Answer:
3(3x - 7)
Step-by-step explanation:
9x - 21
GCF of 9 and 21 is 3
3(3x - 7)
I hope this helps!
Identify all of the functions below. { ( 5 , 1 ) , ( 2 , 2 ) , ( 6 , 6 ) , ( 3 , 4 ) , ( 1 , 1 ) } x y 7 3 0 5 1 3 5 5 3 0 { ( 5 , 1 ) , ( − 5 , 2 ) , ( 2 , 6 ) , ( 6 , 4 ) , ( − 2 , 1 ) } { ( 5 , 1 ) , ( 2 , 2 ) , ( 2 , 6 ) , ( 2 , 4 ) , ( 1 , 1 ) } { 3 , 5 , 9 , 7 , 7 } x y 2 3 2 5 1 3 8 2 5 0
The relations and tables that represent a function include the following:
A. {(5, 1), (2, 2), (6, 6), (3, 4), (1, 1)}.
B. x 7 3 0 5 1
y 3 5 5 3 0
C. {(5, 1), (−5, 2), (2, 6), (6, 4), (-2, 1)}.
What is a function?In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range).
In this context, the given relation {(5, 1), (2, 2), (2, 6), (2, 4), (1, 1)} is not considered as a function because it has the same input variable (domain) that is mapped to different output variable (range) i.e (2, 2) and (2, 6).
Additionally, the given relation {3, 5, 9, 7, 7} would be classified as a set and not a function.
In conclusion, the table shown below does not represent a function because the same input variable (domain) that is mapped to different output variable (range) i.e (2, 3) and (2, 2).
x 2 3 2 5 1
y 3 8 2 5 0
Read more on function here: brainly.com/question/3632175
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Given that events A and B are independent with P(A)=0.55 and P(B)=0.72P determine the value of P(A|Brounding to the nearest thousandth
What are all the zeros of the function f(x)= x^2 −x−56=0
The Solution.
The given function is
[tex]f(x)=x^2-x-56=0[/tex]Solving quadratically using the factorization method, we get
[tex]f(x)=x^2-8x+7x-56=0[/tex][tex]f(x)=x(x-8)+7(x-8)=0[/tex][tex](x+7)(x-8)=0[/tex][tex]\begin{gathered} x+7=0,\text{ or x -8 =0} \\ x=-7,\text{ or x = 8} \end{gathered}[/tex]Hence, the zeros of the function are -7 or 8
1 2 4 5 6 7 9 10 Write 3 and 2 fifths as an improper fraction and as a mixed number. 17 3 2 b. 15 2 3 5 13 3. 3 5. 2 5. 5. a. d. 17 5 Please select the best answer from the choices provided A С . D
To write three and two fifths
Solution:
Three is a whole number and two-fifths is a proper fraction
[tex]\begin{gathered} \text{Thr}ee\text{ = 3} \\ Two-fifths=\frac{2}{5} \\ \text{Thr}ee\text{ and two-fifths = 3}\frac{2}{5} \end{gathered}[/tex]Therefore, three and two-fifths as a mixed number is;
[tex]3\frac{2}{5}[/tex]As an improper fraction,
[tex]\begin{gathered} 3\frac{2}{5}=\frac{(5\times3)+2}{5} \\ =\frac{15+2}{5} \\ =\frac{17}{5} \end{gathered}[/tex]Therefore, three and two-fifths as an improper fraction is 17/5.
Th
Which best describes one way to show 1/3 shaded.
Draw a circle, cut into 3 equals parts and shade 1 part
The graph of the function()=1/ has origin symmetry as well as which of the following symmetries?A. y-axisB. x-axisC. y=x
We will graph a plot of this expression, we have:
[tex]undefined[/tex]The graph is neither symmetric to the x-axis nor the y-axis. Hence, y = x
12² × 5 + 5 .........
The solution to the given expression will be,
[tex]12^2\times5+5=144\times5+5=720+5=725[/tex]Find the slope and y-intercept write y-intercept as order pair
The slope and y-intercept of a line.
