ABCD is rotated counterclockwise about the origin. By how many degrees
was ABCD rotated?

Answer:

[tex]12[/tex]

Step-by-step explanation:

[tex]\sqrt{12} \times\sqrt{12}[/tex]

[tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{a}=a,\:\quad \:a\ge 0[/tex]

[tex]\sqrt{12}\sqrt{12}=12[/tex]

[tex]=12[/tex]

The value of [tex]\sqrt{12} * \sqrt{12}[/tex] is equal to 12

To solve this problem, we have to convert the surds to radicals and then use the law of indices on this.

[tex]\sqrt{12} * \sqrt{12}= 12^\frac{1}{2} * 12^\frac{1}{2}[/tex]

This law is given as

[tex]a^m+a^n = a^(^m^+^n^)[/tex]

let's substitute the values in this question.

[tex]12^\frac{1}{2}*12^\frac{1}{2}[/tex]

Let's apply the law and solve the radical

[tex]12^\frac{1}{2}*12^\frac{1}{2} = 12^(^\frac{1}{2}^+^\frac{1}{2}^)\\[/tex]

Solve the fractions

[tex]\frac{1}{2}+\frac{1}{2}=1[/tex]

substitute the values and solve

[tex]12^\frac{1}{1}=12[/tex]

from the calculations above, the value of the radical is 12.

Learn more on laws of indices here;

https://brainly.com/question/10339517

Answer:

The second one. 30 minutes ÷ 6 miles.

Step-by-step explanation:

You want to find how long it took Jamaal to run one mile.

30 minutes ÷ 6 miles = 5 minutes.

So Jamaal can run one mile in 5 minutes.

Option B, 30mins/6miles

Answer:

39.2m

Step-by-step explanation:

The ratio would be 14/20 which is 0.7. So, you would take 56 and multipy it by 0.7 to get 39.2.

Answer:

39.2

Step-by-step explanation:

ok so you are given 2 triangles that are proportional

the 20 m side and the 56 m side go together

so this leaves 14 and L

so the ration is 2.8

multiply 14 by 2.8 and you get 39.2

Answer:

the answer is

7

Step-by-step explanation:

why is it 7 it is cause -10+7=3

Answer:

7

the answer is 7 because -10+7=-3

Answer:

-16.1y + 14

Step-by-step explanation:

–7(2.3y − 2)

=> -16.1y + 14

Therefore, -16.1y + 14 is the simplified form.

Hoped this helped

[tex]GeniusUser[/tex]

Answer:

53

Step-by-step explanation:

sorry if im incorrect

Answer:

15%

Step-by-step explanation:

[tex]\frac{138}{120}[/tex]×100=

1.15

115%

Increase in 15%

Answer:

B

Step-by-step explanation:

The heaviest pig on the farm weighs 100 pounds

Answer:

49

Step-by-step explanation:

9*7=63

7*7=49

There are 49 questions did Jackson answer correctly.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

Jackson answered every 7 out of 9 questions correctly on a Spanish Quiz.

Total number of questions = 63

Now,

Let number of correct questions = x

So, By the definition of ratio, we can formulate;

⇒ 7 : 9 = x : 63

Solve for x as;

⇒ 7 : 9 = x : 63

⇒ 7 / 9 = x / 63

⇒ 7 × 63 / 9 = x

⇒ x = 7 × 63 / 9

⇒ x = 7 × 7

⇒ x = 49

Thus, There are 49 questions did Jackson answer correctly.

Learn more about the ratio visit:

https://brainly.com/question/2914376

#SPJ2

Answer:

See answer below

Step-by-step explanation:

R3:  If parallel lines, then alternate interior angles is congruent

S4:  AC ≅ AC

R5:   ASA

Answer:

Answer:

safe speed for the larger radius track u= √2 v

Explanation:

The sum of the forces on either side is the same, the only difference is the radius of curvature and speed.

Also given that r_1= smaller radius

r_2= larger radius curve

r_2= 2r_1..............i

let u be the speed of larger radius curve

now, \sum F = \frac{mv^2}{r_1} =\frac{mu^2}{r_2}∑F=

r

1

mv

2

=

r

2

mu

2

................ii

form i and ii we can write

v^2= \frac{1}{2} u^2v

2

=

2

1

u

2

⇒u= √2 v

therefore, safe speed for the larger radius track u= √2 v

Answer: JGI

Step-by-step explanation:

An adjacent angle are angles that share a vertex and side. FGI and JGI share the vertex G and the segment GI

Have a good day!

Answer: All of the them except for the last relation.

Step-by-step explanation: For a relation to be a function, it can have y-values repeat but not x-values. In the last relation, you have (6,-6,), (-3,12), (6,-1), (-8,13). Notice that the x-value of 6 repeats 2 times in this relation. You can graph this relation and use the vertical line test  and you will notice that it will touch the graph more than one time. Therefore, relations 1-4 represents functions and relation 5 does not.

Hope this explanation helps.

