What is the volume of this prism?
3 cm
3 cm
20 cm
13 cm
13 cm
6 cm

5x² + x - 6 = 0

Δ = 1² - 4*5*(-6) = 121 = 11²

x' = (-1 - 11) / (2x5) = -12/10 = - 6/5

x" = (-1 + 11) / (2x5) = 10/10 = 1

=> D

The values of x will the function [tex]f (x) = 5x^2 + x - 6[/tex] equal zero are x = - 6/5 and x = 1. Hence option D is true.

Used the concept of a quadratic equation that states,

An algebraic equation with the second degree of the variable is called a Quadratic equation.

Example; ax² + bx + c = 0

Given that the quadratic equation,

[tex]f (x) = 5x^2 + x - 6[/tex]

Now for the values of x at which the function equals zero, we have to find the zeroes of the function by using the factorization method.

[tex]f (x) = 5x^2 + x - 6[/tex]

[tex]f (x) = 5x^2 + (6 - 5)x - 6[/tex]

[tex]f (x) = 5x^2 + 6x - 5x - 6[/tex]

[tex]f (x) = x (5x + 6) - 1 (5x + 6)[/tex]

[tex]f (x) = (5x + 6) (x - 1)[/tex]

Hence, the value of zeroes,

[tex]5x + 6 = 0[/tex]

[tex]5x = - 6[/tex]

[tex]x = \dfrac{- 6}{5}[/tex]

And, [tex]x - 1 = 0[/tex]

[tex]x = 1[/tex]

So, the value of x is x = - 6/5 and x = 1. Hence option D is true.

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Answer:

The solution is x = 2

Step-by-step explanation:

i) 3x+2y=4

ii) 2x-y=5

Let's isolate y for the second equation

2x-y=5

2x-5 = y

y = 2x-5

Now use this y and substitute it in the first equation.

3x+2y=4

3x + 2(2x-5) = 4

3x + 4x - 10 = 4

7x / 7 = 14 / 7

x = 2

Answer:

A) -4,-4/3,-4/9,-4/27

B) converge

C) no idea

The factored form of the equation 9x⁴y - 6x³y² + 3x²y³ is 3x²y(3x²-2xy+y²).

The product of a constant and two linear expressions in factored form. The roots of the function are the parameters and the x-intercepts of the graph. Often Factoring is referred to as the process of converting a quadratic function to factored form.

We need to write the given expression [tex]9x^4y-6x^3y^2 + 3x^2y^3[/tex] in the factored form, therefore, we will take the common terms out of the given expression,

1. Taking 3 as the common term, we will get,

[tex]9x^4y-6x^3y^2 + 3x^2y^3\\\\= 3 (3x^4y-2x^3y^2 + x^2y^3)[/tex]

2. Taking x² as the common term

[tex]= 3 (3x^4y-2x^3y^2 + x^2y^3)\\\\= 3x^2(3x^2y-2xy^2+y^3)\\\\[/tex]

3. Taking y as the common term,

[tex]= 3x^2(3x^2y-2xy^2+y^3)\\\\= 3x^2y(3x^2-2xy+y^2)\\\\[/tex]

Hence, the factored form of the equation 9x⁴y - 6x³y² + 3x²y³ is 3x²y(3x²-2xy+y²).

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Answer:

5(9)+4= 45+4.....= 49

Step-by-step explanation:

Answer:

12.

Step-by-step explanation:

3, 4, and 12 all divide into 12 .

Answer:

Yes

Step-by-step explanation:

4(3) - 28 = -16

12= -16 + 28

12 = 12

Hope that helps!

Step-by-step explanation:

please mark me as brainlest

Answer:

x = 51

Step-by-step explanation:

If the mean = 11.5, then that means all numbers added together divided by four = 11.5. Let's write this algebraically:

[tex]\frac{12.5+(-10)+(-7.5)+x}{4}=11.5[/tex]

Now, let's solve for x:

[tex]12.5-10-7.5+x=11.5(4)[/tex]

[tex]-5+x=46[/tex]

[tex]x=51[/tex]

I hope this helps!

Answer:

X=3

[tex] {3}^{2} + 6(3) - 3 \\ 9 + 18 - 3 \\ 27 - 3 \\ = 24[/tex]

Answer:

Proportional

Step-by-step explanation:

[tex]\frac{10}{24}= \frac{5}{12}[/tex] the ratio is 2:1

5 x 2 = 10

12 x 2=24

The ratios are proportional.

Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!

Stay Brainy!

−Kallmekrish

Answer:

The given ratios are proportional

Step-by-step explanation:

To consider the fractions as "proportional", they must be equivalent. Let us assume that the fractions are equivalent. Then, we get;

[tex]\implies \dfrac{10}{24} = \dfrac{5}{12}[/tex]

When using cross multiplication, we get;

[tex]\implies \dfrac{10}{24} = \dfrac{5}{12}[/tex]

[tex]\implies 10 \times 12 = 24 \times 5[/tex]

When simplified, we get;

[tex]\implies 10 \times 12 = 24 \times 5[/tex]

[tex]\implies 120 = 120 \ \checkmark[/tex]

Therefore, the relationship is proportional.

Answer:

1/4; 25%

Step-by-step explanation:

if a year has four seasons we can say that there are 4 possibilities

spring appears once

this means that the probability that a day chosen at random will be in spring would be 1 out of 4

or 25%

Answer:

Umm..... sorry but.....my answer came.......

The probability that the number picked is divisible by 3 or 5 is 0.555.

Probability sampling is defined as a sampling technique in which the researcher chooses samples from a larger population using a method based on the theory of probability.

An integer number is chosen randomly between 1 and 1000.

The number of numbers divisible by 3, which is;

[tex]\rm \dfrac{1000}{3}=3333.3 = 333[/tex]

The number of numbers divisible by 5, which is;

[tex]\rm \dfrac{1000}{5}=200[/tex]

The probability that the number picked is divisible by 3 or 5 is;

[tex]\rm Probability=\dfrac{Number \ divisble \ by \ 3+ Number \ divisble \ by \ 5}{1000}\\\\ Probability =\dfrac{333+200}{1000}\\\\Probability=\dfrac{533}{1000}\\\\Probability=0.533[/tex]

Hence, the probability that the number picked is divisible by 3 or 5 is 0.555.

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Answer:

x2+x-2

Step-by-step explanation:

i had this question before

The number of btus which are needed to cool Lucia’s apartment shown in the three-dimensional model are 20,400 btus.

Volume of rectangular prism is the amount of quantity, which is obtained in it in the 3 dimensional space.

Volume of a rectangular prism is the product of its width, height and length.

[tex]V=w\times h\times l[/tex]

Here, (w) is the width of the base (l) is the length and (h) is the height of the rectangular prism.

A three-dimensional model of Lucia’s apartment is shown. The image is attached below for the apartment. The three section are there in the apartment. The volume of this apartment is,

[tex]V=[(20\times12)+(20-9)\times16+(20\times20)]\times10\\V=8160\rm\; ft^3[/tex]

To cool the whole apartment, an air conditioner must provide 2.5 btus per cubic foot. To cool, the 8160 cubic foot apartment the btus needed are,

[tex]n=8160\times2.5\\n=20400\rm\; btus[/tex]

Hence, the number of btus which are needed to cool Lucia’s apartment shown in the three-dimensional model are 20,400 btus.



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Answer:

20,400 BTUs

Step-by-step explanation:

A vertical stretch of scale factor 2, followed by a translation of 4 units left and 1 unit down is written as:

g(x) = 2*f(x + 4) - 1

For a general function f(x), a vertical stretch of scale factor K is written as:

g(x) = K*f(x).

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

So, if we start with a function f(x) and we stretch it vertically with a scale factor of 2, we get:

g(x) = 2*f(x)

Then we translate it 4 units left:

g(x) = 2*f(x + 4)

Then we translate 1 unit down:

g(x) = 2*f(x + 4) - 1

This is the equation for the transformation.

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Answer:

i dont know use the internet

Step-by-step explanation:

this is the right way

Answer:

height of tress is 20 feet

Step-by-step explanation:

because tan = perpendicular/ height

we see option only 20 feet satisfy it

Answer:

Option D :- 20 feet

Step-by-step explanation:

[tex] \sf \tan ( \theta) = \frac{height}{distance} [/tex]

[tex] \rightarrow \sf \: \tan (\theta) = \frac{20}{50} [/tex]

[tex] \sf \: height \: = 20 \: ft[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♫[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \frac{1}{2} (5 + 13) - 4.5[/tex]

[tex]\qquad \sf  \dashrightarrow \: \frac{1}{2} (18) - 4.5[/tex]

[tex]\qquad \sf  \dashrightarrow \: 9 - 4.5[/tex]

[tex]\qquad \sf  \dashrightarrow \:4.5[/tex]

[tex]\qquad \sf  \dashrightarrow \:(5 + 11) - (24 - 15) \times 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:16 - (9 \times 3)[/tex]

[tex]\qquad \sf  \dashrightarrow \:16 - 27[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 11[/tex]

[tex]\qquad \sf  \dashrightarrow \: {6}^{2} + (3 \times 7) - (9 \div 3)[/tex]

[tex]\qquad \sf  \dashrightarrow \:36 + 21 - 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:57 - 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:54[/tex]

Answer:

According to question if we observe, number of red sweets are the least

It 's only 1%

Step-by-step explanation:

On average, people visit Thrillville 2 more times per year than Funland.

To determine how many more times per year, on average, do people visit Thrillville than Funland, the following calculation must be performed:

Therefore, on average, people visit Thrillville 2 more times per year than Funland.

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Answer:

Step-by-step explanation:

29-9=20

9-(-11)=20

50×-20=-1000

-1000+29=-971

Answer:

x<3 and x>2

Step-by-step explanation:

write the symbols this < and > to get the correct answer

Answer:

y = -7.235451 x^2 + 402.5542 x - 2382.736

Answer:

Step-by-step explanation:

Formulae

Area of a triangle = 1/2 x base x height

Area of a rectangle = width x length

Question 1

Surface area of square based pyramid = area of base + 4 × area of triangle

⇒ SA = (6 × 6) + 4(1/2 × 6 × 14)

         = 36 + 168

         = 204 yd²

Question 2

Surface area of a cuboid = 2 × base area + 2 × end area + 2 × side area

⇒ SA = 2(10 × 6) + 2(6 × 3) + 2(10 × 3)

         = 120 + 36 + 60

         = 216 mm²

Extra credit question

Surface area of a triangular based prism = base area + 2 × triangle area + 2 × side areas

base area = 3 × 10 = 30 mm²

triangle area = 1/2 × 3 × 2 = 3 mm²

side area = 10 × 2.5 = 25 mm²

⇒ total SA = 30 + (2 × 3) + (2 × 25)

                 = 30 + 6 + 50

                 = 86 mm²

❍ Concept :-

We can solve these questions by using the formulas of area of triangle and rectangle, which will make our work easier. So, we know that,

⠀

[tex] \blue{ \underline{ \boxed{ \begin{array}{cc} \sf1. ~Area_{Triangle} = \dfrac{1} {2} \times b \times h \qquad \: \: \: \: \: \: \: \\ \\ \\ \sf2. \: Area_{Rectangle} = Length \times Breadth \end{array}}}} \\ \\ [/tex]

Using these formulas and figuring out the number of triangles and rectangles in each shape, we will solve this question.

⠀

✰ Solution :-

⠀

1. In this square pyramid, if we closely observe, we will get to know that there are 1 rectangle and 4 triangular faces. Thus,

⠀

[tex]\sf \hookrightarrow Area=6 \times 6 + 4( \dfrac{1}{2} \times 6 \times 14) \\ \\ \\ \sf \hookrightarrow Area=36 + 168 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {204 \: yd}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ [/tex]

⠀

2. Now, here, we can use the formula of total surface area for cuboid, i.e.

⠀

TSA = 2( lb + bh + hl )

⠀

[tex]\sf \hookrightarrow Area=2(10 \times 6 + 6 \times 3 + 10 \times 3) \\ \\ \\ \sf \hookrightarrow Area=2(60 + 18 + 30) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=2 \times 108 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {216 \: mm}^{2} \: \: \qquad \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

⠀

Extra Credit Question.

⠀

Here, we can find out the total surface area by finding,

⠀

Base area i.e. length x breadth ( B.A. )

Side area i.e. length x breadth ( S.A. )

triangular area = 1/2 x b x h ( T.A. )

⠀

Now,

⠀

TSA = BA + 2 x S.A. + 2 x T.A.

⠀

[tex]\sf \hookrightarrow Area=(10 \times 3) + 2(10 \times 2.5) + 2(\dfrac{1}{2} \times 3 \times 2) \\ \\ \\ \sf \hookrightarrow Area= 30 + 2 \times 25 + 2 \times 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=30 + 50 + 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {86 \: mm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

Answer:

Step-by-step explanation:

Answer:

The answer would be 1/4% or 25%.

Step-by-step explanation:

The reason why is that there were 20 students in the class. 5 people wanted to work in groups. That is 25% of the students. That is why 25% or 1/4% is your answer.