=========================================
Explanation:
We could use the AC factoring method here. Multiply the first coefficient (10) with the last term (3) to get 10*3 = 30.
We need to find factors of 30 that add to 11
1+30 = 31
2+15 = 17
3+10 = 13
5+6 = 11
we have found the pair of factors that add to 11. So we'll break the 11x into 5x+6x and then use factor by grouping method
10x^2 + 11x + 3
10x^2 + 5x + 6x + 3
(10x^2 + 5x) + (6x + 3)
5x(2x + 1) + 3(2x + 1)
(5x+3)(2x+1)
We see the two factors are 5x+3 and 2x+1.
To check the answer, use either the box method, distribution, or FOIL rule to expand out (5x+3)(2x+1) and you should get 10x^2+11x+3 again.
--------------------------------
As an alternative, you can solve 10x^2+11x+3 = 0 through any method you prefer (graphing, completing the square, quadratic formula). The quadratic formula is the best option as it works for any quadratic. The two solutions you should get are x = -3/5 and x = -1/2
Using x = -3/5 and x = -1/2, we can do the following
x = -3/5 becomes 5x = -3 after multiplying both sides by 5, then you add 3 to both sides to get 5x+3 = 0x = -1/2 becomes 2x = -1 after multiplying both sides by 2, and then turns into 2x+1 = 0 after adding 1 to both sidesNote how we have the 5x+3 and 2x+1 as found in the section above. At this point we can stop as we found the factors needed. I'm using the zero product property which says that if A*B = 0, then either A = 0 or B = 0.
How many times larger is 5 × 106 than 5 × 102?
Answer:
1.03921568627
Step-by-step explanation:
The box plots show the high temperatures in January and March for Denmark in degrees Fahrenheit. Box plots titled Average Daily Temperatures in Denver in March and January with horizontal axis labeled temperature in degrees fahrenheit ranges from 45 to 80. March box plot with minimum approximately at 55 and maximum approximately at 75, its interquartile range is approximately between 60 and 70, and the median is between 60 and 65. January box plot is with minimum approximately 55 and maximum approximately at 70, its interquartile range is approximately between 57 and 65, and its median is approximately between 60 and 65. Which can you tell about the mean temperatures for these two months? The mean temperature for March is higher than January's mean. The low median for January pulls the mean temperature below March's mean temperature. There is not enough information to determine the mean temperatures. The high range for March pulls the mean temperature equal to January's mean temperature.
Answer:
The mean temperature for March is higher than January's mean.
Step-by-step explanation:
I took the test. trust me and you will be set free ;D
The vertex of the parabola below is at the point (-3, -5). which of the equations below could be the one for this parabola?
A. x = -3(y + 5)^2
B. y = (x + 3)^2 -5
C. y = (x - 5)^2 + 3
D. y = (x + 3)^2 + 5
Answer:
Step-by-step explanation:
The coordinates of a vertex are (h, k). If our vertex is (-3, -5), then h = -3 and k = -5. The vertex form of a parabola is
[tex]y=(x-h)^2+k[/tex] so if we fill in our h and k values, the equation becomes
[tex]y=(x-(-3))^2+(-5)[/tex] and, simplified, is
[tex]y=(x+3)^2-5[/tex]
Choice B.
Please help Asap. Will give brainiest if answered correctly with a math question
TV = VX.
3x-24 = 2x + 1
Add 24 to both sides:
3x = 2x + 25
Subtract 2x from both sides:
X = 24
VX = 2(25) + 1 = 50 + 1 = 51
The answer is 51
Answer:
51
Step-by-step explanation:
Since it is an isosceles triangle the two sides are equal
3x - 24 = 2x + 1
x = 25
2(25) + 1 = 51
The life of a Radio Shack record player is normally distributed with a mean of 3 years and a standard deviation of 1 years. Radio Shack guarantees its record players for 2 years.
The life of a Radio Shack record player is normally distributed with a mean of 3 years and a standard deviation of 1 years. Radio Shack guarantees its record players for 2 years.
Find the probability that a record player will last less than 2 years?
