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If Lillian has a rectangular garden with an area of 10x² +33x – 7 square feet.The expressions that would represent the length and width of the garden will be (5x-1)(2x+7)

It is defined as the combination of constants and variables with mathematical operators.

It is given that, Lillian has a rectangular garden with an area of 10x² +33x – 7 square feet.

We have to find the expression representing the length and width of the garden.

[tex]=10x^2+33x-7 \\\\ =\left(10x^2-2x\right)+\left(35x-7\right) \\\\ =2x\left(5x-1\right)+7\left(5x-1\right)\\\\ =\left(5x-1\right)\left(2x+7\right)[/tex]

The area of the rectangular garden is,

A = L × B

Comparing the expression with the obtained expression we get the expressions that would represent the length and width of the garden as,

A= (5x-1)(2x+7)

Thus, if Lillian has a rectangular garden with an area of 10x² +33x – 7 square feet. The expressions that would represent the length and width of the garden will be (5x-1)(2x+7)

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Step-by-step explanation:

4x is the equivalent expression if thats an option

An equation in slope-intercept form of the line that is parallel to the one given and passes through the given point is  y=7x+5.

x - axis interception points of [tex]$7 x+5: \quad\left(-\frac{5}{7}, 0\right)$[/tex]

y - axis interception point of [tex]$7 x+5: \quad(0,5)$[/tex]

X-Intercepts: [tex]$\left(-\frac{5}{7}, 0\right)$[/tex], Y Intercepts: (0,5)

Slope of [tex]$7 x+5: \quad m=7$[/tex]

Steps

7x+5

What is line equation?

For a line equation for the form of y=m x+b, the slope is m. m=7

The first step to answering this question is to find the slope of the first line. To do that, we need to put it in slope-intercept form.

y=7x+5  => y=7x+5

So the slope of this line is 7. Perpendicular lines have a negative reciprocal slope, so the slope of the perpendicular line is 7. Using that and the point (1,3) we can make an equation for the line in point-slope form:  We can then convert this into slope intercept form.

=> y=7x+5

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The perimeter of the triangle is 24 units.

What is a triangle?

Triangle is bounded area by three sides. If length of all sides is not equal, then the triangle is known as an obtuse triangle.

The vertices of the triangle are A(-4,4), B(4,4), and C(4,-2)

The formula distance between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²]

The length of line segment AB is √[(4 - (-4))² + (4 - 4)²] = √8² = 8 units

The length of line segment BC is √[(4 - 4)² + (-2 - 4)²] = √6² = 6 units

The length of line segment AC is √[(4 - (-4))² + (-2 - 4)²] = √[8² + 6²] = √100  = 10 units.

The perimeter of a triangle is sum of all sides of the triangle.

The perimeter of the triangle is

AB + BC + AC

= 8 + 6 + 10

= 24 units

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Answer:

25

solution

50=3x

or, 50/3=x

or, x=16.66

hence,imran father will 16 years

The explicit formula for the given arithmetic sequence is aₙ = 23 + (n - 1)11. Here the first term is a1 = 23 and the common difference is d = 11.

The explicit formula for an arithmetic sequence gives the nth term of the sequence. I.e.,

aₙ = a1 + (n - 1)d

Here a1 is the first term; d is a common difference, it is calculated by

d = aₙ₊₁ - aₙ = aₙ₋₁ - aₙ

The given sequence is 23, 34, 45, 56,...

Here the first term a1 = 23

So, the common difference between the terms in the sequence is

d = 34 - 23 = 11

Then, the explicit formula for the given sequence is

aₙ = a1 + (n - 1)d

⇒ aₙ = 23 + (n - 1)11

Therefore, the nth term of the explicit formula for the given arithmetic sequence is aₙ = 23 + (n - 1)11.

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Answer:

yes seems like you understand

Answer:

yes

Step-by-step explanation:

yes

The cost of 4.25 grams of potatoes is £0.00238

From the question, we have the following parameters that can be used in our computation:

2.5kg of potatoes cost £1.40

This means that the unit rate can be calculated as

Unit rate = Cost/Amount

So, we have the following representation

Unit rate = 1.40/2.5

The cost of 4.25 grams is calculated as

Cost = Unit rate * Amount

So, we have the following representation

Cost = 4.25 * 1.40/2.5

Convert to grams

Cost = 4.25 * 1.40/2500

Evaluate

Cost = 0.00238

Hence, the cost is 0.00238

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Probability that exactly 2 will end up being replaced under warranty is 0.14781.

