(8x 2 −15x)−(x 2 −27x)=ax 2 +bxleft parenthesis, 8, x, squared, minus, 15, x, right parenthesis, minus, left parenthesis, x, squared, minus, 27, x, right parenthesis, equals, a, x, squared, plus, b, x If the equation above is true for all values of xxx, what is the value of b-ab−ab, minus, a ?

Answer:

y = 2x + 1

Step-by-step explanation:

From the table attached,

x          y            Difference [tex][d=(y_2-y_1)][/tex]

-1         -1                   -

0          1              1 - (-1) = 2

1           3             3 - 1 = 2    

2          5             5 - 3 = 2

Since,there is a common difference 'd' = 2

Therefore, this table represents a linear equation.

Let the equation is,

y = mx + b

where 'm' is the slope and 'b' is the y-intercept.

Two points lying on the linear equation are (-1, -1) and (0, 1)

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

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

m = 2

And y-intercept 'b' = 1 unit

Therefore, equation of the line will be,

y = 2x + 1

Answer:

54.528

Step-by-step explanation:

Answer:

Row 10 and in column F

Step-by-step explanation:

rows 1 and 3 are decreasing and we are looking for an increase so we can cross those out immediately.

However we do see a pattern in rows 2 to 4 (add 8) so if we add 8 for 3 more rows than we get 37 but add 8 more and we get 45.

from 37 to 43 is 6 more than 37 so we have 4 columns but if we add 3 more we get the 6 columns also column f.

Hope this helps!

Answer:

see below

Step-by-step explanation:

3, 12, 48, 192

We are multiplying by 4 each time  (12/3 =4)

The 5th term

192 *4 =768

The 6th term

768 *4 =3072

The th term

3072 *4 =12288

To find the common ratio, take the second term and divide by the first

2/4 = 1/2

The common ratio is 1/2

Problem 1

---------------------------

Explanation:

The first term is a = 3 and the common ratio or multiplier is r = 4. We start with 3 and multiply each term by 4 to get the next one. The nth term of this geometric sequence is

a(n) = a*(r)^(n-1)

a(n) = 3*(4)^(n-1)

Plug in n = 7 to get the seventh term

a(7) = 3*(4)^(7-1)

a(7) = 3*(4)^6

a(7) = 3*4096

a(7) = 12288

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

Problem 2

----------------------

Explanation:

To find the common ratio, we pick any term but the first one and divide it over its previous term

r = common ratio

r = (second term)/(first term) = 2/4 = 1/2 = 0.5

r = (third term)/(second term) = 1/2 = 0.5

r = (fourth term)/(third term) = 0.5/1 = 0.5

Each term is cut in half to get the next one.

Answer:

E) 45

Step-by-step explanation:

Since b is 90 degrees, and lines CB and BA are equal (as seeen with the 2 lines across them) we can assume that this angle is 45 degrees, half or 90 degrees.

Angle C is also equal to angle A

Answer:

E

Step-by-step explanation:

Using the fact that the sum of angles in a triangle is 180 degrees, we can write the following equation to solve for 3x:

3x + 3x + 90 = 180

3x + 3x = 90

2 * 3x = 90

3x = 45°

Answer:

a) 148.52

Step-by-step explanation:

If sum of two angles is 180, then they are supplementary

Ratio = 10 : 47

Smaller angle = 10x

Larger angle = 47x

10x + 47x = 180

57x = 180

Divide  both sides by 57

x = 180/57

x = 3.16

Larger angle = 47x = 47 * 3.16 = 148.52

Answer:

4.10526315789

Step-by-step explanation:

Answer: 4.10526315789

Step-by-step explanation:

━━━━━━━☆☆━━━━━━━

▹ Answer

-1 - 1/2x

▹ Step-by-Step Explanation

3x ÷ x - 4 + x - 3 ÷ 2x

Divide and Rewrite:

3 * 1 - 4 + x - 3 ÷ 2 * x

Calculate:

3 - 4 + x - 3/2x

-1 + x - 3/2x

= -1 - 1/2x

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

Step-by-step explanation:

[tex]\frac{3x}{x-4}+\frac{x-3}{2x}[/tex]

Make them into common denominators. To do so, multiply by the LCM of the denominators. The LCM of the denominators is (x-4)(2x). Thus, we multiply 2x to the first term and (x-4) to the second:

[tex](\frac{2x}{2x}) \frac{3x}{x-4}+(\frac{x-4}{x-4}) \frac{x-3}{2x}[/tex]

Simplify:

[tex]\frac{6x^2}{2x(x-4)}+\frac{x^2-7x+12}{2x(x-4)} \\=\frac{7x^2-7x+12}{2x(x-4)}[/tex]

And this cannot be simplified further (you can also distribute the denominator if preferred).

