Answer:
Hey there!
4a^2-20a+25 can be factored to (2a-5)(2a-5). Thus, the side length of the square is 2a-5. Basically, we want to find two of the same binomials that can multiply to get 4a^2-20a+25. For example, 2a times 2a = 4a^2, and you can use the foil method to solve for the rest.
4a^2 - 20a +25
(2a)^2 - 20a + (-5)^2
(2a - 5)^2
(9a2 − 16b2) is just a difference of squares, and can be factored to (3a+4b) and (3a-4b). The difference of squares formula can give us this.
Let me know if this helps :)
Answer:
Step-by-step explanation:
Part A
[tex]4a^{2} -20a+25\\\\=(2a)^2-2(5)(2a)+5^2[/tex]
does that seems familiar?
it's because it's a perfect square that can be factorized as
[tex](2a-5)^2[/tex]
so the length of each side is
2a-5 both of them
Part B
[tex]9a^2-16b^2[/tex]
[tex](3a)^2-(4b)^2[/tex]
that's a difference of squares you know [tex]x^2-y^2=(x-y)(x+y)[/tex]
so
[tex](3a-4b)(3a+4b)[/tex]
so the lengths are
3a-4b and 3a+4b
the sides of an angle are
Answer:
the vetrex
Step-by-step explanation:
Consider a group of students playing a game of tug-of-war, in which two teams pull on a rope to find which team is strongest. Each of the statements that follows describes what happens during the tug-of-war. Evaluate each statement and select the statements that are accurate.
HII PLEASE HELP ME IN THIS
Step-by-step explanation:
(i) Sum the forces at point M in the x direction.
∑F = ma
-T sin 30° − T sin 30° + 5 N = 0
2T sin 30° = 5 N
T = 5 N
(ii) Sum the forces on the ring in the x direction.
∑F = ma
T sin 30° − N = 0
N = 2.5 N
Sum the forces on the ring in the y direction.
∑F = ma
T cos 30° − mg − Nμ = 0
Nμ = T cos 30° − mg
2.5 μ = 5 cos 30° − 2
μ = 0.932
(iii) Sum the forces on the ring in the y direction.
∑F = ma
T cos 30° − m₁g − m₂g + Nμ = 0
m₂g = T cos 30° − m₁g + Nμ
m (10) = 5 cos 30° − 2 + (2.5)(0.932)
m = 0.466 kg
m and n are both integers. Select all the statements that are true if m and n are also equal to each other. m - n = n - m OR +m (- n) = m - n
OR 0 = m - n OR m + n = 0
Answer:
The true statements are;
(i) m - n = n - m
(ii) +m (-n) = m - n
(iii) 0 = m - n
Step-by-step explanation:
We are given that m and n are both integers and we have to select all the statements that are true if m and n are also equal to each other.
(i) The given situation is: m - n = n - m
LHS = m - n
= m - m {because m and n are equal}
= 0
RHS = n - m
= n - n {because m and n are equal}
= 0
Hence, the given statement is true because LHS = RHS = 0.
(ii) The given situation is: +m (- n) = m - n
LHS = +m (- n)
= m - n
= m - m {because m and n are equal}
= 0
RHS = m - n
= n - n {because m and n are equal}
= 0
Hence, the given statement is true because LHS = RHS = 0.
(iii) The given situation is: 0 = m - n
LHS = 0
RHS = m - n
= m - m {because m and n are equal}
= 0
Hence, the given statement is true because LHS = RHS = 0.
(iv) The given situation is: m + n = 0
RHS = 0
LHS = m + n
= m + m {because m and n are equal}
= 2m
Hence, the given statement is not true because LHS [tex]\neq[/tex] RHS.
#1) m - n = n - m
#2) +m (-n) = m - n
#3) 0 = m - n
hope this HELPS!!!!!!!
Solve the following equation algebraically
Answer:
the right answer is d
Step-by-step explanation:
please give 5 star i need it
Damien worked at a grocery store earning $9.00 an hour. He worked 30 hours a week and was paid every two weeks. He paid $62 in taxes and had a $50 savings account deduction. How much were Damien's taxes and deductions?
Answer:
Answer: $428.00
Step-by-step explanation: First, we need to calculate the person’s total hours, (30 x 2 = 60 hours) then the money per hour (60 x 9) then take away the taxes and account deductions.
