Unlimited
Factor by grouping (sometimes called the ac-method).
4x² + 3x - 10
First, choose a form with appropriate signs.
Then, fill in the blanks with numbers to be used for grouping.
Finally, show the factorization.
Form:
o
Ax? +
1 x + x - 10
Х
$
4x
+
x - l * - 10
4x?
[ x + x - 10
4x?
x - 10
Factorization:

Answer:

-2

Step-by-step explanation:

The value of c is -4, therefore the additive inverse should be added to get the answer 0

The roots of the quadratic equation x² – 2x + c = 0 are a and –b. Then the value of c is a² – 2a.

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

For which values of c does the quadratic equation

x² – 2x + c = 0 ...1

Two roots of opposite signs

Let the two roots of the opposite signs be a and –b

x = a, –b

Then we have factorized the equation,

(x + b)(x – a) = 0

On solving, we have

x² + (b – a)x – ab = 0 ...2

In comparing equation 2 with equation 1, we have

⇒  b – a = –2

⇒ b = –2 + a

and

⇒ c = a(a – 2) = a² – 2a

More about the quadratic equation link is given below.

https://brainly.com/question/2263981

Answer:

x > 1

Step-by-step explanation:

3 - 2x < 1

- 2x < 1 - 3

- 2x < - 2

Divide - 2 on both sides,

- 2x / - 2 > - 2 / - 2

x > 1

Answer:

x>1

Step-by-step explanation:

Hence, x>1

Step-by-step explanation:

Given that he dimension is

9 1/2 inches wide

and 14 inches wide.

half way from 9.5 inches is

4.75in

half way from 14 inches is

7in

Therefore he put the picture at 4.75in from the top and 7in from the sides

Answer:

a.[tex]-7 < x < 7[/tex]
b.[tex]-12 < x < 6[/tex]
c. Two answers are: y < -3 or y > 19
d. Two answers are x ≤ -17/3 or x ≥ 19/3
e. -4 ≤ y ≤ 5/2

Step-by-step explanation:

Given the following questions:

Question one:

[tex]|x| < 7[/tex]
x is less than 7
[tex]=-7 < x < 7[/tex]

Question two:

[tex]|x+3| < 9[/tex]
[tex]x+3 > -9[/tex]
[tex]3-3=0[/tex]
[tex]-9+-3=-12[/tex]
[tex]x > -12[/tex]

[tex]x+3 < 9[/tex]
[tex]3-3=0[/tex]
[tex]9-3=6[/tex]
[tex]x < 6[/tex]
x is greater than -12, while less than 6
[tex]-12 < x < 6[/tex]

Question three:

[tex]|y-8| > 11[/tex]
[tex]y-8 < -11[/tex]
[tex]-8+8=0[/tex]
[tex]-11+8=-3[/tex]
[tex]y < -3[/tex]

[tex]y-8 > 11[/tex]
[tex]-8+8=0[/tex]
[tex]11+8=19[/tex]
[tex]y > 19[/tex]
Two answers are: y < -3 or y > 19

Question four:

|3x - 1| ≥ 18
3x - 1 ≤ -18
-1 + 1 = 0
-18 + 1 = -17
3x ≤ -17
x ≤ -17/3

3x - 1 ≥ 18
-1 + 1 = 0
18 + 1 = 19
3x ≥ 19
x ≥ 19/3
Two answers are: x ≤ -17/3 or x ≥ 19/3

Question five:

|4y + 3| ≤ 13
|4y + 3| ≤ 13 = -13 ≤ 4y + 3 ≤ 13
-13 ≤ 4y + 3 ≤ 13
4y + 3 ≥ -13
3 - 3 = 0
-13 + - 3 = -16
4y ≥ -16
4 ÷ - 16 = -4
y ≥ -4

4y + 3 ≤ 13
3 + -3 = 0
13 - 3 = 10
4y ≤ 10 = 10/4 ÷ 2 = 5/2
y ≤ 5/2
-4 ≤ y ≤ 5/2

Hope this helps.

Answer:

for the 1st one, m=10 and b=2 because from the word problem it says it starts at 10 which would be 10 on the y axis being where the line would pass through and spending 2 a week would be the slope because he is losing 2 per week its a negative slope so y=10x-2.

for the second one m=48 and b=44 its just like the last one but with different numbers but comment if you want me to explain it but the answer is y=48x-44.

The mean measurement is the average value of the leaves

The possible measurement of the 6th leaf is 13.3

The dataset is given as:

14.2, 13.8, 12.6, 13.4 and 11.5

Sort the data elements

11.5, 12.6, 13.4, 13.8 and 14.2

Calculate the mean

[tex]\bar x = \frac{11.5 + 12.6 + 13.4 + 13.8 + 14.2}{5}[/tex]

[tex]\bar x = \frac{65.5}{5}[/tex]

[tex]\bar x = 13.1[/tex]

So the mean is 13.1 and the median is 13.4

For the mean to increase, the 6th dataset must be greater than 13.1.

For the median to decrease, the 6th dataset must be less than 13.4

From the list of given options, the element that satisfy the above highlights is 13.3

Hence, the possible measurement of the 6th leaf is 13.3

Read more about mean and median at:

https://brainly.com/question/14532771

the sum of two complementary angles is 90°

so 28 + ? = 90

? = 62°

here'

complementry angle means those whose sum is 90

here one angle is given so,

another angle =90-28

that is 72.ans

Answer:

283024

Step-by-step explanation:

First do 532^7

The answer is 12060947473224100000

Next, do 532^-8

The answer is 1/6416424055755230000000

Multiply that number by the first number

(I don't want to type that all out again)

The answer is 1/532

Now, do the last problem. 532^3

The answer is 150568768

Multiply that number by 1/532

The answer is 283024

Hope I helped :)

Please consider Brainliest :)

(it took me so long to type that)

Answer:

Option b - $163.07

Step-by-step explanation:

Given :  A loan of $7,500 with an 11% interest rate compounded monthly over a period of 5 years.

To find : Monthly payment

Solution : Formula to find monthly payment

Monthly Payment = Amount / Discount factor

Discount factor

where ,

Amount = $7500

Rate= 11%=0.11

Time = 5 years

Now, put i and n in Discount factor ,

Monthly payment,

Therefore, Option b is correct monthly payment = $163.07

Answer:

The answer is $163.07

Step-by-step explanation:

To find the monthly payment:

[tex]i = \frac{0.11}{12} = 0.0091[/tex]

Time = 5 years

5 x 12 = 60

Discount factor

[tex]D = \frac{1-(1 + i) -^{n}}i[/tex]

[tex]D = \frac{1 - (1+ 0.009)-^{60} }{0.009} \\[/tex]

[tex]D = \frac{0.421}{0.009} = 46.77[/tex]

Monthly payment

[tex]\frac{7500}{46.77} = $163.07[/tex]

The correlation that exists between the temperature and the number of fruits sold is positive but is almost negligible.

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

A result of zero indicates no relationship at all, therefore, independent variable.

We know that the correlation coefficient is given by the formula,

[tex]r =\dfrac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}[/tex]

r = correlation coefficient

[tex]x_{i}[/tex] = values of the x-variable in a sample

[tex]\bar{x}[/tex] = mean of the values of the x-variable

[tex]y_{i}[/tex] = values of the y-variable in a sample

[tex]\bar{y}[/tex] = mean of the values of the y-variable

Calculate the value of [tex](x_i-\bar{x})(y_i-\bar{y}),\ (x_i-\bar{x})^2,{ \rm and}\ (y_i-\bar{y})^2[/tex] each separately, and then find the sum of them as shown below, therefore, the formula can be written as,

[tex]r =\dfrac{571.5}{261.5\times 1566.833333}= 0.0014[/tex]

Hence, the correlation that exists between the temperature and the number of fruits sold is positive but is almost negligible.

Learn more about Correlation Coefficients:

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Answer:

1. positive

2. 2.2

3. 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

First we make the denominators the same:

2/3 = 10/15

2/5 = 6/15

Ratio: 6/15 : 10/15

Have a great day!!

Please rate and mark brainliest!!

Answer: D

Step-by-step explanation:

x=32 degrees

Step-by-step explanation:

Angles in equilateral triangles are equal, each angle is 60 degrees

2x-4 =60

+4

2x = 64

÷2

x = 32

Also, y will be 12 (12x5=60)

Hope this helps!

