Answer:
Common difference = 2
21st term = 73
Explicit rule : a(n) = 31 + 2n
Three terms in the sequence after 73: 77,77,79
Step-by-step explanation:
Given:
33, 35, 37, 39
If the sequence is arithmetic it has a common difference ( same difference on each value)
d= Common difference = 35 - 33 = 37 - 35 = 39 - 37 = 2
d = 2
Explicit formula:
a(n) = a1 + d (n - 1 )
Where:
a1= first term = 33
d = common difference = 2
Replacing:
a(n)= 33 + 2 (n - 1 )
a(n) = 33 + 2n - 2
a(n) = 31 + 2n
21st term:
a(21) = 31 + 2 (21) = 31+ 42 = 73
To obtain the three terms in the sequence after 73, add the common difference 3 times.
73 + 2 = 75
75+2= 77
77 + 2 = 79
Answers:
Common difference = 2
21st term = 73
Explicit rule : a(n) = 31 + 2n
Three terms in the sequence after 73: 77,77,79
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A bill for $1,896 is paid on 12 monthly installments. the same amount must be paid each month. each installment will be divided equally between two people. how does each person pay each month
Each person pays $79 each month.
A bill for $1,896 is paid in 12 monthly installments.
the same amount must be paid each month.
for, per month installment to be paid equals $1,896/12= $ 158
also given that, each installment will be divided equally between two people, then,
each installment for one person is equal to $ 158 /2=$79
so, $79 each person pays each month.
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in a city, building P is 455 feet taller than two times the height of building Q. the height of building P is 879 feet. what is the height of building Q
Answer:
212 ft
Step-by-step explanation:
[tex]455+2Q=879 \\ \\ 2Q=424 \\ \\ Q=212[/tex]
I need help , my teacher doesn’t teach so we just copy what we can . Am I can’t find M
Need help on this question ASAP PLEASE
Answer:
N/A
Step-by-step explanation:
which question of the three do you need the answer for?
whats the measurement?
Answer:
The measure of BXD is 45°.
Step-by-step explanation:
[tex]x + 20 + x + 30 = 95 - x[/tex]
[tex]2x + 50 = 95 - x[/tex]
[tex]3x + 50 = 95[/tex]
[tex]3x = 45[/tex]
[tex]x = 15[/tex]
So the measure of angle BXD is 15 + 30, or 45°.
what is the domain for f: y=4 x^(2)+12 x-5
The domain of the function f(x) = 4 · x² + 12 · x - 5 is the set of all real numbers.
How to determine the domain of a polynomic function
Functions are characterized by three features:
Domain - The input of all values of x such that the function f(x) exists.Range - The output of all values of y associated with the function f(x).Relations - Relations between the input and output sets.In this problem we need to find the set of all x - values of the polynomic function described in the statement. According to function theory, polynomials are continuous and their domain are always the set of all real numbers.
The domain of the polynomic function is the set of all real numbers.
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2) I read 120 pages yesterday and 132 pages today.
85 pages were left to read.
O How many pages did I read yesterday and today?
Answer:
A total of 252 pages
Step-by-step explanation:
In other words, 120 pages of a book were read yesterday and 132 pages of a book were read today. There are still 85 pages left to read in order to finish the book.
This word problem may seem tricky because it throws in the “85 pages left to read”, but you don’t have to pay attention to that because all the actual question is asking is for you to add the number of pages you already read.
To figure out how many pages were read in total, you must add.
So, 120 + 132 = 252
To do this addition problem mentally:
1. Add the 100s place, so 100 + 100 = 200
2. Add the 10s place, so 20 + 30 = 50
3. Add the 1s place, so 0 + 2 = 2
4. Add up all the sums that you got, so 200 + 50 + 2 = 252
You read 120 pages yesterday and 132 pages today. The values are correct.
What is an expression?An expression is a grouping of one or more mathematical or logical operators, operands (values, variables, or other expressions), and brackets in mathematics and computer programming that denote a computation that can be evaluated to generate a value.
Let x be the number of pages that you read yesterday, and let y be the number of pages that you read today.
From the problem, we know that:
x + y = 120 + 132 (the total number of pages you read over the two days)
x + y + 85 = total number of pages in the book
We can simplify the second equation by combining like terms:
x + y + 85 = total number of pages in the book
x + y = total number of pages in the book - 85
We can substitute the first equation into the second equation to eliminate x + y:
120 + 132 = total number of pages in the book - 85
252 = total number of pages in the book - 85
total number of pages in the book = 252 + 85 = 337
Now we can substitute this value for the total number of pages in the book into the first equation to solve for x and y:
x + y = 120 + 132
x + y = 252
We can solve for one variable in terms of the other by subtracting y from both sides:
x = 252 - y
Now we can substitute this expression for x into the equation x + y = 252 and solve for y:
252 - y + y = 252
y = 132
So you read 120 pages yesterday and 132 pages today.
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4+3x<22 find the solution for the inequlity
Answer:x<6
Step-by-step explanation:
Step-by-step explanation:
4+3x<22
3x<22-4
3x<18
3x÷3<18÷3
x<6
Match the diagrams to the correct congruence. Note that some diagrams may have more than one answer (select all that apply).
C. The image shows two right triangles with one pair of congruent leg and congruent hypotenuse. Therefore, the congruence is HL.
D. This shows two right triangles that share one side (a leg) and have the other leg also congruent to each other. Therefore, their congruence is LL and SAS (leg, right angle, leg).
E. This shows two triangles with a pair of congruent sides, a pair of congruent angles, and they have a common side, therefore congruent since they are the same.
So, their congruence is SAS.
F. This shows two right triangles sharing the same hypotenuse, and with a pair of congruent angles. Therefore, their congruence is HA.
G. This shows two right triangles with congruent hypotenuses, one congruent pair of legs, and two congruent pairs of angles (if we include the right angle).
So, their congruence is HA and HL.
H. The two triangles here have a right angle, a pair of congruent sides, and a pair of angles that are opposite by vertex, so they are also congruent angles.
Therefore, their congruence is ASA.
take another guess: a student takes a multiple-choice test that has 10 questions. each question has four choices. the student guesses randomly at each answer. round the answers to three decimal places.
Value of P(5) is 0.058 by probability.
What is a math illustration of probability?
The likelihood or chance of an event happening is known as probability. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.Given that ,
p = 1 / 4 = 0.25
1 - p = 1 - 0.25 = 0.75
n = 10
Using binomial probability formula ,
P(X = x) = ((n! / x! (n - x)!) * px * (1 - p)n - x
(a) x = 5
P(X = 5) = ((10! / 5! (10 - 5)!) * 0.255 * (0.75)10 - 5
= ((10! / 5! (5)!) * 0.255 * (0.75)5
= 0.058
P(5) = 0.058
(b)
P(X > 3) = 1 - P(X \leq 3)
= 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)
= 1 - 0.776
= 0.224
P(ore than 3) = 0.224
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The complete question is-
Take another guess: A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Round the answers to three decimal places Part 1 of2 (a) Find P(5) P(5)- Part 2 of2 (b) Find P(More than 3) P(More than 3)
What is the equation of the line that passes through the points (-3 , 9) and (9 , -1)? Write in your answer in slope - intercept form.
Please help
(College Algebra)
The equation of the line that passes through the points (-3,9) and (9,-1) is y= -5x/6 + 39/6 .
The equation of line passing through two points (a,b) and (c,d) is given by the equation
(y-b)=m(x-a) ,
where m is the slope of the line ..
the slope m is (d-b)/(c-a)
In the question ,
it is given that
the required line passes through the points (-3,9) and (9,-1)
by formula m= (-1-9)/9-(-3)
= -10/12
So substituting the values in the formula the equation of the line becomes
y-9 = -10/12*(x-(-3))
12*(y-9) = -10*(x+3)
12y - 12*9 = -10x-30
12y-108= -10x -30
12y = -10x-30+108
12y = -10x + 78
On Dividing both sides by 12 , we get
y= -10x/12 + 78/12
y= -5x/6 + 39/6
Therefore , the equation of the line in slope intercept form that passes through the points (-3,9) and (9,-1) is y= -5x/6 + 39/6 .
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Someone please give me the answer to this
The ascending order of the given numbers is 2×[tex]10^{-4}[/tex] <0.004< 4×[tex]10^{-2}[/tex] < 0.042 < 0.24
The first number = 0.24
The second number = 4×[tex]10^{-2}[/tex]
The second number is the form of scientific notation. To compare the numbers, all the numbers should be in same form. So we have to convert the scientific notation to the decimal form
4×[tex]10^{-2}[/tex] = 0.04
The third number = 0.042
Third number is decimal form
The fourth number = 2×[tex]10^{-4}[/tex]
Convert the scientific notation to the decimal form
2×[tex]10^{-4}[/tex] = 0.0002
The fifth number = 0.004
The order of the numbers from least to greatest
= 2×[tex]10^{-4}[/tex] <0.004< 4×[tex]10^{-2}[/tex] < 0.042 < 0.24
Hence, the order of the given numbers from least to greatest is 2×[tex]10^{-4}[/tex] <0.004< 4×[tex]10^{-2}[/tex] < 0.042 < 0.24
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Chuck is making a salad to go with his soup. The recipe calls for 2.1 cups of lettuce per person and 0.56 ounces of salad dressing per cup of lettuce.
If 11 dinner guests want salad, how many ounces of dressing will be necessary? Round the answer to the nearest whole ounce.
The number of ounces necessary when 11 dinner guests want salad is 104 ounces.
How to illustrate the information?It should be noted that 1 cup = 8 ounces. Therefore, 2.1 cups will be:
= 2.1 × 8 = 16.8 ounces.
The recipe calls for 2.1 cups of lettuce per person and 0.56 ounces of salad dressing per cup of lettuce.
Therefore, if 11 dinner guests want salad, the number of ounces of dressing that will be necessary will be:
= 16.8 × 0.56 × 11
= 104
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PLEASE HELP ME ITS REALLY IMPORTANT 30 PTS
The 15 most populous states in the United States have an average population of 14.15 million, with a standard deviation of 8.75 million. Virginia and Washington have populations of 8.38 million and 7.17 million, respectively. Texas and Pennsylvania have z-scores of 1.52 and −0.15, respectively.
Part A: List these four states in order from smallest to largest populations. (4 points)
Part B: Explain your reasoning mathematically and be sure to include all necessary calculations.
Answer:
A.-0.15
1.52
7.17
8.38
8.75
14.15
2 x 10 to the negative 6 power times what number is equal to 6 x 10 to the negative 4 power?
By using division, 2×[tex]10^{-6}[/tex] times 300 is equal to 6×[tex]10^{-4}[/tex]
Scientific notation is a form of writing a very larger number or very smaller number in a simpler form. The general form of the scientific notation is a number from 1 to 10 is multiplied by a power of 10.
Consider the unknown number as x
The first number = 2×[tex]10^{-6}[/tex]
The result of 2×[tex]10^{-6}[/tex] times x = 6×[tex]10^{-4}[/tex]
So the equation will be
2×[tex]10^{-6}[/tex] × x = 6×[tex]10^{-4}[/tex]
Move 2×[tex]10^{-6}[/tex] to the right hand side of the equation
x = 6×[tex]10^{-4}[/tex] ÷ 2×[tex]10^{-6}[/tex]
Here we have to use the division
x = 300
Hence, by using division, 2×[tex]10^{-6}[/tex] times 300 is equal to 6×[tex]10^{-4}[/tex]
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If 2x + y = 5, what is the value of 4x
Answer:
10 - 2 y
Step-by-step explanation:
I need help with the picture below.
Answer:
Scientific form = 3.001 X 10^5
Expanded Form = 300100
Step-by-step explanation:
Answer:315.105
Step-by-step explanation:3.001
x105
-----------
315.105
The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 2 units, then what is the value of k?
k = 2
k equals one half
k = −2
k equals negative one half
Reason:
To shift down 2 units, we go from f(x) = (0.5)x to g(x) = (0.5)x - 2.
The -2 at the end means we subtract 2 from each y coordinate.
Compare this to g(x) = (0.5)x - k to find that k = 2.
please help me FASTTT
Answer:
k=40
Step-by-step explanation:
Answer : Each week the amount goes up by $40
find slope of the line for (-2,-3) (4,-3)
Hello !
Answer:
[tex]\Large\boxed{\sf Slope\ =0}[/tex]
Step-by-step explanation:
Considering two points [tex]\sf A(x_A, y_A)[/tex] and [tex]\sf B(x_B, y_B)[/tex], the slope of the line that passes through A and B is given by [tex]\sf m=\frac{y_B-y_A}{x_B-x_A}[/tex].
Given :
A(-2,-3)B(4,-3)Now we can calculate the slope with the previous formula :
[tex]\sf m=\frac{-3-(-3)}{4-(-2)}[/tex]
[tex]\sf m=\frac{0}{6}[/tex]
[tex]\boxed{\sf m=0}[/tex]
The slope of the line is 0.
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Have a nice day
Please hurry!!
simpilfy. m√p + n√p - √p
A. (m+n-1)√p
B. (m-n-1)√p
C. (m-n+1)√p
Answer:
A
[tex]{ \tt{m \sqrt{p} + n \sqrt{p} - \sqrt{p} }} \\ = { \tt{ \sqrt{p} (m + n - 1)}}[/tex]
Answer:
yh it's A the other guy's right
Step-by-step explanation:
The points (0,k) and (1,4) fall on a line with a slope of 9. What is the value of k?
Answer:
k = -5
Step-by-step explanation:
Slope of a line is given by
[tex]\dfrac{y_2 - y_1}{x_2-x_1}[/tex]
where (x₁, y₁) and (x₂, y₂) are two points on the line
This is commonly referred to as rise/run
Given two points(0, k) and (1,4) and told that the slope is 9 we get
[tex]9 = \dfrac{4-k}{1-0}\\\\9 = \dfrac{4-k}{1}\\\\9 = 4 -k\\\\\text{Subtract 5 from both sides to get }\\9 - 4 = 4 - 4 - k\\\\5 = -k\\\\ k = - 5\\\\[/tex]
4. Which of the following is the graph of y> -+3
a refrigerator was originally priced at $250. it was then put on sale for 20% of. what is the number of dollars in the final price of the refrigerator if an additional 15% is taken off from the sale price?
two chocolate chip cookies and three brownies cost a total of 9.50. One chocolate chip cookie and two brownies cost a total of 6.00. What is the price of a chocolate chip cookie and a brownie? Show all work
Answer:
Step-by-step explanation:
Let Chocolate=X, Brownie=Y
2X+3Y=9.50 (Eq 1)
X+2Y=6.00 (Eq 2)
Multiplying Eq 2 by 2
2(X+2Y=6.00) (Eq 3)
Subtracting Eq 3 by Eq 1
2X+3Y=9.50
2X+4Y=12.00
0-Y= -2.5
Y=2.5
Putting Value of Y in Eq 2
X+2(2.5)=6.00
X+5=6
X=6-5
X=1
1. A grocery store sells salmon for $7.84 per pound. What would be the cost of 2 2/5
pounds of salmon?
In linear equations, 18.816 is the cost of 2 2/5 pounds of salmon.
What are instances of linear equations?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y).A linear equation's graph will always be a straight line. Definition of a Linear Equation.When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1.grocery store sells salmon = $7.84 per pound
the cost of 2 2/5 pounds of salmon = [tex]2\frac{2}{5}[/tex] × 7.84
the cost of 2 2/5 pounds of salmon = 12/5 * 7.84
the cost of 2 2/5 pounds of salmon = 12 * 1.568
the cost of 2 2/5 pounds of salmon = 18.816
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Anyone know the answer for this
Answer:
<1 = 150 degrees
<2 = 150 degrees
Step-by-step explanation:
Angle 1 and the 150 degree angle are equal. The reason is because they are on the same side of the transversal (the slanted line) and they are both above the parallel line that makes the up. They are called corresponding angles.
Angle 2 and angle 1 are equal because they are opposite each other. The term used in math is vertically opposite.
Riley is also making boxes to hold baseballs. She wants the dimensions of her boxes
to be 4 x 6 x 3 units. How many balls can one of Riley's boxes hold?
The volume of the box is 105 cubic units.
What is volume of cuboid ?The amount of space inside a cuboid is calculated using the term "cuboid volume." Having length, breadth, and height, the cuboid is a three-dimensional shape. A shape with a certain length, breadth, and height will be obtained if we start with a rectangular sheet and keep stacking them. Length x Width x Height is the formula for calculating the cuboid's volume.
Given that : The dimensions of her boxes to be 4 x 6 x 3 units.
The volume of cuboid=7×5×3=105 cubic units.
so ,The volume of the box is 105 cubic units.
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Determine the range of f(x) = |x| − 4. {y | −∞ < y < ∞} {y | −4 ≤ y < ∞} {y | 0 < y < ∞} {y | 4 < y < ∞}
The range of the function f(x) = |x| − 4 is {y | −4 ≤ y < ∞}.
Given the function is: f(x) = |x| − 4
first find the domain of the function.
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.
domain= (−∞,∞)
Then, range is he set of all representations of domain elements or the set of all function outputs constitutes the range of the function f.
range = {y | −4 ≤ y < ∞}.
Hence we get the range of the function as {y | −4 ≤ y < ∞}.
.
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∠A and \angle B∠B are vertical angles. If m\angle A=(2x+20)^{\circ}∠A=(2x+20)
∘
and m\angle B=(3x+1)^{\circ}∠B=(3x+1)
∘
, then find the value of x.
Answer:
the answer is x=19 writing more bc I need more characters