EXERCISE 81 Solve each of the following word problems: 1) A triangular shaped roof is 4 metres in all sides. What is its perimeter
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Step-by-step explanation:

180-(90° +32°)

180- 122= 58

triangle =180°

180° - (58° +58°)

180° - 116°= 64°

Answer:

x=64

Step-by-step explanation:

∠A = 180-(90°+32°)

=> ∠A=180-122= 58

Angle sum property in Triangle=180°

=> x = 180° - (58°+58°)

=> x = 180° - 116°= 64°

the sum of triangle is 180:

[tex]y + 40 + y + 30 = 180 \\ 2y + 70 = 180 \\ 2y = 180 - 70 \\ 2y = 110 \\ y = \frac{110}{2} \\ y = 55[/tex]

Answer:

[tex] \rm Numbers = 4 \ and \ -3.[/tex]

Step-by-step explanation:

Given :-

The sum of two numbers is 1 .

The product of the nos . is 12 .

And we need to find out the numbers. So let us take ,

First number be x

Second number be 1-x .

According to first condition :-

[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]

Hence the numbers are 4 and -3

Step-by-step explanation:

[tex]numbers \: = x \: and \: y \\ x \times y = - 12......(1) \\ x + y = 1..... ..(2) \\y = 1 - x \\ put \: this \: in \: (1) \\ x(1 - x) = - 12 \\ x - {x}^{2} = - 12 \\ - x + {x}^{2} - 12 = 0 \\ factorise \\ {x}^{2} - 4x + 3x - 12 = 0 \\ x(x - 4) + 3(x - 4) = 0 \\ (x - 4)(x + 3) = 0 \\ x = + 4 \: or \: - 3 \\ thank \: you[/tex]

Answer:

1/4, 1/2 and 1/3

Step-by-step explanation:

Rational numbers are numbers that can be expressed in the form a/b

So for ease of answering, we can just select values closer to the extremes given

so we can have 1/4, 1/2 and 1/3

These three numbers are all greater than the minimum extreme (-2/3) and less than the maximum extreme

Answer:

Step-by-step explanation:

[tex]\dfrac{7}{25} =0.28=28\%\\\\\dfrac{2}{3} \approx 0.67=67\%\\\\\dfrac{3}{8} =0.375=37.5%[/tex]

Answer:

See Explanation

Step-by-step explanation:

Given

Let

[tex]S \to[/tex] Strawberry

[tex]B \to[/tex] Banana

[tex]S : B = 2 : 3[/tex]

Solving (a):

Complete the table

The table, to be complete, is not given; so, I will generate one myself.

[tex]\begin{array}{cccccc}S & {2} & {3} & {4} & {5} & {6} \ \\ {B} & {3} & {4.5} & {6} & {7.5} & {9} \ \end{array}[/tex]

The table is generated as follows:

[tex]S : B = 2 : 3[/tex]

Multiply by 1.5

[tex]S : B = 2 * 1.5 : 3 * 1.5[/tex]

[tex]S : B = 3 : 4.5[/tex]

Multiply by 2

[tex]S : B = 2*2 : 3*2[/tex]

[tex]S : B = 4 : 6[/tex]

And so on....

In summary, whatever factor is multiplied to S must be multiplied to B; in order to keep the ratio constant

Solving (b): Why the amount are proportion

Because the ratio is constant and it remains unchanged all through.

1 and -1 are the only rational numbers which are their own reciprocal.[tex] \: [/tex]

Answer:

no .... 20% is .2 not .02

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

1^3 + 2^3 + 3^3= 1+8+27

9+27= 36

Answer:

50000000000000000000000000000*50000000000000000000000000000*50000000000000000000000000000=1.25e+86

Hope This Helps!!!

Answer:

1) 1 ≥ 2·x

2) 6·x ≥ 3 + 8·x - 4

3) 1/2 ≥ x The third option and the first number line inequality diagram, please see attached drawing of the number line created with MS Visio

Step-by-step explanation:

The given inequality is presented as follows;

6·x ≥ 3 + 4·(2·x - 1)

By expanding the right hand side of the inequality, we get;

6·x ≥ 3 + 8·x - 4

4 - 3 = 1 ≥ 8·x - 6·x = 2·x

∴ 1 ≥ 2·x

1/2 ≥ x

Therefore, the correct options are;

1) 1 ≥ 2·x

2) 6·x ≥ 3 + 8·x - 4

3) 1/2 ≥ x The third option and the first number line inequality diagram

Answer:

You would pour 50.3 in^3 of juice

Step-by-step explanation:

The term ‘cubic’ indicates volume

so in the context of this question, we are to calculate the volume of the cylinder, then we divide by 2

Mathematically, we have the volume of the cylinder as;

V = pi * r^2 * h

r = 2 inch

h = 8 inch

Since we are dividing the volume by 2 (exactly half full)

V = 1/2 * pi * 2^2 * 8

V = 50.3 in^3

Answer:

10 square meters will have a standard deviation of 1.897.

Step-by-step explanation:

Standard deviation for n instances of a variable:

If the standard deviation for one instance of a variable is [tex]\sigma[/tex], for n instances of the variable, the standard deviation will be of [tex]s = \sigma\sqrt{n}[/tex]

The standard deviation of the number of flaws per square yard is 0.6

This means that [tex]\sigma = 0.6[/tex]

For the 10 square yards will a standard deviation of

[tex]n = 10[/tex], so:

[tex]s = \sigma\sqrt{n} = 0.6\sqrt{10} = 1.897[/tex]

10 square meters will have a standard deviation of 1.897.

Step-by-step explanation:

The number 0 is called a. zero polynomial. binomial.

zigya

Answer: D. between 4.79 and 4.8

Step-by-step explanation:

The square root of 23 (√23) is 4.79583152331. We can obviously eliminate A and B. C and D is left. C is wrong because if we approximate the square root of 23, which is 4.79583152331, we get 4.79. 4.79 > 4.78, so it can't be C. Hope this helps :)

i'm on the same test-

Answer:

3/9

Step-by-step explanation:

P(G,G) = 1/3 × 1/3 = 1/9

P(B,B) = 1/9

P(Y,Y) = 1/9

P(same colour) 1/9 + 1/9 + 1/9 = 3/9

Answer:

<BAC = 36degrees

Step-by-step explanation:

Find the diagram attached

The sum of the interior angle is equal to the exterior. Hence;

<B + <C = <DAB

6x+40 + x+20 = 180 - 3x

7x+60 = 180 - 3x

7x+3x = 180 - 60

10x = 120

x = 120/10

x = 12

Get <BAC

<BAC = 180 - (180-3x)

<BAC = 180-180+3x

<BAC = 3x

<BAC = 3(12)

<BAC = 36degrees

Answer:

12

Step-by-step explanation:

Given

[tex]\frac{1}{2}[/tex] x - [tex]\frac{5}{4}[/tex] + 2x = [tex]\frac{5}{6}[/tex] + x

Multiply through by 12 ( the LCM of 2, 4, 6 ) to clear the fractions

6x - 15 + 24x = 10 + 12x

Answer:

12

Step-by-step explanation:

[tex]12( \frac{1}{2}x - \frac{5}{4} +2x= \frac{5}{6} + x)[/tex]

6x-15+24x=10+12x

Answer:

27y^12

Step-by-step explanation:

you multiply the exponents together

in this case: 4×3=12

and then multiply the base number by 3 as well.

Hi there!

[tex]\large\boxed{f''(x) = 2 - \frac{4}{x^{3}}}[/tex]

[tex]f(x) = x^2 - \frac{2}{x}[/tex]

Recall the power rule:

[tex]\frac{dy}{dx} x^n = nx^{n-1}[/tex]

Rewrite the function for ease of differentiation:

[tex]f(x) =x^2 - 2x^{-1}[/tex]

Use the power rule:

[tex]f'(x) = 2x + 2x^{-2}[/tex]

Take the derivative once more:

[tex]f''(x) = 2 - 4x^{-3}[/tex]

Rewrite:

[tex]f''(x) = 2 - \frac{4}{x^{3}}[/tex]

Answer:

2

Step-by-step explanation:

a prime factor is a factor that is a prime number

a prime number is a number that will have a fraction in the quotient if it's divided by any number other than itself

2 is the only prime factor shared between 8 and 12

Answer:

Average speed = [tex]\frac{(x+y)}{2}[/tex] miles per hour

Step-by-step explanation:

Formula to calculate the average speed of an object is,

Average speed = [tex]\frac{\text{Total distance covered}}{\text{Time taken to cover this distance}}[/tex]

If I travel with the speed of x mph for t hours,

Total distance covered = Speed × Time

                                       = [tex]x\times t[/tex]

                                       = [tex]xt[/tex] miles

Similarly, if I travel with the speed y mph for t hours,

Total distance covered = [tex]yt[/tex] miles

Total distance covered by me = [tex](xt+yt)[/tex] miles

Total time taken to cover this distance = [tex]t+t[/tex]

                                                                 = [tex]2t[/tex] hours

Therefore, expression for the average speed will be,

Average speed = [tex]\frac{xt+yt}{2t}[/tex]

                          = [tex]\frac{(x+y)t}{2t}[/tex]

                          = [tex]\frac{x+y}{2}[/tex] miles per hour

1. a = 68

b = 112

c = 68

2. a = 127

3. a = 35

b = 40

c = 35

d = 70

4. a = 20

b = 70

c = 20

d = 70

e = 110

5. a = 90

b = 90

c = 42

d = 48

e = 132

6. a = 70

b = 55

c = 25

Answer:

A

Step-by-step explanation:

Answer:

Following are the solution to the given point:

Step-by-step explanation:

The formulated null hypothesis would be that the reported average do not differ significantly

[tex]H_o : \mu = \$3262\\\\H_a : \mu < \$3262 \ \text{(One tailed test)}[/tex]

Answer:

She has 9 choices for each different cheese.

For each of these cheeses there are 9 different wines,

So 9 * 9 = 81 and there are

81 possible different choices

An absolute value graph looks like a V. If the number attached to the x is positive, then the graph opens upwards. If the number attached to the x is negative, then the graph opens downwards.

In this case, the graph opens downwards.

To find the vertex, look at the |x - 1| part of the equation. This tells us that x is shifted 1 to the right (opposite of the sign). And, the 3 outside of the absolute value bars tells us that the graph is also shifted up 3. Therefore, the vertex is (1, 3).

Next, we need to figure out how to graph it. That's where the -2 in front comes in. We know the graph faces downwards already. So, from the vertex, we will go down 2 spaces and left or right 1 depending on the side you are working on. Continue this pattern just like you would graphing the slope of a regular line, but this one is two sided.

If you need to view the graph for further help, I would recommend an online graphing calculator such as Desmos.

Hope this helps!

Answer:

28.62*0.057=1.63134

so about 1.63

Hope This Helps!!!