The equation of a line can be expressed as:
y = mx + b
Where m is the slope and b is the y-intercept. The slope of a line that passes through the points (x1,y1) and (x2,y2) is calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The figure shows a horizontal red line. We only need two points (or ordered pairs) to calculate the slope. Let's get them from the graph: (0,-5) and (2,-5).
Calculate the slope:
[tex]m=\frac{-5-(-5)}{2-0}=\frac{-5+5}{2}=0[/tex]The slope is 0.
The y-intercept, as shown in the equation of the line, is the value of y when x=0.
Looking at the graph, we can identify the value of y=-5 when x=0. In fact, y=-5 for any value of x.
Thus, the y-intercept as an ordered pair is (0,-5)
I need help with my math
Let's evaluate the point into the equation in order to check if it satisfies it.
[tex]\begin{gathered} y=4x+2;_{\text{ }}(2,10) \\ x=2,y=10 \\ so\colon \\ 10=4(2)+2=8+2=10 \\ 10=10 \\ This_{\text{ }}is_{\text{ }}true \end{gathered}[/tex]Therefore, the ordered pair is a solution to the equation
Rashad is having a picnic for 62 guests. He plans to serve each guest at least one hamburger. Ifeach package, p, contains eight hamburgers, wirte the inequality that could be used to determinehow many packages of hamburgers Rashad will need to buy.a. What are the key words and information needed to solve this problem? (2 points)b. Write the inequality that describes this situation. (2 points)C. How many packages of hamburgers will Rashad need to purchase to feed his guests? Work outthe problem, showing all of your work, including computation and explanation. (4 points)
a. What are the keywords and information needed to solve this problem?
The keywords are the words that allow us to solve the problem, So they are:
The picnic is for 62 guests
Each guest will receive at least 1 hamburger
Every package contains 8 hamburgers
b. Write the inequality that describes this situation.
Now, we can formulate an equation for the number of hamburgers H that each guest is going to receive if Radash buys p packages:
H = 8p/62
Because 8p is the number of total hamburgers and there are 62 guests.
Then, we know that H needs to be at least 1, so:
H ≥ 1
8p/62 ≥ 1
c. How many packages of hamburgers will Rashad need to purchase to feed his guests?
Then, we need to solve for p as:
Multiplying by 62 on both sides:
(8p/62)*62 ≥ 1 * 62
8p ≥ 62
Dividing by 8:
8p/8 ≥ 62/8
p ≥ 7.75
Therefore, Radash needs to buy at least 8 packages of hamburgers.
Answers:
a. The picnic is for 62 guests
Each guest will receive at least 1 hamburger
Every package contains 8 hamburgers
b. 8p/62 ≥ 1
c. At least 8 packages
you mix 1/2 cup of oats for every 1/4 cup of honey to make 12 cups of granol. How much oats and honey do you use?
Given that you mix 1/2 cup of oats for 1/4 cup of honey to make 12 cups of granol, we can write this as:
[tex]undefined[/tex]Multiply the following polynomials: i) (3x-8)•(4x+7)= ii) (4x + 7)² = iii) (3x –8)•(3x+8)=
Multiply the following polynomials;
(1)
[tex]\begin{gathered} (3x-8)\times(4x+7) \\ =(3x\times4x)+(3x\times7)-(8\times4x)-(8\times7) \\ =12x^2+21x-32x-56 \\ =12x^2-11x-56 \end{gathered}[/tex](2)
[tex]\begin{gathered} (4x+7)^2 \\ =(4x+7)(4x+7) \\ =(16x^2+28x+28x+49) \\ =16x^2+56x+49 \end{gathered}[/tex](3)
[tex]\begin{gathered} (3x-8)(3x+8) \\ =9x^2+24x-24x-64 \\ =9x^2+0-64 \\ 9x^2-64 \end{gathered}[/tex]what is the experimental probability of selecting the name Alex?
We can calculate the probability as the ratio between the positive outcomes (selecting Alex, in this case) and the total possible outcomes.
In one draw, Alex has a chance of 1 in 4, as only one of the four papers has his name on it.
