Answers
Answer:
Step-by-step explanation:
9x^3,15x^5= 3x^3
The GCF is constructed by multiplying all the factors that are common to all the given expressions, exponentiated to the smallest power.
In our example, the following factors are common to all the given expressions: 3, x^3
Therefore, the GCF is equal to 3x^3.
Related Questions
A line passes through the given points. Write an equation for the line in point-slope form. Then rewrite the equation in slope-intercept form. (4, –2), (9, –8)
Answers
Answer:
Step-by-step explanation:
(-8+2)/(9-4)= -6/5
y + 2 = -6/5(x - 4)
y + 10/5 = -6/5x + 24/5
y = -6/5x + 14/5
Barbara Cusumano worked 60 hours last week. Of those hours, 40 hours were paid at the regular-time rate of $12.50 an hour, 18 hours at the time-and-a-half rate, and 2 hours at the double-time rate. What was Barbara's gross pay for the week?
Answers
Answer:
$887.50
Step-by-step explanation:
Her gross pay is the sum of the pay amounts for each of the hour amounts:
pay = 40(12.50) +18(12.50)(1.5) +2(12.50)(2)
= (12.50)(40 +18(1.5) +2(2)) = 12.50(40 +27 +4) = 12.50(71)
pay = 887.50
Barbara's gross pay for the week was $887.50.
The length and width of a book cover are 22.2 centimeters and 12 centimeters respectively. The actual length (and width) can be 0.3 unit less than the measured length (and width) or 0.3 unit greater than the measured length (and width). a. Find the minimum and maximum possible lengths and widths of the book cover. b. Calculate the minimum and maximum possible areas of the book cover.
Answers
Part (a)
The length is supposed to be 22.2 cm, but it could be 0.3 cm less
So 22.2 - 0.3 = 21.9 cm is the smallest value for the length. This is the lower bound of the length.
The upper bound is 22.2 + 0.3 = 22.5 cm as it is the largest the length can get.
-------------
Use this for the width as well
The width is supposed to be 12 cm, but it could be as small as 12-0.3 = 11.7 cm and as large as 12+0.3 = 12.3 cm
-------------
Answers:smallest length = 21.9 cmlargest length = 22.5 cmsmallest width = 11.7 cmlargest width = 12.3 cm============================================
Part (b)
Use the smallest length and width to get the smallest possible area
smallest area = (smallest width)*(smallest length) = 11.7*21.9 = 256.23
-------------
Repeat the same idea but for the largest length and width to get the largest possible area
largest area = (largest width)*(largest length) = 12.3*22.5 = 276.75
-------------
Answers:smallest area = 256.23 square cmlargest area = 276.75 square cmDrag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match each angle measure in degrees with its equivalent measure in radians.
Answers
Answer:
315° = 7π/4 rad80° = 4π/9 rad225° = 5π/4 rad324° = 9π/5 radStep-by-step explanation:
Find the attachment in the diagram below,
In order to get the right match, we will use the conversion
180° = πrad
- For angle 315°;
If 180° = πrad
315° = a
Cross multiplying
180a = 315π rad
a = 315π rad/180
a = 63π/36 rad
a = 7π/4 rad
Hence 315° = 7π/4 rad
- For angle 80°;
If 180° = πrad
80° = b
Cross multiplying
180b = 80π rad
b = 80π rad/180
b = 8π/18 rad
b = 4π/9 rad
Hence, 80° = 4π/9 rad
- For angle 225°;
If 180° = πrad
225° = c
Cross multiplying
180c = 225π rad
c = 225π rad/180
c = 15π/12 rad
c = 5π/4 rad
Hence, 225° = 5π/4 rad
- For angle 324°;
If 180° = πrad
324° = d
Cross multiplying
180d = 8324π rad
d = 324π rad/180
d = 27π/15 rad
d = 9π/5 rad
Hence, 324° = 9π/5 rad
Find the area of quadrilateral...
Answers
Answer:
Total area = 29.8 sq. units
Step-by-step explanation:
area of each triangle = sqrt(s * (s-a) * (s-b) * (s-c))
to get the value of s, use the semi-perimeter = s = perimeter / 2
Total area = area of triangle ABD + area of triangle ACD
semi-perimeter of ABD = (3.48 + 8.66 + 8.6) / 2 = 10.37
semi-perimeter of ABD = (3.54 + 8.84 + 8.6) / 2 = 10.49
area of triangle ABD = sqrt(10.37 * (10.37-3.48) * (10.37-8.66) * (10.37-8.6))
area of triangle ABD = 14.7 sq. units
area of triangle ACD = sqrt(10.49 * (10.49-3.54) * (10.49-8.84) * (10.49-8.6))
area of triangle ACD = 15.08
Total area = 14.7 + 15.1
Total area = 29.8 sq. units
Which statement best illustrates using the vertical line test to determine if the graph below is a function of x? The graph is not a function of x because the line x = 0 intersects the graph at two points. The graph is a function of x because the line x = 5 does not intersect the graph. The graph is not a function of x because the line y = 0 intersects the graph at two points. The graph is a function of x because the line y = 5 does not intersect the graph.
Answers
Answer:
The graph is not a function of x because the line x = 0 intersects the graph at two points.
Step-by-step explanation:
This graph is not a function because it fails the vertical line test, since several vertical lines would intersect the graph at 2 points.
This answer choice is correct, as the line x = 0 intersects the graph at 2 points, (0, 2) and (0, -2).
Answer:
A
Step-by-step explanation:
Use the drawing tool(s) to form the correct answer on the provided graph. The function f(x) is shown on the provided graph. Graph the result of the following transformation on f(x). f(x) + 6
Answers
Answer:
[tex]f(x)=x+6 \\[/tex]
Step-by-step explanation:
The transformation is a translation 6 units up.
[tex]f(x)=x+6 \\[/tex]
We can use the parent function f(x)=x, which is a linear function to graph this function.
Then just translate the function 6 units up.
Answer:
on the x-axis to the left -1 and on the y-axis up 4
Step-by-step explanation:
Start from the -2 on the y-axis and go up on the y-axis 6 times and you should be at 4 on the y-axis. But to finish the problem you have to figure out the first line.
To do that start from the -2 on the y-axis then count up till its on a corner in the graph (rise 4 up on the y-axis then to the right once) so the fraction is 4/1
so rise 6 on the y-axis, you should be at 4 then use the formula rise/run 4/1
step 1 go up 6 times y-axis
step 2 use 4/1 rise from the 4 on the y-axis the run 1 to the right
It was 100% when I did it
Musah stands at the center of a rectangular field.He takes 50 steps north,then 25 steps West and finally 50 on a bearing of 315°. Sketch Musah's movement How far west is Musah's final point from the center? How far north is Musah's final point from the center?
Answers
Answer:
The distance of Musah's final point from the center in the west direction is 60.355 steps
The distance of Musah's final point from the center in the north direction is 85.355 steps
Step-by-step explanation:
Given that :
Musah stands at the center of a rectangular field.
He takes 50 steps north, then 25 steps West and finally 50 on a bearing of 315°.
The sketch for Musah's movement is seen in the attached file below.
How far west is Musah's final point from the centre?
In order to determine how far west is Musah's,
Let d be the distance of how far west;
Then d = BC + CD cos θ
In the North West direction,
cos θ = cos 45°
d = 25 + 50( cos 45°)
d = 25 + 50([tex]\dfrac{1}{\sqrt{2}}[/tex] )
d = 25 + 50( 0.7071)
d =25 + 35.355
d = 60.355 steps
How far north is Musah's final point from the center?
Let d₁ be the distance of how far North;
Then d₁ = AB + CD sin θ
d₁ = 50 + 50 sin 45°
d₁ = 50 + 50([tex]\dfrac{1}{\sqrt{2}}[/tex] )
d₁ = 50 + 50( 0.7071)
d₁ = 50 + 35.355
d₁ = 85.355 steps
A study found that the expected annual income in a certain area is $17,255. Which of the following statistical measurements most likely led to this conclusion? Mean, range, median or mode?
Answers
Answer:
Mean
Step-by-step explanation:
mean is the average of numbers put together and divided by the total amount of numbers, when finding the average annual income using the mean would be most effective
PLEASE ANSWER QUICKLY ASAP
READ THE QUESTION CAREFULLY PLEASE
Answers
Answer:
140°
Step-by-step explanation:
total angle of a hexagon is 720. We know already 510°. That leaves 210°. The ratio between the two angles is 2:1, therefore angle CDE is 140° and angle DEF is 70 °
Answer:
140°
Step-by-step explanation:
We know that all of these angles here are part of a hexagon, meaning that their angle measures will all add up to 720°.
We can use what we already know and find what CDE and DEF will add up to.
[tex]145+90+160+115=510\\720-510=210[/tex]
Now, assuming x is the measure of DEF, we can create an equation for this.
[tex]x + 2x = 210\\3x = 210\\x = 70[/tex]
This is the measure of DEF, but it asks for CDE, which is twice the size of DEF. So
[tex]70\cdot2=140[/tex]
We can double check this is right by adding up all the measures.
[tex]145+90+160+115+140+70=720[/tex]
Hope this helped!
Complete the statements. f(4) is . f(x) = 4 when x is
Answers
Answer:
x=4
Step-by-step explanation:
it's a identity function because it is in the form of f(x)= x ,so the value of x is 4.
Please help me with this problem. I will give brainliest!
Answers
Answer:
centre = (11, 0 ), radius = 3
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - h)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
(x - 11)² + y² = 9 ← in standard form
with (h, k ) = (11, 0 ) and r² = 9 ⇒ r = [tex]\sqrt{9}[/tex] = 3
centre = (11, 0 ) and r = 3
Combine the radicals. 3√5-8√5+2√5
Answers
Answer: [tex]-3\sqrt{5}[/tex]
-3 times the square root of 5
=============================================
Explanation:
Let [tex]x = \sqrt{5}[/tex]
Replace all the root 5 terms with x and we go from
[tex]3\sqrt{5}-8\sqrt{5}+2\sqrt{5}[/tex]
to
[tex]3x-8x+2x[/tex]
From here, combine like terms to get
[tex]3x-8x+2x = -5x+2x = -3x[/tex]
and the last thing to do is replace the x with sqrt(5)
[tex]-3x = -3\sqrt{5}[/tex]
Meaning that,
[tex]3x-8x+2x = -3x[/tex]
[tex]3\sqrt{5}-8\sqrt{5}+2\sqrt{5} = -3\sqrt{5}[/tex]
Just need to calculate the area of the shaded region, thanks
Answers
Answer:
Area of the shaded region= 82.2 cm²
Step-by-step explanation:
Please see attached picture for full solution.
Which of the following describe an angle with a vertex at A?
Check all that apply.
OA. ZABC
B. ZCAB
C. ZACB
D. ZBAC
Answers
Answer:
D) BAC is the correct answer as A is at the middle.
All of the options describe an angle with a vertex at A.
What is a vertex?In geometry, a vertex is a point where two or more lines, curves, or edges meet to form an angle or a corner.
It is the common endpoint of two or more rays, line segments, or sides of a polygon.
We have,
All of the options describe an angle with a vertex at A.
In each option, A is the vertex of the angle.
The letters that come before and after A indicate the other two points that form the angle. So:
∠ABC is an angle with vertex A and points B and C on either side.
∠CAB is an angle with vertex A and points C and B on either side. (Note that the order of the letters is reversed from option A.)
∠ACB is an angle with vertex A and points C and B on either side. (Note that the order of the letters is reversed from option B.)
∠BAC is an angle with vertex A and points B and C on either side. (Note that the letters are in a different order than option A.)
Thus,
All of the options describe an angle with a vertex at A.
Learn more about vertex here:
https://brainly.com/question/30940247
#SPJ5
42. How many solutions does this system of
equations have?
3x + 4y= 7
-3x – 4y = 7
A) 0
B) 1
C) 2
D) Infinite
Answers
Answer:
[tex]\Large \boxed{\mathrm{A) \ 0 }}[/tex]
Step-by-step explanation:
3x + 4y = 7
-3x - 4y = 7
Add both equations.
0x + 0y = 14
0 = 14
There are no solutions.
Answer:
A) 0
Step-by-step explanation:
Adding both equations.
0 + 0 = 14
0 = 14 (no solutions)
The price of a stock decreased by 60 cents one week, decreased 10 cents the next week, and decreased another 20 cents the following week. What is the average change in the price of the stock over the three weeks? need to know right now ASAP!! –270 cents per week –90 cents per week –87 cents per week –30 cents per week
Answers
Hi there! Hopefully this helps!
----------------------------------------------------------------------------------------------------------
It decreased by 30 cents per week.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The average rate of change is calculated as:
the ratio of the sum of the change in the three weeks divided by the number of weeks. (The number of weeks being 3)
Rate of change = [tex]\frac{-60 -10 -20}{3}[/tex].
(-60 + -10 + -20 = -90). So, to simplify it:
[tex]\frac{-90}{3}[/tex] = -30
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Incase you are confused:
Since the average rate of change is negative, this means that the stock price has decreased.
when a watch is sold at ksh.126 a loss of x% is made if sold at ksh.154 aprofit of x%is realized .find the buying price
Answers
Answer:
ksh 140.
Step-by-step explanation:
when a watch is sold at ksh.126 a loss of x%. This can be summarised as follow:
Selling price (Sp) = ksh 126
Percentage loss = x%
Cost price (Cp) =?
Percentage loss = Cp – Sp/Cp x 100
x% = Cp – 126/Cp .......(1)
if sold at ksh.154 a profit of x% is realized. This can be summarised as follow:
Selling price (Sp) = ksh 154
Percentage gain = x%
Cost price (Cp) =?
Percentage gain = Sp – Cp/Cp x 100
x% = 154 – Cp/Cp..... (2)
Equating equation 1 and 2, we have:
x% = Cp – 126/Cp .......(1)
x% = 154 – Cp/Cp..... (2)
Cp – 126/Cp = 154 – Cp/Cp
Cross multiply
Cp(Cp – 126) = Cp(154 – Cp)
Cancel out Cp
Cp – 126 = 154 – Cp
Collect like terms
Cp + Cp = 154 + 126
2Cp = 280
Divide both side by 2
Cp = 280/2
Cp = 140
Therefore, the cost price otherwise known as the buying price is ksh 140.
In a given set of data, if the variance is 25, what is the standard deviation? *
Answers
Explanation: apply the square root to the variance to get the standard deviation
standard deviation = sqrt(variance)
variance = (standard deviation)^2
Based on the variance of the set of data and the definition of standard deviation, the standard deviation here must be 5.
Standard deviation allows us to measure how far apart variables are in a data set.
It is calculated as:
= √Variance
= √25
= 5
In conclusion, the standard deviation is 5 .
Find out more at https://brainly.com/question/14283696.
If Ab = 54, find MC.
Answers
Answer:
MC = 45
Step-by-step explanation:
Δ ABH and Δ MCH are similar and the ratios of corresponding sides are equal, that is
[tex]\frac{AB}{MC}[/tex] = [tex]\frac{AH}{MH}[/tex] , substitute values
[tex]\frac{54}{MC}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )
6MC = 270 ( divide both sides by 6 )
MC = 45
what is (a x b) x c, if a = 11, b = 9, and c = 1? PLEASE HELP!!!
Answers
Answer:99
Step-by-step explanation:(11×9)×1=99
Answer:
The answer is 99Step-by-step explanation:
(a x b) x c
a = 11, b = 9, and c = 1
In order to solve substitute the values of a , b and c into the above expression
That's
( 11 × 9) × 1
Solve the terms in the bracket first
99 × 1
We have the final answer as
99Hope this helps you
2. Which of the following number is divisible by 6?
O. A. 672
O B. 813
O C. 7312
O D. 1234
Answers
Answer:
A - 672
Step-by-step explanation:
Any number divisible by both 3 and 2 is divisible by 6.
in triangle ABC A-B= 15 degree, B-C= 30 degree find A,B,C
Answers
Answer:
A=80 , B=65, C=35
Step-by-step explanation:
A-B=15 ⇒A=B+15
B-C=30⇒-C=30-B ⇒C=B-30
the sum of angle of a triangle = 180
A+B+C=180 ( substitute A and C)
B+15+B+B-30=180
3B-15=180
3B=180+15
B=195/3=65
C=B-30 ⇒ C=65-30=35
A=B+15=65+15=80
check : A+B+C=180
80+65+35=180 ( correct)
Shireen starts from 100 and writes a series of numbers in which EACH NUMBER IS 4 MORE THAN THE NUMBER AFTER IT. Shireen's series will be A.100, 104, 108, 112, B.100, 104, 100, 104, C.100, 96, 92, 88, D.100, 400, 800, 1200,
Answers
Answer:C. 100, 96, 94, 90.
Step-by-step explanation:
If shireen starts at 100, and if the number is 4 more than the number after it. You must subtract 4 to the previous number to get the next number.
So= 100-4= 96
= 96-4= 94
=94-4 = 90
ANSWER IS= 100, 96, 94, 90, etc....
I hope this helps!
BRAINLIEST!!
Factor completely 16x2 + 40x + 25. (4x − 5)(4x − 5) (2x − 5)(2x − 5) (2x + 5)(2x + 5) (4x + 5)(4x + 5) And this one please!
Select the polynomial that is a perfect square trinomial. 36x2 − 4x + 16 16x2 − 8x + 36 25x2 + 9x + 4 4x2 + 20x + 25
Answers
Answer:
(4x + 5)²
4x² + 20x + 25
Step-by-step explanation:
Step 1: Factor 16x² + 40x + 25
(4x + __)(4x + __)
What multiplies to 25 and adds up to 40 with 4 multiplied as coefficient?
(4x + 5)(4x + 5) or (4x + 5)²
Step 2: Factor perfect square trinomial
36x² - 4x + 16 --> 4(9x² - x + 4) No
16x² - 8x + 36 --> 4(4x² - 2x + 9) No
25x² +9x + 4 --> 25x² + 9x + 4 No
4x² + 20x + 25 --> (2x + 5)(2x + 5) or (2x + 5)² Yes
Answer:
(4x + 5)(4x + 5).
4x^2 + 20x + 25.
Step-by-step explanation:
16x^2 + 40x + 25
= (4x + 5)(4x + 5)
= (4x + 5)^2.
36x^2 − 4x + 16: To be a perfect square trinomial, the factors would have to be (6x + 4) or (6x - 4). Since the value of b is only -4, this is NOT a perfect square trinomial.
16x^2 − 8x + 36: To be a perfect square, factors would have to be (4x + 6) or (4x - 6). Since the value of b is only -4, this is NOT a perfect square.
25x^2 + 9x + 4: To be a perfect square, factors have to be (5x + 2) or (5x - 2). Since b is positive, factors would be (5x + 2)(5x + 2) = 25x^2 + 20x + 4. 20x is not equal to 9x, so this is NOT a perfect square.
4x^2 + 20x + 25: Perfect square would have to have factors (2x + 5) or (2x - 5). b is positive, so factors are (2x + 5)(2x + 5) = 4x^2 + 10x + 10x + 25 = 4x^2 + 20x + 25. This IS a perfect square!
Hope this helps!
How many significant figures does each value contain? 5.6803 kg has significant figures. 0.00047 seconds has significant figures. 0.240 miles has significant figures.
Answers
Answer:
5.6803 has five significant figures.
0.00047 has two significant figures.
0.240 has three significant figures.
What are Significant Figures?Significant figures are numbers that are necessary to express a true value.
Place the values in scientific notation.
[tex]5.6803 * 10^{0} = 5.6803\\\\4.7 * 10^{-4} = 0.00047\\\\2.4 * 10^{-1}=0.240[/tex]
Explanation5.6803
The zero that is within 5.6803 is "trapped," meaning it is in between two nonzero digits. Therefore, all five digits are significant figures.
This answer is also already in scientific notation because 5.6803 satisfies the inequality [tex]1 < x < 10[/tex], which decides if a number is correctly written in scientific notation or not.
0.00047
The zeroes that precede the 4 and the 7 are not significant because they are dropped in scientific notation and are not trapped by other nonzero digits. Therefore, only two digits of this value are significant.
0.240
Since the zero at the end of 0.240 is a trailing zero, it is significant along with the 2 and the 4. The zero that precedes these digits and the decimal point is not significant. Therefore, only three digits of this value are significant.
Therefore:
5.6803 has five significant figures.
0.00047 has two significant figures.
0.240 has three significant figures.
waht is the gcf of 4x^5 + 7x^3
Answers
Answer:
Step-by-step explanation:
4x^5 + 7x^3
x^3(4x^2 + 7)
The GCF is x^3
s
If point C is between points A and B and AB = 41, AC = 5x, BC = 3x – 7,
what is the value of x?
I NEED HELP ASAP
Answers
Answer:
x=6
Step-by-step explanation:
We know that point C is in the middle of point A and point B.
That means that when these two equations are added they should be equal to the length of AB which is 41.
5x+3x-7=41
add 7 to both sides
8x=48
divide both sides by 8.
x=6
If two of the ordered pairs was removed which two data points will cause the correlation to decrease the most? Select Two points
1) Data point A
2) Data point B
3) Data point C
4) Data point D
Answers
Answer:
1. Data point A
4. Data point D
Step-by-step explanation:
In a scatter plot, the closer the clustered data points are close to the best line of fit, the greater the correlation that would exist between the two variables.
If we are to draw a best line of fit in the scatter plot that is shown above, the closest data points amongst data points A, B, C, D, and E, that would be close to the best line of fit are data points A and D.
Therefore, removing data point A and point D would cause the correlation to decrease the most.
10. The probability of buying pizza for dinner is 34% and the probability of buying
a new car is 15%. The probability of buying a new car given that you eat pizza for
dinner is 42%. What is the probability of eating pizza for dinner given that they
buy a new car?
Answers
Answer:
The probability of eating pizza given that a new car is bought is 0.952
Step-by-step explanation:
This kind of problem can be solved using Baye’s theorem of conditional probability.
Let A be the event of eating pizza( same as buying pizza)
while B is the event of buying a new car
P(A) = 34% = 0.34
P(B) = 15% = 15/100 = 0.15
P(B|A) = 42% = 0.42
P(B|A) = P(BnA)/P(A)
0.42 = P(BnA)/0.34
P(B n A) = 0.34 * 0.42 = 0.1428
Now, we want to calculate P(A|B)
Mathematically;
P(A|B = P(A n B)/P(B)
Kindly know that P(A n B) = P(B n A) = 0.1428
So P(A|B) = 0.1428/0.15
P(A|B) = 0.952
