What is the remainder when the polynomial 8 x^2 +4x−3 is divided by 2x−1 ?

slope = [tex]\frac{4}{3}[/tex] and equation of line is

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

calculate the slope m using the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = 2, 7 ) and (x₂, y₂ ) = (- 1, 3 )

m = [tex]\frac{3-7}{-1-2}[/tex] = [tex]\frac{-4}{-3}[/tex] = [tex]\frac{4}{3}[/tex]

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

calculate m using the gradient formula

with (x₁, y₁ ) = (- 4, - 3) and (x₂, y₂ ) = (0, 3 )

m = [tex]\frac{3+3}{0+4}[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex]

the line crosses the y-axis at (0, 3 ) hence c = 3

y = [tex]\frac{3}{2}[/tex] x + 3 ← equation of line

The expected value of business profit is the sum of probability times profit:

... 0.2×(-10,000) + 0.4×0 + 0.3×5,000 + 0.1×8,000

... = -2000 + 1500 + 800

... = 300 . . . dollars

The expected value of the business return is slightly positve, so Claire should invest in the business.

Answer:

The answer above is correct

- 57 - 12i

distribute the parenthesis

= 81i² - 36i + 24 + 24i

[ note that i² = (√- 1 )² = - 1 ]

= - 81 - 36i + 24 + 24i ( collect like terms )

= - 57 - 12i

Answer:

D^^

Step-by-step explanation:

Edge

Divide the total amount she has by how much she needs per batch.

When dividing fractions, flip the second one over and then multiply straight across.

9/10 / 1/4 becomes: 9/10 x 4/1

9/10 x 4/1 = 36/10 = 3 6/10 = 3 3/5

She can make 3 more batches and have 3/5 of a teaspoon left over.

Answer:

The correct answer would be -15

Step-by-step explanation:

Although you have the multiplication symbols here, if we were to use subtraction as your instructions indicate, we would just complete the operations from left to right.

14 - 25 - 4

-11 - 4

-15

call that number x.

[tex]\frac{1}{2}\frac{x}{3}=10\\\frac{x}{3}=20\\x=60[/tex]

(1)

both equations express y in term of x, hence equate the right sides

- 8x = 3x ( subtract 3x from both sides )

- 11x = 0 ( divide both sides by - 11 )

x = 0

substitute x = 0 into y = 3x → y = 0

solution is : (x, y ) → (0, 0)

(2)

both equations express y in terms of x, hence equate the right sides

- 4x - 12 = - 7x ( add 7x to both sides )

3x - 12 = 0 ( add 12 to both sides )

3x = 12 ( divide both sides by 3 )

x = 4

substitute x = 4 into y = - 7x → y = - 28

solution is : (x, y ) = (4, - 28 )

The slope is 8/5 because you are increasing 8 units in the y axis and 5 units in the x direction. So the equation here would be d = 8/5t which means for every increase in t by 1, d will increase by 8/5.

MN = 6 in

add the parts of the ratio, 1 + 2 + 3 = 6

divide AB by 6 to find 1 part of the ratio

[tex]\frac{18}{6}[/tex] = 3 ← 1 part

AM = 3 in ← 1 part

MN = 2 × 3 = 6 in ← 2 parts

NB = 3 × 3 = 9 in ← 3 parts

and 3 + 6 + 9 = 18 in = AB

The correct answer is "His teacher advised it because he did not have time to tutor Euler privately." I just did the assignment and got it correct.

While in college, Euler work through advanced math books on his own because his teacher advised it because he did not have time to tutor Euler privately.    

Leonhard Euler was a renowned Swiss mathematician who made significant contributions to various branches of mathematics. While in college, Euler worked through advanced math books on his own not because of his father or the quality of education, but because his tutor, Johann Bernoulli, advised it. Bernoulli recognized Euler's talent and encouraged him to pursue mathematics independently, as Bernoulli did not have enough time to tutor Euler privately.

Answer:

Total liters of salt in [tex]2.64*10^20[/tex] liters of water is [tex]9.24*10^18[/tex].

