the length of a rectangle is six times it’s width. If the perimeter of the rectangle is 112 yards, find it’s length and width.

Given:

Given that the measure of the exterior angle F is 142°

We need to determine the measure of ∠DFE

Measure of ∠DFE:

The ∠DFE and the exterior angle F are linear pairs.

Thus, the linear pair of angles add up to 180°

Hence, we have;

[tex]\angle DFE+142^{\circ}=180^{\circ}[/tex]

Subtracting both sides of the equation by 142, we get;

[tex]\angle DFE=38^{\circ}[/tex]

Hence, the measure of ∠DFE is 38°

Thus, Option a is the correct answer.

Answer:

I think its 23o

Step-by-step explanation:

Answer:

d is correct for me

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Multiply 11 by 2 to get to 22; do the same to 4

Answer:40%

total 60

24 is 40% of 60

Answer:

40

Step-by-step explanation:

24/60 x 100

40%

Answer: The answer is the first one d= 1/50w.

Step-by-step explanation: 3/5 divided by 30 is 1/50 as a fraction. This is the unit rate. 1/50 milligrams per pound. Hope this helps!:))

Answer:

it would be D=1/50 W

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

A=[tex]\frac{bh}{2\\}[/tex]

A=[tex]\frac{5.5*4}{2}[/tex]

A=[tex]\frac{22}{2}[/tex]

A=11

Answer:

A=11in²

Step-by-step explanation:

Answer:

Option B, [tex]-11g + 15[/tex]

Step-by-step explanation:

Step 1:  Distribute

[tex]-g - 5(2g - 3)[/tex]

[tex]-g + (-5 * 2g) + (-5 * -3)[/tex]

[tex]-g - 10g + 15[/tex]

[tex]-11g + 15[/tex]

Answer: Option B, [tex]-11g + 15[/tex]

Answer:

5900 meters < Sarita < 6500 meters

Step-by-step explanation:

Given

Tomás = [tex]6\frac{1}{2} km[/tex]

Jackie = 8,000 m

Joseph = 5.9 km

Mai Yee = 2,790 m

Where km and m represent kilometers and meters respectively

Required

How far could Sarita have ran

First, we'll convert the distance covered by each individuals to one units (Preferably meters)

We'll need to convert distance covered by Tomás and Joseph because they're given in kilometers.

Since 1 km = 1000 m, then we have

Tomás = [tex]6\frac{1}{2} km[/tex]

Tomás = [tex]6\frac{1}{2} * 1000 m[/tex] (Convert fraction to decimal)

Tomás = [tex]6.5 * 1000 m[/tex]

Tomás = 6500 m

Joseph = 5.9 km

Joseph = 5.9 * 1000 m

Joseph = 5900 m

Now that we have the same unit all through, the next step is to list them out

Tomás = 6500 m

Jackie = 8,000 m

Joseph = 5900 m

Mai Yee = 2,790 m

Then, we rearrange in ascending order (from smallest to biggest)

Mai Yee = 2,790 m

Joseph = 5900 m

Tomás = 6500 m

Jackie = 8,000 m

The condition given in the question is that Sarita ran farther than 2 of the people in the table and slower than the other 2

This means that Sarita ran farther than the least 2 "Mai Yee and Joseph"

And at the same time Sarita covered lesser distance than the highest 2 "Tomás and Jackie"

This means that distance covered by Sarita is greater than distance covered by Joseph and less than distance covered by Tomás

Since no option is given, I'll represent the answer using inequality

Recall that

Joseph = 5900 m

Tomás = 6500 m

Sarita could have ran a distance greater than 5900 meters and less than 6500 meters

Distance covered by Sarita: 5900 < Sarita < 6500

Answer:

See below.

Step-by-step explanation:

Formula:

[tex] a_n = 3(n + 4) [/tex]

First term: n = 1

[tex] a_1 = 3(1 + 4) = 15 [/tex]

Second term: n = 2

[tex] a_2 = 3(2 + 4) = 18 [/tex]

Third term: n = 3

[tex] a_3 = 3(3 + 4) = 21 [/tex]

Fourth term: n = 4

[tex] a_4 = 3(4 + 4) = 24 [/tex]

Tenth term: n = 10

[tex] a_{10} = 3(10 + 4) = 42 [/tex]

The explicit formula is [tex]a_{n}[/tex] = 4 + (n - 1)3 first four terms will be 4, 7, 10, and 13 and the 10th term will be 31.

