The factored form of 3w - 15, after factoring out the Greatest Common Factor, is 3(w - 5).
To factor out the greatest common factor (GCF) from the expression 3w - 15, we first need to determine the GCF of the two terms.
In this case, the GCF of 3w and 15 is 3. Both terms are divisible by 3.
To factor out the GCF, we divide each term by the GCF:
3w/3 - 15/3
Simplifying further, we have:
w - 5
Therefore, the factored form of 3w - 15, after factoring out the GCF, is 3(w - 5).
Factoring out the GCF is a process that involves identifying the highest common factor of all the terms in an expression and dividing each term by that factor. This helps simplify the expression and can make it easier to work with or further factorize if needed.
In this case, the GCF was 3, so we divided both terms by 3 to factor it out, resulting in the simplified expression w - 5.
To learn more about the greatest common factor;
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The complete question:
Find out the factored form of the following expression,
3w – 15
Factoring out the GCF
Angel rode his bike 8 km South 5 km East how long did it take Angel to get back
1.CONVERT TO SCIENTIFIC NOTATION2.CONVERT TO STANDARD NOTATION
a. 895,000,000,000a. 3.65 x 108
Answer:
Step-by-step explanation:
a. 8.95 x 10^11
b. 3.65 x 10^8= 365,000,000
Answer:
a. 8.95 x 10^11
b. 3.65 x 10^8= 365,000,000
Step-by-step explanation:
what is the differnence between (-2)^2 and -2^2 in math
Answer:
(-2)^2 = 4-2^2 = -4Step-by-step explanation:
The first is (-2)(-2) = 4.
The second is -(2)(2) = -4.
The order of operations says exponents are evaluated first. An exponent signifies repeated multiplication of the base.
_____
If your calculator is working correctly, it will show you the difference.
__
Beware spreadsheet programs. They don't always follow the order of operations when evaluating formulas. Parentheses are often required to keep them honest.
Answer: The one with perinthesis is bigger because you would do the negative first and you would have nothing to take away from
Step-by-step explanation:
15. _TYU and ZUYB form a linear pair. The mZTYU = 5x - 4 and mZUYB =
3x + 10. Find the degree measure of each angle. HINT: draw a picture.
Upload your work in canvas assignment.
Answer:
∠TYU = 104.75°∠UYB = 75.25°Step-by-step explanation:
A picture on scratch paper works as well as any.
__
The sum of the two angles is 180°:
(5x -4) +(3x +10) = 180
8x = 174 . . . . . . collect terms, subtract 6
x = 21.75 . . . . . .divide by 8
Then the angle measures are ...
∠TYU = 5(21.75) -4 = 104.75°
∠UYB = 3(21.75) +10 = 75.25°
_____
Check
The total is 104.75 +75.25 = 180, as required.
Answer:
104.75 +75.25 = 180
Step-by-step explanation:
(1 point) Find f if f′′(x)=2+cos(x),f(0)=3,f(π/2)=−6.
On a shelf there are 40 chips. 30 of them are cheddars flavored . What is the percentage of those that are cream cheese flavored?
Answer:
Hey there!
30/40 are cheddar flavored, so 10/40 are cream cheese flavored.
10/40=25, so 25% of the chips are cream cheese flavored (assuming that the rest of the chips are all cream cheese flavored)
Let me know if this helps :)
Find two numbers with a sum of 65. Twice the smaller number is 10 more than the larger number.
Answer:
40 and 25Step-by-step explanation:
Let the two numbers be x and y. If the sum of the numbers is 65, then;
x+y = 65........ 1
Given twice the smaller number is 10 more than the larger number, this can be written as 2x = 10+y (taking x as the smallest and y as the largest)
Therefore 2x = 10+y
x = 10+y/2 ....... 2
Substitute equation 2 into 1 to have;
10+y/2 +y = 65
Find the LCM
(10+y+2y)/2 = 65
10+3y/2 = 65
cross multiply
10+3y = 130
3y = 130 -10
3y = 120
y = 120/3
y = 40
Since 2x =10+y
2x = 10+40
2x = 50
x = 50/2
x = 25
Therefore the two numbers are 40 and 25
Answer:
40 and 25
Step-by-step explanation:
The midpoint of AB is M(3, 3). If the coordinates of A are (2, -1), what are the
coordinates of B?
Step-by-step explanation:
Hey there!!
It's so simple.
While finding the coordinates of any point if the midpoint is there it will be much easier. You must remember the midpoint formulae.
Let's simply work with it.
Here, A (2,-1) and midpoint M(3,3) are given.
Let another coordinate be B(x,y).
By midpoint formulae,
[tex]midpoint(x.y) = \frac{x1 + x2}{2} ,\frac{y1 + y2}{2} [/tex]
Putting their values,
[tex]m(3 , 3) = \frac{2 + x}{2} , \frac{ - 1 + y}{2} [/tex]
As they are equal, equating with their corresponding elements we get,
[tex]3 = \frac{2 + x}{2} [/tex]
6= 2 + x
x = 6-2
Therefore, the value of a is 4.
Again,
[tex]3 = \frac{ - 1 + y}{2} [/tex]
6 = -1 + y
Therefore, the value of y is 7.
Therefore, the coordinates are B (4,7)
Hope it helps....
Answer:
The coordinates of B is (4, 7)
Step-by-step explanation:
To find the answer for B, you have to do the inverse of the midpoint formula, which is M equals (x1 multiplied by x2, over 2; y1 multiplied by y2, over 2).
If you substitute in A's coordinates for x1 and y1, you come up with (3, 3) = (2+x, over 2; and -1+y, over 2)
If the x coordinate answer for AB was 3, you can create an equation like this to solve for B's x coordinate: 2+x over 2 equals 3.
you multiply 2 by 3 to get 6---> 2+x=6-----> x=4
If the y coordinate for AB was also three, you can create another equation to solve for B's y coordinate: -1+y over 2 equals 3.
you multiply 2 by 3 to get 6 again---->so -1+y=6---->y=7
so the answer for B's coordinates is (4, 7).
Calculus 2 Master needed, evaluate the indefinite integral of: [tex]\int\( (lnx)^2} \, dx[/tex] So far I had applied the integration by parts and got: [tex](ln x )^2*x - \int\ x*((lnx)^2/2)}[/tex] do we do integration by parts again? also, do we simplify the x at my current stage? steps shown would be appreciated
Answer:
[tex]\displaystyle \int (\ln(x))^2\, dx=x(\ln(x)^2-2\ln(x)+2)+C[/tex]
Step-by-step explanation:
We want to evaluate the integral:
[tex]\displaystyle \int\left(\ln x\right)^2 \, dx[/tex]
We can use Integration by Parts. Rewriting the integral yields:
[tex]\displaystyle =\int 1\cdot (\ln(x))^2\, dx[/tex]
Recall that IBP is given by:
[tex]\displaystyle \int u\, dv = uv - \int v \, du[/tex]
Let u be (ln(x))². And let dv be (1) dx. Therefore:
[tex]\displaystyle du = 2\ln x \cdot \frac{1}{x}\, dx[/tex]
Simplify:
[tex]\displaystyle du=\frac{2\ln(x)}{x}\, dx[/tex]
And:
[tex]dv=(1)dx\Rightarrow v = x[/tex]
Therefore:
[tex]\displaystyle \int (\ln(x))^2\, dx=\underbrace{\ln(x)^2}_{u}\underbrace{x}_{v}-\int\underbrace{x}_{v}\cdot \underbrace{\frac{2\ln(x)}{x}\, dx}_{du}[/tex]
Simplify:
[tex]\displaystyle =x\ln(x)^2-2 \int\ln(x)\, dx[/tex]
We can perform IBP again. Let u = ln(x) and v = 1. Hence:
[tex]\displaystyle du = \frac{1}{x} \, dx[/tex]
And:
[tex]dv=(1)dx\Rightarrow v = x[/tex]
Thus:
[tex]\displaystyle =x\ln(x)^2-2\left(x\ln(x)-\int (x)\frac{1}{x}\, dx\right)[/tex]
Simplify:
[tex]\displaystyle =x\ln(x)^2-2\left(x\ln(x)-\int (1)\, dx\right)[/tex]
Evaluate:
[tex]=x\ln(x)^2-2(x\ln(x)-x)+C[/tex]
Simplify:
[tex]\displaystyle =x\ln(x)^2-2x\ln(x)+2x[/tex]
Factor:
[tex]=x(\ln(x)^2-2\ln(x)+2)[/tex]
Therefore:
[tex]\displaystyle \int (\ln(x))^2\, dx=x(\ln(x)^2-2\ln(x)+2)+C[/tex]
a garden table and bench costs $842 combined. the garden table costs $92 more that the bench. what is the cost of the bench?