Answer:
the probability that a record player will last less than 2 years is 0.1586
Step-by-step explanation:
Given that:
A mean which is normally distributed = 3
and a standard deviation = 1
The objective is to find that a record player will last less than 2 years
Let X be the random variable
i.e
[tex]P(X<2) = P( \dfrac{X - \mu}{\sigma}<\dfrac{X - \mu}{\sigma})[/tex]
[tex]P(X<2) = P( \dfrac{2 - \mu}{\sigma}<\dfrac{2 - 3}{1})[/tex]
[tex]P(X<2) = P( Z< \dfrac{-1}{1})[/tex]
[tex]P(X<2) = P( Z< -1)[/tex]
From the standard normal tables :
[tex]P(X<2) = 1- P( Z< 1)[/tex]
[tex]P(X<2) = 1- 0.8414[/tex]
P(X < 2) = 0.1586
Therefore; the probability that a record player will last less than 2 years is 0.1586
You are fencing a rectangular puppy kennel with 25 ft of fence. The side of the kennel against your house does not need a fence. This side is 9 ft long. Find the dimensions of the kennel.
Answer:
9 by 8 ft
Step-by-step explanation:
if you subtract the 9 ft for the side opposite your house you are left with 16. divide 16 by 2 for the sides sticking out from your house. the answer is 8 so the cage would be 9ft by 8ft
HELP URGENT PLEASE! The Lees have purchased a new home for $360,000, and put a down payment of $50,000 on it. They have a mortgage for the balance, amortized over 20 years at 5.25%. If the Lees pay off the mortgage at the end of the 20 years, how much interest will they have paid in total? USE TVM SOLVER
Answer:
$191,340.80
Step-by-step explanation:
Step 1
We find the amount that is paid monthly by the Lee's
We are told in the question that:
Cost of the house =$360,000
Down payment = $50,000
We are also told, the balance left after the down payment was made = Mortgage that is amortized at an
Interest rate of 5.25%
Time = 20 years
Hence, Mortgage amount = $360,000 - $50,000 = $310,000
Formula for monthly payment =
M= P[r(1+r)^n/((1+r)^n)-1)]
M = the total monthly mortgage payment.
P = the principal loan amount.
r = your monthly interest rate.
= rate/12
=5.25%/12 = 0.0525/12
= 0.004375
n = number of payments
= number of years × number of months
= 20 × 12 = 240 payments
Formula for monthly payment =
M= P[r(1+r)^n/((1+r)^n)-1)]
M = 310,000[0.004375(1 + 0.004375)^240/((1 + 0.004375)^240 ) - 1]
M = $2,088.92
Therefore, the monthly payment by the Lee's is $2,088.92
Step 2
We calculate the Total Amount paid by the Lee's in 20years because we are told in the question that they paid off their mortgage after 20 years
Total Amount paid = Monthly payments × Number of payments
= $2,088.92 × 240
= $501,340.80
Step 3
The third and final step is to calculate the Total interest paid for 20 years
Total Interest = Total amount paid - Mortgage amount
= $501,340.80 - $310,000
Total Interest: $191,340.80
Therefore,the interest will they have paid in total is $191,340.80
plz help asap, thank you
Answer:
57
Step-by-step explanation:
The answer is 57 because if angle 4 is 123 and angle 4 is equal to angle 3 then angle 3 is also 123. Then you would subtract 180 - 123 which is equal to 57.
Answer:
TKL is 57°
Step-by-step explanation:
since angle 3 is equal to angle 4 and angle 4 equals 123°, then angle 3 is 123°
subtract 123 from 180 then you get 57
97 students choose to attend one of three after school activities: football, tennis or running. There are 45 boys. 36 students choose football, of which 11 are girls. 41 students choose tennis. 15 girls choose running. A student is selected at random. What is the probability this student chose running? Give your answer in its simplest form.
Answer:
20/97
Step-by-step explanation:
Since we are only looking at students in general that choose running, the question is more simple than it seems. We can ignore every phrase that is gender specific because it doesn't apply to our question. All we need to know is that there are:
97 students
36 who chose football
41 who chose tennis
And we just need to find the number that chose running
97-(36+41)=20
20 students chose running
20/97
The graphed line shown below is y=-3x+6...Which equation, when graphed with the given equation, will form a system that has no solution?
Answer:
The equation, when graphed together with the line y=-3x +6, which will form a system of equations with no solution is y=-3(x +6), meaning the second option on the picture.
Step-by-step explanation:
hope this helps!
Answer: 2 or B
Step-by-step explanation:
ada is conducting an experiment to determine the boiling point of salt water. she fills two identical pots of water with equal amounts of water. in one pot, she adds salt. she then puts the pots of water over a flame and records the temperature for each pot of water when it begins to boil. what is the treatment?