The probability is 1/4 or 0.25.
(b)A sight-seeing ship is stopped in the water for an hour, miles from the shore. Then the captain heads the ship back to the shore at a constant rate. The ship docks at the shore for a while and then returns to the open sea.Choose the graph that gives the best representation.
We have the following information from the question:
• A sight-seeing ship is stopped in the water for an hour, miles from the shore.
,• Then the captain heads the ship back to the shore at a constant rate.
,• The ship docks at the shore for a while and then return to the open sea.
Then we have to choose the graph that best represents the situation.
To do this, we need to analyze the three situations separately by knowing that on the y-axis we have graphed a distance relative to the shore (dependent variable), and on the x-axis, we have the time as an independent variable:
1. A sight-seeing ship is stopped in the water for an hour, miles from the shore:
If we see this situation, we have to check a distance larger than zero at x = 0. Then we have to see a horizontal line for an hour since the ship is stopped in the water for an hour, and this is because the ship is stopped, and the ship remains in the same place for an hour.
2. Then the captain heads the ship back to the shore at a constant rate:
It means that the ship will shorten the distance with respect to the shore, and this will be verified at a constant rate. Then we need to check in the graph a segment with a negative slope.
3. The ship docks at the shore for a while and then return to the open sea:
We need to check on the graph that the distance from the shore will be zero, and then we will have a horizontal line since the ship will remain for a while in the shore. Then the ship will return to the open sea, and we will check that the distance to shore will increase constantly.
Therefore, the graph that gives the best representation is the second graph from the left, that is:
Therefore, in summary, the
A set of data items normally distributed with a mean of 60. Convert the data item to a z-score, if the data item is 47 and standard deviation is 13.
To answer this question, we need to remember what the z-score is. The formula for it is as follows:
[tex]z_{\text{scorre}}=\frac{x-\mu}{\sigma}[/tex]We have that:
• mu is the population mean
,• x is the raw score we want to normalize or convert into a z-score
,• sigma is the population standard deviation.
Then, since we have that the mean is equal to 60, the raw score, x, is equal to 47, and the standard deviation is 13, then, we have that the z-score is:
[tex]z_{\text{score}}=\frac{47-60}{13}=\frac{-13}{13}\Rightarrow z_{score}=-1[/tex]Then, the z-score is equal to -1. That is, x is one standard deviation below the population mean.
write an equation of the circle
Take into account that the general equation of a circle is given by:
(x - h)² + (y - k)² = r²
where h and k are the values of the coordinates of the point (h,k), which is the center of the circle in the coordinate system.
You can notice in the given image, that the center of the circle is the point (5,4), then, the values of k and h are:
h = 5
k = 4
moreover, you can notice that the radius of the circle is 4, then
r = 4
replace the values of h, k and r in the equation of a circle:
[tex]\begin{gathered} (x-5)^{2}+(y-4)^{2}=4^{2} \\ (x-5)^{2}+(y-4)^{2}=16 \end{gathered}[/tex]The last equation is the required expression for the equation of the given circle.
f(x) = x +4g(x) = 3x2 – 7Find (f .g)(x).A. (f-9)(x) = 3.73 – 28O B. (f.g)(x) = 3x2 + 12x2 – 7x - 28OC. (f.g)(x) = 3.r3 +28O D. (f.g)(x) = 3.7° + 12.2 - 72 +28
Recall that:
[tex](f\cdot g)(x)=f(x)\cdot g(x)\text{.}[/tex]Substituting f(x)=x+4 and g(x)=3x²-7 we get:
[tex]\begin{gathered} (f\cdot g)(x)=_{}(x+4)(3x^2-7), \\ (f\cdot g)(x)=3x^3-7x+12x^2-28, \\ (f\cdot g)(x)=3x^3+12x^2-7x-28. \end{gathered}[/tex]Answer: Option B.
What is the midpoint of the segment shown below?
-10
(-8,-7)
(-7,-8) -10-
10
OA (-15-15)
A.
O B. (-15,-15)
O C. (-15, -15)
OD. (-15, -15)
Remember that the formula to calculate the midpoint between two points is given by
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]substitute given coordinates
[tex]\begin{gathered} M(\frac{-8-7}{2},\frac{-7-8}{2}) \\ \\ M(-\frac{15}{2},-\frac{15}{2}) \end{gathered}[/tex]The answer is option BWhat is the LCM needed to find a common denominator for 5/6 + 3/8 quick
Answer:
Step-by-step explanation:
The lowest common denominator of 38 and 56 is 24. This allows us to convert the two fractions into 924 and 2024 for the purpose of adding and subtracting them.
The LCM is 24
Reason: 6*8/2 = 48/2 = 24
We multiply the denominators 6 and 8, then divide by 2 which is the GCF of the denominators.
Then we can use this to add the fractions
5/6 + 3/8
(5/6)*(4/4) + (3/8)*(3/3)
20/24 + 9/24
(20+9)/24
29/24
Therefore, 5/6 + 3/8 = 29/24
There are 39 fewer 2nd graders than 3rd graders. There are 67 2nd graders. How many 3rd graders are there?
ANSWER
106 3rd graders
EXPLANATION
Let the number of 2nd graders be x.
Let the number of 3rd graders be y.
We have that there are 39 fewer 2nd graders than 3rd graders. This means that:
x = y - 39
There are 67 2nd graders. This means that:
x = 67
This means that:
67 = y - 39
y = 67 + 39
y = 106
Therefore, there are 106 3rd graders.
area of the square is 81 square inches. length of one side is represented by X. what is the value of x?
The area of a square is given by:
[tex]A=l^2[/tex]Where:
l = length of one of its sides:
Since the area is 81, and the length of one of its sides is x, then:
[tex]81=x^2[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{81}=\sqrt[]{x^2} \\ 9=x \\ x=9 \end{gathered}[/tex]Determine the equation in slope intercept form
I need help with a algebra 1 testThe graph of linear f passes through the point (1,-9) and has a slope of -3what is the zero of fanswers are24-6-2
hello
to solve this question, we can simply use the equation of a slope on this
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ y=y-\text{coordinate} \\ x=x-\text{coordinate} \end{gathered}[/tex]now we can simply bring out our data and then proceed to input in and solve for c
[tex]\begin{gathered} y=mx+c \\ y=-9 \\ x=1 \\ m=-3 \\ y=mx+c \\ -9=-3(1)+c \\ -9+3=c \\ c=-6 \end{gathered}[/tex]from the calculations above, the answer to this question is -6 which corresponds to option c.
NB; the point at which is referred as the zero of a graph is known as the intercept. This is the point at which graph crosses the x-axis
Find the surface area of the pyramid. Round your answer to the nearest hundredth.
Okay, here we have this:
Considering the provided information, we are going to calculate the surface area of the pyramid, so we obtain the following:
Let's use the following formula to find the surface area:
Surface area=Area of the base+1/2*Perimeter of the base*Slant Height
Replacing:
Surface area=(12.2ft¨* 12.2 ft)+1/2 * (12.2 ft * 4) * 9.5ft
Surface area=148.84 ft² + 1/2 * 48.8 ft * 9.5 ft
Surface area=148.84 ft² + 231.8 ft²
Surface area=380.64 ft²
Finally we obtain that the correct answer is the first option.
can someone please help I've gone through 4 different teachers
a) see graph below
b) The coordinate of F" = (12/13, 0)
c) cos(D") = 12/13
sin(D") = 5/13
tan(D") = 5/12
Explanation:Given:
A triangle on a coordinate with the units on the vertical and horizontal axis unlabeled
To find:
To label the diagram D"E"F" and determine the coordinates of F"
To label the diagram, we will use the previous diagrams and solutions.
From the information given, the new diagram is similar to the triangle DEF
For similar triangles, the ratio of their corresponding sides will be equal. Also, the corresponding angles are also equal
This means D corresponds to D", E corresponds to E" and F corresponds to F"
labeling the diagram:
b) To get the coordinates of F', we will use the similarity theorem about ratio of corresponding sides:
we have the hypotenuse = 1
the adjacent or base = not given
To get the base, we will use cosine ratio (CAH)
cos D" = adj/hyp
let the adjacent = b
cosD" = b/1
From previous solution of cos D and cos D', the result was 12/13
equating the ratio:
[tex]\begin{gathered} cosD^{\prime}^{\prime}\text{ = }\frac{b}{1}\text{ } \\ cos\text{ D = 12/13} \\ cos\text{ D = cos D'' \lparen similarity theorem\rparen} \\ \frac{b}{1}\text{ = }\frac{12}{13} \\ b\text{ = 12/13} \end{gathered}[/tex]This means the x coordiante of E" = 12/13
Next, we will find the opposite
sin D" = opp/hyp
sinD'' = opp/1
sin D = 5/13
sin D = sin D" (similarity theorem)
[tex]\begin{gathered} \frac{5}{13}=\frac{opp}{1}\text{ } \\ opp\text{ = 5/13} \end{gathered}[/tex]The coordinates of D"E"F":
The coordinate of F" = (12/13, 0)
How: This was determined using the similarity theorem. Comparing the ratio of the corresponding sides of triangle DEF with triangle D"E"F".
cos(D") , sin(D") and tan(D") will have same value as cos (D), sin(D) and tan (D) respectively.
This is because they are similar triangles and the corresponding angles in similar triangles are equal
cos(D") = 12/13
sin(D") = 5/13
tan(D") = 5/12
What is the amplitude of the sine funtion y=2 sin(4x)
A. 4
B. 2
C. r/2
D. r/4
Answer:
it´s C
Step-by-step explanation: Just took the test trust
What is the m stand for in -3 = m-14
Step 1:
Write the equation
- 3 = m - 14
Step 2: Collect similar terms
- 3 = m - 14
m = -3 + 14
m = 11
Final answer
m = 11
The price of a toy is increased by 20%. The resulting price is later decreased by $40.00. If the original price of the toy is $60.00, what is the final price of the toy ?
Answer
Final price of the toy = $32.00
Explanation
The price of a toy is increased by 20%
The resulting price is then decreased by $40.00
Original Price = $60.00
The price of a toy is increased by 20%
Resulting price after this increase = 1.2 (60) = $72
The resulting price is then decreased by $40.00
Final Price = 72 - 40 = $32.00
Hope this Helps!!!
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 137 millimeters, and a standard deviation of 8 millimeters.If a random sample of 31 steel bolts is selected, what is the probability that the sample mean would be greater than 133.5 millimeters? Round your answer to four decimal places.
The probability that the sample mean would be greater than 133.5 is 0.9926
Explanation:Given:
Mean = 137
Standard deviation = 8
Sample = 31
To find the probability that the sample mean would be greater than 133.5, we have:
[tex]\begin{gathered} z=\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}} \\ \\ =\frac{133.5-137}{\frac{8}{\sqrt{31}}}=-2.4359 \\ \\ P(X>133.5)=1-P(z<-2.4359) \\ =1-0.0074274 \\ \approx0.9926 \end{gathered}[/tex]The cost of a pound of nails increased from $2.40 to $2.53. What is the percent of increase to the nearest whole-number percent?
The formula to find the percent increase of two values is:
[tex]\text{ Percent Increase }=\frac{\text{ New price - Old price}}{\text{ Old price}}\cdot100[/tex]In this case, we have:
[tex]\begin{gathered} \text{ Old price }=\text{ 2.40} \\ \text{ New price }=\text{ 2.53} \end{gathered}[/tex][tex]\begin{gathered} \text{ Percent Increase }=\frac{2.53-2.4}{2.4}\cdot100 \\ \text{ Percent Increase }=\frac{0.13}{2.4}\cdot100 \\ \text{ Percent Increase }\approx0.054\cdot100\Rightarrow\text{ The symbol }\approx\text{ is read 'approximately'} \\ \text{ Percent Increase }\approx5\% \end{gathered}[/tex]Therefore, the percent of increase to the nearest whole-number percent is 5%.