The problem states that 20% are likely to need warranty service, and of the 20% that need repair, 40% are likely to need to be replaced. This implies that 8% of the total are likely to need warranty service and be replaced (.20)(.40)=0.08

Therefore, p=0.08

n=10

and x=2 then we have to put the values in the formula,

We now plug all of this into formula , then we get

b(x;n,p) = [tex]\left \{ {{n} \atop {x}} \right. }px(1-p) to the power n-x\\[/tex]

and we get ,

So,

b(2;10,0.08) = (10 2)(0.08)²(1-0.08) to the power 10-2

=45(0.0064)(0.92)to the power 8≈0.14781

So, the probability is 0.14781

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Answer:

option a is correct i.e 6.25 = 25/4

Step-by-step explanation:

= 6.25

= 625 / 100

both being divisible by 5

we get

= 25/4

If the initial population of a town is 100,231 and it grows with a doubling time of 98 years, the population after 31 years is  124803

The initial population of the town = 100231 people

The doubling time = 98 years

We have to find the population in 31 year

The exponential function will be

f(t) = fo(2)^(t/98)

f(t) is the population of the town in t years

fo is the population of the town in t = 0 years

t is the number of years

2 because it doubling time

The value of t = 31 years

Substitute the values in the function

f(31) = 100231×(2)^(31/98)

Do the arithmetic operations

f(31) = 100231 × 1.245

f(31) = 124803.23

f(31) ≈ 124803

Therefore, the population after 31 years is 124803

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Answer:

(x - 3) (x - 9)

Step-by-step explanation:

x² - 12x + 27

x² - 3x - 9x + 27

x(x - 3) - 9(x - 3)

(x - 3) (x - 9)

Thus, The answer is (x - 3) (x - 9)

Step-by-step explanation:

The sum of two consecutive integers if n is the first integer.

consecutive means immediately after, so we have:

n

n + 1

The sum is written as:

n + n + 1

Grouping like terms, we have:

(n + n) + 1

2n + 1

Answer:

38

Step-by-step explanation:

76% of 50 is 38

Answer: 38 games

Step-by-step explanation: The answer is actually pretty simple to get to. You just need to find 76% of 50. Let x be the amount of games they have won this year. The equation is: x= 0.76*50. Why it is 0.76 instead of 76 is because percent is always out of 100 that is why the max is 100%. So 0.76 is the same as 76/100 which is also 76%. Back to the equation: x = 0.76*50. If you solve the equation which is just 0.76*50, you would get 38. 38 is how many games they won in the season.

When we apply coupon before promotional discount, we have to pay $396.

When we apply promotional discount first and then coupon, we have to pay $392

Given,

The coupon amount = $40

Promotional discount = 10%

The rent per hour = $100 + 20% gratuity

The rent for 4 hours including gratuity = (100 × 4) + (100 × 4 + 10/100) = $480

We have to find the amount for the situations given below;

a) The coupon is applied before the promotional discount;

Here,

Coupon deduction;

480 - 40 = $440

Promotional discount deduction;

10% of 440 = 44

Then,

440 - 44 = $396

We have to pay $396.

b) The promotional discount is applied before coupon;

Here,

Promotional discount deduction;

10% of 480 = 48

Then,

480 - 48 = $432

Coupon deduction;

432 - 40 = $392

We have to pay $392.

Therefore,

When we apply coupon first and then promotional discount, we have to pay $396

When we apply promotional  discount before coupon, we have to pay $392.

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Answer: significant

Step-by-step explanation:

Max profit would be 54 type 1 and 88 type 2

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

given:

Let x be the amt of type 1 and y be the amt of type 2.

Then, Storage constraints

x ≤ 100

y ≤ 150

and, Mixing constraint:

62x + 44y ≤ 7220

44y = 7220-62x

y = 164 - 1.4x

and, Packaging constraint:

78x + 46y ≤ 8260

46y = 8260 - 78x

y = 180 - 1.7 x

Then, The objective functions for each corner of the region

solve:

62x + 44y = 7220

78x + 46y = 8260

So, x=54,y=88

Hence, Max profit would be 54 type 1 and 88 type 2

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The vertex and the range of y = |x - 5| + 4 are (b) (5, 4); 4 ≤ y < ∞

The equation is given as

y = |x - 5| + 4

The above equation is an absolute value function

An absolute value function represented as

y = a|x - h| + k

Where

Vertex = (h, k)

This means that the vertex is

Vertex = (5, 4)

Remove the x value

y = 4

Because the leading coefficient is positive, then the vertex is a minimum

i.e.

y ≥ 4

So, the range is 4 ≤ y < ∞

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Answer: I think C

Step-by-step explanation:

The algebraic expression for the increase in this month's finance charge due to higher APR is  0.001x  .

In the question ,

it is given that ,

Kristin's credit rating was lowered ,

and the credit card company raised the APR from 14% to 15.2% ,

the average daily balance in this month is = $x .

the finance charge for 14% APR is = x*(14%/12)

= 0.01167x

the finance charge for 15.2% APR is = x*(15.2%/12)

= 0.01267x

So , the increase in finance charge is = 0.01267x - 0.01167x  

= 0.001x

Therefore , the algebraic expression is 0.001x  .

