The distance between points (3,7) and (x1,y1) is the square root of (x1 - 3)2 + (y1 - 7)2

True or False?

Answer:

option B

option D

Step-by-step explanation:

1)

First we will remove radical sign as[tex]\sqrt[n]{x}=x^{\frac{1}{n} }[/tex] and then multiply the powers.

[tex]\sqrt[3]{4^{5}}=(4^{5})^{\frac{1}{3}}=4^{\frac{5}{3} }[/tex]

2)

The "power rule" tells us that to raise a power to a power, just multiply the exponents.

([tex]4^{15}[/tex])[tex]^{\frac{1}{3}}=4^{15.\frac{1}{3}}=4^{5}[/tex]

Answer:

Step-by-step explanation:

[tex]\[\frac{1+2\sqrt{-3} }{1+\sqrt{-3} } =\frac{1+2\sqrt{-3} }{1+\sqrt{-3} } \times \frac{1-\sqrt{-3} }{1-\sqrt{-3} } =\frac{(1+2\sqrt{-3})(1-\sqrt{-3} ) }{1^{2}-(\sqrt{-3})^{2}   } =\frac{1+2\sqrt{-3}-\sqrt{-3}-2(\sqrt{-3}  )^{2}  }{4} =\frac{1+\sqrt{-3}+6 }{4} =\frac{7+\sqrt{-3} }{4} \][/tex]

[tex]

6(x+xy)-5(y+2xy)=6x+6xy-(5y+10xy) \\

6x+6xy-5y-10xy \\

\boxed{6x-5y-4xy}

[/tex]

Answer:

To solve this problem you would have to distribute the 5 and the 6. Once that is completed you would find the matching pairs and add or subtract them.

The answer is: 6x-4xy-5y

Step-by-step explanation:

Final answer:

The zeros of f(x) = x^3 - 4x^2 - 5x + 20 are 4 and (-1 +/- sqrt(21)) / 2.

Explanation:

The given function is f(x) = x^3 - 4x^2 - 5x + 20. To find the zeros of the function, we need to solve the equation f(x) = 0. One way to find the zeros is by using synthetic division or polynomial long division. However, in this case, we can use factoring by grouping to simplify the equation:

f(x) = (x^3 - 5x) + (-4x^2 + 20)

f(x) = x(x^2 - 5) + (-4)(x^2 - 5)

f(x) = (x - 4)(x^2 + x - 5)

Setting each factor equal to zero, we have:

x - 4 = 0  ---> x = 4

x^2 + x - 5 = 0

Using the quadratic formula, we can find the solutions of the quadratic equation:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

Plugging in the values a = 1, b = 1, and c = -5, we get:

x = (-1 +/- sqrt(1^2 - 4(1)(-5))) / (2(1))

x = (-1 +/- sqrt(1 + 20)) / 2

x = (-1 +/- sqrt(21)) / 2

So, the zeros of f(x) = x^3 - 4x^2 - 5x + 20 are x = 4 and x = (-1 +/- sqrt(21)) / 2.

To translate a triangle by moving it 5 units to the right and 2 units up, you add 5 to the x-coordinates and 2 to the y-coordinates of all its vertices.

To translate  riangle ABC by moving it 5 units to the right and 2 units up, you would perform the following steps:

This transformation doesn't change the shape or size of  riangle ABC; it merely repositions it on the coordinate plane.

Answer:

A

Hope This Helps!  Have A Nice Day!!

