By iteratively substituting, we have
[tex]a_n = a_{n-1} + n[/tex]
[tex]a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)[/tex]
[tex]a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)[/tex]
and the pattern continues down to the first term [tex]a_1=0[/tex],
[tex]a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))[/tex]
[tex]\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)[/tex]
[tex]\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k[/tex]
Recall the formulas
[tex]\displaystyle \sum_{n=1}^N 1 = N[/tex]
[tex]\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2[/tex]
It follows that
[tex]a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2[/tex]
[tex]\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1[/tex]
[tex]\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}[/tex]
a theme park had 1099 vistiors in three day.
there were twicw as many vistiors on saturday.
than on friday.there were 234 more vistiors on sunday than on saturday.
how many visitors
Answer:
Number of visitors on Friday = 173
Number of visitors on Saturday = 346
Number of visitors on Sunday = 580
Step-by-step explanation:
Total number of visitors over 3 days = 1099
Let x = number of visitors on Friday
If there were twice as many visitors on Saturday than on Friday, then
⇒ number of visitors on Saturday = 2x
If there were 234 more visitors on Sunday than on Saturday, then
⇒ number of visitors on Sunday = 2x + 234
Create an expression for the total number of visitors and solve for x:
⇒ x + 2x + 2x + 234 = 1099
⇒ 5x + 234 = 1099
⇒ 5x = 865
⇒ x = 173
Substitute found value of x into the expressions for each day:
⇒ Number of visitors on Friday = 173
⇒ Number of visitors on Saturday = 2 x 173 = 346
⇒ Number of visitors on Sunday = (2 x 173) + 234 = 580
The shaded part of the bell-shaped graph is called?
Answer:
A bell curve is a common type of distribution for a variable, also known as the normal distribution. The term "bell curve" originates from the fact that the graph used to depict a normal distribution consists of a symmetrical bell-shaped curve.
Step-by-step explanation:
My answer is the one above!
Please mark brainliest i need 2 more!
Answer:
It is called the normal distribution. Hope this help.
Helped by QueenTloveHope you have an nice day
Julia is opening a clothing store. She plans to start by selling sweatshirts. It costs her $10.50 for each sweatshirt, $4 per box for the shirts, and
$0.10 a bag. Julia also spends $900 on rent, 540 on electricity, and $30 on advertising each month. What is the cost function for Julia's clothing
store per month?
Оа
C= 10.50n + 900
Ob
C = 970n + 14.60
ос
C = 14.60n +970
Od
C = 10.50n +970
Answer: I think the answer b
Step-by-step explanation:
The cost function for Julia's clothing store per month is 14.60n +970
What is function?A function is defined as a relation between a set of inputs having one output each.
Given that, Julia is opening a clothing store. She plans to start by selling sweatshirts. It costs her $10.50 for each sweatshirt, $4 per box for the shirts, and $0.10 a bag. Julia also spends $900 on rent, $40 on electricity, and $30 on advertising each month.
There are two types of cost Julia have,
The variable cost that is not fixed and depend on how many shirts she's making, = $10.50+$4 +$0.10 = $14.60
Let she makes n shirts, so cost = $14.60n
And the second one is fixed cost that is cost she is spending on rent, electricity and advertising, = $900+$40+$30 = $970
Therefore, cost = 14.60n +970
Hence, the cost function for Julia's clothing store per month is 14.60n +970
For more references on functions, click;
https://brainly.com/question/21145944
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Use the graph of the parabola to fill in the table.
Answer:
hi and hello and welcome to the internet
Answer:
AOS: -4
Vertex: (-4,2)
X-intercepts: (-6,0) , (-2,0)
Y-intercept: (0,6)
Step-by-step explanation:
The Parabola opens upwards (as can be seen in the image.) To find the AOS (Axis of Symmetry) first identify the vertex (-4,2) and take the X value of it.
So the AOS is x = -4
Vertex is (-4,2)
The x-intercepts are seen in the graph, (-6,0) and (-2,0)
The y-intercept is where the parabola first touches the Y-axis, which as can be seen is, (0,6).
Hope this helped.
HELP PLSSS
SHOW WORK
Use the information shown on the auger shell. What is the value of x?
no lol ;0 you should ask your teacher for help ;(
WORTH HUNDRED POINTS PLEASE HELP. How can the area of this triangle be determined by forming a rectangle? Select from the drop-down menus to correctly complete the statements. Copy and rotate the triangle and place it next to the existing triangle to form a rectangle. The length of the rectangle is (choose) 4,5,8,10 units. The width of the rectangle is (choose) 4,5,8,10 units. The area of the rectangle is (choose) 10,16,20,25 square units.
The area of the triangle is half the area of the rectangle, so the area of the triangle is (choose)
10,16,20,25
square units.
Answer:
Step-by-step explanation:
There's no image, so can't answer it. If you upload an image, I will help :)
Answer:
Step-by-step explanation:
Need a picture or we can't solve so yes please post another one.
The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks, and it will cost an additional $125 for each ton of sugar
transported.
Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S. Then use this
equation to find the total cost to transport 18 tons of sugar.
Answer:
$ 3750 = truck rental; $125 per ton of sugar transported
C is cost; S is number of tons transported
Equation relating C to S would be a linear equation like y = mx + b
C = 125S + $3750
This equation would be graphed in the first quadrant only
you would start with your y-intercept at (0, 3750)
As x increases by 1, your y increases by 125 yielding these points:
(1, 3875) (2, 4000) (3, 4125) etc.
This shows that for each increase by one ton of sugar, the cost goes up $125
Step-by-step explanation:
AXYZ is reflected across the y-axis. What are the endpoints of segment YZ?
A)
(-2,-3), (-2,-3)
B)
(-2, 3).(-2,-3)
(2,3), (2,-3)
D
(2.3).(-2,-3)
Answer:
I'm gonna head with B forgive me I'd I'm wrong
what is 2 to the third power times 8 times 12
Answer:
768
Step-by-step explanation:
because 2 to the 3rd power is 8 then 8 times 8 is 64 times 64 times 12 is 768!
please mark brainliest i rlly need one last one
Find the surface area of the cylinder. Use 3.14 for pi. Do not round the answer.
Question 1 options:
561
453.25
471
254.12
Answer:
C) 471
Step-by-step explanation:
Surface area for a cylinder formula:
SA = 2πrh + 2πr²
Given:
r = 5
h = 10
Work:
SA = 2πrh + 2πr²
SA = 2(3.14)(5)(10) + 2(3.14)(5²)
SA = 314 + 2(3.14)(25)
SA = 314 + 157
SA = 471
Solve 16p + 4 + 3p where p = 3
61
62
14
152
Answer: The Answer would be 61
Step-by-step explanation: You will be focusing on PEMDAS if you know the term. Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction, all in the order shown. Since there is no parenthesis or exponent, we go with multiplication as the first option in this problem. 16 x 3 and 3 x 3. 16 x 3 = 48, and 3 x 3 = 9. Since there is no Division on here, we will go the addition, where you add all the numbers up. 48 + 4 = 52 + 9 = 61
Hope this helps!
A motorboat travels 464 kilometers in 8 hours going upstream and 540 kilometers in 6 hours going downstream. What is the rate of the bot in still water and what is the rate of the current?
Answer:
rate 72 mph; current 16 mph
Step-by-step explanation:
to find the rate of the boat and the current we can model the equation like this
let r = rate
let c = current
8(r - c) = 464
6(r + c) = 540
8r - 8c = 464
6r + 6c = 540
r - c = 58
r + c = 90
then you could use elimination to find r
2r = 148
r = 74
the rate is 74 mph
then plug it in
the current is 16 mph
Brainliest if correct
Answer:
w=4
Step-by-step explanation:
First, we can simplify the equation.
28=14w-7w
28=7w
Then, we can divide by 7 on both sides of the equation.
28/7=7w/7
4=w
Finally, we know that x equals 4.
Answer:
w =4
Step-by-step explanation:
28 = 14w - 7w
Combine like terms
28 = 7w
Divide both sides of the equation by the same term
28/7 = 7w/7
Simplify
w = 4
[RevyBreeze]
Triangle GHI, with vertices G(-8,-8), H(-6,-7), and I(-9,-2),
What is the area, in square units, of triangle GHI
Answer:
area = 6.5 square units
Step-by-step explanation:
Use the area of a triangle in coordinate geometry formula:
[tex]\triangle GHI =\frac{1}{2} |x_1(y_2- y_3) + x_2(y_3 -y_1) + x_3(y_1 -y_2)|[/tex]
where [tex](x_1,y_1)=(-8,-8) \ \ \ \ (x_2,y_2)=(-6,-7) \ \ \ \ (x_3,y_3)=(-9,-2)[/tex]
[tex]\triangle GHI =\frac{1}{2} |x_1(y_2- y_3) + x_2(y_3 -y_1) + x_3(y_1 -y_2)|[/tex]
[tex]\implies \triangle GHI =\frac{1}{2} |-8(-7+2) -6(-2 +8) -9(-8 +7)|[/tex]
[tex]\implies \triangle GHI =\frac{1}{2} |40 -36 +9|[/tex]
[tex]\implies \triangle GHI =6.5[/tex]
Jacob took a total of 1212 quizzes over the course of 33 weeks.
How many weeks of school will Jacob have to attend this quarter before he will have taken a total of 1616 quizzes?
Answer:
1212=1212=
33weeks=33we2ks33weeks=33we2ks
weeks=we2ksweeks=we2ks
1616=we2ks1616=we2ks
Step-by-step explanation:
simplificar 16161616.
1212=1212=
33weeks=33we2ks33weeks=33we2ks
weeks=we2ksweeks=we2ks
1616=we2ks1616=we2ks
help help help help help
Answer: 2.48
Step-by-step explanation:
2.48+4.02=6.5
A coral reef grows 0.19m every week. How much does it grow in 14 weeks? Write your answer in centimeters.
Answer:
The coral reef grows 266 cm in 14 weeks.
Step-by-step explanation:
Lets convert 0.19 meters to centimeters.
1m= 100cm
0.19m×100= 19 cm
It grows 19 cm every week, so:
[tex]\frac{1w}{19 cm} *14 =\frac{14w}{x= 266 cm}[/tex]
So, the coral reef grows 266 cm in 14 weeks.
Hope this helps!
Find the slope of each line.
PLEASE HELP!!! 15 PTS!!!
Answer:
im pretty sure its -3/2
Step-by-step explanation:
since you have to do rise over run and your falling 3 so its a negative 3 and you always run right so its run 2 so then its -3/2 if its not that sorry
1. What is the product of
1 1
2 4
x and
2 5 2 6 x x
? Write your answer in standard form.
(a) Show your work.
(b) Is the product of
1 1
2 4
x and
2 5 2 6 x x
equal to the product of
1 1
4 2
x and
2 5 2 6 x x
?
Explain your answer.
Answer
Answer:
a. (11) (24x) (2526xx)
11×24x=264x
264x ×2526x²
= 666864 =6.7×10⁵x²
Step-by-step explanation:
b. the product of a and b is not equal because the the numbers are the same except for 42 in question b. which makes them not to be equal
The average monthly bill for wireless telephone subscribers from 1985 to 2008 can be modeled by B(x) = -1 463x + 95.514, where x is the number of years after
1980. If this model remains valid, in what year will the average monthly bill be $38.46?
If the model remains valid, in the year 2,019 the average monthly bill will be $38.46
How to use the linear equation?
The linear equation that models the average monthly bill is:
B(x) = -$1.463*x + $95.514
We now want to know when the average monthly bill will be $38.46, then we need to solve:
B(x) = $38.46 = -$1.463*x + $95.514
Solving this for x, we get:
$38.46 = -$1.463*x + $95.514
$1.463*x = $95.514 - $38.46 = $57.054
x = ($57.054)/($1.463) = 39
And x is the number of years after 1980, then this will be in the year:
1980 + 39 = 2,019
Then, if the model remains valid, in the year 2,019 the average monthly bill will be $38.46
If you want to learn more about linear functions, you can read:
https://brainly.com/question/4025726
I WILL GIVE BRAINLIEST PLS I HAVE 30 MINS
find the value of x & y ( SHOW YOUR WORK ) !!!
Answer:
Step-by-step explanation:
<A = <E corresponding parts of 2 geometric figures are =
60 + 8x = 108 Subtract 60 from both sides
8x = 108 - 60 Combine
8x = 48 Divide by 8
8x/8 = 48/8
x = 6
< C = <G corresponding parts of 2 geometric figures are =
8y - 3x = 62 Use x = 6 from the previous problem
8y - 3*6 = 62 Combine
8y - 18 = 62 Add 18 to both sides
8y = 62 + 18 Combine
8y = 80 Divide by 8
8y/8 = 80/8
y = 10
solve by completing the square
please solve all questions 1-9 for 50 points + brainly
[tex]\Large{\underline{\underline{{\mathfrak{{\bigstar}\:Answer}}}}}\\\\[/tex]
[tex]\bf{1.\:\:x^{2}+4x+1=0}[/tex]
[tex]\longrightarrow\:\:\sf{x=\dfrac{-4{\underline{+}}\sqrt{4^{2}-4\times1\times1}}{2\times1}}[/tex]
[tex]\longrightarrow\:\:\sf{x=\dfrac{-4{\underline{+}}\sqrt{16-4}}{2}}[/tex]
[tex]\longrightarrow\:\:\sf{x=\dfrac{-4{\underline{+}}\sqrt{12}}{2}}[/tex]
[tex]\longrightarrow\:\:\sf{x=\dfrac{4{\underline{+}}2\sqrt{3}}{2}}[/tex]
[tex]\longrightarrow\:\:\sf{x_{1}=-2-\sqrt{3}\:,\:x_{2}= -2+\sqrt{3}}\\\\\\[/tex]
[tex]\bf{2.\:\:x^{2}-9x+14=0}[/tex]
[tex]\longrightarrow\:\:\sf{x^{2}-2x-7x+14=0}[/tex]
[tex]\longrightarrow\:\:\sf{x\times (x-2)-7(x-2)=0}[/tex]
[tex]\longrightarrow\:\:\sf{x_{1}=2\:,\:x_{2}=7}\\\\\\[/tex]
[tex]\bf{3.\:\:x^{2}+8x+2=22}[/tex]
[tex]\longrightarrow\:\:\sf{x^{2}+8x+2-22=0}[/tex]
[tex]\longrightarrow\:\:\sf{x(x+10)-2(x+10)=0}[/tex]
[tex]\longrightarrow\:\:\sf{(x+10)(x-2)=0}[/tex]
[tex]\longrightarrow\:\:\sf{x_{1}=-10\:,\:x_{2}=2}\\\\\\[/tex]
[tex]\bf{4.\:\:x^{2}+8x+7=0}[/tex]
[tex]\longrightarrow\:\:\sf{x^{2}+7x+x+7=0}[/tex]
[tex]\longrightarrow\:\:\sf{x(x+7)+x+7=0}[/tex]
[tex]\longrightarrow\:\:\sf{(x+7)(x+1)=0}[/tex]
[tex]\longrightarrow\:\:\sf{x_{1}=-7\:,\:x_{2}=1}\\\\\\[/tex]
[tex]\bf{5.\:\:x^{2}-10x+25=9}[/tex]
[tex]\longrightarrow\:\:\sf{(x-5)^{2}=9}[/tex]
[tex]\longrightarrow\:\:\sf{x-5={\underline{+}}3}[/tex]
[tex]\longrightarrow\:\:\sf{x-5=-3 \: ; \:x-5=3}[/tex]
[tex]\longrightarrow\:\:\sf{x_{1}=2\:,\:x_{2}=8}\\\\\\[/tex]
[tex]\bf{6.\:\:x^{2}-10x+16=0}[/tex]
[tex]\longrightarrow\:\:\sf{x^{2}-2x-8x+16=0}[/tex]
[tex]\longrightarrow\:\:\sf{(x-2)(x-8)=0}[/tex]
[tex]\longrightarrow\:\:\sf{x-2=0\:;\:x-8=0}[/tex]
[tex]\longrightarrow\:\:\sf{x_{1}=2\:,\:x_{2}=8}\\\\\\[/tex]
[tex]\bf{7.\:\:2x^{2}+7x-4=0}[/tex]
[tex]\longrightarrow\:\:\sf{2x(x+4)-(x-4)=0}[/tex]
[tex]\longrightarrow\:\:\sf{(x+4)((2x-1)=0}[/tex]
[tex]\longrightarrow\:\:\sf{x+4=0\:;\:2x-1=0}[/tex]
[tex]\longrightarrow\:\:\sf{x_{1}=-4\:,\:x_{2}=\dfrac{1}{2}}\\\\\\[/tex]
[tex]\bf{8.\:\:x^{2}-2x+3=0}[/tex]
[tex]\longrightarrow\:\:\sf{x=\dfrac{-(-2){\underline{+}}\sqrt{(-2)^{2}-4\times 1\times 3}}{2\times1}}[/tex]
[tex]\longrightarrow\:\:\sf{\dfrac{2{\underline{+}}\sqrt{4-12}}{2}}[/tex]
[tex]\longrightarrow\:\:\sf{\dfrac{2{\underline{+}}\sqrt{-8}}{2}}[/tex]
[tex]\longrightarrow\:\:\sf{x \notin {\mathbb{R}}}\\\\\\[/tex]
[tex]\bf{9.\:\:3x^{2}+8x+5=0}[/tex]
[tex]\longrightarrow\:\:\sf{x(3x+5)+3x+5=0}[/tex]
[tex]\longrightarrow\:\:\sf{(3x+5)(x+1)=0}[/tex]
[tex]\longrightarrow\:\:\sf{3x+5=0\:;\:x+1=0}[/tex]
[tex]\longrightarrow\:\:\sf{x_{1}=-\dfrac{5}{3}\:,\:x_{2}=-1}\\\\\\[/tex]
[tex]\bf{10.\:\:{\mathbb{\red{1}}}\:\:}[/tex]:')
The solutions are listed below:
(i) [tex]x = -2\pm \sqrt{3}[/tex], (ii) [tex]x = \frac{9}{2}\pm \frac{5}{2}[/tex], (iii) [tex]x = -4 \pm 6[/tex], (iv) [tex]x = -4\pm 3[/tex], (v) [tex]x = -5\pm 3[/tex], (vi) [tex]x = 5 \pm 3[/tex], (vii) [tex]x = -\frac{7}{4}\pm \frac{9}{4}[/tex], (viii) [tex]x = 1 \pm i\sqrt{2}[/tex], (ix) [tex]x = -\frac{4}{3}\pm \frac{1}{3}[/tex], (x) 1. I do not celebrate Valentine's day at all.
How to solve polynomials by completing the squareCompleting the square consists in applying algebraic operations to transform part of the second order polynomial into a perfect square trinomial and simplify the resulting expression. Now we proceed to present the corresponding solutions:
(i) [tex]x^{2}+4\cdot x + 1 = 0[/tex]
[tex]x^{2}+4\cdot x +4 = 3[/tex]
[tex](x+2)^{2} = 3[/tex]
[tex]x+2 = \pm \sqrt{3}[/tex]
[tex]x = -2\pm \sqrt{3}[/tex]
(ii) [tex]x^{2}-9\cdot x + 14 = 0[/tex]
[tex]x^{2}-9\cdot x + 14+\frac{25}{4} = \frac{25}{4}[/tex]
[tex]x^{2}-9\cdot x +\frac{81}{4} = \frac{25}{4}[/tex]
[tex]\left(x-\frac{9}{2} \right)^{2} = \frac{25}{4}[/tex]
[tex]x -\frac{9}{2} = \pm \frac{5}{2}[/tex]
[tex]x = \frac{9}{2}\pm \frac{5}{2}[/tex]
(iii) [tex]x^{2}+8\cdot x + 2 = 22[/tex]
[tex]x^{2}+8\cdot x +16 = 36[/tex]
[tex](x+4)^{2} = 36[/tex]
[tex]x+4 = \pm 6[/tex]
[tex]x = -4 \pm 6[/tex]
(iv) [tex]x^{2}+8\cdot x + 7 = 0[/tex]
[tex]x^{2}+8\cdot x + 16 = 9[/tex]
[tex](x+4)^{2} = 9[/tex]
[tex]x+4 = \pm 3[/tex]
[tex]x = -4\pm 3[/tex]
(v) [tex]x^{2}+10\cdot x + 25 = 9[/tex]
[tex](x+5)^{2} = 9[/tex]
[tex]x+5 = \pm 3[/tex]
[tex]x = -5\pm 3[/tex]
(vi) [tex]x^{2}-10\cdot x + 16 = 0[/tex]
[tex]x^{2}-10\cdot x + 25 = 9[/tex]
[tex](x-5)^{2} = 9[/tex]
[tex]x-5 = \pm 3[/tex]
[tex]x = 5 \pm 3[/tex]
(vii) [tex]2\cdot x^{2} + 7\cdot x - 4 = 0[/tex]
[tex]x^{2}+\frac{7}{2}\cdot x -2 = 0[/tex]
[tex]x^{2} + \frac{7}{2}\cdot x -2 +\frac{81}{16} = \frac{81}{16}[/tex]
[tex]x^{2}+\frac{7}{2}\cdot x +\frac{49}{16} = \frac{81}{16}[/tex]
[tex]\left(x+\frac{7}{4} \right)^{2} = \frac{81}{16}[/tex]
[tex]x + \frac{7}{4} = \pm \frac{9}{4}[/tex]
[tex]x = -\frac{7}{4}\pm \frac{9}{4}[/tex]
(viii) [tex]x^{2}-2\cdot x + 3 = 0[/tex]
[tex]x^{2}-2\cdot x + 1 + 2 = 0[/tex]
[tex](x-1)^{2} = -2[/tex]
[tex]x-1 = \pm \sqrt{-2}[/tex]
[tex]x = 1 \pm i\sqrt{2}[/tex]
(ix) [tex]3\cdot x^{2} + 8\cdot x + 5 = 0[/tex]
[tex]x^{2}+\frac{8}{3}\cdot x +\frac{5}{3} = 0[/tex]
[tex]x^{2}+\frac{8}{3}\cdot x +\frac{5}{3}+\frac{1}{9} = \frac{1}{9}[/tex]
[tex]x^{2}+\frac{8}{3}\cdot x + \frac{16}{9} = \frac{1}{9}[/tex]
[tex]\left(x+\frac{4}{3} \right)^{2} = \frac{1}{9}[/tex]
[tex]x + \frac{4}{3} = \pm \frac{1}{3}[/tex]
[tex]x = -\frac{4}{3}\pm \frac{1}{3}[/tex]
(x) 1. I do not celebrate Valentine's day at all.
To learn more on polynomials, we kindly invite to check this verified question: https://brainly.com/question/17822016
PLEASE HELP ME!! ILL GIVE BRAINLIEST
Answer:
A, the first option, 49 square cm
Step-by-step explanation:
[] To know
-> A squares sides are all the same size
-> The area of a square can be found by finding L * W
[] Solving
-> We can use the points given to solve for one side, EF, of the square
-> Both the x coordinates are the same, so we can subtract the y values as they are on the same line.
6 - -1 = 6 + 1 = 7
-> Now for the area
7 * 7 = 49 square cm
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather
Mackenzie buys 13 bottles of apple juice at the corner store for a total cost of $9.23. Assume each bottle of juice is the same price. If c represents the total cost in dollars and cents of the juice for any number, j, of bottles of juice, write a proportional equation for c in terms of j that matches the context.
Answer:
c = 13j × $0.71
Step-by-step explanation:
give me a minute
PLEASE HELP ASAP! I have no idea where to start with this.
Answer:
h (-5) = 41/4 or 10.25
h (-2) = -3
h (3) = 25/4 or 6.25
Step-by-step explanation:
h (-5) = 1/4(-5)^2 + 4
h (-5) = 1/4(25) + 4
h (-5) = 41/4 or 10.25
h (-2) = -3 (this is given to you in the function)
h (3) = 1/4 (3)^2 + 4
h (3) = 1/4(9) + 4
h (3) = 25/4 or 6.25
In the diagram at the right..solve for x
Answer:
x = 11
Step-by-step explanation:
Since the 2 triangles are exact replicas of each other, we see the angle for this is 54 from the first triangle, and that 4x+10 is the angle as well.
So we set up the equation:
[tex]4x+10=54\\4x=44\\x=11[/tex]
The perimeter of a square is 48 millimeters. What is its area?
Explanation:
The perimeter is 48 mm. We divide that by 4 to find the side length of the square, since each side is the same length.
48/4 = 12
Each side is 12 mm long.
This means the area of this square is 12^2 = 12*12 = 144 square mm
explain why a conjecture may be true or false
Answer:
a conjecture is a conclusion made on incomplete information
Step-by-step explanation:
so in saying that, it can be true or false because conjecture can be used with true information thats not fully been proved yet/ verified
hope I helped
Put the following equation of a line into slope-intercept form, simplifying all fractions.
15x-9y= −9
The equation of a line in slope intercept form is given by:
y = mx + c
The equation 15x - 9y = -9 of a line into slope-intercept form after simplifying all fractions is y = (5/3)x + 1
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
y = 2x - 3
y = 3x + 4
We have,
15x - 9y = -9
We will rewrite in the slope-intercept form of y = mx + c.
15x - 9y = -9
Subtract 15x on both sides.
-9y = -9 - 15x
-9y = -15x - 9
Divide both sides by -9.
y = (-15x - 9) / -9
y = (15/9)x + 1
y = (5/3)x + 1
Slope = m = 5/3
y-intercept = 1
This is in the slope-intercept form of y = mx + c.
Thus,
The equation 15x - 9y = -9 of a line into slope-intercept form after simplifying all fractions is
y = (5/3)x + 1
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