Answer:

The last one

Step-by-step explanation:

K so first look at y intercept which is +5, so we eliminate A and C, then the graph opens up so the b in ax+bx+c has to be positive which is D

the point ( 0 ; 5 ) in on the curve

so f(0) = 5

choice between :

x² - 2x + 5 or x² + 2x + 5 then :

we have the point (1 ; 4)

with x² - 2x + 5

f(1) = 1² - 2*1 + 5 = 1 - 2 + 5 = 4

so it's correct

=> x² - 2x + 5 is the right one

Answer:

y = -2(x + 1)^2 + 8

Step-by-step explanation:

The equation of a parabola can be written in the form;

y = a(x-h)^2 + k

where a is the multiplier (h,k) is the vertex

so h = -1 and k = 8

Plug in these values

y = a(x + 1)^2 + 8

So to get the value of a, we use the point where the parabola passes through which is the point (1,0)

Simply substitute the values of x and y

0 = a(1 + 1)^2 + 8

0 = a(2)^2 + 8

-8 = 4a

a = -8/4

a = -2

So therefore the equation of the parabola is ;

y = -2(x + 1)^2 + 8

The required equation of parabola with given vertex and point of passing is [tex]y=-2(x+1)^{2}+8[/tex].

Given data:

The vertex of parabola is, (-1, 8).

The vertex is passing through (1, 0).

We know that standard equation parabola is,

[tex]y=a(x-h)^{2}+k[/tex]

Here, a is any multiplier, h and k are the vertices.

From the given problem,

h = -1

k = 8

So substituting the values as,

[tex]y=a(x-(-1))^{2}+8\\y=a(x+1)^{2}+8[/tex]..............................................(1)

To obtain the value of a, we use the point where the parabola passes through which is the point (1,0). Here, x = 1 and y =0.

So,

[tex]0=a(1+1)^{2}+8\\\\a = -2[/tex]

Substitute the value of a in equation (1) as,

[tex]y=(-2)(x+1)^{2}+8\\\\y=-2(x+1)^{2}+8[/tex]

Thus, the required equation of parabola is  [tex]y=-2(x+1)^{2}+8[/tex].

learn more about the parabola here:

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Answer:

8

Step-by-step explanation:

x = -2

the y to (-2,y) is 8

Answer:

b = 100°

should be the answer

I know it is probably to late for your answer but if you are on Solving and Reasoning with Complex Numbers: Tutorial in Edmentum, then the answer for part D on the first lesson activity is this word for word.

This equation generalizes the patterns seen in part D, where a and b represent real numbers:

(a + bi)(a − bi) = a2 + b2.

Hope this helps good luck

Answer:

Your answer should be 4:9

Step-by-step explanation:

Good luck.

Answer:

c

Step-by-step explanation:

let the other angle be x degree

bigger angle = x +36°

According to the question,

x+36° + x° = 180°

=> 2x = 180–36

=> x = 144/2

=> x = 72°

Measure of the bigger angle = x + 36

= 72° + 36°

= 108°

Answer:

multiply both sides by 3

Step-by-step explanation:

i would multiply 3 on both sides to cancel the fraction out so i dont have to work with fractions

Answer:

multiply both 3 sides

Step-by-step explanation:

real simple m

Answer:

car

Step-by-step explanation:

Answer:

-1.6

Step-by-step explanation:

Because the additive inverse of any positive number is it's negative number

Flipping the bulbs is an illustration of sequence and patterns

17 bulbs would remain on.

The sequence of turning the bulbs off and on, would change the state of the bulbs until the 300th process.

While changing the state of the bulbs, the bulb at the perfect square positions would remain on.

There are 17 perfect square numbers between 1 and 300 (inclusive)

Hence, 17 bulbs would remain on.

Read more about sequence and patterns at:

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Answer:

[tex]x=3,\:y=7[/tex]

Step-by-step explanation:

[tex]\begin{bmatrix}8x+3y=45\\ 2x+3y=27\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}x=\frac{45-3y}{8}[/tex]

[tex]\begin{bmatrix}2\cdot \frac{45-3y}{8}+3y=27\end{bmatrix}[/tex]

[tex]\begin{bmatrix}\frac{45+9y}{4}=27\end{bmatrix}[/tex]

[tex]y=7[/tex]

[tex]\mathrm{For\:}x=\frac{45-3y}{8}[/tex]

[tex]\mathrm{Substitute\:}y=7[/tex]

[tex]x=\frac{45-3\cdot \:7}{8}[/tex]

[tex]x=3[/tex]

[tex]\mathrm{The\:solutions\:are}:[/tex]

[tex]x=3,\:y=7[/tex]

Answer:

17

Step-by-step explanation:

5x2=10

8 1/2x2=17

Answer: answer witten in the picture attached to this......