Answer:
HYPOTHESIS
Step-by-step explanation:
Which of the following is the function of f(x)?
Answer:
f(x) = 8(x-3)
Step-by-step explanation:
F^ -1 ( x) = x/8 +3
Let y = x/8+3
To find the inverse
Exchange x and y
x = y/8+3
Solve for y
x-3 = y/8+3-3
x-3 = y/8
Multiply each side by 8
8(x-3) = y/8 * 8
8(x-3) = y
The inverse of the inverse is the function so
f(x) = 8(x-3)
Answer:
[tex]\boxed{f(x) = 8(x-3)}[/tex]
Step-by-step explanation:
[tex]y=\frac{x}{8} +3[/tex]
Switch variables.
[tex]x=\frac{y}{8} +3[/tex]
Make y as subject.
Subtract 3 from both sides.
[tex]x-3=\frac{y}{8}[/tex]
Multiply both sides by 8.
[tex]8(x-3)=y[/tex]
Marci has taken out a loan of $5,000 for a term of 24 months (2 years) at an interest rate of 8.5%. Use the amortization table provided to
complete the statement.
Monthly Payment per $1,000 of Principal
Rate | 1 Year 2 Years 3 Years 4 Years 5 Years
6.5% $86.30 $44.55 $59.35 $23.71 $19.57
7.0% $86.53 $44.77 $31.88 $23.95 $19.80
7.5% $86.76 $45.00 $51.71 $24.18 $20.04
8.0% $86.99 $45.23 $31.34 $24.41 $20.28
8.5% $87.22 $45.46 $24.65 $24.65 $20.52
9.0% $87.45 $45.68 $31.80 $24.89 $20.76
Marci's monthly payment will be $
and her total finance charge over the course of the loan will be $
Answer:
$227.30$455.20Step-by-step explanation:
The table tells you that Marci's monthly payment on a 2-year loan at 8.5% will be $45.46 on each $1000 borrowed. For her $5000 loan, her monthly payment will be 5 times the table value, or ...
monthly payment = $5000/$1000 × $45.46
monthly payment = $227.30
__
Her total of 24 payments will be ...
total repaid = 24 × $227.30 = $5,445.20
That amount is $445.20 more than the amount borrowed, so that is Marci's finance charge.
__
Marci's monthly payment will be $227.30, and her total finance charge will be $455.20.
HELP ME PLLEEEEASE I BEG
Your math teacher caught you text messaging in class, again, so the teacher is making you give a presentation to your math class next week. Your assignment is to analyze the scatter plot that shows people's ages and the number of text messages sent in a day. In 3-5 sentences, explain what you see in the scatter plot below.
Answer: If a scatterplot is included in the assignment
The dots plotted on the graph might closely follow the graph of exponential decline. There is a large number of texts per day by 19-20-21 year-olds, but the number seems to decline exponentially as age increases. With a little work, it may be possible to plot the curve and write an equation to model the decline.
Step-by-step explanation: Look at some graphs of exponential decay. Also consider harmonic and hyperbolic decay. The trend in the data is evident. The main challenge is to look at the data and create an equation that models it.
Which graph represents the function f(x)=|x−3|+1 ?
Answer:
the first one (in quadrant 1, pointing upwards)
Step-by-step explanation:
since the function is positive the graph will be facing upwards and start off at 1
find answer is fast friends
Answer:
see explanation
Step-by-step explanation:
The restriction a ≠ 0 and b ≠ 0 is applied since division by zero would make
[tex]\frac{a}{b}[/tex] and its reciprocal [tex]\frac{b}{a}[/tex] undefined, thus meaningless
Shelley and David have a sweet tooth. Shelley spent \$2.65 for 15 sour keys and 2 chocolate bars. David bought 3 chocolate bars and 10 sour keys for \$3.35 at the same store. Find the cost of each chocolate bar and each sour key at this store. If you need 8 chocolate bars and 24 sour keys to give to friends coming to your birthday party, how much will they cost you at this store?
Answer:
Chocolate bars: $0.95 each
Sour keys: $0.05 each
Total cost for 8 chocolate bars and 24 sour keys: $8.80
Step-by-step explanation:
sour keys=x
chocolate bars=y
15x+2y=2.65
10x+3y=3.35
multiply the second equation by 1.5
15x+4.5y=5.025
2.5y=2.375
y=0.95
Chocolate bars are $0.95 each.
