Why would the polynomial, "[tex]x^2+5x-24[/tex]" factor out to (x-3)(x+8)?
Step-by-step explanation:
5x can also be written as " -3x + 8x " so:
[tex]x^2+5x-24 = x^2-3x+8x-24[/tex]
Using the distributive property:
[tex]x(x-3)+8(x-3)[/tex]
Then again, using the distributive property (but in reverse):
[tex](x-3)(x+8)[/tex]
The two numbers that the middle term should be split into in order to factor can be found by listing out pairs of factors for the product of the last term and the coefficient of the first term, and using the two factors whose sum is the middle term.
For eg (because that was a bit text heavy):
The product of the last term and the first coefficient (1 * (-24)) is -24
the factors of -24 include (and their sum)
-1, 24 (23)
1, -24 (-23)
-2, 12 (10)
2, -12 (-10)
-3, 8 (5)
3, -8 (-5)
-4, 6 (2)
4, -6 (-2)
The middle coefficient is 5 and the sum of the factors -3 and 8 are 5, so split 5x into -3x + 8x to be able to factor how I showed before.
Determine the modulus of each of the complex numbers in the matching pairs. List these moduli in order from smallest to largest. Use the letters of the matching pair in your listing.
Suppose m = 2 + 6i, and |m + n| = 3√10 , where n is a complex number.
a. What is the minimum value of the modulus of n?
√10
Provide one example of the complex number, n.
A = J → 2 + 6i
B = F →75
C = H → -3 - i
D = I → 1 + i
E = G → 5 + 5i
these are my matching pairs
Answer:
the modulus of a complex number z = a + bi is:
Izl= √(a²+b²)
The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:
m = 2 + 6i
n = a + bi
Im + nl = 3√10
√(a² + b²+ 2²+ 6²)= 3√10
√(a^2 + b^2 + 40) = 3√10
squaring both side
a²+b²+40 = 3^2*10 = 9*10 =90
a²+b²= 90 - 40
a²+b²=50
So,
|n|=√(a^2 + b^2) = √50
The modulus of n must be equal to the square root of 50.
now
values a and b such
a^2 + b^2 = 50.
for example, a = 5 and b = 5
5²+5²=25+25= 50
Then a possible value for n is:
n = 5+5i
Let n be x+yi
So
√(a²+b²+2²+6²)=3√10√a²+b²+40=3√10a²+b²+40=90a²+b²=50Minimum value is 5+5i as 5²+5²=50
Find the diameter and circumference
9 m
Answer:
d = 18, c = 56.55
Step-by-step explanation:
Solution
d=2r=2·9=18
C=2πr=2·π·9≈56.54867
Estimate the circumference of the circular base of the object. Round to the nearest hundredth if necessary.
D battery with radius 0.65 in.
circumference: ___ in.
Answer:
4.09
Step-by-step explanation:
Circumference=
[tex]2\pi \times r[/tex]
The circumference of the circular base of the object is 4.082 in
What is circumference?The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center.
Given that, we need to find the circumference of the circular base of the object, whose radius is 0.5 in
The circular object is referred as circle, the circle's circumference is its boundary length measured in unit whose power is always 1, like m, cm, km etc.
Here, if we calculate the circumference of the object, we will get,
The circumference of any circular object given by :-
C = 2π×radius
C = 2×3.14×0.65 = 4.082 in
Hence, the circumference of the circular base of the object is 4.082 in
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find the volume of the prism
Answer:
volume = 108
Step-by-step explanation:
simple: volume = base x height
9 x 12 = 108
Answer 1452
Step-by-step explanation:
im not sure if im correct but the formua is V = L x W x H which is volume equal lenth multiplied by with multiplied by height. so 12 x 11 x 11
What are the solutions of the equation 3x^2 +13x=10 ?
PLEASE HELP ME
Describe the sequence in words:
5,9,13,17,21...
can someone help it would be very helpful
Answer:
Use formula
area of trapezium=(a+b)/2×h
Step-by-step explanation:
1)
area of trapezium=(a+b)2×j
(8×4)/2×696in²as this u can calculate all of yr areas.
stay safe healthy and happy.ASAP -Which is the best estimate of 2 Pi^2
Answer:
C budddyyyyyy
Gieco saves you 15% on car insurance
lol sorry i just had to
I don’t understand what to do because this is worded very strangely. Could somebody help?
In a survey, 200 college students were asked whether they live on campus and if they own a car. Their responses are
summarized in the following table
Is there evidence that college students who don't own a car tend to not live on campus more than students who live on
campus?
A. Yes, because the percentage of students who don't own a car and don't live on campus is greater than the percentage of students who
don't own a car and live on campus.
B. Yes, because the percentage of students who don't own a car and don't live on campus is less than the percentage of students who
don't own a car and live on campus.
C. No, because the percentage of students who don't own a car and don't live on campus is less than the percentage of students who
don't own a car and live on campus.
D. No, because the percentage of students who don't own a car and don't live on campus is greater than the percentage of students who
don't own a car and live on campus.
HELP
find the value of x in a circle 8,x, 20,36
Answer:
8.8 i think
Step-by-step explanation:
Find the mode of these numbers:
4,4,6,6,2,2,6,2,4,2
Answer:
Hello! answer: 2
Step-by-step explanation:
The mode is just the number shown the most in the set of numbers so 2 is the mode because 2 is shown the most Hope that helps!
Solve this inequality. 7d-1<6d
Answer: d < 1
I used A app and it said that
Find the surface area of the composite solid.
Answer:
1240.4 mm²Step-by-step explanation:
[tex]440.4 + 5\cdot(\frac12\cdot16\cdot20)=440.4+800=1240.4\ mm^2[/tex]
Evaluate w - (w - 8) + v, when w = 11 and v = 16.
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Answer:
24
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
help I don’t know the answer
HeLP PLEASE OH LORD ITS TIMED 20 POINTS AM I RIGHT??? IF NOT WHATS THE ANSWER
Answer:
you are correct :D
Step-by-step explanation:
Find the value of x in the triangle
Answer:
x+23+80=4x+17
x+103=4x+17
103-17=4x-x
86/3=x
x=28.66
Step-by-step explanation:
Translate algebraic words to symbols.
Six times y divided by x squared
A. 6y - X2
B. 6y + 2x
C. (6 + y)/2x
D. 6y/x2
Answer:
D
Step-by-step explanation:
Answer:
D. 6y/x²
Step-by-step explanation:
6×y= 6y
x squared =x²
PLS HELP ME I NEED THIS DONE IN A FEW MINUTES
Answer:
(2,2)
Step-by-step explanation:
Midpoint formula, and plug in the numbers.
Hope this helps.
(x1+x2)/2,(y1+y2)/2
(1+3)/2,(3+1)/2
4/2,4/2
(2,2)
Find the Circumference of a circle with a Diameter of 9 inches Group of answer choices 9 pi inches 9 pi inches^2 9 pi inches^3 108 pi inches
Answer: [tex]9\pi\ in.[/tex]
Step-by-step explanation:
Given
The diameter of a circle is [tex]d=9\ in.[/tex]
So, the radius is [tex]r=\frac{d}{2}=4.5\ in.[/tex]
The circumference is given by [tex]2\pi r[/tex]
Insert the values
[tex]\Rightarrow 2\pi \cdot 4.5\\\Rightarrow 9\pi \ in.[/tex]
Thus, the circumference of the circle is [tex]9\pi\ in.[/tex]
PLEASE HELP!!!!!! !!!:!;!!;!
Answer: the dark blue one
Step-by-step explanation:
Find the area of this triangle
Answer:
6km² sounds like a reasonable answer
can someone help me with all these!im giving brainliest:)
Step-by-step explanation:
1a.2.b.1/2 base×heightc.2 ×1/2 base×heightbase×heightb.
1m=100cm1m²=100cm×100cm1m²=10000cm²0.25m²=0.25×10000cm²0.25m²=2500cm²C.
.3.area of rectangle button+area of back+area of top d.total surface area =base×height+area of rectangle button+area of back+area of topPlease help me! DO NOT SEND LINK!
Answer:
Area is 40
perimeter is 26
Step-by-step explanation:
area = l×w
[tex]8 \times 5 = 40[/tex]
Perimeter = 2L +2W
[tex]2 \times 8 + 2 \times 5 \\ 16 + 10 \\ 26[/tex]
Renee can sew a 25-square-foot quilt in 16 hours. Genera can sew the same size quilt in 12 hours. How long would it take them to sew the quilt working together? Rate (Quilts per Hour) Time (Hours) Fraction Completed Renee One-sixteenth x Genera One-twelfth x 6 hours 6 and six-sevenths hours 8 and six-sevenths hours 28 hours
Answer:
Step-by-step explanation:
Renee can sew a 25-square-foot quilt in 16 hours. Genera can sew the same size quilt in 12 hours. How long would it take them to sew the quilt working together? Rate (Quilts per Hour) Time (Hours) Fraction Completed Renee One-sixteenth x Genera One-twelfth x 6 hours 6 and six-sevenths hours 8 and six-sevenths hours 28 hours
This is calculated as:
1/ number of hours for Renee + 1/ number of hours for Geneva = 1/ Total number of hours that they can do it together
= 1/16 + 1/12 = 1/T
Lowest common denominator = 192
= 12 + 16/192 = 1/T
= 28/192 = 1/T
Cross Multiply
28T = 192 × 1
T = 192/28
T = 6 24/192 hours
Answer:
its b
Step-by-step explanation:
i just took the test :)
What 3/8 x 4 3/6 x 4?
➪6.75
__________~ ʜᴀᴘᴘʏ ʟᴇᴀʀɴɪɴɢ ~
1. If it takes 56 square inches of paper to wrap a label around a can of soup that is 7 inches tall, how far
is it around the can?
A.6 inches
inches
B. 10 inches
C. 8 inches
D. 9 inches
Answer:
c 8 inches
Step-by-step explanation:
Can I please have help. I need these answers.
Answer:
1st: not
2nd: not
3rd: slope-intercept
4th: slope-intercept
Answer:
Read Below
Step-by-step explanation:
1) Slope Intercept
2) Slope Intercept
3) Not Slope Intercept
4) Not Slope Intercept
tudents in a fitness class each completed a one-mile walk or run. The list shows the time it took each person to complete the mile. Each time is rounded to the nearest half-minute.
5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5
Which statements are true about a histogram with one-minute increments representing the data? Select three options.
A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes.
The histogram will have a shape that is left-skewed.
The histogram will show that the mean time is greater than the median time of 7.4 minutes.
The shape of the histogram can be approximated with a normal curve.
The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
Answer:
A, D, E
Step-by-step explanation:
GOT IT RIGHT ON EDGE
The true statement about the histogram are
(a) the median and the mean are approximately equal(d) the histogram would have an approximately normal curve(e) there are more data elements between 6 and 9.How to interpret the histogram?The dataset is given as:
5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5
Using a statistical calculator, we have the following summary:
Mean = 7.43
Median = 7.5
Notice that the median and the mean are approximately equal
i.e. 7.43 ≈ 7.5
When the mean and the median are equal, the histogram would have an approximately normal curve
Also, when the dataset is sorted, we have:
5.5, 5.5, 6, 6, 6.5, 7, 7, 7.5, 7.5, 8, 8, 8.5, 9, 9.5, 10
Notice that there are more data elements between 6 and 9.
Hence, the true statement about the histogram are (a), (d) and (e)
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