Expand the expression 3(n + 7)

Hello,

We have : (a + b)² = a² + 2ab + b²

4x² + 20x + 25 = (2x)² + 2 × 2x × 5 + 5² = (2x + 5)² → answer B

Here, we have a = 2x and b = 5 !

Answer:

[tex]\textsf{b.} \quad (2x+5)^2[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]4x^2+20x+25[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].

[tex]\implies ac=4 \times 25=100[/tex]

[tex]\implies b=20[/tex]

Factors of 100 that sum to 20:   10 and 10

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies 4x^2+10x+10x+25[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 2x(2x+5)+5(2x+5)[/tex]

Factor out the common term (2x + 5):

[tex]\implies (2x+5)(2x+5)[/tex]

Simplify:

[tex]\implies (2x+5)^2[/tex]

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Answer: 60

Step-by-step explanation: 12L+1/2=72.5

72.5-24-8.5+20

72.5-24=48.5-8.5=40

40+20=60

To start solving the exercise, we obtain as data:

We apply as a formula:

We apply the formula and solve:

Therefore, the area of the circle is 27 ft².

Answer: 27ft²

Step-by-step explanation: Soln:

Given that,

π=3

Radius(r)=3ft.

We have,

A = π r²

A = 3* (3)²

A=3*9

A=27ft²

Answer:

17x-70/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is

$194 (start) / 100 (100%) = $1.94 (1%)

$1.94 * 7 = $13.58 (7%)

$13.58 * 13 (13 years) = $176.54

$194 (start) + $176.54 (interest) = $370.54

the interest on $194 at 7% interest rate for 13 years is approximately $176.54.

To find the interest on $194 at an annual interest rate of 7% for 13 years, we can use the formula for simple interest:

Interest = Principal * Rate * Time

Where:

Principal = $194 (initial amount)

Rate = 7% (convert to decimal: 7% = 0.07)

Time = 13 years

Now, plug in the values:

Interest = $194 * 0.07 * 13

Calculate the interest:

Interest = $194 * 0.91

Interest ≈ $176.54

So, the interest on $194 at 7% interest rate for 13 years is approximately $176.54.

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The domain of the notation [tex]s(x) = \sum\limits^{\infty}_{n=1} n^{-x}[/tex] is the set of all real values

The sum notation is given as:

[tex]s(x) = \sum\limits^{\infty}_{n=1} n^{-x}[/tex]

From the above notation, the smallest value of n is 1.

This means that the variable x can take any real value as it value

Hence, the domain of the notation [tex]s(x) = \sum\limits^{\infty}_{n=1} n^{-x}[/tex] is the set of all real values

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Answer:

The answer to your question is 3.5 m

Step-by-step explanation:

1 m= 100 cms

so 350 cms  = 3.5 m

I hope this helps and have a good day!

Answer:

[tex]\textsf{b.} \quad 3x+5y=2[/tex]

Step-by-step explanation:

Define the given points:

[tex]\textsf{let}\:(x_1,y_1)=(4,-2)[/tex]

[tex]\textsf{let}\:(x_2,y_2)=(-1,1)[/tex]

Use the slope formula to determine the slope of the line:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-(-2)}{-1-4}=\dfrac{1+2}{-1-4}=-\dfrac{3}{5}[/tex]

Use the point-slope formula to determine the equation of the line.

[tex]\implies y-y_1=m(x-x_1)[/tex]

Substitute the found slope and point (4, -2):

[tex]\implies y-(-2)=-\dfrac{3}{5}(x-4)[/tex]

[tex]\implies y+2=-\dfrac{3}{5}(x-4)[/tex]

Multiply both sides by 5:

[tex]\implies 5(y+2)=-3(x-4)[/tex]

Expand the brackets:

[tex]\implies 5y+10=-3x+12[/tex]

Add 3x to both sides:

[tex]\implies 5y+10+3x=-3x+12+3x[/tex]

[tex]\implies 3x+5y+10=12[/tex]

Subtract 10 from both sides:

[tex]\implies 3x+5y+10-10=12-10[/tex]

[tex]\implies 3x+5y=2[/tex]

Answer:

[tex]\sqrt{10}[/tex]

Step-by-step explanation:

5 - 2x^2 = -15

2x^2 = 20

x^2=10

x= [tex]\sqrt{10}[/tex]

Answer

20 is 5%

1 fifth of hunderd that is 20%

=20%

Answer:

Step-by-step explanation:

PQS and RQS are supplementary

PQS +68=180

PQS =112

x+ 112+TSQ=180

4x=3x+TSQ

TSQ=x which means

2x+112=180

2x=68

x=34

The congruent triangles are solved and the measure of HI ≅ FG and the measure of DH ≅ BF

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle being constructed be ΔCBA

Let the second triangle being constructed be ΔDEL

Now , the measures of the corresponding sides of the congruent triangles will be in the same ratio

So , measure of HI ≅ measure of FG

And , the measure of DH ≅ the measure of BF

Hence , the ∠D is congruent to ∠B

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Answer:

b.  x + (x + 2) + (x + 4) = 39

Step-by-step explanation:

Definitions

The sum of three consecutive odd integers

Let x be the first odd integer.

As there is a difference of 2 between consecutive odd integers, the next odd integer after x will be (x + 2).

Therefore, the next odd integer after (x + 2) will be (x + 2) + 2 = (x + 4).

So "the sum of three consecutive odd integers is thirty-nine" is:

x + (x + 2) + (x + 4) = 39

To solve

⇒ x + (x + 2) + (x + 4) = 39

⇒ x + x + 2 + x + 4 = 39

⇒ 3x + 6 = 39

⇒ 3x = 33

⇒ x = 11

Therefore, the three consecutive odd numbers are 11, 13 and 15.

Answer:

ospe4mhe is taht he iaoe

Answer:

Synecdoche means in which a part of something is substituted for the whole (as hired hand for "worker")

Answer:

A) The median is one of the values listed in the table

Step-by-step explanation:

The median is the middle number in an ordered data set. Since the number of date in the table is a even number, both 75 and 76 is the middle number.  To find the median of an set of data that has an even number of sets, you just add the 2 middle numbers together and divide by 2. So like:

75+76=151

151/2=75.5

75.5 is the median but its not listed in the table, so A.

Answer:

(14/3, 7/3)

Step-by-step explanation:

8-3=5, and 5/3+3=14/3.

5--3=8, and 8/3+5=7/3.

This has a ratio of 1:2 because the length is divided into three and 1 is separate from the other two.

Answer:

Step-by-step explanation

Lines LP and QM are parallel, meaning KLP and QMN are supplementary

So KLP +QMN=180

3x+72=180

3x=108

x=36

Answer:B

Step-by-step explanation:

Answer:

A = pi(r)^2

A = pi(40)^2

A = 1,600pi sq. ft.

Therfore the answer is C.) 1,600 pi sq. ft.

I hope this helps you!!

Answer:

C - 1600[tex]\pi[/tex] sq. ft.

Step-by-step explanation:

Since the answer has to be in terms of pi, we can exclude that from the equation.

The formula to find the area of a circle is [tex]\pi r^2[/tex] where r is the radius. If we plug in 40 for r, we get 1600[tex]\pi[/tex].

Mr. Rodriguez's bill after receiving a discount of 12 1/2% on each item is $140.30.

To calculate Mr. Rodriguez's bill after receiving a discount of 12 1/2% on each item, we need to find the discounted price for each item and then add them together to get the total bill.

First, let's calculate the discount for each item:

Jacket: 12.5% of $69.50

Discount on jacket = 12.5/100 * $69.50 = $8.69

Tie: 12.5% of $15.50

Discount on tie = 12.5/100 * $15.50 = $1.94

Raincoat: 12.5% of $75.35

Discount on raincoat = 12.5/100 * $75.35 = $9.42

Now, subtract the discounts from the original prices to get the discounted prices for each item:

Jacket price after discount = $69.50 - $8.69 = $60.81

Tie price after discount = $15.50 - $1.94 = $13.56

Raincoat price after discount = $75.35 - $9.42 = $65.93

Finally, add the discounted prices of all items to find the total bill:

Total bill = $60.81 + $13.56 + $65.93 = $140.30

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Answer: 62.8in

Step-by-step explanation:

The formula for circumference is C=2πr. Put the values of 10 in for r and 3.14 in for pi, and you get an equation that looks like C=2(3.14)(10). Solving this equation gets you 62.8.

Answer:

62.8

Step-by-step explanation:

Circumference=2rpi

c=2*10*pi

c=20*pi

c=20*3.14

c=62.8

Each girl washes 3 shirts. The 18 shirts are divided equally among the 6 girls

After putting 14 shirts in the washing machine, there are 32 - 14 = 18 shirts left to wash. These 18 shirts are shared equally among 6 girls. To find out how many shirts each girl washes, we divide the total number of shirts (18) by the number of girls (6):

Number of shirts washed by each girl = Total shirts / Number of girls

Number of shirts washed by each girl = 18 / 6

Number of shirts washed by each girl = 3

Each girl washes 3 shirts. The 18 shirts are divided equally among the 6 girls, so each girl washes the same number of shirts.

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Answer:

$120

Step-by-step explanation:

48 pineapples shared equally by 2 people.

48/2 = 24

Each friend got 24 pineapples.

24 × $5 = $120

Answer: $120

Answer: $120

Step-by-step explanation:

Step 1: Find how many 1 person gets (pineapples per person)

48 pineapples divided by 2 people= 48÷2= 24 pineapples each.

Step 2: Money made by 1 person

He has 24 pineapples to sell because that's how many he is supposed to receive. he sells all of them for $5 each, so the total money he makes is 5x24= $120

Checks:

120÷24= 5

the pineapples are 5 dollars each (this is correct).

Hope this helps!