Answer: C(10,7)
Reason:
We can numerically compute both C(10, 3) and C(10, 7) and we would get 120 for each result.
Use the nCr combination formula
[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]
In general we have the rule C(n, r) = C(n, n-r)
Find the Greatest Common Factor of Two or More Expressions
In the following exercises, find the greatest common factor.
1. 8,18
Answer:
The GCF is 2.
Step-by-step explanation:
In my opinion, one of the easier ways to find the greatest common factor of two numbers is to get the prime factors of both and multiply the common ones. The prime factorization of 8 is 2*2*2, and the prime factorization of 162 is 2*3*3 (you can make a factor tree for both of these numbers to verify this). The only common prime factor for both of these numbers is 2, which means the greatest common factor of 8 and 18 is 2.
11. (08.03)
What are the factors of 3x² + 10x + 3? (4 points)
O (3x - 1)(x-3)
O (3x - 3)(x - 1)
O (3x + 1)(x+3)
O (3x+3)(x + 1)
Step-by-step explanation:
[tex] = 3 {x}^{2} + 10x + 3[/tex]
[tex] = 3 {x}^{2} + 9x + x + 3[/tex]
[tex] = 3x(x + 3) + 1.(x + 3)[/tex]
[tex] = (x + 3)(3x + 1)[/tex]
[tex] = (3x + 1)(x + 3)[/tex]
The answer is C.
Which of the following ordered pairs is not a solution of the system of inequalities?
y> x² - 4x-5
y< -x - 5x+6
OA) (1,-5)
B) (-1,6)
OC) (1, -7)
OD) (1,7)
The ordered pair that is not a solution of the system of inequalities is the one in option D (1, 7).
Which of the following ordered pairs is not a solution of the system?
Here we have the system of inequalities:
y > x² - 4x-5
y < -x² - 5x+6
If at least one of the inequalities is false for the given ordered pairs, then the ordered pair is not a solution for the system.
Then we only need to evaluate all the ordered pairs on the given inequalities and see when we have one that is false.
If you look at the pair D (1, 7) and we evaluate that on the second inequality, we get:
7 < (1)² - 5*1 + 6
7 < -2
This is false, then (1, 7) is not a solution of the sytem.
The correct option is D.
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If the measure of angle 2 is 92 degrees and the measure of angle 4 is (one-half x) degrees, what is the value of x? 2 lines intersect to form 4 angles. from top left, clockwise, the angles are 1, 4, 3, 2. 46 88 92 184
The value of x is 184.
What is the value of x?
Given Information
The measure of angle 2 = 92°
The measure of angle 4 = (x/2)°
From the figure, it can be seen that angle 2 and 4 make vertically opposite angles.
Vertically Opposite Angles
The pair of angles that are formed by two intersecting lines and are opposite to each other are defined as vertically opposite angles. The values of vertically opposite angles are always equal.
Here, in this case, ∠1 and ∠3 make a pair of vertically opposite angles. ∠2 and ∠4 form another pair of vertically opposite angles. Hence,
∠4 = ∠2
(x/2) = 92
x = 92 × 2
x = 184
Thus, the value of x is 184.
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Answer:
184
Step-by-step explanation:
edge
Gotta have answer ASAP!!!
“Tell the three ways of naming an angle”
Answer:
1 the vertex point if there are no other angles at the vertex that be confused.
2 three letters with the vertex as the center letter and the other letters representing points from each side.
3 a small number if one is given in the angle.
Answer:
Three Ways to Name an Angle:
1) By its Vertex
2) By the Three Points of the Angle (The Middle Point Must Be the Vertex)
3) By a Letter or Number Written Within the Opening of the Angle.
Step-by-step explanation:
In the picture, t || s, m∠1 = 10x + 2, and m∠2 = 12x – 22. Find the measure of angle 2.
Answer:
122
Step-by-step explanation:
Given information, line t is parallel to line s.
angle 1 and angle 2 are alternate angles and so their measure is equal to each other:
10x + 2 = 12x - 22 transfer like terms to the same side of the equation
2 + 22 = 12x - 10x
24 = 2x divide both sides by 2
12 = x to find the measure of angle 2 replace x with the value we found
12*12 - 22 = 122
While working at Jimmy John's last week, Hal noticed that he was running out of lettuce and became suspicious that the manufacturer was underfilling the lettuce bags. To see if the bags have the stated weight of 15 pounds, he randomly selected 13 bags and found a sample mean of 14.39 pounds with a sample standard deviation of 0.539 pounds. Is this
Yes, it is true that Jimmy John was underfilling the lettuce bags with sample mean of 14.39 pounds and sample standard deviation of 0.539.
Given sample mean =14.39 pound, sample standard deviation=0.539 and stated weight=15 pounds.
We know that mean is the number which comes after dividing sum of numbers divided by numbers. Standard deviation shows how much dispersed data is. Firstly we observe through mean and because it is less than 15, it means Jimmy John's had underfilled in atleast one bag otherwise if he had not underfilled the mean may come greater than or equal to 15 pounds.
Now come along standard deviation, we can observe that standard deviation is also low means the points are not in such a way that one point lies at 15 and other one is 25. It also shows underfilling of lettuce bags.
Hence it is true that Jimmy John had underfilled the lettuce bags.
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write the equation of a circle with a center at (1,-9) and a radius of 12
The equation of the circle is (x - 1)^2 +(y + 9)^2 = 144
How to determine the circle equation?The given parameters are:
Center, (a,b) = (1, -9)
Radius, r = 12
The circle equation is calculated as:
(x - a)^2 + (y- b)^2 = r^2
This gives
(x - 1)^2 +(y + 9)^2 = 12^2
Evaluate the exponent
(x - 1)^2 +(y + 9)^2 = 144
Hence, the equation of the circle is (x - 1)^2 +(y + 9)^2 = 144
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What is the relationship between a and b?
answer may also be none of the above
Answer:
Supplementary angles
Step-by-step explanation:
The two angles combined form a line and their measures add to 180°.
Answer: Supplementary angles
Farmers Jay, Peter and Sam own rectangular farms, as indicated in the figure. Jay owns 2 acres of land, Peter owns 4 acres and sam owns 6 acres. Find the areo of the comman pasture
The area or the common pasture will be 12 acres.
How to calculate the area?Based on the information given, the formula to use will be:
ab/ac = 2/4
b/c = 1/2 .... i
Also, ab/bd = 2/6
a/d = 1/3 .... ii
Multiply both equation
1/2 × 1/3 = 1/6
Therefore, the area will be
= 6 × 2
= 12 acres
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Of the 500 sample households, 7 had three or more large-screen TVs. Among the sample households, 121 had no car, 172 had one car, and 207 had two or more cars. Estimate the percentage of households in the town with one or more cars; attach a standard error to the estimate. If this is not possible, explain why not.
Hence, The percentage of households in the town with one or more cars = 75.8%, a standard error to the estimate= 1.92%
Total sample households = 500
Households in the town with one car = 172
Households in town with two or more cars =207
Households in the town with one or more cars = 172 + 207
= 379
The percentage of households in the town with one or more cars =
(379 / 500)*100 = 75.8%.
A standard error to the estimate = 1.92%.
Hence, The percentage of households in the town with one or more cars = 75. , a standard error to the estimate= 1.92%
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What is the length of the hypotenuse for the triangle shown? Write your answer in simplest radical form. Show all of
your work for full marks. (Hint: Use Pythagorean Theorem).
Answer:
Step-by-step explanation:
do a squared plus b squared = c squared like
2 and 5 thingy squared by 2 + 6 squared = c squared
unsquare c and you get your answer
Add the following polynomials, then place the answer in the proper location on the grid
14x^2 - 8x + 3
-6x^2 + 7x - 11
The addition of the polynomials 14x² - 8x + 3 and - 6x² + 7x - 11 is 8x² - x - 8
Polynomial(14x^2 - 8x + 3) + (-6x^2 + 7x - 11)
= 14x² - 8x + 3 - 6x² + 7x - 11
collect like terms= 14x² - 6x² - 8x + 7x + 3 - 11
= 8x² - x - 8
Therefore, the addition of the polynomials 14x² - 8x + 3 and - 6x² + 7x - 11 is 8x² - x - 8
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Need help with this geometry question.
Answer:
x = 80
Step-by-step explanation:
if ray RU bisects <QRS that means it divided the angle into two equal parts
then we can write the following equation to find the value of x:
<SRU = <QRU
50 = (x/2 + 10) subtract 10 from both sides
40 = x/2 multiply both sides with 2
80 = x
<QRS = 100 because it's the sum of <SRU and <QRU
x-11<36 need help on this equation
Answer:
x<47
Step-by-step explanation:
Take -11 to the side which 36 is. Once it crosses it stops being negative and becomes positive so the equation becomes x<36+11 which is x<47
A flower garden measures 14cm by 20cm. There is a path 2m wide all round it. Find the area of the path.
Answer:
152 m²
Step-by-step explanation:
Area of flower garden
Assuming the flower garden is rectangular and its dimensions are measured in meters:
width of garden = 14 mlength of garden = 20 m[tex]\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\\implies \textsf{Area of flower garden} & = \sf 14 \times 20\\& = \sf 280\:\:m^2 \end{aligned}[/tex]
Total area of path and garden
If there is a 2 m wide path all around the garden, the dimensions of the total area will be the dimensions of the garden extended by 4 m:
width = 14 m + 2 m + 2 m = 18 mlength = 20 m + 2 m + 2 m = 24 m[tex]\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\\implies \textsf{Total area} & = \sf 18 \times 24\\& = \sf 432\:\:m^2 \end{aligned}[/tex]
Area of path
To calculate the area of the path, subtract the area of the garden from the total area:
[tex]\begin{aligned}\implies \textsf{Area of path} & = \sf Total\:area-Area\:of\:garden\\& = \sf 432-280\\& = \sf 152\:\:m^2 \end{aligned}[/tex]
how many moles of sucrose (C12 H22 O11) would be in 8.7 L of a 1.1 M solution of sucrose
Answer:
9.57 moles
Step-by-step explanation:
There is 1.1 mole per liter....
1.1 M/ l * 8.7 L = 9.57 moles
5. The perimeter of a room is measured and found
to be 652 inches. Trim for the room is sold by
the foot. How many feet of trim must be
purchased so that the room can be trimmed?
(A) 50 ft
(B) 54 ft
(C) 55 ft
(D) 60 ft
Answer: C
Step-by-step explanation:
12in is 1 ft
652/12 is 54r4
so atlease 55
8/3 + (-9/4) reduce to simplest form
Triangles A C B and M Q R are shown. Sides A B and M R are congruent. Angles C A B and M R Q are 42 degrees. Angle C B A is 53 degrees. Angle M Q R is 85 degrees.
Are the triangles congruent? Why or why not?
Yes, all the angles of each of the triangles are acute.
Yes, they are congruent by either ASA or AAS.
No, AngleB is not congruent to AngleQ.
No, the congruent sides do not correspond.
2 triangles are connected at one side. The triangles have 2 congruent sides and 1 congruent angle. The first triangle is rotated and then translated down to form the second triangle.
By ASA postulate it can be say that the triangle ABC and triangle MRQ are congruent
What is Angle Sum Property?The sum of all three angles(interior) of a triangle is 180 degrees, and the exterior angle of a triangle measures the same as the sum of its two opposite interior angles.
Using Angle Sum Property, in ΔMRQ
<M + <R + <Q= 180
<M + 42 + 85 = 180
<M = 180 -42
<M= 53°
Now, In ΔMRQ and ΔABC
<A= <R ,
<B = <M
AB = MR
Hence, By ASA criteria ΔMRQ ≅ ΔABC
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write the equation 12^-2 in simplest form
Answer:
0.00694444444444444444444444444444
Rounded to the nearest thousandths: 0.007
Step-by-step explanation:
Use calculator.
Hope this helps!
If not, I am sorry.
The average velocity of 25 taxies is 40 km/hr and the velocity of 35 trucks is 30 km/ hr. find the combined average velocity of both types of vehicles.
Answer:
70 km/hr
Step-by-step explanation:
You just have to add both of the average velocity as you are finding the combined average velocity of both vehicles
The cost of attending an amusement park is $10 for children and $20 for adults. On a particular day, the attendance at the amusement park is 30,000 attendees, and the total money earned by the park is $500,000. Use the matrix equation to determine how many children attended the park that day. Use the given matrix equation to solve for the number of children’s tickets sold. Explain the steps that you took to solve this problem.
A matrix with 2 rows and 2 columns, where row 1 is 1 and 1 and row 2 is 10 and 20, is multiplied by matrix with 2 rows and 1 column, where row 1 is c and row 2 is a, equals a matrix with 2 rows and 1 column, where row 1 is 30,000 and row 2 is 500,000.
Based on the figures above, the numbers of children that attended the park that day is 10,000.
What is the matrix equation about?
Fist we have to use the determinant to solve for c and as such:
[tex]\frac{det.\frac{30000}{500000} \frac{1}{20} }{det. \frac{1}{10} \frac{1}{20} }[/tex]
=[tex]\frac{30000 x 20 - 500000 x 1}{1 x 20 - 1 x 10}[/tex]
= 100000/10
=10,000
Therefore, Based on the figures above, the numbers of children that attended the park that day is 10,000.
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do any questions that you can from any page!!!! I will still give you the points! Show your work, please!!!! literally do whatever you can!!!!!
Answer:
I think that the awnser to 59 is 24x⁴-15x²+27x
Factor the polynomial: x2+7x+12 A (x + 3)(x + 4) B (x + 2)(x + 6) C (x + 1)(x + 12) D (x + 7)(x + 12)
Answer:
a: (x + 3)(x + 4)
Step-by-step explanation:
assuming x^2 + 7x + 12 is the equation you are factoring
you would first multiply a * c
a is 1
b is 7
c is 12
1 * 12 = 12
then you take b and find what adds up to b but multiplies to ac
what adds up to 7 but multiplies to 12
3 and 4
so
you split the equation up like this
x^2 + 3x + 4x + 12
then you factor
x(x + 3) + 4(x + 3)
because x + 3 and x + 3 are the same we can do this
(x + 4)(x + 3)
that is your equation
so a is your answer
it doesnt matter if you have the (x + 3) or (x + 4) in the front
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option A, (x + 3)(x + 4)}[/tex]
-------------------------------------------------------------------------------------------------------------
In order to factor the polynomial we need to first split the middle term so it add up to 7 but multiplies to 12. We know that 3 and 4 can do that. We would the factor by grouping which would give us our final answer.
[tex]x^2 + 7x + 12[/tex]
[tex]x^2 + 4x + 3x + 12[/tex]
[tex]x(x + 4) + 3(x + 4)[/tex]
[tex](x + 3)(x + 4)[/tex]
Answer: [tex]\textsf{Option A, (x + 3)(x + 4)}[/tex]
Find the equivalent expression of the following: x3 (x2 + 5x + 7)
x5 + 5x3 + 7x2
x6 + 5x4 + 7x3
x5 + 4x4 + x4 + 8x3 – x3
x5 + 3x4 + x4 + 6x3 + x3
The equivalent expression of x^3 (x^2 + 5x + 7) is x^5 + 4x^4 + x^4 + 8x^3 - x^3
How to determine the equivalent expression?The expression is given as:
x^3 (x^2 + 5x + 7)
Expand the expression
x^3 * x^2 + x^3 * 5x + x^3 * 7
Evaluate the product
x^5 + 5x^4 + 7x^3
Expand the expression
x^5 + 4x^4 + x^4 + 8x^3 - x^3
Hence, the equivalent expression of x^3 (x^2 + 5x + 7) is x^5 + 4x^4 + x^4 + 8x^3 - x^3
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Which compound inequality is represented by the graph?
←
-5-4-3-2-1 0 1 2 3 4 5
O-3
O-3 < x≤1
O x≤-3 or x>1
Ox<-3 or x ≥ 1
The compound inequality represented by the graph shown in the image below is 5 < x < 9
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The image shown represents a compound inequality. It represents:
x > 5 and x < 9
The compound inequality represented by the graph shown in the image below is 5 < x < 9
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If a > b > c > d, then which is larger, a+c or b+d ? Can we tell from a > b > c > d which of a+d and b+c is larger?
Answer:
1. a+c is larger than b+d
2. No way to tell whether a+d or b+c is larger.
Step-by-step explanation:
1. Which is larger, a+c or b+d?
Let a, b, c, and d be any numbers such that [tex]a > b > c > d[/tex].
Specifically, note that [tex]a > b[/tex], and subtracting b from both sides of the inequality, observe that [tex]a-b > 0[/tex].
Similarly, [tex]c > d[/tex], and subtracting d from both sides of the inequality, observe that [tex]c-d > 0[/tex].
From this, add "a-b" (a positive number, as proven above) to both sides of the inequality.
[tex](a-b)+(c-d) > (a-b)+0[/tex]
Addition by zero (the additive identity) doesn't change anything, so the right side remains "a-b"...
[tex](a-b)+(c-d) > a-b[/tex]
... and "a-b" is positive...
[tex](a-b)+(c-d) > a-b > 0[/tex]
... so, by the transitive property of inequality...
[tex](a-b)+(c-d) > 0[/tex]
Recall that subtraction is addition by a negative number...
[tex]a+(-b)+c+(-d) > 0[/tex]
...and that addition is associative and commutative, so things can be added in any order, so the middle two terms on the left side can be rearranged...
[tex]a+c+(-b)+(-d) > 0[/tex]
Adding b + d to both sides of the inequality
[tex](a+c+(-b)+(-d))+(b+d) > 0+(b+d)[/tex]
... and simplifying
[tex]a+c > b+d[/tex]
So, a+c is larger than b+d.
2. Which is larger, a+d or b+c?
Consider the following two examples:
Example 1
Suppose a=10; b=3; c=2; d=1.
Note that [tex]a > b > c > d[/tex] ([tex]10 > 3 > 2 > 1[/tex]) and, also observe that [tex]a+d=(10)+(1)=11[/tex], and [tex]b+c=(3)+(2)=5[/tex], so a+d is larger than b+c.
Example 2
However, suppose a=10; b=9; c=8; d=1.
Note that [tex]a > b > c > d[/tex] ([tex]10 > 9 > 8 > 1[/tex]) but that [tex]a+d=(10)+(1)=11[/tex], and [tex]b+c=(9)+(8)=17[/tex], so a+d is smaller than b+c.
So, in one example, a+d is bigger, and in the other, a+d is smaller. Therefore, there is no way to tell which of a+d or b+c is larger from only the given information.
3a
From the information given, determine which triangles, if any, are
congruent and state by which rule. If the triangles cannot be shown
to be congruent, write, "Cannot be determined" and explain.
Answer: [tex]\triangle COA \cong \triangle DOB[/tex] by the rule ASA
Step-by-step explanation:
[tex]\overline{CO} \cong \overline{OD}[/tex] (given)
[tex]\angle ACO \cong \angle ODB[/tex] (given)
[tex]\angle COA \cong \angle BOD[/tex] (vertical angles)
So, [tex]\triangle COA \cong \triangle DOB[/tex] by the rule ASA.
HELP HELP HELP
EASY 18 POINTS!
Solving Quadratic Equations Algebraically Explain how to determine the solutions to a quadratic equation, algebraically. Create a problem with a quadratic equation that you would solve algebraically and solve it.
Step-by-step explanation:
So a quadratic equation in factored form is generally given in the form: [tex]a(x-b)(x+c)[/tex]. Sometimes x may have a coefficient but I'll just create a simple quadratic equation. In this form it's easy to see that the solutions to the equation are b and -c, because if you input them in as x, you'll get one of the factors equal to 0, and it'll make the y-value zero, thus it's a solution. So b and c can literally be anything. But for this example I'll chose 3 and 6 to keep it simple. Inputting these as b and c you'll get: [tex]a(x-3)(x+6)[/tex]. Now the value of a will determine the stretch/compression, but to keep it really simple I'll just say that a=1. So now all you have to do is expand the two factors. When you expand them you'll get it in the form: [tex](x-b)(x+c) = x^2+cx-bx-bc[/tex] by using the foil method. So if you expand the two factors in this example you'll get: [tex]x^2+6x-3x-18[/tex] which simplifies to [tex]x^2+3x-18[/tex]. So cool now we have our equation. Now it's time to solve it, you can either factor it (since you literally just had it in factored form), or use the quadratic formula I'll show both methods
Factoring:
When you factor an equation in the form: [tex]ax^2+bx+c[/tex]. You usually multiply the coefficients a and c. Then you'll find factors of ac that add up to b. In this example ac is really just c because a is 1...
So given the equation: [tex]x^2+3x-18[/tex] You want to look for factors of -18 that add up to 3. And whenever you have a negative number as AC you really want to look for factors that have a distance of b which in this case is 3. For example I would say that 9 and 3 have a distance of 6. And then after that depending on whether b is negative or positive. I can choose which factor will be negative and which will be positive. If b was 6 well then 9 would have to be positive and 3 would be negative, but if b was -6 then 9 would have to be negative and 3 would have to be positive.
So in this example look for factors that have "distance" of 3. Well 6 and 3 have a "distance" of 6 so I know those 2 will be the factors. Since 3 is positive that means 6 will be positive, and 3 will be negative. so they add up to 3 and multiply to get -18
AC factors that add up to 3 and multiply to -18: 6 and -3
Now write it in factored form using the two factors:
[tex](x-3)(x+6)[/tex]
Now set up each factor equal to 0 and solve for x:
[tex]x-3 = 0\\x=3[/tex]
[tex]x+6=0\\x=-6[/tex]
This gives you the two solutions: x=3 and x=-6
Quadratic Formula:
The quadratic formula is usually used when a equation can't be easily factored. The quadratic formula gives both zeroes in the equation: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]. Notice the plus or minus sign next to the square root? That's where the the two solutions will come from, or possibly one solution if it's at the vertex. or maybe even no real solutions if the quadratic never intersects the x-axis.
Ok so let's identify a, b, and c. We're given the equation: [tex]x^2+3x-18[/tex]. so a=1, b=3, and c=-18. Plugging these values into the equation you get:
[tex]x=\frac{-(3)\pm\sqrt{(3)^2-4(1)(-18)}}{2(1)}\\[/tex]
Simplifying it a bit gets you the equation:
[tex]x=\frac{-3\pm\sqrt{81}}{2}[/tex]
Simplifying the radical gives you:
[tex]x=\frac{-3\pm9}{2}[/tex]
Use the positive sign:
[tex]x=\frac{-3+9}{2}\\x=\frac{6}{2}\\x=3[/tex]
Use the negative sign:
[tex]x=\frac{-3-9}{2}\\x=\frac{-12}{2}\\x=-6[/tex]
This gives you the two solutions x=3, and x=-6