Answer:

  4 cm

Step-by-step explanation:

At 12 cm depth, the depth is 12/15 = 4/5 of the height of the container.

When the container is tipped on its side, so its height is 5 cm, the depth will still be 4/5 of the height.

  (4/5)(5 cm) = 4 cm

The depth will be 4 cm.

THIS IS THE COMPLETE QUESTION BELOW;

Rosemary walks each week for exercise. Let d represent the distance walked and h represent the number of hours spent walking.

Last week: walked 18 miles in 6 hours

This week: d = 2.5h

Which statement must be true?

A.This week, she walked a greater distance.

B. Last week, she walked a greater distance

C. This week, she walked at a faster pace.

D. Last week, she walked at a faster pace

Answer

OPTION B is correct

B)Last week, she walked a greater distance

Step-by-step explanation:

We were told Rosemary walks each week for exercise.

From the question,

✓d represented the distance walked

✓h represent the number of hours spent walking.

A)Last week: she walked 18 miles in 6 hours

Then, if she walks 18 miles in 6 hours, we can be expressed as (18miles/6hour)

= 3 miles per hour

B)This week: d = 2.5h

This implies that she she walked 2.5 miles per hour this week since the distance is expressed in miles and time in hours.

So we can conclude that last week she walked 3 miles per hour which is more greater than 2.5 miles per hour which she walks this week.

Therefore, OPTION B is correct, (Last week, she walked a greater distance)

Answer:

It's b

Step-by-step explanation:

Answer:

5x^2 +24x +1

Step-by-step explanation:

First you'll want to find the area of the larger rectangle, and then you'll subtract the area of the smaller rectangle (which is not shaded) to get your answer.

Larger Rectangle:

A = length * width

A = (2x + 3)(4x - 5) = (8x^2 - 10x + 12x - 15) = 8x^2 + 2x - 15

Smaller Rectangle:

A = length * width

A = (x - 8)(3x + 2) = (3x^2 + 2x - 24x - 16) = 3x^2 - 22x - 16

Larger Rectangle minus Smaller Rectangle:

(8x^2 + 2x - 15) - (3x^2 - 22x - 16)

5x^2 +24x +1

Answer:

Yes

Step-by-step explanation:

Answer:

y < -4

Step-by-step explanation:

-5y+6>26

subtract 6 from each side

-5y+6-6>26-6

-5y > 20

Divide each side by -5. remembering to flip the inequality

-5y/-5 < 20/-5

y < -4

Answer:

The graph will shift 9 units to the right

Sorry about my hand writing

Answer: It moves 9 units to the right

Step-by-step explanation:

It moves 9 units to the right is because if it's inside parentheses it moves right/left instead of up/down. I also talked to my Algebra Teacher about it and got it right in the final test.

Answer:

$60

Step-by-step explanation:

Answer:

60$

Step-by-step explanation:

3 gallons per hr

multiply by 4

12gl  per 4hrs

5 dl per gl

multiply by 12

60 dl per 12 gl

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

   ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                  PEACE!

Answer:

[tex]b = \frac{(d-c)}{a}[/tex]

Step-by-step explanation:

ab + c = d

Subtract c from both sides

ab + c - c = d -c

         ab = d - c

Divide both sides by 'a'

[tex]\frac{ab}{a}=\frac{d-c}{a}\\\\b = \frac{(d-c)}{a}[/tex]

Answer:

b = (d - c)/a

Step-by-step explanation:

just took this test

Answer:

Step-by-step explanation:

The shape could be divided into a rectangle and a trapezoid ( bottom part )

Let's find the area of the given shape:

Area of the given shape = [tex] \mathsf{ (l \times b) + \frac{1}{2} (b1 + b2)h}[/tex]

plug the values

[tex] \mathsf{ = (3.5 \times 9) + \frac{1}{2} (9 +9 - (5 + 2) \times 2}[/tex]

[tex] \mathsf{ = (3.5 \times 9) + \frac{1}{2} (9 + 2)(2)}[/tex]

[tex] \mathsf{ = 31.5 + \frac{1}{2} \times 11 \times 2}[/tex]

[tex] \mathsf{ = 31.5 + 11}[/tex]

[tex] \mathsf{ = 42.5 \: {units}^{2} }[/tex]

Hope I helped!

