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Answer:

y - 1 = (3/5)x

Step-by-step explanation:

First find the slope of this line.  As we move from (0, -2) to (5, 1), x (the 'run') increases by 5 and y (the 'rise') increases by 3.  Thus, the slope of this line is m = rise / run = 3/5.

Using the point-slope formula for the equation of a straight line:

y - 1 = (3/5)(x - 5), or

y - 1 = (3/5)x                This can also be written as 5y - 5 = 3x, or

y = (3/5)x + 1

Answer:

[tex]B.\ x^3 - 2x^2 - 4x + 1[/tex]

Step-by-step explanation:

Given

Polynomials A to D

Divisor: x - 2

Required

Which of polynomial A - D has a remainder of -7

We start by equating the divisor to 0

[tex]x - 2 = 0[/tex]

Make x the subject of formula

[tex]x = 2[/tex]

Next is to substitute 2 for x in the polynomials to get the remainder;

[tex]A.\ 4x^3 + 2x^2 + 5[/tex]

[tex]4(2)^3 + 2(2)^2 + 5[/tex]

Open Brackets

[tex]4 * 8 + 2 * 4 + 5[/tex]

[tex]32 + 8 + 5[/tex]

[tex]Remainder = 45[/tex]

[tex]B.\ x^3 - 2x^2 - 4x + 1[/tex]

[tex](2)^3 - 2(2)^2 - 4(2) + 1[/tex]

Open Brackets

[tex]8 - 2 * 4 - 4 * 2 + 1[/tex]

[tex]8 - 8 - 8 + 1[/tex]

[tex]Remainder = -7[/tex]

[tex]C.\ 3x^2 + 6x - 2[/tex]

[tex]3(2)^2 + 6(2) - 2[/tex]

Open Brackets

[tex]3 * 4 + 6 * 2 - 2[/tex]

[tex]12 + 12 - 2[/tex]

[tex]Remainder = -2[/tex]

[tex]D.\ -2x^3 + 4x^2 + 3x - 2[/tex]

[tex]-2(2)^3 + 4(2)^2 + 3(2) - 2[/tex]

Open Brackets

[tex]-2 * 8 + 4 * 4 + 3 * 2 - 2[/tex]

[tex]-16 + 16 + 6 - 2[/tex]

[tex]Remainder = 4[/tex]

From the calculations above, the polynomial with a remainder of -7 when divided by [tex]x - 2[/tex] is [tex]B.\ x^3 - 2x^2 - 4x + 1[/tex]

The value of the polynomial [tex]x^3-2x^2-4x+1[/tex] is -7 at x = 2. So, option B is correct.

Important information:

According to the Remainder Theorem, if a polynomial is p(x) is divided by (x-c), then the remainder is p(c).

If polynomials have a remainder of -7 when divided by x – 2. So, the value of the polynomial must be -7 at x = 2.

Substitute x = 2 in the first polynomial.

[tex]4(2)^3+2(2)^2+5=45\neq -7[/tex]

Substitute x = 2 in the second polynomial.

[tex](2)^3-2(2)^2-4(2)+1=-7[/tex]

Substitute x = 2 in the third polynomial.

[tex]3(2)^2+6(2)-2=22\neq -7[/tex]

Substitute x = 2 in the fourth polynomial.

[tex]-2(2)^3+4(2)^2+3(2)-2=4\neq -7[/tex]

Only the value of the second polynomial is -7 at x = 2. Therefore, the correct option is B.

Find out more about 'Remainder Theorem' here:

https://brainly.com/question/4515216

Answer:

first term a=4

Step-by-step explanation:

Sum of the first 6 terms S6 = 15624

common ratio r= 5

n= 6

first term a=?

Formula: S6= a(r^n-1)/r-1

15624 = a( 5^6-1)/5-1

15624 = a(15625-1)/4

15624= a( 15624)÷4

15624= 15624a÷4

Cross multiply

15624×4 = 15624a

62496 = 15624a

divide both sides by 15624

62496÷15624 = 15624a÷15624

4 = a

a= 4

Answer:

Required angle measures 39°

Step-by-step explanation:

Let's say, x measures the angle between the hypotenuse and the common base of two triangles.

Sin(x) = 5/8

x = 39°

This angle is complementary to the angle other than theta (let's say y) in the required triangle.

90 - x = y and 90 - theta = y

>>> Theta = x

Best Regards!

Answer:

A and e

Step-by-step explanation:

Answer:

Please see details below

Step-by-step explanation:

Notice that since you have drawn mid-segments for all sides of the triangles, the three smaller triangles generated at the vertices, are all similar triangles to the large one (XYW).

Let's look at what happens with the smaller triangles:

Triangle QXR is similar to XYW, since the side QR has to be parallel to the big side WY. By construction, the side XQ is half of the side XW, therefore all sides of the smaller triangle *QXR formed must maintain the same proportion. Then side QR is half of side WY which makes side WY = 2 (2.93 cm) = 5.86 cm.

