the H.C.F OF 64,96,128
Answer:
32
Step-by-step explanation:
[tex] 64= 2^6[/tex]
[tex] 96= 2^5\times 3[/tex]
[tex] 64= 2^7[/tex]
Common factor = [tex] 2^5[/tex]
Therefore,
H.C.F OF 64,96,128 = [tex] 2^5[/tex] = 32
3. John receives a day worth of pay, p, for 4 days of newspaper delivery. He spent half of his money on gas. Then he
spent $5 on coffee. Now he has $35 left. How much does John get paid each day for newspaper delivery?
a. Write an expression for the amount of money John earns for 4 days.
b. Use part a to write an expression to represent spending half of his money on gas.
c. Use part b to write an expression to represent spending $5 on coffee.
d. If John has $35 left, write an equation that can be used to find how much John gets paid each day. Solve.
Answer:
a. [tex]Total = 4P[/tex]
b. [tex]Gas = 2P[/tex]
c. [tex]2P - 5[/tex]
d. [tex]P = 20[/tex]
Step-by-step explanation:
Given
[tex]Amount\ received = P[/tex]
[tex]Number\ of\ days = 4[/tex]
[tex]Coffee = \$5[/tex]
[tex]Amount\ Left = \$35[/tex]
Calculating (a); the total amount earned;
[tex]Total = Amount * Days[/tex]
[tex]Total = 4 * P[/tex]
[tex]Total = 4P[/tex]
Calculating (b): Money Spent on Gas
From the question, we understand that 1/2 of his earnings is spent on gas;
Hence;
[tex]Gas = \frac{1}{2} * Total[/tex]
Substitute 4P for Total
[tex]Gas = \frac{1}{2} * 4P[/tex]
[tex]Gas = 2P[/tex]
Calculating (c): Expression for coffee
First, we need to calculate the amount left after buying Gas;
[tex]Amount = Total - Gas[/tex]
[tex]Amount = 4P - 2P[/tex]
[tex]Amount = 2P[/tex]
From this amount, he bough coffee of $5;
Hence; he's left with
[tex]2P - 5[/tex]
Calculating (d): Calculating his daily earnings
After (c) above, he has $35 left
So, we have
[tex]2P - 5 = 35[/tex]
Add 5 to both sides
[tex]2P - 5 + 5= 35 + 5[/tex]
[tex]2P = 40[/tex]
Divide through by 2
[tex]P = 20[/tex]
Hence, his daily earnings is $20
A group of college students is volunteering for Homes for the Community during their spring break. They are putting the finishing touches on a house they built. Working alone, Wade can paint a certain room in 6 hours. Rhonda can paint the same room in 3 hours. How long will it take them working together to paint the room? Round your answer to the nearest hundredth if necessary.
Answer:
2 hours.
Step-by-step explanation:
From the question given,
Wade can do the work alone in 6 hours.
Rhonda can do the same work in 3 hours.
Next, we shall determine how much work is done by Wade and Rhonda in 1 hour each. This is illustrated below:
If Wade can do the work alone in 6 hours.
Then Wade can do 1/6 of the work in 1 hour.
If Rhonda can do the same work in 3 hours.
Then Rhonda can do 1/3 of the work in 1 hour.
Next, we shall determine the work done by Wade and Rhonda when they work together. This is illustrated below:
Wade's 1 hour work = 1/6
Rhonda's 1 hour work = 1/3
Therefore, work done by Wade and Rhonda together in 1 hour = 1/6 + 1/3 = 3/6 = 1/2
Since they completed 1/2 of the work in 1 hour, it means they will complete the work in 2 hours.
PLEASE HELP ME, I DON'T UNDERSTAND!
Hello,
First of all, dividing by 0 is not defined we will take x different from 1/3 (because -1+3x= 0 <=> x = 1/3)
Then, dividing this polynomial by (-1+3x) means that you have to have Q(x), a polynomial of degree 1 and R a real number such that
[tex]\dfrac{9x^2-6x+2}{-1+3x}=Q(x)+\dfrac{R}{-1+3x}\\\\\text{We can multiply by (-1+3x)}\\\\9x^2-6x+2=(-1+3x)Q(x)+R[/tex]
Either you do the division and you can select the correct answer or you check the different answer to identify the correct one.
For instance, for the first answer, let's estimate
[tex](-1+3x)(3x-3)+\dfrac{-1+3x}{3x-1}\\\\=-3x+3+9x^2-9x+1\\\\=9x^2-12x+4[/tex]
and this is not equal to our initial polynomial, so this is not the correct answer.
Second Answer.
[tex](-1+3x)(3x-1)+\dfrac{-1+3x}{3x-1}\\\\=-3x+1+9x^2-3x+1\\\\=9x^2-6x+2[/tex]
And this is our initial polynomial. So this is the [tex]\large \boxed{\sf \bf \text{correct answer}}[/tex]
Thank you.
PS: in this example, you can even notice the following (so it makes the division trivial)
[tex](3x-1)^x=9x^2-6x+1 \\\\\text{So}\\\\9x^2-6x+2= (3x-1)^2+1\\\\\text{And, then.}\\\\\dfrac{9x^2-6x+2}{-1+3x}=3x-1+\dfrac{1}{3x-1}[/tex]
Cooper bought a washing machine with a sticker price of $900. If he paid $12
a week for two years, what was the approximate markup rate on the washing
machine?
A. 27.9%
B. 38.7%
C. 69.3%
D. 72.1%
1 year = 52 weeks. 2 years would be 104 weeks.
$12 per week x 104 weeks = $1248 total.
1248 - 900 = $348
348 /900 = 0.3866 = 38.7%
The answer is B
find the sum of the interior angles of a regular hexagon and hence the size of each interior angle
Answer: (a) 720°, (b) 120°
Step-by-step explanation:
A hexagon is a polygon with six sides.
Formula for finding the interior angle of a polygon = ( 2n - 4 )complementary
= ( 2n - 4 ) 90
complimentary angle is 90° or
= ( n - 2 )supplementary
supplementary angle is 180° . Now solving the question now since n = 6
we now put it in any of the formula above
( 2 x 6 - 4 ) x 90 = ( 12 - 4 ) x 90
= 8 x 90
= 720° or
( 6 - 2 ) x 180 = 4 x 180
= 720°.
The second part of the question, each size of the interior angle
= ⁷²⁰/₆
= 120°
When a number is increased by 3 and that number is doubled, the result is -8. What was the original number?
Answer:
The original number is -7.
Step-by-step explanation:
In this section, we are trying to figure out a mysterious number. Let's call this number y. To find the value of y, we need to create an equation. Our equation will be based on clues hidden in the text. So, what do we know?
- A number, aka y, is increased by 3. (y+3)
-That number is doubled. 'That number' refers to the answer of y+3. So, (y+3)x2.
-Finally, the end result is -8.
Great! Now we know our equation: 2(y+3)=-8. We need to figure out what y equals, so let's isolate the y term with some algebra.
2(y+3)=-8; Original formula
2y+6=-8; Distribute the (y+3)
2y=-14; Carry the 6 to the other side of the equation.
y=-7: Divide
Thus, our mysterious number is -7. Hope this helps:)))
Let (6,-5) be a point on the terminal side of θ. Find the exact values of sin θ, sec θ, and tan θ.
Answer:
sinθ = -5/√61
secθ = √61/6
tanθ = -5/6
Step-by-step explanation:
From the given coordinate (6, -5), x = 6 and y = -5. This shows that the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.
Let us get the value of the radius 'r' first before calculating the trigonometry identities.
Using the Pythagoras theorem;
[tex]r^2 = x^2 + y^2\\r^2 = 6^2 + (-5)^2\\r^2 = 36+25\\r^2 = 61\\r = \sqrt{61}[/tex]
Using SOH, CAH, TOA to get the trigonometry identities;
Given x = 6, y =5 and r = √61
[tex]sin \theta = opp/hyp = y/r\\sin \theta = 5/\sqrt{61} \\[/tex]
Since sin θ, is negative in the fourth quadrant, [tex]sin \theta = -5/\sqrt{61} \\[/tex]
[tex]cos \theta = adj/hyp = x/r\\cos \theta = 6/\sqrt{61} \\[/tex]
[tex]sec \theta = \frac{1}{cos \theta} \\sec \theta = \frac{1}{6/\sqrt{61} } \\sec \theta = \frac{\sqrt{61} }{6}[/tex]
For tanθ:
[tex]tan \theta = \frac{opp}{adj} = \frac{y}{x} \\tan \theta = \frac{5}{6}\\[/tex]
Since tan θ, is negative in the fourth quadrant, [tex]tan \theta = -5/6[/tex]
[tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex],
[tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]
[tex]TAN\Theta=\frac{-5}{6}[/tex].
Given coordinate of point be (6, -5).
So the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.
Since (6, -5) is on the terminal side that puts us in the fourth quadrant. If we plot that point and draw a diagonal to it from the origin, we will be able to draw a right triangle with that diagonal as the hypotenuse.That means the adjacent side is 6 and opposite side it -5.
By Pythagorean theorem, we find that the hypotenuse
[tex]H=\sqrt{6^{2} +(-5)^{2} }[/tex]
[tex]H=\sqrt{61}[/tex]
We know from trigonometric ratios,
[tex]SIN\Theta=\frac{Perpendicular}{hypotenuse} \\[/tex]
[tex]SIN\Theta=\frac{5}{\sqrt{61} }[/tex]
Since [tex]SIN\Theta[/tex] is negative in 4th quadrant,
so,
[tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex]
Similarly,
[tex]SEC\Theta=\frac{hypotenuse}{base}[/tex]
[tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]
And,
[tex]TAN\Theta=\frac{perpendicular}{base}[/tex]
[tex]TAN\Theta=\frac{-5}{6}[/tex]
Hence, [tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex], [tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex] and [tex]TAN\Theta=\frac{-5}{6}[/tex].
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What is 325.623 rounded to the nearest tenth?
real numbers are ____ integers
OPTION A: Always
OPTION B: Sometimes
OPTION C: Never
Answer:
B
Step-by-step explanation:
Which of the following equations represents a line parallel to the line given by y=5x +9?
Answer:
y = 5x + 1
Step-by-step explanation:
Lines that are parallel to each other on a graph would have the same slope but different y-intercepts. When option A's equation is graphed along with the line given in the question, the lines appear to be parallel.
Option A should be the correct answer.
Which expression is equivalent to (73)5 • 74 ?
This question is incomplete because the options are missing; here is the complete question:
Which expression is equivalent to (73) 5 • 74?
Select each correct answer:
73 • 5 + 4
73 + 5 + 4
73 + 5 • 74
73 • 5 • 74
The answer to this question is 73 • 5 • 74
Explanation:
The symbol • represents multiplication, this implies the numbers 5 and 74 should be multiplied when solving this operation. Moreover, if the expression is simplified the same symbol or a multiplication symbol should be used.
Moreover, the lack of a symbol between these numbers and 73 indicates multiplication. Indeed, in algebra and some fields of mathematics, the multiplication symbol is omitted, and two numbers standing side by side with no symbol indicate the multiplication. Thus, it is correct to place a multiplication symbol between 73 and the other numbers.
Find the sum of the sequence. 42+43+44+45+...+107
Answer:
4917
Step-by-step explanation:
Given sequence:
42, 43, 44, 45, ..., 107This is AP with common difference of 1, the first term of 42 and the last term of 107
Number of terms:
107 - 42 + 1 = 66Sum of the terms:
Sₙ= 1/2*n*(a₁+aₙ)Sₙ= 1/2*66*(42+107) = 4917Answer is: 4917
can u answer this plz
Answer:
The answer is 14 :)
Step-by-step explanation:
We have,
∠PQS = 90°∠PQR = 76°Find the measure of ∠ x ?
∠PQR + ∠RQS = ∠PQS
⇒ 76° + x = 90°
⇒ x = 90° - 76°
⇒ x = 14°
Three weeks ago John bought stock at 4944; today the stock is valued at 4971g. We could say the stock is performing at which of the
following?
A. Below par
B. Above par
C. On par
D. Par equality
Answer:
Step-by-step explanation:
B: Above par. Stock has gained a bit of value since it was purchased.
What is the standard form of nine million, twenty thousand, twenty-nine
Answer:
9000000+20000+20+9
Step-by-step explanation:
3. Find which of the following are in proportion:
(1) 12, 16, 6,8
Answer:
thus, the ratios 8 : 16 and 6 : 12 are equal
Step-by-step explanation:
8 : 16 and 6: 12
8 : 16 = 1/2
6: 12= 1/2
Thus, the ratios 8 : 16 and 6 : 12 are equal
identify the values of the coefficents in the quadratic equation 5x^2=4x+7
Answer:
5, -4, and -7
Step-by-step explanation:
5x² = 4x + 7
The standard form of a quadratic equation is
y = ax² + bx +c, where
a, b, and c are the coefficients.
If we convert your quadratic to the standard form, it becomes
5x² - 4x - 7 = 0
The coefficients are 5, -4, and -7.
There are 5 different pairs of gloves, where left and right are distinguishable. Select 4 of the 10 gloves. (a) How many are there to select 2 pairs of gloves? (b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
Answer:
(a) How many are there to select 2 pairs of gloves?
10 ways
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
130 ways
Step-by-step explanation:
We solve the above questions using Combination
Combination = C(n, r) = nCr
= n!/n! ×(n - r)!
(a) How many are there to select 2 pairs of gloves?
We have 5 pairs of gloves. Therefore, the number of ways to select 2 gloves =5C2
= 5!/2! × (5 - 2)!
= 5!/2! × 3!
= 5 × 4 × 3 × 2 × 1/(2 × 1) × (3 × 2 × 1)!
= 10 ways.
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
We are told to select 4 gloves out of the 10 gloves = 10C4
We have 5 pairs, we need to make sure that two out of the selected 4 make a pair = 5 × 2⁴
= 80
Hence,
10C4 - 5C4
= [10!/4! × (10 - 4)!] - 80
= 210 - 80
= 130 ways
Emily wants to use multiplication to solve 1/5 divided by 3=a
Answer:
[tex]a = \frac{1}{15}[/tex]
Step-by-step explanation:
Hey there!
To solve the given we'll use keep change flip.
[tex]\frac{1}{5} / 3 = a\\\\\frac{1}{5} *\frac{1}{3} = a\\\\\frac{1}{15} = a[/tex]
Hope this helps :)
Given
f(x) = 3x + 10 and g(x) = x - 2, find f (g(5))
-10
23
None of these.
The value of the function f (g (5)) will be 10.
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The function are,
f(x) = 3x + 10 and g(x) = x - 2
Now,
Solve the function as;
f (g (5)) = f (5 - 2)
= f (3)
= 3 × 3 + 10
= 9 + 10
= 10
Thus, The value of the function f (g (5)) will be 10.
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Can Someone please help me....Like pretty please....It would mean everything to me, Please help me out 1. 2. 3. 4. 5.
================================
Explanation:
SSS stands for "Side side side" indicating there are 3 pairs of sides that are same length. Visually we use tickmarks to show how the sides pair up. Eg: sides that have 1 tickmark only are the same length. If we know that all 3 pairs of sides are congruent, then we have enough info to conclude the triangles are congruent.SAS means "side angle side". The angle is between the two sides. The sides in question are the ones with tickmarks to indicate how they pair up. We have two angles and a side between them. So we use ASA this time. It stands for "Angle side angle". This is slightly different from AAS.We'll use AAS here. The side is not between the two angles. So this is why AAS is different from ASA. Some books may call "AAS" as "SAA", but they're the same thing. HL stands for hypotenuse leg. This only applies to right triangles (since the hypotenuse is a special term for the longest side of a right triangle). The hypotenuse is always opposite the 90 degree angle. This is the only time when SSA will work. Otherwise, SSA is ambiguous and it is not a valid congruence theorem.What is the y-intercept of the graph of the following data? a (-1, 0) b (0, 3) c (0, -3) d (1, 6).
Answer:
b
Step-by-step explanation:
The y- intercept is the point on the y- axis where the graph crosses.
On the y- axis the x- coordinate is always zero.
From the table when x = 0 , y = 3, thus
(0, 3 ) is the y- intercept → b
A super-secret handshake is set up with every other person in a cabin. You and another person in the cabin have one handshake. Now there are 14 total people in the cabin. How many handshakes will there be in all?
Answer: 7 handshakes in all.
Step-by-step explanation:
If you and another person have one shake and there are 14 total people in the cabin that means that there will be 7 handshakes in all.
simplify -4(x+6)+2(x-2)
Answer:
[tex]-2x-28[/tex]
Step-by-step explanation:
We can apply the distributive property then combine like terms for a simpler equation.
[tex]-4(x+6)+2(x-2)\\\\-4x-24+2x-4\\\\-2x-28[/tex]
Hope this helped!
Answer:
-2x -26
Step-by-step
Simplify.
-104
3(+ 1)?
Enter your answer, as a simplified fraction, in t
Please I need it now
Answer: I'll explore two options here. Your question wasn't entirely clear. If you meant a regular 2 step equation, this would be your answer:
-104(3+1)
-104(4)
416
However, if you meant -104/(3+1) this would be your answer:
-104 ÷ (3+1)
(3+1) = 4
-104 ÷ 4 = -26
Hope this helped!
Change the decimal to fraction form or mixed number form and reduce if possible 73.437
Answer:
73.437= 74 437/1000
Step-by-step explanation:
73.437 to fraction.
Let's acknowledge the presence of a decimal and how many digit we have after the decimal point.
Actually, the numbers after the decimal point will determine the amount of 10s to be divided with.
What I'm saying is this
73.437= 74 437/1000
In this case, 437 is a prime number
So
73.437= 74 437/1000
PLZ HELP ASAP!! (Algebra)
Answer:
the relation is a function since one input provides us with only one output
outputs are the range since we know that range is the set of all possible outcomes
solve this equation x-3=4
Answer:
x-3= 4
x= 4+3
Answer: x= 7
Answer:
x=7
Step-by-step explanation:
x-3=4
Adding 4on both sides
x-3+3=4+3
x=7
Hope it will help you :)
For the scale factor n = 3, select a line segment other than LK that is not a vertical or horizontal line segment. Next, compute the slope m of your
line segment in the preimage and the image using the slope formula m= Show your work.
Answer:
Plato
Step-by-step explanation:
The line segment chosen is HI. Its image is H'I'. The slope of preimage HI is -1.25 and the slope of the image H'I' is -1.25.
What is the scale factor?The Scale Factor is used to scale shapes in different dimensions. We study different geometrical shapes in geometry, both two-dimensional and three-dimensional. The scale factor is a metric for comparing figures with similar appearances but differing scales or metrics.
What are images and preimages?The image of a transformation is the shape after the transformation. The preimage of a transformation is the shape before the transformation. The image is scale factor times preimage.
How do we determine the slope of a line?A line passing through the points (x₁, y₁) and (x₂, y₂) will have a slope
m = (y₂ - y₁)/(x₂ - x₁).
How do we solve the given question?We are asked to select a line segment other than LK, which is not a vertical or horizontal line segment, for the scale factor n = 3.
So, we have to select a preimage( other than LK), and its image (3 times the preimage).
So we select the preimage as HI and its image as H'I', as the scale factor between them is n = 3, and HI is not a vertical or horizontal line segment.
Now, we calculate their slopes.
For the preimage HI (slope is m₁):
HI passes through the points (2, 0) and (0, 2.5). Substituting these values in the slope formula, we get
m₁ = (2.5-0)/(0-2) = -2.5/2 = -1.25.
For the image H'I' (slope is m₂):
HI passes through the points (6, 0) and (0, 7.5). Substituting these values in the slope formula, we get
m₂ = (7.5-0)/(0-6) = -7.5/6 = -1.25.
∴ The line segment chosen is HI. Its image is H'I'. The slope of preimage HI is -1.25 and the slope of the image H'I' is -1.25.
NOTE: The slopes of images and preimages are always the same as the image is just an enlarged or diminished form of the preimage.
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