Best regards!

Answer:

Perimeter = 32 meters

Step-by-step explanation:

1 meter = 1m = 100 cm = 100 centimeters

400cm = 400/100 = 4 meters

Rectangle Perimeter = 2(legth + width)

                                   = 2(12 + 4)

                                   = 2*16

                                    = 32 meters

Answer:

C. C only

Step-by-step explanation:

Well to determine if the given graphs are functions we need to do the vertical line test to all the graphs,

A. This fails the vertical line test because the vertical line could pass through 2 points on the lines.

B. this also fails because a vertical line could pass through 2 points.

C. This passes because the vertical line doesn’t touch 2 points.

Answer:

D: 4x² - 4x + 1

Step-by-step explanation:

(2x - 1) ( 2x - 1)

4x² - 2x - 2x + 1

4x² - 4x + 1

The correct answer is d) 4x2 - 4x + 1.

The area of a square is found by squaring the side length:

(2x-1)? = (2x-1)(2x-1) = 2x*2x - 2x*1 - 2x*1 - = 1(-1) = 4 x 2 - 2x - 2x + 1 = 4x2-4x+1

Answer:

216

Step-by-step explanation:

When you say "6 raised to 3", it means you multiply 6, 3 times. Meaning:

6✖️6✖️6=216

Hope this helped!

Have a nice day:)

Answer:

Step-by-step explanation:

You gave very clear instructions on how to draw this graph, so that's what I did. What you need to remember in particular with limits is that you do not care in the least what happens AT the x value of 2, only what happens as it is being approached. Because we are asked the limit as x is approaching from the left and the right, this is a one-sided limit question. In order for the limit to exist as x approaches 2 (NOT from the left or the right), the limit would have to agree from the left and the right, and this one doesn't. Having said that there is "a horizontal line crossing the y-axis at 5 that ends at the open point (2, 5)..." is a limit approaching x from the left. Therefore,

[tex]\lim_{x \to 2^-} f(x)=5[/tex]

Having also said there is "...another horizontal line starting at the open point (2, -3) and continues to the right..." is a limit approaching x from the right. Therefore,

[tex]\lim_{x \to 2^+} f(x)= -3[/tex]

The closed point at (2, 1) is where x IS, and remember that we don't care about what happens AT x. So disregard this point in limits.

Answer:

Step-by-step explanation:

It is not perfectly linear because the difference between the y values is not constant. However, when you use the regression function on your calculator and enter the L1 values as your x's and the L2 values as your y's and use the LinReg equation, you get an r-squared value of .999900 and an r value of .999950. So it linear, with your answer being "linear, because the r value for the linear model is closest to 1".

In this question, we have two columns, you giving the time and the other the distance. We have to identify it the relationship is linear or exponential.

First, I am going to explain when we have a linear relation and when we have an exponential relation, then we observe the data and solve this question, getting the following correct answer:

linear, because the r value for the linear model is closest to 1

Linear and exponential data:

If the absolute value of the change assume close values, it is linear.

If the rates are, it is exponential.

Data:

t = 1 -> d = 530

t = 2 -> d = 1050

t = 3 -> d = 1600

t = 4 -> d = 2110

t = 5 -> d = 2650

Subtractions:

2650 - 2110 = 540

2110 - 1600 = 510

1600 - 1050 = 550

1050 - 530 = 520

Divisions(rates):

2650/2110 = 1.25

2110/1600 = 1.32

1600/1050 = 1.52

1050/530 = 1.98

The rates change considerably more than the subtractions, so it is linear relationship, and the correct option is:

linear, because the r value for the linear model is closest to 1.

For more on linear/exponential growths, you can check https://brainly.com/question/24282972

Answer:

1.) P = 8g + 50

2.) Find the attached file for the graph.

Step-by-step explanation:

Let the profit = P

And g = good sold.

Given that each yo-yo sells for $8.00

The rate or the slope of the equation will be 8

Also, it is given that they must pay a clerk $50.00 a day to sell them. A flat rate of 50 dollars is an intercept of the equation.

Using the general linear equation of

Y = mX + C

The equation for the profit the store will make in a day will be.

P = 8g + 50

Please find the attached file for the graph

Step-by-step explanation:

theanswer is 64 degrees

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

You don't get a free answer. I am, after all, a high school math teacher, so there has to be a lesson in with this.