Answer:
$375 is what i got on
The bad debt ratio for a financial institution is defined to the dollar value of loans defaulted divided by the total dollar value of all loans made. Suppose that a random sample of 7 Ohio banks is selected and that the bad debt ratios (written as percentages) for these banks are 6%, 8%, 5%, 9%, 7%, 5% and 8%. Banking officials claim that the mean debt ratio for all Midwestern banks is 3.5 percent and the mean bad debt ratio for Ohio banks is higher. Set up the null and alternative hypotheses needed to attempt to provide evidence supporting the claim that the mean bad debt ratio for Ohio banks exceed 3.5 percent. (a) H0: μ ≤ [ Select ] % versus Ha: μ > [ Select ] %. (b) Discuss the meanings of a Type I error and a Type II error in this situation. Type I : Conclude that Ohio's mean debt ratio is [ Select ] 3.5 % when it actually is 3.5%. Type II : Conclude that Ohio's mean debt ratio is [ Select ] 3.5 % when it actually is 3.5%.
Answer:
Step-by-step explanation:
From the information given:
Consider X to be the random variable denoting the bad debt ratios for Ohio Bank.
Then, [tex]X \sim N ( \mu, \sigma ^2)[/tex]
Thus the null hypothesis and the alternative can be computed as:
Null hypothesis:
[tex]H_o : \mu \leq3.5\%[/tex]
Alternative hypothesis
[tex]H_1 : \mu > 3.5\%[/tex]
The type I and type II error is as follows:
Type I:
The mean bad debt ratio is > 3.5% when it is not
Type II:
The mean bad debt ratio is ≤ 3.5% when it is not.
The test statistics can be calculated by using the formula:
[tex]t = \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
where;
sample size n = 7
mean = 6+8+5+9+7+5+8 = 48
sample mean [tex]\overline x =\dfrac{48}{7}[/tex]
[tex]\overline x[/tex] = 6.86
sample standard deviation is :
[tex]s = \sqrt{\dfrac{\sum( x -\overline x)^2}{n-1}}[/tex]
[tex]s = \sqrt{\dfrac{( 6 -6.86)^2+( 8-6.86)^2+ ( 5 -6.86)^2 + ...+( 7 -6.86)^2+ ( 5 -6.86)^2+( 8 -6.86)^2 }{7-1}}[/tex]
s = 1.573
population mean [tex]\mu = 3.5[/tex]
Therefore, the test statistics is :
[tex]t = \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \dfrac{6.86- 3.5}{\dfrac{1.573}{\sqrt{7}}}[/tex]
[tex]t = \dfrac{3.36}{\dfrac{1.573}{2.65}}[/tex]
[tex]t = \dfrac{3.36\times {2.65}}{{1.573}}[/tex]
t = 5.660
At significance level of 0.01
[tex]t_{0.01} = 3.707[/tex]
P - value = P(T > 5.66)
P - value = 1 - (T < 5.66)
P - value = 1 - 0.9993
P-value = 0.0007
Therefore, since [tex]t_{0.01} < t[/tex] , we reject the null hypothesis and conclude that the claim that the mean bad debt ratio for Ohio banks is higher than the mean for all financial institutions is true.
Find the value of x. (3x-9)(x+7)
Answer:
The answer to this question is 23
Step-by-step explanation:
The reason is because....
23x3= 69
69-9=60
60+ (x+7)
23+7=30
30+60=90
The angle shown is a 90 degree angle therefore this is your answer.
last year ,rita opened an investment account with $400 At the end of the year the amount in the account had decreased by 28.5% how much is this decrease in dollars? how much money way in her account at the end of last year
Answer:
Step-by-step explanation:
decrease=400×0.285=114.000 $
amount at the end=400-114=286 $
A homeowners association charges a $3.85 fee for each day your payment is late. If a bull is paid 13 days late, then how much will the homeowners association charge in late fees?
Answer:
$50.05
Step-by-step explanation:
Since you have to pay $3.85 per day, and you pay it 13 days late, then you would multiply $3.85 and 13.
3.85*13= 50.05
Total amount of late charges fee is $50.05
Given that;Amount pay for late charges = $3.85
Number of days = 13 days
Find:Total amount of late charges fee
Computation:Total amount of late charges fee = Amount pay for late charges × Number of days
Total amount of late charges fee = 3.85 × 13
Total amount of late charges fee = $50.05
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Rewrite 4/10 : 1/25 as unit rate
Answer: 10
Explanation:
remember that when you have a divided fraction, you can change de numerator and denominator so your fractions be like this:
4/10 * 25/1 = 100/10
10*1
100/10= 10
this happens because when you have a fraction that is being divided, it's also like you are cross multiplying, just like the resolution upwards, then you get 100 divided by 10, which is 10.
I hope it helps you. :)
D) Solve for k.
4(K + 11) - -2 = 6
K=
Answer: K=23
Step-by-step explanation:
Answer:
k=9
Step-by-step explanation:
4k+44 because you distribute the 4 to the parenthesis
new equation: 4k+44-2=6
add 2 to 6 which would be 8 because you have to get k by itself
4k+44=8 subtract 44 from 8
-36=4k
divide by four
k=-9
if the equation is really 4(k+11)--2=6
do the same first steps so 4k+44
but the -2 would become positive cuz of the double negative
so:
4k+44+2=6
4k+46=6
subtract 46 from 6
4k=-40
divide -40 by 4
k=-10
What is the next number 5, -20, 80, -320, 1280 _
The population of a town increased from 3600 in 2006 to 4500 in 2011. Find the absolute and relative (precent) increase.
what grade math is this????????????????????
4x - 3y = 6 ,7x + 3y =27
Answer:
Step-by-step explanation:
4x - 3y = 6
7x + 3y = 27
11x = 33
x = 3
7(3) + 3y = 27
21 + 3y = 27
3y = 6
y = 2
(3,2)
Answer:
x=3 and y=2
Step-by-step explanation:
Let's solve your system by substitution.
4x−3y=6;7x+3y=27
Step: Solve4x−3y=6for x:
4x−3y=6
4x−3y+3y=6+3y(Add 3y to both sides)
4x=3y+6
4x /4 = 3y+6 /4 (Divide both sides by 4)
x= 3 /4 y+ 3 /2
Step: Substitute
3 /4 y+ 3 /2 for x in7x+3y=27:
7x+3y=27
7( 3 /4 y+ 3 /2 )+3y=27
33 /4 y+ 21 /2
=27 (Simplify both sides of the equation)
33 /4 y+ 21 /2 + (−21 /2 )
=27+ (−21 /2) (Add (-21)/2 to both sides)
33 /4 y= 33 2
33/4y=33/2
33 /4 =33/4 (Divide both sides by 33/4)
y=2
Step: Substitute 2 for y in x= 3 /4 y+ 3 /2
x= 3 /4 y+ 3 /2
x= 3 /4 (2)+ 3 /2
x=3 (Simplify both sides of the equation)
Answer:
x=3 and y=2
HOPE THIS HELPS!!!! :)
<333333333333333
5. Solve: 16 * 22 / 2
Answer:
176
Step-by-step explanation:
Usually you'll follow PEMDAS & the left->right rule, however, as you are only multiplying and dividing, it does not matter.
22/2 = 11
11 * 16 = 176
176 is your answer.
~
Answer:
176
Step-by-step explanation:
PEMDAS : first Multiply 16 & 22 which equals 352. Then Divide 352 by 2 which equals 176.
Find its inverse, and state the domain and range.
(7,-1) and ( 21,-5) what is the slope
Answer:
-2/7
Step-by-step explanation:
Going from (7,-1) to ( 21,-5) we see x (the 'run') increasing by 14 and y (the 'rise') decreasing by 4. Thus, the slope of the line connecting these two points is m = rise/run = -4/14, or -2/7.
A football is kicked vertically upward from a height of 4 feet with an initial speed of 65 feet per second. The formula h=4+65t−16t2 describes the ball's height above the ground, h, in feet, t seconds after it was kicked. Use this formula to find the ball's height 2 seconds after it was kicked. The ball's height, 2 seconds after it was kicked, was nothing feet. I NEED EXTREME HELP PLEASE !!!
Answer: h = 70ft
Step-by-step explanation: To find the height the ball reached after 2 seconds, substitute variable t for 2 and calculate height:
[tex]h=4+65t-16t^{2}[/tex]
[tex]h=4+65.2-16.2^{2}[/tex]
[tex]h=4+65.2-16.4[/tex]
[tex]h=4+130-64[/tex]
h = 70
After 2s, the football reached a height of 70 feet.
Answer:
if its for 3 seconds the answer is 55
Step-by-step explanation:
Write the expression in words 5-y
Answer:
five minus y
Step-by-step explanation:
Answer:
y less than five
Step-by-step explanation:
thats your answer, please trust me
Which name describe only those numbers highlighted on the number line.
Answer: negative numbers
Explanation: Notice that on the number line, 0 is in the middle, all numbers to the left of 0 are negative, and all numbers to the right of 0 are positive.
Since the numbers highlighted only include numbers
to the left of 0, negative numbers are shown here.
Pregunta 4 (1 punto)
4.) Fill in the blank
2(x+7) = 2x + _
оа
a) 7
b) 14
c
c) 7x
d) 14x
Od
Answer:
7....................
if f(x)=4x^2-6
find f(3)
Answer:
f(3) = 30Step-by-step explanation:
f(x) = 4x² - 6
To find f(3) substitute the value of x that's 3 into f (x) that is for every x in f (x) replace it with 3
We have
f(3) = 4(3)² - 6
= 4(9) - 6
= 36 - 6
We have the final answer as
f(3) = 30Hope this helps you
Answer: f(3) = 30
Step-by-step explanation:
Hi guys, can anyone help me with this? Many thanks:)
Step-by-step explanation:
y = √—16x²+8x—2√8x+1+2In this exercise, lines m and n are parallel. Find the measure of each numbered angle.
ITS 9 PARTS
1 = 62° ( Vertically Opposite Angles )
10 = 62° ( Corresponding Angles )
9 = 10 = 62° ( Vertically Opposite Angles )
6 = 95° ( Vertically Opposite Angles )
7 = 180° - 95° = 85° ( Linear Pair )
8 = 7 = 85° ( Vertically Opposite Angles )
5 = 8 = 85° ( Corresponding Angles )
3 = 5 = 85° ( Vertically Opposite Angles )
4 = 180° - ( 9 + 7 )
4 = 180° - ( 62° + 85° )
4 = 180° - 147°
4 = 33° ( Angle Sum Property )
2 = 4 = 33° ( Vertically Opposite Angles )
Which angles are complementary to each other?
Answer:
angle CDA and angle BDC
mark this as brainliest!
Answer:
∠CDA and ∠BDC as their sum equals 90°
Step-by-step explanation: