6x + y=4x+ 11y, write a formula for h(x) in terms of x

Answer:

  a) maximum; the parabola opens downward

  b) positive; it must lie above the x-axis

  c) x = 1.5

Step-by-step explanation:

The x-intercepts of a function are the points where the graph of the function crosses the x-axis. The y-values there are zero.

The "differences" of a function are related to the average slope between adjacent points. Second differences are related to the rate of change of the slope of the function. When second differences are negative, as here, the slope of the quadratic function is decreasing, becoming more negative. We say the curvature of the function is negatve, and that it opens downward.

__

If the graph of the parabola opens downward, and it crosses the x-axis, it must have a maximum that is a positive value of y.

__

The graph of a parabola is symmetrical about its vertex. That means points on the same horizontal line are the same distance from the line of symmetry, which must go through the vertex. The x-coordinate of the vertex will be the x-coordinate of the midpoint between the two x-intercepts:

  x = (-2 +5)/2 = 3/2

The x-coordinate of the vertex is x = 1.5.

______

Additional comment

The attachment shows a table with three evenly-spaced points on the curve. The calculations show first differences (d1) and second differences (d2). You can see that the sign of the second diffference is negative, in agreement with the given conditions.

Answer:

Difference in weight is 24 once

Step-by-step explanation:

got it right

Answer:

12

Step-by-step explanation:

5^2+b^2=13^2

25+b^2=169

169-25=144

b=12

(yes, this is also a triple)

Answer:

y = -2x + 16

Step-by-step explanation:

Slope-intercept form is:

Where m = slope

b = y-intercept

To find the slope of the line containing (7,2) and (2,12), we have to find the slope, m.

Now, to find the y-intercept (b), insert m = -2 into the equation and one of the given points:

let's use point (7,2) to find b:

Now, we can find the equation of this line:

Answer:

y=-2x+16

Step-by-step explanation:

First we should find the slope.

We can use the formula (y2-y1)/(x2-x1)

(12-2)/(2-7)=10/-5=-2

So, the slope is -2.

From there, we can plug in one of the points into the standard slope-intercept equation, y=mx+b, along with the slope we already found

y=-2x+b

12=-2(2)+b

12=-4+b

b=16

So, the slope-intercept equation is y=-2x+16

Answer:

Area = 12 + 6.25π ft², Perimeter = 6 + 5π ft

Step-by-step explanation:

Area:

So I would break this shape into a triangle and a circle (the two semi-circles make a full circle).

Formula for Area of a Triangle: base · height ÷ 2

6 · 4 ÷ 2 = 24 ÷ 2 = 12

Formula for area of a circle: π · radius²

π · (5/2)² = 6.25π

Area of entire shape: Triangle + Circle

Area = 12 + 6.25π ft²

Perimeter:

So the perimeter is made up of the base of the triangle plus the circumference of the circle.

Base of Triangle: 6

Formula for circumference: 2rπ

5 · π = 5π

Perimeter = 12 + 5π ft

Answer:

D  In step 3

Step-by-step explanation:

Given polynomial:  x² - 2x - 15 = 0

Step 1:  factor the polynomial ⇒ (x + 3)(x - 5) = 0

Step 2:  x + 3 = 0  and  x - 5 = 0

Step 3:  x = -3  and x = 5

x - 5 = 0

Add 5 to both sides:

⇒ x - 5 + 5 = 0 + 5

⇒ x = 5

Answer:

a) Greatest Common factor = 3

b) Greatest Common factor = x

c) Greatest Common factor = xy

Step-by-step explanation:

a)

We can write the equation "3x² - 9x + 12" into three parts and we factor them:

3x² =  [tex]3\times\:x\times\:x[/tex]

9x = [tex]3\times\:3\times\:x[/tex]

12 = [tex]2\times\:2\times\:3[/tex]

Common factor = 3

b)

We can write the equation "5x² + 3x" into two parts and we factor them:

5x² = [tex]5\times\:x\times\:x[/tex]

3x = [tex]3\times\:x[/tex]

Common factor = x

c)

We can write the equation "x²y - xy²" into two parts and we factor them:

x²y = [tex]x\times\:x\times\:y[/tex]

xy² = [tex]x\times\:y\times\:y[/tex]

Common factor = xy or x ⋅ y

#1

3 is common

GCF=3

#2

Nothing common except x and 1

#3

GCF=xy

The window that has the shape of a kite has the area of the glass as 648 centimetre squared.

Area can be defined as the space occupied by a flat shape or the surface of an object. Therefore,

The window is the shape of a kite. Therefore, the square meters of the glass used for the window is the area of the window(kite).

Therefore,

area of kite = ab / 2

where

Therefore,

a = 18 + 18 = 36 cm

b = 15 + 21 = 36 cm

area of the window = 36 × 36 / 2 = 1296 / 2 = 648 cm²

learn more on area here:https://brainly.com/question/2494000

Answer:

[A] It will take 24 minutes for Joe and Charmaine to meet again at the starting line.

[B] Joe will complete 2 laps

[C]  Charmaine will complete 3 laps.

Step-by-step explanation:

Factor two numbers 12 and 8:

12 = 2×2×3

8 = 2×2×2

Find LCM of 12 and 8:

Lcm of 12 and 8 - 2×2×3×2 = 24

Therefore,

[A] How much time does it take for them to meet again at the starting line?

It will take 24 minutes for Joe and Charmaine to meet again at the starting line.

[B] How many laps does Joe complete

Joe will complete 2 laps

[C] How many laps does Charmaine complete?

Charmaine will complete 3 laps.

~lenvy~

Step-by-step explanation:

number of boys = total no. of students - no. of girls

= 900 - 300

= 600

ratio of boys and girls = no. of boys : no. of girls

= 600 : 300

= 200

= 600 : 900

= 200: 300

= 2:3

= 300 : 900

= 1:3

= 300 : 600

Two hemispheres will be equal to a spheres, hence the volume of 10 hemispheres is 266.581 cubic inches

Given Data

Let us find the volume of sphere

Volume = 4/3 *πr^3

Volume = 4/3*3.124* 4^3

Volume = 4/3*3.124*64

Volume =266.581 cubic inches

Learn more about hemispheres here:

https://brainly.com/question/25641436

Answer:

PA = 8 cm

Step-by-step explanation:

First, create a right triangle with legs OA and SA and hypotenuse OS. Use the Pythagorean Theorem to get the length of OS. Since this is a pythagorean triple (3-4-5) triangle, the hypotenuse is 5, meaning that OS is 5 cm long. Because OS and OP are both radii of the circle, they are equal. So, OP = 5 cm. Finally, simply add OA and OP to get PA:

OA + OP = PA

3 + 5 = PA

PA = 8 cm

Answer:

the 45 degree angle is in the first quadrant, the coordinates are (√2/2, √2/2) (square root of 2 on the top, 2 on the bottom)

Answer:

The answer should be 15, since each week the number goes up by 15.

I see a pattern here! Let me show you - multiply 15 by the week number (1, 2, 3, 4, ...), and you have y.

For example, 15 x 3 (for week 3) is 45, as shown by the y value.

So all we must do is multiply 15 by 5, and voila! We'll have our answer. Which, by the way, is 75.

I hope this answers your question!

-Toremi

In Cartesian coordinates, the volume is

[tex]\displaystyle \iiint_R \mathrm dV[/tex]

where R is the set

[tex]R = \left\{(x,y,z) \, : \, -4\le x\le4 \text{ and } -\sqrt{16-x^2} \le y \le \sqrt{16-x^2} \text{ and }\right. \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~\left.-\sqrt{16-x^2-y^2} \le z \le \sqrt{16-x^2-y^2} \right\}[/tex]

Converting to spherical coordinates, we take

[tex]\begin{cases}x=\rho\cos(\theta)\sin(\phi) \\ y=\rho\sin(\theta)\sin(\phi) \\ z = \rho\cos(\phi)\end{cases}[/tex]

and we can compute the Jacobian to find

[tex]dV = dx\,dy\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi[/tex]

and the set R transforms to

[tex]R' = \left\{(\rho,\theta,\phi) \,:\, 0\le \rho\le4 \text{ and }0\le\theta\le2\pi \text{ and } 0\le\phi\le\pi\right\}[/tex]

The new integral and hence the volume is then

[tex]\displaystyle \iiint_R \mathrm dV = \iiint_{R'} \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi \\\\ = \boxed{\int_0^\pi \int_0^{2\pi} \int_0^4 \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi}[/tex]

The two vertices (-5, 8) and (-5, -6) of the rectangle have the same x-coordinates

The distance between the two vertices is 14 units

The vertices are given as:

(-5, 8) and (-5, -6)

The distance between the two vertices is calculated using:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

So, we have:

d = √[(-5 + 5)^2 + (8 + 6)^2]

Evaluate the sum

d = √196

Evaluate the square root

d = 14

Hence, the distance between the two vertices is 14 units

Read more about distance at:

https://brainly.com/question/7243416

Answer: 14

Step-by-step explanation:

Answer:

A.  Complementary and Adjacent

B.  ∠KLM = 22°  and  ∠MLN = 68°

Step-by-step explanation:

Question A

As ∠KLN is a right angle, ∠KLN = 90°

⇒ ∠KLM + ∠MLN = 90°

When the sum of two angles is 90°, they are called complementary angles.

∠KLM and ∠MLN have a common side of ML and a common vertex (corner point) L.

When two angles have a common side and a common vertex but do not overlap in any way, the are called adjacent angles.

Question B

First find n:

∠KLM + ∠MLN = ∠KLN

⇒ 2n + (6n + 2) = 90

⇒ 2n + 6n + 2 = 90

Combine like terms:

⇒ 8n + 2 = 90

Subtract 2 from both sides:

⇒ 8n = 88

Divide both sides by 8:

⇒ n = 11

Now substitute the found value of n into the expressions for the two angles:

⇒ ∠KLM = 2(11) = 22°

⇒ ∠MLN = 6(11) + 2 = 68°

Answer:

8 po yan po sagot ko .. correct me if I wrong

Answer:

i dont understand i need pic

Answer:

the most closest answer is D because the formula is 3.14 x radius² x height

Step-by-step explanation:

if its right can I have brainliest

Using the Fundamental Counting Theorem, it is found that [tex]1.11 \times 10^{13}[/tex] different telephone numbers would be avaiable worldwide.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem:

Hence, the number of different telephone numbers that would be avaiable is given by:

[tex]N = n_1n_2 = 1.11 \times 10^3 \times 10^{10} = 1.11 \times 10^{13}[/tex]

[tex]1.11 \times 10^{13}[/tex] different telephone numbers would be avaiable worldwide.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

Answer:

blank = 0.23

Step-by-step explanation:

to do this you can divide both sides by 100

23/100 is 0.23

blank = 0.23

Answer:

0.23 or 23/100

Step-by-step explanation:

1) Start by setting up an equation

We'll say that x represents the blank.

100x = 23

2) Solve

100x = 23

Divide both sides by 100

x = 0.23 or 23/100

Answer:

16

Step-by-step explanation:

12 divided by 2 x 3 - (7 - 5)

6 x 3 - 2

18 - 2

16

Answer:

answer 16

Step-by-step explanation:

12 ÷ 2 x 3 - ( 7 - 5 ) is it right?
---------------------------------------------

Solving from left to right

12 ÷ 2 x 3 - ( 7 - 5 )
6 x 3 - (+2)
18 - 2

16

Answer:

Infinitely many solutions

Step-by-step explanation:

To solve for x, start by expanding the left-hand side of the equation.

2(x +5)= 2x +10

2(x) +2(5)= 2x +10

2x +10= 2x +10

Subtracting 10 from both sides:

2x= 2x

Divide both sides by 2:

x= x

Thus, x has infinitely many solutions.

Answer:

-2/5

Step-by-step explanation:

5x - 2y = -10

-2y = -5x - 10

y = 5/2x + 5

m = 5/2

Perpendicular lines have slopes that are negative reciprocals of one another. For example, 5 would become -1/5 and 1/3 would become -3.

If m = 5/2

Perpendicular line m = -2/5

Hope this helps!

Answer:

The slope of the line perpendicular to this line is -2/5.

Step-by-step explanation:

5x - 2y = -10

Let's simplify this equation to be in slope-intercept form: y = mx + b.

Start by adding 2y to both sides of the equation.

Next, add 10 to both sides of the equation.

Divide both sides of the equation by 2.

The slope of this line is the coefficient of x; in this case, it is 5/2.

If we want to find the slope of the line perpendicular to this line, we take the opposite (change the sign) reciprocal (flip the fraction).

The slope 5/2 becomes -2/5.

Therefore, the slope of a line perpendicular to the line whose equation is 5x - 2y = -10 is -2/5.

Answer:

Step-by-step explanation:

it shows that the line is the same becuase it is perfectly lined up :)

38.1 units^2

Step-by-step explanation:

you can use the formula: 1/2(ab)(sin c)

plug it in: 1/2(16*7)(sin 138)

simplify: 57sin138

plug it into your calculator: 38.1 (rounded)

If you found this answer helpful, I would appreciate if you gave me the brainliest award :D.

Answer:

37.5

Step-by-step explanation:

For acellus

Answer:

B and F.

Step-by-step explanation:

2x^2 + 7x + 3 = 0

2x^2 + 6x + x + 3 = 0

2x(x + 3) + 1(x + 3) = 0

(2x + 1)(x + 3) = 0

x = -1/2, -3.

Answer:

[tex]\sf -3x+4y=12[/tex]

Step-by-step explanation:

x-intercept is when y = 0   →   (-4, 0)

y-intercept is when x = 0   →   (0, 3)

[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{3-0}{0-(-4)}=\dfrac34[/tex]

Substitute one of the points and the found slope into the point-slope form of a linear equation:

[tex]\implies \sf y-y_1=m(x-x_1)[/tex]

[tex]\implies \sf y-0=\dfrac34(x-(-4))[/tex]

[tex]\implies \sf y=\dfrac34(x+4)[/tex]

[tex]\implies \sf 4y=3(x+4)[/tex]

[tex]\implies \sf 4y=3x+12[/tex]

[tex]\implies \sf -3x+4y=12[/tex]