The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).

The arithmetic progression has wider use in mathematics for example sum of natural numbers.

Natural number = 1,2,3,4,5,6,7,8...

Now it has the same difference between any two consecutive terms d =2-1 = 3-2.

Let's say

First term = 4

Common difference = 3

Then

The nth term of the AP will be

[tex]a_{n}[/tex] = 4 + (n - 1)3

First term: n = 1

a₁ = 4

Second term: n = 2

a₂ = 7

Third term: n = 3

a₃ = 10

Fourth term: n = 4

a₄ = 13

Tenth term: n = 10

a₁₀ = 31

Hence, the explicit formula is [tex]a_{n}[/tex] = 4 + (n - 1)3 first four terms will be 4, 7, 10, and 13 and the 10th term will be 31.

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[tex]-3x+5<17\\-3x<12|:(-3)\\x>-4[/tex]

x∈(-4;+∞)

/\/\/\/\/\/\/\/\/\/\/\

P.S. Hello from Russia :^)

Answer:

16

Step-by-step explanation:

2:3=x:24

2/3=x/24

(24)(2/3)=x

x=16

Final answer:

The product of 4/9 and 72 is found by multiplying 4 by 72 and then dividing by 9, giving us the final answer of 32.

Explanation:

To find the product of 4/9 and 72, you multiply the two numbers together. Here's how you do it:

Write the multiplication expression: 4/9 × 72.

Since 72 is the same as 72/1, you can think of this as multiplying two fractions: (4/9) × (72/1).

Multiply the numerators together: 4 × 72 = 288.

Multiply the denominators together: 9 × 1 = 9.

Combine the results to find the fraction form of the answer: 288/9.

Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is 9: 288 ÷ 9 = 32.

The product of 4/9 and 72 is 32.

Answer:

∠XDQ : 41°

∠UXD: 139 °

Step-by-step explanation:

Allow me to rewrite your answer for a better understanding and please have a look at the attached photo.

A segment XD is drawn in rectangle QUAD as shown  below.

What are the measures of ∠XDQ and ∠UXD ?

My answer:

As we can see in the photo, ∠ADX = 49° and ∠ADU =90°

=>  ∠XDQ = ∠ADU - ∠ADX

= 90°  - 49°  = 41°

In the triangle ADX, we can find out the angle of ∠DXA

= 180° - ∠DAX - ∠ADX

= 180° - 90° - 49°

= 41°

=> ∠UXD = 180° - ∠DXA  (Because UA is a straight line)

=180° - 41°  

= 139 °  

Answer:y=9(8)^x

Step-by-step explanation:

The exponential function that passes through the points (0,9) and (3,4608) is y = 9 * 8^x. This was determined by using the given points to find the values of a and b in the function y = ab^x.

To write an exponential function that passes through the points (0,9) and (3,4608), we start with the general form y=abx. Using the given points, we can set up two equations based on their coordinates. The first point (0,9) leads to the equation 9 = a * b0, which simplifies to 9 = a since anything raised to the power of 0 is 1. The second point (3,4608) gives us 4608 = a * b3.

Now that we know a = 9, we can substitute it into the second equation to find the value of b: 4608 = 9 * b3. Dividing both sides by 9, we get 512 = b3, which leads to b = 8 after taking the cube root of 512. Thus, the exponential function we are looking for is y = 9 * 8x.

Answer:3

Step-by-step explanation:

2x8=16

There are 5 people in total

16/5=3.2

Whole number so 3 slices

Answer: the answer is A (4)

Answer:

The correct answer is 8 inches

Step-by-step explanation:

Answer:

copper=3kg

nikhil=5/4 kg

zinc=3/4 kg

Step-by-step explanation:

copper:nikhil:zinc

12:5:3

let x be one value

12x+5x+3x=5

20x=5

x=5/20=1/4

12*1/4=12/4=3

5*1/4=5/4=1 1/4

3*1/4=3/4

To make 5 kg of the alloy, you would need:

A ratio is a mathematical comparison of two quantities or values. It expresses the relationship or proportion between the quantities being compared. Ratios can be represented in different forms, such as fractions, decimals, or as a colon (:).

Let's calculate the amounts for each metal:

Copper:

The ratio indicates that for every 12 parts of the alloy, 1 part should be copper.

So, the amount of copper needed

= 12/20 x 5

= 3 Kg

Nickel:

For every 5 parts of the alloy, 1 part should be nickel.

