[tex]\bf \begin{array}{|cl|ll} \cline{1-2} term&value\\ \cline{1-2} f(1)&\\ f(2)&\\ f(3)&7\\ f(4)&7r\\ f(5)&7rr\\ &252\\ \cline{1-2} \end{array}\qquad \qquad 7rr=252\implies 7r^2=252\implies r^2=\cfrac{252}{7} \\\\\\ r^2=36\implies r=\sqrt{36}\implies r=6 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|cl|ll} \cline{1-2} term&value\\ \cline{1-2} f(1)&\stackrel{\frac{7}{6}\div 6}{\cfrac{7}{36}}\\ &\\ f(2)&\stackrel{7\div 6}{\cfrac{7}{6}}\\ &\\ f(3)&7\\ f(4)&42\\ f(5)&252\\ f(6)&1512\\ \cline{1-2} \end{array}[/tex]
notice, once we know what the common factor "r" is, from the 3rd term we can simply multiply it by "r" to get the next term, and divide the 3rd term by "r" in order to get the previous term, namely the 2nd term, and then divide the 2nd by "r" to get the 1st one.
Photo Attached! Help with my algebra please!
Answer:
A
Step-by-step explanation:
(x−2) means the graph is shifted 2 units to the right.
+3 means the graph is shifted 3 units up.
So the graph of g(x) is shifted 2 units right and 3 units up.
A certain city has a population of 10000 and increases by 4% per year. What will the population be 5 years later? (The answer has been simplified.)
53782
12167
12000
30000
Answer:
Option B is correct.
Step-by-step explanation:
A city has population = 10000
Population increase each year = 4%
So, Population increase after 1 year = 10000 * 4%
= 10000*4/100
= 400
Adding in the current population:
10000+400 = 10,400
Population increase after 2 year = 10,400*4%
= 10400*4/100
= 416
Adding in the current population:
10400+416 = 10816
Population increase after 3 year = 10,816*4%
= 10816*4/100
= 433
Adding in the current population:
10816+433 = 11,249
Population increase after 4 year = 11,249*4%
= 11249*4/100
= 450
Adding in the current population:
11249+450 = 11,699
Population increase after 5 year = 11,699*4%
= 11699*4/100
= 468
Adding in the current population:
11699+468 = 12167
So, the population after 5 yeras will be 12167.
Option B is correct.
The population of the city will be approximately 12,167 people after 5 years, calculated by using the formula for exponential growth with a 4% annual increase from the initial population of 10,000.
The question involves calculating the future population of a city that is experiencing exponential growth over a period of time. To find the population of a city 5 years later when the population increases by 4% per year, we use the formula for exponential growth, which is:
P = [tex]P0 * (1 + r)^t[/tex]
Where:
P is the future population
P0 is the initial population (which is 10,000)
r is the annual growth rate (which is 4% or 0.04)
t is the number of years (which is 5)
Using the formula, we calculate:
P = 10,000 × (1 + 0.04)⁵
P = 10,000 × (1.04)⁵
P = 10,000 × 1.2166529
P = 12,166.529
So, the population will be approximately 12,167 people 5 years later.
If $125 is invested at an interest rate of 18% per year and is compounded continuously, how much will the investment be worth in 2 years? Use the continuous compound interest formula A = Pert.
Answer:
$179.17
Step-by-step explanation:
You already know the formula but you have it typed incorrectly. The rt is raised as a power to the e. Just in case you didn't know that. Filling in our formula with what we have gives us:
[tex]A(t)=125e^{(.18)(2)[/tex]
Simplify that power to .36 and we have
[tex]A(t)=125e^{.36}[/tex]
Now raise e to the power of .36 on your calculator and get
A(t)= 125(1.433329415) and
A(t) = $179.17
Answer:
C 179 is the answer.
Step-by-step explanation:
What is the value of x? Enter your answer in the box x=
Answer: 45°
Step-by-step explanation:
There are 180 degrees in a triangle so
180-80=100-55=45°
Please help me out please!! :)
Starting from the Pythagorean identity, we deduce
[tex]\sin^2(x)+\cos^2(x) = 1 \iff \cos^2(x) = 1-\sin^2(x) \iff \cos(x) = \pm\sqrt{1-\sin^2(x)}[/tex]
If we plug in the value 7/10 for sin(x), we have
[tex]\cos(x) = \pm\sqrt{1-\dfrac{49}{100}} = \pm\sqrt{\dfrac{51}{100}}=\pm\dfrac{\sqrt{51}}{10}[/tex]
Hot air ballon 280 feet away as it rises up into the sky. At first, the balloon is at an angle of elevation of 12 degrees. A few minutes later, the balloon rises to angle of elevation of 60 degrees. What is the change in altitudes between Steve's two observations?
Answer:
Step-by-step explanation:
This is right triangle trig. The reference angle is 12 in one case and 60 in the other, but the horizontal distance doesn't change in either one, and neither does what you are looking for, which is the height of the balloon in both cases of the angle differences. And if you're looking for the difference in the height, you'll find both and subtract the smaller from the larger.
The height is across from the reference angle and the horizontal distance is adjacent to the reference angle, so the trig identity you want is tangent. Set up according to the angle measure of 12 degrees:
[tex]tan(12)=\frac{x}{280}[/tex] and
280 tan(12) = x
x = 59.5 ft
Now for the angle measuring 60 degrees:
[tex]tan(60)=\frac{x}{280}[/tex] and
280 tan(60) = x
x = 484.9
The difference between the two heights is 425.5 feet.
(14x^(2)-21x)/(2x-3)
need answer now please! show work
Answer:
7x
Step-by-step explanation:
Sorry this is the best way I could show the work as the equation maker on this site does not support doing something in this format
To divide the expression (14x^2 - 21x) by (2x - 3), you can use long division to get the answer 7x.
Explanation:To divide the expression (14x^2 - 21x) by (2x - 3), we can use long division. Here are the steps:
Divide (14x^2) by (2x) to get 7x.Multiply (2x - 3) by 7x to get 14x^2 - 21x.Subtract (14x^2 - 21x) - (14x^2 - 21x) to get 0.Therefore, the answer is 7x.
Question 78 find the value of x
For this case we have that by definition, the volume of a parallelepiped is given by:
[tex]V = l * w * h[/tex]
Where:
l: It's the long
w: It is the width
h: It's the height
From the figure we have the following data:
[tex]V = 975 \ ft ^ 3\\h = 9 \ ft\\w = 4ft\\x =?[/tex]
We must find the value of the length of the parallelepiped:
[tex]975 = x * 4 * 9\\975 = 36x\\x = \frac {975} {36}\\x = 27.083[/tex]
Answer:
[tex]x = 27.1 \ ft[/tex]
One day at lunch, the cafeteria sold thirty-four 1-pint containers of milk. The cafeteria also sold forty-eight 12-fl-oz bottles of water. Did the cafeteria sell more fluid ounces or milk? How many more?
Fluid ounces, 47 more
The graphs of f(x) and g(x) are shown below: graph of function f of x equals x squared minus x minus 12. Graph of function g of x equals 3.4 times x minus 6.6 What are the solutions to the equation f(x) = g(x)?
a) x = −1, 5.4
b)x = −3, 4
c)x = −1, 2
d)x = −10, 12
Answer:
Option a) x = −1, 5.4
Step-by-step explanation:
we have
[tex]f(x)=x^{2} -x-12[/tex]
[tex]g(x)=3.4x-6.6[/tex]
equate f(x) and g(x)
[tex]x^{2} -x-12=3.4x-6.6[/tex]
Solve the quadratic equation by graphing
The solutions are x=-1 and x=5.4
see the attached figure
Answer:
x= -1, 5.4
Step-by-step explanation:
[tex]f(x)= x^2-x-12[/tex]
[tex]g(x)= 3.4x -6.6[/tex]
f(x) is a quadratic equation and g(x) is a linear equation
To find f(x)= g(x) we need to find the point where the graph of f(x) and g(x) intersects.
The quadratic equation f(x) and linear equation g(X) intersects at two points
from the graph f(x)= g(x) at x= -1 and x=5.4
Please help me out with this
Answer:
y=6x-2
Step-by-step explanation:
to find the 6 you have to see the difference in the y values and the y values are going up by 6 each time. the -2 comes from the y intercept. to find the y intercept you have to see when x=0 which in this table is -2
hope i helped
y = 6x - 2. The equation that describes how x and y are related is given by y = 6x - 2.
If we look the table of the image, we can see that the graph that describes the relation between x and y is a straight line.
The set of infinite points aligned in the same direction is known as straight line and its main equation has the form y = mx + b, where m is the slope, and b the y-intercept.
In order to solve this problem, we need to find the slope which is [tex]m = \frac{y_{2}-y_{1} }{x_{2}- x_{1}}[/tex]
Solving m for two points of the straight line, Let's take (0, -2) and (1, 4):
[tex]m = \frac{4-(-2)}{1 - (0)}=\frac{6}{1} \\m = 6[/tex]
We can see if we take two points in order from the table always obtain the value m = 6, which means for each unit of x, y increase 6 units.
To find the y- intercept (0, y), from the table of the image we can see when x = 0, y = -2.
Writing the equation y = mx + b, with m = 6 and b = -2:
y = 6x -2
Find the value of x, rounded to the nearest tenth
Answer:
x=12.5
Step-by-step explanation:
The given triangle is a right angle triangle.
We cannot use the Pythagoras theorem as the lengths of all sides are not known. We will use triangular ratios here to solve the given problem.
As it is clear from the diagram that x is the hypotenuse of the triangle and 11 is the length of the base. We will use a ratio in which base and hypotenuse are used.
So,
cos θ= base/hypotenuse
cos 28=11/x
x=11/cos28
x=11/0.8829
x=12.45
Rounding off to nearest 10
x=12.5
In every right triangle, a leg is given by the multiplication between the hypothenuse and the sine of the opposite angle, or the cosine of the adjacent one.
So, in this case, we have
[tex]11 = x\cos(28)[/tex]
Solving for x, we have
[tex]x = \dfrac{11}{\cos(28)}\approx 12.5[/tex]
Write the equation of the quadratic function with roots 6 and 10 and a vertex at (8, 2).
Answer:
https://socratic.org/questions/how-do-you-write-the-equation-of-the-quadratic-function-with-roots-6-and-10-and-
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
Given the roots are x = 6 and x = 10, then
the factors are (x - 6) and (x - 10)
The quadratic is then the product of the roots
y = a(x - 6)(x - 10) ← a is a multiplier
To find a substitute (8, 2) into the equation
2 = a(2)(- 2) = - 4a ( divide both sides by - 4 )
a = - [tex]\frac{1}{2}[/tex]
Hence
y = - [tex]\frac{1}{2}[/tex](x - 6)(x - 10) ← expand factors
y = - [tex]\frac{1}{2}[/tex](x² - 16x + 60) ← distribute
y = - [tex]\frac{1}{2}[/tex] x² + 8x - 30
A line passes through (1, –5) and (–3, 7). a. Write an equation for the line in point-slope form. b. Rewrite the equation in slope-intercept form. y – 5 = 3(x + 1); y = 3x + 8 y + 5 = –3(x – 1); y = –3x – 2
see picture attached.
i hope this helped !!
ANSWER
Point-slope form:
[tex]y + 5 = -3(x - 1)[/tex]
Slope-intercept form;
[tex]y = - 3x - 2[/tex]
EXPLANATION
The point-slope form of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]
We need to find the slope using the formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
Let us substitute the point (1, –5) and (–3, 7).
This implies that,
[tex]m = \frac{7 - - 5}{ - 3 - 1} [/tex]
[tex]m = \frac{12}{ - 4} = - 3[/tex]
The point slope form now becomes,
[tex]y - - 5 = - 3(x - 1)[/tex]
[tex]y + 5 = -3(x - 1)[/tex]
To find the slope intercept form, we expand to obtain;
[tex]y = - 3x + 3 - 5[/tex]
[tex]y = - 3x - 2[/tex]
Which graph shows a car traveling at 50 miles per hour?
Answer:
If you could insert a picture of the graphs that would help! thank you!
Step-by-step explanation:
in order to solve he following system of equations by subtraction, which of the following could you do before subtracting the equations so that one variable will be eliminated when you subtract them? 4x-2y=7, 3x-3y=15
Answer:
To eliminate x multiply the first equation by 3 and the second equation by 4
To eliminate y multiply the first equation by 3 and the second equation by 2
Step-by-step explanation:
We are given a system of linear equations;
4x-2y=7
3x-3y=15
solving by elimination means that we shall be getting rid of one of the variables in order to determine the other. In this case we can either eliminate x or y. In order to eliminate any of these variables, we first must make their coefficients equal in both equations. To eliminate x;
Multiply the first equation by 3 and the second equation by 4.
To eliminate y;
Multiply the first equation by 3 and the second equation by 2.
when dealing with two rational expressions that have different denominators, how would you find a common denominator. What effect would that have on the numerators of the expression
Answer:
you mulitple the two bottomz by the other number
example 3/4 and 2/8
8 is a common mulitple so 3/4 becomes 6/8 and now they have common denominators
Step-by-step explanation:
example 3/4 and 2/8
8 is a common mulitple so 3/4 becomes 6/8 and now they have common denominators
and the numerator gets multipled with the same number as the denominator
Karl participated in a two-day charity walk. His parents donated money for each mile he walked. Karl walked 2 1 4 miles on the first day and 5 1 2 miles on the second day. His parents donated $62. How much money did his parents pay for each mile?
Answer:
$8/mile
Step-by-step explanation:
Total distance walked was 2 1/4 mi + 5 1/2 mi = 7 3/4 mi. Please note: you must use the " / " symbol to indicate division; "2 1 4" is unclear.
$62
Unit rate = $ per mile = --------------- = $8/mile
7 3/4 mi
A rectangular box is 4 cm ?wide, 4 cm ?tall, and 12 cm long. What is the diameter of the smallest circular opening through which the box will? fit?
Answer:
The smallest box dimensions are 4 x 4 cm.
Find the diagonal and this would be the diameter of the smallest circle.
Using the Pythagorean theorem:
4^2 + 4^2 = c^2
16 + 16 = c^2
c^2 = 32
c = √32
c = 5.658 cm ( Round answer as needed.)
3/4 + (1/3 \ 1/6) - (- 1/2) =
Answer:
3 1/4
Step-by-step explanation:
I'll assume you meant 3/4 + (1/3 / 1/6) - (- 1/2) and not 3/4 + (1/3 \ 1/6) - (- 1/2)
So we start with 3/4 + (1/3 / 1/6) - (- 1/2)
The toughest part is (1/3 / 1/6) , but remember that when dividing with a fraction, it's like multiplying by the inverse of that fraction, so...
[tex]\frac{1/3}{1/6} = \frac{1}{3} * \frac{6}{1} = \frac{6}{3} = 2[/tex]
Then we return to the original problem with the new value for the parenthesis:
3/4 + 2 + 1/2 = 3/4 + 8/4 + 2/4 = 13/4 or 3 1/4
Answer:
The correct answer is 3 1/4
Step-by-step explanation:
It is given that,
3/4 + (1/3 \ 1/6) - (- 1/2)
To find the value of given expression
3/4 + (1/3 \ 1/6) - (- 1/2) for finding the answer we have to find the value of
(1/3 / 1/6) = 1/3 * 6/1 = 2
3/4 + (1/3 \ 1/6) - (- 1/2 = 3/4 + 2 + 1/2
= 3/4 + 8/4 + 2/4 = (3 + 8 + 2)/4 = 13/4 = 3 1/4
The correct answer is 3 1/4
You have a total of 45 dimes and quarters. You have 3 more quarters than dimes. Which system of equations can you use to find the number x of quarters and number y of dimes you have? Use the system to determine how much money you have in quarters and dimes.
Let's call dimes x and the quarters x+3 since we have 3 more of them.
x+x+3=45
2x=42
x=21
we have 21 dimes and 23 quarters
21*0.10=2.1
23*0,25=5.98
if we add those together it equals 8.08
Answer:
$8.10
Step-by-step explanation:
Let d and q represent the # of dimes and quarters, respectively. Then write equations reflecting this story:
q = d + 3, and d + q = 45. Substitute d + 3 for q in the second equation, obtaining:
d + d + 3 = 45, or 2d = 42, or d = 21. Then there are 21 dimes and 24 quarters. That comes to $2.10 + $6.00, or $8.10.
HELP !!! | 20 Points.
Joshua has a ladder that is 17 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 16.5 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 70°. Will the ladder be safe at this height? Show your work.
Answer:
No. The ladder is too steep.
Step-by-step explanation:
Length of ladder = 17 feet. This is the hypotenuse.
Side a of a right triangle = 16.6
To answer this, you need one of the trigonometric functions.
Opposite = 16.5
hypotenuse = 17
The function you need is the sine function.
Sin(theta) = opposite / hypotenuse
sin(theta) = 16.5 / 17
Sin(theta) = 0.97059
theta = sin-1(0.07059)
theta = 76.07
No the ladder is too steep.
Answer:
The ladder will not be safe.
Step-by-step explanation:
The ladder is 17 ft long
The top of the ladder is 16.5 ft above the ground
The ladder makes a right triangle of height = 16.5 ft and hypotenuse = 17 ft
To find the angle the ladder makes with the ground,
Height ÷ hypotenuse = sin angle
i.e [tex]\frac{16.5}{17}[/tex] = sin angle
[tex]sin^{-1}[/tex] angle = 76.1°
So the ladder is not safe since the angle it makes with the ground is greater than 70°.
According to the fundamental theorem of algebra, how many roots does the polynomial f(x)=x4+3x2+7 have over the complex numbers, and counting roots with multiplicity greater than one as distinct? (i.e f(x)=x2 has two roots, both are zero).
The polynomial f(x)=x^4+3x^2+7 has four roots over the complex numbers according to the fundamental theorem of algebra, counting roots with multiplicity greater than one as distinct. This is consistent with the theorem's stipulation that a polynomial of degree n has exactly n roots.
Explanation:The subject of this question is the fundamental theorem of algebra which belongs to the domain of Mathematics, specifically the study of polynomials. As indicated in the question, we have a function, f(x), which represents a polynomial of degree 4 as shown by the highest exponent. According to the fundamental theorem of algebra, a polynomial of degree n has exactly n roots, counting multiplicity. This means a function f(x)=x4+3x2+7, which is a fourth degree polynomial, will have four roots over the complex numbers.
This is also true per the theorem when roots with multiplicity greater than one are considered distinct. For example, f(x)=x2 is a polynomial of degree 2; it has two roots, both are zero, hence the two roots are counted as two distinct roots.
While the quadratic formula is used for finding roots of second degree polynomials, it is not directly applicable here since we are dealing with a fourth degree polynomial.
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A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle. (x + 5)x = 104 x2 + 5x – 104 = 0 Determine the solutions of the equation. What solution makes sense for the situation? x = What are the dimensions of the rectangle? width = inches length = inches
Answer:
Step-by-step explanation:
x² + 5x – 104 = 0
Factor using the AC method. Here, a = 1 and c = -104. Multiplied together, ac = -104. Factors of -104 that add up to +5 are +13 and -8.
(x + 13) (x - 8) = 0
x = -13, 8
A negative width doesn't make sense, so x = 8. Therefore, the width is 8 inches and the length is 5 more than that, or 13 inches.
Answer:
width = 8
length = 13
Step-by-step explanation:
All that is left to do is factor the results that you have
x^2 + 5x - 104 = 0
You need two numbers that are fairly close together (ignore the sign differ by 5) and multiply to 104.
The two numbers are 8 and 13
More formally stated, the quadratic can be factored to
(x + 13)(x - 8) = 0
x - 8 =0
x - 8 + 8 = 8 + 0
x = 8
x + 13 = 0 has no meaning.
That means that the width ( a positive number ) = 8
The length is 5 more = 13
Celia and Jake bought 4 pizzas that cost $7 each and bread sticks that cost $3 they spilt the cost between them. Which equations could be used to find how much each paid? Let T stand for the total coat and E stand for the amount each paid.
Answer:
E = (3b+28)/2
T=3b+28
E= t/2
Step-by-step explanation:
The coat of the 4 pizzas would be $28, and an unknown amount of breadsticks that cost 3 dollars each.
Im going to use B as the amount of breadsticks bc i dont know what its supposed to be but that should be the correct answer.
T=3b+28
E= t/2
can you help me will mark brainlyist
Answer:
see below
Step-by-step explanation:
The functions for these tables are, respectively, ...
f(x) = 5 - x
f(x) = 3x
f(x) = (x -1)² . . . . . a quadratic relation
f(x) = 4x² . . . . . . a quadratic relation
We assume the intention is that the terminology "quadratic variation" mean "proportional to the square of x". In that case, only the last function has such variation.
What is the value of x if 15 = 5x + 45 ?
Answer:
x=6
Step-by-step explanation:
15 = 5x + 45
/5 /5
15 = x + 9
-9 -9
6 = x
The value of x = 6
How to write repeating decimals as fractions
Answer:
You take the repeating group of digits and divide it by the same number of digits but formed only by 9s.
Step-by-step explanation:
Let's say you have 0.111111111111...., your repeating pattern is 1, that consists of one digit (1). You take that digit and you divide it by 9:
1/9 is the fraction equivalent to 0.111111111111111...
Let's say you have 0.12121212121212...., the repeating pattern is 12, that consists of 2 digits (12). You take those 2 digits and divide them by 99:
12/99 is the fraction equivalent to 0.12121212121212...
which can be reduced to 4/33
If you have 0.363363363363..., your repeating pattern is 363, which is 3 digits, so you divide 363by 999:
363/999 is the fraction equivalent to 0.363363363363...
which can be simplified to 121/333
To write a repeating decimal as a fraction, multiply the decimal by a suitable power of 10 to eliminate the repeating part, subtract the original equation from the new equation, solve for the variable, and simplify the fraction if possible.
Explanation:To write a repeating decimal as a fraction, you can use a trick that involves using a variable to represent the repeating part of the decimal. Let's take an example of the repeating decimal 0.3333...
Let x be the repeating decimal: x = 0.3333...Multiply both sides of the equation by a power of 10 that will eliminate the decimal part. In this case, we can multiply by 10 to get: 10x = 3.3333...Subtract the original equation from the new equation to eliminate the repeating part: 10x - x = 3.3333... - 0.3333... => 9x = 3Solve for x by dividing both sides of the equation by 9: x = 3/9Simplify the fraction if possible: x = 1/3Therefore, the repeating decimal 0.3333... can be written as the fraction 1/3. This method can be applied to any repeating decimal to convert it into a fraction.
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The ratio of men to women working for a company is 5 to 7. If there are 156 employees total, how many women work for the company?
I hope it’s correct
Answer:
65 men
91 women
Step-by-step explanation:
the ratio is 5 to 7 and there are 156 total
5+7 is 12
so this gives us
5/12*156=65 men
7/12*156=91 women
65 + 91 = 156
What is the cosine ratio for angle F?
hope this answer your question :)
ANSWER
[tex]\cos( \angle \: F) = \frac{5}{13}[/tex]
EXPLANATION
The side length adjacent to <F is 5 units.
The length of the hypotenuse is 13 units.
The cosine ratio is
[tex] \cos( \angle \: F) = \frac{adjacent}{hypotenuse} [/tex]
This implies that:
[tex] \cos( \angle \: F) = \frac{5}{13}[/tex]
The fourth choice is correct.