The same reasoning is valid when we compare triangle RYS with the larger triangle XYW: side RS of the small triangle is half of side XW of the large triangle, That is: XW = 2 (2.04 cm) = 4.08 cm

Similarly, small triangle SWQ is similar to XYW, and the side QS has to be half of side XY, therefore side XY = 2 (2.28 cm) = 4.56 cm

Then, the perimeter of triangle XYW is:

XY + YW + XW= 4.56 cm + 5.86 cm + 4.08 cm = 14.5 cm

Answer:

I think it is 5

Step-by-step explanation:

Answer:

It's (B) Rhombus and (D) Rectangle

Step-by-step explanation:

Answer:

probability of getting no heads: 1/ 8

probability of at least two tails: 1/4

Step-by-step explanation:

To calculate the probability of getting no heads, multiply the probability of not getting heads for each coin. A coin has two sides: heads and tails; the probability of not getting heads would be 1/2.

1. Multiply the probabilities for each coin

1/2 · 1/2 · 1/2 = 1/8

To calculate the probability of getting at least two tails, multiply the probability of getting tails for two coins and the probability of flipping either heads or tails for the remaining coin. Because it is at least two tails, the remaining coin can flip to either heads or tails.

1. Multiply the probabilities for each coin

1/2 · 1/2 · 2/2 = 1/4

Answer:

The domain is -418 < a < 8848 where a is an integer.

Step-by-step explanation:

We see from the data given that the  domain of T(a) takes both positive and negative integer values ( 8848 meters and  -418 meters); T(a) never gets decimal values (and in real life thy won't be of much use because we are not looking for that much accuracy).

So the appropriate number type for the domain of T(a) would be integers. And if you are interested, the domain is -418 < a < 8848.

Answer:

A =  0    -7                             b=   0     -7

      3     2d                                   3      2d    

Let's calculate A and B:

Calculte (AB)^(-1):

Calculte B^(-1) and A^(-1):

so:

(AB)^(-1) = B^(-1) * A^(-1)

Answer:

d

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

5(x-1)-2

Put x as 3 and evaluate.

5(3-1)-2

5(2)-2

10-2

= 8

Answer:

solution,

X=3

[tex]5(x - 1) - 2 \\ putting \: the \: value \: of \: x \\ = 5(3 - 1) - 2 \\ = 5 \times 2 - 2 \\ = 10 - 2 \\ = 8[/tex]

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▹ Answer

3x + 5

▹ Step-by-Step Explanation

8x - 2 - 5x + 7

= 3x - 2 + 7

= 3x + 5

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer: For the equation to have one solution, use any number that does not contain 3x.

Step-by-step explanation:

8x - 2 - 5x + 7

Combine like terms

3x + 5

The correct answer is $307.5

Explanation:

The total of the bond after 20 years is $150 plus the interests during this time (105% of $150). This last value can be calculated by multiplying the percentage (105) by the total ($150) and dividing it into 100% (total percent represented by $150. The process is shown below:

[tex]150 = 100[/tex]%

[tex]x = 105[/tex]%

[tex]x = \frac{150 x 105}{100}[/tex]

[tex]x = 157.5[/tex]

This means the total money in interest is $157.5 and this added to $150 is equivalent to $307.5

Answer:

see explanation

Step-by-step explanation:

The statements tells us that w is inversely proportional to v and the equation relating them is

v = [tex]\frac{k}{w}[/tex] ← k is the constant of proportion

To find k use the condition v = 9, w = 5, that is

9 = [tex]\frac{k}{5}[/tex] ( multiply both sides by 5 )

45 = k

v = [tex]\frac{45}{w}[/tex] ← equation of proportion

When w = 4 , then

v = [tex]\frac{45}{4}[/tex] = 11.25

Answer:

Step-by-step explanation:

[tex]sin \: 54 = \frac{opposite \: side}{hypotenuse} [/tex]

[tex]sin \: 54 = \frac{h}{10} [/tex]

[tex]0.8090 = \frac{h}{10} [/tex]

[tex]h = 10 \times 0.8090[/tex]

[tex]h = 8.09[/tex]

[tex]h = 8.1[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

h = 8.1 m

Step-by-step explanation:

Sin 54 = [tex]\frac{opposite }{hypotenuse}[/tex]

Where opposite = h, hypotenuse = 10 m

0.809 * 10 = h

=> h = 8.1 m

Tenemos que sean x e y los lados de la huerta entonces el perímetro sería:

P = 2*x + 2*y

Sabemos que el perimetro es 140, reemplazando:

140 = 2*x + 2*y

x + y = 70

despejamos y, nos queda:

y = 70 - x

Ahora tenemos que el área sería:

A = x*y

reemplazamos y:

A = x*(70 - x)

A = 70*x - x^2

Esta sería la ecuación que modela el área de la huerta.

Derivamos e igualamos a 0:

0 = 70 - 2*x

x = 70/2

x = 35

ahora calculamos y:

y = 70 - 35

y = 35

El área máxima sería:

A = 35*35

A = 1225 m^2

Answer:

A relation

Step-by-step explanation:

A relation can be defined as a pairing of numbers in a data set. The pairing of numbers are the domain and the range.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer: The bottom option, the graph.

