Find the vertex form of y=-x^2-10x-21

Answer:

Step-by-step explanation:

1 option 2c

1. The equation of a circle with center (h,k) and radius r units is given by

[tex](x-h)^2+(y-k)^2=r^2[/tex]

The given circle has center (5,-2) and a radius r=3 units.

We substitute these values into the formula to get:

[tex](x-5)^2+(y--2)^2=3^2[/tex]

This simplifies to:

[tex](x-5)^2+(y+2)^2=9[/tex]

The correct answer is A.

2.  The given circle has center (3,-5) and radius r=8 units.

We substitute the given values into the formula to obtain:

[tex](x-3)^2+(y--5)^2=8^2[/tex]

We simplify to get:

[tex](x-3)^2+(y+5)^2=64[/tex]

The correct answer is C

3. The given circle has equation:

[tex](x+8)^2+(y+9)^2=169[/tex]

We can rewrite this equation as:

[tex](x--8)^2+(y--9)^2=13^2[/tex]

Comparing this to

[tex](x-h)^2+(y-k)^2=r^2[/tex]

The center is (-8,-9) and the radius is 13.

The correct answer is A.

4. The given circle has equation:

[tex](x-7)^2+y^2=225[/tex]

We can rewrite this equation as:

[tex](x-7)^2+(y-0)^2=15^2[/tex]

Comparing this to

[tex](x-h)^2+(y-k)^2=r^2[/tex]

The center is (7,0) and the radius is 15.

The correct answer is B.

5. The given circle has center (-2,6) and passes through (-2,10).

We can use the number line to find the radius.

[tex]r=|10-6|=4[/tex]

[tex](x-h)^2+(y-k)^2=r^2[/tex]

We substitute the center and the radius into the formula to get:

[tex](x--2)^2+(y-6)^2=4^2[/tex]

This simplifies to:

[tex](x+2)^2+(y-6)^2=16[/tex]

The correct answer is A

6. The given circle has center (1,2) and passes through (0,6).

We can use the distance formula to find the radius.

[tex]r=\sqrt{(1-0)^2+(2-6)^2}=\sqrt{17}[/tex]

[tex](x-h)^2+(y-k)^2=r^2[/tex]

We substitute the center and the radius into the formula to get:

[tex](x-1)^2+(y-2)^2=\sqrt{17}^2[/tex]

This simplifies to:

[tex](x-1)^2+(y-2)^2=17[/tex]

The correct answer is C

Answer:Two <‘s supplementary to equal <‘are=

I got this correct on Odyssey:)

Answer:

Option B.

Step-by-step explanation:

∠1 and ∠3 are supplementary and ∠2 and ∠4 are supplementary.

Because they are exterior sides in opposite rays.

In other words ∠1 + ∠3 = 180° and ∠2 + ∠4 = 180°

and it is given that ∠1 ≅ ∠2

So ∠3 ≅ ∠4

Since Two angles supplementary to equal angles are equal will be the reason.

Option B is the correct option.

The greatest common factor between 14 and 24 is 2 because

The factors of 14 that divides 14 without a remainder are 1,2, and 7

The factors of 24 that divides 14 without a remainder are 1,2,3,4,6,8,and 12

Therefore 2 is the greatest factor between 14 and 24.

For this case we have that by definition, the Greatest Common Factor or GFC of two numbers is given by the biggest factor that divides both without leaving residue. We should look for the GFC of 14 and 24.

14: 1,2,7,14

24: 1,2,3,4,6,8,12,24

Thus, it is observed that the GFC of both numbers is 2.

Answer:

2

[tex]

f(x)=3x^2-24x+36 \\

0=3(x-2)(x-6) \\

0=(x-2)(x-6)

[/tex]

There will be 2 solutions.

[tex]

x-2=0\Longrightarrow\boxed{x_1=2} \\

x-6=0\Longrightarrow\boxed{x_2=6}

[/tex]

Hope this helps.

r3t40

The zeros of the function f(x) = 3x^2 - 24x + 36 are found using the quadratic formula to be x = 6 and x = 2.

