Given,
[tex]x^2-8x+15=0[/tex]To find the roots
[tex]\begin{gathered} x^2-8x+15=x^2-3x-5x+15 \\ =x(x-3)-5(x-3) \\ =(x-3)(x-5) \end{gathered}[/tex]The required roots are,
[tex](x-3)(x-5)[/tex]с C' B' A B D' D The distance from A to B is 10 and the distance from A to B'is 2. What is the scale factor? 1/5 4 5 1/4
In this problem, we have that
the center of the dilation is pointed A ----> because the intersection segments c
so
the scale factor is equal to
scale factor=AB'/AB
substitute given values
scale=2/10
scale =1/5Perform the matrix operation.2 3Given A =25and B =04-1 6find 2A + B.A4 103 1610]B-3 11D4 142 22
step 1
Find 2A
Multiply by 2 each number of the matrix A
so
2A= 4 6
4 10
step 2
Find out the sum 2A+B
so
2A+B= (4+0) (6+4)
(4-1) (10+6)
2A+B= 4 10
3 16
therefore
the answer is the option A
How did the reporter state probability for rain last week compared to the actual results
Answer:
The probability of rain was less than the actual results
Explanation:
Given that it rained on Monday, Tuesday, Thursday, and Friday, the actual probability of rain is 4 out of 7 days.
If the reporter stated that the probability of rain was 3 out of days, we can see that the probability of rain the reporter stated was less than the actual result of 4 out of 7 days
View the tables:How are the values in each table growing?Which table shows common differences? Explain your reasoning.Which one shows common factors? Explain your reasoning.
In first table, where the height of the water is considered, every minute the water rises by 3 cm.
In second table, where possible outcome is considered, for increase in one coin the outcome increases by a factor of two.
The first table, where the height of the water is considered, shows common difference. As it increases equally every minute.
The second table, where possible outcome is considered,shows a common factor as all the values are divisible by 2. So the common factor is 2.
I don't understand problem like this : h >4
Solution
For this case we can assume that x = number of minutes that Ebony waited
Then the correct sequence is given by
Identify the variable as the number of minutes, x. Identify the inequality symbol as greater than. Identify the constant as 56 minutes. Write the inequality as x >56
Order of operations was it evaluated correctly? 10 - 2(5+11)= 10-2(16)= 10 -32= -22EXPLAIN your reasoning Please this is due today thank you
10 - 2(5+11)
Step 1
first, you need to eliminate the () by making the operation inside, it is an addition
10-2(5+11)
10-2(16)
then,
Step 2
do the operation related to the (), it is multiplication, rember a(b) = a*b = (a)b = (a)*(b), the meaning is the same.
10-2(16)
10-32
Step 3
finally, do the subtraction
Mario loaned Juan $21,890 at an interest rate of 14% for 164 days. How much will juan pay Mario at the end of 164 days? Round youranswer to the nearest cent. Note: Assume 365 days in a year and 30 days in a month.
For the interest calculation we shall apply the simple interest formula which is;
[tex]\begin{gathered} I=P\times R\times T \\ \text{Where;} \\ P=\text{Initial amount borrowed} \\ R=\text{rate of interest (expressed as decimal)} \\ T=\text{Time in years} \end{gathered}[/tex]The initial amount is $21890, the rate is 14% (that is 0.14) and the time is 164/365 of a year.
Therefore, the interest calculated would be;
[tex]\begin{gathered} I=P\times R\times T \\ I=21890\times0.14\times\frac{164}{365} \\ I=3064.6\times\frac{164}{365} \\ I=1376.9709589 \\ I\approx1376.9\text{ (rounded to the nearest cent)} \end{gathered}[/tex]The interest payable at the end of 164 days is $1,376.90 (rounded to the nearest cent).
Therefore, the amount Juan would pay back is;
if a rectangle with an area of 42 units^2 has a length of seven units what is the rectangles primeter?
EXPLANATION
Let's see the facts:
The area of the rectangle is equal to 42 squared units.
Length = 7 units
The perimeter is given by the following relationship:
[tex]\text{Perimeter}=2\cdot(\text{length}+\text{width)}[/tex]But i don't know the width, so i can find it by isolating from the area formula as follows:
[tex]\text{Area}=\text{length}\cdot\text{width}[/tex]Isolating the width:
[tex]\text{Width}=\frac{Area}{\text{length}}=\frac{42}{7}=6\text{ units}[/tex]So, width = 6 units
Finally the perimeter is:
[tex]\text{Perimeter = 2(7+6) = 2(13)=26 units}[/tex]The perimeter is 26 units
Write the given function as the composition of two functions.y=√15 + 6xChoose the correct answer below.OA. If f(x) = -√x and g(x) = 15+ 6x, then y = f(g(x)].1B. If f(x)=√x and g(x) = -OC. If f(x) =³√xCOD. If f(x) = -115+ 6x'then y = f[g(x)].and g(x)= 15+ 6x, then y = f[g(x)].and g(x) = 15+ 6x, then y = f[g(x)]....
Given:
[tex]y\text{ = -}\sqrt[3]{15+6x}[/tex]To find:
the functions that give the above composite function
f(g(x)): substitute x in f(x) with g(x)
This means g(x) will be 15 + 6x which will be substituted into function f(x)
[tex]\begin{gathered} f(x)\text{ = -}\sqrt[3]{x} \\ g(x)\text{ = 15 + 6x} \\ \\ Check: \\ f(g(x)):\text{ substitute x in g\lparen x\rparen with f\lparen x\rparen} \\ f(g(x))\text{ = -}\sqrt[3]{15\text{ + 6x}} \end{gathered}[/tex][tex]f(x) = x + 7[/tex]Substitute the value a. f(5)b. f(-1)c. f(-3)
Answer
a) f(5) = 12
b) f(-1) = 6
c) f(-3) = 4
Explanation
We are given the function
f(x) = x + 7
We are then asked to evaluate a number of valus of x for the function
a) f(5)
f(x) = x + 7
f(5) = 5 + 7 = 12
b) f(-1)
f(x) = x + 7
f(-1) = -1 + 7 = 6
c) f(-3)
f(x) = x + 7
f(-3) = -3 + 7 = 4
Hope this Helps!!!
Linear function gis shown in the graph. Write the slope-Intercept form of the equation representing this function.
To find the equation of the line in slope intercept form the first step is to find the slope of the given line:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]In this formula, m is the slope of the function, y2 and y1 are the y coordinates of 2 points on the line, and x2 and x1 are the x coordinates of the same 2 points, for example, they can be (-1,3) and (0,1):
[tex]m=\frac{1-3}{0-(-1)}=-\frac{2}{1}=-2[/tex]The slope of the line is -2.
Now, we can use the y intercept of the graph of g, which is 1.
The slope intercept form of the equation follows the following general structure:
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y intercept. Use the known values to replace them on the equation. The intercept form of the equation is:
[tex]y=-2x+1[/tex]You have 4929 songs in your computers music library. The songs have a mean duration of 246.3 seconds with a standard deviation of 111.42 seconds. One of the songs is 391 seconds long. What is its z-score?
5. What are the zeros of the polynomial function f(x) = x³ - 2x² - 4x + 8? (Select all that apply.)
□ (√2,0)
(2,0)
(0,0)
(-2,0)
Answer:
(2, 0), (-2, 0)
Step-by-step explanation:
f(x) = x³ - 2x² - 4x + 8
(x³ - 2x²) (-4x + 8)
x²(x - 2) - 4(x - 2)
(x² - 4) (x - 2)
(x + 2)(x - 2)(x - 2)
(x + 2) (x - 2)²
x = -2, 2 multiplicity of 2
I hope this helps!
Twice a number, decreased by 4, is at least 12. Which of the following is a solution?8576
Answer:
8
Explanation:
Let the number = n
Twice the number decreased by 4:
[tex]2n-4[/tex]The phrase 'at least' means the expression above can either be equal to or greater than 12.
Thus, the given statement as inequality is:
[tex]2n-4\geq12[/tex]We then solve the inequality for n.
[tex]\begin{gathered} \text{ Add 4 to both sides} \\ 2n-4+4\geq12+4 \\ 2n\geq16 \\ \text{ Divide both sides by 2} \\ \frac{2n}{2}\geq\frac{16}{2} \\ n\geq8 \\ \implies n=(8,9,10,\cdots) \end{gathered}[/tex]The number that is a solution is 8.
What is the radius and diameter of the following circle?18 cmRadius =cmDiameter =cm
We are given the diameter of the circle = 18 cm
Radius = Diameter /2 = 18 /2 = 9 cm
Please help me with this timed practice problem.The first step have different options: substract, distribute, divide, add.
From the starting equation to the first step we can see that the only change was made on the left side of the equation.
We can see that the distributive property of multiplication is being applied to the parenthesis.
So, the "-2"is being distributed to the 5x and the 8.
So, the correct options in step 1 is distribute.
In step 2, we can see that the 6x on the left side are not there anymore and the -10x on the left turned into -16x. That is, we substracted 6x from both sides. Thus, the correct option on Step 2 is substract.
In Step 3, the -16 is not on the left side anymore and the 30 from the right side is in place of the 14. So, we added 16 to both sides in this step, and the correct alternative is add.
Now, on Step 4 we had -16x that turned into x and a denominator of -16 appeared on the right side, so we have divided both sides by -16. The correct alternative on Step 4 is divide.