Given the true/false statements are true (facts), select the best logical induction made from thoses statements: Mo likes oranges, jai likes oranges, Ben like oranges.
Answer:
People like oranges
Step-by-step explanation:
Given:
Mo likes oranges. Jai likes oranges. Ben likes oranges.
We have a few different options;
Option A: People don't like other fruit, such as apples. This can't be possible because we have only been given people who like oranges.
Option B: People on like oranges. This can't be possible because only is the case where people do not like any fruit except oranges, and we are not sure of this.
Option C: People like oranges. This can be possible because Mo, Jai, and Ben likes oranges
Option D: People like fruit. This can't be possible because we are not sure if people like all fruits or not
People like oranges.
What is Induction?the action or process of inducting someone to a position or organization.
How to determine?We have a few different options;
Option A: People don't like other fruit, such as apples. This can't be possible because we have only been given to people who like oranges.
Option B: People like oranges. This can't be possible because only is the case where people do not like any fruit except oranges, and we are not sure of this.
Option C: People like oranges. This can be possible because Mo, Jai, and Ben like oranges
Option D: People like fruit. This can't be possible because we are not sure if people like all fruits or not
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b-3+4b=34
Solve equation
Answer:
b = 7.4
Step-by-step explanation:
b - 3 + 4b = 34
combine like terms:
5b - 3 = 34
5b = 37
divide by 5:
b = 7.4
Answer:
b=7.4
Step-by-step explanation:
1. Combine like terms
5b-3=34
5b=37
2. Isolate x value by dividing
b=7.4
The area of rectangular is 46 square inches.if the length is 4 times the width . Then find the dimensions of the rectangular
Answer:
the rectangle's width is approximately 3.39 inches
and the length is approximately 13.56 inches.
Step-by-step explanation:
Recall that the area of a rectangle is Length times Width
If we name the length "L" and the width "W", we have:
L * W = 46
Also: "the length is 4 times the width" can be written in math form as:
L = 4 * W
and now we can replace the length L by 4 * W in the formula for the area:
[tex]L\,*\,W = 46\\(4\,W) \,W = 46\\4\,W^2=46\\W^2=\frac{46}{4} =11.5\\W=\sqrt{11.5} \\W\approx 3.39[/tex]
and now we find the value of L:
[tex]L=4\.(3.39) = 13.56[/tex]
Therefore, the rectangle's width is approximately 3.39 inches
and the length is approximately 13.56 inches.
If the side of an equatorial triangle is L then express the perimeter of the triangle in terms of L.
Answer:
3L
Step-by-step explanation:
Perimeter is the sum of side lengths
Since the triangle is equilateral, it has all sides equal and each has length of L
So perimeter is:
P= L+L+L = 3LThe density of an object has the equation d = m/v. If an object has a mass of 20 g and a volume of 3.5 cm^3, what is its density?
Answer:
[tex]\Large \boxed{\mathrm{5.71 \ g/cm^3 }}[/tex]
Step-by-step explanation:
[tex]\sf \displaystyle density = \frac{mass}{volume}[/tex]
[tex]\displaystyle \rho = \frac{m}{V}[/tex]
[tex]\sf Mass \rightarrow 20 \ g \\ Volume \rightarrow 3.5 \ cm^3[/tex]
[tex]\displaystyle \rho = \frac{20}{3.5}[/tex]
[tex]\rho \approx 5.71[/tex]
Density is defined as the mass per unit volume of an object and It is calculated using the equation: density (d) = mass (m) / volume (v).
In this scenario, the mass of the object is given as 20 grams and the volume is given as 3.5 cm^3. To find the density, we can substitute these values into the equation: density =[tex]20 g / 3.5[/tex] cm^3 To simplify the unit of the measurement, we can convert cm^3 to mL (since 1 cm^3 is equal to 1 mL).
Thus, the equation becomes: density = [tex]20 g / 3.5[/tex] mL Calculating the division: density ≈ 5.71 g/mL Therefore, the density of the object is approximately 5.71 g/mL.
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What is the solution to the equation by -2(y + 1) = 3(y – 2) + 6?
Answer: y= -2.5
Step-by-step explanation:
Distribute the -2 and 3 into the parentheses. -6 + 6 cancels out so you are left with 3y on the right side. Add 2y to the right side leaving you with -2=5y. Divide both sides by -2
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{ y = - 0.4}}}}[/tex]Step-by-step explanation:
[tex] \sf{ - 2(y + 1) = 3(y - 2) + 6}[/tex]
Distribute -2 through the parentheses
Similarly, Distribute 3 through the parentheses
⇒[tex] \sf{ - 2y - 2 = 3y - 6 + 6}[/tex]
Since two opposites add up to zero , remove them
⇒[tex] \sf{ - 2y - 2 = 3y}[/tex]
Move 3y to Left hand side and change it's sign
Similarly, move -1 to right hand side and change it's sign
⇒[tex] \sf{ - 2y - 3y = 2}[/tex]
Collect like term
⇒[tex] \sf{ - 5y = 2}[/tex]
Divide both sides of the equation by -5
⇒[tex] \sf{ \frac{ - 5y}{ -5 } = \frac{2}{ - 5} }[/tex]
Calculate
⇒[tex] \sf{ - 0.4}[/tex]
Hope I helped!
Best regards!
Which equation can pair with X- y=-2 to create a consistent and dependent system?
O 6x + 2y = 15
0 -3x + 3y = 6
O _8x – 3y = 2
O 4x – 4y = 6
Calculate the total installment price the carrying charges in the number of months needed to save them money at the monthly rate to buy the item below for its cash price the computer with the cash price of 750 offered on the installment plan for 39 per month for 24 months
Answer:
the total installment is $936 the carrying charges are $186 the monthly rate to buy the items are 19.23 or 20 monthsStep-by-step explanation:
$39 for 24 months comes to ...
$39 × 24 = $936
The "carrying charges" are the difference between the cash price and the installment price:
$936 -750 = $186
Saving at the rate of $39 per month, it would take ...
$750/$39 = 19.23 months about 20 months to save up the cash price.
Often, such savings would come from a once-a-month paycheck, so it would take more than 19 such paychecks to save the required amount.
hope it will help :)
You need to construct an open-top rectangular box with a square base that must hold a volume of exactly 475 cm3. The material for the base of the box costs 8 cents/cm2 and the material for the sides of the box costs 6 cents/cm2. The dimensions for a box that will minimize the cost of the materials used to construct box are:
Answer:
The dimensions of the box are:
x = 8,93 cm and h = 5,95 cm
C(min) = 850,69 cents
Step-by-step explanation:
The volume of the box is:
V = x²*h where x is the side of the square base and h the height
then h = V/ x² ⇒ h = 475 / x²
The total cost of box C is:
C = C₁ + 4*C₂ Where C₁ and C₂ are the costs of the base and one lateral side respectevily
Then cost C = 8*x² + 4* 6*h*x
The cost C as a function of x is
C(x) = 8*x² + (24* 475 /x² )*x
C(x) = 8*x² + 11400/x
Tacking derivatives on both sides of the equation
C´(x) = 16*x - 11400/x²
C´(x) = 0 ⇒ 16*x - 11400/x² = 0
16*x³ = 11400 ⇒ x³ = 11400/16
x³ = 712,5
x = 8,93 cm
and h = 475 / (8,93)² ⇒ h = 5,95 cm
C(min) = 8*79,77 + 4* ( 8,93)*5,95
C(min) = 638,16 + 212,53
C(min) = 850,69 cents
To check if value x = 8,93 would make C(x) minimum we go to the second derivatives
C´´(x) = 16 + 22800/x³ > 0
Then we have a minimum of C at x = 8,93
A refrigerator is priced at 525.50 there is a 7% sales tax rate
Answer:
562.29
Step-by-step explanation:
you would just multiply 525.50 by 7 which is 3678.5 and divide that by 100 which is 36.785 and add that to 525.50 which is 562.285 which can be rounded to 562.29
20 POINTSSSSSSSSSSS AND BRAINLIESTTTTTTTTTTTTTSSSSSSSSSSSSSS
Answer:
C
Step-by-step explanation:
Since the exponent on the 10 is negative, we need to move the decimal point to the left instead of the right. After moving the decimal point on the 2.5 to the left 4 places, we see that the answer is 0.00025.
cual de estos tipos de mentalidad puede contribuir a superar situaciones de no inclusión porque
La mentalidad de crecimiento, ya que a diferencia de la mentalidad fija, nos permite ver en otras personas la mentalidad de mejorar y perseverar.
The equation $y = -6t^2 + 51t$ describes the height (in feet) of a projectile launched from the surface of Mars at 51 feet per second. In how many seconds will the projectile first reach 108 feet in height?
Answer:
4 OR 4.5 SECONDS
Step-by-step explanation:
Use the given data to find the minimum sample size required to estimate a population proportion or percentage.
Margin of error 0.03: confidence level 95%; and unknown
Answer:
1067
Explanation:
The formula that will be used to calculate the sample size if population proportion isn't given is expressed as;
Sample size n = |Z|² × 0.25/E² where;
Z is the z-score at 95% confidence
E is the margin of error
Given parameters
Z score at 95% confidence interval = 1.96
E = 0.03
Substituting the given values into the formula to get the sample size n we will have;
n = 1.96²×0.25/0.03²
n = 3.8416×0.25/0.0009
n = 0.9604/0.0009
n = 1067.11
n ≈ 1067
Hence, the minimum sample size required to estimate a population proportion is approximately 1067
2 What operation should be done first to solve 6x + 5 = 35?
o
Subtract 5
O Add 5
Multiply by 6
O Divide by 6
Answer:
subtract 5
Step-by-step explanation:
subtract 5 from each side of the equal sign..
Answer:
the answer is subtract 5
Step-by-step explanation:
17.
An urn contains eight red, six white, and four green balls. Four balls are drawn at random.
(a) Compute P(all four are red).
(b) Compute P(exactly two are red and exactly two are green).
(c) Compute P(exactly two are red or exactly two are green).
(a) The probability that all four balls are red is
(Type an integer or a decimal. Round to two decimal places as needed.)
(b) The probability that there are exactly two red balls and exactly two green balls is
(Type an integer or a decimal. Round to two decimal places as needed.)
(c) The probability that there are exactly two red balls or exactly two green balls is
(Type an integer or a decimal. Round to two decimal places as needed.)
Complete Question
An urn contains eight red, six white, and four green balls. Four balls are drawn at random.
(a) The probability that all four balls are red is
(Type an integer or a decimal. Round to two decimal places as needed.)
(b) The probability that there are exactly two red balls and exactly two green balls is
(Type an integer or a decimal. Round to two decimal places as needed.)
(c) The probability that there are exactly two red balls or exactly two green balls is
Answer:
(a) The probability that all four balls are red is
0.023
(b) The probability that there are exactly two red balls and exactly two green balls is
0.055
(c) The probability that there are exactly two red balls or exactly two green balls is
1.398
Step-by-step explanation:
An urn contains
Red balls = 8
White balls = 6
Green balls = 4
Total number of balls = 18 balls
(a) The probability that all four balls are red is?
The probability that a ball drawn is red = 8/18
The probability of drawing a ball that is not red = 1 - 8/18 = 10/18
The probability that all the 4 balls drawn are red = 8/18 × 7/17 × 6/16 x 5/15
= 1680/73440
= 0.022875817
Approximately = 0.023
(b) The probability that there are exactly two red balls and exactly two green balls is
There are 6 ways by which this can be achieved. Where R = Red balls and G = Green Balls
RRGG
GGRR
RGRG
GRGR
RGGR
GRRG
P(Exactly two red balls and two green balls) = P(Exactly two red balls × Exactly two green balls)
=[ (8/18 × 7/17) ×( 4/16 × 3/15)] × 6 ways
= 672/73440 × 6 ways
= 0.0091503268 × 6 ways
= 0.0549019608
Probability of drawing out exactly two two red balls and two green balls is
= 0.055
(c) The probability that there are exactly two red balls or exactly two green balls is
P(Exactly two red balls or two green balls) = P(Exactly two red balls + Exactly two green balls)
P(Exactly two red balls or two green balls) = P(Exactly two red balls or Exactly two green balls)
=[ (8/18 × 7/17) + ( 4/16 × 3/15)] × 6 ways
=0.1830065359 + 0.05
= 0.2330065359 × 6 ways
= 1.3980392154
≈1.398
Charmaine can knit 15 rows in 22 minutes. Create a ratio table and then estimate about how many full rows could she knit in 90 minutes?
Answer:
61 rows
Step-by-step explanation:
Set up a proportion:
[tex]\frac{15}{22}[/tex] = [tex]\frac{x}{90}[/tex]
Cross multiply:
22x = 1350
x = 61.36
= approx. 61 rows
What is the ratio of 2 feet to 4 yards?
Answer:
1:6
Step-by-step explanation:
1 yard = 3 feet. 4 yards = 12 feet.
Ratio of 2 feet:12 feet = 1:6 Ans D
The ratio of 2 feet to 4 yards is 1 : 6
How to determine the ratio?The ratio is given as:
Ratio = 2 feet : 4 yards
Convert yard to feet
Ratio = 2 feet : 4 * 3 feet
Evaluate
Ratio = 2 feet : 12 feet
Divide the ratio
Ratio = 1 : 6
Hence, the ratio of 2 feet to 4 yards is 1 : 6
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Which type of transformation is shown?
Answer:
Translation
Step-by-step explanation:
The object is only moved, which is what happens when a translation occurs
A diagonal of a rectangle is 8cm and forms an angel measuring 30 with one side.Find the area of the rectangle.
Answer:
16 * √3 cm² or approximately 27.71 cm²
Step-by-step explanation:
Given the 8 cm length of the diagonal and the 30° (π/6 radians) angle with one of the sides, we can calculate the width and height of the rectangle using:
8 * cos(π/6) = 8 * ((√3)/2) = 4 * √3
8 * sin(π/6) = 8 * (1/2) = 4
Multiply those two values together to get the area and you get
16 * √3 cm²
after running 3/5 of a race the runner only has 4 miles left how long was the race
Answer:
10 miles
Step-by-step explanation:
3a/5 + 4 = a
a = race long
4 = a - 3a/5
4 = 5a/5 - 3a/5
4 = 2a/5
4*5/2 = a
a = 10
The length of the entire race is 10 miles.
Let length of race = r
Miles left after running 3/5 of race :
r - 3r/5 = 4We can solve the expression thus :
r - 3r/5 = 4
r - 3r = 4 * -5
r - 3r = -20
-2r = -20
divide both sides by -2 to isolate r
r = 10
Hence, the length of the entire race is 10 miles.
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The temperature on Monday was 5 Degrees. The temperature on Thursday was - 8 degrees. Was the overall change in the temperature positive, negative, or 0? Why ? *
Answer:
Negative change
Step-by-step explanation:
Given
[tex]Monday\ Temperature = 5\ deg[/tex]
[tex]Thursday\ Temperature = -8\ deg[/tex]
First, we need to calculate the overall change in temperature
This is calculated by subtracting the initial temperature from the final temperature
[tex]Overall\ Change = Thursday\ Temperature - Monday\ Temperature[/tex]
[tex]Overall\ Change = -8\ deg - 5\ deg[/tex]
[tex]Overall\ Change = -13\ deg[/tex]
The overall change shows a negative change in the temperature.
This is as a result of a drop in temperature from Monday to Thursday
Find (f-g)(x) for the following functions. f(x) = x2-2x-24 g(x) = x+4
Answer:
(f-g)(x) = x² - 3x - 24Step-by-step explanation:
f(x) = x² - 2x - 24
g(x) = x + 4
To find (f-g)(x) subtract g(x) from f(x)
That's
(f-g)(x) = x² - 2x - 24 - ( x + 4)
(f-g)(x) = x² - 2x - 24 - x - 4
Group like terms
We have
(f-g)(x) = x² - 2x - x - 24 - 4
Simplify
We have the final answer as
(f-g)(x) = x² - 3x - 28Hope this helps you
Multiply
11 x 34.12
I’m so confused?
Answer:
[tex]34.12 * 11 = 375.32[/tex]
Step-by-step explanation:
Given
11 * 34.12
Required
Multiply
To start with, we have to ignore the decimal points;
So, we have
3412
* 11
---------------
3 4 1 2
3 4 1 2
------------------------
3 7 5 3 2
The next step is as follows;
34.12 is in 2 decimal places
11 is has no decimal (0 decimal place)
Add the decimal places together
[tex]Decimal\ Place = 2 + 0 = 2[/tex]
This implies that the result will be in 2 decimal placed;
Hence:
[tex]34.12 * 11 = 375.32[/tex]