The zeros of the function f(x) = 3x2 \- 24x + 36 are the values of x for which f(x) equals zero. To find the zeros, we set the quadratic equation equal to zero and solve for x. This can be done using the quadratic formula x = (-b \\pm (sqrt{b2 \(- 4ac})/(2a), where a = 3, b = -24, and c = 36. Applying the quadratic formula:

Therefore, the zeros of the function are x = 6 and x = 2.

The length of the edge of the bases is x = 4 and x=1.79.

The volume of a rectangular box can be calculated if you know its three dimensions: width, length, and height.

The volume of a box with a square base and a height of 2 cm is 32cm for box A and the volume of a box with a square base and a height of 10cm is 32cm.

What is the length of the edge of the bases?

The volume of the box = length × width × height

Therefore, we are going to make use of Equation (1) to determine the solution to this question, so that we have;

For Box A; We are given our volume to be equal to 32cm^3, height = 2cm, length and width = x cm.

For Box B IS;

[tex]\rm 32 = 2x^2\\\\x^2 = 16\\\\x^2=4^2\\\\x=4[/tex]

Here  Length = width.

For box B;

[tex]\rm 32 = 10x^2\\\\x^2=\dfrac{32}{10}\\\\x^2=3.2\\\\x=1.79[/tex]

Hence, the length of the edge of the bases is x = 4 and x=1.79.

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[tex]

s=\frac{\Delta{y}}{\Delta{x}}=\frac{9-7}{4+2}=\boxed{\frac{2}{6}=\frac{1}{3}}

[/tex]

Hope this helps.

r3t40

Answer:

The value of y when x = 5 and z = 16 is 272

Step-by-step explanation:

* Lets Talk about the direct variation

- y is varies jointly (directly) as x and z, that means there are direct

  relation between y , x and z

- y increases if x increases or z increases

∴ y ∝ x × z

- To change this relation to equation we use a constant k

∴ y = k (x) (z), where k is the constant of variation

- To find the value of k we substitute the values of x , y and z in

  the equation above

∵ y = 136 when x = 5 and z = 8

∴ 136 = k × 5 × 8

∴ 136 = 40 k ⇒ divide both sides by 40

∴ k = 3.4

- Substitute this value in the equation

∴ y = 3.4 (x) (z)

∵ x = 5 , z = 16

∴ y = 3.4 (5) (16) = 272

∴ The value of y when x = 5 and z = 16 is 272

Answer:

The correct answer is B.

Step-by-step explanation:

If y varies jointly as x and z, then we can write the join variation equation.

[tex]y=kxz[/tex], where 'k' is the constant of proportionality.

If y = 136 when x = 5 and z = 8,then

[tex]136=k(5)(8)[/tex],

[tex]\implies 136=40k[/tex]

[tex]\implies \frac{136}{40}=k[/tex]

[tex]\implies \frac{17}{5}=k[/tex].

The variation equation now becomes:

[tex]y=\frac{17}{5}xz[/tex]

when x = 5 and z = 16, then

[tex]y=\frac{17}{5}(5)(16)[/tex]

[tex]y=17(16)[/tex]

[tex]y=272[/tex]

The correct answer is B.

Answer:

485 ft

Step-by-step explanation:

step 1

Find the distance from the base of the building to the base of the radio tower

Let

x -----> the distance from the base of the building to the base of the radio

we know that

tan(36°)=254/x

x=254/tan(36°)=349.60 ft

step 2

Find the distance from the base of the tree to the base of the radio tower

Let

x -----> the distance from the base of the tree to the base of the radio tower  

we know that

tan(62°)=254/x

x=254/tan(62°)=135.05 ft

step 3

Find the distance from the base of the building to the base of the tree

Adds the distances

349.60 ft+135.05 ft=484.65 ft

Round to the nearest foot

484.65 ft=485 ft

The final distance is approximately 485 feet.

Calculating the Distance from the Building to the Tree

To determine the distance from the base of the building to the base of the tree given the angles of elevation to the top of the radio tower, we can use trigonometry.

Let the height of the radio tower be 254 feet. Assume the distance from the base of the building to the base of the tower is x feet, and the distance from the base of the tree to the base of the tower is y feet.

Step-by-Step Solution:

Using the angle of elevation from the building, 36°, we can write:

tan(36°) = 254 ÷ x

Solving for x: x = 254 / tan(36°)

Using the angle of elevation from the tree, 62°, we can write:

tan(62°) = 254 ÷ y

Solving for y: y = 254 / tan(62°)

Calculate the values:

tan(36°) ≈ 0.7265

x = 254 / 0.7265 ≈ 349.6 feet.

tan(62°) ≈ 1.8807

y = 254 ÷ 1.8807 ≈ 135.1 feet.

The total distance from the base of the building to the base of the tree is x + y:

Total distance = 349.6 + 135.1 ≈ 485 feet.

Thus, the distance from the base of the building to the base of the tree is approximately 485 feet.

A function of the form f(x)=ab^x is called an exponential exponential growth function, when b is greater than 1

What is an exponential function?

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ in mathematics, where x is the independent variable.

It is given the exponential function :

f(x) = abˣ  and b>1

Therefore, If the base (b) is greater than one is called an exponential growth, if it smaller than one it called an exponential decay.

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Need the table, please include an attachment!

Answer:

(C) Y=26.9x-1.3 is the answer

Step-by-step explanation:

Answer:

Option 3: 300 phones

Step-by-step explanation:

Given

Phone produces each day: 1000

Number of phones that were checked = 30

Defective phones = 9

So the probability of defective phones will be calculated by dividing the number of defective phones by total number of phones checked.

So, the probability of defective phones

= 9/30

= 0.3 or 30%

So, from 1000 phones the defective phones will be:

1000*0.3

= 300 Phones ..

Answer:

18 Inches total of rope

Step-by-step explanation:

9+9=18

or

9 x 2 = 18

You can do this two ways:

1. You can multiply 9 (how long the rope is) by 2 (how many ropes you have. so...

length of rope * number of ropes

9 * 2 = 18

2. Or you  can add 9 plus nine together and it will give you the same answer. so...

9 + 9 = 18

Hope this helped!

Answer: B

Step-by-step explanation: edge2022

Answer:

The CORRECT answer is False

Step-by-step explanation:

I just took the test and got it correct!!

cos x + i sin x in the range 0 to 2pi will be unique so false.

Complex numbers exist the numbers that exist expressed in the form of a+ib where, a, and b are real numbers, and 'i' exists an imaginary number named “iota”. The value of i = (√-1).

The abbreviated polar form of a complex number exists z = rcis θ, where r = √(x2 + y2) and θ = tan-1 (y/x).

The range is the difference between the highest and lowest values in a set of numbers. To find it, subtract the lowest number in the distribution from the highest.

The range in statistics for a given data set is the difference between the highest and lowest values. For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8. Thus, the range could also be defined as the difference between the highest observation and lowest observation.

Hence, cos x + i sin x in the range 0 to 2pi will be unique so false.

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Answer:

21. D

22. A

Step-by-step explanation:

Answer:

None of the statements are true​

Step-by-step explanation:

Given statements are:

I. The difference between -14 and -8.3 is positive.

II. -14 + 8.3 has the same value as the difference between -1.4 and -8.3.

III. The between -8.3 and -14 has the same value as the difference between -1.4 and -8.3.

Test for statement (I).

difference = -14-(-8.3) = -14+8.3 = -5.7

which is negative so statement I is FALSE.

Test for statement (II).

-14+8.3 = 5.7

difference = -14-(-8.3) = -14+8.3 = -5.7

which are different so statement II is FALSE.

Test for statement (III).

difference = -8.3-(-14) = -8.3+14 = 5.7

which is different than difference value -5.7 for statement I.

so statement III is FALSE.

So the correct choice is "None of the statements are true​".

Answer:

70 times

Step-by-step explanation:

12 * 5 = 60

28 * 5 = 140

140/2 = 70

According to the question,

Friend clap,

then,

→ [tex]12\times 5 =60 \ times[/tex]

→ [tex]28\times 5 = 140 \ times[/tex]

In 0.5 minutes, he clap.

= [tex]\frac{140}{2}[/tex]

= [tex]70 \ times[/tex]

Thus the response above is appropriate.

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R; all quadratic functions are going to have ranges and domains of *ALL REAL NUMBERS*.

Step-by-step explanation:

The highest point of a parabola is at the vertex.

x = -b / (2a)

x = -1 / (2×-0.0023)

x ≈ 217.4

y = (217.4) − 0.0023 (217.4)²

y ≈ 108.7

The horizontal distance can be found when the potato lands (y=0):

0 = x − 0.0023x²

0 = x (1 − 0.0023x)

x = 0, x ≈ 434.8

So the potato reaches a maximum height of 108.7 m and travels a horizontal distance of 434.8 m.

The height point of the trajectory is 217.39 meters and the horizontal distance the potato travels before hitting the ground is 434.78 meters.

To find the height point of the trajectory and the horizontal distance the potato travels before hitting the ground, we can use the equation y=x-0.0023x^2 to represent the trajectory. Since the trajectory is a parabola, the height point corresponds to the vertex of the parabola. To find the vertex, we can use the formula x = -b / (2a), where a = -0.0023 and b = 1. To find the horizontal distance the potato travels before hitting the ground, we need to find the x-intercepts of the parabola, which correspond to the points where y = 0.

First, let's find the height point:

Using the formula x = -b / (2a) and substituting the values, we get:

x = -1 / (2 * (-0.0023)) = 217.39 meters

Now, let's find the horizontal distance:

Setting y = 0 and solving for x, we get:

0 = x - 0.0023x^2

0 = x(1 - 0.0023x)

x = 0 or x = 434.78 meters

Therefore, the height point of the trajectory is 217.39 meters and the horizontal distance the potato travels before hitting the ground is 434.78 meters.

Answer:

Question 1: x = 3

Question 2: x = -4

Question 3: x = -2

13: x=3

14: x=-4

15: x=-2

All I did was use an calculator to find out the missing variables or u could have just put all the answer chooses in it and see which one is right.

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=2,143.57 \end{cases}\implies 2143.57=\cfrac{4\pi r^3}{3}\implies 6430.71=4\pi r^3 \\\\\\ \cfrac{6430.71}{4\pi }=r^3\implies \sqrt[3]{\cfrac{6430.71}{4\pi }}=r\implies \stackrel{\pi =3.14}{7.9999956 \approx r}\implies \stackrel{\textit{rounded up}}{8=r}[/tex]

Answer:

[tex]9x^{2}+3x-20=(3x+5)(3x-4)[/tex]

Step-by-step explanation:

We need to drag the tiles and place them in boxes to form the correct pairs.

The given options are:-

1) [tex]9x^{2}+3x-20[/tex]

2) [tex](4x-3y)^{2}[/tex]

3) [tex](3x+5)(3x-4)[/tex]

4)[tex](3x+2)(9x^{2} -6x+4)[/tex]

First we simplify the all given factor and then compare with provided options

2) [tex](4x-3y)^{2}[/tex]

=[tex]16x^{2}+9y^{2}-24xy[/tex]

3) [tex](3x+5)(3x-4)[/tex]

[tex]9x^{2}-12x+15x-20[/tex]

[tex]9x^{2}+3x-20[/tex]

Here we can see equation (3) match with (1)

so, [tex]9x^{2}+3x-20=(3x+5)(3x-4)[/tex]

Hence, the correct match is shown in figure-1

The expressions that are equivalent should be matched as follows;

9x² + 3x - 20 ↔ (3x + 5)(3x - 4)

In order to match the equivalent expressions, we would have to either expand or factor each of the given expressions as follows;

9x² + 3x - 20

By applying the sum-product pattern, we have:

9x² + 15x - 12x - 20

By writing the common factor from the two pairs, we have:

(9x² + 15x) + (-12x - 20)

3x(3x + 5) - 4(3x + 5)

(3x + 5)(3x - 4)

Next, we would expand the expression (4x - 3y)²;

(4x - 3y)(4x - 3y)

16x² - 12xy - 12xy + 9y²

16x² - 24xy + 9y²

9y² - 24xy + 16x²

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Answer:

Figure A sides are 1/4 the size of Figure B

The top of Figure A = 4, the top of Figure B = 1.

Divide 1 by 4 to get the scale factor, which is 1/4 as a fraction or 0.25 as a decimal.

Step-by-step explanation:

Answer:

The first blank is "y", the second blank is "x", and the third blank is 1:3.

The value of 's' is calculated using the formula s = re, where e is the angle in radians and r is the radius in meters, which can also be determined statistically.

The value of s in the given physics problem represents the distance between two objects separated by an angle, when they are a certain distance r apart. According to the information and by using the formula s = re, where e is the angle in radians and r is the radius in meters (converted from millimeters), we can substitute the known values to find s. Since S = 80×109 N/m² is the shear modulus and given the small value of Kåp, we assume that s will be significantly small compared to 0.040. Additionally, the value of s can also be found using statistical methods, as indicated by a computer or calculator output showing s = 16.4 as the standard deviation in a set of residuals.

ANSWER

c. never

EXPLANATION

When we have

[tex]\frac{a}{b}[/tex] in mathematics, we call b the divisor.

In mathematics, division by zero is not defined.

We cannot divide a function, or a number by zero and get a value.

That is why, there is the restriction, b≠0

Therefore, zero is never a divisor.

The correct answer is C

Answer: 15

Step-by-step explanation

Answer:

Step-by-step explanation:

[tex]\underline{+\left\{\begin{array}{ccc}2x+3y=9\\-2x+2y=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad5y=15\qquad\text{divide both sides by 5}\\.\qquad\qquad\boxed{y=3}[/tex]

MN is 63 mm.

Since triangles MPQ and NQP are similar, we have the following

proportion:

[tex]\frac{MQ}{NP} = \frac{QP}{MN}[/tex]

Substituting the given values, we have:

[tex]\frac{30}{10} = \frac{21}{MN}[/tex]

Solving for MN, we get:

[tex]MN = \frac{21 \times 30}{10} = 63 mm[/tex]

Therefore, MN is 63 mm.

Answer:

Choice A. P = I² · R where

Step-by-step explanation:

Electrical power is the rate at which the electrical force does work. So what is electrical work? That's the work [tex]W[/tex] that the electrical force do when it moves charges [tex]Q[/tex] across a potential difference [tex]V[/tex]:

W = [tex]V\cdot Q[/tex].

The power is the rate at which the electrical force do the work:

[tex]\displaystyle P = \frac{W}{t} = V \cdot \frac{Q}{t}[/tex].

On the other hand, current [tex]I[/tex] is the charge through a cross-section of the circuit in unit time. By the definition of current:

[tex]\displaystyle\frac{Q}{t} = I[/tex].

[tex]\displaystyle P =V \cdot \frac{Q}{t} = V\cdot I[/tex].

Consider Ohm's Law:

[tex]V = I \cdot R[/tex].

Therefore

[tex]\displaystyle P = V\cdot I = (I \cdot R) \cdot I = I^{2}\cdot R[/tex].

Choice-A is one of several useful, correct formulas for electrical power.  It's true in AC circuits as well as DC ones.

Answer:

48 cm²

Step-by-step explanation:

Let's call the width and height of the rectangle w and h.

w / h = 3 / 4

2w + 2h = 28

Solve the system of equations with substitution.

w = 3/4 h

2 (3/4 h) + 2h = 28

3/2 h + 2h = 28

7/2 h = 28

h = 8 cm

So the width is:

w = 3/4 (8)

w = 6 cm

So the area is:

A = wh

A = 48 cm²