To eliminate the biggest common factor, use the distributive property: Solution: 16 + 36 = 4 (4 + 9)
To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Due to that,
To remove the most significant common factor, we must use the distributive property.
Given expression:16 + 36
1, 2, 4, 8, and 16 make up the number 16.
1, 2, 3, 4, 6, 9, 12, 18, and 36 make up the number 36.
Then, 4 is the most prevalent component.
distributed property
The formula is ab + bc
subtracting 4 from the supplied expression.
Therefore, the distributive property is used.
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What is the axis of symmetry and vertex for the function f(x)=3(x-2)^2+4?
Answer:
Axis of symmetry: x = 2
Vertex: (2,4)
Step-by-step explanation:
helpp. The Eiffel Tower in Paris, France is 1063 feet tall. If you took an elevator 3/4 the way up the tower, how far from the ground would you be in feet?
If the Height of Eiffel Tower in Paris is 1063 feet tall and we took an elevator 3/4 up the tower then we would be 797.25 feet from the ground.
Given The height of the Eiffel Tower is 1063 feet tall. We have taken an elevator that is 3/4 up the tower.
Height is the measurement of someone from head to foot or from base to top. It is the distance upward.
Height of The Eiffel tower is 1063 feet.
We have taken 3/4 up the elevator.
Then the height from ground to us can be calculated by multiplying 1063 by 3/4 which will be as under:
=1063*3/4
=729.25 feet
Hence if the height of the Eiffel Tower is 1063 feet then we would be 729.25 up from the ground if we have taken elevator 3/4 up the tower.
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At what values of x, does f(x) = 0?
a. 0
b. -1
c. -8
d. 4.2
e. 4
f. 2
Answer:
B E F
Step-by-step explanation:
as the graphic shows, f(x) = 0 means that the y value is 0. and that means these are the points, where the curve intersects the x-axis.
they are already marked in the graphic :
for x = -1, 2, 4
Which phrase best describes the translation from the graph y = (x – 5)2 + 7 to the graph of y = (x + 1)2 – 2?
The parent. function shifted up by 6 units to produce x + 1 and to the left by 9 units
What is translation?This is a way of changing the position of an object on an xy-plane.
Given the parent function expressed as y = (x – 5)^2 + 7
From the resulting image after translation, we can see that the parent. function shifted up by 6 units to produce x + 1 and to the left by 9 units
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What is the recursive formula for the geometric sequence with this explicit formula?
For the given geometric sequence, we have:
[tex]a_1 = 9\\\\a_n = (-1/3)*a_{n-1}[/tex]
So the correct option is B.
Which is the recursive formula?Here we have the geometric sequence:
[tex]a_n = 9*(-\frac{1}{3} )^{(n - 1)}[/tex]
To get the initial value of the geometric sequence, we just need to replace n by 1, so we get:
[tex]a_1 = 9*(-\frac{1}{3} )*(1 - 1) = 9[/tex]
Now, notice that the common ratio is (-1/3), this means that each term of the sequence is (-1/3) times the previous term.
[tex]a_n = (-1/3)*a_{n-1}[/tex]
Then the correct option is B.
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One car travels 30 meters east in 5 seconds. A second car travels 42 meters west in 7 seconds. During their respective periods of travel, the cars must have had the same _______________.
The cars must have had the same Average Speed
Average speed is the mean value of the speed of a body over a period of time. The formula for average speed is needed since the speed of a moving body is not constant and varies across a period of time. Even with varying speed, the values of total time and the total distance covered can be used, and with the help of the formula for average speed, we can find a single value to represent the entire motion.
The average speed of a body is equal to the total distance covered, divided by the total time taken. The formula for average speed is given as:
[tex]\frac{Total distance covered by the object}{Total time taken}[/tex]
Given :-
Distance covered by A = 30 metersTime taken by A = 5 secondsDistance covered by B = 42 metersTime taken by B = 6 secondsSubstituting the given values in the formula for A and B respectively we get
Average Speed of A = [tex]\frac{30}{5}[/tex] m/s = 6 m/s
Average Speed of B = [tex]\frac{42}{7}[/tex] m/s = 6m/s
Thus the cars must have had the same Average Speed.