Answer:

Step-by-step explanation:

5

(Answer:5)The greatest common factor of 15 and 5 is, 5

Answer:

[tex]\large\boxed{A.\ \dfrac{x+2}{x+5}}[/tex]

Step-by-step explanation:

[tex]x^2+3x+2=x^2+x+2x+2=x(x+1)+2(x+1)=(x+1)(x+2)\\\\x^2+6x+5=x^2+x+5x+5=x(x+1)+5(x+1)=(x+1)(x+5)\\\\\dfrac{x^2+3x+2}{x^2+6x+5}=\dfrac{(x+1)(x+2)}{(x+1)(x+5)}\qquad\text{cancel}\ (x+1)\\\\=\dfrac{x+2}{x+5}[/tex]

Answer:

see explanation

Step-by-step explanation:

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex], thus

sinA = [tex]\frac{2\sqrt{19} }{20}[/tex] = [tex]\frac{\sqrt{19} }{10}[/tex]

--------------------------------------------------------------------------------------------

cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex], thus

cosA = [tex]\frac{18}{20}[/tex] = [tex]\frac{9}{10}[/tex]

-------------------------------------------------------------------------------------------

tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex], thus

tanA = [tex]\frac{2\sqrt{19} }{18}[/tex] = [tex]\frac{\sqrt{19} }{9}[/tex]

Answer: I have 4 cookies, I but 3 more cookies, how many cookies do I have now? I have 7 cookies

Step-by-step explanation:

A story problem where the answer is 7 is given above.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have number 7.

The question problem is as follows -

There are 77 chocolates and 11 childrens. How many chocolates should be given to each child such that each one gets equal number of chocolates.

Solution -

Assume each child gets [x] chocolates. Then -

11x = 77

x = 7

Therefore, a story problem where the answer is 7 is given above.

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7.8889 I think so so I divided 2.84%39=7.8889

Final answer:

To find the 2010 cost of filling a gas tank based on 1970 prices, divide the 1970 total cost by the price per gallon to find the number of gallons, then multiply that by the 2010 price per gallon. The cost to fill the same tank in 2010 would be $47.34.

Explanation:

The question is asking to calculate the cost of a full tank of gas in 2010 based on the cost from 1970. To find out how much it would cost in 2010, we need to first determine the number of gallons that could be bought for $6 in 1970 at $0.36 per gallon. This can be calculated by dividing $6 by $0.36, which equals 16.67 gallons (approximately). Now, assuming the tank size has not changed, to find out the cost in 2010, we multiply the number of gallons by the 2010 price per gallon. Thus, 16.67 gallons multiplied by $2.84 per gallon equals $47.34.

Answer:

B) 17

Step-by-step explanation:

9857/82=120.....

120*82=8940

9857-9840=17

ANSWER

B) 17

EXPLANATION

We want to find the remainder when, 9857 is divided by 82.

We carry out the long division as shown in the attachment.

We can see that

[tex]9857 = 82 \times 120+ 17[/tex]

Hence the remainder is 17.

The correct answer is B.

Answer:

The diameter of a circle with an area of 804.25 cm is 32 cm

Step-by-step explanation:

We know that formula for area of circle is:

Area of Circle = πr^2

804.25 =  3.14 * r^2

=> r^2 = 804.25 / 3.14

r^2 = 256.13

Taking square root on both sides

√r^2 = √256.13

r = 16.0

and r is half of diameter i.e

r = diameter / 2

=> diameter = 2r

so, diameter = 2 * 16

diameter = 32 cm

So, the diameter of a circle with an area of 804.25 cm is 32 cm.

The diameter is approximately [tex]\(32.02\)[/tex] cm, calculated from [tex]\(d = 2 \times 16.01\)[/tex], where [tex]\(r \approx 16.01\)[/tex] cm.

To find the diameter of a circle with an area of 804.25 cm², follow these steps:

Step 1:

Recall the formula for the area [tex](\(A\))[/tex] of a circle: [tex]\(A = \pi r^2\)[/tex], where r is the radius of the circle.

Step 2:

We're given the area [tex]\(A = 804.25\)[/tex] cm². Rearrange the formula to solve for [tex]\(r\)[/tex]: [tex]\(r = \sqrt{\frac{A}{\pi}}\)[/tex].

