Answer:
Step-by-step explanation:
If we divide 24 by 6, we get 4, which is the other factor of 24 when given the one factor of 6. Same goes here. In order to find out what the other factor of [tex]y^2-10y+24=0[/tex] is when given one factor of y - 4, we simply divide the second degree polynomial by y - 4 to get the quotient. The quotient, then, is the other factor. Synthetic division is the easiest way to do this.
If y - 4 is the factor, then by the Zero Product Property, y - 4 = 0 and y = 4. Setting up synthetic division:
4| 1 -10 24
____________
The rule is to start by bringing down the first term, multiplying it by the number outside, then putting that product up under the next term in line:
4| 1 -10 24
4
1
Then add the column, multiply the sum by the number outside, and put that product up under the next term in line:
4| 1 -10 24
4 -24
1 -6
And add the last column and that is the remainder. We get a 0 remainder. That means that y - 4 goes evenly into the polynomial and the other factor we are looking for is found in the numbers under the addition line. These numbers are the leading coefficients of the depressed polynomial, the polynomial that serves as the other factor: 1y - 6.
Therefore, the 2 factors that multiply together to give us [tex]y^2-10y+24=0[/tex] are (y - 4)(y - 6) and we can check ourselves by multiplying this out by FOILing to see if the result is the polynomial we started with. It is, so we're all done!
Answer:
its ( y-6 )
Step-by-step explanation:
well if you use the FOIL method you will get that answer. also i took the test and got a 100 so there u go.
Which expression is equivalent to
Answer:
[tex]\frac{(x+2)}{(x-1)}[/tex]
Step-by-step explanation:
[tex]\frac{x^2 + x -2}{x^2 -2x+1}[/tex] =
[tex]\frac{(x+2)(x-1)}{(x-2)(x-1)}[/tex] =
[tex]\frac{(x+2)}{(x-1)}[/tex]
Solve the equation 5x + 2(2x -23) = -154
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
5x+2(2x-23)=-1545x+4x-46=-1549x-46=-1549x=-154+469x=-108x=[tex]\sf{\dfrac{-108}{9} }[/tex] x=-12Answer:
x = -12
Step-by-step explanation:
5x + 2(2x - 23) = -154
Distribute;
5x + 4x - 46 = -154
Collect like terms
9x - 46 = -154
Add 46 to both sides;
9x = -108
Divide both sides by 9
x = -12
PLEASE HELP!
Record the lengths of the sides of ΔABC and ΔADE.
I would appreciate it.
AB: 20
BC: 12
AC: 16
AD: 10
DE: 6
AE: 8
A particular strain of bacteria triples in population every 45 minutes Assuming you start with 50 bacteria in a Petri dish how many bacteria will there be in 4.5 hours
Answer:
4.5 hours in minutes = 270
Every 45 minutes, bacteria triples
You start with 50
Divide 270 (total time) by 45 (every time bacteria triples)
270/45 = 6
36,450 bacteria
Thank you guys for helping me !! Can you help me with this question ?
Answer:
(A). x² + y² - 4x + 6y - 3 = 0
Step-by-step explanation:
(x - 2)² + (y + 3)² = 4²
x² - 4x + 4 + y² + 6y + 9 - 16 = 0
x² + y² - 4x + 6y - 3 = 0
Solve the system of equations using substitution.
y = x + 6
y = –2x – 3
Answer:
x = -3
y= 3
Step-by-step explanation:
y = x + 6 -----------------------(I)
y = -2x - 3 ---------------------(II)
Substitute y =x +6 in equation (II)
x + 6 = -2x - 3
Add 2x to both sides
x + 2x +6 = -3
Combine like terms
3x + 6 = - 3
Subtract 6 from both sides
3x = - 3 - 6
3x = -9
Divide both sides by 3
x = -9/3
x = -3
Plug in s = -3 in equation (I)
y = -3 + 6
y = 3
99999+999=????????????????????????????
Answer:
100998 is the answer.
I hope this help u.
Answer:
100998
Step-by-step explanation:
₁ ₁ ₁ ₁ ₁
99999
+ 999
100998
you can also think of it as
99999(+1) + 999(-1)
100000+998
100998
Please help 50 points!
d=10
Answer:
Solution given:
[tex]\sqrt{25+3x}=d+2x[/tex]
squaring both side
25+3x=(d+2x)²
when x=-3
25+3*-3=(d+2*-3)²
25-9=(d-6)²
16=(d-6)²
[tex]\sqrt{16}=d-6[/tex]
4=d-6
d=4-6
d=10
Answer:
d = 6
Step-by-step explanation:
[tex] \sqrt{25 + 3( - 3)} = d + 2( - 3) \\ 4 = d - 6 \\ d = 10[/tex]
hopefully this makes sense
:)
simplify m√p + n√p - √p
Answer:
[tex]{ \tt{m \sqrt{p} + n \sqrt{p} - \sqrt{p} }} \\ = { \tt{ \sqrt{p}(m + n - 1) }}[/tex]
What is the vertex of the function f(x) = -|x + 7| − 4?
A.
(-7,-4)
B.
(7,4)
C.
(-7,4)
D.
(7,-4)
Answer:
it would be
D.
(7,-4)
Mark me as brainliest pleases
Answer:
it would be A (-7,-4)
Step-by-step explanation:
pleaseee help mee helpp meeee
Answer:
i can help you i know this answer
(06.04 MC) Dennis drew the line of best fit on the scatter plot shown below: What is the approximate equation of this line of best fit in slope-intercept form?
Answer:
Step-by-step explanation:
In order to write the equation of this line, we need to pick 2 points on the graph where the line goes right through the intersection of the grids. Actually, you only need 1 of these, because the line goes through at (0, 15). Another point then can be (6, 6). Locate this point so you know what I means when I say that the line goes right through where the grids intersect at x = 6 and y = 6 (as opposed to somewhere in the middle of one of these grids). Find the slope between these 2 points:
[tex]m=\frac{6-15}{6-0}=-\frac{9}{6}=-\frac{3}{2}[/tex]
Since there's only one choice with that slope, that is the choice you want.
Nick works part-time at a bookstore. His pay varies directly with the number of hours worked. In one week, he earned $120 for 8 hours of work.
a) Define two variables for this relation.
b) Describe the rate of change in words.
c) Determine an equation to represent the relation:
d) Use the equation to determine how many hours Nick must work to earn $345
Answer:
23 hoiurs
Step-by-step explanation:
Given data
a. The two variables are
1. Number of hours worked
2. The amount earned
b. The rate is given as
=120/8
=$15 per hour
c. The equation is given as
rate=Amount earned/ number of hours worked
15= 345/hours
make hours subject of the formula we have
hours= 345/15
hours= 23 hours
Hence he must work for 23 hours
the price of a box of cereal incresed by 45% if the original price of the box of cereal was 5$ what is the new price?
Answer: 7.25
Step-by-step explanation:
Make six prime numbers using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 once each.
~can you plz explain?!
Answer:
2, 3, 5, 7, 11, 13.
Step-by-step explanation:
A prime number is a number that you don't get a whole number when divided by 2 but you do get a whole number when divided by prime numbers such as 3,5,7,11... Basically a number with two factors, it can only be divided by 1 or themselves. for example:
9/2 = 4.5 (this is not a whole number so it might be a prime.
9/3 = 3 (it works when divided by a prime number.
another:
8/2 = 4 (it gives a whole number when divided by 2 therefor, it can't be a prime number.
Answering:
There are 6 prime numbers at the top^^^^.
One possible answer is 2, 3, 5, 41, 67, 89
Another possible answer is 2, 3, 5, 47, 61, 89
Other answers may be possible.
=============================================================
Explanation:
This is a trial and error type of problem. Though with practice it's not as blind of randomly guessing.
We have 9 values here. If we paired them up, then we can form at most 4 pairs (since 9/2 = 4.5 rounds down to 4). That means we won't be able to form six two-digit primes. Some of the primes must be single digits.
We can have 3 single digit primes and 3 two-digit primes since 3+2*3 = 9.
The single digit primes are: 2, 3, 5, 7
Let's say 2 and 5 are definitely locked down to be the single digit group. I'm doing this since we can't have 2 or 5 as the units digit. If the units digit is 2, then 2 is a factor and it's not prime. Similarly, if 5 is the units digit, then 5 is a factor and that two digit value is not prime.
For good measure, we'll throw 3 in there as well and see what happens.
------------------
The digits we have left are: 1, 4, 6, 7, 8, 9
The number 14 isn't prime, but 41 is prime
67 is prime so that's another two values off the list
lastly, 89 is prime so that works as well.
So one possible sequence is 2, 3, 5, 41, 67, 89
Notice how we can swap the 1 and 7 to go from 41,67 to 47,61; this gets us two other primes. So another possible answer is 2, 3, 5, 47, 61, 89
------------------
Side note: having the list of primes on a reference sheet is a handy recommendation. You only need to go up as high as 97 which is the largest two digit prime.
Which of the following is the number of sides for a regular polygon that will
not form a regular tessellation?
A. 6
B. 4
C. 7
D. 3
Answer:
A
Step-by-step explanation:
A
The number of sides for a regular polygon that will not form a regular tessellation is 7. The correct option is C.
What is a polygon?A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.
A tessellation or tiling is the seamless covering of a surface, frequently a plane, with one or more geometric shapes, known as tiles. One regular polygon can be used to create a single regular tessellation. Two or more regular polygons are used in a semi-regular tessellation.
Triangles, squares, and hexagons are the only three regular tessellations.
Now, the name of the polygon having 3, 4, and 6 sides is triangle, square, and Hexagon. Therefore, the only regular polygon that will not form a regular tessellation is heptagon, which has 7 sides.
Hence, the number of sides for a regular polygon that will not form a regular tessellation is 7.
Learn more about Polygon here:
https://brainly.com/question/10441863
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What is the graph of the solution set of the inequality?
Answer:
The Tasty Beans Coffee House being planned for the corner of SE 12th and Main will ruin a perfectly nice neighborhood. Besides the fact that Tasty Beans already has coffee shops all over the city, it will pull business away from local coffee houses that have been here for decades. In addition, there is already a parking problem on that street, and the new business will just add to the congestion. They're planning a drive-up window, too, and that will mean a steady stream of traffic in a very high-volume area. Ask anyone walking down the street, and they'll tell you this is a bad idea. I speak for my whole neighborhood when I say, "Go away, Tasty Beans!"
Step-by-step explanation:
Which best explains why all equilateral triangles are similar?
O All equilateral triangles can be mapped onto each other using dilations.
O All equilateral triangles can be mapped onto each other using rigid transformations.
O All equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations.
O All equilateral triangles are congruent and therefore similar, with side lengths in a 1:1 ratio.
Answer:
the correct answer is option 1.
The correct explanation is: All equilateral triangles are congruent and therefore similar, with side lengths in a 1:1 ratio.
What are similar triangles?Those triangles look the same but are different in size.
And in similar triangles,
the corresponding sides are in proportion to each other and the corresponding angles are equal to each other.
In an equilateral triangle, all three sides are congruent, and all three angles are congruent.
Therefore, any equilateral triangle can be transformed into any other equilateral triangle through a combination of translations, rotations, and reflections, without changing the size or shape of the triangle.
Thus, all equilateral triangles are similar, with side lengths in a 1:1 ratio, since they have the same shape but may differ in size.
To learn more about similar triangles;
https://brainly.com/question/14926756
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Find the length of the hypotenuse of a right angle triangle if remaining side are 3 cm and 4 cm.
Answer:
5 cm
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
let h be the hypotenuse , then
h² = 3² + 4² = 9 + 16 = 25 ( take the square root of both sides )
h = [tex]\sqrt{25}[/tex] = 5
{(5,2), (-2,4), (2, -7)}
Domain:
Range:
Answer:
Step-by-step explanation:
The domain are all the x values in order, no repeats allowed:
D = {-2, 2, 5}
Same thing for the range, except these are the y values:
R = {-7, 2, 4}
The coordinates stated this way don't match up to what they are in coordinate form, but they don't have to.
Answer:
Domain : {-2,2,5}
Range:{ -7,2,4}
Step-by-step explanation:
The domain is the inputs
Domain : {-2,2,5}
The range is the outputs
Range:{ -7,2,4}
find value of the variable
Answer:
x=10
Step-by-step explanation:
16/24=(x-2)/12
or, 16/2=x-2
or, 8=x-2
or, x-2=8
or, x=10
Answered by GAUTHMATH
7. If the supplement of an angle is 69, then find its complement.
Answer:
no solution
Step-by-step explanation:
Supplementary angles add to 180
Let x be the supplement
x+69 = 180
x = 180-69
x =111
The complement of an angle means they add to 90
111+y = 90
y = 90-111
y =-21
But an angle cannot be negative so there is no solution
Answer:
21 degrees.
Step-by-step explanation:
To find the complementary angle you have to subtract the given angle from 90.
so,
90 - 69 = 21.
Extra info: if you need to find the supplementary angle you need to subtract the given angle from 180.
The air in poultry-processing plants often contains fungus spores. Inadequate ventilation can affect the health of the workers. The problem is most serious during the summer. To measure the presence of spores, air samples are pumped to an agar plate and "colony-forming units (CFUs)" are counted after an incubation period. Here are data from two locations in a plant that processes 37,000 turkeys per day, taken on four days in the summer. The units are CFUs per cubic meter of air.
Day Day 2 Day 3 Day 4
Kill room 3175 2526 1763 1090
Processing 529 141 362 224
The spore count is clearly higher in the kill room. Give sample means and a 99% confidence interval to estimate how much higher the spore count is in the kill room?
Answer:
-611.031 < μd < 4260.031
Step-by-step explanation:
This is a matched pair design :
______Day1 Day 2 Day 3 Day 4
x1 Kill room 3175 2526 1763 1090
x2 Processing 529 141 362 224
First we obtain the difference, d ;
d = (x1 - x2)
d = 2646, 2385, 1401, 866
The mean difference, dbar = Σd/ n = 7298 / 4 = 1824.5
The standard deviation of difference,
Sd = √(Σx-dbar)²
Using calculator, Sd = 834.086
The 99% confidence interval :
Mean ± margin of error
dbar ± margin of error
Margin of Error = Tcritical * Sd/√n
Tcritical at 99%, df = n-1 ; df = 4-1 = 3
Tcritical = 5.84
Margin of Error = 5.84 * 834.086/√4 = 2435.53112
Confidence interval = 1824.5 ± 2435.53112
(-611.031 ; 4260.031)
PLS HELP!
When rolling a single number cube, what are the odds, in simplest form, in favor of rolling a 4 or a 5? A. 1:1 B. 1:2 C. 1:3 D. 1:5
Answer: 1:3
Step-by-step explanation:
The odds are 2/6 because you’re given 2 choices from the 6 side die you can then simplify that fraction to 1:3
Plz help out will give brainliest
Answer:
10 degrees = C
Step-by-step explanation:
Total internal angles add to 180 degrees.
Add all values of c and set equal to 180.
18c = 180.
c=10
Answer:
c = 10
Step-by-step explanation:
3c + 6c + 9c = 180 degrees. Every triangle has 180 degrees.
18c = 180 Combine the like terms. Divide by 18
18c/18 = 180/18
c = 10
Find the value of x. Round the length to the nearest tenth.
Answer:
[tex]x=opposite\: side\: of \:22[/tex]
[tex]16=hypotenese[/tex]
[tex]sin22=opp/hyp[/tex]
[tex]sin22=\frac{x}{16}[/tex]
[tex]\Longrightarrow x=16\times sin22[/tex]
[tex]x=5.99[/tex]
[tex]x=6.0[/tex]
[tex]OAmalOHopeO[/tex]
Please Solve:
x^2-4x-5=0
The total enclosed area is ____ square units. Round to the nearest tenths place (1 decimal place).
Answer: 47.6
Is this right?
Answer:
siis corretoed
Step-by-step explanation:
Instructions: Find the measure of the indicated angle to the nearest degree.
29 and 17
Answer:
30º
Step-by-step explanation:
because it is a right triangle, we can use trig functions to solve
tan^{-1}=17/29=30.379
Integrate the following.[tex]\int\limits^a_b {sin(x)} \, dx[/tex]
Answer: -cos(a)+cos(b)
Step-by-step explanation:
To integrate is the same as saying to find the antiderivative.
[tex]\int\limits^a_b {sin(x)} \, dx[/tex] [antiderivative of sinx is -cosx]
[tex]-cos(x)|_b^a[/tex] [include boundaries]
[tex]-cos(a)+cos(b)[/tex]
Therefore, the integral would be -cos(a)+cos(b).
