Answer:
Hey there!
Arithmetic sequences are made up of terms that are added or subtracted, and geometric sequences are made up of terms that are multiplied or divided.
Given this info, we can see that we go from 10 to -5. Because we know that this is geometric, we see that we must divide by -2 in our sequence.
We can see that this is true because -5/-2=5/2.
Now, we could simply continue dividing by negative two to get our answer, which is -5/16.
You could easily do that with a calculator, but if you had to find a term that was farther from the first term, that would take forever to do with a calculator, so there is an equation that you can use and plug in your numbers to find the answer quickly.
, where is the number of term in the sequence (6 in this problem), a is the first term of the sequence (10), and r is the common ratio (-1/2).
I hope this helps!
Step-by-step explanation:
given f(x)=2/x^2+3x-10.
which of the following is true?
Of(x) is positive for all x < -5
Of(x) is negative for all x < -5
Of(x) is positive for all x < 2
Of(x) is negative for all x > 2
The function f(x)=2/x²+3x-10 is negative for all x < -5 option second "is negative for all x < -5" is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
[tex]\rm f\left(x\right)=\dfrac{2}{x^2}+3x-10[/tex]
f(x) is positive for all x < -5
Plug x = -4
f(-4) = -21.875
The above statement is not true
f(x) is negative for all x < -5
Plug x = -4
f(-4) = -21.875
The above statement is true
f(x) is positive for all x < 2
Plug x = 1
f(1) = -5
The above statement is not true
f(x) is negative for all x > 2
Plug x = 3
f(3) = -0.777
The above statement is not true
Thus, the function f(x)=2/x²+3x-10 is negative for all x < -5 option second "is negative for all x < -5" is correct.
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Darnell's graduation picnic will cost $12 if it has 6 attendees. If there are 7 attendees, how much will Darnell's graduation picnic cost? Solve using unit rates
Answer:
$14
Step-by-step explanation:
6 attendees divided by the cost of 12 = $2 per attendee
If 7 attendees are joining times $2 per person =$14
Sonji bought a combination lock that opens with a four-digit number created using the digits 0 through 9. The same digit cannot be used more than once in the combination.
If Sonji wants the last digit to be a 7 and the order of the digits matters, how many ways can the remaining digits be chosen?
Answer:
504 ways
Step-by-step explanation:
We know that since Sonji wants the last digit to be 7 and that numbers don't repeat, there are only 9 possibilities for the first digit, 8 possibilities for the second digit, 7 possibilities for the third digit, and 1 possibility for the fourth digit (which is 7).
Using the Fundamental Counting Principle, there are 9*8*7*1 = 504 ways for the remaining digits to be chosen.
Answer:
B. 504
Step-by-step explanation:
Have a good day!
Betty invests $45,000 into a cd which has an interest rate of 6.3% that compounds monthly for a total of 5 years. how much will betty have after the 5 years? (rount to the nearest dollar)
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45000\\ r=rate\to 6.3\%\to \frac{6.3}{100}\dotfill &0.063\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases} \\\\\\ A=45000\left(1+\frac{0.063}{12}\right)^{12\cdot 5}\implies A=45000(1.00525)^{60}\implies A\approx 61611[/tex]
Sketch the graph of y = negative 2 x squared + x + 1 using your graphing calculator. What are the x-intercepts of this graph? a. (1, 0) and (-0.5, 0) c. There are no x-intercepts b. (-2.5, 0) and (-2, 0) d. (-1.5, 0) and (-0.5, 0)
The x-intercept is (1, 0) and (-0.5, 0).
The correct option is (a)
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
Given function is:
f(x)= [tex]-2x^{2}+x+1[/tex]
So, The graph of this equation is attaches below.
The x- intercepts of this graph
[tex]\mathrm{X\:Intercepts}:\:\left(-\frac{1}{2},\:0\right),\:\left(1,\:0\right)[/tex]
or
X intercepts: (1, 0) and (-0.5, 0)
Hence, the x-intercept is (1, 0) and (-0.5, 0).
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What is the mean absolute deviation of the data set? Round to the nearest hundredth if necessary.
The mean absolute deviation, rounded to the nearest hundredth, is: 11.67 calories.
How to Find the Mean Absolute Deviation?To find the mean absolute deviation, find the mean of the data then find the average distance of each data point from the mean.
Given the data, 61, 42, 52, 27, 35, 23:
Mean = (61 + 42 + 52 + 27 + 35 + 23)/6
Mean = 240/6
Mean = 40
Mean absolute deviation = [(61 - 40) + ( 42 - 40) + ( 52 - 40) + ( 27 - 40) + ( 35 - 40) + ( 23 - 40) 6 = (21) + (2) + (12) + (13) + (5) + (17)] / 6 = 70/6
Mean Absolute Deviation = 11.67 calories.
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if f(x)=x²+2x-4 and g(x) = -4x+1, what is (g-f)(x)?
A x²+6x-5
B. x2-2x-3
C. x²-6x+5
D.-x²-6x+5
The (g-f)(x) is option D: - x² - 6x + 5.
What are terms in polynomials?Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.
Given;
f(x) = x²+2x-4
g(x) = -4x+1,
Then the subtraction of the two function;
g(x) - f(x)
= -4x+1 - (x²+2x-4 )
= -4x+1 - x²- 2x + 4
= - x² - 6x + 5
Hence, the correct option is D: - x² - 6x + 5.
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For an upcoming field trip to the science center, the school will allow students to select one extra activity. The school surveys a random sample of 25 students to determine about how many tickets of each kind they will need to buy.
The total amount that would be spent on all the activities is $1605.40.
What is the total amount?The total amount that would be spent on movies = (14/25) x 1200 x 1.55 = $1041.60
The total amount that would be spent on planetarium tickets = (7/25) x 1200 x 1.05 =352.80
The total amount that would be spent on backstage passes = (4/25) x 1200 x 1.10 =211.20
Total amount = 211.20 + 352.80 + $1041.60 = $1605.40
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Name something that you cannot find when looking at a box and whisker plot
Answer:
how many are of each number
Step-by-step explanation:
because it just shows the range, and the average, and the quarters, you can't really tell how many of the "item" of associated with each number
what is the answer to this? i've been stuck on it forever
Answer:
42 degrees.
Step-by-step explanation:
70 = 3x + 33 + 5x + 13
70 = 8x + 46
8x = 24
x = 3
m∠ABC = 9 + 33 = 42 degrees.
Type the correct answer in each box. use numerals instead of words. what are the x-intercept and vertex of this quadratic function? g(x) = -5(x-3)^2 write each feature as an ordered pair: (a,b). the x-intercept of function g is . the vertex of function g is .
Considering the given quadratic function, we have that:
The x-intercept is (3,0).The vertex is (3,0).What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the function is given by:
g(x) = -5(x - 3)²
Hence h = 3, k = 0, and the vertex is (3,0).
What are the x-intercepts of a function g(x)?They are the values of x for which g(x) = 0, hence:
-5(x - 3)² = 0
(x - 3)² = 0
Applying the root to both sides:
x - 3 = 0.
x = 3.
The x-intercept is (3,0).
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Suppose a charity received a donation of $22.9 million. If this represents 48% of the charity's donated funds, what is the total amount of its donated funds?
Round your answer to the nearest million dollars.
Hedya is 4 times as old as Hannah, and Hannah is 1.5 times as old as Hadassah. If the sum of their ages is 102, how old is Hadassah?
Step 1: Choose a point on the line, such as (2, 5).
Step 2: Choose another point on the line, such as (1, 3).
Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is StartFraction one-half EndFraction.
Step 4: Substitute those values into the point-slope form.
y – y1 = m(x – x1)
y – 3 = y minus y 1 equals m left-parenthesis x minus x 1 right-parenthesis. (x – 1)
Which of Talia’s steps is incorrect?
Step 1 is incorrect because it uses a point that is not on the line.
Step 2 is incorrect because it uses a point that is not on the line.
Step 3 is incorrect because it shows an incorrect ratio for the slope.
Step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form.
The step of Talia that's incorrect is: C. step 3 because the slope ratio she calculated is incorrect.
What is the Slope?The slope of a line (m) = rise/run = change in y / change in x.
Calculating the slope using two points on the line, (2, 5) and (1, 3), we should have:
Slope (m) = (5 - 3)/(2 - 1)
Slope (m) = (2)/(1)
Slope (m) = 2
This shows that the ratio of the slope calculated by Talia was wrong. The step that is incorrect is: C. Step 3
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solution for -4 5/6 +5 1/3
Answer:
1/2
Step-by-step explanation:
to solve this equation you must find the greatest common factor or gcf to make the denominators the same
that happens to be 6
so
-4 5/6 + 5 2/6
then you add
you can break them up at add them like this
(-4 + 5) + (-5/6 + 2/6)
1 + -3/6
-3/6 is also -1/2
1 + -1/2
1/2
that is your answer
How many cups are equal to 1/2 of a pint ?
Answer:
0.5 =12.0095
pint U.S Cup
I think im right but I hope this helps! ^^
Reuben attached a wire between two poles on a hill as shown which is the closest to x the distance between the two poles
The closest to x the distance between the two poles is gotten as; x = 75 ft
How to utilize trigonometric ratios?
From the Brainly link attached, we can see the diagram and we can say that;
We are given a right angled triangle with;
A known angle of; θ = 20°
Length of the hypotenuse = 80
Now, we want to find the length of the base x. Thus, we will use trigonometric ratio to get;
cos θ = x/hypotenuse
Thus;
cos 20 = x/80
x = 80 cos 20
x = 75.17 ft ≈ 75 ft
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Measure of the following
Answer: [tex]35^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle BIG=90^{\circ}[/tex] since the lines are perpendicular, meaning that [tex]m\angle HIG=90-30-25=\boxed{35^{\circ}}[/tex]
Over what interval is the function in this graph constant?
OA. -3≤x≤2
B. -4sxs-2
OC. -2≤x≤3
OD. -5≤x≤5
A function assigns the value of each element of one set to the other specific element of another set. The correct option is B.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The interval of the function for which the given graph is constant is when the value of x is less than -2 and when the value is greater than -4. Therefore, we can write this interval as -4< x < -2.
Hence, the correct option is B.
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Find f¹(x) for the function
f(x) = -4.
2
f¹(x) = [?]x + [ ]
Answer:
[tex] {f}^{ - 1}(x) = 2x + 8[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{x}{2} - 4 \\ \\ y = \frac{x}{2} - 4 \\ \\ y = \frac{x - 8}{2} \\ \\ x = 2y + 8 \\ \\ {f}^{ - 1} (x) = 2x + 8[/tex]
The Raymond family is building a pool in their backyard. If the contractor
chargest $2 per cubic foot to excavate, how much money will it cost to dig out
the hole for the pool?
19 ft
14.5 ft
4 ft
5 ft
12 ft
Answer:
2020
Step-by-step explanation:
(12×5×14.5+7×4×5)×2=
2020
Solve for system of equations. y = x²-3x + 4
x + y = 4
Answer:
Step-by-step explanation:
x²-3x+4+x=4
x²-3x+x=4-4
x²-2x=0
x²-x=0/2
x²-x=0
x=0
Solve the given inequality and graph the solution on a number line. -X/2 -3/2 = 5/2
No Links:
show how to solve the equation in the picture
[tex]\left(3\cdot8\cdot x\right)^7\\\\\left(3\cdot2\cdot4\cdot x\right)^7\\\\\left((3\cdot2)\cdot4\cdot x\right)^7\\\\\left(6\cdot4\cdot x\right)^7\\\\6^7\cdot4^7\cdot x^7\\\\[/tex]
In the second step, I rewrote 8 as 2*4. Then after that I regrouped terms so that the (3*2) can pair up together. This of course turns into 6. After that point, we have 6, 4 and x multiplied together as the base.
The last step uses the rule that [tex](a*b*c)^d = a^d*b^d*c^d[/tex], in other words, we apply the exponent d to each term inside the parenthesis. Each term inside gets its own exponent.
An example: [tex](2*4*6)^3 = 2^3*4^3*6^3[/tex]
23.21
Which equation represents the relationship between the number of liters, x, and the number of liquid pints, y?
O y = x + 5.55
Oy=x-5.55
O y = 2.11x
O Y - 211
The equation that represents the relationship between the number of liters, x, and the number of liquid pints, y is y = 2.11x
How to determine the equation?The attached table of values represents the missing piece in the question.
Start by calculating the rate of change using:
m = (y2 - y1)/(x2 - x1)
This gives
m = (14.77 - 10.55)/(7- 5)
Evaluate
m = 2.11
The equation is then calculated using:
y = m(x - x1) + y1
This gives
y = 2.11(x - 5) + 10.55
Evaluate
y = 2.11x - 10.55 + 10.55
y = 2.11x
Hence, the equation that represents the relationship between the number of liters, x, and the number of liquid pints, y is y = 2.11x
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PLEASE HELP MEEE ❗‼️‼️❗‼️
Find RS
A) 38
B) 35
C) 37
D) 40
The interior angles sum to 180°, so the missing angle has measure
180° - 106° - 12° = 62°
Use the law of sines to find RS:
sin(106°)/RS = sin(62°)/34 ⇒ RS = 34 sin(106°)/sin(62°) ≈ 37
Please help me on this
Answer:
4
Step-by-step explanation:
16/4
The lines shown below are parallel. If the green line has a slope of -27, what is
the slope of the red line?
10-
O A.-/7/7
OB.
10
O C. /
OD.
7
3
-10-
5
15
713
B.-
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.
The correct option is A.
What is a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.
The slope of the parallel line is always equal. Given the slope of the green line is -3/7, also, it is parallel to the red line. Therefore, the slope of the red line is -3/7.
Hence, the correct option is A.
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A yardstick measures distance to 1/4, or 0.25, of an inch. What is the most
appropriate way to report a length measured using this yardstick?
The most appropriate way to report a length measured by using this yardstick is to write the measurement in decimals (0.25) rather than in fraction (¼).
What is measurement?Measurement is a process through which the size, dimensions, or other physical quantities of magnitude that are associated with an object is taken, especially for use in a scientific research and experiment.
In Mathematics, a yardstick refers to a graduated measuring stick that has its length equal to one yard.
In this scenario, the most appropriate way to report a length measured by using this yardstick is to write the measurement in terms of decimals (0.25), so as to make easy approximations of the distance possible.
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In which two of these numbers does the digit
6 have a value of 0.6?
16.7
61.28 14.63 28.16 96.77 85.62
Answer:
Step-by-step explanation:
In this numbers:
14.63
85.62
The two numbers where the digit 6 has a value of 0.6 are 14.63 and 85.62.
To determine in which two numbers the digit 6 has a value of 0.6, we need to examine the place value of 6 in each number.
Let's go through each number:
1. 16.7: The digit 6 is in the tens place, so its value is 6 * 10 = 60 (not 0.6).
2. 61.28: The digit 6 is in the ones place, so its value is 6 (not 0.6).
3. 14.63: The digit 6 is in the tenths place, so its value is 6 * 0.1 = 0.6.
4. 28.16: The digit 6 is in the hundredths place, so its value is 6 * 0.01 = 0.06.
5. 96.77: The digit 6 is in the tens place, so its value is 6 * 10 = 60 (not 0.6).
6. 85.62: The digit 6 is in the tenths place, so its value is 6 * 0.1 = 0.6.
The two numbers where the digit 6 has a value of 0.6 are 14.63 and 85.62.
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