r=-1}[/tex]

Answer:

The correct option is 1.

Step-by-step explanation:

Let the amount invested in utility bound be x. So, the amount invested in saving account is (10000-x).

It is given that the yearly income from the two investments is same.

[tex]\text{9\% of x}=\text{6\% of (10000-x)}[/tex]

[tex]\frac{9}{100}\times x=\frac{6}{100}\times (10000-x)[/tex]

[tex]\frac{9x}{100}=600-\frac{6x}{100}[/tex]

[tex]\frac{9x}{100}+\frac{6x}{100}=600[/tex]

[tex]\frac{15x}{100}=600[/tex]

[tex]15x=60000[/tex]

[tex]x=4000[/tex]

The amount invested in utility bound is $4000.

[tex]10000-x=10000-4000=6000[/tex]

The amount invested in saving account is $6000.

Answer:

B 2 < x < 6

Step-by-step explanation:

six times an integer is between 12 and 36.  Between does not include so we use <   not ≤

12 < 6x < 36

Divide all sides by 6

12/6 < 6x/6 < 36/6

2 < x < 6

Answer:

If there are 31 days in this month, it is January

Step-by-step explanation:

The converse of a statement is when you switch the conclusion with the hypothesis. If you do this, you get:

If there are 31 days in this month, it is January.

This is false btw. December has 31 days, and it's not January

The converse of the statement 'If it is January, then there are 31 days this month' is 'If there are 31 days this month, then it is January'. This is done by reversing the order of the 'if' (antecedent) and 'then' (consequent) parts of the statement.

The converse of the conditional statement 'If it is January, then there are 31 days this month.' is 'If there are 31 days this month, then it is January.'

In a conditional statement, the order of the 'if', known as the antecedent, and the 'then', known as the consequent, makes up the statement's direction. The converse of a conditional statement simply flips or reverses this order. It's important to note that the truth of the original statement does not guarantee the truth of its converse.

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Answer:

13n - 6 is your correct answer

The written statement 'six less than the product of 13 and a number' is translated into the algebraic expression 13n - 6, where 'n' represents the unknown number.

The student is asking to translate a written statement into a mathematical expression using a variable. The statement is 'six less than the product of 13 and a number' and we are using the variable n to represent the unknown number. To form this expression, first consider the 'product of 13 and a number', which is written as 13n. Then, to represent 'six less than' this product, you would subtract 6 from it, resulting in the expression 13n - 6.

It would have taken Homer 8 hours and 24 minutes to fix the deck himself.

Given that Homer and Mike were replacing the boards on​ Mike's old deck, and Mike can do the job alone in 1 hour less time than Homer, and they worked together for 6 hours until Homer had to go home, and Mike finished the job working by himself in an additional 6 hours, to determine how long would it have taken Homer to fix the deck​ himself, the following calculation has to be done:

Therefore, it would have taken Homer 8 hours and 24 minutes to fix the deck himself.

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Answer:

13 3/4 servings

Step-by-step explanation:

Stephen has  1  1/10 kg of tofu.

He uses 2/25 kg in each serving.

We will divide to figure out how many servings he can make

1 1/10 ÷ 2/25

We need to change the mixed number 1 1/10 to an improper fraction

1 1/10 = (10*1 + 1) /10 = 11/10

11/10 ÷2/25

Copy dot flip

11/10 * 25/2

275/20

Divide the top and bottom by 5

55/4

We will change this back into an improper fraction

4 goes into 55   13 times   with 3 left over

13 3/4

He can make 13  3/4 servings

Answer:

He translated them the wrong way.

It should of gone up 2 and right 2 not down 2 and left 2.

The correct coordinates would be (A' = 3,0) (B' = 3, -3) (C' = 2, -2)

Please mark brainliest would rly help.

Step-by-step explanation:

Answer:

A. x > 0

Step-by-step explanation:

As long as the number (x) is a number greater than 0, the inequality would be correct. Take for example, 1 (a number greater than 0)

4^1 = 4; 2^1 = 2; 4 > 2

Another example is 2

4^2 = 16; 2^2 = 4; 16 > 4

etc.

