Answer:
all values of b
Step-by-step explanation:
6b < 36 or 2b + 12 > 6.
First solve the one on the left
6b < 36
Divide by 6
6b/6 < 36/6
b <6
Then solve the one on the right
2b + 12 > 6
Subtract 12 from each side
2b+12-12 >6-12
2b >-6
Divide by 2
2b/2 >-6/2
b >-3
b<6 or b >-3
Rewriting
b>-3 or b<6
b > -3 is an open circle at -3 with a line going to the right
b < 6 is an open circle at 6 with a line going to the left
The or means we add the lines together
We have a line going from negative infinity to infinity
all values of b
Answer:
All real numbers b ∈ [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
First we solve the following inequality
[tex]6b < 36[/tex]
Divide by 6 both sides of the inequality
[tex]b<\frac{36}{6}\\\\b<6[/tex]
The set of solutions is:
[tex](-\infty, 6)[/tex]
Now we solve the following inequality
[tex]2b + 12 > 6[/tex]
Subtract 12 on both sides of the inequality
[tex]2b + 12-12 > 6-12[/tex]
[tex]2b> -6[/tex]
Divide by 2 on both sides of the inequality
[tex]\frac{2}{2}b> -\frac{6}{2}[/tex]
[tex]b> -3[/tex]
The set of solutions is:
[tex](-3, \infty)[/tex]
Finally, the set of solutions for composite inequality is:
[tex](-\infty, 6)[/tex] ∪ [tex](-3, \infty)[/tex]
This is: All real numbers [tex](-\infty, \infty)[/tex]
What is 2/3 times 3/5 in simplest form
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2}{3}[/tex] × [tex]\frac{3}{5}[/tex]
Cancel the 3 on the numerator/denominator of the fractions leaving
[tex]\frac{2}{1}[/tex] × [tex]\frac{1}{5}[/tex] = [tex]\frac{2}{5}[/tex]
Answer:
2 over 5
Step-by-step explanation:
Write the sum using summation notation, assuming the suggested pattern continues. -9 - 4 + 1 + 6 + ... + 66
Answer:
Summation notation is:
[tex]\sum_{n=1}^{16}[5(x-1)-9][/tex]
If you prefer it a little more simplified:
[tex]\sum_{n=1}^{16}(5x-14)[/tex]
Step-by-step explanation:
First my favorite part, finding a pattern between the consecutive terms.
This is an arithmetic series because the terms are going up by 5 each time.
So arithmetic sequence, think linear equations:
x | y
1 -9
2 -4
3 1
4 6
..................
n 66
We are going to have to find that n but will will eventually...
The equation for a line in point slope form is [tex]y-y_1=m(x_x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point on the line and m is the slope.
We are already have the slope is 5 (the slope is the common difference in arithmetic sequence).
I'm going to use the first point (1,-9).
So the equation in point slope form is [tex]y-(-9)=5(x-1)[/tex]
Subtract 9 on both sides:
[tex]y=5(x-1)-9[/tex]
Now we need to know how many terms we are adding so what is x if y=66.
[tex]66=5(x-1)-9[/tex]
Add 9 on both sides:
[tex]75=5(x-1)[/tex]
Divide both sides by 5:
[tex]15=x-1[/tex]
Add 1 on both sides:
[tex]16=x[/tex]
We have 16 terms in this sequence where the 16th term is 66.
Summation notation is:
[tex]\sum_{n=1}^{16}[5(x-1)-9][/tex]
You could simplify the 5(x-1)-9.
Distribute: 5x-5-9
Add like terms: 5x-14
Answer:
Step-by-step explanation:
5x^2 - 9 - 7x^2 - x + 1
Answer:
−2x^2−x−8
Step-by-step explanation:
5x^2 - 9 - 7x^2 - x + 1 = −2x^2−x−8
5*x^2-9-7*x^2-x+1 = (-2*x^2)-x-8
What is the area of △ABC ? Enter your answer, as a decimal, in the box. Round only your final answer to the nearest tenth. units² Triangle A B C has leg A C labeled 10 and leg B C labeled 17. Angle A C B is labeled 25.1 degrees.