Step-by-step explanation:

A relation is something that gets input from a set, called domain (usually the x) and "transforms" them into an output, from a set called the range.

Now, a relation is only a function if, for all the elements x in the domain, each one of them has only one element y in the range associated to it.

For example, in the first set we can see that the value x = 1 appears two times, it is related to different values in the range, then this is not a function.

The second relation is not a function.

the third relation is:

x = 3*y^2 - 7

This is a function, but in this relation x is the output and y the input, so this is a function of y.

In the fourth relation we can see a graph, this is a function (each value in the domain is related to only one in the range), and in the horizontal axis we can see a x, so this is a function of x.

Answer:

D

Step-by-step explanation:

The lower bound is the smallest value that rounds up to the given value.

Given value = 4m

The lower bound would be 3.5m

Any number less than .5 rounds down, any number greater to or equal to 0.5 rounds up, so if you have 3.5 or higher it rounds to 4

Answer:

A ≈ 3215.36

Step-by-step explanation:

A = πr²

Radius - D/2

Radius - 64/2 → 32

A = 3.14(32)²

A = 3215.36

Hope this helps! :)

Answer:

3215.36 um²

Step-by-step explanation:

d = 2r => r = d/2 = 64/2 = 32 um

A = π·r²

= 3.14·32²

= 3.14·1024

≈ 3215.36 um²

Answer: 168 hours

Step-by-step explanation:

There are 24 hours in a day.  Thus, simply multiply 7*24 to get 168.

Hi there! Hopefully this helps!

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Answer: There are 168 hours in 7 days.

Since there 24 hours in a day, Multiply 24 times 7 and you get 168.

Example : 24 x 7 = 168.

Answer:

B

Step-by-step explanation:

Since the diagonals of a rhombus bisect each other, that means P is the midpoint of LN. Therefore, LP = 1/2 * LN = 1/2 * 30 = 15.

Answer:

<B = 47°

<C = 28°

b = AC = 28.0

Step-by-step explanation:

Given:

∆ABC

AB = c = 18

BC = a = 37

<A = 105°

Required:

Length of AC = b

measure of angle B and angle C

SOLUTION:

==>Use the sine rule, sin A/a = sinC/c to find the angle of C:

SinA = sin(105) = 0.9659

a = 37

sinC = ?

c = 18

0.9659/37 = sinC/18

Cross multiply

0.9659*18 = 37*sinC

17.3862 = 37*sinC

Divide both sides by 37

17.3862/37 = sinC

0.4699 = sinC

sinC = 0.4699

C = Sin-¹(0.4699)

C = 28.0° (nearest tenth)

==>Find angle B using sum of angles in a triangle:

Angle B = 180 - (105+28)

Angle B = 180 - 133

Angle B = 47°

==>Find length of b using sine rule, b/sinB = c/sinC:

SinC = sin(28) = 0.4695

SinB = sin(47) = 0.7314

c = 18

b = ?

b/0.7314 = 18/0.4695

Cross multiply

b*0.4695 = 18*0.7314

b*0.4695 = 13.1652

Divide both sides by 0.4695

b = 13.1652/0.4695

b = 28.0 (nearest tenth)

Answer:

a) x = 10

Step-by-step explanation:

En este romboide, el angulo A es igual a el angulo C, y el angulo ABC es igual a el angulo CDA.

Entonces, el angulo C es 7x.

En un triangulo, los angulos se suman para ser 180 degrados. En el triangulo BCE, hay un angulo recto.

7x + 2x + 90 = 180

7x + 2x = 90

9x = 90

x = 10

Espero que este te ayude!

Answer:

Step-by-step explanation:

f-  -3u=21 divide each side by (-3)

-3u/-3=-21/3

u=-7

g) 23+a=12  use subtraction method , subtract 23 from both sides

23-23+a=12-23

a=-11

h) -9+b=15  use additional method, add 9 to both sides

-9+9+b=15+9

b=26

Answer:

x = 6/5

y = 8/5

Step-by-step explanation:

3x - y = 2

2x + y = 4

Add the equations, cancelling y.

5x = 6

x = 6/5

Put x as 6/5 in the second equation and solve for y.

2(6/5) + y = 4

12/5 + y = 4

y = 4 - 12/5

y = 8/5

Answer:

A 5% raise can be written as 1.05 so the new salary is 25100 * 1.05 = $26355.

Answer:

x² - 8x+ 16 = 5

x² - 8x + 16 - 5 = 0

x² - 8x + 11 = 0

Using the quadratic formula

x = -b±√b² - 4ac / 2a

a = 1 , b = - 8 c = 11

x = --8±√(-8)² - 4(1)(11) / 2(1)

x = 8 ± √ 64 - 44 / 2

x = 8±√20 / 2

x = 8 - √ 20 / 2 or x = 8 + √ 20 / 2

x = - √ 5 + 4 or x = √5 + 4

Hope this helps