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Related Questions
5⁄6 · n = 10 (solve for n)
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When you divide 5/6 and 10 you get 12.
To check your answer multiply 5/6 and 12 and you will get 10.
N=12
Explain what needs to happen to the inequality sign when dividing or multiplying by a negative number. a. nothing happens c. change the inequality sign to an equals sign b. flip the inequality sign d. the inequality needs to be graphed on a number line
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so the answer is B
Answer:
(B) flip the inequality sign.
Step-by-step explanation:
If we consider an inequality such that [tex]-x\leq7[/tex], then if we multiply the inequality with a negative number such as [tex]-1[/tex], then the inequality becomes [tex]x\geq-7[/tex].
Also, if we divide the above inequality [tex]-x\leq7[/tex], by a negative number that is [tex]-1[/tex], then the inequality becomes [tex]x\geq-7[/tex].
Therefore, if we multiply or divide an inequality by a negative number, then it flips the inequality sign.
Hence, option (B) is correct.
One number is 6 less than another. their sum is 12 find the larger number
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y=x-6
x+y=12
x+x-6 =12
2x-6=12
2x=18
x=18/2 =9
x=9
y =9-6 =3
9+3 =12
Larger number is 9
in a certain county, the number of charter schools is 4 less than twice the number of alternative schools. We know that there are 48 charter schools in the county. How many alternative schools are in the county?
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Answer:
There are [tex]26[/tex] alternative schools in the country
Step-by-step explanation:
Let
x------> the number of charter schools
y-----> the number of alternative schools
we know that
[tex]x=48[/tex]
[tex]x=2y-4[/tex] -----> equation A
substitute the value of x in the equation A and solve for y
[tex]48=2y-4[/tex]
[tex]2y=48+4[/tex]
[tex]2y=52[/tex]
[tex]y=26[/tex]
Factor completely 36x2− 121.
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Factorising (a² - b²) gives (a+b)(a-b)
Factorising 36x² - 121 gives (6x+11)(6x-11)
Line LJ is a diameter of circle K. If tangents to circle K are constructed through points L and J, what relationship would exist between the two tangents? Explain.
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If tangents are constructed through points L and J, then the tangents are perpendicular to the diameter and parallel to each other.
A ship travels 10 miles from Point A to Point B, makes a turn of 112, and travels 16 miles to Point C. If the ship travels directly from Point C back to Point A, how many miles will it travel on the last leg of the trip (from Point C to Point A)? Round your answer to the nearest tenth of a mile.
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[tex] 10^{2} + b^{2} = 16^{2} [/tex]
and [tex]100+ b^{2} =256[/tex]
and [tex] b^{2} =256-100[/tex]
so [tex] b^{2} =156[/tex]
Take the square root of both sides to find that b = 12.5
What is the factored form of the expression k^2 - 9h^2
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a^2 - b^2 = (a+b) (a-b)
So, what we need to do here is apply this equation:
k^2 - 9h^2 =
k * k - (3h)^2 =
(k + 3h) (k - 3h)
How do I solve this
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so, hmm which are those? let's check, let's set the denominator to 0, and solve for "x".
[tex]\bf x^2+6x-7=0\implies (x+7)(x-1)=0\implies x= \begin{cases} -7\\ 1 \end{cases} \\\\\\ \textit{let's check, } x=-7\quad \cfrac{(-7)+2}{(-7)^2+6(-7)-7}\implies \cfrac{-5}{49-42-7}\implies \cfrac{-5}{0} \\\\\\ x=1\quad \cfrac{(1)+2}{(1)^2+6(1)-7}\implies \cfrac{3}{1+6-7}\implies \cfrac{-3}{0}[/tex]
How much water can be held by a cylindrical tank with a radius of 12 feet and a height of 30 feet?
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Permutations!!
If 9 actors must sit together how many ways are there to seat 13 people around the table?
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To calculate the number of ways to seat 13 people around a table with 9 actors sitting together, we treat the 9 actors as one unit and then arrange the five units around the table, resulting in (4! * 9!) different possible arrangements.
Explanation:The question asks us to calculate the number of ways to seat 13 people around a table if 9 actors must sit together. This can be approached as a permutations problem in combinatorics.
Firstly, treat the 9 actors as one unit since they must sit together. With this in mind, we effectively have 5 units to arrange: the group of 9 actors and the remaining 4 individuals. As the seating arrangement is around a circular table, we can fix one person's seat and arrange the remaining units. As a result, there are (5-1)! ways to arrange these units since circular permutations eliminate the concept of a distinct 'starting' point that linear permutations have.
Now we need to consider the arrangements of the 9 actors within their group. Since their relative positions to each other matter, they can be permuted in 9! ways.
Therefore, the total number of seating arrangements would be the product of the two permutations: (5-1)! * 9!.
Calculating this gives us (4!) * 9! = (4*3*2*1) * (9*8*7*6*5*4*3*2*1) different possible arrangements.
Toby gets 78 votes, which is 52% of the total votes cast. How many students voted in Toby’s grade?
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52% = 0.52
78/0.52 =150
150 students voted
Why does a bag of chips puff up in an airplane?
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Which expression is equivalent to (cos x)(tan(–x))?
A. -sin x
B. sin x
C. -csc x
D. csc x
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[tex][cos(x)][tan(-x)][/tex] is the same as [tex][cos(x)][ -\frac{sin(x)}{cos(x)}] [/tex]
We can now cancel out the cos(x), which leaves us only with -sin(x) remaining. So your answer is A.
A model for a company's revenue is R=-15p^2+300p+12,000, where p is the price in dollars of the company's product. What prize will maximize revenue?
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[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} R = &{{ -15}}p^2&{{ +300}}p&{{ +12,000}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)[/tex]
so the Revenue will be the highest at [tex]\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}[/tex] and that will happen at the price of [tex]\bf -\cfrac{{{ b}}}{2{{ a}}}[/tex]
[tex]R(p)=-15 p^{2}+300p+12,000[/tex]
Move the 12,000 over to the other side and set the equation equal to 0:
[tex]-15 p^{2}+300p=-12,000[/tex]
In order to complete the square, the leading coefficient on the squared term has to be a 1 and it's a -15, so we have to factor that out:
[tex]-15( p^{2}-20p)=-12,000 [/tex]
Now it's ready to complete the square on it. Do this by taking half the linear term, squaring it, and then adding it in. Our linear term is 20p. Half of 20 is 10 and 10 squared is 100, so we will add in 100 on the left. Let's do this next step in two parts:
[tex]-15( p^{2}-20p+100)=-12,000 [/tex]
That's not quite complete yet because if we add in 100 inside the parethesis on the left we have to add in that same amount on the right. But on the left, we didn't just add in 100, we added in -15 TIMES 100 cuz we can't just forget about the -15 we factored out. That looks like this then:
[tex]-15( p^{2}-20p+100)=-12,000-1,500 [/tex]
The whole reason for doing this is to create a perfect square binomial on the left which is what we have done. The perfect square binomial is this (and we are going to do the subtraction on the right at the same time):
[tex]-15(p-10)^{2}=-13,500[/tex]
If we move the right side over to the left we get this:
[tex]-15(p-10) ^{2}+13,500=0 [/tex]
which gives us a vertex of (10, 13,500). That means that at a price of $10, the max revenue will be $13,500. See how beautifully that works out!??
Indicate the equation of the given line in standard form. The line that contains the point Q( 1, -2) and is parallel to the line whose equation is y - 4 = 2/3 (x - 3)
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y = mx + b
slope(m) = 2/3
(1,-2)...x = 1 and y = -2
sub and find b, the y int
-2 = 2/3(1) + b
-2 = 2/3 + b
-2 - 2/3 = b
-6/3 - 2/3 = b
- 8/3 = b
equation is : y = 2/3x - 8/3...but we need it in standard form
y = 2/3x - 8/3
-2/3x + y = -8/3...multiply by -3
2x - 3y = 8 <== standard form
If you guess an answer on two multiple choice questions with the options a, b, or c, what is the probability of you guessing the answer to both questions correctly?
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(1/3) x (1/3) = 1/9
Jake has proved that a function, f(x), is a geometric sequence. How did he prove that?
A He showed that an explicit formula could be created.
B He showed that a recursive formula could be created.
C He showed that f(n) ÷ f(n − 1) was a constant ratio.
D He showed that f(n) − f(n − 1) was a constant difference.
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C. He showed that f(n)/(f(n-1) was a constant ratio.
what is the slope of a line that passes through (-4,-13) and (19,11)
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m (gradient) = (y1 - y2) / (x1 - x2)
where (x1, y1) is the coordinate of the first point, and (x2, x2) is the coordinate of the second point
in your question:
x1 = -4
x2 = 19
y1 = -13
y2 = 11
m = (-13 -11) / (-4 -19) = -24 / -23 = 24/23 or 1.04 (2d.p.)
hope that helps :)
Answer:
24/23
Step-by-step explanation:
- vs - = + after -24,-23 =
Answer = 24, 23
It costs $35$35 per hour to rent a boat at the lake. You also need to pay a $25$25 fee for safety equipment. You have $200$200. For how long can you rent the boat?
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Sophie has a hard rubber ball whose circumference measures 13 inches. she wants to store it in a box. what is the number of cubic inches in the volume of the smallest cube- shaped box with integer dimensions that she can use?
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Because the circumference of the ball is 13 inches, therefore
2πr = 13
r = 13/(2π) = 2.069 in
In order to fit the ball into a cube-shaped box with integer dimensions, each side of the box should measure 3 inches (the next integer greater than 2.069).
The volume of the cube-shaped box is 3³ = 27 in³.
Answer: The volume is 27 in³.
What are the explicit equation and domain for a geometric sequence with a first term of 3 and a second term of −9?
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r = -9/3 = -3
an = a1 * r^(n - 1)
a1 = 1st term = 3
r = common difference = -3
now sub
an = 3 * -3^(n - 1) <== ur formula
domain : all integers where n > = 1 <==
Answer: [tex]\ a_{n}=3(-3)^{n-1}[/tex]
Step-by-step explanation:
Given: A geometric sequence with its first term [tex]a_1=a=3[/tex]
and second term [tex]a_2=-9[/tex]
We know that the common ratio in of a geometric sequence=[tex]\frac{a_{n}}{a_{n-1}}[/tex]
Thus, common ratio [tex]r=\frac{-9}{3}=-3[/tex]
We know that the explicit rule for geometric sequence is written as
[tex]a_{n}=ar^{n-1}\\\Rightarrow\ a_{n}=3(-3)^{n-1}..[\text{by substituting the values of 'a' and 'r' in it }][/tex]
Thus, the explicit rule for the given geometric sequence is [tex]\ a_{n}=3(-3)^{n-1}[/tex] for every n ,a natural number.
URGENT!!!!!!!!!!11!! Plz HElP
A school typically sells 500 yearbooks each year for $50 each. the economics class does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price.the revenue for the yearbook sales is equal to the number of yaerbooks sold times the price of the yearbook. let x represent the number of $5 decreases in price. if the expression that represents the revenue is written in the form r(x)=(500+ax)(50-bx). find the values of a and b.
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What is the prime factorization of -96? tell me how do u get the answer
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the prime factorization of -96 is : - 3×2^5
Answer: -1 x 2^5 x 3
Step-by-step explanation: To find the prime factorization of -96, we need to first factor out -1, which gives us 1 x (-1) x 2 x 2 x 2 x 2 x 2 x 3. Then, we can rewrite -1 as -1^1, and combine the 2's to get 2^5. So the prime factorization of -96 is -1^1 x 2^5 x 3.
Remember, negative numbers can also have prime factorizations.
A comic-strip writer churns out a different number of comic strips each day. For 16 days, the writer logged the number of comic strips written each day (sorted low to high): {1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7}. What type of skew can be observed in this distribution?
positive skew
negative skew
zero skew
skew cannot be observed
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We have the data set already in ascending order, so finding the quartiles is quite straight forward.
We have Q₁ = 2, Q₂ = 3, Q₃ = 5 (refer to the first picture below)
The box plot is given in the second picture and from this plot, we can see that the data tail slightly on the right, and this shows a positive skew.
What are the vertical asymptotes of the function f(x) = the quantity of 2 x plus 8, all over x squared plus 5 x plus 6? x = −3 and x = −2 x = −3 and x = 2 x = 1 and x = −2 x = 1 and x = 2?
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Find the area of a square with apothem 9 in. Round to the nearest whole number.
281 in2
305 in2
458 in2
324 in2
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So, if the apothem is 9in, the length of the side is 2 * 9in = 18 in.
And, the area of the square is (length of the side)^2 = (18 in)^2 = 324 in^2
Answer: 324 n^2
Answer:
The area of the square is 324 square inches.
Step-by-step explanation:
The apothem of the square is 9 inches.
The side of the square is twice the length of the apothem.
Hence, the side of the square is given by
[tex]a=2\times 9=18\text{ in}[/tex]
The area of a square is the given by
[tex]A=a^2\\A=18^2\\A=324\text{ in}^2[/tex]
Therefore, the area of the square is 324 square inches.
PLEASE CAN SOMEONE HELP!!!????
Use elimination to solve for x and y:
−2x−y=9
2x−9y=1
My Choices are....
a. (−4,−1)
b. (−1,−4)
c. (5,1)
d. (−1,−7)
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-2x-y=9
2x-9y=1 +
0x-10y=10
-10y=10
divide by -10
y=-1
sub back
-2x-y=9
-2x-(-1)=9
-2x+1=9
-2x=8
divide by -2
x=-4
y=-1
(x,y)
(-4,-1)
A
The values of x and y after solving both the equations by the elimination method are -4 and -1. So option A is correct
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
Two linear equations
−2x − y = 9
2x − 9y = 1
by using elimination method,
−2x − y = 9
2x − 9y = 1
0 - 10y = 10
y = -1
2x − 9× -1 = 1
2x = -8
x = -4
Hence, the values are, -4 and -1
To know more about Equation check:
https://brainly.com/question/1529522
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Flying against the wind, a jet travels 4400mi in 8 hours. Flying with the wind, the same jet travels 5820mi in 6 hours. What is the rate of the jet in still air and what is the rate of the wind?
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820 - W = 620
W = 820 - 620 = 200 miles per hour The jet in still air flies at a rate of 820 mph(miles per hour)The wind speed is 200 mph(miles per hour)
Accuracy is a measure of how close an answer is to the actual or expected value
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:)