Show the pair of straight lines are perpendicular.
C number.

Answer:

48cm²

Step-by-step explanation:

PQ=(24-5-5)/2=7

This means PR is 14 and US is 10.

The height of the parallelogram is base times height, so 28/7=4

Now we just look at it as one big parallelogram.

4(14+10)/2=48 cm²

Answer:

<

Step-by-step explanation:

Answer:

{-3.5, 3.5}

Step-by-step explanation:

Interpreting

|-x| = 3.5

gives

3.5 = +(-x)  or 3.5 = -(-x)

or

x = + / - 3.5

so the answer is

{-3.5, 3.5}

Answer:

A

Step-by-step explanation:

Answer:  b) {-3, 0.5}

Step-by-step explanation:

The new equation is the original equation plus 6.  Move the original graph UP 6 units.  The solutions are where it crosses the x-axis.

[tex]\text{Original equation:}\quad f(x)=\dfrac{15}{x}-\dfrac{9}{x^2}\\\\\\\text{New equation:}\quad\dfrac{15}{x}+6=\dfrac{9}{x^2}\\\\\\.\qquad \qquad f(x)= \dfrac{15}{x}-\dfrac{9}{x^2}+6[/tex]

+6 means it is a transformation UP 6 units.  

Solutions are where it crosses the x-axis.

The curve now crosses the x-axis at x = -3 and x = 0.5.

Answer:

We could rewrite 7/2 as 7a + 2

Step-by-step explanation:

Complex numbers is when real numbers [i.e: 1, 1/2, 200, 5/7, etc..) and an imaginary numbers [numbers that give a negative result when squared] are combine together.

Answer:

b) 36 inches

Step-by-step explanation:

Length  of the  wire = Outside circumference of the cylindrical tube * length of the cylinder

= 4 * 9

= 36 inches

Length of the wire will be same to the surface area of the cylinder

Surface area of cylinder = circumference * length

Answer:

855.298 m^3

Step-by-step explanation:

The volume of a cylinder equation is piR^2H.

So pi5.5^2×9

855.298 m^3

Answer:

Step-by-step explanation:

y = 2x + 4a/6b   y=(12xb+4b )/6b

6yb=12x+4a

a=(-12xb+6yb)/4=

a=3yb/2 -3xb

x=y/2-a/3b

b=2a/(3y-6x)

the solution is for every variable

Answer:

6

Step-by-step explanation:

The Fundamental theorem of Algebra states that a polynomial of degree n has n roots. These can be real, complex or both.

f(x) = 2[tex]x^{6}[/tex] - 3x³ + 1 - 2[tex]x^{5}[/tex] ← is a polynomial of degree 6

Thus the maximum number of real roots is 6

Answer:

$45.

Step-by-step explanation:

When the TV is bought on hire purchase, you deposit $35 and pay $30 monthly. There are 12 payments. 12 * 30 = $360. 360 + 35 = $395.

Since cash would've cost $350, the amount of money saved by paying cash is 395 - 350 = $45.

Hope this helps!

Answer:

[tex]H_{o}[/tex]: Larger proportion of news media = democrats

Ha : Large proportion of news media [tex]\neq[/tex] democrats  

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis.

Answer:

The correct option is;

We cannot infer a cause and effect relationship because we do not have a control group

Step-by-step explanation:

The treatment in research involves giving stimulus known as treatment to a group or portion of the sample which are then known as the treatment group while the remaining portion of the the sample are exempted from the stimulus. A successful treatment manipulation is one where members of the treatment group perform higher in the measured metrics of the research than members of the control group.

Given that the researchers gathered data from a random sample of drivers and measurement of several variables  including the explanatory  variable of the of the research without subjecting a sample to a treatment or having a control group we cannot infer a cause and effect relationship as there are no control group

Answer:

Step-by-step explanation:

If the number of representatives of a multi-level marketing company as a function of the number of days that have passed can be modeled by the exponential function R(d) = 150(1.03)^d, to calculate the number of representatives that the company have after 75 days, we will substitute d = 75 into the modeled equation.

R(75) = 150(1.03)^75

R(75) = 150*9.1789

R(75) = 1,376.835

Hence, the company have about 1377 representatives after 75 days.

Answer:

Step-by-step explanation:

can you at least telllus what is in the drop box

Answer:

O B. 17 units

Step-by-step explanation:

The chord is AC and the radius of the circle is perpendicular to the chord at B. AB = 8.5 units. According to the perpendicular bisector theorem, if the radius of a circle is perpendicular to a chord then the radius bisects the chord. This means that chord AC is bisected by the radius of the circle at point B. The length of the circle is calculated using:

[tex]AB=\frac{AC}{2}\\ AC=2*AB\\cross multiplying:\\AC = 2*8.5\ units\\AC = 17 \ units[/tex]

The length of the chord is 17 units.

Answer:

The answer is 17 units :D

Step-by-step explanation:

Answer:

153.586 close to 154 students

Step-by-step explanation:

mean=61

standard deviation =10

sample 450 students , x between 61 and 71

(x-mean)/deviation for score 61 and 71

61-61/10=0

71-61/10=1

the z-scores is between 0 and 1 ( use calculator)

the percentage is 0.3413 close to 34%

number of students that score between 61 and 71=

450*0.3413= 153.586 close to 154 students

Answer:

Step-by-step explanation:

Question:

7^1/5

The number given has an exponent of a fraction: fraction exponent = 1/5

Since the top is one, the number 7 stays the same. = 7^1 = 7

The bottom is a 5. This means it is to the fifth root.

Answer = D

Hope this helped,

Kavitha

Answer: If 36/7 is one of the options, choose that one.

If the question involves an exponent, you should use the "caret" which is ^ found above the 6 on a keyboard. [Shift + 6]. That helps avoid confusion.

Step-by-step explanation: 7 is equal to 35/5 because 7×5=35

Add 1/5 and you end up with 36/5. A Common rational number.

7^(1/5) = the 5th root of 7. A very small irrational number!

Answer:

tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]

The height of the blimp above the ground is h = 153.884 yard

No,  the fans will not be able to read the advertisement.

The exact angle if the blimp is at 150 feet is 45.74°

Step-by-step explanation:

From the summary of the information given :

The angle of elevation from a point directly under the goal post is 72° and the blimp will be directly above the 50 yard line.

That statement above being illustrated in the attached diagram below for better understanding.

a. Which trigonometric ratio would you use to calculate how high the blimp will be above the 50 yard line?

The trigonometric ratio that can be used to calculate how high the blimp will be above the 50 yard line is :

tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]

b. How high above the ground is the blimp?

Using the above derived trigonometric ratio,

tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]

[tex]tan \ 72^0 = \dfrac{h}{50}[/tex]

[tex]h =tan \ 72^0 \times {50}[/tex]

[tex]h =3.07768 \times {50}[/tex]

h = 153.884 yard

The height of the blimp above the ground is h = 153.884 yard

c. In order to be able to read the advertisement on the side of the blimp the highest the blimp can be is 150 feet.

Will the fans be able to read the advertisement?

No,  the fans will not be able to read the advertisement.

This is  because, 153.884 yard to feet

=  153.884 × 3

= 461.652 feet which is more than the maximum given 150 feet.

If not, what possible angle of elevation could we use?

The possible angle of elevation can be determined by taking the tangent of the trigonometric ratio.

SO

tan θ = [tex]\dfrac{h}{150}[/tex]

tan θ = [tex]\dfrac{153.884}{150 \ feet}[/tex]

tan θ =  1.026

θ = tan ⁻¹ (1.026)

θ = 45.74°

d. What is the exact angle if the blimp is at 150 feet?

The exact angle if the blimp is at 150 feet is 45.74°

Answer:

$35

Step-by-step explanation:

Using the formula provided, d=(p−c)÷2 (where d is the discount, p is the original price, and c is the store's cost for the dress.) we can determine the discount.

The original price is 120,

d=(120−c)÷2

The store's cost is 50,

d=(120−50)÷2

So we subtract 120 and 50 to get

d=(70)÷2

70 divide by two is

d= 35

The discount is $35

Answer:

[tex]\approx[/tex] 11 litres of water will fit inside the container.

Step-by-step explanation:

As per the given figure, we have a container formed with combination of a right angled cone placed at the top of a right cylinder.

Given:

Height of cylinder, [tex]h_1[/tex] = 15 cm

Diameter of cylinder/ cone, D = 26 cm

Slant height of cone, l = 20 cm

Here, we need to find the volume of container.[tex]\\Volume_{Container} = Volume_{Cylinder}+Volume_{Cone}\\\Rightarrow Volume_{Container} = \pi r_1^2 h_1+\dfrac{1}{3}\pi r_2^2 h_2[/tex]

Here,

[tex]r_1=r_2 = \dfrac{Diameter}{2} = \dfrac{26}{2} =13\ cm[/tex]

To find the Height of Cylinder, we can use the following formula:

[tex]l^2 = r_2^2+h_2^2\\\Rightarrow h_2^2 = 20^2-13^2\\\Rightarrow h_2^2 = 400-169\\\Rightarrow h_2^2 = 231\\\Rightarrow h_2=15.2\ cm \approx 15\ cm[/tex]

Now, putting the values to find the volume of container:

[tex]Volume_{Container} = \pi \times 13^2 \times 15+\dfrac{1}{3}\pi \times 13^2 \times 15\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 15+\pi \times 13^2 \times 5\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 20\\\Rightarrow Volume_{Container} = 10613.2 \approx 10613\ cm^3[/tex]

Converting [tex]cm^{3 }[/tex] to litres:

[tex]10613 cm^3 = 10.613\ litres \approx 11\ litres[/tex]

[tex]\approx[/tex] 11 litres of water will fit inside the container.

Answer:

30.045

Step-by-step explanation:

the length of rectangle=140 which is also the diameter of circle

R=d/2=140/2=70 ( which is the width of rectangle)

perimeter of rectangle=2l+2w=140+280=420

perimeter of semicircle=πr+d=70π+140=359.911

the difference between two perimeter

(perimeter of rectangle- perimeter of semi circle) =

420-359.911=60.089

since only one shaded area :

60.089/2=30.0445 close to 30.045

Answer:

Real interest rate = -1%

Step-by-step explanation:

Real interest rate=Nominal interest rate - inflation rate

From the above,

Nominal interest rate=1%

Inflation rate=2%

Real interest rate=Nominal interest rate - inflation rate

=1% - 2%

= -1%

Real interest rate = -1%

Real interest rate shows you what it really costs borrowers to pay back their loans.

if the real interest rate is greater than zero, the amount you pay back is worth more in real terms than the money you borrowed.

if the real interest rate is below zero as in the above case, the amount you will pay back is less worth in real terms than the money you borrowed.

Answer:

0.431 inches

Step-by-step explanation:

We were given the following values:

Height the tennis ball was dropped = 100in

Rebound height = 58in

We have to find the rebound ratio

= 58in/100in = 0.58

The formula to be used

Height on nth bounce = Initial height × (Rebound ratio)ⁿ

Where n = number of bounce

Height on the 10th bounce = 100 × (0.58)^10

Height on the 10th bounce = 0.4308042069inches

Approximately, the height on the 10th bounce = 0.431 inches.

Answer:

[tex]\sf x=\frac{1}{10}[/tex]

Step-by-step explanation:

Rewrite expression with bases of 4.

[tex]\sf{4^{\frac{3}{4} }} \times \sf({4^\frac{1}{2} )^x =(4^2)^{\frac{2}{5} }[/tex]

Apply law of exponents, when bases are same for exponents in multiplication, add the exponents. When a base with an exponent has a whole exponent, then multiply the two exponents.

[tex]\sf{4^{\frac{3}{4} }} \times \sf{4^{\frac{1}{2} x}=4^{\frac{4}{5} }[/tex]

[tex]\sf{4^{\frac{3}{4} +\frac{1}{2} x}=4^{\frac{4}{5} }[/tex]

Cancel same bases.

[tex]\sf \frac{3}{4} +\frac{1}{2} x=\frac{4}{5}[/tex]

Subtract 3/4 from both sides.

[tex]\sf \frac{1}{2} x=\frac{1}{20}[/tex]

Multiply both sides by 2.

[tex]\sf x=\frac{1}{10}[/tex]

Step-by-step explanation:

2^{2*3/4} × 2^{x}=2^{4×2/5}

2^{3/2} × 2^{x}= 2^{8/5}

2^{3/2+x}=2^{8/5}

equate powers

{3+2x}/2= 2^2

5{3+2x}= 2{8}

15+10x=16

collect like terms

10x=16-15

10x=1

divide both sides by 10

x=1/10

x=0.1

Question:

Find the value of the letter in each of the following and give reasons for the steps involved:

1 2 A

+ 6 A B =

A 0 9

Answer:

128 + 681 =  809

Step-by-step explanation:

Here, let's use the general form of numbers where any  letter must represent one value and each digit must be represented by just one letter.

