Find the vertex of the parabola y=x^2 + 5x + 10

Answers

Answer 1

The coordinates of the vertex of the given parabola [tex]y=x^2+5x+10[/tex] will be [tex](\dfrac{5}{2},\dfrac{15}{4})[/tex].

What is the vertex of a parabola?

Vertex of the parabola is the point of intersection of symmetry axis of the parabola and the parabola itself.

The given equation of parabola is [tex]y=x^2 + 5x + 10[/tex].

To get the coordinates of vertex of this parabola, we have to write the equation of parabola in the standard form.

So, write the equation of parabola in its standard form as,

[tex]y=x^2 + 5x + 10\\y=x^2+2\times \dfrac{5}{2}x+\dfrac{25}{4}-\dfrac{25}{4}+10\\y=(x-\dfrac{5}{2})^2+\dfrac{15}{4}\\(y-\dfrac{15}{4})=(x-\dfrac{5}{2})^2[/tex]

The standard form of parabola is,

[tex]y-b=(x-a)^2[/tex] where (a, b) is the coordinate of the vertex.

So, by comparing the equations, the vertex of the parabola will be [tex](\dfrac{5}{2},\dfrac{15}{4})[/tex].

Therefore, the coordinates of the vertex of the given parabola [tex]y=x^2+5x+10[/tex] will be [tex](\dfrac{5}{2},\dfrac{15}{4})[/tex].

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Find The Vertex Of The Parabola Y=x^2 + 5x + 10

Related Questions

You are out to dinner at Nick’s Pizza with a group of 5 friends. The total cost for pizza and sodas is $38.50. Your waiter did a great job and you would like to leave a 20% tip. Total =

Answers

Answer:
I believe 7.7
Step-by-step explanation:

lmk if it helps

In circle H with m/GHJ = 70 and GH = 10 units, find the length of arc GJ.
Round to the nearest hundredth.

Answers

Answer:

GH8 remains 70 and gh remains 10

Step-by-step explanation:

there is no five or more

Find the volume of the oblique cylinder as pictured below with a = 10 cm, h = 17 cm. Do not include units in your answer. Use 3.14 for pie and round your answer to the nearest hundredth. Do not include units in your answer

Answers

The volume of the oblique cylinder that has the given dimension is: 5,338 cm³.

What is the Volume of an Oblique Cylinder?

Volume = πr²h, where h is the height and r is the radius of the oblique cylinder.

Given the following:

Radius (r) = a = 10 cmHeight (h) = 17 cm

Volume of oblique cylinder = πr²h = (3.14)(10²)(17)

Volume of oblique cylinder = 5,338 cm³

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If a 714-mile trip takes 17 hours, the average speed is?

Answers

Answer:

42 mph

Step-by-step explanation:

brainliest/crown please :)

Mia has two cylindrical bird feeders. Her red bird feeder has a diameter of 10 inches and is 8.3 inches tall. What is the volume of the red bird feeder?

Answers

The volume of the red bird feeder will be equal to V=651.88 cubic inches

What is volume?

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length,width and height of the cube or Cuboid.

It is given that:-

Diameter = 10 inches

Height =  8.3 inches

Volume=?

Since the feeder is cylindrical so the volume will be calculated as:-

[tex]\rm Volume=\dfrac{\pi }{4}d^2H\\\\\\Volume=\dfrac{\pi }{4}(10)^2(8.3)\\\\\[/tex]

V=651.88 cubic inches

Hence volume of the red bird feeder will be equal to V=651.88 cubic inches

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Alannah picked out 10 apples that cost a total of $5. On her way to the checkout counter, she decided she really wanted 12 apples. If all the apples are the same price, how much will Alannah pay for 12 apples? Explain how each child came up with their answer?

Answers

6 dollars for 12

Step-by-step explanation:

if she paid 5 dollars for 10, you would do 10/ 5 which would get you 2 dollars per apple so she would pay 6dollars for 12 apples

Can anyone help me with this please?

Answers

Step-by-step explanation:

since there are answer options we don't need to formally solve the system of equations, we only need to try the first point of every option, and see, where the equations are true.

if we cannot find it for the first point, then we would need to try the same thing for the serving points.

let's put (0, 6) into the first equation :

-2×0² + 6 = 6

6 = 6 true

let's put it into the second equation ;

4×0² + 3×6 = 28

18 = 28 false

that eliminates the first 2 answers.

let's put (-1, 4) into the first equation :

-2×(-1)² + 4 = 6

-2×1 + 4 = 6

-2 + 4 = 6

2 = 6 false

that eliminates the third answer.

let's put (-1, 8) into the first equation :

-2×(-1)² + 8 = 6

-2 + 8 = 6

6 = 6 true

let's put it into the second equation :

4×(-1)² + 3×8 = 28

4 + 24 = 28

28 = 28 true

and because the square function delivers the same result for -1 and +1, it is also true for the second point.

and the 4th answer is therefore correct.

Five more than a number p is less than 17.

Answers

Answer:

2x-15

Step-by-step explanation:

Found it on a Phrase translator to equations.

1. Are the side lengths congruent?





2. Are the opposite sides parallel?







3. Are the adjacent sides perpendicular?





4. The most specific name for this quadrilateral is:

Answers

Answer:

opposite sides are congruentopposite sides are paralleladjacent sides are not perpendicularthe figure is a parallelogram

Step-by-step explanation:

An easy way to determine the nature of the quadrilateral is to look at the lengths and midpoints of the diagonals. Adding and subtracting the coordinates of one end point from the other can tell what you need to know.

The diagonals of a parallelogram are mutual bisectors. The diagonals of a rhombus are perpendicular. The diagonals of a rectangle are congruent.

__

diagonal AC

The difference of end points of diagonal AC is ...

  C -A = (7, 2) -(-6, 1) = (13, 1)

The sum of the end points of diagonal AC is ...

  C +A = (7, 2) +(-6, 1) = (1, 3)

diagonal BD

The difference of end points of diagonal BD is ...

  B -D = (0, 7) -(1, -4) = (-1, 11)

The sum of end points of diagonal BD is ...

  B +D = (0, 7) +(1, -4) = (1, 3)

comparison of diagonals

midpoints

The two diagonals have the same end point sum, (1, 3), meaning their midpoints are coincident. The figure is a parallelogram.

lengths

The lengths of the diagonals will be the same if the sum of squares of the coordinates of the end-point differences are the same.

  Σ(C -A)² = 13² +1² = 170

  Σ(B -D)² = (-1)² +11² = 122 ≠ 170 . . . . . not a rectangle

perpendicularity

The diagonals will be perpendicular if the "dot product" of the end-point differences is zero.

  x1·x2 +y1·y2 = 13(-1) +1(11) = -2 ≠ 0 . . . . not a rhombus

The most specific name for this quadrilateral is parallelogram.

_____

Opposite sides of a parallelogram are congruent and parallel.

Adjacent sides of a rectangle are perpendicular. This is not a rectangle, so adjacent sides are not perpendicular.

A parallelogram that is not a rectangle or rhombus is described most specifically as a parallelogram.

What is the value of the rational expression below when xis equal to 4?
x-12/x-8

Answers

Answer:

= -7

Step-by-step explanation:

given x = 4

12/4 = 3

4 - 3 - 8 = -7

find the area of the figure. use 3.14 for pi.
a 133.5
b 188.5
c 149.25
d 94.25

Answers

Answer:

  d.  94.25 in²

Step-by-step explanation:

The area of this composite figure is the sum of the areas of a semicircle and a triangle. Each of those areas can be found using the appropriate formula:

  semicircle: A = (π/2)r²

  triangle: A = 1/2bh

__

semicircle

The semicircle has a radius equal to half its diameter. The radius is (10 in)/2 = 5 in. Its area is ...

  A = (3.14/2)(5 in)² = 39.25 in²

triangle

The area of the triangle with base 11 in and height 10 in is ...

  A = 1/2bh

  A = 1/2(11 in)(10 in) = 55 in²

total area

The area of the figure is the sum of the areas of the semicircle and triangle, so is ...

  figure area = (39.25 in²) +(55 in²)

  figure area = 94.25 in²

How many solutions does this system have?
x-3y=4
-2x+6y=3
O one
O two
O an infinite number
Ono solution

Answers

Answer:

two solutions B

Step-by-step explanation:

x-3y=4

-2x+6y=3

Graph the function y = x+2+5. Which point lies on the graph?

A-
(-2,5)

B-
(3,6)

C-
(7,6)

D-
(0,5)

Answers

Answer:

A

Step-by-step explanation:

Given equation :

y = x + 2 + 5y = x + 7

Evaluating the options

A (-2, 5)

5 = -2 + 75 = 5Correct!

Define an axiom in geometry

Answers

Answer:

In mathematics or logic, an axiom is an unprovable rule or first principle accepted as true because it is self-evident or particularly useful.

Match the trigonometric ratios with their values based on the triangle shown in the diagram.

Answers

The trigonometric ratios with their values are based on the triangle will be sin D = 4 / 5, sin C = 3 / 5, sin D x cos D = 12 / 25, tan C x tan D = 1, and cos C x tan D = 16 / 15.

What is trigonometry?

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The triangle is given below.

Then the trigonometric ratios with their values are based on the triangle shown in the diagram and will be

sin D = 4 / 5

sin C = 3 / 5

sin D x cos D = 4 / 5 x 3 / 5

sin D x cos D = 12 / 25

tan C x tan D = 3 / 4 x 4 / 3

tan C x tan D = 1

cos C x tan D = 4 / 5 x 4 / 3

cos C x tan D = 16 / 15

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The beginning balance in a person's checking account was -10 dollars. After writing three checks for 8, 10 and 17 dollars and making a deposit of 90 dollars, what was the new balance in the account?

Answers

Answer:

45

Step-by-step explanation:

he have -10$ that means he have loan

he withdraw 8,10and 17 dollars

now his balance is -45$

now he deposited 90 dollars

now

=90-45$

=45$

How does the graph of f(x) = -4^5x - 3 differ from the graph of g(x) = -4^5x?

A. The graph of f(x) is shifted three units to the right of the graph of g(x).

B. The graph of f(x) is shifted three units down from the graph of g(x).

C. The graph of f(x) is shifted three units up from the graph of g(x).

D. The graph of f(x) is shifted three units to the left of the graph of g(x).

Answers

Using translation concepts, it is found that the correct option is given by:

B. The graph of f(x) is shifted three units down from the graph of g(x).

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the parent function is:

[tex]g(x) = -4^{5x}[/tex]

The translated function is:

[tex]f(x) = -4^{5x} - 3[/tex]

3 was subtracted from the original function, which means that the translated function was shifted 3 units down, and option B is correct.

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the graph of y=sin x and y=cos x are identical except for a horizontal shift

Answers

I think it will be 31

Find the volume of this please

Answers

Answer: 436.8

Step-by-step explanation:

The linear inequality y <-2/3+ 2 is graphed. Which is a solution for the inequality

Answers

Answer:

C. (0;0).

Step-by-step explanation:

(0;0) only.

if to substitute the given coordinates into the given inequality and calculate the result, then the left side equals to the right side. Except (0;0).

Which of the following sets does not contain any irrational numbers?
PICTURE OF SETS SHOWN BELOW.

Thank you so much

Answers

Answer:

C

Step-by-step explanation:

infinite numbers

pi

square root of 80

^all irrational

Which expression is another way to write 10,000?

10 × 10 × 10

10 × 10 × 10 × 10

10 × 10 × 10 × 10 × 10

10 × 10 × 10 × 10 × 10 × 10

Answers

EXPRESSION

==============================

[tex] \large \sf \underline{Question:}[/tex]

Which expression is another way to write 10,000?

==============================

[tex] \large \sf \underline{Answer:}[/tex]

[tex] \qquad\quad\large \bold{10 \times 10 \times 10 \times 10}[/tex]

==============================

[tex] \large \sf \underline{Solution:}[/tex]

By getting the answer you just multiply 10 directly by 10 until you get what you are looking for;

[tex] \rm{10 \times 10 = \pmb{100}}[/tex][tex] \rm{ 100 \times 10 = \pmb{1000}}[/tex][tex] \rm{1000 \times 10 = \pmb{10000}}[/tex][tex] \rm { \underline{ \pmb{10 \times 10 \times 10 \times 10 = 10000}}}[/tex]

Hence, proven.

==============================

Answer:

Step-by-step explanation:

10000

There is some algebra in it I think! Thanks!! (I’ll add extra points and brainly just ask:)

Answers

Answer:

C. 27

Step-by-step explanation:

27 + 23 = 50

:)

Answer: hii :)

i know this oneeeee ^^ your answer is 27 <3

Step-by-step explanation:

Move all terms not containing x to the right side of the equation.

hopefully this helps you

- Matthew ~

Two similar polygons have a scale factor of three. The smaller polygon has an area of 42 cm² and perimeter of 50 cm. what is the area of the larger polygon? and what is the perimeter of the larger polygon?

