The following points are rotated about the origin through 90° in clockwise direction. Find the new coordinates,
A. A(1,3), B(5,3), and C(3, 1)
B. A' (3,-1), B'(-5, -3), and C (1.-3)
C. A'(3,-1), B (3,-5), and C(1, -3)
D. O A'(3, 1), B'(3,5), and C(1,3)

[tex]\huge \boxed{g=\frac{x-2}{3} }[/tex]

Answer:

[tex]g=\frac{x-2}{3}[/tex]

Step-by-step explanation:

Hi there!

[tex]x=3g+2[/tex]

We can make g the subject by using inverse operations to cancel values out. For example, 2 is being added to 3g. To move it, we can subtract 2 from both sides:

[tex]x-2=3g+2-2\\x-2=3g[/tex]

Now, to move the 3, divide both sides by 3:

[tex]\frac{x-2}{3}=\frac{3g}{3} \\\frac{x-2}{3}=g[/tex]

I hope this helps!

Answer:

He received 10 dimes and 15 quarters.

Step-by-step explanation:

Dimes = $0.10

Quarters = $0.25

Variable x = dimes

Variable y = quarters

Create a pair of linear equations:

0.10x + 0.25y = 4.75

x + y = 25

Isolate any variable, using an equation of your choice:

x + y = 25

x = 25 - y

Plug in this new value of x into the other equation:

0.10(25 - y) + 0.25y = 4.75

Use the distributive property:

2.5 - 0.10y + 0.25y = 4.75

Combine like terms:

2.5 + 0.15y = 4.75

Isolate variable y:

0.15y = 2.25

y = 15

Plug in the value of y into any equation:

x + y = 25

x + 15 = 25

Isolate variable x:

x = 10

Answer:

B

Step-by-step explanation:

Given the three integrals, we want to determine which integrals necessarily have the same value.

We can let the first integral be itself.

For the second integral, we can perform a u-substitution. Let u = x + a. Then:

[tex]\displaystyle du = dx[/tex]

Changing our limits of integration:

[tex]u_1=(0)+a=a \text{ and } u_2 = (b+a)+a = b+2a[/tex]

Thus, the second integral becomes:

[tex]\displaystyle \int_{0}^{b+a}f(x+a)\, dx = \int_a^{b+2a} f(u)\, du[/tex]

For the third integral, we can also perform a u-substitution. Let u = x + c. Then:

[tex]\displaystyle du = dx[/tex]

And changing our limits of integration:

[tex]\displaystyle u_1=(a-c)+c=a \text{ and } u_2=(b-c)+c=b[/tex]

Thus, our third integral becomes:

[tex]\displaystyle \int_{a-c}^{b-c}f(x+c)\, dx = \int_{a}^{b} f(u)\, du[/tex]

Since the only difference between f(x) and f(u) is the variable and both the first and third integral have the same limits of integration, our answer is B.

Answer: Becomes four times

Step-by-step explanation:

Given

Speed is doubled for a moving object

Suppose initial speed is u

Increased speed is 2u

Kinetic Energy is given by

[tex]\Rightarrow K=0.5mu^2[/tex]

When speed is doubled

[tex]\Rightarrow K'=0.5m(2u)^2\\\Rightarrow K'=(0.5mu^2)\times 4\\\Rightarrow K'=4K[/tex]

Kinetic energy becomes four times

Answer:

24

Step-by-step explanation:

Multiply the side length by the dilation

36 x 2/3

72/3

Simplify

72/3 = 24

Your answer is correct

Step-by-step explanation:

Hope it is helpful to you

Answer: 2/3

Step-by-step explanation:

1/4 (3/12) plus 5/12 = 8/12

which can be simplified by 4

Answer:

19

Step-by-step explanation:

You will need expand so you can plug in the givens

Quotient rule: log(b^7)-[log(a^5c^6)]

Product rule: log(b^7)-[log(a^5)+log(c^6)]

Distribute: log(b^7)-log(a^5)-log(c^6)

Power rule: 7log(b)-5log(a)-6log(c)

Plug in: 7(4)-5(3)-6(-1)

Simplify: 28-15+6

Simplify: 13+6

Simplify: 19

Answer:

FG ≈ FL (Both are hypotenuse, supposed to be equal in order to the congruency to become HL)

Answered by GAUTHMATH

Answer:

To find width when given perimeter and length you must multiply the length by two and subtract that amount from the perimeter. Then divide the new number by two.