(6.6 x 10^8)÷(2.0 x 10^4)
Given:
[tex]\frac{6.6\times10^8}{2.0\times10^4}[/tex]Simplify the expression
[tex]\frac{6.6\times10^8}{2.0\times10^4}=\frac{6.6}{2.0}\times\frac{10^8}{10^4}[/tex]Solve the expression by applying the law of indices
[tex]\frac{6.6\times10^8}{2.0\times10^4}=\frac{6.6}{2.0}\times10^{8-4}[/tex]Simplify further
[tex]\begin{gathered} \frac{6.6\times10^8}{2.0\times10^4}=3.3\times10^{8-4} \\ \frac{6.6\times10^8}{2.0\times10^4}=3.3\times10^4 \end{gathered}[/tex]Therefore, the answer is
[tex]3.3\times10^4[/tex]Which of the following represents the slope of the line 2x - 5y = 10
mini lesson[tex]y = - 3x - 10[/tex]math
so we have to replace y. we get
[tex]\begin{gathered} 2x+5=-3x-10 \\ 2x+3x=-10-5 \\ 5x=-15 \\ x=-\frac{15}{5}=-3 \end{gathered}[/tex]if x=-3, we get that y is
[tex]y=2\cdot-3+5=-1[/tex]so the solution is
[tex](-3,1)[/tex]Use the given data to make a box-and-whisker plot.5, 4, 16, 21, 10, 6, 15
Given the set of data:
5, 4, 16, 21, 10, 6, 15
Let's create a box-and-whisker plot from the given data.
The box and whisker plot has the following properties:
Let's solve for the following:
• Minimum value or lower extreme:
This is the smallest value in the data set.
Here, the minimum value is 4.
• Maximum value or upper extreme:
This is the greatest number in the data set.
Here, the greatest number is 21.
• Median:
This is the middle value after arranging the data in ascending order(from lowest to greatest).
Arranging in ascending order, we have:
4, 5, 6, 10, 15, 16, 21
The middle number above is = 10
Therefore the median is 10.
• Lower quartile:
The lower quartile is the median of the lower half of the data.
To find the lower quartile, let's list the lower half of data first.
Lower half:
4, 5, 6
The median of the lower half of the data is 5.
Therefore, the lower quartile is 5.
• Upper quartile:
The upper quartile is the median of the upper half of the data set.
Upper half of the data set:
15, 16, 21
The median is 16.
The upper quartile is 16.
Therefore the box and whisker plot created from the given data set is:
Option B is correct.
ANSWER:
B
PLEASE ANSWER QUICK WILL GIVE Brain
n73=8.76
Answer:
n=639.48
Step-by-step explanation:
i love my life
Answer: 8.33--
Step-by-step explanation:
73/8.76
8.) Rotate 90' clockwise about the orgin:ADEOriginal NewCoordinates CoordinatesA: () A: (___)B: () B: (__)D:() D:(__)E:( _ :) E: (_,_)V:( _,-) V:( _,-)R: (___) R' (_._)RB2
We have six points that fall in a figure
The original coordinates of this points are:
A: ( -3, 2)
B: ( -3, -4)
D: ( 1, 3)
E: (7, 2)
V: ( 4, 8)
R: ( 3, -2)
To find the new coordinates we must bear in mind that the points must be rotated 90° clockwise.
So, we need to use the next formula to find the new points:
[tex]P(x,y)\to-90^{\circ}\to P^{\prime}(y,-x)[/tex]Finally,
The new coordinates of the points are:
A': ( 2, 3)
B': ( -4, 3)
D': ( 3, -1)
E': ( 2, -7)
V': ( 8, -4)
R': ( -2, -3)
Write an inequality for the word problem and answer the question about the inequality. The faculty team scored less than half as many points as the varsity team. A total of 100 points was scorered. If x represents the number of points that the varsity team scored Could x = 60
From the exercise we can indentify the following
• x, = number of points that the varsity team scored
,• y ,= number of points that the faculty team scored
[tex]\begin{gathered} x+y=100\to(1) \\ y<\frac{1}{2}x\to(2) \end{gathered}[/tex]Let's clear y in (1) to be able to replace in (2)
[tex]\begin{gathered} y=100-x\to(1) \\ 100-x<\frac{1}{2}x\to(1)\text{ in (2)} \\ \frac{1}{2}x+x>100 \\ \frac{3}{2}x>100 \\ x>\frac{100\cdot2}{3} \\ x>\frac{200}{3} \\ x>66.6666 \\ x>67 \end{gathered}[/tex]The answer is x cannot be equal to 60 because they have to be at least 67 points to comply with the inequalityWhat is the center of the data?Number of Green Candies in a Bag:O101112131415The center is0):tivity
Given:
10, 11, 12, 13, 14, 15
Find the center of the data.
To find the center of the data,
Determine the point on the graph of the unit circle that corresponds to pi. Then find cos pi and sin pi, and state which functions are undefined for pi.
The entire unit circle measures 2pi, then, pi corresponds to the half of the unit circle. It is located at the point (-1,0).
The cosine of pi is equal to the x-coordinate, and the sin of pi is equal to the y-coordinate of the point pi.
Since it is located at (-1,0) thus the cos(pi)=-1 and sin(pi)=0.
The functions that are undefined for pi are those which have sin(pi) as denominator, let's check:
[tex]\begin{gathered} \csc (\pi)=\frac{1}{\sin(\pi)}=\frac{1}{0}=undef \\ \cot (\pi)=\frac{\cos (\pi)}{\sin (\pi)}=\frac{-1}{0}=undef \end{gathered}[/tex]AMAn art teacher has 9 3/5 gallons of paint to pour into containers. If each container holds3/5 gallon, how many containers can they fill?Answer type: Mixed numberSubmit Answerattempt 1 out of
So they can fill 16 containers.
1) If an art Teacher has
9 3/5 gallons
Each container holds
3/5 gallons
2) Firstly, let's turn that mixed number into an improper fraction
9 3/5 = (5 x 9+3) /5 = 48/5
Given that each container holds 3/5, then let's divide
48/5 ÷ 3/5 = 48/5 x 5/3 =16
If we hadn't turned
9 3/5 ÷ 3/5 = 16
3) So they can fill 16 containers.
÷
tenemos $5000 en una cuenta. A final de cada mes se ingresa un 5% del dinero que hay en la cuenta en dicho momento. Calcular el dinero que habrá en la cuenta después de un trimestre¿ en que porcentaje ha subido la cantidad inicial?
Al final del primer mes tenemos:
5000 + 5000*0.05 = 5250
Al final del segundo mes:
5250 + 5250*0.05 = 5512.5
Y al final del tercer mes nos queda:
5512.5 + 5512.5*0.05 = 5788.125
El dinero que habra en la cuent despues de un trimestre es $5788.125
Para calcular en que porcentaje ha subido la cantidad inicial, dividimos la cantidad extra obtenida despues de un trimestre entre la cantidad inicial:
[tex]\begin{gathered} \frac{788.125}{5000}=0.157625 \\ \text{Expresado en porcentaje:} \\ 0.157625\cdot100=15.7625 \end{gathered}[/tex]Ha subido en un 15.7625%
How do you work the following problem:517 37/50 + 312 3/100? and I also need to turn in to a decimal
Calculate the following sum of mixed fractions:
[tex]517\frac{37}{50}+312\frac{3}{100}[/tex]Before adding the fractions, we should express them as improper fractions:
[tex]517+\frac{37}{50}+312+\frac{3}{100}[/tex]We can add the integers 517+312=829
And now the fractions:
[tex]\frac{37}{50}+\frac{3}{100}[/tex]Expand the first fraction to have a denominator 100:
[tex]\frac{2\cdot37}{2\cdot50}+\frac{3}{100}=\frac{74}{100}+\frac{3}{100}=\frac{77}{100}[/tex]Now we simply join the integer part with the proper fraction:
[tex]829\frac{77}{100}[/tex]It's the final answer
Let's elaborate on the sum:
[tex]\frac{37}{50}+\frac{3}{100}[/tex]We need to make both denominators equal and then add the numerators easily
For example:
[tex]\frac{3}{8}+\frac{4}{8}=\frac{7}{8}[/tex]Note the fraction 37/50 does not have the same denominator as 3/100
How can we make them equal?
Multiply by 2
both the 37 and 50
To express the result as decimal, we divide the fraction and add it to the integer:
[tex]829\frac{77}{100}=829+\frac{77}{100}=829+0.77=829.77[/tex]Determine if the set of number of days in January, J, and the set B={6,9,15,10,1,0,8,4,11} is equivalent
equivalent sets are those that have the same cardinality, that is, the same number of elements
The width of a rectangle is 5x-4. The perimeter is 14x+4. What is the length
Given:
The width of rectangle is w = 5x - 4.
The perimeter of rectangle P = 14x + 4.
Explanation:
The formula for the perimeter of rectangle is,
[tex]P=2(L+w)[/tex]Substitute the expression in formula to determine the length of rectangle.
[tex]\begin{gathered} 14x+4=2(L+5x-4) \\ L+5x-4=\frac{14x+4}{2} \\ L=7x+2-5x+4 \\ =2x+6 \end{gathered}[/tex]So length of rectangle is 2x + 6.
Answer: 2x + 6