Answer:
66
Step-by-step explanation:
The sequence you provided seems to be arithmetic as it increases as 4 each term. Assuming 1 is the first term the equation would be [tex]a_{n}=1 + 4(n-1)[/tex]. You could just take the first 6 terms and add them together since you already have 4 values calculated and you could calculate the other 2 by adding 4. This would give you
(1 + 5 + 9 + 13 + 17 + 21) = 66
But there's an easier way to do it. You could use the formula [tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]. You can calculate [tex]S_6[/tex] by plugging in those values. You would need to calculate [tex]a_6[/tex] before hand, but you can calculate that using the formula I defined above. Which in general is [tex]a_n = a_1 + d(n-1)[/tex] where d is like the slope, or how much it changes each term. So if you calculate [tex]a_6[/tex] you'll get [tex]1+4(6-1) = 1+4(5) = 21[/tex]. Now plug this into the series formula above and you get [tex]S_6 = \frac{6(1+21)}{2}=\frac{6(22)}{2}=\frac{132}{2}=66[/tex] which is exactly what you get if you add the first 6 terms as shown above when you do it manually.
[tex]\text{First let's find two more terms, because we have only six. We can do that by}\\\text{adding 4:: 13+4=17; 17+4=21}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{Now we just add the terms: 1+5+9+13+17+21}[/tex]
[tex]\rule{300}{1.7}\\\text{66}[/tex]
A tree is making a shadow 22 feet long. The angle of elevation from the tip of
the shadow to the top of the tree is 50°.
feet. Round your answer to the nearest
The height of the tree is about
foot.
Answer:
26.2 feet
Step-by-step explanation:
tan(50°) = h/22
h = 22 × tan(50°) = 26.2 feet
Need help! The answer is D, can anyone explain in detail how?
Answer:
D
Step-by-step explanation:
0.0378÷0.21=0.18
this is 18 hundredths
but its 180 thousandths
Explanation:
Now--this is an awfully odd way to word a question.
BUT, it is solvable!
digits have "place values" in numbers, let's focus on after the decimal point:
_ . _ _ _ _ _ '
we know this can go on forever, but we don't need it to (for this problem, that is)
_ . _ _ _
_ . {tenths} {hundredths} {thousandths} ........
we want to know how many thousandths we have:
the answer to this problem (0.0378 / 0.21) is 0.18
{let's consider what we know about place values:}
"10" can be thought of as ten-ones
and "1" can be thought of as ten tenths
{the reason it's always ten __ is that we use a base-ten system, and there are only ten options for each digit [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] }
so, 10 could be thought of as ten ones, which could each be thought of as ten tenths--meaning that 10 is the same thing as 100 tenths
[if you ignore the decimal point, it becomes more clear]:
10.0 [100]
likewise, 10.00 is 1000 hundredths; and 10.000 is 10,000 thousandths
--------
okay, back to our problem:
how many thousandths make up 0.18?
Let's write this out to the thousandths place:
0.180
if we use our tactic of ignoring the decimal, we are left with 0180 [of course, a "0" before a number has no value, so we can rewrite it as 180], or 180
so, 0.18 is really composed of 180 thousandths, which is how option D is the answer
hope this helps!! :)
{let me know if there's anything else you would like me to explain about this!}
What is the interval in which both f (x) and g(x) are positive?
A. (–1, ∞)
B. (2, ∞)
C. (3, ∞)
D. (–∞, 2) ∪ (2, ∞)
Need help with number 2 please!!!
Answer:
Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.
Step-by-step explanation:
The graph of function f(x) is the parent function.
(Parent functions are the simplest form of a given family of functions).
The graph of g(x) is related to the graph of f(x) by a series of transformations. To determine the series of transformations, work out the steps of how to go from f(x) to g(x).
Transformations
For a > 0
[tex]\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of }\:a \\& \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\& \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a \end{aligned}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
Parent function:
[tex]f(x)=x^3[/tex]
Step 1
Multiply the parent function by 6:
[tex]\implies 6f(x)=6x^3[/tex]
Therefore, this is a vertical stretch by a factor of 6.
Step 2
Now make the function negative:
[tex]\implies -6f(x)=-6x^3[/tex]
Therefore, this is a reflection in the x-axis.
Step 3
Finally, add 2 to the function:
[tex]\implies -6f(x)+2=-6x^3+2[/tex]
Therefore, the function has been translated 2 units up.
Conclusion
Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.
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Share £20 in the ratio 2:3
Answer:
£8 : £12
Step-by-step explanation:
2:3 means that there are 5 parts in total. Let parts be represented as p. 5p = £20, p = £4. That meant 2 parts = £8 and 3 parts = £12. Hence to share £20 in the ratio 2:3 is £8 : £12
A. 6x 10y=9
B. 6x=9
C. -10y = 15
D. 2x= 15
Answer:
6x = 9
Step-by-step explanation:
4x-5y = 12
2x+5y = -3
Add the equations together
4x-5y = 12
2x+5y = -3
-------------------
6x + 0y = 9
6x = 9
Answer:
B. 6x = 9
Step-by-step explanation:
4x - 5y = 12
+ 2x + 5y = -3
____________
6x + 0 = 9
Hence, option B. 6x = 9 is the correct answer.
The Function h is defined by the following rule.
h(x) = 2x-2
Complete the function table.
Answer:
[tex]\fbox {See below} \downarrow[/tex]
Step-by-step explanation:
[tex]\textsf {The function is :}[/tex]
[tex]\boxed {h(x) = 2x - 2}[/tex]
[tex]\textsf {Finding the missing values :}[/tex]
[tex]\mathsf {h(-4) = 2(-4) - 2 = -10}[/tex][tex]\mathsf {h(-2) = 2(-2) - 2 = -6}[/tex][tex]\mathsf {h(1) = 2(1) - 2 = 0}[/tex][tex]\mathsf {h(4) = 2(4) - 2 = 6}[/tex][tex]\mathsf {h(5) = 2(5) - 2 = 8}[/tex][tex]\textsf {The table :}[/tex]
[tex]\left[\begin{array}{ccc}x&f(x)\\-4&-10\\-2&-6\\1&0\\4&6\\5&8\end{array}\right][/tex]
Simplify
[tex]\left(\frac{123}{321}\right)\left(\frac{456}{654}\right)\left(\frac{789}{987}\right) \left(\frac{123}{321}\right)^{-1}\left(\frac{456}{654}\right)^{-1}\left(\frac{789}{987}\right)^{-1}[/tex]
Answer:
1
Step-by-step explanation:
using the rule of exponents
[tex](\frac{a}{b}) ^{-1}[/tex] = [tex]\frac{b}{a}[/tex] , then
[tex]\frac{123}{321}[/tex] × [tex]\frac{456}{654}[/tex] × [tex]\frac{789}{987}[/tex] × [tex]\frac{321}{123}[/tex] × [tex]\frac{654}{456}[/tex] × [tex]\frac{987}{789}[/tex]
[ [tex]\frac{123}{321}[/tex] × [tex]\frac{321}{123}[/tex] = 1 , [tex]\frac{456}{654}[/tex] × [tex]\frac{654}{456}[/tex] = 1 , [tex]\frac{789}{987}[/tex] × [tex]\frac{987}{789}[/tex] = 1 ]
= 1 × 1 × 1
= 1
how to make 27 using 1,2,3,4 only once
Answer:
1) (4 - 2 + 1)^3
2) 3^2(4 - 1)
3) 3^4/2 + 1
It can be either one of those
Answer:
(2 * 4 + 1) * 3 =Step-by-step explanation:
how to make 27 using 1,2,3,4 only once
Remember Pemdas
(2 * 4 + 1) * 3 =
(8 + 1) * 3 =
9 * 3 =
27
The measure of B is (3x-4)° and the measure of D is (2x-6)°. What are the measures of angles B and D?
Answer:
5x - 10
Step-by-step explanation:
→ Find the sum of the expression
3x - 4 + 2x - 6
→ Collect all the x terms
3x + 2x - 4 - 6
→ Simplify
5x - 10
Use the Change of Base Formula to solve each equation.
3x = 27.3
Answer:
9.1
Step-by-step explanation:
3(9.1)=27.3
27.3÷3=×
×=9.1
Determine if an exponential would be an appropriate model for the data shown in each scatter plot. Select one that applies.
Answer:
Graph 1: No, a linear model would be more appropriate.Graph 2: YesGraph 3: No, a quadratic model would be more appropriate.an airplane that is flying at an altitude of 30 000 ft is beginning to descend at a rate of 1000 feet per minute. a helicopter is beginning its trip, starting at an altitude of zero feet. the helicopter ascends more slowly than the airplane, going up at a rate of 500 feet per minute. after how many minutes will the airplane and the helicopter be at the same altitude
Using linear functions, it is found that the airplane and the helicopter will be at the same altitude after 20 minutes.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The functions that gives the height of the airplane and the helicopter, after t minutes, is given by:
A(t) = 30000 - 1000t.H(t) = 500t.They will be equal when:
A(t) = H(t).
Hence:
30000 - 1000t = 500t
1500t = 30000
t = 30000/1500
t = 20 minutes.
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There are 230 calories in a 48 gram packet of M&M's. How many calories are in a 33.6 gram bag?
Answer:
161 calories
Step-by-step explanation:
1) Divide 230 by 48
4.791666666666667
2) multiply 4.791666666666667 by 33.6
161
Done! Your answer is 161 calories in a 33.6 gram bag. Or just 161.
Hope this helps!
Find the area of the shaded portion of the
figure. All angles are right angles.
Dimensions are in inches.
3
8
5
Answer:
22 [in.²]
Step-by-step explanation:
1. the required area can be calculated as
A=A1-A2, where A1- area of big quadrilateral, A2-area of the small quadrilateral;
2. A=5*8-3*6=40-18=22 [in²].
please help me write an equation for this polynomial graphed
The equation of the given polynomial is f(x)=(x+2)(x+1)(x-3).
here we have given the graph of the
The roots of the given polynomial is
x=-2,x=-1 and x=3
What is the polynomial?A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Therefore the equation of the polynomial is
f(x)=(x+2)(x+1)(x-3)
Therefore the equation of the given polynomial is f(x)=(x+2)(x+1)(x-3).
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The equation for this polynomial graphed will be P(x) = a(x + 2)(x + 1)(x – 3)³.
What is polynomial?A polynomial expression is an algebraic expression with variables and coefficients.
The graph of the polynomial is given below.
From the graph, the roots of the polynomial will be -2, -1, and 3.
Then the factor of the polynomial will be
(x + 2), (x + 1), and (x – 3)
Then the polynomial will be
P(x) = a(x + 2)(x + 1)(x – 3)³
More about the polynomial link is given below.
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The diameter of a bicycle wheel is 63 cm. How much distance will it cover in 20revolutions?
Answer:
1256 cm
Step-by-step explanation:
First we must find the perimeter, because the perimeter is equal to 1 revolution.
The perimeter of any circle is Pi(Diameter)
3.14*20
62.8 cm is the perimeter of the bike wheel.
Because the perimeter is basically a revolution, we can multiply 62.8 by 20 to get:
1256 cm
What is the slope of the line through (1,-2) and (-3,-2)?
-1/2
Step-by-step explanation:
m = y2-y1/x2-x1
-3+2/3-1
m=-1/2
Hii!
_________________________________________________________________
Answer: Slope = 2 - Choice [C] ✅
Step-by-step explanation:
Do you need to know the slope of the line through (1,-2) and (-3,-2)? No problem! Luckily, there's a formula to find this!
The slope formulaThe slope formula "[tex]\sf \cfrac{y2-y1}{x2-x1}[/tex]", is the formula we'll use to find the slope.
Let's stick in the values we know
[tex]\sf m= \cfrac{-2-2}{-3-(-1)}[/tex]
Simplify
[tex]\sf m=\cfrac{-4}{-3+1}[/tex]
Simplify
[tex]\sf m=\cfrac{-4}{-2}[/tex]
[tex]\sf m= \cfrac{4}{2}[/tex]
[tex]\sf m=2[/tex] ✅
--
Hope that this helped! Best wishes.
--
PS. If you want to learn more, refer to this link:
✨brainly.com/question/18192642?referrer=searchResults
--
If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a certain city, where p(x)= 155-(x/10):
a. find an expression for the total revenue from the sale of x thousand candy bars.
b. find the value of x that leads to maximum revenue
c. find the maximum revenue
The expression for the total revenue from x thousand sales is 155,000x - 100x².
The value of x is 775 cents and the maximum revenue is $60,062,500.
What is the maximum revenue?First, come up with an expression for total revenue from x thousand sales:
= (155 - x /10 ) × x × 1,000 units
= 155,000x - 100x²
The value of x would then be:
Derive the function from the total revenue function to give:
0 = 155,000 - 200x
x = 775 cents
The maximum revenue is therefore:
= 155,000(775) - 100(775)²
= $60,062,500
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A 6-sided number cube is rolled twice. What is the probability of getting a 3 on the first roll and a 4 on the second roll? 2.8% 16.7% 20% 33.3%
Answer: 2.8%
Step-by-step explanation:
On the first roll, probability to get a 3 is 1/6.
On the second roll probability to get a 4 is also 1/6.
To get both of these numbers together, you need to multiply the two probabilities.
1/6 x 1/6 = 1/36.
1/36 = ~2.8
2.8%
Answer: 2.8%
Step-by-step explanation: I got it right on the test.
Please state the equation of the line in standard form
Answer:
See below
Step-by-step explanation:
Slope = rise / run
from 0,-1 to 1.5 , 0
this is 1 / 1.5 = 2/3
y xis intercept = -1
y = 2/3 x -1 Slope intercept form
2/3 x - y = 1 another form
2x - 3y = 3 Standard form (I think this is 'standard form' ....yah?)
Let the Universal set be the letters a through j: U = (a, b, ..., i, jJ. Let A = (b, e, g, i), B = {a, b, e, f), and C = {a, e, i, ji) List the elemefits of the set An (BU C)
Answer:
A ∩ (B U C) = {b , e , i}
Step-by-step explanation:
A = {b , e , g , i}
B = {a , b , e , f}
C = {a , e , i , j}
We note B U C ,The union of the two sets B and C
which is the set that contains all elements
that are in B or in C .
The easiest way to determine B U C :
Step1 : (write all the elements of B and C side by side)
B U C = {a , b , e , f , a , e , i , j}
Step2 : (delete the repeated elements)
B U C = {a , b , e , f , i , j}
FINDING A ∩ (B U C) :
it’s the set of elements that exist in both sets
A and B U C simultaneously:
A = {b , e , g , i}
B U C = {a , b , e , f , i , j}
Then
A ∩ (B U C) = {b , e , i}
what is 4³ writ
ten in expanded form?
Answer:
4^3 written in expanded form is 4*4*4
Mark as Brainliest please
Answer: 64
Step-by-step explanation:
Hii!
Do you need to know what 4^3 written in expanded form is? No problem!
4^3=4*4*4 (the ^3 tells us to multiply the base (which is 4 here) times 3)
The answer is 64.
Hope that this helped! Best wishes.
--
The value of x for the function f(x) = 100+ 0.3x is 210, when
f(x) = 121. True Or False
Answer:
false
Step-by-step explanation:
the answer is x=70
0.0000000019 written in scientific notation is
Answer:
1.9x10^8
hope I helped
Answer:
0.0000000019= 1.9*10^ -9
Find the area of triangle PQR.
Step-by-step explanation:
To get the angle of QPR, we subtract 90-60=30. This proves that the triangle is a 30,60,90, as angle QRP must be 60°. To get the area, we must know the length and width. These can be derived from a known relationship within 30,60,90 triangles.
[tex]qp = \frac{\sqrt{3}}{2} n[/tex]
[tex]qr = \frac{1}{2} n[/tex]
[tex]pr = n[/tex]
because half of pr is 10, we can conclude that n is 20. So we plug 20 into N for QP and QR, and get values of
[tex]qp = 5 \sqrt{3} [/tex]
[tex]qr = 5[/tex]
Now we multiply (l*w)/2 and get:
[tex] \frac{(5 \sqrt{3} \times 5)}{2} = 21.65 \: units[/tex]
Solve the following system of equations. -7x+5y=-11; -4x+3y= -7
Answer:
X = (-2) Y = (-5)- 7x + 5y= (-11) -------(1)
-4x + 3y,= (-7) ----------(2)
Solving by using elimination methodMultiplying eq 1 with 3 and eq 2 with 5
3( -7x + 5y) = 3(-11)
5(- 4x + 3y) = 5(-7)
-21x + 15y = (-33)
-20x + 15y,= (-35)
Subtracting both the eq.
-x = 2
x = (-2)
Putting this value in eq. 1
- 7x + 5y= (-11)
-7(-2)+ 5y= (-11)
14 + 5y = (-11)
5y = (-11) - 14
5y= (-25)
y = (-5)
Which model represents 2 . 36 ÷ 4 ?
A. Three groups each have three tens and 4 ones.
B. There are three groups of five tens and 9 ones in each group.
C. There are four groups of three tens and six ones.
D. There are three groups of five tens and nine ones in each group
A hibernating animal lost 4 pounds. Write a signed number to represent this weight change
Answer: -4 pounds
Step-by-step explanation:
The hibernating animal lost 4 pounds. This means we are 4 below wherever the animal's weight was in the beginning. This can be represented with a negative number;
-4 pounds
S
2
Question 10 of 10
What is the value of p?
90
125
OA. 125°
O B. 55°
O C. 45°
O D. 35°
SUBMIT
Answer:
D
Step-by-step explanation:
You do 180-125 to find the angle (because its a straight line) and then you get 55, then you have a right angle so you have 90 and then you do:
55+90+p=180
and then you get
145 +p=180
180-145=35
p=35