Step-by-step explanation:

Answer:

[tex]HE || LP[/tex]

Step-by-step explanation:

Given

[tex]HE \cong LP[/tex]

Required

Which proves that [tex]HELP[/tex] is a parallelogram

We have:

[tex]HE \cong LP[/tex]

The given sides must also be parallel i.e.

[tex]HE || LP[/tex]

Hence, (c) is correct

#1. Vertical

#2. Adjacent, Complementary

#3. Adjacent, Linear Pair, Supplementary

---A linear pair forms a line, which is equal to 180 degrees

#4. Adjacent

#5. Vertical, Complementary

#6. Vertical, Supplementary

---There is a 90 degree angle within this problem. If one angle is 90 degrees, then they are all 90 degrees, which makes the sum of angle 1 and 2 = 180. So, they are supplementary.

Hope this helps!

The relationship between angle 1 and 2 are as follows:

1. ∠1 ≅ ∠2 (vertical angles)

2. ∠1 and ∠2 are adjacent and complementary angles.

3. ∠1 and ∠2 are linear pairs and supplementary angles

4. ∠1 and ∠2 are adjacent angles

5. ∠1 and ∠2 are vertical angles

6. ∠1 and ∠2 are vertical angles and supplementary angles.

1.

Therefore,

∠1 ≅ 2 (vertical angles)

2.

Therefore,

∠1 and ∠2 are adjacent and complementary angles.

3.

∠1 and ∠2 are linear pairs and supplementary angles.

4.

∠1 and ∠2 are adjacent angles

5.

∠1 and ∠2 are vertical angles

6.

∠1 and ∠2 are vertical angles and supplementary angles

learn more on angles here: https://brainly.com/question/18166236?referrer=searchResults

Step-by-step explanation:

Let √2 + √3 be a / b.

a and b are co - primes.

a and b have 1 as a common factor.

√2 + √3 = a / b

( √2 + √3 )^2 = ( a / b )^2

(√2)^2 + (√3)^2 + 2.√2.√3 = a^2 / b^2

2 + 3 + 2.√2.√3 = a^2 / b^2

5 + 2.√2.√3 = a^2 / b^2

2.√2.√3 = ( a^2 / b^2 ) - 5

2.√2.√3 = ( a^2 - 5b^2 ) / b^2

√2.√3 = ( a^2 - 5b^2 ) / 2b^2

a and b are not co - primes, as they more than 1 as a common factor.

So,

√2 + √3 is irrational.

Hence, proved.

Answer:

Smaller angle = 53.2

Larger angle = 126.8

Step-by-step explanation:

Lets say x is the measure of the supplement. Since we know they're supplementary, we know their angle measure sum will equal 180. We can set up our equation like this [tex]x + (x-73.6) = 180[/tex]. Note: (x - 73.6) is the measure of the smaller angle. By solving, we get 126.8 degrees for the measure of the supplement. If we plug in the value of x into (x-73.6), we get 53.2 degrees as the angle measure of the smaller angle.

Answer:

A.15/8

Step-by-step explanation:

the answer is 15/8

Answer:

D.

[tex]{ \tt{ \cos( \theta) = \frac{adjacent}{hypotenuse} }} \\ \\ { \tt{ \cos( \theta) = \frac{8}{ \sqrt{ {15}^{2} + {8}^{2} } } }} \\ \\ { \tt{ \cos( \theta) = \frac{8}{ \sqrt{289} } }} \\ \\ { \tt{ \cos( \theta) = \frac{8}{17} }}[/tex]

Answer:

25+144+X=180°

169+X=180°

X= 180-169

Therefore, x= 11°

checking process: (25+144+11= 180°)

Answer:

x = 11 i beileve!

Step-by-step explanation:

Answer:

A. 15.7 ft

Step-by-step explanation:

circumference = 2πr

radius= half the diameter 5/2=2.5

2(3.14)(2.5)=15.7 ft

Answer:

The angle in decimal form is 167.009°.

Step-by-step explanation:

We know an angle in terms of integer angles, minutes and seconds, whose conversion into decimal degrees is expressed by the following formula:

[tex]\theta = n + \frac{m}{60}+\frac{s}{3600}[/tex] (1)

Donde:

[tex]n[/tex] - Integer angle, in sexagesimal degrees.

[tex]m[/tex] - Minutes.

[tex]s[/tex] - Seconds.

If we know that [tex]n = 167[/tex], [tex]m = 0[/tex] and [tex]s = 31''[/tex], then the angle in decimal form is:

[tex]\theta = 167^{\circ}+\frac{0}{60}^{\circ} + \frac{31}{3600}^{\circ}[/tex]

[tex]\theta = 167.009^{\circ}[/tex]

The angle in decimal form is 167.009°.