~

Answer:

A. x > 0

Step-by-step explanation:

see graph

4^x > 2^x

Replace 4 with 2^2

2^2^x > 2^x

a^b^x = a^(b*c)   so

2^ 2x > 2^x

If the bases are the same, the exponents must keep the same ratio

2x>x

This is true if x>0

Answer:

y = [tex]\frac{-2}{3} + 10[/tex]

Step-by-step explanation:

A line perpendicular to 2x = 1 - 3y has the same gradient (or slope). To find this we must isolate the y:

Move the -3y over to the other side making it a +3y:

3y + 2x = 1

Move the +2x over to the other side making it a -2x:

3y = -2x + 1

Divide everything by 3:

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

So the gradient is [tex]\frac{-2}{3}[/tex]

Now as the points are given, (9 , 4)

The equation of the line so far is:

y = mx + c

4 = [tex]\frac{-2}{3}[/tex](9) + c

4 = -6 + c

Move the -6 over making it a +6:

4 + 6 = c

c = 10

So that means the full equation is:

y = [tex]\frac{-2}{3} + 10[/tex]

Answer:

Harry is 2 years old and Jim is 6 years old.

Step-by-step explanation:

set up the equations. let harry be h and jim be j.

h+4=j

j+2=2(h+2)

plug in the j from the first equation.

you should get h=2 (harry is two years old)

if h+4=j, 2+4=j. so j=6 (jim is six years old)

Answer:

Harry is 2 years old and Jim is 6 years old.

Step-by-step explanation:

Let x years be Harry's age now and y years be Jim's age now.

1. In 4 years, Harry’s age will be x+4 years. If in 4 years, Harry’s age will be the same as Jim’s age is now, then

[tex]x+4=y.[/tex]

2. In 2 years, Jim's age will be y+2 years and Harry's age will be x+2 years. If in 2 years, Jim will be twice as old as Harry will be, then

[tex]y+2=2(x+2).[/tex]

Solve the system of two equations:

[tex]\begin{array}{l}x+4=y\\y+2=2(x+2).\end{array}[/tex]

Substitute y=x+4 into the second equation:

[tex]x+4+2=2(x+2),\\ \\x+6=2x+4,\\ \\6-4=2x-x,\\ \\x=2[/tex]

and [tex]y=2+4=6.[/tex]

Answer:

4 (x + 1)

Hope That Helps!

Answer:

In the attachment!!

Hope this helps!!

Answer:

The answer is 2.4

Step-by-step explanation:

Divide 1.2x10^5 by 4.9x10^3 and you should get the answer of 2.44.

Hope this helps

Answer:

i think the answer is 85

hope this helps

Step-by-step explanation:

Answer:

85 is a composite number

Step-by-step explanation:

3 = 1 × 3

5 = 1 × 5

19 = 1 × 19

71 = 1 × 19

85 = 1 × 85 = 5 × 17

The x in the formula is the depth.

You are given two different depths, replace x with the depths, solve for T, then subtract the to find the difference:

At 1200 meters the temperature is:

T = 4500/1200 = 3.75 degrees

At 3750 meters the temperature is:

T = 4500 / 3750 = 1.20 degrees.

The difference in temperature between the two depths is:

3.75 - 1.20 = 2.55 degrees C.

Answer:

B $13

Step-by-step explanation:

Julie has 16.73  That is approximately 17 dollars

She buys a purse that is 4.12.   That is approximately 4 dollars

17 -4 = 13

She will have approximately 13 dollars left

The length of the third side can be any value in the interval:

4 < x  <10

For any triangle whose side lengths are A, B, and C, the triangular inequality says that the sum of the lengths of any two sides must be larger than the length of the other side, then:

A + B > C

A + C > B

C + B > A

Here we know that the side lengths are 3, 7 and x.

Then we can write:

3 + 7 > x

x + 3 > 7

x + 7 > 3

Solving these, we can write:

10 > x

x > 7 - 3 = 4

x > 3 - 7 = -4

Then the range of possible values of the third sides are:

4 < x  <10

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Answer:

A movie ticket costs $9.

A snack costs $2.

Step-by-step explanation:

So the word problem is asking us to find the cost of a movie ticket and a snack, therefore we will label the cost of a movie ticket as "m" and the cost of a snack as "s".

In the word problem we are given two equations:

2m (movie ticket cost) + 3s (snack cost) = $24

&

3m (movie ticket cost) + 4s (snack cost) = $35

To figure out the cost of a snack we need to get the variables in both equations to be "opposites", so we use substitution.

We multiply everything in the first equation by 3 which gives us:

6m + 9s = $72

And in order to make the other equation the opposite we multiply everything in the second equation by -2 giving us:

-6m + -8s = $-70

Now we add both equations since the variables for m are opposites.