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Answer:

D

Step-by-step explanation:

the numerator of the exponent is the exponent of x

the denominator is the the index of the root

If the store buys 200 shirts for $2400 and sells for $20 each then the percent markup is = 66.67%   .

In the question ,

it is given that ,

the number of shirts that departmental store buys is = 200 shirts .

the cost price for 200 shirts is = 2400

So , the cost for 1 shirts is = 2400/200 = $12 ,

the selling price for 1 shirt is = $20 ,

the percent markup can be calculated using the formula ,

percent markup  = (selling price - cost price)/(cost price)  × 100 ,

= (20 - 12)/12 × 100

= 8/12 × 100

= 800/12

= 66.66666

≈ 66.67 % .

Therefore , percent markup is 66.67% .

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The required total cost of packaging each comforter is $89.20.

Activity estimated indirect activity costs allocation base estimated quantity of allocation base,

materials handling $ 12,600 number of parts 4,200 parts

Cost per part = $ 12,600/4,200 =  $3

assembly$ 55,440 number of parts 4,200 parts,

Cost per part = $ 55,440/4,200 =  $13.20

packaging $10,920 number of comforters 1,050 comforters each comforter consists of 4 parts

Cost per part =$10,920 /1,050 = $10.40

Then, For all cost of 4 parts,

Materials handling = ($3 x 4) = $12

Assembly = ($13.20 x 4) = $52.80

Packaging = ($10.40 x 1) = $10.40

Total overhead cost = $75.20

And Direct materials cost = $14.00

So, total manufacturing cost =  $75.20 + $14.00 =  $89.20

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Answer:

4 more years

Step-by-step explanation:

you were born in 2008, you should be 14 now or soon, by the end of the year. So 4 in 4 years you would be 18.

Answer: Simple, you are 14 right? So 4 more years

Step-by-step explanation:

Add 14+4 and you'll get 18.

The number of boys were  1750 boys  and the number of girls were 700 girls  .

In the question ,

it is given that ,

the ratio of the number of girls to the number of boys is 2 : 5.

So , the number of boys is = 5x

and the number of girls is = 2x ,

also given that , the total number of students is = 2450

So , According to the question ,

5x + 2x = 2450

7x = 2450

Dividing both sides by 7 ,

we get ,

x = 2450/7

x = 350 ,

Hence , the number of girls = 2(350) = 700

and the number of boys is = 5(350) = 1750 .

Therefore , there are 700 girls and 1750 boys .

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Step-by-step explanation:

you do understand that the diameter of a circle is simply 2 times the radius, yes ?

imagine a circle and you draw a radius line (from the center of the circle to the circle arc).

and now imagine to draw another radius line, just in the opposite direction.

when you look at the result, you have 1 straight line going from the circle arc to the circle arc and passing through the center of the circle. that is what a diameter is.

how long is it ? well, we drew 2 radius lines to create this line. so, it is 2×radius long.

so, the diameter of the seal is

2×2 = 4 yards

At 6 gallons per minute, the hose moves water.

Our tutors' response was given

X gallons per minute is what we'll suppose the hose can provide.

288 : 48 = x : 1

x = 288/48

x = 6 gal/min.

At 6 gallons per minute, the hose moves water.

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∠c = 100° (Since ∠c and ∠100° are opposite angles)

∠c - ∠b = 70° (∠b =30° since ∠b and ∠30° make 60°)

∠a = 30° (Since ∠a and ∠30° vertically opposite angles)

What are opposite angles?

Angles, where two lines cross that are directly opposite one another, are known as opposite angles. The vertex, where the lines come together to produce the angle, is the location of the junction. Vertical angles are another name for opposite angles. Congruent angles are those that have opposite angles that are equal or have the same measurement. For instance, A and C are referred to be opposite angles in the parallelogram ABCD. B and D are the opposing angles in a similar way.

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Answer: taxes

Step-by-step explanation:

Answer:

51/3

Step-by-step explanation:

Angles opposite congruent sides of a triangle are congruent.

[tex]x+17=4x-34 \\ \\ 17=3x-34 \\ \\ 51=3x \\ \\ x=51/3[/tex]

Answer:

a.6x+3=27

b.x=4

c. Morgan has 6 packs of erasers, each pack has 4 erasers, and after Avery gives her three more erasers, she has a total of 27.

Step-by-step explanation:

a.6x+3=27

6x=24

b.x=4

c. Morgan has 6 packs of erasers, each pack has 4 erasers, and after Avery gives her three more erasers, she has a total of 27.