Solve the equation by factoring:
x² – 5x = 14
a. x= -2 or 7
b. x= 2 and -7
C. X= -2 or -7
d. x = 2 or 7

Answer:

[tex]\large \boxed{\sf \ \ \ x-y=-2\sqrt{7} \ \ \ }[/tex]

Step-by-step explanation:

Hello,

it took me some time to understand the correct equations, I believe that you mean

[tex]x+y=4\\\\x^2+y^2=22\\\\x^4=y^4-176\sqrt{7}[/tex]

So let's play with these equations

[tex]x^4=y^4-176\sqrt{7}\\\\<=>y^4-x^4=176\sqrt{7}\\\\<=>y^4-x^4=(y^2)^2-(x^2)^2=(y^2-x^2)(y^2+x^2)=(y-x)(y+x)(x^2+y^2)\\\\=176\sqrt{7}[/tex]

So

[tex]x-y=-\dfrac{176\sqrt{7}}{(x+y)(x^2+y^2)}=-\dfrac{176\sqrt{7}}{4*22}=-2\sqrt{7}=-5.291503...[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Total number of flash = 50 flash

Step-by-step explanation:

Given:

Time taken of a flash = 3/5 minute = 3/5 × 30 = 36 sec

Total time = 30 minute = 30 × 60= 1800 sec

Find:

Total number of flash in 30 minutes

Computation:

⇒ Total number of flash = Total time / Time taken of a flash

⇒ Total number of flash = 1800 / 36

⇒ Total number of flash = 50 flash

Answer:

m<ABC > m<ACB (angle property of a triangle)

Step-by-step explanation:

Given that: ΔABC

                  AB = AX

Prove: m<ABC > m<ACB

From the given diagram,

ΔABX is an isosceles triangle (two congruent sides and angles)

<AXB = m<ABX = [tex]90^{o}[/tex] (isosceles triangle property)

AC = AX + XC

Thus,

AC > AB

m<ABC = m1 + m3 ≥  [tex]90^{o}[/tex]

m<ACB < [tex]90^{o}[/tex] (acute angle property)

Therefore since in a triangle the longest side is opposite to the greatest angle, then;

m<ABC > m<ACB (angle property of a triangle)

Answer:

-4

Step-by-step explanation:

y = -4x + 6 is the equation and -4 is the slope

Answer:

a)16      (2*2*2*2= 16)

b)16  (-4*-4-16)(-+-=+)

c)500 (5*5*5=125        125*4=500)

d)0.49  (0.7*07)

e)480  (4^=16     9^=81  121^0=1          16+81 -1 =96     96*5=480)

f)5^2  or 25 (a^m/ a^n=a^m-n)

g) 11^14 (reason same as the f one)

h)8.20

i) 4(-4*16=64)

j)900

Answer:

Uncle is 34. Nephew is 10.

Step-by-step explanation:

Let u equal the age of the uncle, and n equal the age of the nephew.

First, two years ago, the sum of their ages was 40. We can represent this by subtracting 2 from each variable. Thus:

[tex](u-2)+(n-2)=40[/tex]

[tex]u+n-4=40[/tex]

[tex]u+n=44[/tex]

Next, in two years time, the uncle will be three times as old as his nephew. We can represent this by adding 2. Thus:

[tex]u+2=3(n+2)[/tex]

We now have a system of equations and can solve accordingly.

First, from the first equation, we can determine that:

[tex]u=44-n[/tex]

We can substitute this into the second equation.

[tex](44-n)+2=3(n+2)[/tex]

[tex]46-n=3n+6[/tex]

[tex]40=4n[/tex]

[tex]n=10[/tex]

Thus, the nephew's age is 10.

And the uncle's age is 44-10 or 34.

Answer:

(0, 6)

Step-by-step explanation:

The solution is the point of intersection of the lines.

(0, 6)

Answer:

zero residual equals zero mean

A line of best fit is a straight line that shows the appropriate correlation among scatter plots of a given data. It is majorly used when the plotted points are not linear, it can be used to express the relationship between dependent and independent variables.

The sum of the residuals should be close to zero because it shows that the line of best fit is accurately drawn. Thus, it implies that there is a linear relationship between the two variables. Since he residual is close to zero, the graph could be said to be a linear graph.

The question is not typed properly! Complete question along with answer and step by step explanation is provided below.

Question:

Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495 and standard deviation 118 .

You choose an SRS of 100 students and average their SAT Critical Reading scores. If you do this many times, the standard deviation of the average scores you get will be close to

a. 118

b. 118/100=1.18

c. 118/√100= 11.8

d. cannot be determined

Answer:

The standard deviation of the sample would be  

[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]

The correct option is (c)

Therefore, the standard deviation of the average scores you get will be close to 11.8

Step-by-step explanation:

From the given information,  

The population mean SAT critical reading score is

[tex]\mu = 495[/tex]

The population standard deviation is

[tex]\sigma = 118[/tex]

You choose an SRS of 100 students and average their SAT Critical Reading score.

[tex]n = 100[/tex]

Since the sample size is quite large then according to the central limit theorem,

The mean sample will be the same as the population mean  SAT critical reading score.

[tex]\bar{x} = \mu = 495[/tex]

The standard deviation of the sample would be  

[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]

The correct option is (c)

Therefore, the standard deviation of the average scores you get will be close to 11.8

Answer:

JL = 32

Step-by-step explanation:

We are told in the above question that:

In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.

From the attached diagram, we can see that

JL : JK = JK: JM

Therefore,

JL/ JK = JK /JM

Where JL = Unknown

JK = 24

JM = 18

JL/ 24 = 24/18

Cross Multiply

24 × 24 = JL × 18

Divide both sides by 18

JL = (24 × 24) /18

JL = 576/18

JL = 32

Answer:

$8000 worth of sales

Step-by-step explanation:

We know Jack needs to make $1000 in 40 hours. We also know he makes 5% commission, meaning he gets 5% of the money from a sale, and that he makes $15/h.

First, lets find how much made from his hourly pay.

40 * $15 = $600

Now subtract that from how much he needs,

$1000 - $600 = $400

He still needs $400 from commissions. We know he makes 5% commission, so we can find the total value of the sales he'd need by multiplying 400 by 20 since 5% x 20 = 100%, aka the total value. $400 x 20 = $8000 in sales.

Answer:

  -63

Step-by-step explanation:

Compare ...

  f(x) = x^2 -3x +18

to the standard form ...

  f(x) = ax^2 +bx +c

and you will see that ...

  a = 1, b = -3, c = 18.

__

The value of the discriminant is ...

  d = b^2 -4ac

  d = (-3)^2 -4(1)(18) = 9 -72 = -63

The discriminant is -63.

Answer:

To solve a triangle is to find the lengths of each of its sides and all its angles. The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle. The cosine rule is used when we are given either a) three sides or b) two sides and the included angle.

Step-by-step explanation:

We just saw how to find an angle when we know three sides. It took quite a few steps, so it is easier to use the "direct" formula (which is just a rearrangement of the c2 = a2 + b2 − 2ab cos(C) formula). It can be in either of these forms:

cos(C) =  a2 + b2 − c22ab

cos(A) =  b2 + c2 − a22bc

cos(B) =  c2 + a2 − b22ca

Answer:

Law of cosines, two sides and the included angle known

Step-by-step explanation:

double check that the question is exactly the same to make sure you get the question correct

"If ∠P is given and the values of r and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for p."

Answer:

[tex]7\sqrt{2}[/tex] meters

Step-by-step explanation:

This is a 45 45 90 triangle. This means that two sides of the triangle are equivalent. In this type of triangle, the two equal sides are represented by [tex]a[/tex] and the hypotenuse that you are trying to find (u) is represented by [tex]a\sqrt{2}[/tex]

Therefore, your answer is [tex]7\sqrt{2}[/tex] in simplest radical form.

Answer:

u= 7[tex]\sqrt{2}[/tex]

Step-by-step explanation:

The missing side is u

sin 45° = [tex]\frac{\sqrt{2} }{2}[/tex]

so :

Answer:

He will have 13 packages containing 3 pairs of headphones and 1 music player each.

Step-by-step explanation:

He has 39 pairs of headphones and 13 music players.

He wants to sell both set of items in identical packages.

To do this he has to divide them in such a way that the same number of both set of objects are in every box.

Let us find the ratio of the pairs of headphones to music players:

39 : 13 = 3 : 1

Therefore, dividing the pairs of headphones into 3 parts and the music players into 1 part, he can have identical packages.

So, he will have 13 packages containing 3 pairs of headphones and 1 music player each.

Answer:

Step-by-step explanation:

graph attached

Answer:

graph y

Step-by-step explanation:

Answer:

its G(2)

Step-by-step explanation:

Gg

Answer: the answer is A

Step-by-step explanation:

Answer:

Pascal's triangle is a triangular array of the binomial coefficients. It is used to find combinations.

Answer:

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.

Step-by-step explanation:

Answer:

6root(2)/25

Step-by-step explanation:

5^-2 = 1/25

3(root(8)) = 6(root(2))

so you get 6(root(2))(1/25)

= 6(root(2))/25

The required simplified value of the given expression is 0.34 or  6√2 / 25.

Given that,
Expression to simply ios given,
5⁻² x 3√8

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Simplification =>
= 5⁻² x 3√8
= 1/ 5⁻² x 3 x 2 √2
= 6√2 / 25
= 0.34

Thus, the required simplified value of the given expression is 0.34 or  6√2 / 25.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Answer:

C, D, and F

Step-by-step explanation:

The roots of the cubic polynomial are 1, (5+√17)/2, and (5-√17)/2 options (C), (D), and (F) are correct.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have a cubic or third-degree polynomial:

F(x) = x³ - 6x² + 7x - 2

To find the all possible roots of the cubic polynomial

By using the trial and error method:

Plug x = 1

F(1) = 1 - 6 + 7 - 2

F(1) = 8 - 8

F(1) =0

x = 1 is one of the roots of the polynomial.

We can write the cubic polynomial in the factored form:

F(x) = (x - 1)(x² -5x + 2)

We have a quadratic polynomial:

= x² -5x + 2

To find the roots of the quadratic polynomial use the quadratic formula:

a= 1, b = -5, and c =2

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\rm x = \dfrac{-(-5) \pm\sqrt{(-5)^2-4(1)(2)}}{2(1)}[/tex]

After solving:

x = (5+√17)/2

x = (5-√17)/2

Thus, the roots of the cubic polynomial are 1, (5+√17)/2, and (5-√17)/2 options (C), (D), and (F) are correct.

Learn more about Polynomial here:

brainly.com/question/17822016

#SPJ5

Answer: A

Step-by-step explanation:

2x²-2x-9=0

this is a quadratic equation so we will use the quadratic formula .

 Δ= b²-4*a*c

let's calculate Δ to khow how many solutions this equations have .

 Δ= (-2)²-4*2*(-9)

    = 76

 we notice that 76>0

so this equation has two solutions :  (-b-√76)/4 and (-b+√76)/4

the trick here is to notice that :

[tex]\sqrt{76}[/tex] = [tex]\sqrt{19*4}[/tex]

      = [tex]\sqrt{19} *\sqrt{4}[/tex]

      = 2[tex]\sqrt{19}[/tex]

Now we will simplify Δ by factoring by 2

so the answer is a .

Answer:

16/64 i think

Step-by-step explanation:

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Total Marks = 64

Correct = 48

Incorrect = 64-48

=> 16

Fraction of Incorrect Answers:

=> [tex]\frac{16}{64}[/tex]

In simplest form:

=> [tex]\frac{1}{4}[/tex]

Answer:

T ≥ 8x

50 ≥ 8x .......1

x ≤ 6

Liam can buy lunch for 6 people.

Step-by-step explanation:

Let x represent the number of people Liam can buy lunch for.

Given;

Lunch cost per person r = $8 per person

The total amount he has T = $50

The cost of buying lunch for c people is;

C = $8 × x

C = 8x

Therefore, to be able to buy lunch for them, the total cost C must be less than the total amount he has.

T ≥ C

Substituting C, we have;

T ≥ 8x

50 ≥ 8x ,.......1

Solving the inequalities;

8x ≤ 50

x ≤ 50/8

x ≤ 6.25

To the nearest whole number;

x ≤ 6

Liam can buy lunch for 6 people.

Answer:

answer is b). y = 100+ 0.05x

Step-by-step explanation:

Answer:

y ≥ -2/3x +3

Step-by-step explanation:

incline is -2/3

and intercept with y-axis is 3

so the equation of the line is

y = -2/3x +3

Since the intended area in the graph I above the line, we now know enough to find the right one question:

y ≥ -2/3x +3

Answer: y>-2/3x+3 because the line is dotted its >

Answer:

Step-by-step explanation:

[tex]y = 1/2x +3\\m =1/2\\m_1m_2 = -1\\1/2m_2 =-1\\m_2= -2\\(10 ,-5)\\x = 10\\y = -5\\y = mx+b \\-5 = -2(10) + b\\-5=-20+b\\-5+20 =b\\b = 15\\m = -2\\Substitute -given -values- into- slope -intercept-form\\y = mx+b\\y = -2x+15[/tex]

Answer:

y=x+5

Step-by-step explanation:

Hey there! :)

Answer:

C) 74 units.

Step-by-step explanation:

MT is congruent to KT because the diagonals of a quadrilateral bisect each other. Therefore:

8y + 18 = 12y - 10

Subtract 8y from both sides:

18 = 4y - 10

Add 10 to both sides:

28 = 4y

Divide both sides by 4:

28/4 = 4y/4

y = 7 units. Plug this into the equation for MT:

8(7) + 18 = 74 units.

Answer:

74

Step-by-step explanation:

Set up the equations

8y + 18 = 12y -10

Combine like terms

28 = 4y

Divide each side by 4

y=7

Plug in the value of y in the equation of 8y + 18 since that's the value for MT

8(7) + 18 = 74

Hope this helps!

4                    1                    1

---  kg    x    -----      =         ------   kg = 0.05 kg = 50 g

10                    8                  20