Step-by-step explanation:

If 1 liter of water contains [tex]3.5*10^-2[/tex] amount of salt,

Then,

[tex]2.64*10^20[/tex] liters of water will contain,

[tex]3.5*10^-2[/tex] should be multiplied by [tex]2.64*10^20[/tex].

Therefore,

Total liters of salt in [tex]2.64*10^20[/tex] liters of water is [tex]9.24*10^18[/tex].

x Greater-than-or-equal-to 12

A closed circle is used on the graph.

The arrow on the graph points right.

The inequality representation is x ≤ 2.6 and has been graphed.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of before example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

The graph of inequality has a closed circle at 2.6, and the ray moves to the left.

The closed circle represents that point x = 2.6 is included.

Suppose the variable is x then x ≤ 2.6 represents the inequality.

Hence "The inequality representation is x ≤ 2.6 and has been graphed".

For more about inequality,

brainly.com/question/20383699

#SPJ2

The table can be filled in as follows:

[tex]\begin{array}{r|cccc}x(days)&1&2&3&4\\g(x)=3^x&3&9&27&81\\f(x)=3x+5&8&11&14&17\end{array}[/tex]

After 3 days, Kim's savings already exceeds Ben's, and is increasing at a faster rate. The appropriate descriptor is ...

... Kim will save more than Ben

_____

An exponential function increases faster than any polynomial function. (A linear function is a polynomial function.)

If Kim keeps up her savings for 28 days, her account balance will exceed the US Gross National Product of more than $20 trilliion. (Exponential functions tend to increase very rapidly!) Meanwhile, Ben's savings will be $89 on day 28.

_____

Please note the discrepancy in the problem statement. The verbiage says "days", but the table shows "years".

(a)

his profits increase annually by 2.5%, thus the profits each year form a geometric sequence with r = 1.025

that is 100 + 2.5 = 102.5% = 1.025

[tex]a_{n}[/tex] = 35000 × [tex](1.025)^{n-1}[/tex] ← explicit rule

(b)

[tex]a_{12}[/tex] = 35000 × [tex](1.025)^{11}[/tex] = 45923....

Profits after 12 years ≈ $46000

Charlotte will need 3 buffet menus to host 75 people!

y = - [tex]\frac{1}{2}[/tex] x - 34

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 68, 0 ) and (x₂, y₂ ) = (0, - 34 )

m = [tex]\frac{-34-0}{0+68}[/tex] = [tex]\frac{-34}{68}[/tex] = - [tex]\frac{1}{2}[/tex]

the y-intercept = (0, - 34 ) ⇒ c = - 34

y= - [tex]\frac{1}{2}[/tex] x - 34

Answer:

Y=-.5x-34

Step-by-step explanation:

this is because you can do y2-y1/x2-x1 to get slope

-34/68

Which equals one half so currently

Y=-1/2x

To get the y intercept we can look at the number when x=0 so it would be -34. So here is the equation

Y=-.5x-34

Answer:

B. x = 5 and y = -13

Step-by-step explanation:

Equating real parts, we have ...

... x + 4 = 9

... x = 9 - 4 . . . . subtract 4

... x = 5

___

Equating imaginary parts, we have ...

... yi +9i = -4i

... yi = -4i -9i = -13i . . . . subtract 9i

... y = -13 . . . . . . . . . . . divide by i

[tex](x+yi)+(4+9i)=9-4i \\\\x+4+yi+9i=9-4i\\\\x+4+(y+9)i=9-4i\\\\x+4=9 \wedge y+9=-4\\\\x=5 \wedge y=-13 \Rightarrow \text{B}[/tex]

Parallel lines have the same slope, so the slope of the new line is 1/2.

The line passes through (0,4), and this gives the y-intercept, which would equal 4.

The equation now would be: y = 1/2x + 4

( anything )² = anything × anything

5² = 5 × 5 = 25

x = [tex]\frac{3}{4}[/tex]

distribute the parenthesis on left side of equation and simplify

5x - 2x - 2 = [tex]\frac{1}{4}[/tex]

3x - 2 = [tex]\frac{1}{4}[/tex] ( add 2 to both sides )

3x = [tex]\frac{1}{4}[/tex] + 2 = [tex]\frac{9}{4}[/tex] ( divide both sides by 3 )

x = [tex]\frac{9}{4}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{3}{4}[/tex]

Answer:

i think its d

Step-by-step explanation:

Answer:

I think it is C triangle ABD and triangle ADC. I hope that helped.