    6m + 9s = $72

+  -6m + -8s = $-70

   s = $2

Now we put s back into one of our original equations and to do that I am going to use 2m + 3s = $24

2m + 3s (2) = $24   ----> 2m + 6 = $24

Now, in order to get the value of m, we need to get rid of the 6 by  subtracting 6 from both sides of the equation.

2m= $18

Now we divide by 2 on both sides to get m by its self.

m= $9

And to check to make sure we are right:

2m (9) + 3s (2) = $24

$18 + $6 = $24 (true)

A movie ticket costs 9$ and a snack costs 2$.

A movie ticket costs $6 and a snack costs $4.

To solve this problem, we can set up a system of linear equations based on the information given. Let's denote the cost of a movie ticket as t and the cost of a snack as s.

From the question, we have two equations:

1. For two movie tickets and three snacks, the total cost is $24:

[tex]\[ 2t + 3s = 24 \][/tex]

2. For three movie tickets and four snacks, the total cost is $35:

[tex]\[ 3t + 4s = 35 \][/tex]

Now, let's solve this system of equations. We can start by isolating one of the variables in one of the equations. For example, we can solve the first equation for s:

[tex]\[ 2t + 3s = 24 \][/tex]

[tex]\[ 3s = 24 - 2t \][/tex]

[tex]\[ s = \frac{24 - 2t}{3} \][/tex]

Now we can substitute this expression for s into the second equation:

[tex]\[ 3t + 4\left(\frac{24 - 2t}{3}\right) = 35 \][/tex]

Multiplying through by 3 to clear the fraction, we get:

[tex]\[ 9t + 4(24 - 2t) = 105 \][/tex]

[tex]\[ 9t + 96 - 8t = 105 \][/tex]

[tex]\[ t = 105 - 96 \][/tex]

[tex]\[ t = 9 \][/tex]

Now that we have the cost of a movie ticket, we can substitute [tex]\( t = 9 \)[/tex] back into our expression for s:

[tex]\[ s = \frac{24 - 2(9)}{3} \][/tex]

[tex]\[ s = \frac{24 - 18}{3} \][/tex]

[tex]\[ s = \frac{6}{3} \][/tex]

[tex]\[ s = 2 \][/tex]

Therefore, a movie ticket costs $6 and a snack costs $4.

The complete question is

A group of friends bought 2 movie tickets and 3 snacks for a total of $24. Another group bought 3 movie tickets and 4 snacks for a total of $35. What is the cost of a movie ticket and the cost of a snack?

Answer:

On her 60th birthday, she would have earned $83048.5.

Step-by-step explanation:

The formula to calculate the compound interest is:

[tex]A=P(1+\frac{r}{100} )^{n}[/tex]  --- (1)

where A is Principal and interest, r is the rate of interest and n is the number of years compounded.

For our problem,

P = 25000,

r = 0.05 and

n = 60 - 30 = 30

Substitute these values in (1), we get,

[tex]A=25000(1+0.05)^{30}[/tex]

[tex]=25000(1.05)^{30}[/tex]

= 25000(4.32194)

= 108048.5

Compound Interest = Amount - Principal

= 108048.5 - 25000

= 83048.50

Hence, on her 60th birthday, she would have earned $83048.5.

Answer:

The interest in 30 years be 8305000 cent.

Step-by-step explanation:

Formula

[tex]Amount = P(1+r)^{t}[/tex]

Where P is the principle , r is the rate of interest in the decimal form and t is the time.

As given

On her 30th birthday, Ann Marie opened a new compound interest account with $25,000.

The account pays 5% interest annually.

If Ann Marie retires on her 60th birthday and close the account at that time .

P = $25000

5% is written in the decimal form.

[tex]= \frac{5}{100}[/tex]

= 0.05

r = 0.05

As  Ann Marie open account on his 30 th birthday and close it at its 60 th birthday .

Thus

t = 60 - 30

t = 30 years

Put all the value in the formula

[tex]Amount = 25000(1+0.05)^{30}[/tex]

[tex]Amount = 25000(1.05)^{30}[/tex]

[tex]Amount = 25000\times 4.322 (Approx)[/tex]

[tex]Amount = \$ 108050[/tex]

As

Amount = Principle + Interest

Putting the value

$108050 = $25000+ Interest

$108050 - $25000 = Interest

Interest = $83050

As 1 dollar = 100 cent

Convert $83050 convert into cent .

$83050 = 83050 × 100

             = 8305000 cent.

Therefore the interest in 30 years be 8305000 cent.

Answer:

10% discount

Step-by-step explanation:

3x+4/5

-24+4/5=-20/5=-4

-4-4=-8.

-8+2(-8)=-8-16=-24 or B.

Answer:

- 2  1/10

Step-by-step explanation:

-2/5 -x -9/10

Let x = 4/5

-2/5 - 4/5 - 9/10

Combine like terms

-6/5 - 9/10

Get a common denominator of 10

-6/5 * 2/2 - 9/10

-12/10 - 9/10

-21/ 10

Change this to a mixed number

10 goes into 21   2 times with 1 left over

-2 1/10

Answer:

- 2  1/10

Step-by-step explanation:

Answer:

x = 2 or x = 1 or x = -1 or x = 3/2   thus from the answers given only A: applies

Step-by-step explanation:

Solve for x over the real numbers:

2 x^4 - 7 x^3 + 4 x^2 + 7 x - 6 = 0

The left hand side factors into a product with four terms:

(x - 2) (x - 1) (x + 1) (2 x - 3) = 0

Split into four equations:

x - 2 = 0 or x - 1 = 0 or x + 1 = 0 or 2 x - 3 = 0

Add 2 to both sides:

x = 2 or x - 1 = 0 or x + 1 = 0 or 2 x - 3 = 0

Add 1 to both sides:

x = 2 or x = 1 or x + 1 = 0 or 2 x - 3 = 0

Subtract 1 from both sides:

x = 2 or x = 1 or x = -1 or 2 x - 3 = 0

Add 3 to both sides:

x = 2 or x = 1 or x = -1 or 2 x = 3

Divide both sides by 2:

Answer:  x = 2 or x = 1 or x = -1 or x = 3/2

[ Answer ]

$25 An Hour

[ Explanation ]

We already know the total amount he has right now. We also know how long he has worked at his job. To solve, we can use division.

Divide 1500 by 60

1500 / 60

= 25

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Answer:

1500 ÷ 60 = 25

Step-by-step explanation:

He worked for 60 hours and got $1500, 1500 divided by 60 equals 25 dollars each hour.

Answer: y > x, y > 2

The horizontal line goes through 2 on the y axis. This boundary line is represented by the equation y = 2, since every point on this line has a y coord of 2. The shading above it means that the inequality is y > 2. Every point in the shaded region of y > 2 has a y coord that is larger than 2.

The other inequality is y > x because we shade above the dashed boundary line y = x, which is that slanted dashed line.

Combining the two regions of y > 2 and y > x leads to what is shown.

Final answer:

The question regarding systems of inequalities is incomplete, but linear inequalities like y < x or y > 2 can be graphically represented. The same is true for linear equations, with options A, B, and C all depicting linear forms.

Explanation:

The question which system of inequalities is shown seems to be missing some context or parts, but in general, inequalities can be represented on a graph and used to describe the relationship between variables. When dealing with linear inequalities, such as y < x or y > 2, these can be shown graphically with a line dividing the plane into two regions: one where the inequality is true and the other where it is false. For instance, y < x would be represented by a line that slopes upward to the right, and the region below this line (where y is less than x) is shaded. Similarly, for y > 2, a horizontal line is drawn at y=2, and the area above this line is shaded, indicating where y is greater than 2.

When looking at linear equations, all the options A. y = -3x, B. y = 0.2 + 0.74x, and C. y = -9.4 - 2x are indeed linear, as they can all be written in the form y = mx + b, where m and b are real numbers and represent the slope and y-intercept of the line, respectively.

Answer:

t = 1 3/7 hours

Step-by-step explanation:

For plane 1

distance = rate *t

d1 = 40 *t

For plane 2

distance = rate * time

d2 = 100 * t

We know that d1+d2 = 200  (the planes will meet)

We know that the times will be the same because the leave at the same time.

Substitute in d1 =40t and d2 = 100t into  d1+d2 = 200

d1+d2 = 200

40t + 100t = 200

Combine like terms

140t = 200

Divide each side by 140

140t/140 = 200/140

t= 200/140

t= 20/14

t = 10/7

t = 1 3/7 hours

Answer:

1 3/7 hours is the answer :)

Step-by-step explanation: