Step-by-step explanation:
Equation: y= [tex]-x^2+3x+9[/tex]
To create a parabola:
Does your parabola open up or down: If up, a>0 if down, a<0
This one opens down.
Is there a vertical strech or vertical compression:
No
What is the y-intercept: (0,9)
What strategy: Quadratic formula
Why?: You can fully factor the equation. You just get
-([tex](x^2-3x-9)[/tex] which isn't factorable.
Use the quadratic formula, where a= -1, b= 3, and c=9 to show your work.
Quadratic formula: [tex]\frac{-b+\sqrt{b^2-4ac} }{2a} \frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\frac{-(3)+\sqrt{(3)^2-4(-1)(9)} }{2(-1)}[/tex] and [tex]\frac{-(3)-\sqrt{(3)^2-4(-1)(9)} }{2(-1)}[/tex]
[tex]\frac{-3+\sqrt{9-4(-9)} }{-2}[/tex] and[tex]\frac{-3-\sqrt{9-4(-9)} }{-2}[/tex]
[tex]\frac{-3+\sqrt{9+36} }{-2}[/tex] and [tex]\frac{-3-\sqrt{9+36} }{-2}[/tex]
[tex]\frac{-3+\sqrt{45} }{-2}[/tex] and[tex]\frac{-3-\sqrt{45} }{-2}[/tex]
[tex]\sqrt{45}[/tex] = [tex]\sqrt{9 (5)} = 3\sqrt{5}[/tex]
[tex]\frac{-3+3\sqrt{5} }{-2}[/tex] and [tex]\frac{-3-3\sqrt{5} }{-2}[/tex]
Cancel the negatives (-3) and (-2)
[tex]\frac{3 +3\sqrt{5} }{2} or\frac{3 -3\sqrt{5} }{2}[/tex] = end result
Good luck!
Find the value of y.
168
X
y = [? ]°
Answer:
Y=96Step-by-step explanation:
The required value of y = 192°.
In a circle angle angle of arc x =168°. Angle of arc y is to be determine.
The angle can be defined as line inclined over other line by certain measure called angle.
Here, a circle has angle= 360°
x +y =360°
y = 360°-x
y = 360°-168°
y = 192°
Thus, the required value of y = 192°.
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PLZZZZZZZZZZ HLPPPPPPPPP MEEEEEEEEEE what is the factorization of the polynomial graphed below? assume it has no constant factor. write each factor as a polynomial in descending order.
Answer:
(x-5)(x-8)(x+2)=0
Step-by-step explanation:
first look at the x intercept to find the factor
x:-2,5,8
x=-2 then x+2=0
x=5 then x-5=0
x=8 then x-8=0
(x-5)(x-8)(x+2)=0
check for y in the polynomial when x=0
x^3-11x^2+14x+80
x=0 y=80 ( correct according to the graph
Which point of intersection is the solution to the system that of equations y= 2/5x-1/2 and y=-1/3x+2/3
Answer:
x = 35/22
y = 3/22
Step-by-step explanation:
y= 2/5x-1/2 ................(1)
y=-1/3x+2/3 ...............(2)
10*(1)
10y = 4x -5 ...................(1A)
3*(2)
3y = -x +2 ....................(2A)
To find intersection, solve for y & x
4(2A) + (1A)
12y+10y = -4x+4x +8-5
22y = 3
y = 3/22
Substitute in (1)
3/22 = 2/5x -1/2
multiply by 110
15 = 44x - 55
70 = 44x
x = 70/44 = 35/22
A central angle of a circle intercepts an arc of length 18 centimeters. The radius of the circle is 9 centimeters. What is the measure of the central angle in radians?
Answer:
.44444444
Step-by-step explanation:
πr²=full circumference
18/π(9)²=x/2π
What is the area of the triangle in the diagram?
Answer:
[tex]\frac{(a-b)^2+b^2}{a^2}[/tex]
which agrees with the first choice (A) in your list of possible answers
Step-by-step explanation:
Notice that the area of the outer square is given by the square of it side [tex](a)[/tex].Then the outer area is given by: [tex]a^2[/tex]
Now, the inner square's area we calculate by subtracting from the outer area four equal right angle triangles (those shaded in grey in the figure provided). Each of such right angle triangles have an area given by the general formula of a triangle's area:
[tex]Area_{triangle}= \frac{base\,*\,height}{2} =\frac{(a-b)\,b}{2} =\frac{ab-b^2}{2}[/tex]
Therefore the internal square's area is:
[tex]a^2-4\frac{ab-b^2}{2} =a^2-2ab+2b^2[/tex]
And then the quotient of this are over the larger square area becomes:
[tex]\frac{a^2-2ab+2b^2}{a^2} =\frac{a^2-2ab+b^2+b^2}{a^2}=\frac{(a-b)^2+b^2}{a^2}[/tex]
I need help please! The sequence 6,18,54,162, ... shows the number of pushups Kendall did each week, starting with her first week of exercising (a) What is the recursive rule for the sequence (b) What is the iterative rule for the sequence
Answer:
a: 3
b. 6973568802
Step-by-step explanation:
a₁ = 6 , r = 3 , a₂₀ =?
Result:
a₂₀ = 6973568802
Explanation:
To find a₂₀ we use the formula
aₙ = a₁ · r ^ⁿ⁻¹
In this example we have a₁ = 6 , r = 3 , n = 20. After substituting these values to above
formula, we obtain:
aₙ = a₁ · r ^ⁿ⁻¹
a₂₀ = 6 · 3 ^²⁰⁻¹
a₂₀ = 6 · 1162261467
a₂₀ = 6973568802
There are three cards. One is green on both sides, the second is red on both sides and the third is red on one side and green on the other. We choose a card at random and we see one side (also chosen at random). If the side we see is green, what is the probability that the other side is also green
Answer:
0.667
Step-by-step explanation:
According to Bayes theorem:
Since there are three cards, the probability that the side is green = 1/3
For the first card, if one side is green, the probability that the other side is also green = 1 (both sides are green)
For the second card, if one side is green, the probability that the other side is also green = 0 (both sides are red)
For the third card, if one side is green, the probability that the other side is also green = 1/2 (one side is green and the other side is red)
[tex]P(G_k/A)=\frac{P(G_k)P(A/G_k)}{\Sigma_{i=1\ to\ m} P(G_i)P(A/G_i)} \\P(B_1/A)=\frac{P(G_1)P(A/G_1)}{P(G_1)P(A/G_1)+P(G_2)P(A/B_2)+P(G_3)P(A/G_3)}\\ P(B_1/A)=\frac{1/3*1}{(1/3*1)+(1/3*0)+(1/3*1/2)=\frac{1/3}{1/2} }=0.667[/tex]
what is the slope of A line that passes through the points (−1, 2) and (3, 10)
Answer:
2
Step-by-step explanation:
(y2-y1) / (x2-x1)
(10-2) / (3-(-1))
8/(3+1)
8/4
2
Answer:
2
Step-by-step explanation:
(x¹, y¹) (x², y²) = (-1,2) (3,10)
Slope = (y²-y¹) ÷ (x²-x¹)
= (10 - 2) ÷ (3 -(-1))
= 8 ÷ 4
= 2
Hi everyone please help me with two questions,THX...this is for 6th grade
Answer:
A. 12 for every 7
Step-by-step explanation:
There are 12 peas in her bowl.
There are 7 peas in her hair.
The ratio of peas in her bowl to peas in her hair is 12 for every 7.
It costs $1.58 to buy a bag of popcorn. Which of the following equations shows the amount of money needed, z, to buy n bags of popcorn? z = 1.58 + n n = 1.58 + z z = 1.58n n = 1.58z
Answer:
z = 1.58n
Step-by-step explanation:
To find the total amount (z), the cost of a bag (1.58) must be multiplied by the number of bags (n).
z = 1.58n
Answer:
1.58 times the number of bags you're buying will give you how much money it all is: z=1.58n
Vincent wants to put 75 photograph in an album. A full page holds 6 photo graphs. what is the smallest number of pages vincent uses? (67)(72)(51)(42)(73)(64)(60)(20)(69)
Answer:
He needs just 13 pages
That is round up to not more than 20 pages will be the smallest
Step-by-step explanation:
Vincent wants to put 75 photograph in an album.
And a full page holds 6 photo graphs.
If 6 photographes is one page
Then 75 photographes =( 75*1)/6
75 photographes = 75/6
75 photographes= 12.5
12.5 pages will hold 75 photographes but nothing like 12.5 pages.
To the nearest page = 13 pages
Anybody pls solve this question and explanation btw.
Answer:
[tex]Vol=883.6875\,\, cm^3\\[/tex]
Step-by-step explanation:
Recall that the volume of a whole sphere is given by the formula:
[tex]Vol_{sphere}=\frac{4}{3} \pi\,R^3[/tex]
then, the volume of a semi-sphere would be half of the formula above:
[tex]Vol=\frac{2}{3}\, \pi\,R^3[/tex]
Now, the radius R is given by half of the semi-sphere diameter: 15/2 = 7.5 cm.
which makes our calculation:
[tex]Vol=\frac{2}{3}\, \pi\,R^3=\frac{2}{3}\, \pi\,(7.5\,cm)^3=883.6875\,\, cm^3\\[/tex]
which of these figures does NOT have line symmetry
Answer:
Figure D does not have line of symmetry
Answer:
You are correct, it is D
Step-by-step explanation:
What is the surface area of a sphere with a radius of 13 units?
A. 6767 units2
B. 10147 units
C. 8451 units2
D. 5077 units2
I hope this helps you
Sphere Surface Area Formula is
4.pi.r^2
4.pi.13^2
4.pi.169
676.pi
The surface area of the sphere with radius 13 units is S = 676π units²
What do you mean by a Sphere?A sphere is a three-dimensional geometrical object that is perfectly round in shape. A sphere is a fully spherical, three-dimensional geometrical object. Every point on its closed surface is equally spaced from the centre, which is the only point on the surface.The distance from the center to any point on the surface of the sphere is known as the radius of the sphere..
Surface Area of a Sphere = 4πr²
Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
They are used to represent many natural and man-made objects such as planets, basketballs, and molecules.
Let the data be ,
Let r = 13 units be the sphere's radius.
Let S be the sphere's surface area.
And , Surface Area of a Sphere = 4πr²
On simplifying , we get
S = 4π ( 13 )²
S = 4π ( 169 )
S = 676π units²
Thus, the sphere's surface area is S = 676 units2.
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What is the original price of a packet of biscuits bought for Rs230 including 6% tax
Answer:
Rs216.98
Step-by-step explanation:
If Rs230 is including the 6% tax then 230 = 106%
230 / 106 = 1% = 2.1698
2.1698 X 100 = 100% = 216.98
The original price of a packet of biscuits will be Rs216.98.
What is the percentage?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that the original price of a packet of biscuits bought for Rs230 including 6% tax.
The original price will be calculated as below:-
If Rs230 is including the 6% tax then 230 will be equal to 106 percent as below:-
230 = 106%
Then 1 percent will be equal to the ratio of 230 and 106 as below,
1% = 230 / 106= 2.1698
Divide 230 by 106 and to calculate the original price multiply by 100.
2.1698 X 100 = 100% = Rs216.98
Therefore, the original price of a packet of biscuits will be Rs216.98.
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Find the volume of the cone.
Radius: 3 m, Slant Height: 5 m
Round to the nearest whole number.
Volume =[?] m3
Answer:
Volume of cone = 37.7m^3
Which best describes how the graph of g(x) =1/9sqrt(x) relates to the graph of the parent function, f(x) =sqrt(x) ? The graph of g(x) is shrunk vertically by a factor of 1/9. The graph of g(x) is stretched vertically by a factor of 1/9. The graph of g(x) is shrunk vertically by a factor of 1/3. The graph of g(x) is stretched vertically by a factor of 1/3.
Answer:
The graph g(x) is vertically shrunk by a factor of 1/9.
Step-by-step explanation:
Parent Graph: f(x) = a√(bx - c) + d
Since we are only modifying a, we are dealing with vertical shrink (a < 1) and stretch (a > 1). Since 1/9 < 1, we have a vertical shrink by a factor of 1/9.
The correct description is:
"The graph of g(x) is shrunk vertically by a factor of 1/9"
How do dilations work?
There are two types of dilations.
Vertical dilation:
For a function f(x), a vertical dilation of scale factor k is written as:
g(x) = k*f(x).
Where if k > 1, we have a dilation, if 0 < k < 1, we have a contraction.
Horizontal dilation:
For a function f(x), a horizontal dilation of scale factor k is wrtten as:
g(x) = f(x/k).
Where if k > 1, we have a dilation, if 0 < k < 1, we have a contraction.
Here we have:
f(x) = √xg(x) = (1/9)*√xSo we can see that g(x) is a vertical contraction of scale factor 1/9.
Then the correct option is:
"The graph of g(x) is shrunk vertically by a factor of 1/9"
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The perimeter of a triangular field is 84 m, if the ratio of its sides are 13: 14:15, Find the area of the field. *
Answer:
[tex]Area = 336\ m^2[/tex]
Step-by-step explanation:
If the ratio of the sides is 13:14:15, we can say that the length of each side is 13x, 14x and 15x.
Then, if the perimeter is 84 m, we have:
[tex]P = 13x + 14x + 15x = 84[/tex]
[tex]42x = 84[/tex]
[tex]x = 2[/tex]
The length of each side is:
[tex]13x = 26\ m[/tex]
[tex]14x = 28\ m[/tex]
[tex]15x = 30\ m[/tex]
Now, to find the area of the field, we can use the following formula:
[tex]Area = \sqrt{p(p-a)(p-b)(p-c)}[/tex]
Where a, b and c are the sides and p is the semi perimeter:
[tex]p = P/2 = 42\ m[/tex]
So we have that:
[tex]Area = \sqrt{42(42-26)(42-28)(42-30)}[/tex]
[tex]Area = 336\ m^2[/tex]
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
the function has two real roots and crosses the x axis in two places.
Step-by-step explanation:
Using the general quadratic formula;
[tex]x = \frac{-b\pm \sqrt{b^2 -4ac}}{2a}[/tex]
for a quadratic equation
[tex]ax^2 +bx+c=0[/tex]
given the quadratic function below;
[tex]G(x) = -x^2 +4x+2[/tex]
the roots of the equation can be calculated by applying the quadratic formula.
[tex]x = \frac{-4\pm \sqrt{4^2 -(4*-1*2)}}{2*-1}\\x = \frac{-4\pm \sqrt{16 -(-16)}}{-2}\\x = \frac{-4\pm \sqrt{32}}{-2}\\x = 4.449 \\or\\x = -0.449\\[/tex]
Therefore, the function has two real roots and crosses the x axis in two places.
Attached is the graph of G(x) for more understanding.
Please can you help me, it would be greatly appreciated.
Answer:
20 cm^2.
Step-by-step explanation:
If the scale factor is 2 each of the sides of the figure will be increased by a factor 2.
So each side will have a length of 2 * 1 = 2 centimeters.
It will consist of 5 squares of dimension 2*2 = an area of 4 cm^2
So the area of the new cross is 5*4 = 20 cm^2.
We can also calculate the area directly by multiplying by 2^2 ( the scale factor)squared.)
The original area = 5 so the area of the enlarged figure = 5 * 2^2 = 20 cm^2.
cual es la secuencia creciente de los divisores primos de 2520
Answer:
The answer is "[tex]2^3 \times 3^2 \times 5 \times 7\\\\[/tex]"
Step-by-step explanation:
Given:
2520
Prime factor=?
Prime factor of 2520 is:
[tex]= 2 \times 2 \times 2\times 3\times 3 \times 5 \times 7\\\\= 2^3 \times 3^2 \times 5 \times 7\\\\[/tex]
Evan, Claire, Jaya and Tim are running a 3km relay race.
Evan ran 9/10 of a km
Claire ran 7/9 of a km
Jaya ran 2/3 of a km
What fraction of a km does Tim need to run to finish the race?
Try to answer ASAP please, thank you.
Answer:
Tim needs to finish 59/90
Step-by-step explanation:
Add together what Evan Claire and Jaya ran
9/10 + 7/9+ 2/3
The common denominator is 90
9/10 (9/9) +7/9 *10/10 + 2/3 *30/30
81/90 + 70/90 + 60/90
211/90
We need 3 km = 3 *90/90 = 270 /90
270/90 - 211/90 = 59/90
1. What is the equation for the following graph
use photo for graph
x = 4 is the answer because the y coordinate is zero and at x axis it intersects at 4..
please mark it as brainliest ❤️❤️ and follow me..
Answer:
x=5 is the answer
Step-by-step explanation:
hope this helped
The angle measurements in the diagram are represented by the following expressions.
MY
ZA = 5.7 - 15
ZB = 2x + 21
Pro
Pro
Tea
Solve for x and then find the measure of B:
Answer:
x = 12
m(∠B) = 45°
Step-by-step explanation:
Given question is incomplete; find the complete question in the attachment.
In the figure attached two lines 'l' and 'm' are the parallel lines and line 'n' is a transverse.
Angles A and B are the "Alternate exterior angles" which will equal in measure.
m(∠A) = m(∠B)
(5x - 15) = (2x + 21)
5x - 2x = 15 + 21
3x = 36
x = 12
Since, m(∠B) = (2x + 21)
= (2×12) + 21
= 24 + 21
= 45°
Therefore, x = 12 and measure of angle B will be 45°.
what is two plus two
Answer:
4 is the answer to your question
Step-by-step explanation:
(ANSWER ASAP) Which table represents a linear function? graph 1 graph 2 graph 3 graph 4
Answer:
D)
Step-by-step explanation:
Use desmos in the future to help you determine if all of those coordinate make a straight line.
A chef planning for a large banquet thinks that 2 out of every 5 dinner guesis will order his soup appetizer he excepts 800 guests at the banquet
Answer:
320 people
Step-by-step explanation:
[tex]\frac{2 people}{5 people}[/tex]=[tex]\frac{x}{800 people}[/tex]
solve for x by using cross multiplication
-multiply 2 by 800 to get 1,600
-divide 1,600 by 5 people to get 320
your answer is 320 people
Please help i will give out brainliest
Answer:
A
Step-by-step explanation:
To determine if a point lies on the curve, substitute the x- coordinate into the equation. If the value obtained is equal to the y- coordinate then the point lies on the curve, that is
A
y = ([tex]\frac{3}{2}[/tex] )² = [tex]\frac{9}{4}[/tex] ≠ [tex]\frac{9}{2}[/tex] ← not on line
B
y = (- 1)² = 1 ← lies on line
C
y = 4² = 16 ← lies on line
D
y = ([tex]\frac{1}{2}[/tex] )² = [tex]\frac{1}{4}[/tex] ← lies on line
help plz quick i will mark u brainllest
Answer:
1st one
Step-by-step explanation:
I don't do explanations just answer it mate.
Answer:
hi! your answer should be C. CA ≈ EC
Step-by-step explanation:
"C." just makes the most sense. CA and EC are equal lengths. A, B, and D are not equal. So it has to be C. Hope this helps :)
Nine less than the quotient of two and a number x.
Answer:
Hey there!
Your answer would be x/2 - 9
Answer:
2 ÷ x - 9
Step-by-step explanation:
Quotient of two is written as = 2 ÷ x
Nine less is written as = -9
Final answer = 2 ÷ x - 9
Hope this helped! :)