Find two numbers whose product is 110, and whose sum is 21.

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:

C. 00

Step-by-step explanation:

Using power rule....

y = x²

y' = 2x        

Solving for y' - 2x......

y' - 2x

2x - 2x

0

I hope this helps!

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~

A hypothesis testing is a statistical inference that uses data from a sample to draw conclusions.

It should be noted that hypothesis testing simply means a statistical act where an assumption is made regarding a parameter.

In this case, a hypothesis testing is a statistical inference that uses data from a sample to draw conclusions. The null hypothesis predicts no effect while the alternative hypothesis states the research predictions.

Learn more about hypothesis on:

https://brainly.com/question/11555274

Answer:

[tex]\sqrt{113}\\[/tex]

Step-by-step explanation:

[tex]distance= \sqrt{(5-[-3])^2+(2-[-5])^2}\\\\distance= \sqrt{(8)^2+(7)^2}\\\\distance= \sqrt{64+49}\\\\distance= \sqrt{113}\\[/tex]

Answer:

There is a 1/250 chance that his ticket will be chosen

There is a 249/250 chance that his ticket will not be chosen

Step-by-step explanation:

Hope that helps!

Answer:

(x - 5)(x - 7x)

Step-by-step explanation:

x - 12x + 35 = 0

x - 12x + 35 = 0

x - 5x - 7x + 35= 0

x ( x - 5) -7x(x + 5)

(x - 5)(x - 7x)

Answer:

Difference in weight is 24 once

Step-by-step explanation:

got it right

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

Answer:

Step-by-step explanation:

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

Answer:27

Step-by-step explanation:

Its pretty simple. Perimeter is the addition of all the sides. Add 4+9+8+6 to get 27.

Answer:

6 ⋅ 16

This is the sum of the areas of the 6 square faces.

The surface area of the cube in the figure given is 96 squared units

The surface area of a cube is calculated by finding the total area of all six faces. Since all sides of a cube are equal in length, you can use the formula:

Surface area of a cube = 6 × (side length)²

In other words, you square the length of one side of the cube and then multiply it by 6 to get the total surface area.

Let's say the side length of the cube is "s," then the formula becomes:

Surface area of a cube = 6 × s²

In the question given, we can calculate the surface area of this cube as;

Surface area = 6 * s²

s = 4

Surface area = 6 * 4²

Surface area = 6 * 16 = 96 unit²

Learn more on surface area of cube here;

https://brainly.com/question/410493

#SPJ2

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:

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

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:

[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]

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]

Answer:

86.28 degrees

Step-by-step explanation:

Angle between vectors is

[tex] \cos(x) = \frac{cross \: product}{magnitudes \: multiplied} [/tex]

The cross product is

[tex]4 + 0 - 3 = 1[/tex]

The magnitudes of first vector is

[tex] \sqrt{1 {}^{2} + 2 {}^{2} + 3 {}^{2} } = \sqrt{14} [/tex]

The second vector magnitude is

[tex] \sqrt{17} [/tex]

So the magnitudes multiplied is

[tex] \sqrt{14} \times \sqrt{17} = \sqrt{238} [/tex]

So our equation will be

[tex] \cos(x) = \frac{1}{ \sqrt{238} } [/tex]

[tex]x = \cos {}^{ - 1} ( \frac{1}{ \sqrt{238} } ) [/tex]

X is about 86.28 degrees

The amount at which the dress will sell for in the boutique is $6716.25.

The total cost of beading = 180 x 25% x $40 = $1800

The total cost of ruffles = 35% x 180 x $35 = 2205

Time left for making embroidery and sewing = (100% - 35% - 25%)/2 = 20%

The total cost of embroidery = 20% x 180 x $20 = $720

The total cost of sewing = 20% x 180 x $18 = $648

Total cost = 5373

Selling price = 1.25 x 5373 = $6716.25

To learn more about percentages, please check: https://brainly.com/question/25764815

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:

13

Step-by-step explanation:

the two lines with y in them are the same length

6y = y+65

5y = 65

y = 13

Answer:

D

Step-by-step explanation:

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:

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

Answer:

The answer is 310

Step-by-step explanation:

Example of distributive property of division

The 1,860 is broken down into 1800 & 60

1800 divided by 6            +               60 divided by 6

1800 divided by 6 = 300        +         60 divided by 6  = 10

300 + 10 = 310

Answer:

The answer is 29.25%.

Step-by-step explanation:

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