Now substitute the y value in one of the equations
15x+2(0.95)=2.65
15x+1.9=2.65
15x=0.75
x=0.05
Sour keys are $0.05 each.
For the second part of the question, just multiply the number of chocolate bars by the cost and same thing with the sour keys and add them.
Final answer: $8.80
If 2x = 60, find the value of 6 - 7x
Answer:
- 204
Step-by-step explanation:
2x = 60
x = 30
6 - 7(30) = -204
Answer:
-204
Step-by-step explanation:
Step 1- Solve for the value of x
2x = 60
Divide 60 by 2 so x is by its self
x = 30
Step 2- Plug in 30 for x in the second equation
6 - 7(30)
6 - 210
-204 is the answer
NEED HELP ASAP!!! I GIVE GOOD POINTS
Answer:
70
Step-by-step explanation:
Devi’s mother is three times as old as Devi. Five years ago, Devi’s mother was four times as old as Devi was then. Find their present ages
Answer:
Devi's present age = 15 years
Devi's Mother's present age = 45 years
Step-by-step explanation:
Let the present age of Devi be x years.
Therefore, mother's present age = 3x
Five years ago:
Devi's age = (x - 5) years
Mother's age =( 3x - 5) years
According to the given condition:
Five years ago:
Devi's mother's age = 4 times Devi's age
3x - 5 = 4( x - 5)
3x - 5 = 4x - 20
20 - 5 = 4x - 3x
15 = x
x = 15 years
3x = 3* 15 = 45 years
Hence,
Devi's present age = 15 years
Devi's Mother's present age = 45 years
The pentagon ABCDE is dilated to the image A'B'C'D'E' with the center of the dilation at the origin.
Select all true statements
The scale factor of the dilation is 1/4
The line EA is parallel to the E’A’ because EA passes through the center of the dilation
Since the line C’D’ falls on the line CD, the scale factor is. It applied on the line CD
The scale factor of the dilation is 1/2
The line CD is not parallel to the line C’D’ because CD passes through the center of the dilation
Now I’m no genius but I‘m pretty sure the answers are “c” and “d”
Ya’ll have a good day or night, whichever one!
The true statement for the Pentagon in the given graph is
The scale factor of the dilation is 1/2 with the center at the origin(0,0).
Dilation:Dilation implies resize of any object.
It may increase or decrease the object by a particular value.The particular value is called the scale factor. Properties of Dilation of figure:Parallel lines in the dilated figure remain the same as in the original figure.The dilation of any figure does not vary from each angle of the figure.The midpoints of the dilated figure remain the same as that of the original figure.True statement:The scale factor of the dilation of the pentagon is 1/2.
Reason:The pentagon with vertices A(0.5,4.5), B(2,3), C(1,0), D(-2,0), E(-3,3) when multiplied by 1/2 we get The vertices of the dilated pentagon as A'(0.25,2.25), B'(1,1.5), C'(0.5,0), D'(-1,0), E(-1.5,1.5). When we plot the points A'B'C'D'E' in the graph, obtain the dilated pentagon with a center at the origin. Wrong statement with Reasons:The scale factor of the dilation is not 1/4 because when we multiply the vertices of pentagon ABCDE by 1/4 we are not getting the dilated points as in the graph.The line EA is parallel to E'A' but,1. The line EA does not passes through the center of the dilation
at origin(0,0), which can be clearly seen from the given graph.
2. For two lines to be parallel it is not necessary for one of the
lines to pass through the origin.
The line C'D' is parallel to CD as we should see the figure in a 3-dimensional way and it also follows the properties of dilation of a figure.Hence the scale factor of the given pentagon is 1/2.
To learn more about the Dilation of polygons:
https://brainly.com/question/3020085?referrer=searchResults
#SPJ2
how to do this question plz answer
Answer:
(a) See net below
(b) 38 cm^2
Step-by-step explanation:
(a) see completed net below.
It's like a pizza box when finishd.
Fold the two sides (left, right, 1*3) up.
Fold the bottom part added up to form a side.
Fold the very bottom rectangle to form the top face.
(b) Total surface area
= top and bottom faces of 12 cm^2 each+ 2 sides of 3 cm^2 + 2 sides of 4 cm^2 each
= 2*12 + 2*3 + 2*4
= 24 + 6 + 8
= 38 cm^2
On a coordinate plane, a piecewise function has 3 lines. The graph shows cleaning time in hours on the x-axis and total cost in dollars on the y-axis. The first line has an open circle at (0, 50) and continues horizontally to a closed circle at (2, 50). The second line has an open circle at (2, 100) and continues horizontally to a closed circle at (6, 100). The third line has an open circle at (6, 200) and continues horizontally to a closed circle at (8, 200). The graph represents the cleaning costs charged by a housekeeping service. Which statement is true of the cost function? A cleaning time of 2 hours will cost $100. A cleaning time of 6 hours will cost $150. Cost is a fixed rate of $100 for jobs requiring more than 2 hours, up to a maximum of 6 hours. Cost is a fixed rate of $200 for jobs that require at least 6 hours.
Answer:
C. (2, 6] hour jobs cost $100
Step-by-step explanation:
Let's consider each of these statements in view of the graph:
A cleaning time of 2 hours will cost $100. -- The closed circle at (2, 50) tells you the cost of a 2-hour job is $50, not $100.A cleaning time of 6 hours will cost $150. -- The closed circle at (6, 100) tells you the cost of a 6-hour job is $100, not $150.Cost is a fixed rate of $100 for jobs requiring more than 2 hours, up to a maximum of 6 hours. -- The line between the open circle at (2, 100) and the closed circle at (6, 100) tells you this is TRUE.Cost is a fixed rate of $200 for jobs that require at least 6 hours. -- "At least 6 hours" means "greater than or equal to 6 hours." The closed circle at (6, 100) means a 6-hour job is $100, not $200.Answer:
(0,8) first option and 50,100 or 200 in the second option
Step-by-step explanation:
THIS IS URGENT! PLEASE help me with this question!!!
In an examination 1/3 of the total student used unfair means and out of which 1/4 caught red handed while cheating. If 5 student caught red handed then find the total number of student appeared in exam
Answer:
total number of students =60
Step-by-step explanation:
total number of students 60
used unfair means 1/3= 20
1/4 caught red handed 1/4 of 20= 5
80 people took a driving test. 70 of them passed the test. What percentage failed the test?
Answer:
12.5% failed
Step-by-step explanation:
Convert the fraction 10 out of 80 into a decimal to become the percentage
Answer: 87.5% failed driving test is 12.5%
Step-by-step explanation:
Please answer this in two minutes
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Inverse Trigonometry Function.
So here, we get as
SinX = 1/2
X = Sin^-1(1/2)
X= 30°
Find the product of all positive divisors of 288.
Answer:
The answer is 1.514571894×10^21.
Step-by-step explanation:
Here, the divisors of 288 are,
1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288.
now, their product =1×2×3×4×6×8×9×12×16×18×24×32×36×48×72×96×144×288
=1.514571894×10^21.
is answer.
Hope it helps...
Answer:
Step-by-step explanation:
2 * 3 * 4 * 6 * 8 * 9 * 12 * 16* 18 * 24 * 32 * 36 * 48 * 96 * 144
Some teachers would include 288. I would not.
You can get the actual answer by using the calculator that came with your computer. An ordinary calculator will not work because the answer will come out in scientific notation.
657,366,253,849,018,368 is the answer.
Parallelogram L M N O is shown. Angle L is (x + 40) degrees and angle O is (3 x) degrees. What is the measure of angle O in parallelogram LMNO? 35° 75° 105° 155
Answer:
C, 105 Degrees
Step-by-step explanation:
So the two opposite sides of a parallelogram is equal to each other and the two adjacent angles are supplementary. So if (x+40)+3x=180, this means that 4x+40=180. This gives us 4x=140, so x=35. If we plug it back into the equation it ascertains as such: 3(35)= 105. The answer for this question and angle O is 105 degrees, or C.
The measure of angle O in this parallelogram is 105°.
The properties of a parallelogramThe opposite angles of a parallelogram are equal.The Opposite sides of the parallelogram are equal and parallel.The diagonals of the parallelogram bisect each other.The Sum of the angles = 360°
Solution
Because the properties says that opposite angles are equal.
Angle L = (x + 40)
angle O = (3 x)
Applying the first property
x+40+x+40+3x+3x = 360
collect the like termsx+x+3x+3x+40+40 = 360
8x+80 = 360
8x = 360-80
8x = 280
Divide through the equation by 8
x = 280/8
x = 35
The question wants us to find the value of angle O
O = 3x
O = 3*35
= 105
The value of angle O is equal to 105°
Read more on parallelograms here:
https://brainly.com/question/970600