So, the amount of nickel needed

= 5/20x 5

= 1.25 Kg

Zinc:

For every 3 parts of the alloy, 1 part should be zinc.

So, the amount of zinc needed

= 3/20 x 5

= 0.75 Kg

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Step-by-step explanation:

Theoretical probability : Theoretical probaility is the value expected from an outcome or an equation assuming perfect conditions. It is based on theories and hypotheisi and not based on real life incidents.

Experimental probability : When we performa n experiment, the values we get are experimental probability. These are actual rsults of the eperiemnt under study

Independent probability : Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur.

Dependent probability: If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.

Since the results of the experiment are used and based on the above definitions. we should use experiement probabiity (Option B) to predict he probability of the next number showing on the top face

Answer:

48 cm

Step-by-step explanation:

The midsegment of a trapezoid is calculated as

[tex]\frac{sumofbases}{2}[/tex], thus

XY = [tex]\frac{34+62}{2}[/tex] = [tex]\frac{96}{2}[/tex] = 48 cm

Answer:

see explanation

Step-by-step explanation:

The opposite angles of the inscribed quadrilateral are supplementary, thus

∠ A + ∠ C = 180°, substitute values

14z - 7 + 8z = 180

22z - 7 = 180 ( add 7 to both sides )

22z = 187 ( divide both sides by 22 )

z = 8.5

Thus

∠ A  = 14z - 8 = 14(8.5) - 7 = 119 - 7 = 112°

∠ C = 8z = 8(8.5) = 68°

∠ D = 10z = 10(8.5) = 85°

The sum of the 4 interior angles = 360°, thus

∠ B = 360° - (112 + 68 + 85)° = 360° - 265° = 95°

Thus

∠ A = 112°, ∠ B = 95°, ∠ C = 68°, ∠ D = 85°

9.24 days does it take 500 grams of the isotope to decay to 250 grams.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculation

Given that

The isotope thulium-167 is used in laser scans for medical treatments

The rate of decay is 0.075

The isotope thulium-167 is used in laser scans for medical treatments.

If we started with 500 grams then we are looking for when only 250 grams are left so

y = y₀e^(-0.075t)

y₀ represents the initial amount of radioactive material

250 = 500e^(-0.075t)

0.5 = e^(-0.075t)  

Now take the natural log of both sides which gives us,

ln0.5 = -0.075t

t = ln0.5/(-0.075)

t = 9.24 days

Hence, 9.24 days does it take 500 grams of the isotope to decay to 250 grams.

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The shadow length of Kyle is 1.2 feet,if a lighthouse is 150 feet tall and cast a shadow of 30 feet. Kyle is standing next to a lighthouse and is 6 feet tall.

Step-by-step explanation:

The given is,

                  A lighthouse is 150 feet tall.

                  Cast a shadow of 30 feet.

                  Kyle is 6 feet tall.

Step:1

                 Ref the attachment,

                 From triangle ABC,

                               tan ∅ = [tex]\frac{Opp}{Adj}[/tex]......................(1)

                 Where, Opp = AB = 150 feet

                                Adj = BC = 30 feet

                 Equation (1) becomes,

                              tan ∅ = [tex]\frac{150}{30}[/tex]

                                        = 5

                                     ∅ = [tex]tan^{-1}[/tex] 5

                                     ∅ = 78.69°

                 ∅ is same for both ABC and PQR triangle.

                 From triangle PQR,

                               tan ∅ = [tex]\frac{Opp}{Adj}[/tex]......................(1)

                 Where, Opp = PQ = 6 feet

                                Adj = QR = x

                 Equation (1) becomes,

                      tan 78.96° = [tex]\frac{6}{x}[/tex]

                                     5 = [tex]\frac{6}{x}[/tex]

                                     x = [tex]\frac{6}{5}[/tex] = 1.2

                 Shadow length of Kyle, x = 1.2 feet

Result:

           The shadow length of Kyle is 1.2 feet, if a lighthouse is 150 feet tall and cast a shadow of 30 feet. Kyle is standing next to a lighthouse and is 6 feet tall.

Answer:

55

Step-by-step explanation:

180-25=55

Answer: 55

Step-by-step explanation:

Answer:

a=15

Step-by-step explanation:

5a-10b=45

5a-10*3=45

10*3=30

5a-30=45

+30

5a=75

75/5=15

a=15

Answer:

A=15

Step-by-step explanation:

Answer:

55/3 its a fraction hope this helps

Step-by-step explanation: