Three math questions

Answer:

77.  [tex]\cot^{6} x = \cot^{4} x \csc^{2}x - \cot^{4} x[/tex]Proved

78.  [tex]\sec^{4}x \tan^{2} x = \sec^{2}x [\tan^{2}x + \tan^{4}x ][/tex] Proved

79. [tex]\cos^{3} x\sin^{2} x = [\sin^{2}x - \sin^{4}x] \cos x[/tex] Proved.

80. [tex]\sin^{4}x - \cos^{4}x = 1 - 2\cos^{2}x + 2 \cos^{4} x[/tex] Proved.

Step-by-step explanation:

77. Left hand side

= [tex]\cot^{6} x[/tex]

= [tex]\cot^{4} x \times \cot^{2} x[/tex]

= [tex]\cot^{4}x [\csc^{2}x - 1][/tex]  

{Since we know, [tex]\csc^{2} x - \cot^{2}x = 1[/tex]}

= [tex]\cot^{4} x \csc^{2}x - \cot^{4} x[/tex]  

= Right hand side (Proved)

78. Left hand side

= [tex]\sec^{4}x \tan^{2} x[/tex]

= [tex]\sec^{2} x [1 + \tan^{2}x] \tan^{2} x[/tex]  

{Since [tex]\sec^{2}x - \tan^{2}x = 1[/tex]}

= [tex]\sec^{2}x [\tan^{2}x + \tan^{4}x ][/tex]

= Right hand side (Proved)

79. Left hand side  

= [tex]\cos^{3} x\sin^{2} x[/tex]

= [tex]\cos x[1 - \sin^{2} x] \sin^{2} x[/tex]

{Since [tex]\sin^{2}x + \cos^{2} x = 1[/tex]}

= [tex][\sin^{2}x - \sin^{4}x] \cos x[/tex]

= Right hand side

80. Left hand side  

= [tex]\sin^{4}x - \cos^{4}x[/tex]

= [tex][\sin^{2}x + \cos^{2}x]^{2} - 2\sin^{2} x \cos^{2}x[/tex]

{Since [tex]\sin^{2}x + \cos^{2} x = 1[/tex]}

= [tex]1 - 2\cos^{2} x[1 - \cos^{2}x ][/tex]

= [tex]1 - 2\cos^{2}x + 2 \cos^{4} x[/tex]

= Right hand side. (Proved)

Answer:

The numbers are 40 and 49

Step-by-step explanation:

Smaller number = x

Larger number = y

Let's write our system of equations:

x + y = 89

3x = y + 71

***************************

x = 89 - y

Substituting x in the 2nd equation and solving for y:

3 (89 - y) = y + 71

267 - 3y = y + 71

-3y - y = 71 - 267 (Like terms)

-4y = - 196

y = -196/-4

y = 49

Solving for x in the 1st equation:

x + y = 89

x + 49 = 89

x = 89 - 49

x = 40

The numbers are 40 and 49

150 cm ......... 100 %

165 cm ...............x %

x = 165×100/150 = 16500/150 = 110 %

Answer:

10%

Step-by-step explanation:

Subtract 150 from 165, which gives 15.

Then, do 15/150 = 0.1

Convert decimal to percent by moving the decimal point two spaces back. 0.1 becomes 10%.

Answer:

[tex]S'(4,6)[/tex]

Step-by-step explanation:

Dilation rules :

For a pre-image point [tex](x,y)[/tex] which is dilated by a scalar factor of [tex]k[/tex] about the origin, the corresponding point of the image can be given by [tex](kx,ky)[/tex]

Pre-image point [tex](x,y)\rightarrow (kx,ky)[/tex] Image point

Given points of quadrilateral PQRS.

P(2,10)

Q(6,8)

R(6,3)

S(2,3)

The quadrilateral is dilated about the origin by a scalar factor of 2.

The co-ordinates of point S' after dilation can be given by:

[tex]S(2,3)\rightarrow S'((2\times2),(2\times3))[/tex]

Thus [tex]S'(4,6)[/tex] (Answer)

Answer:

As jitumahi456 states B).(4, 6) is the correct answer.

Step-by-step explanation:

I took the test on edg.

Answer:

im pretty sure its c

Step-by-step explanation:

Answer:

There is 1 pear for every green apple! So in this ratio there would be 1 pear!

Step-by-step explanation:

-viridiancat4, an 8th grader! :)

1. It's True. Since it's 485 gallons every 6.5 minutes, then to find 1 minute you would do 485/6.5 which is approximately 74 gallons.

2. It's False. 85% of 33500 is 28475 gallons. If you divide that by 74, since that's the number of gallons per minute, you get approximately around 384 minutes. Since you want the time in hours, you divide 384 by 60, and you get the decimal 6.4. Since 6 hours is greater than 4 hours, it's false.

3. It's False. 64% of 33500 is 21440 gallons. 48% of 33500 is 16080 gallons. 21440-16080 is 5360 gallons, not 3360 gallons.

4. It's False. To find the percent of change, you first need to subtract 19800 from 33500, which gives you a result of 13700. Then you divide 13700/33500, which gives you a quotient of approximately 0.41. You multiply that by 100 to find the percent, which is 41%. 41% is not equal to 12%.

5. It's False. Since the unit rate is 74 gallons per minute, you divide 33500 by 74 to see how many minutes it takes. That gives you a quotient of approximately 453 minutes. You divide that by 60 since you want the time in hours, and the quotient of that is 7.55. 7 hours is greater than 5, so it's false.

I'm not too sure about some of them, so you might want to check my math. :)

Answer: x=1.1

Step-by-step explanation:

-2.2 - (-4x - 2) = - (-x - 3.1)

-2.2 + 4x + 2 = x + 3.1

-0.2 + 4x = x + 3.1

+0.2              + 0.2

4x = x + 3.3

-x     -x

3x = 3.3

/3     /3

x = 1.1

hope this helps!

Answer:

linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants)

Step-by-step explanation:

The transformation on the figure is a reflection over the y-axis.

In the image, we can see that we have an original figure in the left side of the y-axis, and then it is reflected over it.

We can see that it is a reflection and not a translation, because the orientation of the figure changes (you can see that in both figures, the 90° is in the side farthest away from the axis).

So the correct option is B, reflection over the y-axis.

If you want to learn more about reflections, you can read:

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Answer: All four runners ran .96 seconds

Step-by-step explanation: The total time of the four runners, divided by the amount of runners.

3.86/4= .965

Answer:

0.0042%

Step-by-step explanation:

We know that 1 pound is equivalent to 16 ounces.

So, 3 pounds of a product is equivalent to (16 × 3) = 48 ounces of the product.

Now, it is given that I add 0.002 ounces of coloring to 3 lbs of product.

So, the required percentage of coloring I used to product is [tex]\frac{0.002 \times 100}{48 + 0.002} = 0.0042[/tex]% (Answer)

Answer:4/5

Step-by-step explanation:

2/15 + 10/15=12/15=4/5

easy right?

Answer:

5/9

Step-by-step explanation:

Answer:

5/9

Step-by-step explanation:

Now we need to make our denominators match.

9 goes into 3 evenly, so we only need to multiply one term to get a common denominator.

Multiply 1 by 3, and get 3, then we multiply 3 by 3 and get 9.

Since our denominators match, we can add the numerators.

2 + 3 = 5

That gives us the sum, which is

5/9

Now, do we need to simplify this fraction?

First, we attempt to divide it by 2...

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

No good. 7 is larger than 5. So we're done reducing.

There you have it! Here's the final answer to 2/9 + 1/3

Answer:  A)

Step-by-step explanation: This is correct because a telescope is a piece of technology use to look further into space

The expression is equivalent to −78x − 198.

To simplify the expression −13(6x + 15) − 3, you can start by distributing the −13 across the terms inside the parentheses:

−13 * 6x = −78x

−13 * 15 = −195

So, the expression becomes:

−78x − 195 − 3

Next, combine the constant terms:

−195 − 3 = −198

The simplified expression is now:

−78x − 198

This expression is equivalent to the original expression −13(6x + 15) − 3. It cannot be further simplified as the terms are not like terms and cannot be combined further. So, the answer is −78x − 198.

The expression represents a linear equation where x is the variable. It can be used to find the value of the expression for specific values of x.

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The number is 1

Step-by-step explanation:

Let x be the required number

Then according to given statement

Five times the difference of twice a number and seven is negative twenty-five.

[tex]5(2x-7) = -25[/tex]

Simplifying

[tex]10x-35 = -25\\[/tex]

Adding 35 on both sides

[tex]10x-35+35 = -25+35\\10x = 10[/tex]

Dividing both sides by 10

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

Verification:

[tex]5[2(1)-7] = -25\\5(2-7) = -25\\5(-5) = -25\\-25=-25[/tex]

Hence,

1 is the number

Keywords: Linear equation

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Answer:

3/8

Step-by-step explanation:

You'd first want to count all the triangles (possibilities) which is 8 total numbers

Then find the even numbers. There is 2, 2, and 4 which is a total of 3 even numbers

The fraction would be 3/8 and it can't be simplified any further

Answer:

3/8

Step-by-step explanation:

This is because, out of 8 results, only 3 of them are even numbers. That is the biggest chance you have at getting an even number.

Answer:

B)No, the estimate should be higher

Answer:

no the estimate should be lower

Correct option:

c.f(x-3)+1

From the options we have either vertical or horizontal shift. So, for this type of transformation we have:

For any real positive number [tex]c[/tex], vertical and horizontal shift in the graph [tex]y=f(x)[/tex] are expressed as follows:

[tex]\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)[/tex]

From these rules, we know that:

[tex]f(x-3)+1[/tex]

would move the graph of the function to the right of the coordinate plane because of [tex]f(x-3)[/tex]. In other words, the transformation is as follows:

[tex]f(x-3)+1[/tex] shifts the graph of [tex]f(x)[/tex] three units to the right and one unit up

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Answer:Bob Owes $186 to the store he purchased an item at

Step-by-step explanation:

Answer:

There is exactly one output for each input.

The graph of a linear function is a straight line.

A linear function has a constant rate of change.

Step-by-step explanation:

Answer:

A,B,D

Step-by-step explanation:

i took the assignment and quiz on ed2020

4 divided by 3/5

pretend that 4 has a denominator which is 1

4/1 divided by 3/5

when dividing always flip over the second fraction

4/1*5/3

multiply the numerators together

4*5=20

multiply the denominators together

1*3=3

answer:

20/3 or 6 2/3

Answer:

-1/2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(3-9)/(7-(-5))

m=-6/(7+5)

m=-6/12

m=-1/2

Answer:25

Step-by-step explanation:

10 plus 9+4+2 will give you 21 and it will have 4 yellow ones left

The digits which a composite number greater than 10 might have include; 1, 2 ,3 and 4.

According to the question;

The number 10 has two place values namely;

In essence, any composite number greater than 10 can have either of 1, 2, 3 and 4 in the ones place.

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Answer:

Differentiation of both the term is [tex]2x+3[/tex]

Step-by-step explanation:

As we have to use first principle of derivatives lets recall the formula.

[tex]f(x)= \lim_{h\to 0}\frac{(x+h)-f(x)}{h}[/tex]

Solving our eqaution.

[tex]y=x^2+3x[/tex]

We will work with [tex]f(x+h)[/tex] then [tex]-f(x)[/tex] separately then put in the above formula.

1.

[tex]f(x+h)=(x+h)^2+3(x+h)[/tex]

[tex](x^2+h^2+2hx+3x+3h)[/tex]

Now [tex]-f(x)[/tex]

[tex]-f(x)=-x^2-3x[/tex]

Plugging the values of both.

