Your sequence has a common difference of -8, so could be considered an arithmetic sequence with first term 79. A formula for the n-th term might be ...
... a[n] = 79 -8(n -1)
or
... a[n] = 87 -8n
A triangle’s longest side is 8cm longer than the shortest side and 5cm linger than the third side. If the perimeter is 56cm find the Length of the three sides
The length of the three sides of the triangle is 17cm, 25cm, and 12cm.
Explanation:To solve this problem, let's assign variables to the three sides of the triangle. Let x represent the shortest side, (x + 8) represent the longest side, and (x - 5) represent the third side.
Using the perimeter given, we can set up an equation:
x + (x + 8) + (x - 5) = 56
Simplifying the equation, we have 3x + 3 = 56, then 3x = 53, and finally x = 17.
Therefore, the three sides of the triangle are:
Shortest side: 17cm
Longest side: 17 + 8 = 25cm
Third side: 17 - 5 = 12cm
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Does anyone know this answer??
For this case we have the following equation:
[tex](2x + 3) ^ 2 + 8 (2x + 3) + 11 = 0[/tex]
Let [tex]u = 2x + 3[/tex]
We have:
[tex]u ^ 2 + 8u + 11 = 0[/tex]
By definition, given an equation of the form [tex]ax ^ 2 + bx + c = 0[/tex]
The quadratic formula, to find the solution can be written as:
[tex]x = \frac{-b+/-\sqrt{b ^ 2-4 (a) (c)} }{2(a)}[/tex]
In this case we have:
[tex]a = 1\\b = 8\\c = 11[/tex]
Substituting in the quadratic formula we have:
See attached image
Answer:
Option B
x = (- 7 ± √5) / 2
use the substitution u = 2x + 3
equation can now be written as
u² + 8u + 11 = 0
solve for u using the quadratic formula with a = 1, b = 8 and c = 11
u = ( - 8 ± √( 64 - 44 ) )/2
= ( - 8 ± √20 )/2 = ( - 8 ± 2√5 ) / 2 = - 4 ± √5
change the variable back into terms of x
2x + 3 = - 4 ± √5 ( subtract 3 from both sides )
2x = - 7 ± √5 ( divide both sides by 2 )
x = ( - 7 ± √5 ) / 2
Use the drop-down menus to complete the statements about the function p(x) = x(x – 1) + 1.
The value of a is–1012 .
The value of b is–1012 .
The value of c is–1012 .
The value of the discriminant is–3–11 5 .
The quadratic function will intersect the x-axis 012 times.
Expanded, the function is ...
... p(x) = x² -x +1
Compared to
... ax² +bx +1
The value of a is 1The vaule of b is -1The value of c is 1The value of the discriminant is b²-4ac = 1²-4·1·1 = -3The quadratic function will intersect the x-axis 0 times._____
The negative discriminant means there are no real roots, hence no x-intercepts.
Answer: The value of a is 1. The value of b is -1. The value of c is 1. The value of the discriminant is -3. The quadratic function will not intersects the x-axis.
Explanation:
The standard form of a quadratic equation is,
[tex]ax^{2} +bx +c[/tex]
It can be written as,
[tex]x^{2} -x+1[/tex]
What is the value of the expression? (5/2)2+3^3/4 Enter your answer in the box.
To evaluate the expression (5/2)^2 + 3^3/4, we simplify each part separately, then add the results. The final value of the expression is 13.
Explanation:To evaluate the expression (5/2)^2 + 3^3/4, we'll start by simplifying each part separately.
The first part, (5/2)^2, means we raise 5/2 to the power of 2. To do that, we multiply the numerator and denominator of 5/2 by itself:
(5/2)^2 = (5/2) x (5/2) = 25/4.
The second part, 3^3/4, means we raise 3 to the power of 3, and divide the result by 4:
3^3/4 = 27/4.
Now we can add the two simplified parts together:
(5/2)^2 + 3^3/4 = 25/4 + 27/4 = 52/4 = 13.
Which situation can be modeled by the inequality 5 + 10w ≥ 45? 50 pts!!!
Final answer:
The inequality models a situation where you have at least 45 dollars and you are adding $10 for each additional unit.
Explanation:
The inequality 5 + 10w ≥ 45 can be modeled by a situation where you have at least 45 dollars and you are adding $10 for each additional unit. Let's solve it step by step:
1. Subtract 5 from both sides of the inequality: 10w ≥ 40.
2. Divide both sides by 10: w ≥ 4.
The solution to the inequality is w ≥ 4. This means that the situation being modeled is where you have at least 4 units of something.
6 divided by the difference of a number and 2, minus 5 divided by a number plus 2, equals 5 times the reciprocal of the difference of the number squared and 4. What is the number? Please help ASAP!!!!!!!!! :(
Answer:
-20
Step-by-step explanation:
Question 2
Marilee spins the arrow on Spinner 1 and then spins the arrow on Spinner 2.
What is the sample space for this experiment?
A.) {A1, A2, B3, B4}
B.) {A1, B2, A3, B4}
C.) {A1, A2, A3, A4, B1, B2, B3, B4}
D.) {A1, B2}
Either A or B on Spinner 1 can be paired with any of 1, 2, 3, 4 on Spinner 2. The appropriate choice is ...
... C.) {A1, A2, A3, A4, B1, B2, B3, B4}
Choose the equation that could be used to solve this problem. The product of a number and 3 is 87. What is the number?
A) 3x = 87
B) x + 3 = 87
C) x 3 = 87
D) x − 3 = 87
A
in mathematics the product of numbers means multiply the numbers
let x be the number, then the product of x and 3 = 3x
the result of this multiplication is 87
so 3x = 87 is the equation to solve the problem
the solution is x = 29
The equation used to solve this problem is 3x = 87. The solution, found by isolating x, is 29.
Explanation:The equation that could be used to solve the problem 'The product of a number and 3 is 87. What is the number?' is 3x = 87. This equation represents 'the product of a number (x) and 3 equals 87'. You would solve this by dividing both sides by 3 to isolate x, resulting in the solution x = 29. Thus, the number that when multiplied by 3 equals 87 is 29.
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Bonita said that the product of 5 6 56 × 1 2 3 23 is 7 3 73 . How can you tell that her answer is wrong?
the last digits of the numbers being multiplied are 6 and 3
resulting in a product of 18
thus the last digit in her answer would have to be an 8 not a 3
Help me plz with problem I need a lot of help with it
Answer:
about 35
Step-by-step explanation:
This question is asking for an estimate, which means you round the number(s) to something convenient to perform the calculation.
Here, 47% is conveniently rounded to 50% = 50/100 = 1/2. Then 1/2 of 70 is ...
1/2·70 = 70/2 = 35
A reasonable estimate of 47% of 70 is 35.
___
As you get more sophisticated in your estimating, you can also estimate the error. This estimate is about 3% (of 70) high, so is high by 3/100·70 = 2.1. That means the real answer is 35 - 2.1 = 32.9.
You could also estimate the error as 3% of 100 = 3/100·100 = 3, so you could say the actual value is between 35-3 = 32 and 35. Since 100 is larger than 70, you know that 3% of 100 is larger than 3% of 70, so this is an over-estimate of the error.
A sequence is defined by the recursive function f(n + 1) = –10f(n).
If f(1) = 1, what is f(3)?
3
–30
100
–1,000
We are given
[tex]f(n+1)=-10f(n)[/tex]
we are given
[tex]f(1)=1[/tex]
At n=1:
we can plug n=1 into formula
[tex]f(1+1)=-10f(1)[/tex]
[tex]f(2)=-10f(1)[/tex]
[tex]f(2)=-10*1[/tex]
[tex]f(2)=-10[/tex]
At n=2:
we can plug n=2 into formula
[tex]f(2+1)=-10f(2)[/tex]
[tex]f(3)=-10f(2)[/tex]
[tex]f(3)=-10*-10[/tex]
[tex]f(3)=100[/tex]................Answer
A function assigns the value of each element of one set to the other specific element of another set. The value of f(3) is 100.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
As the recursive function is given to us, f(n + 1) = –10f(n), also the value of f(1)=1 , therefore, the value of f(2) can be written as,
[tex]f(n + 1) = -10f(n)\\\\f(1 + 1) = -10f(1)\\\\f(2)= -10 \times 1\\\\f(2)=-10[/tex]
Now, the value of f(3) can be written as,
[tex]f(n + 1) = -10f(n)\\\\f(2 + 1) = -10f(2)\\\\f(3)= -10 \times -10\\\\f(3)= 100[/tex]
Hence, the value of f(3) is 100.
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A force of 50 pounds is exerted at an angle of 80 with the horizontal. What is its horizontal component?
a.9 lb.
b.29 lb.
c.49 lb.
Answer:
Option A is the correct answer.
Explanation:
Any vector can be resolved in to two components. Horizontal component and vertical component.
Consider a vector F which is at angle θ⁰ to the horizontal, we can resolve this vector in to two.
Horizontal component = F cos θ
Vertical component = F sin θ
Here we have Force , F = 50 pounds
Angle with horizontal = 80°
Horizontal component = F cos θ = 50* cos 80 = 8.68 pounds
≅ 9 lb.
Option A is the correct answer.
What is 3.242424... as a mixed number
Answer:
3 8/33
Step-by-step explanation:
You want the mixed-number equivalent of the repeating decimal 3.2424....
Repeating decimalA repeating decimal fraction that starts at the decimal point can be converted to a ratio of integers by expressing the repeating digits over the same number of 9s.
Here, the two repeating digits "24" mean the fraction equivalent is ...
0.2424... = 24/99 = 8/33
The mixed number equivalent of 3.2424... is 3 8/33.
__
Additional comment
If the repeating portion does not start at the decimal point, you can use the following technique to do the conversion.
Multiply the original number by 10^n, where n is the number of repeating digits.Subtract the original number from this product. Repeating digits should cancel to zeros.Divide this difference by (10^n) -1 and simplify the resulting fraction.Effectively, this multiplies and divides the number by ((10^n) -1)/((10^n) -1). In the case here, that would be multiplication by 1 in the form 99/99.
3.242424... × 99/99 = 321/99 = 3 8/33
The "321" will be manifested on a calculator as 320.99999.... If you multiply by (100 -1) with pencil and paper, you can see that you get ...
324.2424... - 3.2424... = 321 . . . . . . repeating digits cancel
If the repeat starts somewhere else, you can still use the "fraction with equal number of 9s" technique, but with a multiplier:
3.6242424... = 3.6 + 0.0242424 ... = 3.6 + (1/10)(24/99)
= 36/10 + 8/330 = 3 103/165
<95141404393>
3.242424... as a mixed number is [tex]\(3 \frac{8}{33}\)[/tex].
To express the repeating decimal 3.242424... as a mixed number, we can first write it as an infinite geometric series.
Let x = 3.242424.... Then, multiplying x by 100 gives 100x = 324.242424...
Now, subtract x from 100x:
100x - x = 324.242424... - 3.242424...
99x = 321
Now, solve for x:
[tex]\[ x = \frac{321}{99} \][/tex]
Now, express the fraction [tex]\(\frac{321}{99}\)[/tex]as a mixed number.
[tex]\[ \frac{321}{99} = 3 \frac{24}{99} \]\\Now, simplify the fraction:\[ \frac{24}{99} = \frac{8}{33} \][/tex]
So, 3.242424... as a mixed number is [tex]\(3 \frac{8}{33}\)[/tex].
Which equation represents y = x2 − 10x + 30 in vertex form?
To complete the square, you can add (and subtract) the square of half the x coefficient.
... y = x² -10x + 30
... y = (x² -10x +25) + (30 -25)
... y = (x -5)² +5
Based on data set 3 in appendix b, body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.20°f and a standard deviation of 0.62°f. Using the empirical rule, what is the approximate percentage of healthy adults with body temperatures (a) between 97.58°f and 98.82
The empirical rule tells you 68% of the population is within 1 standard deviation of the mean. Your limits are 1 standard deviation from the mean, so your percentage is ...
... 68%
_____
98.20 - 0.62 = 97.58 . . . 1 standard deviation below the mean
98.20 + 0.62 = 98.82 . . . 1 standard deviation above the mean
Approximately 68% of healthy adults have body temperatures between 97.58°F and 98.82°F, as per the empirical rule which states that about 68% of data falls within one standard deviation of the mean in a bell-shaped distribution.
Using the empirical rule (also known as the 68-95-99.7 rule), we can determine the approximate percentage of healthy adults with body temperatures between 97.58°F and 98.82°F. The empirical rule states that for a bell-shaped distribution:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% falls within two standard deviations.
Approximately 99.7% falls within three standard deviations.
Given that the mean body temperature is 98.20°F and the standard deviation is 0.62°F:
One standard deviation from the mean includes temperatures from 98.20°F - 0.62°F to 98.20°F + 0.62°F, which is 97.58°F to 98.82°F.
Therefore, approximately 68% of healthy adults have body temperatures between 97.58°F and 98.82°F according to the empirical rule.
What is the solution of the system of inequalities
Answer:
There are four (4) whole-number solutions to these inequalities:
... {(4, 1), (5, 0), (6, 0), (7, 0)}
Step-by-step explanation:
These are nicely solved by graphing. Whole numbers are non-negative integers, so x and y can be any values 0, 1, 2, .... The area of overlap on the graph clearly shows that y=0 and y=1 are the only viable choices for y, and that the values for x are limited in each of these cases.
Divide and answer in simplest form: 5 ÷ 3/ 5
8 1/3 you have to do keep, change, flip
[tex]\frac{25}{3}[/tex]
change division to multiplication and turn the fraction upside down
5 ÷ [tex]\frac{3}{5}[/tex]
= 5 × [tex]\frac{5}{3}[/tex] = [tex]\frac{25}{3}[/tex] in simplest form
Solve for y in the equation –11y = –143.
A. –13
B. –12
C. 12
D. 13
Simplify the expression 20/(9-2)
please help! cube root
juan is saving money for a trip. he has already saved 100 he saves 50 each week what would be the rate of change of the situation?
Answer:
The rate of change would be 50
Step-by-step explanation:
The rate of change in any equation is simply the amount in changes for every value of x. Since it goes up by 50 for every increase of the week, it means that the rate of change is 50.
find the range of the function f(x)=2x+7 for the domain -2,3,8
The range is the output value
f(-2) = 2(-2)+7 =3
f(3)= 2(3)+7 = 13
f(8) = 2(8)+7 = 23
The range is 3,13,23
The overall cost of carpet and installation from a particular company is represented by the function, where x represents the square footage of the carpet.
P(x) = $2.90x + $103.00
What is the average rate of change over the interval [2,000, 2,500]?
A. $2.90 per square foot
B. $4.85 per square foot
C. $0.34 per square foot
D. $1.03 per square foot
The function is linear, so its rate of change is the same everywhere. That rate of change is the coefficient of the variable x, so is $2.90. Since the units of x are feet, and the units of P(x) are dollars, the rate of change $2.90 must be ...
... A. $2.90 per square foot
The average rate of change for the given cost function over the interval [2,000, 2,500] is calculated using the slope formula, resulting in an average rate of $2.90 per square foot, corresponding to option A.
Explanation:The question asks to find the average rate of change of the cost function P(x) = $2.90x + $103.00, where x represents the square footage of the carpet, over the interval of [2,000, 2,500 square feet]. To calculate the average rate of change, we use the formula of the slope between two points on the function:
(P(x_2) - P(x_1)) / (x_2 - x_1).
So for the interval [2,000, 2,500], we have:
(P(2500) - P(2000)) / (2500 - 2000) = (($2.90 \times 2500 + $103.00) - ($2.90 \times 2000 + $103.00)) / (2500 - 2000).
This simplifies to:
($7250 + $103 - $5800 - $103) / 500 = $1450 / 500 = $2.90 per square foot.
Therefore, the average rate of change over the interval [2,000, 2,500] is $2.90 per square foot, which corresponds to option A.
7:8:9=__:12:__ find the blanks. They are ratios PLEASE HELP
Answer: [tex]7:8:9 = 10.5:12:13.5[/tex]
Step-by-step explanation:
Suppose, [tex]7:8:9= x:12:y[/tex]
Now according to the ratio, the equations will be........
[tex]\frac{7}{8}=\frac{x}{12}\\ \\ 8x=7*12=84\\ \\ x=\frac{84}{8}=10.5[/tex]
and
[tex]\frac{8}{9}=\frac{12}{y}\\ \\ 8y=9*12=108\\ \\ y=\frac{108}{8}=13.5[/tex]
So, the ratio will be [tex]7:8:9 = 10.5:12:13.5[/tex]
The ratio is [tex]\boxed{7:8:9 = 10.5:12:13.5}[/tex].
Further Explanation:
Given:
The ratio is [tex]7:8:9[/tex] and is equal to [tex]{\text{\_\_\_}}:{\text{12}}:{\text{\_\_\_}}[/tex].
Calculation:
Consider the number in the first blank as [tex]x[/tex].
Consider the number in the second blank as [tex]y[/tex].
Therefore, the ratio is [tex]7:8:9[/tex] and is equal to [tex]{{x}}:{\text{12}}:{{y}}[/tex]
From the given equation the ratio of [tex]7:8[/tex] is equal to the ratio of [tex]x:12[/tex].
Now equate [tex]\dfrac{7}{8}[/tex] and [tex]\dfrac{x}{12}[/tex] to obtain the value of [tex]x[/tex].
[tex]\begin{aligned}\frac{7}{8} &= \frac{x}{{12}} \\ \frac{7}{8} \times 12 &= x \\ \frac{{21}}{2} &= x \\ 10.5 &= x \\ \end{aligned}[/tex]
Therefore, the value of [tex]x[/tex] is [tex]10.5[/tex].
From the given equation the ratio of [tex]8:9[/tex] is equal to the ratio of [tex]12:y[/tex].
Now equate [tex]\dfrac{8}{9}[/tex] and [tex]\dfrac{12}{{y}}[/tex] to obtain the value of [tex]y[/tex].
[tex]\begin{aligned}\frac{8}{9} &= \frac{{12}}{y} \\ \frac{9}{8} &= \frac{y}{{12}} \\ \frac{9}{8} \times 12 &= y \\ \frac{{27}}{2} &= y \\ 13.5&= y \\\end{aligned}[/tex]
Therefore, the value of [tex]y[/tex] is [tex]13.5[/tex].
Hence, the ratio is [tex]\boxed{7:8:9 = 10.5:12:13.5}[/tex].
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Ratio and Proportion
Keywords: number, reciprocal, fraction, ratio, equation, proportion, 7:8:9, fill blank.
The difference between 72 and 16
72 - 16 = 56
-Nicole :) <3
72 - 16 = 56
If a question says "find the difference" it usually means that you can use subtraction :)
Tavon has a gift card for $ 50 that loses $ 2 for each 30-day period it is not used. He has another gift card for $ 40 that loses $ 1.50 for each 30-day period it is not used. a. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal. b. What will the value of each card be when they have equal value?
To find the number of 30-day periods until the value of the gift cards will be equal, we set up and solve an equation. The value of each card will be $10 when they have equal value.
Explanation:To solve this problem, we can set up an equation to represent the value of each gift card over time and find when they will be equal.
Let x be the number of 30-day periods that have passed. After x periods, the value of the first gift card will be $50 - $2x, and the value of the second gift card will be $40 - $1.50x.
Setting the two expressions equal, we get:
$50 - $2x = $40 - $1.50x
Simplifying the equation, we have:
$10 = $0.5x
Dividing both sides by $0.5, we get:
x = 20
So, after 20 periods (or 20 months), the value of each gift card will be equal.
To find the value of each card at that point, we can substitute x = 20 into one of the expressions. Let's use the first gift card:
Value = $50 - $2(20) = $50 - $40 = $10
Therefore, when they have equal value, each gift card will be worth $10.
Find the point, M, that divides segment AB into a ratio of 5:5 if A is at (0, 15) and B is at (20, 0).
A) (35, 10)
B) (20, 10)
C) (10, 7.5)
D) (17.5, 5)
C
a ratio of 5 : 5 simplifies to 1 : 1, which basically means we require the midpoint of the line segment
using the midpoint formula
M = [[tex]\frac{1}{2}[/tex] (0 + 20 ), [tex]\frac{1}{2}[/tex] (15 + 0)] = (10, 7.5 )
Answer:
Option C). (10, 7.5)
Step-by-step explanation:
We have to find the coordinates of point M that divides the segment AB into a ratio of 5:5.
Vertices A and B are (0, 15) and (20, 0)
Ratio 5:5 is simply the ratio 1:1 means point M is the midpoint of segment AB.
So x-coordinate of M will be [tex]\frac{(20+0)}{2}=10[/tex]
and y - coordinate will be = [tex]\frac{(15+0)}{2}=7.5[/tex]
Therefore Option C. (10, 7.5) are the coordinates of point M.
Write the standard form of the equation of a line with slope=-4 and through the point (2, 2)
Show all work
The point-slope form of the equation of a line with slope m through point (h, k) can be written as
... y = m(x -h) +k
For your problem, where m = -4 and (h, k) = (2, 2), this becomes
... y = -4(x -2) +2
... y = -4x +8 +2 . . . . eliminate parentheses
... 4x +y = 10 . . . . . . .add 4x to put into standard form
what is an equation in point-slope form for the line that passes through the points (4,-1) and (-3,4)?
y - 4 = - [tex]\frac{5}{7}[/tex](x + 3 )
the equation of a line in point-slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
to calculate m use the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (4, - 1) and (x₂, y₂ ) = (- 3, 4)
m = [tex]\frac{4+1}{-3-4}[/tex] = [tex]\frac{5}{-7}[/tex] = - [tex]\frac{5}{7}[/tex]
use either of the 2 points as a point on the line
using (a, b) = (- 3, 4 ), then
y - 4 = - [tex]\frac{5}{7}[/tex](x + 3 )
PLEASE HELP! 40 POINTS
In a particular year, a total of 44740 students studied in two of the most popular host countries when traveling abroad. If 5672 more students studied in the most popular host country than in the second most popular host country, find how many students studied abroad in each country!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
I'd start with setting up the equations. Calling x the number of students in most popular country 1, and y in country 2.
x + y = 44740
x - y = 5672
now solve for x1 and x2. You can subtract second from first:
0 + 2y = 39068
y = 19534
so
x = 5672 + 19534 = 25206
Add a sentence to answer it in words.
total students= 44740 divided by 2 countries= 22370 for each country. if were trying to get a difference of 5672 students, then were gonna divide that 5672 by 2 which is gonna = 2836 students. country 1= 22370 students + 2836 of country 2's students. country 2 is 22370 students - 2836 students that we gave to country 1. so now, country 1 ends up with 25206 students, country 2 end up with 19534 students. a difference of 5672.