Mathematics High School

List the intercepts, vertex, and axis of symmetry for each quadratic function whose graph is shown.

Answers

Answer 1
do you have a picture of the actual graph?

Related Questions

Crystal estimated that repairs to her car would cost about $100. The cost of repairs was actually $175. Fill in the box with Crystal's percent error

Answers

percent error=100 times error/predicted

error=175-100=75

predicted=100

percent error=100 times 75/100=75

the answer si 75% error

Prove the Converse of the Pythagorean Theorem using similar triangles. The Converse of the Pythagorean Theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse, the triangle is a right triangle. Be sure to create and name the appropriate geometric figures.

Answers

The Pythagorean Theorem tells us that in a right angle, the sum of the squares lengths of the legs of the triangle equal the squared length of the hypotenuse. 

By angle similarity of triangles we know that if we have three triangles △ADB △ABC △BDC triangles are similar then the sides of the triangles are proportional. AD:AB=AB:AC=AC::BC= BC:DC
AD/AB=AB/AC  AC/BC=BC/DC
Now we cross multiply
AD*AC=AB*ABAC*DC=BC*BC 
This is the same as
AD*AC=AB2AC*DC=BC2
AD*AC+AC*DC=AB2+BC2
Distributive property
AC(AD+DC)=AB2+BC2 
But by construction 
AD+DC=AC
Substituting 
AC*AC=AB2+BC2
So we have
AB2+BC2=AC2 
This proves that the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse. 

Answer:

To prove the Converse of Pythagorean Theorem:

Step-by-step explanation:

1. Draw a right triangle (Triangle ABC)

2. Draw an altitude from and A to the hypotenuse creating 2 new triangles

3. The part that intersects the hypotenuse will be point D, this makes a right angle

Triangle DBA and triangle ABC both have right angles and share angle B, this means that triangle ABC and triangle DBA are congruent by the AA postulate. Since triangle DAC and triangle ABC both have right angles(angle D and angle A) and they share angle C, triangle DAC and ABC are congruent by the AA postulate as well.

The ratios can be set up as:

AC/BC = DC/AC & AB/BC = DB/BA

Once cross multiplied, the result should be:

(AC)² = (BC)(DC) & (AB)² = (BC)(DB)

Now add both sides together to get:

(AC)² + (AB)² = BC(DC) + (BC)(DB)

To make things easier, factor out the like terms:

(AC)² + (AB)² = BC(DC + DB)

When looking at the triangle(must draw to see), it shows that (DC + DB) is actually side BC. This leaves:

(AC)² + (AB)² = BC(BC) → (AC)² + (AB)² = (BC)²

The Pythagorean theorem says that a² + b² = c². Knowing this, on the original triangle, side AB = a, side AC = b, and side BC = c. Knowing this:

(AC)² + (AB)² = (BC)² → a² + b² = c²

This proves the Converse of the Pythagorean Theorem.

So the question says...

Suppose you have ∠SMB and m ∠SMB =125.35 °.

Part A: Determine the angle measure that is complement to ∠SMB, if possible. If ∠SMB does not have a complementary angle, then explain why it does not.

Part B: Determine the angle measure of the supplement of ∠SMB.

Part C: Determine the angle measure of the angle complement to ∠SMB’s supplement.

I’m stuck on this question so if anyone can help me with it that would be greatly appreciated. Thanks!

Answers

Part A. Two angles are complementary if their sum is equal to 90°. Since the angle given is more than 90°, there is no possible complement for a 125.35-degree angle.

Part B. Two angles are supplementary if their sum is equal to 180°. So,
Supplementary angle = 180 - 125.35 = 54.65°

Part C. Complementary angle = 90 - 54.65 = 35.35°

Part A: ∠SMB does not have a complementary angle

Part B: The angle measure of the supplement of ∠SMB is 54.65°

Part C: The angle measure of the angle complement to ∠SMB's supplement is  35.35°

The given angle is ∠SMB and m ∠SMB =125.35 °

For Part A

Complementary angles are angles that sum up to 90°.

To determine the angle measure that is complement to  ∠SMB, we will find the angles that adds up to ∠SMB to give 90°. Since  ∠SMB is already greater than  90°, therefore,  ∠SMB does not have a complementary angle.

For Part B.

Supplementary angles are angles that sum up to 180°.

To determine the angle measure of the supplement of ∠SMB, we will find the angle that adds up to ∠SMB to give 180°. Let the measure of the angle be x, that is

x + 125.35° = 180°

∴ x = 180° - 125.35°

x = 54.65°

∴ The angle measure of the supplement of ∠SMB is 54.65°

For Part C

To determine the angle measure of the angle complement to ∠SMB's supplement, we will determine the measure of the angle that adds up to ∠SMB's supplement to give 90°. Let the angle be y

Then,

y + 54.65° = 90°

(NOTE: ∠SMB's supplement is 54.65°)

∴ y = 90° - 54.65°

y = 35.35°

∴ The angle measure of the angle complement to ∠SMB's supplement is  35.35°

Hence,

Part A: ∠SMB does not have a complementary angle

Part B: The angle measure of the supplement of ∠SMB is 54.65°

Part C: The angle measure of the angle complement to ∠SMB's supplement is  35.35°

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If p||q, solve for x.

Answers

x=10 because both of the angles when added equal 180
The two angles are supplementary because they are corresponding angles(not sure i the term is actually corresponding... i could be something else). Thus 7x-1+13x-19=180 so 20x-20=180 so x=10

Plz see picture and question attached

Answers

the answer is 16m² because the square root of 81 is 9 meaning both width and height of the patio are 9. to find the height of the square patch you do 9 - 5 = 4
because it is square, meaning the width and height are the same, so therefore the width is also 4. to get the area of a square of rectangle, you times the width by the height. 4 × 4 = 16. so the answer is 16m² because the unit is metre so we write m²

You want to embroider a square design. You have an embroidery hoop with a 6 inch diameter. Find the largest value of x so that the entire square will fit in the hoop. Round to the nearest tenth

Answers

Final answer:

The largest size of the square that can be embroidered within the 6 inch hoop is 4.2 inches per side (rounded to the nearest tenth). This is found using geometry principles involving squares and circles.

Explanation:

This question is asking for the side length of a square that will fit within a circle, or in this case, an embroidery hoop, with a certain diameter. This is a concept from geometry that involves the relationship between squares and circles. Essentially, the diameter of the circle becomes the diagonal of the square.

To calculate the side length (x) of the square, we'll use the formula for the diagonal (d) of a square divided by the square root of 2 (d = √2 * x). Since the diameter of the hoop is 6 inches, rearranging the equation gives us x = d / √2 which results in x = 6 / √2 = 4.2 inches (rounded to the nearest tenth)

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1. simplify

9 x 5 + 2 / 8 - 3

by the way " / " means division.

Answers

the answer would be 42.25 because first you multiply 9 and 5, then divide 2 and 8 and add that to 45, then you subtract 3 from that.
Your answer will be 46. Remember PEMDAS. Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. These are the steps you would do a problem like this in. First you would multiply 9x5, because there is no parentheses or exponents. Next, divide. This will leave you with 45+4-3. Next, do your addition and subtraction. There's your answer Hope this helps  :)

Can someone explain to me how to solve these ?

Answers

[tex]\bf 21)\\\\ \cfrac{c}{a}=r+d\implies \cfrac{c}{r+d}=a \\\\\\ 23)\\\\ ka=v+w\implies a=\cfrac{v+w}{k} \\\\\\ 25)\\\\ z=y+mx\implies z-y=mx\implies \cfrac{z-y}{m}=x[/tex]

Which equation would represent this problem?

Five added to 3 times a number is equal to 8 less than 5 times the number

Answers

5+3n=8-5n should be the could answer how I solve it was adding is a plus sigh=n and less than is a minus sign

Find the length of the hypotenuse of a right triangle with legs of lengths 12 ft and 16 ft answer

Answers

Answer:

Step-by-step explanation:

but what ab this one:  Find the length of the hypotenuse of a right triangle with legs of 5 ft and 12 ft.

A right triangle in which one angle is the right angle and the two sides are perpendicular to each other. Hence, the length of the hypotenuse is [tex]20ft[/tex].

What s the right triangle?

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular.

Here, the lengths of the triangle are [tex]12ft[/tex] and [tex]16ft[/tex] .

As we know,

[tex]H^{2}=P^{2}+B^{2}[/tex]      ..........[tex](1)[/tex]

Now, substituting the values in the equation [tex](1)[/tex], we get

[tex]H^{2}=(12)^{2}+(16)^{2}\\H^{2}=144+256\\H^{2}=400\\H=\sqrt(400)\\H=20ft[/tex]

Hence, the length of the hypotenuse is [tex]20ft[/tex].

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What’s the answer pleaseeeeeeeee

Answers

y^2 +6^2 = 12^2

y^2 +36 = 144

y^2 = 108

sqrt(108) = 10.392 = 6sqrt(3)

 Answer is B 6sqrt(3)

Suppose you have 48 feet of fencing to enclose a rectangular dog pen. The function : A = 24x-x^2 , where x = width , gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area ?

PLEASE HELP ASAP!! *if you can give explanation/work it would be great* if not that is okay ..

Answers

check the picture below, that's a parabolic graph of a quadratic equation with a negative leading coeffficient, like this one, the one in the graph is just for initial velocity, but, the highest point is at the vertex for any of these parabolas.

and this one is not exception, so where's the vertex?  what's A or the y-coordinate when the vertex is reached?, well, let's check.

[tex]\bf A=24x-x^2\implies A=-1x^2+24x+0\\\\ \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} A = &{{ -1}}x^2&{{ +24}}x&{{ +0}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left(-\cfrac{24}{2(-1)}~~,~~0-\cfrac{24^2}{4(-1)} \right)\implies \left(12~~,~~ 0+\cfrac{576}{4} \right) \\\\\\ \left(\stackrel{width}{12}~~,~~\stackrel{Area}{144} \right)[/tex]

so, that's the vertex, and when the width is that much, the Area reaches a maximum of that much.
Final answer:

The width that gives the maximum area of the rectangular pen is 12 feet, and the maximum area is 144 square feet.

Explanation:

To maximize the area of a rectangle with a fixed perimeter, you want to make the rectangle as close to a square as possible. This maximizes the area because it distributes the available fencing evenly among the sides, optimizing the area enclosed. The given function, A = 24x - x^2, represents the area of a rectangle with width 'x' and length 'L' where L = (48-2x) / 2.

Maximization or minimization of a function occurs at its turning point. For a quadratic function like ours, the maximum or minimum happens at the vertex. The x-coordinate of the vertex is given by -b/2a. So, in our function A = -x^2 + 24x (which is the same as 24x - x^2), a = -1, b = 24.

Substitution gives: x = -(24) / 2*(-1) = 12 feet. Therefore, the width that gives you the maximum area is 12 feet.

Substitute x = 12 into the function to find the maximum area: A = 24*12 - 12^2 = 288 - 144 = 144 square feet.

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The diagram shows triangle MNP. Which term describes point Q?

Answers

Answer:

(B) Incenter

Step-by-step explanation:

From the given figure, it can be seen that PMN is a triangle where MQ is the angle bisector of ∠NMP, PQ is the angle bisector of∠NPM and NQ is the angle bisector of ∠MNP.

Also, It is equally distant from the three line segments forming the sides of the triangle. Thus, By the definition of incenter, Q can be named as the incedntre of the given triangle PMN.

Since, the centroid, circumcenter and orthocenter does not satisfy the conditions given in the figure, thus Q can not be considered as centroid, circumcenter and orthocenter.

Hence, option B is correct.

Answer:

the answer is incenter

Step-by-step explanation:

took the apex quiz got it correct !

Tanisha bought 4 bundled packs of comic books. The price of each pack was the same. After she bought the packs, her account balance showed a change of −$86.64. What would have been the change to Tanisha's account balance had she bought only 1 bundled pack of comic books?

A) 21.60
B) -21.60
C) 21.66
D) 21.66

Answers

B) -21.60 BC your dividing a positive by a negative

how many times must 24 be added until the sum is 1500

Answers

1500 / 24 = 60
60 times must 24 be added until the sum is 1500
it cant... all i got was 63 times

A number is a multiple of 3 if and only if the number is odd
True or false

Answers

False. 30 is an even number and is a multiple of 3, 3 x 10 = 30. Same with 60, 90, 120, etc. if you keep adding 30. 

What are the characteristics of a gas?
A. a definite shape but no definite volume
B. no definite shape but a definite volume
C. a definite volume and definite shape
D. no definite shape or definite volume

Answers

D. no definite shape or definite volume

Answer:

D

Step-by-step explanation:

according to the rational root theorem, which is a factor of the polynomial f(x) = 3x^3 - 5x^2 - 12x + 20?

Answers

They are:  +-(1,2,4,5,10,20)/+1(1,3)

Which linear system of equations does the matrix represent?

-3 5 | 15
2 3 | -10

Answers

Actually the answer is
-3x + 5y = 15
2x + 3y = -10
Final answer:

The matrix represents the system of linear equations: -3x + 5y = 15 and 2x + 3y = -10.

Explanation:

The matrix represents the system of linear equations. Each row corresponds to an equation and each column to a coefficient of the unknowns. So, the given matrix:

-3  5  |  15
2  3  | -10

Represents the system of linear equations:

-3x + 5y = 15

2x + 3y = -10

Where x and y are the unknown variables that we are trying to solve for.

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What is the common difference of the arithmetic sequence 1/5, 6/5 , 11/5 ,16/5 , ...?

Answers

+ 5/5 each time

hope this helps
The common difference is 1 because if you simplify the improper fractions, each hole number is 1 greater than the one before. So the common difference is 1 or 5/5

Kim was walking down a rocky path for 4 minutes the election dropped steadily altogether it dropped 8 feet what was the chance in elevation per minute for the 4 minutes?

Answers

in 4 minutes it changed 8 feet

 so 8/4 =2 feet per minute change

and since it dropped it would be a negative change so -2 feet per minute

Find an equation of the line containing the point (3,3) and parallel to y = 2 x − 1 y=2x-1.

Answers

y=mx+b
y=2x+b
then substitute x and y
3=2(3) + b
3= 6 + b
b=-3
y=2x-3

Use a quadratic equation to find two real numbers that satisfies the situation. The sum of the two numbers is 2, and their product is –48.

Answers

Final answer:

To find two real numbers whose sum is 2 and product is -48, we form a quadratic equation x^2 - 2x - 48 = 0. Using the quadratic formula, we get two pairs of numbers (8, -6) and (-6, 8) that satisfy the given conditions.

Explanation:

To find two real numbers that satisfy the given conditions, namely their sum being 2 and their product being –48, we can set up a system of equations or use a . Let's denote the two numbers as x and y. We know:

x + y = 2xy = -48

We can express y in terms of x from the first equation: y = 2 - x. Substituting this into the second equation gives us:

x(2 - x) = -48

This simplifies to a quadratic equation:

x^2 - 2x - 48 = 0

Using the, x = (-b ± √(b^2 - 4ac)) / (2a), with a = 1, b = -2, and c = -48, we find the two possible values for x, which in turn gives us the corresponding values for y:

x = (2 ± √(4 + 192)) / 2

x = (2 ± √196) / 2

x = (2 ± 14) / 2

Therefore, the two solutions are x = 8 or x = -6. Since we were looking for two numbers, using x + y = 2, the corresponding y values are y = -6 and y = 8, respectively. Hence, the two pairs of numbers that satisfy the conditions are (8, -6) and (-6, 8).

A bag contains 80 marbles: 40 are red, 20 are blue, and 20 are black. what is the probability of selecting a red or blue marble at random

Answers

40 % out of 80 for red
20% out of 80 for blue

Find the approximate value of the circumference of a circle with the given radius. Use = 3.14. Round your results to one more decimal than in the given radius. 4 inches C = 12.5 inches 12.6 inches 25.1 inches 25.2 inches

Answers

C  = 2 * 3.14 * 4 =   25.1  to nearest tenth ( 1 decimal place)

Answer:

[tex]25.1\ inches[/tex]

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=4\ in[/tex]

substitute

[tex]C=2(3.14)(4)=25.1\ in[/tex] -----> one more decimal than the given radius (nearest tenth)

Which equation can be used to solve for b?

A) tan(30°) = 5/b
B) tan(30°) = b/5
C) tan(30°) = 10/b
D) tan(30°) = b/10

Answers

SOH CAH TOA
tan(x) = opposite / adjacent

the hypotenuse is the longest side of 10, so C and D are not correct.

Side b is adjacent to the 30° angle
Side 5 is opposite of the 30° angle

tan(30) = 5/b

In this exercise we want to calculate the value of angle B, so we have to:

Letter A

So knowing the tangent formula as:

[tex]tan(x) = opposite / adjacent[/tex]

Knowing some information given in the exercise such as:

the hypotenuse is the longest side of 10Side b is adjacent to the 30° angleSide 5 is opposite of the 30° angle

So we have:

[tex]tan(30)=5/b[/tex]

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PLEASE HELP 30 POINTS!!!!!!

Answers

placed them equal to each other.

3x + 6 = 4x - 2                 

6 (+2) = 4x (-3x)

8 = x

plug in x to both of the expressions


3(8) + 6 = 24 + 6 = 30
4(8) - 2 = 32 - 2 = 30  

True

x = 8

hope this helps


B is wrong, because you do not set them equal to 180 ( you set them equal to each other). Next, it is wrong, because they messed up the end too.

hope this helps
Answer:  " x = 8 " 
_______________________________
By examining the image attached, we notice that:
_______________________________________________
The 2 (two) particular angles with the following measurements:
_________________________________________________
1)  4x - 2 ;  and: 

2)  3x + 6 ;  
_________________________________________________
are equal; since they are "alternate interior angles" ; since the 2 (two) horizontal lines in the figure are parallel; and since alternate interior angles are equal in measurement.
___________________________________________
The question asks to solve for "x" ;

As such:

  4x - 2  =  3x + 6  ;

Solve for "x"  ; 

Subtract "3" from each side of the equation ; & add "2" to each side of the equation ; 


   4x - 2 =   3x  + 6  ;
  -3x +2 =  -3x  + 2  ;
_________________________
    1x     =            8  ;  
_________________________

   →  x = 8 .
____________________________________
Now, we can check our answer:
____________________________________
      " 4x - 2  =  3x + 6 " ;

  → Plug in "8" for "x" ; to see if both sides of the equation are equal ;

   4(8) - 2  =?  3(8) + 6 ??

  →  32 - 2 =?  24 +  6 ?? 

  →  30 = ? 30 ?  Yes!
____________________________________________________

If I set a goal of signing up 30% of customers to receive emails. that means that if I speak to 130 customers today I need to collect email addresses from ?

Answers

130*.3 people
^^^^^^^^^

Answer:39

Step-by-step explanation:

130+30%=39

Abigail drives at an average speed of 60 miles per hour for 3 hours. The graph shows her distance versus time. Which statements are true? Check all that apply. As Abigail’s time increases, her distance increases. As Abigail’s time increases, her distance decreases. At 2 hours, Abigail has traveled 120 miles. At 1.5 hours, Abigail has traveled 100 miles. At 3 hours, Abigail has traveled 180 mile

Answers

As Abigail's time increases, her distance increases.

At 2 hours, Abigail has traveled 120 miles.

At 3 hours, Abigail had traveled 180 miles.

The statements are to be checked whether they are true or not.

The true statements are:

As Abigail’s time increases, her distance increases.

At 2 hours, Abigail has traveled 120 miles.

At 3 hours, Abigail has traveled 180 mile

Abigail is driving at a speed of 60 miles per hour for 3 hours.

The function representing the situation will be

[tex]y=60x[/tex]

where,

[tex]y[/tex] is the distance in miles

[tex]x[/tex] is the time in hours

If time increases this means [tex]x[/tex] increases so, distance [tex]y[/tex] will also increase.

At 2 hours [tex]x=2[/tex]

[tex]y=60\times 2=120[/tex]

The distance traveled is 120 miles.

At 1.5 hours [tex]x=1.5[/tex]

[tex]y=60\times 1.5=90[/tex]

The distance traveled is 90 miles.

At 3 hours [tex]x=3[/tex]

[tex]y=60\times 3=180[/tex]

The distance traveled is 180 miles.

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If 5 ounces is equal to 140 grams, then 2 pounds of pizza dough is equal to how many grams?

Answers

907.18 grams are in 2 pounds.
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