Try this solution:

1. m∠A=m∠L; m∠B=m∠M and m∠C=m∠N;

2. m∠B=m∠M=35° and m∠C=m∠N=95°;

3. m∠A=m∠L=180°-(m∠B+m∠C)=180-35-95=50°

answer: 50°

Answer:

a) Error: Moving the decimal point without changing the exponent changes the value of the number. The final number reported is different from the one computed.

b) Correct work: (see below)

... Correct solution: 1.035×10¹¹

Step-by-step explanation:

a) When the decimal point is moved to the left in the mantissa, its value is divided by 10 for each place the decimal point is moved. To keep the overall value of the number the same, the power of 10 must be increased to compensate. The increase in the exponent is the number of places the decimal point is moved left.

In this problem, the decimal point is moved 1 place left, so the exponent needs to be increased from 10 to 11.

b) Correct work:

[tex]\displaystyle(7.14\cdot 10^{10})+(3.21\cdot 10^{10})=(7.14+3.21)\cdot 10^{10}\\\\=10.35\cdot 10^{10}=1.035\cdot 10^{11}[/tex]

I would add 7 to get ...

... 2x² = 16

then divide by 2 to get

... x² = 8

Now, I would take the square root, recognizing that both positive and negative values will solve the problem.

... x = ±√8

The root can be simplified, so we have ...

... x = ±2√2

_____

The above method seemed the most obvious method to me. One could use the quadratic formula, but that seems to involve more operations.

... 2x² -16 = 0 . . . . subtract 9

... x = (-0 ± √(0² -4·2·(-16)))/(2·2) . . . . put the coefficients into the formula

... x = ±(√128)/4 = ±√8 = ±2√2 . . . . . simplify the result

Sample Response/Explanation: I would use the square root property of equality. Because there is no x term, I would just add and divide to get x2 by itself. Then I would take the square root.

2/11 is 0.181818 as a decimal so closest to 0.

Answer:

The answer is the first one which is 0

A. all inherited traits of an organism.

Genes are something you inherit from a family and are passed on. Sometimes you might skip your parents and inherit a trait from a another past relative.

Answer:

about 36.3 feet

Step-by-step explanation:

Let x represent the height of the kite in feet. Then (x-22) is the horizontal distance to the kite. The Pythagorean theorem tells you the string length is related to these distances by ...

... 39² = x² + (x-22)²

... 2x² -44x -1037 = 0 . . . . rearrange to standard form

Using the quadratic formula, the positive solution is ...

... x = (-b+√(b²-4ac))/(2a) . . . . for a=2, b=-44, c=-1037

... x = (44 + √((-44)² -4(2)(-1037)))/(2·2)

... x = 11 + √639.5 ≈ 36.288

The kite is about 36.3 feet above the ground.

Answer:

A.

​Yes, the table shows a probability distribution.

Step-by-step explanation:

Given that a sociologist randomly selects single adults for different groups of​ three.  And the random variable x is the number in the group who say that the most fun way to flirt is in person.

Since sample size is only 3, x cannot be more than 3.

So x can take values as 0 1 2 3

Prob distribution is given as

x P(x)

0 0.092

1 0.338

2 0.418

3 0.152

We find that x values are from 0 to 3.  

Each probability is positive but less than 1.

Also total probability = 1

So this is a perfect probability distribution.

A.

​Yes, the table shows a probability distribution.

Answer:

a. True, b. False, c. True, d. True, e. False,  f. True

Step-by-step explanation:

Partial results of a survey about students who wear glasses are shown in the two-way table.

First we complete the table to understand options easily

               Always     Sometimes     Never     Total

Boys          25                50                52           127

Girls           35                15                 48            98

Total          60                65               100          225

Now we can solve all the options easily.

a.  225 students were surveyed   -         True

b.  25 girls always wear glasses   -          False  (35)

c. 15 girls sometimes wear glasses   -      True

d.  52 boys never wear glasses     -         True

e.  75 boys were surveyed   -                   False  (127)

f. 65 students sometimes wear glasses -True