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Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 21st, 26th, 65th, and 75th percentiles. If needed, round your answers to two decimal digits. Percentile Value 21% 26% 65% 75%
The the 21st, 26th, 65th, and 75th percentiles are 19.45, 21.7, 27.85, and 29.50.
How to compute the percentile?Here, n=8
P21=(21(n+1)100)th value of the observation
=(21⋅9/100)th value of the observation
=1st observation +0.89[2nd-1st]
=15+0.89[20-15
= 19.45
P26 = (26(n+1)100)th value of the observation
=(26⋅9/100)th value of the observation
=2nd observation +0.34[3rd-2nd]
=20+0.34[25-20]
=20+0.34(5)
= 21.7
P65= (65(n+1)100)th value of the observation
=(65⋅9/100)th value of the observation
=5th observation +0.85[6th-5th]
=27+0.85[28-27
= 27.85
P75 = (75(n+1)100)th value of the observation
=(75⋅9/100)th value of the observation
6th observation +0.75[7th-6th]
=28+0.75[30-28]
= 28 + 1.50
= 29.50
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4/15 divided by 1 1/3 + 0.4
Answer: 2/13
Step-by-step explanation:
To solve this word problem expression, we can first convert the mixed number to an improper fraction so it's easier to work with.
1 1/3 = 4/3
Adding 4/3 to 0.4, we get 5.2/3.
4/15 divided by 5.2/3 is 4/26, or 2/13
Sarah received scores of 85, 92 and 78 on her first three exams of the grading period. What is the lowest score Sarah can earn on the next exam for the exam average to be at least a 87 for the grading period.
The storage container below is in the shape of a rectangular prism with a height of 6 feet and a length that is 2 feet more than its width.
Recall that the formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height.
Write the equation that represents the volume of the storage container in terms of its width.
The equation that represents the volume of the storage container(rectangular prism) in terms of its width is 12w + 6w²
How to find the volume of a rectangular prism?volume of a rectangular prism = lwh
where
l = lengthw = widthh = heightTherefore,
h = 6 ft
l = 2 + w
Hence,
volume of the rectangular prism = (2 + w) × w × 6
volume of the rectangular prism = (2w + w²)6
volume of the rectangular prism = 12w + 6w²
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1.
a) Carol and Conrad together have less than $50. Carol has $10 more than Conrad how much money might Conrad have.
b) How much money might Carol have
Simplify by factoring or distributing:
1.) 2(x + 3) =
2.) 2(x + 3 + y) =
3.) −5 (2x − 3) =
4.) –5(–8w + p) =
5.) 20 + 32w =
6.) 84 + 36z =
7.) (2x - 6)(5x + 7) =
8.) (y - 10)(4y + 2) =
The following equation simplified by factoring or distributing:
2x + 62x + 6 + 2y-10x + 1540w - 5p4(5 + 8w)12(7 + 3z)12(7 + 3z)4y² - 38y - 20Factorization1.) 2(x + 3)
= 2x + 6
2.) 2(x + 3 + y)
= 2x + 6 + 2y
3.) −5 (2x − 3)
= -10x + 15
4.) –5(–8w + p)
= 40w - 5p
5.) 20 + 32w
= 4(5 + 8w)
6.) 84 + 36z
= 12(7 + 3z)
7.) (2x - 6)(5x + 7)
= 10x² + 14x - 30x - 42
= 10x² - 16x - 42
8.) (y - 10)(4y + 2)
= 4y² + 2y - 40y - 20
= 4y² - 38y - 20
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Subtract 6x^{2}-7x-2 from 6x^{2}-2x+6
Hello!
Let's subtract!
⇒ 6x² - 2x + 6 - (6x² - 7x - 2)
⇒ 6x² - 2x + 6 - 6x² + 7x + 2
⇒ 5x + 8
∴ The difference will be equal to 5x + 8.
Answer:
Your answer is 5x+8
Step-by-step explanation:
= 6x^2-2x+6 - (6x^2-7x-2)
= 6x^2-2x+6 - 6x^2+7x+2
= 6x^2- 6x^2-2x+7x+6+2
=5x+8
Hope its helpful!
Find the measure of the exterior angle.
Answer:
The exterior angle is 77
Step-by-step explanation:
The measure of the exterior angle of a triangle is equal to the sum of the two opposite interior angles.
2x+11 = x +44
First we need to find x
Subtract x from each side
2x+11-x = x+44
x +11 = 44
Subtract 11 from each side
x+11-11 = 44-11
x =33
Now we can find the exterior angle
2x+11 = 2(33)+11 = 66+11 = 77
The exterior angle is 77
someone please please help me with this !!
9) The x-intercepts are when y=0. From the factored form, we know the x-intercepts are (-1,0) and (3,0).
10) The y-intercept is when x=0. From the standard form, we know the y-intercept is (0, -3).
Jeremy left the house in the morning and the temperature outside was 2 degrees Celcius. Once he returned at night, the temperature was -7 degrees Celcius.
How much did the temperature decrease by?
Answer:
The temperature decreased by 9 degrees.
Step-by-step explanation:
Since the temperature in the morning was 2*C & at night, the temperature was -7*C, the temperature had to decrease using this equation => ||-7 + 2|| = x, with -2 being the temperature loss added as well. All we have to do is 7+2 = x & 9 = x, with x being the temperature drop.
Answer:
9 degrees Celcius
Step-by-step explanation:
The difference between 2 and -7 is 9.
The completed construction of regular hexagon is shown below explain why act is a 30-60-90 triangle
In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg and length of the hypotenuse is twice the length of the shorter leg.
How to explain the reasonACF is a 30º-60º-90º triangle because of the following reasons;
Based on a theorem, in a 30°-60°-90° triangle, it is said that the length of the longer leg is √3 times the length of the shorter leg and length of the hypotenuse is twice the length of the shorter leg,
1 → short leg = 1
2 → hypotenuse = 2
√3 → long leg = √3
Using the Pythagorean theorem., we have that
a² + b² = c²
1² + b² = 2²
b² = 2² - 1²
b² = 4 - 1
b² = 3
√b² = √3
b = √3
Thus, in a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg and length of the hypotenuse is twice the length of the shorter leg.
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The graph of F(x), shown below, has the same shape as the graph of G(x) =
x², but it is shifted to the left 2 units. What is its equation?
F(x)=_
5
A. F(x)=x²+2
B. F(x)=x²-2
C. F(x) = (x-2)²
OD. F(x) = (x + 2)²
Answer: D
Step-by-step explanation:
See attached image.
To solve -3 = -19 + d/5, what steps would you use?
19 add divide multiply subtract
5 add divide multiply subtract
To solve the expression, the steps are add 19 and multiply by 5
How to solve the expressionGiven the equation;
-3 = -19 + d/5
First,
Collect like terms
-3+ 19 = d/5
Add the values on the left side
We have
16 = d/5
Cross multiply
16 × 5 = d
We then have
d = 80
Thus, to solve the expression, the steps are add 19 and multiply by 5
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Please Help Asap!!! I would really appreciate it
Using the given exponential function, it is found that the colony would have 852 bacteria after 10 days.
What is the exponential function?The exponential function for the colonies' size is given as follows:
[tex]F = I(1 + r)^t[/tex]
In which:
I is the initial amount.r is the growth rate.t is the number of time periods.The parameters are given as follows:
I = 55, r = 0.73, t = 5, as 10/2 = 5.
Hence the amount will be given by:
[tex]F = 55(1 + 0.73)^5 = 852[/tex]
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Which statistic is used to determine if there is a significant difference between three or more sets of related scores
The t-test is a type of inference statistic used to determine if there is a significant difference between the means of two groups that may be related to a particular characteristic. The t-test is one of many tests used to test statistical hypotheses.
Inference statistics have two main purposes. Estimates for population groups (for example, the average SAT score for all 11th graders in the United States). Hypothesis testing to draw inferences about the population
One-way ANOVA is a common method for comparing three or more group means. The usual goal is to determine if the mean (or median) of at least one group is different from the other. Subsequent multiple comparison tests are often used to determine where differences occur.
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What is the scale factor from ABC to ADEF?
5
A 3 C
D
15
OA. 2
OB. 3
OC. 3
OD. 1/1/20
E
12
Answer:
OB
Step-by-step explanation:
no clear explanation for this answer. a picture to demonstrate how i archived it will be shared
The scale factor from triangle ABC to DEF would be,
⇒ 1 / 3
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
Two triangle ABC and DEF is shown in figure.
Hence, We can formulate;
The scale factor from triangle ABC to DEF would be,
⇒ AC / DF
⇒ 3 / 9
⇒ 1 / 3
Thus, The scale factor from triangle ABC to DEF would be,
⇒ 1 / 3
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I need help please..
What is the leading coefficient of the polynomial? 5x² + 8x³ +4 - 6x² – 3x5
Answer:
In polynomial function f(x) = 5x² + 2x³ + 4 the leading coefficient is 5.
The leading coefficient of a polynomial is the coefficient of the leading term 5x².
Step-by-step explanation:
The cost of advertising for a radio station is £50+£5 x broadcasting time in minutes use the graph to show the cost of advertising for broadcasting up to 10 minutes of the advert
A function assigns the values. The cost of advertising for 10 minutes will be equal to £100.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Let the number of minutes of advertising be represented by x, and the cost of advertising be represented by y.
Given the function through which the cost of advertising can be determined. Therefore, the cost of advertising for the 10 min program will be when the value of x is 10. Therefore, the cost of advertising for 10 mins will be £100.
Hence, the cost of advertising for 10 minutes will be equal to £100.
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Which of the following is an example of a combination?
A. Selecting the best cake and runner-up best cake from a cake
decorating competition
B. Selecting 5 CDs to take with you on a trip from a collection of 30
CDs
C. The number of orders in which 6 people can arrive at a party if no
one arrives at the same time
D. The number of orders in which triplets can be born
Explanation:
For choice A, order matters. This is because of the positions of first place and second place are different from one another. Since order matters, we have a permutation for choice A and can rule it out.
Choices C and D are ruled out for the same reason.
Choice B is a combination. It doesn't matter what the order of the CDs are. All that matters is the group overall rather than the individual CDs.
Consider functions f and g
Using successive approximation, what is the approximate solution to the equation f(x)= g(x)? Use the graph as a starting point
PLEASE THIS HAS A TIME LIMIT AND GIVE PROOF BECAUSE I REALLY NEED TO GET THIS RIGHT :((
25 POINTS AND WILL MARK BRAINLIEST
Answer:
1)D 2) Can't see the function
x^-4 for x=4
simplify this
Answer:
1/256
Step-by-step explanation:
4^-4 is the same thing as 1/4*1/4*1/4*1/4 which is 1/256
Answer:
1/256
Step-by-step explanation:
4⁻⁴ = 1/(4⁴) = 1/256
In the following exercises, multiply the binomials. Use any method.
247. (p + 12)(p − 5)
Answer:
Hence the expression [tex]$$(p+12)(p-5)=p^2+8p-60$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (p+12)(p-5).We have to multiply the given expression.Multiply the (p+12) by -5, multiply the (p+12) by p then add like terms.[tex]$$\frac{\begin{matrix}{} & {} & p & + & 12 \\ \times & {} & p & - & 5 \\ \end{matrix}}[/tex]
____________
[tex]{\frac{\begin{matrix}{} & - & 5p & - & 60 \\ {{p}^2} & + & 12p & {} & {} \\ \end{matrix}}{\begin{matrix}{{p}^2} & + & 8p & - & 60 \\ \end{matrix}}}$$[/tex]
A line passes through the point (8, -5) and has a slope of 5/4. Write an equation in point-slope form for this line.
ATTACHED IS THE SOLUTION!!