[tex]f(x)= \lim_{h\to 0}\frac{(x+h)-f(x)}{h}[/tex]

[tex]f(x)= \lim_{h\to 0}\frac{(x^2+h^2+2hx+3h+3x)- x^2-3x}{h}=\frac{h^2+2hx+3h}{h}[/tex]

Taking [tex]h[/tex] as common.

[tex]f(x)= \lim_{h\to 0}\frac{h^2+2hx+3h}{h}=h+2x+3[/tex]

Putting [tex]h=0[/tex]

Then

[tex]f(x)=2x+3[/tex] is the final derivative.

This will be same for [tex]y= x^2 + 3x + 8[/tex] as we have to put [tex]8[/tex] only.

2.

[tex]f(x+h)=(x+h)^2+3(x+h)+8[/tex]

[tex](x^2+h^2+2hx+3x+3h)[/tex]

Then [tex]-f(x)=-x^2-3x-8[/tex]

Plugging the values of both.

[tex]f(x)= \lim_{h\to 0}\frac{(x+h)-f(x)}{h}[/tex]

[tex]f(x)= \lim_{h\to 0}\frac{(x^2+h^2+2hx+3h+3x+8)- x^2-3x-8}{h}=\frac{h^2+2hx+3h}{h}[/tex]

Taking [tex]h[/tex] as common.

[tex]f(x)= \lim_{h\to 0}\frac{h^2+2hx+3h}{h}=h+2x+3[/tex]

Putting [tex]h=0[/tex]

Then

[tex]f(x)=2x+3[/tex] is the final derivative.

So both the derivatives are same.

The height of the observer can be taken negligible in case of big measurements. The height of the kite from the ground is 40 meters approximately.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Referring to the figure attached below, we have the vertical distance of the kite from the ground as the length of the side BC.

(assume that the height of the observer flying kite is negligible and that kite's string is straight, and some more basic assumptions)

Using the Pythagoras theorem as the triangle ABC is a right angled triangle as vertical distance means line perpendicular to the ground, we get the length of the line segment BC as:

[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\|BC|^2 = |AC|^2 - |AB|^2\\\\|BC| = \sqrt{|AC|^2 - |AB|^2}\\[/tex]

(positive root since length is a non-negative quantity).

We have |AC| = length of the kite's string = 50 meters

|AB|  = distance of the observer from the point directly above which the kite is flying = 30 meters

Thus, we get the height of the kite from the ground as:

[tex]|BC| = \sqrt{|AC|^2 - |AB|^2}\\|BC| = \sqrt{50^2 - 30^2} = \sqrt{1600} = 40\: \rm \text{(in meters)}[/tex]

Thus,  the height of the kite from the ground is 40 meters approximately.

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Answer:24.5

Step-by-step explanation:

Formula:

H=KV²

8=K×20²(400)

=8/400

=0.02

H=0.02×35²

=24.5

Answer:

The maximum height reached by the golf ball when v = 35 is 24.5 meters.

Step-by-step explanation:

Given : A golf ball, thrown upwards, rises at a speed of v metres per second. The ball reaches a maximum height of h metres.  h is proportional to the square of v.  When v = 20, h = 8.

To find : Work out the maximum height reached by the golf ball when v = 35 ?

Solution :

h is proportional to the square of v i.e. [tex]h\propto v^2[/tex]

[tex]h=kv^2[/tex]

Where, k is the constant of proportionality

When v = 20, h = 8,

[tex]8=k(20)^2[/tex]

[tex]8=400k[/tex]

[tex]k=\frac{8}{400}[/tex]

[tex]k=0.02[/tex]

The equation became [tex]h=0.02v^2[/tex].

Now, when v = 35 the value of h is

[tex]h=0.02(35)^2[/tex]

[tex]h=0.02\times 1225[/tex]

[tex]h=24.5[/tex]

Therefore, the maximum height reached by the golf ball when v = 35 is 24.5 meters.