Answer: [tex]36.1\ units^2[/tex]
Step-by-step explanation:
You need to use the SAS area formula. This is:
[tex]A=\frac{a*b*sin(\alpha)}{2}[/tex]
Given the triangle ABC, you know that:
[tex]a=AC=10\ units\\b=BC=17\ units\\\alpha=\angle ABC=25.1\°[/tex]
Therefore, substituting these values into the formula, you get that the area of the triangle ABC is:
[tex]A=\frac{(10\ units)(17\ units)*sin(25.1\°)}{2}\\\\A=36.1\ units^2[/tex]
Solve each equation. 6x^2+1=13
Answer:
The solution of given equation is x = ±√2
Step-by-step explanation:
It is given that an equation
6x² + 1 = 13
To find the solution of given equation
6x² + 1 = 13 can be written as,
⇒ 6x² = 13 - 1
6x² = 12
x² = 12/6 = 2
x = ±√2
Therefore the solution of given equation is x = ±√2
Form the union for the following sets.
X = {0, 10, 100, 1000)
Y = (100, 1000)
XU Y =
00)
{0, 10)
(100, 1000)
(0, 10, 100, 1000)
[tex]X\cup Y=\{0,10,100,1000\}[/tex]
Which is the better deal? 12 pack of markers for $8.04, 8 pack of markers for $5.60, 24 pack of markers for $14.40, or 16 pack of markers for $10.40
Answer:
$14.40 for 24 markers
Step-by-step explanation:
Lets find the price per marker
$8.04 /12 = .67
$5.60/8 =.70
$14.40 /24 =.60
$10.40/16 =.65
The lowest amount is .60, which is the best deal
$14.40 for 24 markers
simplify : (x^-2y^-4x^3)^-2
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x^{-2}y^{-4}x^3)^{-2}\implies (x^{-2}x^3y^{-4})^{-2}\implies (x^{-2+3}y^{-4})^{-2}\implies (x^{1}y^{-4})^{-2} \\\\\\ \stackrel{\textit{distributing the exponent}~\hfill }{(x^{-2\cdot 1}y^{-2\cdot -4})\implies x^{-2}y^8}\implies \cfrac{1}{x^2}\cdot y^8\implies \cfrac{y^8}{x^2}[/tex]
Box A contained 1.67 kg of flour. Box B contained 8600 g of flour. After same amount of
flour was added to each box, Box B contained 4 times as much flour as Box A. How
much flour was added to each box? Give your answer in kg.
Answer:
The amount of flour added to each box was 0.64 kg
Step-by-step explanation:
Let
x ----> the amount of flour added to each box in kg
Remember that
1 kg=1,000 g
8,600 g=8,600/1,000=8.6 kg
we know that
The linear equation that represent this situation is
(8.6+x)=4(1.67+x)
Solve for x
8.6+x=6.68+4x
4x-x=8.6-6.68
3x=1.92
x=0.64 kg
To solve this problem, we'll use algebra. Let's denote the initial amount of flour in Box A as A and in Box B as B. Also, let the amount of flour added to each box be x (in kilograms).
Given:
A = 1.67 kg
B = 8600 g, which we need to convert to kilograms. Since 1 kilogram is 1000 grams, we get:
B = 8600 / 1000 kg
B = 8.6 kg
After adding x kg of flour to each box, Box B contains 4 times as much flour as Box A. Therefore, we can set up the following equation:
B + x = 4(A + x)
Now, we plug in the values for A and B:
8.6 + x = 4(1.67 + x)
Distribute the 4 on the right side of the equation:
8.6 + x = 6.68 + 4x
Now we'll consolidate like terms:
8.6 - 6.68 = 4x - x
1.92 = 3x
To solve for x, we divide both sides by 3:
x = 1.92 / 3
x = 0.64 kg
So 0.64 kg of flour was added to each box.
18. The table shows the amount of money in a savings account after several weeks
Week
Savings
$125
$140
$155
$170
$185
$200
a. Is the sequence arithmetic or geometric? Explain. Find the common difference or common
b. Write a recursive formula for the sequence
c. Write an explicit formula for the sequence
Answer:
a. Arithmetic
b. [tex]a_{n} = a_{n-1} + 15[/tex]
c. [tex]a_{n} = 15n + 125[/tex]
Step-by-step explanation:
A sequence is arithmetic when the difference between one term and the next is a constant. On the other hand, a sequence is geometric when the next term is found by multiplying the previous by a constant.
In this case, the next term of the sequence can be found by adding $15. Therefore, the sequence is ARITHMETIC ✔️
The recursive formula will be the following: [tex]a_{n} = a_{n-1} + 15[/tex]
The explicit formula is the following: [tex]a_{n} = 15n + 125[/tex]
assume the probability of having a boy or a girl is the same. what is the probability of have a boy then a girl then another girl
Answer:
[tex]\dfrac{1}{8}[/tex]
Step-by-step explanation:
If the probability of having a boy or a girl is the same, then
the probability of having a boy = a probability of having a girl = 1/2.
Let B denote boy and G denote the girl.
The sample space of having three children is:
BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG.
The probabilities of each of those events is
[tex]Pr(BBB)=Pr(BBG)=Pr(BGB)=Pr(GBB)=\\ \\=Pr(BGG)=Pr(GBG)=Pr(GGB)=Pr(GGG)=\\ \\=\dfrac{1}{2}\cdot \dfrac{1}{2}\cdot \dfrac{1}{2}=\dfrac{1}{8}.[/tex]
Emily had $56 in her account. She deposited a $265 check, and bought three equally priced backpacks for her children. The next day, when she checked her balance, it was $243. What was the price of each backpack?
Answer:
$26
Step-by-step explanation:
Start with $56.
Add $265, obtaining a + balance of $321.
Let x represent the unit price of the backpacks. Then:
$321 - 3x = $243.
Combining like terms:
3x = $78
Then x, the price of the individual backpack, was $78/3, or $26.
Jordan is kayaking upstream. The following equation models his speed: f(x) = 2x2 − 4x − 9, where x is Anna's speed relative to land. What is the domain of the function? x ≥ 1 x ≤ −4 x ≥ −9 All real numbers
Answer:
All real numbers
Step-by-step explanation:
The given equation is:
[tex]f(x) = 2 {x}^{2} - 4x - 9[/tex]
where x is Ana's speed.
This is a quadratic function.
A quadratic function is a polynomial function.
All polynomial functions are are continuous and defined for all real values of x.
Therefore the domain of
[tex]f(x) = 2 {x}^{2} - 4x - 9[/tex]
is all real numbers.
Answer:
All real numbers
Step-by-step explanation:
The domain of a continuous parabola is always all real numbers or −∞ ≤ x ≤ ∞ because the ends of the parabola continue forever and when you graph this equation, you see that the ends of the parabola never stops, it continues on and on and on.
Refer to the coordinate system shown below. Write the ordered pair that names point M.
(9,2)
(1,8)
(1,9)
(9.1)
Answer:
(1,9)
Step-by-step explanation:
For this case we must locate the point M in the coordinate system, once we visualize it we count the number of grid that are between the axis "x" and the point M, we have that there are 9 grids, then the coordinate "y" from the point M is 9. Now we count the number of grids between the "y" axis and the point M, we see that there is a grid, so the coordinate "x" of the point M is 1.
Point M: (1,9)
Answer:
Option C
The PTO purchased 6 gallons of ice cream for a party if they served 2/3 cup to each student how many student will be served ice cream?
Please answer fast
Answer:
144 people
Step-by-step explanation:
1 gallon = 4 quarts
6 gallons = 6*4 quarts
6 gallons = 24 quarts
1 quarts= 2 pts
24 quarts = 2*24 = 48 pts
1 pts = 2 cups
48 pts = 48 * 2 cups = 96 cups
We know 6 gallons = 96 cups
96 cups ÷ 2/3 cups per person =
Copy dot flip
96 * 3/2 = 144 people
What is the measure of
Answer:
I think (c) 120 is right answer.
Answer:
C. 120°
Step-by-step explanation:
Since this is an isosceles triangle [two congruent sides], m<B is also 30°. Now, we have to the m<A by using the Interior Angles Theorem [m<1 + m<2 + m<3 = 180°]. So we do this:
60 + m<A = 180; 120 = m<A
I am joyous to assist you anytime.
Which of the following describes a similarity between the British colonies in
India and Palestine during the Cold War?
O
A. After gaining independence, leaders in both former colonies
embraced Soviet-style communism.
O
B. After gaining independence, British authorities in both former
colonies still controlled the government.
O
C. After gaining independence, territory in both former colonies was
divided due to religious conflicts.
O
D. After gaining independence, both former colonies became close
allies of the United States.
Answer:
C. After gaining independence, territory in both former colonies was divided due to religious conflicts
Step-by-step explanation:
The British had India as their colony, and Palestine as their mandate. Once the World War II ended though, the British saw that they are not in a financial position to be able to keep their colonies and mandates, so they decided to grant them independence. The independence didn't went as desired by the locals though, as both India and Palestine got partitioned because of religious reasons. India was partitioned into Hindu and Muslim part, while Palestine and Muslim and Jewish part. The situation in the Indian subcontinent quickly escalated, as well as in Palestine where the Arabs saw the formation of Israel as stealing of their land.
Answer: C. After gaining independence, territory in both former colonies was divided due to religious conflicts.
which is a graph of f(x)=5x-2/x+2with any vertical or horizontal asympototes indicated by the dash lines?
Answer:
See attachment
Step-by-step explanation:
The given function is [tex]f(x)=\frac{5x-2}{x+2}[/tex].
This rational function has a vertical asymptote at where the denominator is zero.
The denominator [tex]x+2=0[/tex] when [tex]x=-2[/tex]
There is vertical asymptote at [tex]x=-2[/tex]
The horizontal asymptote for this rational function is given by the ratio of the leading coefficient of the numerator to the leading coefficient of the denominator.
[tex]y=\frac{5}{1}[/tex]
The horizontal asymptote is [tex]y=5[/tex]
The graph of this rational function is shown in the attachment
Is this right? Or is the answer B?
For this case we must find an expression equivalent to:
[tex]\sqrt [4] {f}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So, rewriting the given expression we have:
[tex]f ^ {\frac {1} {4}}[/tex]
Answer:
Option 1
Answer:
f^(1/4)
Step-by-step explanation:
The fourth power of f, expressed with a rational exponent, is f^(1/4).
solve the equation V/7=3
Answer:
21
Step-by-step explanation:
[tex] \frac{v}{7} = 3[/tex]
Multiplying both sides by 7, we get
[tex] \frac{v}{7} \times 7 = 3 \times 7 [/tex]
The two 7s on the left cancel out to give 1, so
[tex]v = 21[/tex]
Please mark Brainliest if this helps!
An arithmetic sequence has this recursive formula:
A1=6
An=an-1-3
What is the explicit formula for this sequence?
Answer:
A
Step-by-step explanation:
Sn=a(n-1) d
this formula for Calculating arithmetic sequence
Answer: D. [tex]a_n=6+(n-1)(-3)[/tex]
Step-by-step explanation:
Given : An arithmetic sequence has this recursive formula:
[tex]a_1=6 \ \ \; \ a_n=a_{n-1}-3[/tex]
Using the given information, Second term of arithmetic sequence will be :-
[tex]a_2=a_{1}-3=6-3=3[/tex]
That means common difference = [tex]a_2-a_1=3-6=-3[/tex]
The explicit formula for arithmetic sequence is given by :-
[tex]a_n=a+(n-1)d[/tex], where a is the first term and d is the common difference.
Put a= 6 and d= -3, we get
The explicit formula for this sequence :-
[tex]a_n=6+(n-1)(-3)[/tex]
Use complete sentence to describe the net of a rectangular pyramid
Answer:
The net of a rectangular pyramid is consisting of a rectangle, for the base, and there are 4 more triangles that make up the lateral faces, and the triangles make the pyramid.
The average rate of change of g(x) between x = 4 and x = 7 is 5/6. Which statement must be true?
A. g(7)-g(4)=5/6
B. g(7-4)/7-4=5/6
C. g(7)-g(4)/7-4=5/6 D. g(7)/g(4)=5/6
Answer:
[tex]\frac{g(7)-g(4)}{7-4}=\frac{5}{6}[/tex]
So it looks like C.
Step-by-step explanation:
Average rate of a function g(x) on the interval from x=a to x=b is given by the formula:
[tex]\frac{g(b)-g(a)}{b-a}[/tex].
You can even say:
[tex]\frac{g(a)-g(b)}{a-b}[/tex].
So we have from x=4 to x=7, so the formula becomes:
[tex]\frac{g(7)-g(4)}{7-4}[/tex]
We are given this is equal to 5/6.
Answer:
Its C
Step-by-step explanation:
Which statements are true about parallelogram LMNO? Check all that apply.
x = 11
please insert the entire of the question
Answer:
1, 4, 5
Step-by-step explanation:
If y= x-6 were changed to y= x+8, how would the graph of the new fun
compare with the first one?
Answer:
Step-by-step explanation:
The graph of the new function would be the graph of the old one, translated 14 units to the left.
Only a triangle can be the base of a pyramid. True or False
Answer:
True
Step-by-step explanation:
I did it on ap3x and got it right!
Over the last 3 evenings, Keisha received a total of 81 phone calls at the call center. The first evening, she received 6 fewer calls than the second evening. The third evening, she received 3 times as many calls as the first evening. How many phone calls did she receive each evening
Answer:
First: 15
Second: 21
Third: 45
Step-by-step explanation:
In order to create the equation we need to represent the evenings with an alebraic term, in thsi case we are going to represent the second evening with an X
Second evening:x
The first night she got 6 fewer calls than the second: Second-6=x-6
The third night she received 3 times the first: 3(first night)=3(x-6)
The equation is First Night plus second night plus third night equals 81.
[tex]First+second+third=81\\x+(x-7)+3(x-6)=81\\x+x-7+3x-18=81\\5x=81+21+6\\5x=105\\x=\frac{105}{5} \\x=21[/tex]
So the first evening he received 15 calls, the second he received 21 and the third one he received 45.
A store had 100 t-shirts. Each month, 30% of the t-shirts were sold and 25 new t-shirts arrived in shipments. Which recursive function best represents the number of t-shirts in the store, given that f(0) = 100?
The correct recursive function is: [tex]\[ f(n) = f(n-1) \times (1 - 0.30) + 25 \][/tex]
Let's break down the problem:
At the start, there are 100 t-shirts in the store (f(0) = 100).
Each month, 30% of the current stock is sold, and 25 new t-shirts arrive.
So, if we denote the number of t-shirts in the store at the beginning of the nth month as f(n), we can represent the recursive relationship as follows:
f(n) = f(n-1) * (1 - 0.30) + 25
This equation means that the number of t-shirts in the store at the beginning of the nth month is equal to 70% of the number of t-shirts at the beginning of the previous month (because 30% were sold), plus 25 (because 25 new t-shirts arrive).
In this function:
- [tex]\( f(n) \)[/tex] represents the number of t-shirts in the store at the beginning of the nth month.
- [tex]\( f(n-1) \)[/tex] represents the number of t-shirts in the store at the beginning of the (n-1)th month.
- [tex]\( (1 - 0.30) \)[/tex] represents 70% of the t-shirts from the previous month remaining after 30% are sold.
- [tex]\( + 25 \)[/tex] represents the 25 new t-shirts that arrive each month.
Complete question: A store had 100 t-shirts. Each month, 30% of the t-shirts were sold and 25 new t-shirts arrived in shipments. Which recursive function best represents the number of t- shirts in the store, given that f(0)=100?
a-f(n)=f(n-1) 0.3+25,n>0
b-f(n)=100-f(n-1) = ( 3.3+25 n>0
c-f(n)=f(n-1) -( 0.7+25 n>0
d-f(n)=100-f(n-1) - C 7+25 n>0
Given the equation 3x + 1 = 16, solve for x
Answer:
x = 5
Step-by-step explanation:
3x + 1 = 16
Subtracting 1 on both sides of the equation,
3x + 1 – 1 = 16 – 1
Summing algebraically (in this case subtracting by having different signs) on both sides,
3x = 15
Isolating x by dividing both sides by 3
3x / 3 = 15 / 3
Dividing,
x = 5
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
We have the following expression:
[tex]3x+1=16[/tex]
and we need to solve for [tex]x[/tex], so the first thing we have to do (in order to leave the x alone on one side of the equation) is move the +1 to the left sife with the opposite sign (-1):
[tex]3x=16-1\\3x=15[/tex]
now we divide each side by 3, and we get:
[tex]\frac{3x}{3}=\frac{15}{3} \\x=5[/tex]
the answer is [tex]x=5[/tex]
6. The digital sum for the year 1989 is 1 + 9 + 8 + 9 or 27. How many years from 1990 to
2800 have a digital sum of 27?
A.
O
B. 1
C. 2
D. 3
Answer:
c. 2
Step-by-step explanation:
if you mix up the numbers you can find that 1998 is 27. then you have to start adding and subtracting numbers. Your digital sum includes a basic three 9's so, you also have 2799.