Prove that 7 root 3 is an irrational number.​

Find k if (x+1) is a factor of 2x³ + kx² + 1

k = 1

The factor of a polynomial F(x) is another polynomial that divides evenly into F(x). For example, x + 3 is a factor of the polynomial x² - 9.

This is because;

i. x² - 9 can be written as (x - 3)(x + 3) which shows that both (x - 3) and (x + 3) are factors.

ii. If x = -3 is substituted into the polynomial x² - 9, the result gives zero. i.e

=> (-3)² - 9

=> (9) - 9 = 0

Therefore, if (x + a) is a factor of a polynomial, substituting x = -a into the polynomial should result to zero. This also means that, if x - a is a factor of a polynomial, substituting x = a into the polynomial should give zero.

From the question

Given polynomial: 2x³ + kx² + 1

Given factor: x + 1.

Since x + 1 is a factor of the polynomial, substituting x = -1 into the polynomial should give zero and from there we can calculate the value of k. i.e

2(-1)³ + k(-1)² + 1 = 0

2(-1) + k(1) + 1 = 0

-2 + k + 1 = 0

k - 1 = 0

k = 1

Therefore the value of k is 1.

Answer:

d = 17.3 m

Step-by-step explanation:

We can extend Pythagorean theorem to 3 dimensions by writing

[tex] {d}^{2} = {x}^{2} + {y}^{2} + {z}^{2} [/tex]

or

[tex]d = \sqrt{ {x}^{2} + {y}^{2} + {z}^{2} } [/tex]

Since we are dealing with a cube of side 10 m, then

x = y = z = 10 m

so we get

[tex]d = \sqrt{ {10}^{2} + {10}^{2} + {10}^{2} } [/tex]

or

[tex]d = \sqrt{3 \times {10}^{2} } = 10 \sqrt{3} \: m[/tex]

This becomes

d = 17.3 m

Answer:

Side-Side-Side (SSS) Congruence - if three sides of one triangle are congruent to three sides of  another triangle, then the triangles are congruent.

Side-Angle-Side (SAS) Congruence - If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Angle-Side-Angle (ASA) Congruence - If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Angle-Angle-Side (AAS) Congruence - If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

u see which one fits

Answer:  SAS

Step-by-step explanation: because there are Two sides and the angle between them are congruent.

Step-by-step explanation:

The formula for the lateral area of a right cone is :

LA = rs

Where

r is the radius of the base and s is the slant height of the cone

Equivalent expression,

[tex]r=\dfrac{LA}{s}[/tex]

or

[tex]s=\dfrac{LA}{r}[/tex]

Hence, this is the required solution.

Answer:

The answers are C & E

Answer:

x = 146

Step-by-step explanation:

The exterior angle of the triangle is equal to the sum of the opposite interior angles

x = 48+98

x = 146

Answer:

The sum of all the angles in a triangle is 180 degrees,

We know the measures of two angles, 48 and 98

if we add those and then subtract their sum from 180, we can find the third angle which will help us find the exterior angle x

48+98=146

180-146 = 34

now, we have to do 180-34 to find the measure of x.

why? any straight line is 180 degrees.

180-34 = 146

x = 146

hope this is correct and it helps you.

Answer:

the value of increase each time is 1,571.43

Step-by-step explanation:

Given;

original value of the number, A = 1000

final value of the number, N = 12,000

Assuming the number increased equally each time, let the value of increase each time = x

The following linear equation will be obtained to solve for x;

7x + 1000 = 12,000

7x = 12,000 - 1,000

7x = 11,000

x = 11,000/7

x = 1,571.43

Therefore, the value of increase each time is 1,571.43

Answer:

[tex]A: (-3,1)[/tex]

[tex]B:(-1,-1)[/tex]

[tex]d=\sqrt{(-3-(-1)^{2} +(-1(-1))^{2} }[/tex]

[tex]=\sqrt{(-2)^{2}+(2)^{2} }[/tex]

[tex]=\sqrt{4+4}=\sqrt{8}[/tex]

[tex]=2\sqrt{2} =2.8[/tex]

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hope it helps..

have a great day sis ^_^!!!

Answer:

Coordinates of :-

A= (-3,1)

B= (-1,-1)

Distance AB= [tex]\sqrt{-2+3)^{2}+(-1-1)^{2} }[/tex]

OAmalOHopeO

Answer:

No

Yes

Step-by-step explanation:

Let's find the inclination of the 3 lines.

m:

((-4) -3)/(0 - (-4))

-7/4

n:

((-2) -2)/(3 - 1)

-4/2

-2

k:

(1 -(-3)/(4 -(-3)

(1 +3)/4 +3

4/7

Okay, we find the inclination of all the three lines. For two lines be parallel, they have to have the same inclination. The inclination of m = -7/4 and the inclination of n = -2, so they're not parallel. And now, to know if m is perpendicular to k, they inclination have to be the opposite of the inverse of each other, so it means that they have to have opposite signals, and they need to be inverted fractions (for example a/b are inverted to b/a), and they are these two things: m = -7/4 and n = 4/7, so they're perpendicular

Answer:

No, the slopes are not equal.

Yes, the slopes are negative reciprocals.

Step-by-step explanation:

Just did it on edge.

Answer:

25 and 26

Step-by-step explanation:

25+26=51

Hope this helps! :)

Answer and Step-by-step explanation:

We can represent the equation like this:

x + (x + 1) = 51, where x is a number and x + 1 is the consecutive number.

Solve for x.

Add the x's together.

2x + 1 = 51

Subtract 1 from both sides of the equation.

2x = 50

Divide 2 on both sides of the equation.

x = 25

So, the numbers are 25 and 26.

25 + 26 = 51

#teamtrees #PAW (Plant And Water)

Answer: 10.8%

Step-by-step explanation:

The question is asking what the percentage of the down payment is of the purchase price of the house.

For such a question, the purchase price needs to be known.

We shall therefore assume a purchase price and you can use the process to find out your percentage.

Assume the purchase price is $1,000,000.

The percentage would be:

= Down payment / Purchase price * 100%

= 108,000 / 1,000,000

= 10.8%

Answer:

10.8%

Step-by-step explanation:

see above

Answer:

16 and 56

Step-by-step explanation:

gcf of 24 and 48 is 24

gcf of 14 and 32 is 2

gcf of 16 and 28 is 4

Let's find one by one

#1

24 and 48

No

#2

14 and 32

No

#3

GCF is 4

No

#4

16 and 56

Yes

Answer:

15550.88

Step-by-step explanation:

the formula for the volume of a cylinder is πr^2(h), so plug in height and radius, and you have the answer.

Answer:

15550.88

Step-by-step explanation:

You use πr^2 h

Answer:

[tex]x =12.5[/tex]

Step-by-step explanation:

Given

[tex]300x + \frac{500}{7}y =10000[/tex]

[tex]y = 87.5[/tex]

Required

Find x

Substitute [tex]y = 87.5[/tex] in [tex]300x + \frac{500}{7}y =10000[/tex]

[tex]300x + \frac{500}{7}*87.5 =10000[/tex]

[tex]300x + 500*12.5 =10000[/tex]

[tex]300x + 6250=10000[/tex]

Collect like terms

[tex]300x =10000-6250[/tex]

[tex]300x =3750[/tex]

Divide by 300

[tex]x =12.5[/tex]

Answer:

12.5

Step-by-step explanation:

Answer:

If I live in South Carolina then I live in Charleston

Step-by-step explanation:

Just switch them

Answer:

The answer is below

Step-by-step explanation:

∠EFG and ∠GFH are a linear pair, m∠EFG = 3n+ 21, and m∠GFH = 2n + 34. What are m∠EFG and m∠GFH?

Solution:

Two angles are said to form a linear pair if they share a base. Linear pair angles are adjacent angles formed along a line as a result of the intersection of two lines. Linear pairs are always supplementary (that is they add up to 180°).

m∠EFG = 3n + 21, m∠GFH = 2n + 34. Both angles form linear pairs, hence:

m∠EFG + m∠GFH = 180°

3n + 21 + (2n + 34) = 180

3n + 2n + 21 + 34 = 180

5n + 55 = 180

5n = 125

n = 25

Therefore, m∠EFG = 3(25) + 21 = 96°, m∠GFH = 2(25) + 34 = 84°

Answer:

B.6

Step-by-step explanation:

3 + 2x + 22 = x + 17

Combine like terms

25 + 2x = x + 17

Subtract 17 from both sides

8 + 2x = x

Subtract 2x from both sides

8 = -x

Divide both sides by -1

x = -8

Substitute -8 for x in 2x + 22 to find value of QR

2(-8) + 22

Multiply

-16 + 22

Add

QR = 6

The length of QR in the given figure by combining like terms and applying the substitution method, QR = 6

Used the concept of addition and combining like terms in the mathmatical expression.