Answer:

x=13.6

Step-by-step explanation:

By Pythagoras theorem, 5.5^2+x^2=14.7^2. x^2=14.7^2-5.5^2. x=13.6

Answer:

44

Step-by-step explanation:

The difference between 15 and 9 is 6. 5 times the sum of 7 and 3 is 50 because 7+3=10 and 10 times 5 is 50. So if you subtract the difference between 15 and 9 from 50 you get 44.

Step-by-step explanation:

Increase in dollars

19/100 x 472.000 = $89,670

and the current value house is $472,000 + $89,670 = $561,680

Answer:

see image

Step-by-step explanation:

Answer:

80.4

Step-by-step explanation:

tan15=x/300

300tan(15)=80.38

Answer:

D

Step-by-step explanation:

The parent function is

[tex]f(x) = \sqrt[3]{x} [/tex]

g(x) translates to the right 2 units so we can represent this as

[tex] \sqrt[3]{x - 2} [/tex]

G(x) is shifted up 1 so our function is now

[tex] \sqrt[3]{x - 2} + 1[/tex]

Answer:

∠F = 59°

∠E = 31°

DF = ≅ 3  (2.98)

Step-by-step explanation:

Answer:

See both definitions below

Step-by-step explanation:

Let us define science

Science is a body of knowledge, it is a systematic application of knowledge and understanding of the natural and social world following a systematic methodology based on evidence.

Let us define Technology

Simply put, technology is the application of scientific knowledge

Answer:

Simply put, technology is the application of scientific knowledge Step-by-step explanation:

Answer:

[tex] \rm\displaystyle 4\cos( \theta) \cos \left( {2\theta} \right) \cos \left( {4 \theta } \right) [/tex]

Step-by-step explanation:

I assume the question want us to rewrite cosθ+cos3θ+cos5θ+cos7θ by using Sum-to-Product Formula and note that it's not an equation therefore θ can never be specified

===========================

so we want to rewrite cosθ+cos3θ+cos5θ+cos7θ by using Sum-to-Product Formula the good news is that the number of the function of the given expression is even so there's a way to do so, rewrite the expression in parentheses notation:

[tex] \rm\displaystyle \left( \cos( \theta) + \cos(3 \theta) \right) + \left(\cos(5 \theta) + \cos(7 \theta) \right)[/tex]

recall that,Sum-to-Product Formula of cos function:

[tex] \rm \boxed{\displaystyle \cos( \alpha ) + \cos( \beta ) = 2 \cos \left( \frac{ \alpha + \beta }{2} \right) \cos \left( \frac{ \alpha - \beta }{2} \right) }[/tex]

notice that we have two pair of function with which we can apply the formula thus do so,

[tex] \rm\displaystyle \left( 2\cos \left( \frac{ \theta + 3 \theta}{2} \right)\cos \left( \frac{ \theta - 3 \theta}{2} \right) \right) + \left(2\cos \left( \frac{5 \theta + 7 \theta}{2} \right) \cos \left( \frac{5 \theta - 7 \theta}{2} \right) \right)[/tex]

simplify addition:

[tex] \rm\displaystyle \left( 2\cos \left( \frac{4 \theta}{2} \right)\cos \left( \frac{ - 2\theta }{2} \right) \right) + \left(2\cos \left( \frac{12 \theta }{2} \right) \cos \left( \frac{ - 2 \theta}{2} \right) \right)[/tex]

simplify division:

[tex] \rm\displaystyle \left( 2\cos \left( {2 \theta} \right)\cos \left( { - \theta } \right) \right) + \left(2\cos \left( {6 \theta } \right) \cos \left( { - \theta} \right) \right)[/tex]

By Opposite Angle Identities we acquire:

[tex] \rm\displaystyle \left( 2\cos \left( {2 \theta} \right)\cos \left( { \theta } \right) \right) + \left(2\cos \left( {6 \theta } \right) \cos \left( { \theta} \right) \right)[/tex]

factor out 2cosθ:

[tex] \rm\displaystyle 2 \cos( \theta) (\cos \left( {2 \theta} \right) + \cos \left( {6 \theta } \right) )[/tex]

once again apply Sum-to-Product Formula which yields:

[tex] \rm\displaystyle 2 \cos( \theta) (2\cos \left( {4\theta} \right) \cos \left( {2 \theta } \right) )[/tex]

distribute:

[tex] \rm\displaystyle 4\cos( \theta) \cos \left( {2\theta} \right) \cos \left( {4 \theta } \right) [/tex]

and we're done!