Answer:

the amount paid for the loan would be $6700.80

Use the multinomial theorem to compute some polynomial expansions:

(a + b + c)² = a² + b² + c² + 2 (ab + ac + bc)

(a + b + c)³ = a³ + b³ + c³

… … … … … … + 3 (a²b + a²c + ab² + b²c + ac² + bc²)

… … … … … … + 6 abc

(a + b + c)⁴ = a⁴ + b⁴ + c⁴

… … … … … … + 4 (a³b + a³c + ab³ + b³c + ac³ + bc³)

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 12 (a²bc + ab²c + abc²)

Now, given that

a + b + c = 4

a² + b² + c² = 10

it follows that

ab + ac + bc = (4² - 10)/2 = 3

We use this result to simplify the extra terms in the 3rd-degree expansion.

a²b + a²c + ab² + b²c + ac² + bc²

= a (ab + ac) + b (ab + bc) + c (ac + bc)

= a (ab + ac + bc) + b (ab + ac + bc) + c (ab + ac + bc) - 3abc

… … I underline the terms that are added and subtracted … …

= (a + b + c) (ab + ac + bc) - 3abc

= 4 • 3 - 3abc

= 12 - 3abc

Given that

a³ + b³ + c³ = 22

this tells us that

4³ = 22 + 3 (12 - 3abc) + 6abc

4³ = 58 - 3abc

and so

abc = (4³ - 58)/(-3) = -2

from which it follows that

a²b + a²c + ab² + b²c + ac² + bc² = 12 - 3 • (-2) = 18

Now we similarly simplify the extra terms in the 4th-degree expansion.

a³b + a³c + ab³ + b³c + ac³ + bc³

= a² (ab + ac) + b² (ab + bc) + c² (ac + bc)

= a² (ab + ac + bc) + b² (ab + ac + bc) + c² (ab + ac + bc) - a²bc - ab²c - abc²

= (a² + b² + c²) (ab + ac + bc) - (a²bc + ab²c + abc²)

= 10 • 3 - (a²bc + ab²c + abc²)

which means

4⁴ = a⁴ + b⁴ + c⁴

… … … … … … + 4 (30 - a²bc - ab²c - abc²)

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 12 (a²bc + ab²c + abc²)

reduces to

136 = a⁴ + b⁴ + c⁴

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 8 (a²bc + ab²c + abc²)

Now, we know a + b + c = 4 and abc = -2, so we have

a²bc + ab²c + abc² = abc (a + b + c) = -2 • 4 = -8

and so

136 = a⁴ + b⁴ + c⁴ + 6 (a²b² + a²c² + b²c²) + 8 • (-8)

200 = a⁴ + b⁴ + c⁴ + 6 (a²b² + a²c² + b²c²)

Finally, we know that ab + ac + bc = 3. Squaring this gives

(ab + ac + bc)² = 3²

a²b² + a²c² + b²c² + 2 (a²bc + ab²c + abc²) = 9

but we also know that a²bc + ab²c + abc² = -8, so

a²b² + a²c² + b²c² + 2 • (-8) = 9

a²b² + a²c² + b²c² = 25

Therefore, we end up with

200 = a⁴ + b⁴ + c⁴ + 6 • 25

⇒   [[[   a⁴ + b⁴ + c⁴ = 50   ]]

Answer: ok we will help

Step-by-step explanation:

he need our help

Answer:

-1 / 2.

Step-by-step explanation:

The Slope of a line when given two points:

First establish the two points as (X1, Y1) and (X2,Y2)

you can decide which point is (X1, Y1) and which point is (X2,Y2) in any order

So I choose (X1, Y1) = (-10,1) and (X2,Y2) = (0,-4)

Next use this equation to find the difference in rise/run (rise over run): (Y2 - Y1) / (X2 - X1)

Now we're ready to solve by plugging in our points: ( (-4) - 1 ) / ( 0 - (-10) ) **DON'T FORGET negatives attached to numbers when plugging in**

Solve: (-5) / 10 = -5 / 10 or -1 / 2 reduced by taking out a 5 from top and bottom. So your slope is equal to -1 / 2.

Answer:

-1/2

Step-by-step explanation:

Answer:

10 or 10/1

Step-by-step explanation:

1/1000 * 10= 0.01 = 1/100

Answer:

  A.  y ≥ -3x +4

Step-by-step explanation:

The boundary line crosses the y-axis at +4, so the y-intercept of it is +4. This eliminates choices C and D.

The shading is above the line, where y-values are greater than those on the line. This eliminates choice B.

The correct inequality is ...

  A. y ≥ -3x +4

Answer:

x intercept= (-3,0)  y intercept= (0,3)

Step-by-step explanation:

for x intercepts, y should equal zero

for y intercepts, x should equal zero

x intercept: -x+0=3

-x=3

x=-3  (x,y)--> (-3,0)

y intercept: 0+y=3

y=3 (x,y)--> (0,3)

Answer:

Answer:x - intercept (0, -3)

3)y - intercept (3, 0)

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

8m

Step-by-step explanation:

Answer:

220 calories

Step-by-step explanation:

Cross multiply and then divide:

[tex]\frac{14}{22}= \frac{140}{x}[/tex]

140 x 22 = 3080

3080 / 14 = 220

Answer:

see explanation

Step-by-step explanation:

(1)

Using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{4}{6}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{4}{6}[/tex] ) ≈ 41.8° ( to the nearest tenth )

(2)

Using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{29}{14}[/tex] , then

x = [tex]tan^{-1}[/tex] ([tex]\frac{29}{14}[/tex] ) ≈ 64.2° ( to the nearest tenth )

(3)

Using the cosine ratio in the right triangle

cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{25}{40}[/tex] , then

x = [tex]cos^{-1}[/tex] ([tex]\frac{25}{40}[/tex] ) ≈ 51.3° ( to the nearest tenth )