Answer:
[tex]Area = 6x^3+-5x^{2} +6x+5[/tex]
Step-by-step explanation:
Given that:
Length of a rectangle = [tex]3x^2-4x+5[/tex]
Width of rectangle = [tex]2x + 1[/tex]
To find:
Simple polynomial expression for finding the area of rectangle.
Solution:
First of all, we should know about the formula for finding the area of rectangle. Then we should know how to multiply two polynomials.
Formula for area of a rectangle in terms of its length and width is:
[tex]Area= Length \times Width[/tex]
Putting the given values:
[tex]Area = (3x^2-4x+5)(2x+1)[/tex]
Here, we can use the distributive property of multiplication for finding the value of the above multiplication expression.
[tex](A+B)\times (C+D) = A\times C + A\times D+ B\times C + B \times D[/tex]
Therefore, the multiplication of above polynomials can be written as:
[tex]Area = (3x^2-4x+5)(2x+1)\\\Rightarrow Area = 3x^2(2x+1)-4x(2x+1)+5(2x+1)\\\Rightarrow Area = 6x^3+3x^{2} -8x^{2} -4x+10x+5\\\Rightarrow Area = 6x^3+-5x^{2} +6x+5[/tex]
Therefore, the answer is:
[tex]Area = 6x^3+-5x^{2} +6x+5[/tex]
What do you need to do to a variable with a coefficient?
For example: 4n=20.
add
subtract
divide
multiply
Answer:
wouldnt it be 5
Step-by-step explanation:
How many solutions does the quadratic system shown below have ?
Juan wants to solve the equation below using the Distributive Property.
4(6 – x) = 12
What should Juan’s first step be?
A. Multiply 4 by x.
B. Subtract x from 6.
C. Distribute 4 to (6 – x).
D. Subtract 4 from both sides.
Answer:
C. Distribute 4 to (6 - x).
Step-by-step explanation:
Person above is right.
Juan’s first step should be C. Distribute 4 to (6 – x).
What is distributive property of multiplication over addition?Suppose a, b and c are three numbers. Then we have:
a(b + c) = a b + a c
(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)
We are given an equation as;
4(6 – x) = 12
Here Juan wants to solve the equation, using the Distributive Property.
thus, 4(6 – x) = 12
First step is to distribute 4.
4(6) – 4(x) = 12
Then solve;
24 - 4x = 12
x = 3
Hence, Juan’s first step should be C. Distribute 4 to (6 – x).
Learn more about distributive property here;
https://brainly.com/question/5637942
#SPJ2
Combine Like Terms
22+15x=34-17x
Step-by-step explanation:
22+15x=34-17x
So now, the 34 will join the 22 and the 15x will join the -17x
22-34=-17x-15x
-12=-2x
So now, we divide both sides by -2x
and the negative will cancel negative so
x=6
find the compound ratio of 6:5cm and 2:5
Answer:
12:25
Step-by-step explanation:
6/5×2/5
=12/25
12:25
Find the value of n.
Answer:
20cm
Step-by-step explanation:
Answer:
n = 15
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = n + 1 and h = n + 1 - 5 = n - 4 , then
[tex]\frac{1}{2}[/tex](n + 1)(n - 4) = 88 ( multiply both sides by 2 to clear the fraction )
(n + 1)(n - 4) = 176 ← expand the left side using FOIL
n² - 3n - 4 = 176 ( subtract 176 from both sides )
n² - 3n - 180 = 0 ← in standard form
(n - 15)(n + 12) = 0 ← in factored form
Equate each factor to zero and solve for n
n - 15 = 0 ⇒ n = 15
n + 12 = 0 ⇒ n = - 12
However, n > 0 , thus value of n = 15
The price of a necklace was increased by 10% to £154.
What was the price before the increase?
Answer:
answer in attached picture
Answer:
£169.4
Step-by-step explanation:
£154.00 + 10% = 169.4
Brainliest Please??!!??
- ElizabethKate
(5,6) and (−5,12) what is the rate of change??
Answer:
- 0.6
Step-by-step explanation:
Start point: (5,6)
End point: (-5,12)
rate of change = (12-6) / (-5-5) = 6/-10 = - 3/5 = - 0.6
Answer:
The rate of change is -0.6
Step-by-step explanation:
Given
[tex](x_1,y_1) = (5,6)[/tex]
[tex](x_2,y_2) = (-5,12)[/tex]
Required
Determine the rate of change
The rate of change means the slope (m) and it is calculated as thus:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{12-6}{-5-5}[/tex]
[tex]m = \frac{6}{-10}[/tex]
[tex]m = -\frac{6}{10}[/tex]
Simplify the fraction
[tex]m = -\frac{3}{5}[/tex]
[tex]m=-0.6[/tex]
The rate of change is -0.6
PLZ HELP i will brainliest if u answer the 3 question correct
Step-by-step explanation:
1. The formula is 18x3 since there is 3 equal area sides. The volume is 54 (probably)
2. The formula for the pyramid is 3x3x2/3. Which the volume is 6.
3. Same thing the volume is 60 and what i did to get that is 20x3
Hope this helps!
Answer:
Given : A=(1,2)≡(x
1 ,y
1
) and B=(3,−2)≡(x
2
,y
2
)
Let M=(x,y) be the midpoint of AB
x=(
2
x
1
+x
2
) and y=(
2
y
1
+y
2
)
Then, x=
2
1+3
and y=
2
2−2
⟹x=2 and y=0
∴M=(2,0)
∴ Coordinates of the midpoint of AB is (2,0)
Step-by-step explanation:
use the distributive property to rewrite 4(x+9)
Answer:
4x+36
Step-by-step explanation:
4*x+4*9
4x+36
Yo can somebody help me ?
Answer:
x=60
Step-by-step explanation
all the sides are equal and they all add up to 180.
so 180 divided by 3= 60
thus your answer is 60
Kelsey can buy 2 pounds of apples for 7 dollars
Answer:
each pound cost 3.5 dollars
Step-by-step explanation:
7/2
Answer: each pound is 3.50 dollars
Step-by-step explanation: 7.00 divided by 2 is 3.50 dollars
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Micah rows his boat on a river 4.48 miles downstream, with the current, in 0.32 hours. He rows back upstream the same distance, against the current, in 0.56 hours. Assuming his rowing speed and the speed of the current are constant, what is the speed of the current?
3 miles per hour
8 miles per hour
11 miles per hour
14 miles per hour
Answer:
its 3 miles per hour which is A
Step-by-step explanation:
i got it right on the test
"What is the Part to Total Ratio for purple Globbles to total Globbles? There are 5 purple Globbles and 15 Globbles in all. Remember to reduce!"
Answer:
1÷3Step-by-step explanation:
5 purple Globbles and 15 Globbles in total.
Part to Total Ratio for purple:
5÷15 = 1÷3Solve the simultaneous equations:
4x+3y=44
3x+3y=39
x=
and y=
Answer:
X = 5 and Y = 8
Step-by-step explanation:
4x + 3y = 44
3x + 3y = 39
- - -
__________
x = 44 - 39
x = 5........eq 1
Now putting the values in any equation
4 ( 5 ) + 3 y = 44
20 + 3 y = 44
[tex]4(5) + 3y = 44[/tex]
[tex]20 + 3y = 44[/tex]
[tex]3y = 44 - 20[/tex]
[tex]3y = 24[/tex]
[tex]y = \frac{24}{3} [/tex]
[tex]y = 8[/tex]
What is the solution of the equation (4x + 3)2 = 18?
O x = 3 and x = -3
O x = -3 and x = 3
=
2
O x= -3+372 apd x = -3-3,2
4
4
x= 3+372 and x = -3 +372
4
Answer:
Step-by-step explanation:
2(4x+3)=18
8x+6=18
-6 -6
8x = 18
÷8 ÷8
x = 2.25
ive tried multiple ways and they are all different to the provided answers
Work out the answers to:
a) 7 x(-4)
b) (-6) x 8
c) (-5) × (-9)
Answer:
A=-28 B=-48 C=45
Step-by-step explanation:
-(7x4)= -28 so your first step is multiply the positive and the negative equals a negative (+)x(-)=(-) second is to multiply the numbers
-(6)x8= -28 same steps for the first
(-5)x(9) convert it to 5x9=45
Evaluate the expression when m=−6.
m−(−8)=
How would you solve equations with 3 sides or whatever this is
Answer: B. -4 < y < -1
Step-by-step explanation:
1. Subtract 2 from all three sides to isolate the variable in the center of the inequality
5 < 2 - 3y < 14
3 < -3y < 12
2. Divide each of the three sides by -3 to get y by itself, as each of the answers have y as independent.
3 < -3y < 12
-1, y, -4
3. Rearrange
-4 < y < -1 (b)
Simply the expression (5x+9y) - (11x-3y+7)
Answer:
-6+12y-7
Step-by-step explanation:
Who doesn't like short answers, instead of writing a hole paragraph.
Answer:
[tex]-6x + 12y - 7[/tex]
Step-by-step explanation:
[tex](5x + 9y) - (11x - 3y + 7)[/tex]
Lets open the brackets.
[tex]=> 5x + 9y - 11x + 3y - 7[/tex]
Now lets add/substract the like terms only.
[tex]=> 5x - 11x + 9y + 3y - 7[/tex]
[tex]=> -6x + 12y - 7[/tex]
15/40 = x/13,095
solve for x then round to the nearest amount of whole hours.
PLEASE ANSWER ASAP!
Answer:
Step-by-step explanation:
You can cross multiply (15 x 13095) = 40x
196425 = 40x
divide by 40
x = 4,910.625
x = 4,911
Explain please I’ll give brainliest to the best response!!:)
Answer:
Because 4/1 is 4 and 12/3 is 4
Step-by-step explanation:
Answer:
4:1 is equal to 12:3
Step-by-step explanation:
if you divide 12:3 both numbers by 3 it equals 4:1
just picture the smaller squares for the 12:3 with three lines in them
sorry im not that good at exlaining stuff
help almost done....
*will give brainist*
just make sure the answer is correct!!
Sandy has 27 roses, 9 daisies, and 18 tulips. She wants to arrange all the flowers in bouquets. Each bouquet has the same number of flowers and the same type of flower. What is the greatest number of flowers that could be in a bouquet?
Answer:
The greatest number of flowers that could be in a bouquet is 9 flowers
Step-by-step explanation:
We solve the above question using Greatest Common Factor method. We find the factors of 27, 9 and 18. The greatest factor common to the 3 number is our answer.
The factors of 9 are: 1, 3, 9
The factors of 18 are: 1, 2, 3, 6, 9, 18
The factors of 27 are: 1, 3, 9, 27
Then the greatest common factor is 9.
The greatest number of flowers that could be in a bouquet is 9 flowers
What value of x makes the equation true?
3(4x-5)-4x+1=-6
Please show work
Answer:
x = 1
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
3(4x - 5) - 4x + 1 = -6
Step 2: Solve for x
Distribute 3: 12x - 15 - 4x + 1 = -6Combine like terms: 8x - 14 = -6Isolate x term: 8x = 8Isolate x: x = 1Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 3(4(1) - 5) - 4(1) + 1 = -6Multiply: 3(4 - 5) - 4 + 1 = -6Subtract: 3(-1) - 4 + 1 = -6Multiply: -3 - 4 + 1 = -6Subtract: -7 + 1 = -6Add: -6 = -6Here we see that -6 does indeed equal -6.
∴ x = 1 is the solution to the equation.
Why is the percent increase from 45 to 75 not equal to the percent decrease from 75 to 45? Select three options.
UThe amount of change drent for the percent increase and the percent decrease
UThe ratio of the percent increase is not the same as the percent decrease.
OThe ratio for the percent increase has a smaller denominator than the percent decrease.
U The ratio for the percent increase has a different numerator than the percent decrease.
O The original amount for the percent increase is different from the original amount for the percent decrease.
Answer:
work out the difference (increase) between the two numbers you are comparing. Then: divide the increase by the original number and multiply the answer by 100. % increase = Increase ÷ Original Number × 100. If your answer is a negative number, then this is a percentage decrease.
Step-by-step explanation:
Find the sum of the first 40 terms of a geometric sequence where the first term is 16 and the common ratio is 1.1. 704 7,081.48089 7,805.62898 6,423.16445
Step-by-step explanation:
The nth term of a geometric progression can be determined by using the formula:
Tn=arn−1
where: a = first term and r = common ratio
Substitute the given values of first term and common ratio into the formula:
Tn=arn−1
T5=(40)(0.5)5−1
T5=(40)(0.5)4
T5=(40)(0.0625)
T5=2.5
Find the total surface area of this prism where
the cross-section is an isosceles triangle.
13 cm
5 cm
10 cm
24 cm
Answer:
The total surface area of the prism is 620 cm²
Step-by-step explanation:
The total area of the prism = lateral area + 2 (area of the cross-section)
The lateral area = perimeter of the cross-section × height
∵ The cross-section of the prism is an isosceles triangle
∵ The sides of the triangle are 13 cm, 13 cm, 24 cm
∵ The perimeter of the triangle is the sum of its sides
∴ The perimeter = 13 + 13 + 24 = 50 cm
∴ The perimeter of the cross-section = 50 cm
∵ The height of the prism is 10 cm
→ Use the rule of the lateral area above to find it
∴ The lateral area of the prism = 50 × 10 = 500 cm²
∵ The area of the triangle = [tex]\frac{1}{2}[/tex] × base × height
∵ The base of the triangle = 24 cm
∵ The height of the triangle = 5 cm
∴ The area of the triangle = [tex]\frac{1}{2}[/tex] × 24 × 5 = 60 cm²
∴ The area of the cross-section = 60 cm²
→ Substitute the lateral area and the area of the cross-section in the rule
of the total surface area above
∵ The surface area = 500 + 2(60)
∴ The surface area = 500 + 120
∴ The surface area = 620 cm²
∴ The total surface area of the prism is 620 cm²