Take the following:

A = 8

B = 1

Thus, A +B = 8 + 1 = 9

Also add:

8 + 2 = 10

In general form, tens digit is zero and the 1 is carried over.

I.e, A = 1 + 6 + 1 = 8

We can now see that,

A = 8

B = 1

Therefore,

1 2 A

+ 6 A B =

A 0 9

Will be written as:

128 + 681 =  809

D. The line is perpendicular to the plane determined by the two lines.

Remember how you get to 3D space?

You take one axis called x and perpendicularly intersect it with y axis and you get a 2D plane. Now take a 2D plane and perpendicularly intersect it with an axis z and you get 3D euclidean space.

Hope this helps.

Answer:

[tex]7 < x < 37[/tex] -- Triangle 1

[tex]6.5 < x < 19.9[/tex] -- Triangle 2

[tex]22 < x < 46[/tex] -- Triangle 3

[tex]21 < x < 67[/tex] -- Triangle 4

Step-by-Step Explanation:

Given

2 sides of a triangle

1. 22 and 15

2. 13.2 and 6.7

3. 34 and 12

4. 23 and 44

Required

Determine the range of the third side in the above triangles

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]22 + x > 15[/tex]

[tex]22 + 15 > x[/tex]

[tex]15 + x > 22[/tex]

Solving

[tex]22 + x > 15[/tex]

Make x the subject of formula

[tex]x > 15 - 22[/tex]

[tex]x > -7[/tex]

Solving

[tex]22 + 15 > x[/tex]

[tex]37 > x[/tex]

Solving

[tex]15 + x > 22[/tex]

Make x the subject of formula

[tex]x > 22 - 15[/tex]

[tex]x > 7[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]37 > x[/tex] and [tex]x > 7[/tex]

Rewrite both inequalities

[tex]x < 37[/tex] and [tex]7 < x[/tex]

Combine the two inequalities

[tex]7 < x < 37[/tex]

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]13.2 + x > 6.7[/tex]

[tex]13.2 + 6.7 > x[/tex]

[tex]6.7 + x > 13.2[/tex]

Solving

[tex]13.2 + x > 6.7[/tex]

Make x the subject of formula

[tex]x > 6.7 - 13.2[/tex]

[tex]x > -6.5[/tex]

Solving

[tex]13.2 + 6.7 > x[/tex]

[tex]19.9 > x[/tex]

Solving

[tex]6.7 + x > 13.2[/tex]

Make x the subject of formula

[tex]x > 13.2 - 6.7[/tex]

[tex]x > 6.5[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]19.9 > x[/tex] and [tex]x > 6.5[/tex]

Rewrite both inequalities

[tex]x < 19.9[/tex] and [tex]6.5 < x[/tex]

Combine the two inequalities

[tex]6.5 < x < 19.9[/tex]

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]34 + x > 12[/tex]

[tex]34 + 12 > x[/tex]

[tex]12 + x > 34[/tex]

Solving

[tex]34 + x > 12[/tex]

Make x the subject of formula

[tex]x > 12 - 34[/tex]

[tex]x > -22[/tex]

Solving

[tex]34 + 12 > x[/tex]

[tex]46 > x[/tex]

Solving

[tex]12 + x > 34[/tex]

Make x the subject of formula

[tex]x > 34 - 12[/tex]

[tex]x > 22[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]46 > x[/tex] and [tex]x > 22[/tex]

Rewrite both inequalities

[tex]x < 46[/tex] and [tex]22 < x[/tex]

Combine the two inequalities

[tex]22 < x < 46[/tex]

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]23 + x > 44[/tex]

[tex]23 + 44 > x[/tex]

[tex]23 + x > 44[/tex]

Solving

[tex]23 + x > 44[/tex]

Make x the subject of formula

[tex]x > 23 - 44[/tex]

[tex]x > -21[/tex]

Solving

[tex]23 + 44 > x[/tex]

[tex]67 > x[/tex]

Solving

[tex]23 + x > 44[/tex]

Make x the subject of formula

[tex]x > 44 - 23[/tex]

[tex]x > 21[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]67 > x[/tex] and [tex]x > 21[/tex]

Rewrite both inequalities

[tex]x < 67[/tex] and [tex]21 < x[/tex]

Combine the two inequalities

[tex]21 < x < 67[/tex]