α' β
5. A quadratic equation 2x2 = 6x + 3 has two roots p and q. Find the quadratic equations with
roots p2q and pq2?
​

Answer:

28.

Step-by-step explanation:

I just did the question and I got it right. The answer above is right. The image below is where I did the question and has the picture attached next to it too.

*And I accidentally clicked the one star option, that's why it has such a low score.

An isosceles triangle is a triangle where two sides are equal and the angles opposite to the sides are also equal.

The value of y is 28.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

An isosceles triangle is a triangle where two sides are equal and the angles opposite to the sides are also equal.

m∠CAB = 34

m∠CBA = x - 5

m∠ACB = 4y

Triangle ABC is an isosceles triangle.

AC and BC are sides are equal.

This means,

m∠CAB = m∠CBA

34 = x - 5

34 + 5 = x

x = 39

Now,

The sum of the angles in a triangle is 180 degrees.

This means,

34 + (x -5) + 4y = 180

34 + (39 - 5) + 4y = 180

34 + 34 + 4y = 180

68 + 4y = 180

4y = 180 - 68

y = 112 / 4

y = 28

We can cross-check.

34 + 34 + 4 x 28 = 180

34 + 34 + 112 = 180

180 = 180

Thus,

The value of y is 28.

Learn more about triangles here:

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Answer:

nth term of geometric sequence = a(n) = [tex](3/4)(4/3)^{n-1}[/tex]

Step-by-step explanation:

nth term of geometric sequence = a(n)

nth term of geometric sequence = a(n) = [tex]ar^{n-1}[/tex]

Where,

a =  first term

r = common ratio

n = number of term

So,

GP: 3/4, 1, 4/3, 16/9

a = 3/4

r = 1 / [3/4] = 4/3

n = n

nth term of geometric sequence = a(n) = [tex]ar^{n-1}[/tex]

nth term of geometric sequence = a(n) = [tex](3/4)(4/3)^{n-1}[/tex]

Answer:

h = 0.139725

Step-by-step explanation:

Volume of a Cylinder Formula: V = πr²h

You are given V = 20 and r = 6.75.

20 = π(6.75)²h

20/45.5625π = h

h = 0.139725

I'm not sure if this is correct or not.

Answer:

≈1.4 m

Step-by-step explanation:

V= 20 l= 20 000 cm³

d= 13.5 cm ⇒ r= 13.5 cm / 2= 6.75 cm  (assume it is cm)

V= πr²h

h= V/πr²= 20000/3.14*6.75² ≈ 140 cm= 1.4 m

Answer:

1/6

Step-by-step explanation:

An experimental probability is the number of times an event occurred when actually attempted.

So, if Jo does the experiment 60 times and receives 50 unpainted balls, then calculate how many painted balls she got:

60-50 = 10.

So, the probability of picking a painted ball = 10/60 = 1/6

Hope this helps

Answer:

13 units.

Step-by-step explanation:

By Pythagoras:

(x -3)^2  + (x + 4)^2 = (2x - 3)^2

x^2 - 6x + 9 + x^2 + 8x + 16 = 4x^2 -12x + 9

4x^2 - x^2 - x^2  + 6x - 8x - 12x + 9 - 9 - 16 = 0

2x^2 -14x - 16 = 0

2(x^2 - 7x - 8) = 0

2(x -8)(x + 1) =0

x = 8, -1.

As x must be positive we take x = 8

So the hypotenuse is  2(8) - 3 = 13 units long.

Answer: 15.58 miles

Step-by-step explanation:

Given two sides and an included angle, segment AB can be calculated using the cosine rule :

Given a = 15.6 miles, b = 12.3 miles and C=α=66.7°

To find c:

c= √(a^2+b^2-2abcosα

c = √ 15.6^2 + 12.3^2 -(2 × 15.6 × 12.3)cos66.7°

c = √243.36 + 151.29 - 151.79454

c = √242.85545

c = 15.583820

c = 15.58 miles

Answer:

13.56

Step-by-step explanation:

hope that helps

Answer:

270[tex]\sqrt{3}[/tex] cm³

Step-by-step explanation:

A regular hexagon can be cut into 6 equilateral triangles.

The area (A) of an equilateral triangle can be calculated as

A = [tex]\frac{s^2\sqrt{3} }{4}[/tex] ← where s is the side length, here s = 6

A = [tex]\frac{6^2\sqrt{3} }{4}[/tex] = 9[tex]\sqrt{3}[/tex] cm² ← multiply by 6

area of base = 6 × 9[tex]\sqrt{3}[/tex] = 54[tex]\sqrt{3}[/tex] cm²

The volume (V) of the prism is calculated as

V = area of base × height = 54[tex]\sqrt{3}[/tex] × 5 = 270[tex]\sqrt{3}[/tex] cm³

Answer:

y=2(x+2)(x+3)

Step-by-step explanation:

First, we need to factor the right side:

y=2(x^2+5x+6)

Now, we can have an incomplete equation like this:

y=2(x+_)(x+_)

In the blanks, we need to fill out numbers that add to be 5 and multiply to be 6. What are factors of 6? 6 and 1, 2 and 3. Do 6 and 1 add to be 5? No. Do 2 and 3 add to be 5? Yes!

So, our factored form is

y=2(x+2)(x+3)

Answer:

9:20

Step-by-step explanation:

Given:

Surface area of shape A = 9 cm²

Surface Area of shape B = 16 cm²

Ratio of volume of shape A to B = 27:125

Required:

Find the ratio of the height of shape A to the height of shape C.

Ratio of surface area (A:B)² = ratio of linear measures (A:B)

Thus,

(A:B)² = (A:B)

(A/B)² = (A/B)

[tex] (\frac{A}{B})^2= (\frac{9}{16}) [/tex]

Take the square root of both sides:

[tex] (\sqrt{\frac{A}{B}})^2 = (\sqrt{\frac{9}{16}}) [/tex]

[tex] \frac{A}{B} = \frac{3}{4}[/tex]

Ratio of volume of shape B to C = 27:125

Thus,

(B:C)³ = 27:125

[tex] (\frac{B}{C})^3= (\frac{27}{125}) [/tex]

Take the cube root of both sides:

[tex](3\sqrt{\frac{B}{C}})^3 = (3\sqrt{\frac{27}{125}})[/tex]

[tex] \frac{B}{C} = \frac{3}{5}[/tex]

Therefore, ratio of lengths A:B:C =

3:4:C

A:3:5

To make them equivalent, we have:

9:12:C

A:4:20

Therefore, the ratio of the height of shape A to the height of shape C =

9:20

Answer:

5x2x2x2x2x7x7

Step-by-step explanation:

First list all of the prime factors of 1120. You can do this by drawing a factor tree.

The results are:

5,2,2,2,2,7,7

To make 1120 a product of its prime factors, we just have to write it in the form:

5x2x2x2x2x7x7

Hope this helps

Answer:

The HCF of 30 and 40 is 10

Answer:

10

Step-by-step explanation:

Well to find the GCF of HCF which are the same thing we have to make of list of factors of 30 and 40.

Look at the image below

after making the list find the greatest common factor which is 10.

Answer:

so the value of x is 8.3333≈8.3

Step-by-step explanation:

3x:10=5:2

[tex]\frac{3x}{10}=\frac{5}{2}[/tex]

by cross-multiplication

3x×2=5×10

6x=50

6x/6=50/6

x=8.33

i hope this will help you :)

Answer:

I think the answer is b

Step-by-step explanation:

Answer:

b) 5u.

Step-by-step explanation:

El triangulo es 45-45-90, entonces los dos lados son iguales. Si un lado es 8u, el otro lado tambien es 8u.

Entonces, 8u + x = 13u.

x = 13u - 8u

x = 5u

Espero que esto te ayude!

Answer:

√(r+n)/5=m

Step-by-step explanation:

r=5m²-n

adding n on both sides

r+n=5m²-n+n

r+n/5=m²

taking square root on both sides

√(r+n)/5=m

Answer: b, c, and e

Step-by-step explanation:

I hope I helped

The standard form of the equation of straight line is given by

y - 1 = -1/6(x + 4)

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have a table as given in the image attached at the end of answer.

The slope of the line will be -

m = (y₂ - y₁)/(x₂ - x₁)

m = (1 - 2)/(- 4 + 10)

m = - 1/6

The standard form of the equation of straight line is given by -

y - y₂ = m(x - x₂)

y - 1 = -1/6(x + 4)

Therefore, the standard form of the equation of straight line is given by

y - 1 = -1/6(x + 4)

To solve more questions on straight lines, visit the link below-

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[Refer to the image attached for complete question]

Answer:

D to C

Step-by-step explanation:

The radius is half the diameter or the center point to the edge (circumference)

Answer:

DC

Step-by-step explanation:

Answer:

The maximum value of (2·x - 10) is 20

Step-by-step explanation:

Given that the maximum value of f(x) = 20

f(x) = -4·x² + bx + c

We are required to find the maximum value of (2·x - 10)

f'(x) = -8·x + b = 0

x = b/8

f''(x) = -8, therefore, f'(x) is the maximum point

20 = -4·x² +8·x²  + c

20 = -4·(b/8)² + b×(b/8) + c

20 = -b²/16 + b²/8 + c

20 = b²/16 + c

f(2·x - 10) = -4·(2·x - 10)² + b·(2·x - 10) + c

f(2·x - 10) = b·(2·x - 10) + c - (16·x²-160·x +400

Differentiating to find the maximum gives;

f'(2·x - 10) = d(b·(2·x - 10) + c - (16·x²-160·x +400)/dx = 2·b -32·x +160 = 0

x = (2·b +160)/32 = 0.0625·b +5

At the maximum point, therefore, we have;

b·(2·(0.0625·b +5) - 10) + c - (16·(0.0625·b +5)²-160·(0.0625·b +5) +400

At the max value of f(2·x - 10) = b²/16 + c

Since b²/16 + c = 20, we have the maximum value of (2·x - 10) = 20.

Answer:

A,  40.16

Step-by-step explanation:

cosθ = adjacent (BC) / hypotenuse (AB)

cos 17° = BC / 42

BC = 40.16

Answer:

[tex]\boxed{BC = 40.16}[/tex]

Step-by-step explanation:

Cos 17 = [tex]\frac{adjacent}{hypotenuse}[/tex]

Where adjacent = BC, hypotenuse = 42

0.959 = [tex]\frac{BC}{42}[/tex]

BC = 0.959 * 42

BC = 40.16

Answer:

31/12

Step-by-step explanation:

-5/12 - (-9/3)

Distribute the negative sign to the brackets.

-5/12 + 9/3

Make denominators equal and add.

-5/12 + 36/12

= 31/12

Answer:

31/12

Step-by-step explanation:

Find the least common denominator, which is 12, then combine

You have to add the fractions because two negative signs equals to positive

-5/12 + 36/12

-5+36=31

Therefore your answer is 31/12

Hope this helps please mark brainliest!

Answer:

D) $270.00

Step-by-step explanation:

15% of 1800 is 270 which is exactly what the dollar amount of the discount would be

Answer:

D.) $270.00

Step-by-step explanation:

I got this by first turning 15% into its decimal form:

[tex]15%[/tex]% [tex]= .15[/tex]

Once I did this I multiplied the decimal form by the price of the motorcycle.

[tex]1,800[/tex] × ·[tex]15[/tex] = [tex]270[/tex]

Answer:

The function is a direct variation function with a constant of variation of 1.5.

Step-by-step explanation:

I just took the test :/

Answer:

The function is a direct variation function with a constant of variation of 1.5.

Step-by-step explanation:

Step-by-step explanation:

so her minimum 4th score is calculated this way:

[tex] \frac{230 + 185 + 195 + x}{4} = 210 \\ 610 + x = 840 \\ x = 230[/tex]

so in round four

her score should be x in the way that:

x≥230

Answer:

Step-by-step explanation:

Compound Interest Formula, Amount, [tex]A(n)=P(1+r)^n[/tex]

Interest=Amount - Principal

[tex]I=P(1+r)^n-P[/tex]

At the end of 1 year, interest =Rs450, therefore:

[tex]450=P(1+r)-P\\450=P+Pr-P\\450=Pr[/tex]

At the end of 2 years, interest =Rs945, therefore:

[tex]945=P(1+r)^2-P\\945=P(1+r)(1+r)-P\\945=P(1+r+r+r^2)-P\\945=P(1+2r+r^2)-P\\945=P+2Pr+Pr^2-P\\945=2Pr+Pr^2[/tex]

Recall: Pr=450

Therefore:

[tex]945=2(450)+Pr^2\\945-900=Pr^2\\Pr^2=45[/tex]

Comparing Pr=450 and [tex]Pr^2=45[/tex]

[tex]\dfrac{Pr^2}{Pr}= \dfrac{45}{450}\\r=0.1[/tex]

Substitute r=0.1 to obtain P

0.1P=450

P=Rs4500

Therefore:

Answer:

[tex] 7.25 \: units[/tex]

Step-by-step explanation:

[tex]d \bigg(5 \frac{1}{2}, \: \: - 1 \frac{3}{4} \bigg) \\ \\ = d \bigg( \frac{11}{2}, \: \: - \frac{7}{4} \bigg) \\ \\ = d \bigg( \frac{22}{4}, \: \: - \frac{7}{4} \bigg) \\ \\ = \frac{22}{4} - \bigg( - \frac{7}{4} \bigg) \\ \\ = \frac{22}{4} + \frac{7}{4} \\ \\ = \frac{22 + 7}{4} \\ \\ = \frac{29}{4} \\ \\ = 7. 25\: units[/tex]

Answer:

the fifth number is 70

Step-by-step explanation:

mean (average) of first 5 numbers =50 , Then sum of this 5 numbers = 50*5 =250.

The mean  of 4 numbers = 45 . Sum 4 numbers = 45*4 = 180

the fifth number is 250-180=70

(180 +70)/5=50 which is the mean

Answer:

The correct answer is:

b. 6

Step-by-step explanation:

We are given the graph of an exponential function.

We have to find the average rate of change for this exponential function from x = 2 to x = 4.

First of all, let us plot the point on the graph on the points x = 2 and x = 4.

Please refer to the attached diagram.

We can easily find that the value of y at x = 2 is 4.

the value of y at x = 4 is 16.

[tex]\therefore[/tex] the coordinates are (2, 4) and (4, 16).

Let the points be A(2, 4) and B(4, 16)

Now, let us find the average rate of change for exponential function i.e. change in value of y divided by change in value of x from x = 2 to x = 4:

Formula:

[tex]\text{Average rate of change = } \dfrac{\text{Change in y coordinate}}{\text{Change in x coordinate}}[/tex]

[tex]\Rightarrow \dfrac{16-4}{4-2}\\\Rightarrow \dfrac{12}{2}\\\Rightarrow 6[/tex]

So, correct answer is option b. 6

Answer:

B

Step-by-step explanation:

The area of the square can be calculated using S^2 = x^2

The area of the circle is pi * r^2

= 22/7 * (x-1)^2

= 22(x-1)^2/7

So we need the value of x, that will make;

x^2 = 22(x-1)^2/7

In this kind of scenario, since we have options, it is best to test values instead of going through long calculations

Let’s try 2.29

So;

2.29^2 = 22/7(2.29-1)^2

5.2441 = 5.23

So close , but let’s see if any other value will

give us a closer value

Let’s work with 1.66

1.66^2 = 22/7(1.66-1)^2

2.7556 = 1.369

This is far from what we need

Let’s try 0.5

0.5^2 = 22/7(0.5-1)^2

Thus gives a negative answer on the right hand side, so no need trying

And lastly 1.25

1.25^2 = 22/7(1.25-1)^2

1.5625 = 0.1946

So the first test still gives the most probable answer to a decimal place accuracy

Answer:

b. 2.29

Step-by-step explanation:

the answer above is correct please give them the brainiest  

Answer:

B

Step-by-step explanation:

a parabola would be x2 since it is square rooted it would be a curved so the answer would be the second graph

Answer:

month 5

Step-by-step explanation: