A rectangle has a length of 6 and a width of y + 4. Use the distributive property to write an expression to represent the area of the rectangle.

Lydia invested $ 3100 in investment lost 2 % and invested $ 4400 in investment that earned 5 %

Solution:

Given that on two investment totaling $ 7500

Lydia lost 2% on one and earned 5% on the other

Her net annual receipts were $158

To find: amount invested in both investments

Let Lydia invest $ x in first investment where she lost 2 %

Let Lydia invest $ y in second investment where she earned 5 %

Total investment given = 7500

x + y = 7500 ---- eqn 1

Net annual receipt = 158

5 % y- 2 % x = 158

[tex]\frac{5}{100}y - \frac{2}{100}x = 158[/tex]

0.05y - 0.02x = 158 ------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 7500 - y

Substitute x = 7500 - y in eqn 2

0.05y - 0.02(7500-y) = 158

0.05y -150 + 0.02y = 158

0.07y = 158 + 150

0.07y = 308

y = 4400

Thus,

x = 7500 - y

x = 7500 - 4400

x = 3100

Thus she invested $ 3100 in investment lost 2 % and invested $ 4400 in investment that earned 5 %

Final answer:

Lydia invested $3,100 at a 2% loss and $4,400 at a 5% gain. A system of equations is set up and solved using substitution to determine the amount invested in each scenario.

Explanation:

To solve Lydia's investment problem, we need to set up a system of equations based on the given information

Total investment is $7,500.

She lost 2% on one investment and earned 5% on the other.

Her net annual receipts were $158.

Let's define:
x = the amount of money invested at a 2% loss
y = the amount of money invested at a 5% gain

The system of equations can be written as:

x + y = 7500 (the total amount invested)

-0.02x + 0.05y = 158 (the net receipts from the investments)

Multiplying the second equation by 100 to simplify the decimals:

-2x + 5y = 15800

Now we can use the method of substitution or elimination to solve for x and y. For this example, we'll use the substitution method:

Solve for y in the first equation: y = 7500 - x

Substitute y into the second equation: -2x + 5(7500 - x) = 15800

Now solve for x: -2x + 37500 - 5x = 15800

Combine like terms: -7x = 15800 - 37500

-7x = -21700

Divide by -7: x = 3100

Substitute x into y = 7500 - x: y = 7500 - 3100 = 4400

So Lydia invested $3,100 at a 2% loss and $4,400 at a 5% gain.

Answer: 10%

50 is half of 100, so if it decreases 5 dollars from 50, then it has to be 10% of a decrease, or discount.

Hope this helps!

Answer:

10%

Step-by-step explanation:

50-45=5

5/50=1/10=10%

Answer:

20 hours

Because 143.50/7= 20.5

Meaning the most she can work is 20 hours a week

Answer:

Step-by-step explanation:

My frist store wen you I was a little kid and the most main street from this is

Answer:

Answers are in picture, if you want an explanation for anything, just ask.

Step-by-step explanation:

Answer:

Step-by-step explanation:

In the multiplication operation of numbers 435 and 173, the regrouped or carried over amounts are 10 (in units place calculation) and 30 (in tens place calculation). Therefore, the answer corresponds to option B: 20 and 3.

In multiplicaton problems, we often need to 'regroup' or carry values. In the multiplication of 435 and 173, regrouping is necessary. Here's how it's done:

We start by multiplying 5 from 435 with 3 from 173, to get 15. We write down 5 and carry over the 1 (or 10 from 15).

Next, we multiply the 5 in 435 with 7 (the tens-place in 173), which equals 35. We add the carry-over 1 to get 36. We write down the 6 and carry over the 3 (or 30).

Finally, we multiply the 5 in 435 with 1 (the hundreds-place in 173). Then add the carried over 3, resulting in 8.

The process is repeated with the remaining numbers in 435.

So for the multiplication above, the regrouped amounts are 10 and 30, corresponding to option B: 20 and 3.

For more such question on multiplication operation visit:

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Answer:

.875 = 875/1,000 = 7/8

The correct answer is D.

Answer:

[tex] {4}^{ - 3} \times {4}^{2} \times {4}^{5} = {4}^{ - 3 +2 + 5} = {4}^{4} [/tex]

False. The missing exponent is 4.

Answer:

(-20,20)

Step-by-step explanation:

Given coordinates are (-4,4).

Also, we need to dilate by a scale factor of 5.

The term dilation refers to changing the value of coordinate by a scale factor.

If the coordinate is said [tex](x,y)[/tex] and it is going to be dilated by a scale factor [tex]'k'[/tex].

Then the new coordinate will be (kx, ky).

So,

[tex](-4,4)\\\\k=5\\\\(-4\times5,4\times5)=(-20,20)[/tex]

The coordinate [tex](-4,4)[/tex] after dilated by a scale factor [tex]5[/tex] will be [tex](-20,20)[/tex]

Answer:

97-x

Step-by-step explanation:

100-(3+x)

= 100-3-x (- sign is multiplied with the both 3 and x)

= 97-x

Answer:

Step-by-step explanation:

x + 3 = 100

x = 100 - 3

x = 97

Answer:

HI hydrogen iodide

Step-by-step explanation:

H2(gas)+I2(gas)---------->2HI(gas)

Answer:

I don't really know what you were asking; would you mind please clarifying? :)

Step-by-step explanation:

From what I'm guessing from the question is, "Iodine, and hydrogen combine to form hydrogen iodide. In the reverse reaction, hydrogen iodide decomposes back into hydrogen and iodine."

Did that help?

Answer:

[tex]3\frac{3}{4}[/tex] hours.

Step-by-step explanation:

Sean read [tex]\frac{1}{5}[/tex] of a book in [tex]1\frac{1}{2}[/tex] hours.

We are asked to determine the time that Sean requires to read [tex]\frac{1}{2}[/tex] of this book.

If the rate of reading the book is assumed to be constant, then we can use the unitary method to find the answer.

Now, Sean reads [tex]\frac{1}{5}[/tex] of a book in [tex]\frac{3}{2}[/tex] hours.

So, Sean reads the total of the book in [tex]\frac{3}{2} \div \frac{1}{5} = \frac{15}{2}[/tex] hours.  

Hence, Sean reads  [tex]\frac{1}{2}[/tex] of this book in [tex]\frac{15}{2} \times \frac{1}{2} = \frac{15}{4} = 3\frac{3}{4}[/tex] hours. (Answer)

Answer:

[tex]6.7\sqrt{2}\ in[/tex]

Step-by-step explanation:

Let x inches be the length of the side of the square. The area of the square is

[tex]x\cdot x=x^2\ in^2[/tex]

Then

[tex]x^2=44.89\\ \\x=6.7\ in[/tex]

By the Pythagorean theorem,

[tex]d^2=6.7^2+6.7^2\\ \\d^2=44.89+44.89\\ \\d^2=89.78\\ \\d=\sqrt{89.78}=6.7\sqrt{2}\ in[/tex]

Find the length of a side by taking the square root of the area:

Side = sqrt44.89 = 6.7 inches.

Now to find the length of the diagonal multiply the side length by the sqrt of2:

Diagonal = 6.7Sqrt(2) ( exact length)

As a decimal= 9.4752

Answer:

The Area of the base is 16 cm² .

Step-by-step explanation:

Given as :

The surface area of the cuboid = x = 95 cm²

The lateral surface area of the cuboid = y = 63 cm²

Let The Area of the base = z cm²

Now, Let The length of cuboid = l cm

The breadth of cuboid = b cm

The height of cuboid = h cm

According to question

∵ The surface area of the cuboid = 2 ×(length × breadth + breadth × height + height × length)

Or, x = 2 ×(l × b + b × h + h × l)

Or, 95 =  2 ×(l × b + b × h + h × l)

Or,  (l × b + b × h + h × l) = [tex]\dfrac{95}{2}[/tex]          ....1

Similarly

∵lateral surface area of the cuboid = 2 ×(breadth × height + length × height)

Or, y = 2 ×(b × h + l × h)

Or, 2 ×(b × h + l × h) = 63

Or, (b × h + l × h) = [tex]\dfrac{63}{2}[/tex]              ......2

Putting value of eq 2 into eq 1

so,  (l × b +  [tex]\dfrac{63}{2}[/tex] ) = [tex]\dfrac{95}{2}[/tex]    

Or, l × b = [tex]\dfrac{95}{2}[/tex] - [tex]\dfrac{63}{2}[/tex]    

Or,  l × b = [tex]\dfrac{95 - 63}{2}[/tex]

i.e l × b = [tex]\dfrac{32}{2}[/tex]

so, l × b = 16

Now, Again

∵The Area of the base = ( length × breadth ) cm²

So, z =  l × b

i.e z = 16 cm²

So, The Area of the base = z = 16 cm²

Hence,The Area of the base is 16 cm² . Answer

Answer:

4.8 Liters.

Step-by-step explanation:

When pressure is kept constant the volume of a certain quantity of gas is proportional to the absolute temperature of the gas.

So, [tex]\frac{V_{f} }{T_{f}} = \frac{V_{i} }{T_{i}}[/tex] .......... (1)

Where, f denotes the final and i denotes the initial values.

Now, [tex]V_{i} = 3[/tex] Liters,

[tex]T_{i} = 25 + 273 = 298 K[/tex] and  

[tex]T_{f} = 200 + 273 = 473 K[/tex]

Therefore, from equation (1) we get,

[tex]V_{f} = \frac{3 \times 473}{298} = 4.76[/tex] Liters ≈ 4.8 Liters. (Answer)

To calculate Alia's hourly wage, you divide the total amount she earned ($585.60) by the total number of hours she worked (18.3 hours), which results in approximately $32 per hour. This question is related to the subject of Mathematics, specifically rates and ratios.

The subject of this question is Mathematics, specifically the sub-topic of rates and ratios, which includes calculating earnings per hour.

To calculate Alia's earnings per hour, we need to divide her total earnings by the number of hours she worked. Here's a step-by-step explanation:

https://brainly.com/question/1582269

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Final answer:

The diameter of the pizza is 14 inches, its circumference is approximately 43.98 inches, and its area is about 153.94 square inches, calculated using fundamental geometry formulas for circles.

Explanation:

A pizza with a radius of 7 inches is given, and we are tasked with determining its diameter, circumference, and area. These are fundamental geometry calculations related to circles.

The diameter of a circle is twice its radius. So, the diameter of the pizza is 2 × 7 inches = 14 inches.

The circumference of a circle is calculated as π (Pi) times its diameter.

Therefore, the circumference of the pizza is π × 14 inches ≈ 43.98 inches (using π = 3.1416).

The area of a circle is given by π times the square of its radius (πr²).

Hence, the area of the pizza is π × 7² inches² ≈ 153.94 square inches.

These calculations provide a complete geometric understanding of the pizza's properties in terms of diameter, circumference, and area.

Answer:

123 coupons.

Step-by-step explanation:

Divide the total of 164 coupons by 4. 164/4 = 41

Find the amount of coupons sent by multiplying 41 by 3. 41 x 3 = 123

The answer is 123 coupons. (123/164 = 3/4)

Answer:

Step-by-step explanation:

Explanation:

The product of two positive numbers is always positive.

So product of All positive numbers will be always positive.

For Example

( + ) × ( + ) = ( + )

The product of two negative number is always positive.

So product of even negative numbers will be always positive

For example

( - ) × ( - ) = ( + )

Also product of negative and positive is also given as a negative

( - ) × ( + ) = ( - )

and

( + ) × ( - ) = ( - )

Let the Six Positive numbers be

a, b ,c , d, e, f

So the Product of Six Positive numbers will be

[tex](+a)\times (+b)\times (+c)\times (+d)\times (+e)\times (+f)=\textrm{Positive Number}[/tex]

Let the Six Negative numbers be

-a, -b ,-c , -d, -e, -f

So the Product of Six Negative numbers will be

[tex](-a)\times (-b)\times (-c)\times (-d)\times (-e)\times (-f)=\textrm{Positive Number}[/tex]

Therefore the Product's Sign will be

a) Positive ; Positive

Answer:

c) Positive; Positive

Step-by-step explanation:

As we know it is a basic rule in mathematics, that if positive is multiplied by positive it gives a positive result always. So hence, from this rule it is proved that if we multiply 6 positive numbers, we will be getting the product which will be having positive sign. And in the second part of the questions, answer  is that if we multiply 6 negative numbers then the sign remains positive as we know it is also a basic rule in mathematics that when 2 negative numbers are multiplied by each and other then it will give a positive product. So the answer will remain 'c) Positive; Positive''

Answer:

V=20

Step-by-step explanation:

Simplify both sides of the equation.

4−2(v+9)=26

4+(−2)(v)+(−2)(9)=26(Distribute)

4+−2v+−18=26

(−2v)+(4+−18)=26(Combine Like Terms)

−2v+−14=26

−2v−14=26

Step 2: Add 14 to both sides.

−2v−14+14=26+14

−2v=40

Step 3: Divide both sides by -2.

−2v

−2

=

40

−2

v=−20

Paulo's family has 1 hour 45 minutes before the trip to Scenic Lake Park.

To find out how long Paulo's family has before the trip to Scenic Lake Park, we will determine the amount of time between their arrival and the start of the trip.

Paulo's family arrived at the reunion at 8:30 A.M. The trip to Scenic Lake Park starts at 10:15 A.M.

Here's how to calculate the difference between these two times manually:

1. Convert both times to a 24-hour format (if needed):
  - Paulo's family arrival time: 8:30 A.M. is already in the morning, so it stays the same.
  - Trip start time: 10:15 A.M. is also in the morning, so it stays the same.

2. Calculate the hours remaining:
  - From 8 A.M. to 9 A.M. is 1 hour.
  - From 9 A.M. to 10 A.M. is another hour.
  - From 8:30 A.M. to 10 A.M., they have a total of 1 hour and 30 minutes.

3. Calculate the additional minutes remaining:
  - From 10:00 A.M. to 10:15 A.M. is an additional 15 minutes.

4. Add the additional minutes to the total time calculated:
  - They already have 1 hour and 30 minutes, and we add another 15 minutes to this.
  - So, the total time they have before the trip is 1 hour and 45 minutes.

Therefore, Paulo's family has 1 hour and 45 minutes of free time before the trip to Scenic Lake Park starts.

Answer:

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Final answer:

Cami must answer all 12 of the remaining questions correctly to achieve a final score greater than 80% on her exam, having already secured 70% correct from the first 20 questions.

Explanation:

Cami has answered 70% of the first 20 questions correctly, which means she has 14 correct answers. As the final exam has 32 questions in total (20 + 12), to achieve a final score greater than 80%, she needs to get more than 80% of 32 total questions correct, which is more than 25.6 correct answers. Since she cannot get a fraction of a question correct, she needs at least 26 correct answers in total. Given she has already 14 correct, she needs at least 12 more correct answers out of the remaining 12 questions to achieve this score.

Answer:

150.72 cubic centimeter

Step-by-step explanation:

Given:-

Height of cone (h) = 9cm

Diameter of cone(d)=8cm

radius of cone(r)=[tex]\frac{d}{2}[/tex]=[tex]\frac{8}{2} =4cm[/tex]

To calculate= Volume of cone([tex]V_{cone}[/tex])

[tex]Volume\ of\ cone(V_{cone}) =\frac{1}{3} \times \pi \times r^{2} \times h[/tex]

[tex]=\frac{1}{3} \times 3.14\times 4^{2} \times 9[/tex]

Volume of cone([tex]V_{cone}[/tex]) [tex]=150.72\ cubic\ centimeter[/tex]

Therefore paper cone cup can hold 150.72 cubic centimeter of water.

The paper cone cup can indeed hold 150.72 cubic centimeters of water.

The paper cone cup can indeed hold 150.72 cubic centimeters of water. Let's break down the calculation:

1. Given dimensions:

  - Height of the cone (h) = 9 cm

  - Diameter of the cone (d) = 8 cm (which implies a radius (r) of 4 cm)

2. To calculate the volume of the cone, we'll use the formula:

[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \][/tex]

3. Plugging in the values:

[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi \cdot 4^2 \cdot 9 \][/tex]

4. Calculating:

[tex]\[ V_{\text{cone}} = \frac{1}{3} \cdot 3.14 \cdot 16 \cdot 9 = 150.72 \, \text{cubic centimeters} \][/tex]

Therefore, the paper cone cup can indeed hold 150.72 cubic centimeters of water.

Answer:

D

Step-by-step explanation:

1 1/4 + 3/4 + 2/4 + 1/4

1+1+ 3/4

2  3/4

Answer:

The GCF of 7 and 12 is 1.

Answer:

Step-by-step explanation:

GCF of 12 and 7 = 1

If there is no common factor then , GCF will be 1

Answer:

1. First option.

2. First option.

3. First option.

Step-by-step explanation:

1. You need to remember that the Associative Property of Addition states the following:

[tex](a+b)+c=a+(b+c)[/tex]

Notice that you can group the numbers "a", "b" and "c" in any combination.

In this case, given the statement provided in the exercise:

[tex](2 + 3.4) + 6 = 2 + (3.4 + 6)[/tex]

You can identify that it ilustrates the Associative Property of Addition.

2. Remember that:

- Natural numbers are known as "Counting numbers".

- Whole numbers include positive numbers and zero.

 - Integers include the Whole numbers and the negative numbers.

- Rational numbers are those numbers that can be wriitten as a fraction:

[tex]\frac{a}{b}[/tex]

Where "a" is the numerator and "b" is the denominator.

 - Integers are a subset of Rational Numbers.

- Irrational numbers cannot be written as a fraction.

Based on this, you can conclude that [tex]\frac{1}{3}[/tex] is a Rational number.

3. The product is the result of a multiplication.

In this case the word "more than" indicates Addition.

Then, the product of 2 more than "y" and 7 can be expressed as:

[tex]7(y+2)[/tex]

Answer:

On Saturday night it had sold 35 numbers of cups.

Step-by-step explanation:

On the Saturday night the ratio of the number of cones to the number of cups sold is 6 : 5 in Freshly frozen yogurt however on Sunday night the ratio of the number of cones to the number of cups is 4 : 1.

Now, if the Freshly frozen yogurt sold 42 cones on Saturday night then in the ratio of 6 : 5, it sold cups [tex]\frac{5}{6}[/tex] times the number of cones.

Therefore, on Saturday night it had sold [tex]42 \times \frac{5}{6} = 35[/tex] numbers of cups. (Answer)

Answer:

see explanation

Step-by-step explanation:

The equation of proportionality is

y = kx ← k is the constant of proportionality

k = y ÷ x, thus

k = 160 ÷ 25 = 320 ÷ 50 = 480 ÷ 75 = 640 ÷ 100 = 6.4

and

y = 6.4x ← equation of proportionality

Answer:you would times everything on the inside by 5 im pretty sure

Step-by-step explanation: