Answers
Answer:
Part (a)
Given quadratic: [tex]y=x^2+2x-8[/tex]
Factored form
To factor, find two numbers that multiply to -8 and sum to 2: 4 and -2
Rewrite the middle term of the quadratic as the sum of these number:
[tex]\implies y=x^2+4x-2x-8[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies y=x(x+4)-2(x+4)[/tex]
Factor out the common term [tex](x+4)[/tex]:
[tex]\implies y=(x-2)(x+4)[/tex]
Zeros
The zeros of the quadratic polynomial are the x-coordinates of the points where the graph intersects the x-axis, i.e. when y = 0
[tex]\implies y=0[/tex]
[tex]\implies (x-2)(x+4)=0[/tex]
[tex]\implies (x-2)=0\implies x=2[/tex]
[tex]\implies (x+4)=0\implies x=-4[/tex]
Therefore, the zeros are 2 and -4
Vertex
The x-coordinate of the vertex is the midpoint of the zeros.
[tex]\textsf{midpoint}=\dfrac{-4+2}{2}=-1[/tex]
To find the y-coordinate of the vertex, substitute the found value of x into the given equation:
[tex]y=(-1)^2+2(-1)-8=-9[/tex]
Therefore, the vertex is (1, -9)
------------------------------------------------------------------------------------------------
Part (b)
Given quadratic: [tex]y=-x^2-9x-14[/tex]
Factored form
To factor, first factor out -1:
[tex]y=-(x^2+9x+14)[/tex]
Now find two numbers that multiply to 14 and sum to 9: 7 and 2
Rewrite the middle term of the quadratic as the sum of these number:
[tex]y=-(x^2+2x+7x+14)[/tex]
Factorize the first two terms and the last two terms separately:
[tex]y=-(x(x+2)+7(x+2))[/tex]
Factor out the common term [tex](x+2)[/tex]:
[tex]y=-(x+7)(x+2)[/tex]
Zeros
The zeros of the quadratic polynomial are the x-coordinates of the points where the graph intersects the x-axis, i.e. when y = 0
[tex]\implies y=0[/tex]
[tex]\implies -(x+7)(x+2)=0[/tex]
[tex]\implies -(x+7)=0 \implies x=-7[/tex]
[tex]\implies (x+2)=0 \implies x=-2[/tex]
Therefore, the zeros are -7 and -2
Vertex
The x-coordinate of the vertex is the midpoint of the zeros.
[tex]\textsf{midpoint}=\dfrac{-7+(-2)}{2}=-4.5[/tex]
To find the y-coordinate of the vertex, substitute the found value of x into the given equation:
[tex]y=-(-4.5)^2-9(-4.5)-14=6.25[/tex]
Therefore, the vertex is (-4.5, 6.25)
Related Questions
Can someone please answer this for me i will mark you the brainliest
A cylinder has a radius of 6 m and a height of 11 m
what is the approximate area of the cylinder
A: 527.5 m2
B: 640.6 m2
C: 414.5 m2
D: 1243.4 m2.
Answers
Answer:
B!
Step-by-step explanation:
2 times pie times 6 times 6 plus 11 equals 640.9
How many flowers, spaced every 6 inches, are needed to surround a circular garden with a 20-foot radius?
Answers
Choose the expression that is equivalent to 7w2-3/5 (10m2 - 15w – 15) +2w
Answers
Answer:
The answer is C :)
Step-by-step explanation:
An ellipse has focused F1 (-2,4) and F2 (0,7) and the point (4,4) is on the ellipse. Identify the constant sum for the ellipse.
Answers
Answer:
please solve this quickly tommorow is my maths exam
Answer:
11
Step-by-step explanation:
Find the exact value.
sin 9
4
Type + or -
Answers
Step-by-step explanation:
[tex] \sin( \frac{9\pi}{4} ) [/tex]
[tex]0.1230573409[/tex]
2 points
15. Write the ratios for sin X and cos X. You can indicate v by writing "sq.
root" or using alt 251 on your keyboard. You will have two answers. sin X =
and cos X =
Answers
15. Write the ratios for sin X and cos X. You can indicate v by writing "sq.
root" or using alt 251 on your keyboard. You will have two answers. sin X =
and cos X =
please elaborate on your question
A washer and dryer cost a total of $1014. The cost of the washer is two times the cost of the dryer. Find the cost of each item.
Cost of washers
Cost of dryer:
Answers
Answer:
Washer is $676
Dryer is $338
Step-by-step explanation:
1014 divide by 3 gives you 338.
338 x 2 = $676
676 is twice 338.
676 + 338 = 1014
In how many ways could you select 2 of the 6 possible different brands of
orange juice at the store?
Answers
Answer:
15 different ways you can select 2 of 6 brands of orange juice
Step-by-step explanation:
Brand 1
Brand 2
Brand 3
Brand 4
Brand 5
Brand 6
1. (B1, B2)
2. (B1, B3)
3. (B1, B4)
4. (B1, B5)
5. (B1, B6)
6. (B2, B3)
7. (B2, B4)
8. (B2, B5)
9. (B2, B6)
10. (B3, B4)
11. (B3, B5)
12. (B3, B6)
13. (B4, B5)
14. (B4, B6)
15. (B5, B6)
Write an equation of the line in slope-intercept form.
y =
Answers
Therefore the equation is
y = - 4x / 3
3^x= 3*2^x
solve this equation✂️
Answers
Step-by-step explanation:
this is what i get , i hope this will help you
A cube-shaped box is filled with coffee beans. Which equation represents the density of coffee beans in the box? Let c represent the number of coffee beans.
Answers
Answer:
option b I guess
Step-by-step explanation:
D=c/s³ would be the answer
helppppppp!!!!!!!!!!!!!!
Answers
Answer:
20 oz
Step-by-step explanation:
12 + 20 = 32
32 to 20 is equal to 8 to 5
Help with this question
Answers
Answer:
b = 5√3
Step-by-step explanation:
I would honestly just use pythag, but I'll use trig:
tanθ = opposite/adjacent
tan(30°) = 5/b
btan(30°) = 5
b = 5/tan(30°)
b = 5/(√3/3) = 15/√3
b = 15/√3 · (√3/√3) = 15√3/3
b = 5/√3
Check with pythag:
a² + b² = c²
5² + 5√3² = 10²
25 + 25(3) = 100
25 + 75 = 100 ✅
I hope this helps!
You have a bag of gummy worms with 5 green, 3 blue, 6 red, and 2 orange. Which expression represents the probability that you will reach into the bag and pull a red worm, eat it, and then pull a green worm?
Answers
Answer:
[tex]\frac{1}{8}[/tex] I think
Step-by-step explanation:
you have a bag witha a total of 16 gummy worms right? 6 out of 16 of them are red, 5 out of 16 are green.
so you pull out a red one and eat it. the probabilty of you doing that is [tex]\frac{6}{16}[/tex] . keep it in mind that you ate a gummy worm.after enjoying that gummy worm you decide to take another one, but this time, it's green. you know you just ate one right, but you did not replace it now did you? what that means is out of the 16 gummies you had, you are now left with 15 (because you ate one).now you are left with 15 gummy worms. you take a green one out of the packet. the probabilty of you doing that is [tex]\frac{5}{15}[/tex].now that you've got your probabilities all sorted, now it's time to use some basic probability principles. if you ever come across a probability question with the word and, you need to know automatically that you are multiplying. if you ever come across the word or, you are adding. it's always gonna be like this.
so when you multiply your two probabilities, you get the answer [tex]\frac{1}{8}[/tex]
whenever you're dealing with probability, make sure you're aware of things that are being taken. check whether they're being replaced or not. the way I attempted at working it out is how the other probability questions involving replacements are solved, no matter what it is.
I really hope you found this helpful (that is if all I said is correct) :)
The table shows selected values of a piecewise defined function f(x) that increases over the intervals (-∞, 3) and (3,∞). Which of the following statements are true? Select all that apply.
help pls
Answers
Answer: B D F
Step-by-step explanation:
The statement (B), statement (D), statement (F) are true if piecewise defined function f(x) that increases over the intervals (-∞, 3) and (3,∞).
What is piecewise function?A piecewise function is one that has several curve parts in its graph.
It means that, based on the value of the input, it has countless definitions.
A piecewise function, in other words, performs differently depending on the input.
We have given a data for a piecewise function.
From the data:
[tex]\rm \lim_{n \to 3^+} f(x) = 5[/tex]
[tex]\rm \lim_{n \to 3^-} f(x) = 6[/tex]
[tex]\rm \lim_{n \to 2^+} f(x)[/tex] Does not exist because [tex]\rm \lim_{n \to 3^+} f(x)[/tex] and [tex]\rm \lim_{n \to 3^-} f(x)[/tex] are not equal.
Thus, the statement (B), statement (D), statement (F) are true if piecewise defined function f(x) that increases over the intervals (-∞, 3) and (3,∞).
Learn more about the piecewise function here:
brainly.com/question/12561612
#SPJ2
(-5, -5) (1,3) find the distance between each pair of points
Answers
Answer:
10
Step-by-step explanation:
Plug into Distance formula --> √(1 - (-5))^2 + (3 - (-5))^2
---> 10
Which of the following shows the Commutative Property of Multiplication?
(3 × 2) × 7 = 3 × (2 × 7)
4 × (5 + 8) = (4 × 5) + (4 × 8)
4 × 5 = 5 × 4
9 × 7 = 63
Answers
Answer:
The options that show the Commutative Property of Multiplication are:
A) 4x5=5x4
C) (3 x 2) × 7 = 3 ×(2 x 7)
------------------------------
The commutative property of multiplication states that the order in which the factors are multiplied does not change the product, that is:
Of the options, the ones which show it are:
A) 4x5=5x4
C) (3 x 2) × 7 = 3 ×(2 x 7)
In C), on the left side, the first 3 is multiplied by 2, then the result 6 is multiplied by 7, resulting in 42. On the right side, 2 is multiplied by 7, resulting in 14, which is multiplied by 3, resulting in 42.
Step-by-step explanation:
-lukelaws
Answer:
(3 × 2) × 7 = 3 × (2 × 7)4 x 5 = 5 x 4Step-by-step explanation:
These shows the commutative property.
Regardless of which number you group together, the answer remains the same as numbers on each side are identicalHope it helps~
CAN SOMEBODY HELP ME SOLVE THE EQUATION
Answers
Answer:
72.6
Step-by-step explanation:
y = 3.23x + 33.86
y = 3.23 (12) + 33.86
y = 38.76 + 33.86
y = 72.62
Hope this helps!
Choose which statements are true:
I. Every parallelogram is a rhombus.
II. Every rhombus is a parallelogram.
III. Every quadrilateral has 4 sides.
Answers
Answer:
II. Every rhombus is a parallelogram.
III. Every quadrilateral has 4 sides.
Step-by-step explanation:
Not all parallelograms are rhombuses because a rhombus needs to have equal sides, but a parallelogram does not.
The definition of a rhombus is "a parallelogram with opposite equal acute angles, opposite equal obtuse angles, and four equal sides" so all rhombuses are parallelograms.
The definition of a quadrilateral is having four sides, so all quadrilaterals will have four sides.
angles A, B, and Y are in quadrants 1, 2, 3 respectively such that:
tan A= 2
tan B= -4/3
cos Y= -1/3
evaluate the following:
1)cos(2B)
2)tan(2A)
3)cos(Y/2)
4)tan(Y/2)
5)sin(B/2)
6)csc(2B)
7)sec(A/2)
Answers
Answer:
so the lol is the very nice in the lol morning in the 1098 in 1233 because is use the lol in morning.
I don’t understand, can anyone help me?
Answers
Answer:
Step-by-step explanation:
If x = 0, f(x) = -15.
If f(x) = 27, x = 3.
I need help with this anybody please ?
Answers
60
The answer is given in the above picture.
Hope u like it............
a farmer sold 1/4 of his 1500 flock of sheep. how many sheep dd he sell?
Answers
Answer:
375 sheep.
Step-by-step explanation:
To find 1/4 of 1500, you must divide the number by the denominator of the fraction.
1500 ÷ 4 = 375
Sandy wants to carpet the game room in her house. How many square feet of carpet will she need to complete her project if the diameter of the semicircle portion of her room is 10 ft and the base of the triangle is 5 ft? Carpet is only sold in whole number quantities.
Answers
Answer:
52ft²
Step-by-step explanation:
Explanation is in photo
MR X was at the crown of the statue of liberty in an island of New York City. He sighted a cargo ship coming into New York harbor with an angle of depression 35 degree. How far is the cargo ship from the base of the statue of liberty
Answers
Answer:
d = h/1.43
Step-by-step explanation:
Given
Angle of depression = 35°To Find
Distance between cargo ship and base of The Statue of LibertySolving
Let the height of the statue be 'h' and distance between it and the ship be 'd'Upon changing the viewpoint (you'll see why) to the ship viewing the top of the statue, the angle is now (90 - 35)° = 55°Then, upon taking the tan ratio of the angle between them :⇒ tan 55° = h/d
⇒ 1.43 (approx.) = h/d
⇒ d = h/1.43
[∴ Input the value of height in this formula if it is given, and you should be able to get your answer.]
Use the Pythagorean Theorem to find which one of the
following is the hypotenuse c of a right triangle with side
lengths of a = 9 cm and b = 12 cm.
a 12 cm
b 15 cm
C 14 cm
d 17 cm
Answers
Altitude (AB) = 9cm
Base (BC) = 12cm
To FindHypotenuse (AC) = ?
[tex] \fbox \text{According To Pythagoras Theorem = }[/tex]
[tex] \text{(Hypotenuse)² = (Altitude)² + (Base)²}[/tex]
Inserting The Values
[tex] \text{(Hypotenuse)²} =( {9})^{2} + (12) {}^{2} \\ \\ \implies \text{(AC)} {}^{2} = 81 + 144 \\ \\ \implies \text{(AC}) {}^{2} = 225 \\ \\ \implies \text{AC} = \sqrt{225} \\ \\ \implies \text{AC} = 15[/tex]
[tex] \therefore \text{Hypotenuse \: (AC)} = 15 \text{cm}[/tex]
Option B= 15cm is the correct answer
Hope This HelpsThree students are working to find the solution set of this system of equations:
y = 3x + 10
2y = 6x – 4
Use the drop-down menus to complete the statements about each of their methods.
Mia answer choices 1:
-Intersect
-Do not Intersect
-Are the same line
Mia answer choices 2:
-One
-Zero
-Infinetly many
Roberto answer choices 1:
-Can
-Cannot
Delmar answer choies 1:
-sometimes
-never
-always
Delmar answer choices 2:
-One
-Zero
-Infinitely many
Answers
In the equation, Mia correctly graphs the two lines and sees that they do not intersect. This means that the system has zero solution.
How to illustrate the equation?From the complete question, Roberto correctly sees that y cannot be equal to both 10 more than three times a number and 2 less than three times a number at the same time.
Delmar correctly concludes that because 3x + 10 and 3x - 2 will never be equal, the system has zero solution.
Learn more about equations on:
https://brainly.com/question/12444483
What is an intercept?
Answers
A rectangular playground measures 5/8 mile long and 1/4 mile wide. What is the area, in square miles, of the playground?
Answers
Answer:
5/32 square miles or 0.15625 square miles
Step-by-step explanation:
1/4 miles × 5/8 miles
=5/32 square miles or 0.15625 square miles
Help picture below 6 problems will give brainlest
Answers
Step-by-step explanation:
13. 15² = 12² + ?²
225 - 144 = ?²
? = √81
? = 9 feet
16. D. Regular Hexagon