Step 3:

Substitute the given area into the equation: [tex]\(r = \sqrt{\frac{804.25}{\pi}}\).[/tex]

Step 4:

Calculate the radius: [tex]\(r[/tex] ≈ [tex]\sqrt{\frac{804.25}{\pi}}[/tex] ≈ [tex]\sqrt{256.25}[/tex] ≈ 16.01 cm.

Step 5:

Recall that the diameter [tex](\(d\))[/tex] of a circle is twice the radius: [tex]\(d = 2r\)[/tex].

Step 6:

Substitute the calculated radius into the equation: [tex]\(d = 2 \times 16.01\)[/tex].

Step 7:

Calculate the diameter: [tex]\(d[/tex] ≈ [tex]2 \times 16.01[/tex] ≈ [tex]32.02\)[/tex] cm.

Therefore, the diameter of the circle with an area of 804.25 cm² is approximately 32.02 cm.

Answer:

21

Step-by-step explanation:

the range is the highest minus the lowest

27-6=21

Answer:

21 milliliters

Step-by-step explanation:

We first need to arrange the quantities from the least to the largest.

i.e {6, 8, 9, 10, 13, 14, 15, 16, 20, 22, 25, 27}

Range of this set of data is = largest quantity - least quantity = 27 - 6 = 21 milliliters

Answer:

70.58 ft²

Step-by-step explanation:

One pie-shaped sub-area of this octagon has two sides of length 5 ft and a central angle of 360°/8, or 45°.  We need to find the area of one such sub-area and then multiply the result by 8 to find the total area of the octagon.

Picture this pie-shape, this isosceles triangle with two sides of length 5 ft and central angle 45°.  Half of that angle is 22.5°.  Half of the base of this triangle is 5 sin 22.5°, or 1.91; the full base length is twice that, or 3.82.  the height of the triangle is 5 cos 22.5°, or 4.62.

The formula for the area of a triangle is

A = (1/2)(base)(height), which in this case is:

A = (1/2)(3.82 ft)(4.62 ft) = 8.82 ft²

and so the area of the whole octagon is 8(8.82 ft²), or 70.58 ft²

Answer:

D) 70.7

Step-by-step explanation:

I got it right

Answer:13.1

Step-by-step explanation:first note that 13.1 had two parts 13 and 1

13.1 has one digit in the fractional part thus 13.1 is already rounded as much as possible to the nearest tenth the answer is 13.1

Answer:

Do pemdas, (parentheses, exponents, multiplication, division, addition and subtraction). But do whatever is first, which in this case is multiplication.

Step-by-step explanation:

Write the equation out.

    105 x 2 + 66x -72 = ?

    105 x 2 = 210

     210 + 66x - 72

    210 + 66x = 276x

     276x - 72 = 204

      ? = 204

Answer:

C)-2(9+32n)

Step-by-step explanation:

The given expresion is

[tex] - 18 - 64n[/tex]

We can rewrite this expression as:

[tex] - 2 \times 9 + - 2 \times 32n[/tex]

We factor -2 to obtain:

[tex] - 2(9 + 32n)[/tex]

Note that, we can use the distributive property to obtain:

[tex] - 2(9 + 32n) = - 18 - 64n[/tex]

Therefore the correct answer is C)-2(9+32n)

The expression equivalent to (-18)-64n is option A: -2(9-32n). This is because when you distribute the -2 across the terms in the parentheses, it gives you the original expression.

To find which expression is equivalent to (-18)-64n, we can factor out the greatest common factor (GCF) from each term. The GCF of -18 and -64n is -2. Thus, when we factor out -2, we are left with:

(-18)-64n = -2(9 + 32n).

But we have to pay attention to our signs; we should distribute -2 within the parentheses to check our result:

-2 × 9 = -18

-2 × 32n = -64n

Thus, option A -2(9-32n) is the correct equivalent expression, as the negative sign in front of the parentheses will switch the signs of the terms inside when distributed. Options B, C, and D either lack the necessary negative sign or have the incorrect sign for 32n.

Answer:

56.52

Step-by-step explanation:

i did the iready lol

Answer:

2 fluid ounces

Step-by-step explanation:

Answer:

[tex]\large\boxed{256\pi\ sq.in.}[/tex]

Step-by-step explanation:

The formula of a surface area of a sphere:

[tex]S.A.=4\pi R^2[/tex]

R - radius

We have R = 8 in. Substitute:

[tex]S.A.=4\pi(8^2)=4\pi(64)=256\pi\ in^2[/tex]

Answer:

Step-by-step explanation:

18 ft

Answer: 18 ft (technically water isn't measured in feet but who cares :)

Step-by-step explanation: 5*3*2=x-12--------- 30=x+12-----x=18

Answer:

The correct option is option D

Step-by-step explanation:

The volume of a pyramid is:

V=1/3(B)(H)

Where

B:Base = s^2

H:Height = 2/3s

Then:

V=1/3(B)(H) = 1/3(s^2)(2/3s) = 2/9s^3

The correct option is option D

Answer:

answer is V= 2/9 s3 is correct

Answer:

C. Even

Step-by-step explanation:

Any multiple of 2 is an even number.

27 is 3³, so the result cannot be a perfect square.

The product of two numbers, neither of which is 1, cannot be prime.

the answer would be C. An even number

Answer:

The number which produces a given number when cubed.

Step-by-step explanation:

cube root

the number which produces a given number when cubed.

PLZ MARK BRAINLIST!!!

the number which produces a given number when cubed.

Answer:

[tex]\boxed{\tan \theta}[/tex]

Step-by-step explanation:

[tex]\dfrac{\tan \theta }{\sin^{2} \theta + \cos^{2} \theta}[/tex]

Use the trigonometric identity

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

Then,

[tex]\dfrac{\tan \theta }{\sin^{2} \theta + \cos^{2} \theta} = \dfrac{\tan \theta }{1} = \boxed{\tan \theta}[/tex]

The correct option is d. tan θ. The simplified expression is [tex]\(\tan\ \theta\)[/tex].

The expression you provided is:

[tex]\[ \frac{\tan\ \theta}{\sin^2 \theta + \cos^2 \theta} \][/tex]

We know that [tex]\(\sin^2 \theta + \cos^2 \theta = 1\)[/tex] due to the Pythagorean identity for sine and cosine.

So, the expression simplifies to:

[tex]\[ \frac{\tan\ \theta}{1} = \tan\ \theta \][/tex]

Therefore, the correct simplified expression is [tex]\(\tan\ \theta\)[/tex].

The complete question is:

Simplify the trigonometric expression.

[tex]\[ \frac{\tan\ \theta}{\sin^2 \theta + \cos^2 \theta} \][/tex]

Select the correct answer:

a. cos θ +sin θ

b. cot² θ

c. cot θ

d. tan θ

Answer:

5/4

Step-by-step explanation:

look to the right of the graph where the red dot is at then go over to the dot, then you count down until you get to the line.

We can use the points (2, 1) and (4, 6) to solve.

Formula: y2-y1/x2-x1

= 6-1/4-2

= 5/2

Best of Luck!

Answer:

B. 12/5

Step-by-step explanation:

tan=opp. leg/adj. leg

tan 67= 12/5

According to this diagram, the tan67° is 12/5.

⇒  tan67° = perpendicular/base = 12/5.

Hence, the value of tan67° is 12/5.

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Answer:

x=10

Step-by-step explanation:

110 and 8x + 30 are vertical angles, which means they are equal

110 = 8x+30

Subtract 30 from each side

110-30 = 8x+30 -30

80 = 8x

Divide each side by 8

80/8 = 8x/8

10 =x

Answer:

C. Circle

Step-by-step explanation:

A, B, and D are all composed of straight line segments.  However a circle is one continuous, rounded line (not a segment).

A circle is an object that has no line segments.

Hence, a circle is an object that has no line segment.

Therefore, Option C is the correct answer.

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