If JK and LM are congruent and parallel, then JKL and MLK are congruent.
True
False

[tex]Use\\\\(ab)^n=a^nb^n\\\\ (a^n)^m=a^{n\cdot m}\\-------------------\\\\\left(r^{-3}s^2t\right)^4=\left(r^{-3}\right)^4\left(s^2\right)^4(t)^4=r^{(-3)(4)}s^{(2)(4)}t^4\\\\=\boxed{r^{-12}s^8t^4}\to\boxed{\dfrac{s^8t^4}{r^{12}}}[/tex]

To simplify the expression (r⁻³ s² t)⁴, the power of a power rule is used to obtain the result r⁻¹² s⁸ t⁴.

To simplify the expression (r⁻³ s² t)⁴, we apply the power of a power rule, which states that (ab)c = ab*c. Using this rule, we raise each factor within the parentheses to the fourth power:

Therefore, the simplified expression is r⁻¹² s⁸ t⁴.

Answer:

0.9 represents the amount of the original price he is paying. i.e 0.9 of the original price equals the sales price

Step-by-step explanation:

Answer:

C The percent, as a decimal, of the original price that Ray pays

Step-by-step explanation:

Answer: 1.6M kilometers, 8 kilometers

Step-by-step explanation:

Kilometers per mile times miles gives kilometers.

(1.6 kilometers / mile) × M miles = 1.6M kilometers

5×1.6 is 8

Answer:

Rewrite equations:

y=x−1;−4x+3y=−2

Step: Solvey=x−1for y:

y=x−1

Step: Substitutex−1foryin−4x+3y=−2:

−4x+3y=−2

−4x+3(x−1)=−2

−x−3=−2(Simplify both sides of the equation)

−x−3+3=−2+3(Add 3 to both sides)

−x=1

−x

−1

=

1

−1

(Divide both sides by -1)

x=−1

Step: Substitute−1forxiny=x−1:

y=x−1

y=−1−1

y=−2(Simplify both sides of the equation)

Answer:

x=−1 and y=−2

Answer:

Cubic Units

Step-by-step explanation:

Self explanatory

Answer:

the units of volume are always cubic units

Total number of fruits

                      = 15 apples + 7 Oranges + 3 Strawberries + 1 banana + 5 limes + 9 pineapples

= 15+7+3+1+5+9

= 22+3+1+14

= 25+15

= 40 fruits

The total is 40 fruits which should be sent to  (2401 W. Grace Street).

Answer:

The total is [tex]40[/tex] fruits which should be sent to  ([tex]2401[/tex] W. Grace Street)

Step-by-step explanation:

Let

x------->the total number of fruits

Find the total number of fruits

[tex]x=15\ apples + 7\ Oranges + 3\ Strawberries + 1\ Banana + 5\ limes + 9\ pineapples[/tex]

[tex]x=15+7+3+1+5+9[/tex]

[tex]x=40\ fruits[/tex]

Answer: 86.7%

Step-by-step explanation:

[tex]\dfrac{New - Original}{Original}[/tex]

[tex]\dfrac{\$2.24 - \$1.20}{\$1.20}[/tex]

= [tex]\dfrac{\$1.04}{\$1.20}[/tex]

= 0.867

= 86.7%

Answer:  The correct option is (B) -7.

Step-by-step explanation:  We are given to select the correct values of x that make the following rational expression undefined :

[tex]E=\dfrac{16-x}{7+x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

a rational expression is undefined at the points where the denominator becomes zero.

Therefore, the expression (i) will become undefined when

[tex]7+x=0\\\\\Rightarrow x=-7.[/tex]

Thus, the required value of x where the given expression is undefined is -7.

Option (B) is CORRECT.

Answer:

yes

Step-by-step explanation:

for the sticks to form a right triangle, the 3 sticks' lengths must comply w the Pythagoras theorem: hypothesis^2 = first side^2 + second side^2

hypothesis is the longest length so its 10

10^2 = 100 = 36 + 64 = 6^2 + 8^2

so the 3 sticks will form a right triangle

Answer:

6^2+8^2=10^2 so yes

Step-by-step explanation:

In order to test a triangle with lengths 6, 8 and 10 inches is right-angle or not, the Pythagoras equation should be used: a^2+b^2=c^2.

As 6^2+8^2=10^2 so yes, the three sticks will form a right-angle triangle.

Answer:

Figure C

Step-by-step explanation:

Figure A represents a ray because it has arrow only on one end.

Figure B is a line segment because it stops on both ends.

Figure C is a line because it has arrow on both ends.

Figure D is an angle, because it is 2 rays joined at a vertex.

Answer:

sqrt(-80) = 4sqrt(5)i

Step-by-step explanation:

Likely a list of answers should be provided. There are all kinds of possible answers (well 2 perhaps).

Begin by factoring 80 into prime factors.

80: 2*2*2*2*5

For ever pair of 2s, one can be taken outside the square root sign. The other one just disappears.

sqrt(80) = sqrt(2 * 2 * 2 * 2 * 5)

For every pair 2 is taken out of the root sign and the other forgotten

sqrt(2 * 2 * 2 * 2 * 5) = 2 * 2 * sqrt(5) = 4 sqrt(5)

The sqrt(-80) = 4sqrt(5)*sqrt(-1)

There is no real number that can be written as the sqrt(-1). So a number has been defined into existence. sqrt(-1) = i It's a definition, not a real number.

So the end result is sqrt(-80) = 4sqrt(5)i

Answer:

$27402.    

Step-by-step explanation:

We have been given that Berto invested in a precious mineral. The value of the mineral tends to increase by about 11% per year. He invests $40,000 in 2015.

Let us write a function using our given information for the value of minerals.

We are told that the value of minerals increase by 11% every year, so our function will be an exponential function.

Since an exponential function is in form: [tex]y=a*b^x[/tex]; for growth b=(1+r), where r is rate of growth in decimal form.

a= Initial value.  

Let us convert our given rate in decimal form.

[tex]11 percent= \frac{11}{100}=0.11[/tex]

Let G(t) be the growth of minerals t years after 2015.

Upon substituting our given values we will get our function as: [tex]G(t)=40,000*(1+0.11)^t[/tex]

[tex]G(t)=40,000*(1.11)^t[/tex]    

To find the value of Berto's investment in year 2020 by substituting t=5 in our function as 2020-2015=5.

[tex]G(2020)=40,000*(1.11)^5[/tex]

[tex]G(2020)=40,000*1.6850581551[/tex]

[tex]G(2020)=67402.326204\approx 67402[/tex]    

Therefore, the value of his investment in 2020 will be $67402.

Let us find the difference of values of minerals between 2020 and 2015.

67402-40000=27402

Therefore, Berto's investment will be worth $27402 in 2020.

Answer:

Step-by-step explanation:

20742

Answer:

The actual room measurement is 15 yrds by 10 yrds

Then the length is 15 yrds

Step-by-step explanation:

1 feet is equal to 0.3333 yards

The room measure 3 by 2 feet

Scale on blue print 1 ft to 5 yrds.

That's is to say for every ft in the Blue print...it is 5 yrds real.

So it's multipling factor bis five.

The actual measurement will be

5*(3 by 2) yrds

The actual measurement is 15 yrds by 10 yrds .

But the length is 15 yrds and breadth is 10 yrds

Answer would be the third option.

Area of a triangle is half of the base times the height. A=(b·h)/2

In the third option the height is 8 ft. and base is 6 ft. which when multiplied together gets you 48. Half of that is 24.

Answer:

8+8i

Step-by-step explanation:

remove parenthesis

3+i+5+7i

add like terms

8+8i

not sure if you wanted it foiled or like that

Answer:

The call it the Donut Eatting Contest

Step-by-step explanation:

okay the first line on that line is 0 in a min then 1 in a min then 2 in a min then 3 in a min then 4 in a min cause she said how many donuts per min

then on each person that eat that many put a x obove the number

We are given that AB ≅ CB and AD ≅ CD.

We know that BD ≅ BD, so ΔABD ≅ ΔCBD by SSS.

Then ∠1 ≅ ∠2 by CPCTC; and ∠3 ≅ ∠4, also by CPCTC.

Since ∠1 ≅ ∠2, BD is the bisector of (∠1+∠2) = ∠ABC.

Since ∠3 ≅ ∠4, BD is the bisector of (∠3+∠4) = ∠ADC.

From (5), we know BD is the angle bisector of ∠ABC. ΔABC is isosceles, so the bisector of the apex angle is also an altitude and median. That is, point M on BD and AC must be the midpoint of AC by the definition of a median.

Answer:

14/5 or 2 4/5

Step-by-step explanation:

7 3/5 = 38/5

4 4/5 = 24/5

38/5 - 24/5 = 14/5 = 2 4/5

Answer:

union and the second question is intersection

Step-by-step explanation:

Answer:

The union of two sets A and B is the set of elements that are present in A, in B, or in both A and B.

The intersection of two sets A and B is the set of elements that are present in A, in B.

Look at the picture.

ΔABC and ΔDAC are similar. Therefore the sides of the triangles are in proportion:

[tex]\dfrac{AC}{BC}=\dfrac{DC}{AC}[/tex]

AC = x

BC = 5 + 4 = 9

DC = 4

Substitute:

[tex]\dfrac{x}{9}=\dfrac{4}{x}[/tex]          cross multiply

[tex]x^2=(9)(4)\\\\x^2=36\to x=\sqrt{36}\\\\\boxed{x=6\to C)}[/tex]

Answer:

21x+35[tex]\geq[/tex]160

Step-by-step explanation:

(Amount)(time)+(starting total)[tex]\geq[/tex]total

(21)(x)+(35)[tex]\geq[/tex]160

21x+35[tex]\geq[/tex]160

Answer:

A prom ticket at Valley high school cost $160. Bryan is going to save money for his ticket by walking his neighbor’s dog for $21 per week. Bryan has already has saved $35. Which inequality could be used to find the minimum number of weeks Bryan must walk the dog to earn enough to pay for his prom ticket?

A) 21x + 35 ≥ 160  

B) 21x + 35 ≤ 160  

C) 35x + 21 ≥ 160  

D) 35x + 21 ≤ 160

Step-by-step explanation:  THE ANSWER is A

Answer:

$875.00

Step-by-step explanation:

If you want to find out how much commission Anil earned in commissions last month, you must multiply $12,500 by .07 (7%) and it equals $875.00.

Hope that helps!

Answer:  D

Step-by-step explanation:

When dealing with a an exponent in fraction form:

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

1t+45d

i think. could be wrong.

Answer:

[tex]x+1[/tex] meters.

Step-by-step explanation:

Let L be the length of rectangle.

We have been given that the rectangle has an area of [tex]x^{2}-6x-7[/tex] square meters and a width of [tex]x-7[/tex] meters.

Since we know that area of rectangle is the product of its length and width.

[tex]\text{Area of rectangle}=\text{Width* Length}[/tex]

[tex]\text{ Length}=\frac{\text{Area of rectangle}}{\text{Width}}[/tex]

To find the length of our given rectangle we will divide area of rectangle by width of our rectangle.

[tex]L=\frac{x^2-6x-7}{x-7}[/tex]

Let us factor out our numerator by splitting the middle term.

[tex]L=\frac{x^2-7x+x-7}{x-7}[/tex]

[tex]L=\frac{x(x-7)+1(x-7)}{x-7}[/tex]

[tex]L=\frac{(x-7)(x+1)}{x-7}[/tex]

Upon cancelling out x-7 from numerator and denominator we will get,

[tex]L=(x+1)[/tex]  

Therefore, the length of our rectangle will be [tex]x+1[/tex] meters.

Answer:

Mutual Fund

Step-by-step explanation:

A mutual fund is invested by managers in diversity of stocks, bonds and other securities. Mutual fund is an investments that help you grow your money to bigger value. Your money will be used to invest in some companies, products and services to be able to gain more.

It is an investment programmed funded by share holders that trades in diversified holdings and is professionally managed. It pols money from many investors to purchase securities. These investors could be institutional or retail in nature.

Answer:

9

Step-by-step explanation:

Make sure to use PEMDAS.

[tex]6/2(1+2)\\\text{Simplify.}\\3(3)\\\text{Simplify.}\\9[/tex]

Answer:

Joey needs to eat 7 hot dogs per minute to break his own record in next 9 minutes.

Step-by-step explanation:

Joey needs more than 72 hot dogs in 10 minutes to break his own record.That means Joey needs to eat at least 73 hot dogs in 10 minutes.

After 1 minute Joey has eaten = 10 hot dogs.

In remaining 9 minutes balance hot dogs = 73-10 =63

Therefore per minute hot dogs to be eaten = 63/9 =7

So answer is 7 hot dogs per minute to be eaten.

Joey needs to eat  7.00 hot dogs per minute for the next 9 minutes to break his own record.

To break his record, Joey Chestnut needs to eat more than 72 hot dogs in 10 minutes. After the first minute, he has already eaten 10 hot dogs. So, he has 9 minutes left to eat the remaining hot dogs needed to break the record, which is 72 - 10 = 62 hot dogs.

To find out how many hot dogs per minute Joey needs to eat for the next 9 minutes, we divide the remaining number of hot dogs by the remaining time:

Hot dogs per minute = Remaining hot dogs / Remaining time

Hot dogs per minute = 62 hot dogs / 9 minutes

Hot dogs per minute ≈ 6.89 hot dogs per minute

Therefore, Joey needs to eat  7.00 hot dogs per minute for the next 9 minutes to break his own record.

It's important to note that Joey needs to eat more than this calculated rate per minute to ensure he breaks his record, as he cannot consume a fraction of a hot dog. So, he should aim to eat at least 7 hot dogs per minute to secure his victory.