Answer:
D. -4
Step-by-step explanation:
a1 is the first term.
a1 = -10
an = an-1 + 3
The recursive formula means that each term after the first term is 3 more than the previous term.
a2 = a1 + 3 = -10 + 3 = -7
a3 = a2 + 3 = -7 + 3 = -4
Look at the graph below.
what is the slope of the line ?
Answer:
The slope is [tex]-\frac{1}{5}[/tex].
Step-by-step explanation:
Choose 2 points on the graph.
(7,3) and (2,2)
Use slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{2-3}{2-7}[/tex]=[tex]\frac{-1}{-5}[/tex]
The slope is [tex]-\frac{1}{5}[/tex].
Answer:
[tex]\frac{1}{5}[/tex] or [tex]0.2[/tex]
Step-by-step explanation:
The slope refers to the gradient of the line.
There is a formula to find the gradient of a line where m is the gradient:
[tex]m=\frac{y_{2}-y_{1} }{x_{2} - x_{1}}[/tex]
So, we will take two points on the line.
Let's take our first point as (-3, 1) and our second as (7, 3).
Let's work with the [tex]y[/tex] values.
The first [tex]y[/tex] value is 1 and the second [tex]y[/tex] value is 3.
So, in the numerator, they would look like [tex]3 - 1[/tex].
Let's work with the [tex]x[/tex] values.
The first [tex]x[/tex] value is -3 and the second [tex]x[/tex] value is 7.
So, in the denominator, this would look like [tex]7--3[/tex].
Let's use these in the fraction and work out our answer:
[tex]m = \frac{3-1}{7--3} = \frac{2}{10} = \frac{1}{5} = 0.2[/tex]
Therefore, our final answer is [tex]\frac{1}{5}[/tex] or [tex]0.2[/tex].
Write down seven multiplications with an answer of -20
Answer:
-10 x 2
10 x -2
5 x -4
4 x -5
20 x -1
-20 x 1
2 x 2 x -5
Step-by-step explanation:
Answer:
-1 x 20= -20
-20 x 1 = -20
-5 x 4= -20
-4 x 5= -20
-2 x 10= -20
-10 x 2= -20
-2 x 2 x 5 = -20
Step-by-step explanation:
use factors of 20
hope this hepled :)
the cost of 10 water bottles is $55. find the unit cost of the water bottle
Answer:
$5.50
Step-by-step explanation:
For one water bottle you divide the 55 dollars by 10
55/10= 5.5
Answer:
$5.50
Step-by-step explanation:
We must divide to solve so lets do that now :)
55/10 = 5.50
Each bottle will cost 5 dollars and 50 cents :)
Have an amazing day!!
Please rate and mark brainliest!!
This month is October. Which month will 2451 months be later?
Answer:
January
Step-by-step explanation:
The month October is the 10th month,
there is 12 months in a year
2451 / 12 = 204.25
0.25 of a year, 1/4 of the year so 12/4 = 3
2451 months is 204 years and 3 months
3 months after October is January
10 + 3 = 13 where December is 12 and the 13th month is January
The table shows the age of some participants in a quiz competition and the number of questions they could answer correctly:
Age (years) (x)
15 21
17 22 16 19 18
Number of questions they could answer (y) 17 17 17 17 17 17 17
What is the correlation coefficient for the data, and what does it represent?
O0; it represents no correlation between x and y
O1; it represents a linear positive correlation between x and y
O-1; it represents a linear negative correlation between x and y
O1; it represents a linear negative correlation between x and y
Option first "0; it represents no correlation between x and y" is correct there is no relation between x and y.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
[tex]\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}[/tex]
We have:
Age (years) (x) 15 21 17 22 16 19 18
Number of questions they could answer(y) 17 17 17 17 17 17 17
As we can see all y values are the same.
n∑y² = 7(2023) = 14161
(∑y)² = 119² = 14161
If we put the value of the above data the value will become undefined.
Thus, option first "0; it represents no correlation between x and y" is correct there is no relation between x and y.
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PLEASE ANSWER ASAP!!!!!!!
What is the exact value of cos(tan−1(−1))/sin(cos−1(−3√2))?
Enter your answer, as a simplified fraction, in the box.
cos(tan−1(−1))/sin(cos−1(−3√2))=
The exact value of [tex]\dfrac{cos(tan^{-1}(-1))}{sin(cos^{-1}(-\frac{3}{\sqrt{2}})}[/tex] would be root 2.
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Given;
[tex]\dfrac{cos(tan^{-1}(-1))}{sin(cos^{-1}(-\frac{3}{\sqrt{2}})}[/tex]
We know that
The inverse tan(-1) = -π/4
cos(-π/4) = 1/√2
The inverse cos(√3/2) = π//6
sin(π/6) = 1/2
Then substitute
[tex]\dfrac{cos(tan^{-1}(-1))}{sin(cos^{-1}(-\frac{3}{\sqrt{2}})}\\\\[/tex]
[tex]\dfrac{(1/\sqrt{2}) }{(1/2)} \\\\= \sqrt{2}[/tex]
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HELPP URGENT and please explain
Answer:
A) There are two complex solutions.
Step-by-step explanation:
To know how many solutions a quadratic equation has, calculate the discriminant of the equation.
discriminant = b² - 4ac
where a = coefficient of x²
b = coefficient of x
c = constant of equation
if b² - 4ac > 0 , then equation has 2 real roots
if b² - 4ac = 0 , then equation has 1 real, repeated root
if b² - 4ac < 0 , then equation has 2 complex roots
In this case, discriminant = 9² - 4(-2)(-12)
= -15
As -15 < 0, equation has 2 complex roots.
P(x) Q(x) = R(x); if P(x)
72 Am
R(x); if P(x)=x+2 and R(x) = x³ - 3x² - 6x-2, what is Q(x)?
Answer:
Q(x) is = to 11x² that's my answer
Complete the hypothesis about the product of two rational numbers. Select the correct answer from each drop-down menu. The product of two rational numbers is number because multiplying equivalent to the ratio of which is number.
Answer: I hope this helps you in what you're doing.
Step-by-step explanation: Because multiplying two rational numbers results in the ratio of two integers, which is also a rational number, the product of two rational numbers is also a rational number.
Mike mixes paint at a hardware store. A certain shade of orange paint is made by
mixing white, red, and yellow paint in a ratio of 4 to 3 to 2. If Mike wants to make 3
gallons of paint that is this shade of orange, how many gallons of red paint will he
need?
Answer: 1 gallon
Step-by-step explanation:
white: red: yellow
4 : 3 : 2
total units: 9 units
total amount: 3 gallons
one unit: 3/9
= 1/3
no of units of red: 3 units
amount of paint needed: 1/3 x 3
= 1 gallon
If a = 2√3, then the exact value of b is...
Answer:
b = 2
Step-by-step explanation:
using the tangent ratio in the right triangle and the exact value
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{b}{a}[/tex] = [tex]\frac{b}{2\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
b × [tex]\sqrt{3}[/tex] = 2[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
b = 2
Answer:
C. b = 2Step-by-step explanation:Given that a = 2√3.
Let's find value of b...
[tex]\bf \tan( {30}^{o} ) = \cfrac{b}{a} [/tex][tex] \bf \cfrac{1}{ \sqrt{3} } = \cfrac{b}{2 \sqrt{3} } [/tex][tex]\bf b = 2[/tex]______________________32 divided by 4x [16x1/2]-2
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Answer:
The ordered pair which makes both the inequalities true is = (–2, 2)
Step-by-step explanation:
inequalities are the relationships between two expressions which are not equal to one another.
Inequalities are represented by the following relations:
≤: "less than or equal to"<: "less than"≠: "not equal to">: "greater than"≥: "greater than or equal to"an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
so, the option B(-2,2) satisfies the inequalities expressions given in the question
therefore we can conclude that (-2,2) is the ordered pair which ,makes both the given inequalities true.
so the correct answer is (-2,2)
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I need some help with this an explanation would be nice as well thanks
Answer:
Step-by-step explanation:
to collect data about the amont of time spent
Answer:
Probably the first one because the other two questions would be un-reliable
Step-by-step explanation:
What is the completely factored form of x4y – 4x2y – 5y? y(x2 – 5)(x2 1) y(x2 5)(x2 – 1) (x2y – 5)(x2 1) (x2y 5)(x2 – 1)
Answer:
y (x² + 1) (x² - 5)
Step-by-step explanation:
Factorization:Take 'y' from each term.
x⁴y - 4x²y - 5y = y[x⁴ - 4x² - 5]
Now factorize x⁴ - 4x² - 5.
Sum = -4
Product = -5
Factors = -5 , 1
When we add (-5) + 1, it gives (-4) and when we multiply (-5)*1, gives (-5).
x⁴ - 4x² - 5 = x⁴ + x² - 5x² - 5
= x²(x² + 1) -5(x² + 1)
= (x²+ 1) (x² - 5)
x⁴y - 4x²y - 5y = y (x² + 1) (x² - 5)
can someone please help mee
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:Domain = [-9, -1][/tex]
[tex]\qquad \tt \rightarrow \:Range = [-1 , 3][/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Domain = All possible values of x for which f(x) is defined
[ generally the extension of function in x - direction ]
Range = All possible values of f(x)
[ generally the extension of function in y - direction ]
[tex] \large\textsf{For the given graph : } [/tex]
[tex]\qquad \tt \rightarrow \: domain = [ - 9, -1][/tex]
[tex]\qquad \tt \rightarrow \: range= [ -1,3][/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The function a(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. a(b)=14 x b+5/2
A function assigns the values. The inverse of the function in terms of the area will be b=(a/7)-5.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete question is,
The function a(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. a(b)=14 x b+5/2. Write a function in terms of area to find the length of the other side.
The given is the function of the area of the trapezoid, a(b)=14 x b+5/2.
The area of a trapezoid is given as,
Area = Height × [(Sum of parallel sides)/2]
The given function can be written in terms of area as,
[tex]a = 14\times \dfrac{(b+5)}{2}\\\\\dfrac{2(a)}{14} = b+5\\\\\dfrac{2(a)}{14} -5= b\\\\\dfrac{(a)}{7} -5= b[/tex]
Hence, the inverse of the function in terms of the area will be b=(a/7)-5.
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!!HELP PLS!! a triangle has side lengths measuring 3x cm 6xcm and h cm which expression describes the possible values of h in cm? 4x < h < 10x, 10x < h < 4x, h=4x, h=10x
Based on the triangle inequality theorem, the possible values of h in cm is: A. 4x < h < 10x
What is the Triangle Inequality Theorem?Based on the triangle inequality theorem, two sides of a triangle must be equal or more than the third sides.
Given a values of the side lengths of a triangle as, 3x, 6x, and h cm, the possible values would be determined as shown below:
h < 3x + 7x or 7x - 3x < h
h < 10x or 4x < h
The possible values of h would be: 4x < h < 10x.
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the sum of m and n is 32, and the value of m is three times the value of n. what is the value of m and n?
A. m+n=32
n= 3m
B. m+3n=32
m=3n
C. m+n=32
m=3n
D. m+n=3
32m=n
Answer:
The correct set of equations is C.
Step-by-step explanation:
m + n = 32
m = 3n
We have 4n = 32, so n = 8 and m = 24.
Hi, so I know the answer to this problem (now that I got it wrong) but I'm not quite sure why I was wrong, help?
Answer:
[tex]-2x^2-x[/tex]. Your answer was wrong because "x-squared" terms didn't cancel.
Step-by-step explanation:
To solve this problem, set up an equation. We know something is supposed to be added to the expression [tex]2x^2+2x[/tex], and the result should be x. So:
[tex]2x^2+2x+(\text{ ? })=x[/tex]
We want to solve for the question mark... the unknown thing that we're adding to the original expression, in order to get x.
It is uncommon to put question marks in equations to represent quantities. Usually we use a letter. Since x is already being used in the equation, we should pick something else ... we could use "y".
[tex]2x^2+2x+(\text{ } y \text{ })=x[/tex]
...or just...
[tex]2x^2+2x+y=x[/tex]
Algebra allows us to solve the equation and find out what "y" is equivalent to.
To solve, we want to get the "y" by itself. To do so, we try to eliminate the other "terms" from the left side of the equation.
Understanding "terms" & "like terms"
Terms
"Terms" in an equation are either a number multiplied to other things, or just a single number that isn't multiplied to anything else.
For example, the various terms in our equation above are
[tex]2x^2[/tex], [tex]2x[/tex], [tex]y[/tex], [tex]x[/tex]
You might ask why the last things, which don't have a number, are considered terms.
Remember that multiplying by 1 doesn't change anything, so we could imagine each of the last two terms as being 1 times the letter.
So, we can rewrite our equation:
[tex]2x^2+2x+1y=1x[/tex]
Like terms
"Like terms" are terms where the "other stuff the numbers are multiplied to" is the same, so for instance, the [tex]2x[/tex] and the [tex]1x[/tex] are like terms. They are like terms because, the "other stuff" that the numbers are multiplied to are "x" for both terms. Note that [tex]2x[/tex] and [tex]2x^2[/tex] are not "like terms" because the "stuff" is different:
[tex]x[/tex] is different than [tex]x^2[/tex]
"Like terms" are important because only like terms can be "combined" into a single simplified term.
Solving equations
To solve an equation, we isolate what we're solving for, y, by disconnecting the other terms from it, and simplify.
Starting with subtracting 2x from both sides of the equation:
[tex]2x^2+2x+1y=1x\\(2x^2+2x+1y)-2x=(1x)-2x[/tex]
Subtraction is the same as "adding a negative":
[tex]2x^2+2x+1y+(-2x)=1x+(-2x)[/tex]
Since all terms are now connected by addition, we can add in any order we want (because of the Commutative Property of Addition), and we can combine like terms.
Thinking just about the number parts, since [tex]1+(-2)=-1[/tex], then [tex]1x+(-2x)=-1x[/tex].
Returning to our main equation, the right side simplifies:
[tex]2x^2+2x+1y+(-2x)=1x+(-2x)\\2x^2+2x+1y+(-2x)=-1x[/tex]
On the left side: [tex]2x[/tex] and [tex]-2x[/tex] are like terms.
Fact: [tex]2+(-2)=0[/tex]
So, [tex]2x+(-2x)=0x[/tex]
Since anything times zero is just zero, [tex]0x=0[/tex]. Furthermore, adding zero to anything doesn't change it. So when the [tex]2x[/tex] and [tex]-2x[/tex] terms on the left side of our main equation are combined, they "disappear" (While we talked through are a lot of rules/steps to justify why that works, it is common to omit those justifications, and to just combine those like terms and make them disappear.)
So, [tex]2x^2+2x+1y+(-2x)=-1x[/tex] simplifies to:
[tex]2x^2+1y=-1x[/tex]
Similarly for the [tex]2x^2[/tex] term, we subtract from both sides:
[tex]2x^2+1y=-1x\\(2x^2+1y)-2x^2=(-1x)-2x^2\\2x^2+1y+(-2x^2)=-1x+(-2x^2)[/tex]
Combining like terms on the left, they disappear.
[tex]1y=-1x+(-2x^2)[/tex]
There are no like terms on the right.
Since the two terms on the right are added together, we can use the commutative property of addition to rearrange:
[tex]1y=-2x^2+(-1x)[/tex]
Addition of a negative can turn back into subtraction, and simplify multiplication by 1.
[tex]y=-2x^2-x[/tex]
Remembering we chose "y" as the unknown thing we wanted to know, that's why the "correct answer" is what it is.
Verifying an answer
Verifying can double check an answer, and helps explain why the answer you chose doesn't work.
To verify an answer, the original statement said add something to the expression and get a result of "x". So, let's see if the "correct answer" does:
[tex]2x^2+2x+(\text{ } ? \text{ })\\2x^2+2x+(-2x^2-x)\\2x^2+2x+(-2x^2-1x)\\2x^2+2x+(-2x^2)+(-1x)[/tex]
Combining the "x-squared" terms, completely cancels...
[tex]2x+(-1x)[/tex]
Combining the "x" terms, and simplifying...
[tex]1x\\x[/tex]
So it works.
Why isn't the answer what you chose:
[tex]2x^2+2x+(\text{ } ? \text{ })\\2x^2+2x+(-x^2-x)\\2x^2+2x+(-1x^2-1x)\\2x^2+2x+(-1x^2)+(-1x)[/tex]
Combining the x-squared terms, things don't completely cancel...
[tex]1x^2+2x+(-1x)[/tex]
Combining the x terms...
[tex]1x^2+1x\\x^2+x[/tex]
So adding the answer that you chose to the expression would not give a result of "x", which is why it is "wrong"
What is the volume of a cylinder, in cubic feet, with a height of 13 feet and a base
diameter of 4 feet? Round to the nearest tenths place.
Answer:
163.3
Step-by-step explanation:
3.14*r^2*h
h=13
4/2 = 2
r=2
2^2 = 4
3.14*4 = 12.56
12.56*13 = 163.28
Rounded = 163.3
I believe the answer is 163.3
help me with this question please, thank you !
Answer:
2
Step-by-step explanation:
[(27divided by (-3)-9] divided by [15-21}
=[-9-9] divided by 3
= 6divided by 3 = 2
if answer is correct so mark me as brain lest :-)
Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
(b) 3 terms, degree 10
Step-by-step explanation:
When simplifying polynomials, the first thing you look at is the exponents of the variables in each term. (The terms are separated by + or - signs.) Only terms with the same set of exponents can be combined.
When considering the degree of the polynomial, you look at the sum of exponents of the variables in each term. That sum is the degree of the term. The degree of the polynomial is the highest of the degrees of the terms.
__
exponents and degreeThe four terms have variables s and t. If we write the exponents of those variables as an ordered pair, we will have one ordered pair for each term:
5s⁶t² ⇒ (exponent of s, exponent of t) ⇒ (6, 2); degree = 6+2 = 8
6st⁹ ⇒ (1, 9); degree = 1+9 = 10
-8s⁶t² ⇒ (6, 2); degree 6+2 = 8 (this is a like term to the first term)
-6t⁷ ⇒ (0, 7); degree 0+7 = 7
The degrees are 8, 10, 8, 7, so the highest degree is 10. This is the degree of the polynomial.
__
combining termsWe can only combine the terms containing s⁶t². Doing that gives ...
(5 -8)s⁶t² +6st⁹ -6t⁷ = -3s⁶t² +6st⁹ -6t⁷ . . . . . three terms
In "standard form", the terms are written in order of decreasing degree:
6st⁹ -3s⁶t² -6t⁷ . . . . . . 3 terms, degree 10
Necesito la solución.
Practice A
Get a coin and toss it five times. Record the outcomes on the table below. Then, answer the questions that follow.
Head
Tail
1st toss
2nd toss
3rd toss
4th toss
5th toss
Total
Answer:
You can just flip a coin five times either with a real one (heads being a face or a picture and tails being the other side) or online, then put a tick on either heads or tails depending on what you got on that toss. Then just put how many times you got heads in the first question.
Hope this helps I guess.
Venn diagrams ! 3rd times a charm….
Answer:
1. 85 people were surveyed
PLEASE HELP
1-Spin the spinner 20 times, create a table to display the results. What is the experimental probability of spinning yellow?
2-Perform another 20 spins, and record them. What is the new experimental probability of spinning yellow?
3-What is the experimental probability of spinning red or yellow?
Answer:
24
Step-by-step explanation:
Help please due in a couple minutes:,)
Answer:
The amount of air in a leaky tire.
Step-by-step explanation:
The plot shows a decrease with time (I'll assume the x axis is time).
Which of the answer options would one expect a decrease over time.
A leaky tire? YES
Hair length with soda? NO
Cost of a meal when adding appetizers? NO
Answer:
a. the amount of air in a leaky bicycle tire as time increases.
Step-by-step explanation:
since the scatter plot is descending(y), then we can infer whatever is being recorded is decreasing as time goes on (x)
a. is a great example, as you have a leak in a bicycle tire the air will decrease.
b. does not make any rational sense, since soda does not affect an individual's hair length.
c. does not make sense since the plot is getting smaller over time, therefore adding prices (of said appetisers) makes the cost go up not down.
therefore your answer is a. the amount of air in a leaky bicycle tire as time increases.
hope this helps:)
The editor of a school magazine polled randomly selected students in the 8th, 9th, and 10th grades. They were asked which activity they enjoyed the most: watching sports, reading, or listening to music. The two-way frequency table shows the data she collected.
(see attachment for table)
Based on the data in the table, what is the approximate probability that a randomly selected student is in the 9th grade, given that he or she enjoys watching sports the most?
A. 0.39
B. 0.37
C. 0.35
D. 0.33
Answer:
D 0.33
Step-by-step explanation:
based on the table you would just divide 13/39 which is 0.33
I hope i am right
Answer: 0.37
Step-by-step explanation:
Instead of doing 13/39 which is the total number of 9th graders. You have to do 13/35 (35= the total amount of kids who prefer watching sports) because it is saying "what is the approximate probability that a randomly selected student is in the 9th grade, given that he or she enjoys watching sports the most?"