Answers

Step-by-step explanation:

a scale factor applies to every line, that means also to every side of the polygon.

the area of a polygon is always created out of the product (multiplication) of 2 dimensions (or sides).

while a perimeter is a pure sum of sides.

so the perimeter grows by the same factor as the sides : scale factor 3.

the perimeter of the larger polygon is therefore :

50 × 3 = 150 cm

and the area of the larger polygon ?

remember, that the area is always the product of 2 sides (or the sum of products of 2 sides).

and so, the scale factor enters these multiplications twice, and it gets therefore squared : 3×3 = 9.

so, the area of the larger polygon is then

42 × 9 = 378 cm²

Wendy’s Big Bacon Classic contains how many calories after calculating the
nutrients below?
44 grams Carbohydrate= 44×4 =176_ Calories
36 Grams of Fat= 36×9 = 324 _ Calories
37 Grams of Protein= 37×4 =_148__ Calories

4. What is the percentage of total calories that come from fat in question 3?
Fat Calories:__________
% of Total Calories _________
help with number 4 please and explain it goes with the top answer

Answers

Answer:

Fat Calories: 342

50% of Total Calories

Step-by-step explanation:

Total calories:

Carbohydrates:

176

Fat:

324

Protein:

148

Total:

176+324+148=648

648/342 = 2

Meaning that half of the calories come from fat.

PLEASE HELP I NEED QUICK!!!

Answers

5 cups of rice if you look at 1 1/3 it says 5 1/3 cups can be made so 5 cups of rice

3/4 cups of dry rice can make 3 cups cooked rice

1 cup dry ice can make

3÷3/43×4/34cups

Solve for Unknown: x/10=24/39.

Do not put variable, only put the number value to the nearest whole number.

Answers

Answer:

6

Step-by-step explanation:

When you have a proportion (fraction=fraction), you can crossmultiply to solve. See image.

two parallel lines are cut by a transveral.

if the measure of 1 is 45 degrees, what is the measure of 5

135
180
45
90

Answers

The answer is 45. The explanation is that <1 and <5 are congruent or equal because they are parallel.

Answer:

is C). 45

Step-by-step explanation:

fractions were never my strong suit can anyone help?​

Answers

Answer:

See below ~

Step-by-step explanation:

Find the decimal values of the fractions on each side :

Left side                      Right side

⇒ 4/10 = 0.4               ⇒ 2/5 = 0.4

⇒ 1/2 = 0.5                 ⇒ 9/12 = 0.75

⇒ 1/4 = 0.25               ⇒ 2/8 = 0.25

⇒ 3/4 = 0.75              ⇒ 5/10 = 0.5

Hence, the matched fractions are :

4/10 ↔ 2/5

1/2 ↔ 5/10

1/4 ↔ 2/8

3/4 ↔ 9/12

Answer:

Step-by-step explanation:

Consider the equation 5 – 3(2x – 7) = 12 – 5(x – 2). Is x = 2 a solution to this
equation? Is x = 4 a solution to this equation?

Answers

Answer: No (x = 2), Yes (x = 4)

Step-by-Step Explanation:

=> 5 - 3(2x - 7) = 12 - 5(x - 2)

Substitute x = 2 in the Equation :-

5 - 3(2x - 7) = 12 - 5(x - 2)
5 - 3(2(2) - 7) = 12 - 5((2) - 2)
5 - 3(4 - 7) = 12 - 5(2 - 2)
5 - 3(-3) = 12 - 5
5 + 9 = 12 - 5
14 = 7
LHS is not Equal to RHS

Therefore, x = 2 is not a Solution.

Substitute x = 4 in the Equation :-

5 - 3(2x - 7) = 12 - 5(x - 2)
5 - 3(2(4) - 7) = 12 - 5((4) - 2)
5 - 3(8 - 7) = 12 - 5(4 - 2)
5 - 3(1) = 12 - 5(2)
5 - 3 = 12 - 10
2 = 2
LHS is Equal to RHS

Therefore, x = 4 is a Solution.

Answer:

[tex]\sf x=4[/tex]

Step-by-step explanation:

[tex]\sf 5 - 3(2x - 7)=12 - 5(x - 2)[/tex]

To get rid of the parentheses, we'll apply the distributive property. Staring with the left side, multiply -3 by (2x-7).

[tex]\sf 5 - 6x+21=12 - 5(x - 2)[/tex]

5+ 21= 26

[tex]\sf 26 - 6x=12 - 5(x - 2)[/tex]

Now, let's do the same thing to the right side. Multiply -5 by (x-2) »12−5x+10, than add 12+ 10 = 22 .

[tex]\sf 26 - 6x=22 - 5x[/tex]

Combine like terms.

[tex]\sf 26 - x=22[/tex]

Subtract 26 from both sides.

[tex] \sf - x= - 4[/tex]

Multiply both sides by -1.

[tex]\sf x=4[/tex]

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