The discriminant is part of the quadratic formula. It is:

[tex]b^2-4ac[/tex]. If this value is found to be > 0 and a perfect square, there are 2 real roots; if this value is found to >0 and not a perfect square, there are 2 complex roots; if this value is found to be = 0, then there is 1 real root with a multiplicity of 2; and finally, if this value is found to be < 0, then there are 2 imaginary roots. Also, it would help to know that, because we are dealing with the discriminant, which comes from the quadratic formula, and quadratics, by definition, have 2 solutions, you must have 2 solutions listed as the possible roots for the equation. Our equation is:

[tex]-4x^2=-8-10x[/tex] but in order to determine the a, b, and c for the discriminant, that equation has to be in standard form, set equal to 0:

[tex]-4x^2+10x+8=0[/tex]

From this we can see that a = -4, b = 10, and c = 8. Filling in the discriminant:

[tex]10^2-4(-4)(8)[/tex] which gives us a value of

100 - [4(-4)(8)] (don't forget orders of operation here!)

100 - (-128) = 100 + 128 = 228

This value is greater than 0 but is not a perfect square, so there are 2 complex roots. That means that there will be radicals in the solutions.

Answer:

408 bottles

Step-by-step explanation:

the machine can fill 136 bottles in 1 hour, 136×3=408

Answer:

408

Step-by-step explanation:

680 bottles in 5 hours

in three hours:

1 hour =680/5=136

in three hours:it will be 136*3=408

One equation you can use is y = -12x+752 and you plug in x = 8 to find y.

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

Explanation:

x = number of minutes

y = depth of the submarine

Being at sea level means the depth is y = 0. Diving 752 ft below sea level means the depth is y = 752. It's tempting to make this negative since we're below sea level, but depth values are always positive. They are simply distances you are from the surface of the water. Negative distances are never possible. So this concept might be a bit tricky to get used to.

Possibly equally confusing is the fact that the "12 ft per minute" means the slope is -12. This is because the depth is getting smaller as the submarine gets closer to the surface (aka the sub is rising).

The equation is y = -12x+752. The equation is in the form y = mx+b with m = -12 as the slope and b = 752 as the y intercept. Note how the y intercept is the starting depth value.

From here, we plug in x = 8 to find where the sub is

y = -12x+752

y = -12*8+752

y = -96+752

y = 656

The submarine's depth after eight minutes is 656 feet

----------------------

An alternative equation to use is

y = 12x-752

which is very similar to the other one used earlier. All I did was flip the sign of each term. Now y represents the height of the sub. Negative y values indicate we're below the surface of the water. The slope being positive means the submarine is going upward. The negative y intercept indicates we're starting 752 feet below sea level. Plugging in x = 8 will lead to y = -656, which you'll need to make positive (since all depth values are positive).

As you can probably guess, the change from y = -12x+752 and y = 12x-752 is simply multiplying the right hand side by -1, which explains why the signs flip (and explains how the y value sign flips as well)

Answer:

25,886.01 in²

Step-by-step explanation:

The area of shaded region = Area of the outter circle (the larger circle) - area of the inner circle (the smaller circle)

Area of a circle = πr²

Radius of larger circle = PO = 93.4 in

Area of the larger circle = 3.14*93.4² = 27,391.98 in²

Radius of smaller circle = PO - RQ = 93.4 - 71.5 = 21.9

Area of smaller circle = 3.14*21.9² = 1,505.97 in²

Area of shaded region = 27,391.98 - 1,505.97 = 25,886.01 in²

Answer:

x = 2

Step-by-step explanation:

If x is a prime number, then x + 1 is not a prime number.

A counterexample is x = 2.

x = 2

2 is prime

x + 1 = 2 + 1 = 3

3 is also prime

Answer:

Its usual speed is 25 kilometre/hour

Step-by-step explanation:

Let the usual  time duration for a journey of 300 km. = t

Let the usual speed = v

The parameters given are;

The time duration for the 300 km. journey at increased speed = t - 2

The increased speed of the passenger train = v + 5

Distance, d = Speed, v × Time, t

Therefore, we have;

v × t = 300

∴ t = 300/v

Also (v + 5)×(t - 2) = 300

Substituting the value of t = 300/v, we have;

(v + 5)×(300/v - 2) = 300

[tex]- \dfrac{2 \cdot v^2 - 290 \cdot v - 1500}{v} = 300[/tex]

Which gives;

2·v² + 10·v - 1500 = 0

Which is equivalent to v² + 5·v - 750 = 0

Therefore we have;

(v + 30)·(v - 25) = 0  whereby v = -35 or 25 km/h

v = Natural number = 25 km/hour

Therefore its usual speed is 25 kilometre/hour.