Given that,

The length of line segments is,

PQ = 3

QR = (2x + 22)

PR = (x + 17)

Now, from the figure,

PQ = QP + QR

Substitute the given values,

x + 17 = 3 + 2x + 22

Combine like terms

x + 17 = 25 + 2x

Subtract 17 from both sides

x = 8 + 2x

Subtract 2x from both sides

x - 2x = 8

- x = 8

Divide both sides by -1

x = -8

So, for the length of QR,

Substitute - 8 for x in the length of QR,

QR = 2x + 22

= 2(-8) + 22

= -16 + 22

= 6

Learn more about the line segment visit:

https://brainly.com/question/280216

#SPJ4

Answer:

m∠W = 134

Step-by-step explanation:

JGN is congruent to AIW and the names of the triangles are both in the same order. That may sound confusing but this means that:

J = A

G = I

N = W

So, if angle N is 134 then angle W is the same.

Answer:

the missing side is 6

Step-by-step explanation:

Using the Pythagorean theorem, ([tex]a^{2} + b^{2} = c^{2}[/tex]), for right triangles, you get [tex]4^{2} + (2\sqrt{5}) ^{2} = c^{2}[/tex].  Since the square cancels the square root for side b you get [tex](2^{2})*(5)[/tex] which equals 20. This makes your equation go to 16+20 = [tex]c^{2}[/tex]. Then add the numbers to make [tex]36=c^{2}[/tex]  solve for c by taking the square root of both sides to get c = 6.

Answer:

Step-by-step explanation:

h × b × [tex]\frac{1}{2}[/tex] = A   (this is the formula)

2 × 3 × [tex]\frac{1}{2}[/tex] =  3m²

I believe you forgot to mention some information...but hope this helps...

Answer:

Each side is 10 inches because the perimeter is 80 inches, you will have to divide 80 by 8 because octagon is a shape with 8 sides. So 80 divided by 8 is 10..... So the answeer is 10 inches.

Step-by-step explanation:

80÷8=10

brainliest!!!!?

Answer:

∆ABC~=∆PQR

Angle BAC=QPR

answer:

N(t)=2×[tex]1.7^{t}[/tex]

17

15

step by step explain:

before lesson (t=0), she knows 2 words.

after a week (t=1), she knows

2×(1+70%)=3.4 words

after one more week (t=2), she knows

3.4×(1+70%)=5.78 words

one more week later (t=3), she knows

5.78×(1+70%)=9.826 words

and so on ...

from pattern shown above, we know that she knows

2×[tex]1.7^{t}[/tex] words after t weeks

so N(t)=2×[tex]1.7^{t}[/tex]

after 4 weeks (t=4), she knows 2×[tex]1.7^{4}[/tex]=16.7042≈17 words

for learning 5000 words, she need:

2×[tex]1.7^{t}[/tex]=5000

   [tex]1.7^{t}[/tex]=2500

t log(1.7)=log(2500)

         t=[tex]\frac{log(2500)}{log(1.7)}[/tex]

          =14.7448727

          ≈15 (round up)

Answer:

(a) N(t) = 2(1.7)^t

(b) 17

(c) 15

Step-by-step explanation:

(a) N(t) = 2(1.7)^t

There is a 2 because she starts with 2 words. The 1.7 is since her vocabulary grows by 70%. Finally, t represents the weeks. (it is an exponent)

(b) Just plug in the equation

N(4) = 2(1.7)^4

N(4) = 2(8.3521)

N(4) = 16.7042

Round, so it is 17

(c) Once again, plug in the equation

5000 = 2(1.7)^t

2500 = (1.7)^t

use a calculator for the part below

log1.7(2500) = log1.7(1.7)*t

t = log1.7(2500)

t = 14.7448

Round, so it is 15

Answer:

-10

Step-by-step explanation:

i think this is the answer

Answer:

the answer is median (b)

Answer: B)  [tex]0 \le y \le 100[/tex]

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

Explanation:

The range is the set of possible y outputs. Visually, we look for the highest and lowest points to determine that range of y values. The lowest point occurs when y = 0, which is the left-most point of the graph. The highest point is when y = 100 where the peak is.

So we say that y is between 0 and 100, including both endpoints to lead to the inequality [tex]0 \le y \le 100[/tex]

The range in interval notation is [0, 100]. The square brackets say to include the endpoints.

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Side note: The domain appears to be [tex]2.5 \le x \le 9.5[/tex] since the left-most point seems to have the x coordinate x = 2.5 and the right-most point seems to have the x coordinate x = 9.5. The domain is the set of all possible x inputs. So if your teacher was asking about the domain, then the answer would be C.

An attachment would help. Assuming this is the Pythagorean theorem, c would be 10 feet. (6)^2 + (8)^2 = 100 -----> √100 = 10