What are the solutions to the quadratic equation x^2 – 16 = 0?

Answer:

a) x° = 108°

b) vertically opposite angles (C) justifies my answer.

Answer:

The answer is option c.

Its an vertically opposite angle because when two lines intersect eachother then theangles formed opposite to it is called v.o.a (vertically opposite angle)

Hope it helps...

Answer:

The long of the flag is:

15 ft

Step-by-step explanation:

On a three rule:

5 ft is to 8 ft

24 ft is to  A ft

A = 24*5/8

A = 15 ft

related task:  https://brainly.com/question/17139181

Answer:

-3x

Step-by-step explanation:

-3 is the coefficient and x is the variable.  

Answer:

Step-by-step explanation:

Given the system of equation, x + 4 y = 14. and 3 x + 2 y = 12, to solve for x, we can use the elimination method of solving simultaneous equation. We need to get y first.

x + 4 y = 14............ 1 * 3

3 x + 2 y = 12 ............ 2  * 1

Lets eliminate x first. Multiply equation 1 by 3 and subtract from equation 2.

3x + 12 y = 42.

3 x + 2 y = 12

Taking the diffrence;

12-2y =42 - 12

10y = 30

y = 3

From equation 1, x = 14-4y

x = 14-4(3)

x = 14-12

x = 2

It can be seen that the easiest way to get the value of x is by using the first equation and we are able to do the substitute easily because the variable x has no coefficient in equation 1 compare to equation 2 as such it will be easier to make the substitute for x in the first equation.

Answer:

A: The easiest to solve for is x in the first equation.

Step-by-step explanation:

Answer:

7.5 jars

Step-by-step explanation:

There are 25 students in the art class.

Mr Jones is planning that for the project, each of the 25 students will need 0.3 jar of paint.

The amount of paint Mr Jones needs for this project is therefore the product of the number of students in the class by the amount of paint each student needs.

That is:

25 * 0.3 = 7.5 jars of paint

Mr Jones needs 7.5 jars of paint for the art project.

Answer:

You just need to demonstrate that the expression is not equivalent. To do that, we just need to evaluate the expression with a specific number.

[tex]\frac{3}{8}x+2 \neq \frac{3}{2}x+5[/tex]

For [tex]x=0[/tex], we have

[tex]\frac{3}{8}(0)+2 \neq \frac{3}{2}(0)+5\\2 \neq 5[/tex]

Notice that the answer is true because 2 is not equivalent to 5.

Therefore, the expression is actually non-equivalent.

Answer:

The 1st selection is appropriate.

_____

2nd: the rotation would need to be 90° CCW

3rd, 4th: rotation or double reflection will give the original orientation. This figure is reflected an odd number of times, so has its orientation reversed.

Hope it helps.. Mark brainliest

The sequence of transformations are reflection over the y-axis and then a rotation 90 clockwise about the origin.

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

Given that, figure G is rotated 90° clockwise about the origin and then reflected over the x-axis, forming figure H.

Vertices of triangle G are (-3, 1), (-1, 2) and (-2, 5).

The reflection of point (x, y) across the y-axis is (-x, y).

On reflection over x-axis, we get coordinates as (3, 1), (1, 2) and (2, 5)

90° clockwise rotation: (x, y) becomes (y, -x)

On 90° clockwise rotation, we get coordinates as (1, -3), (2, -1) and (5, -2)

Triangle H has points (2, -1), (1, -3), (5, -2).

Hence, the sequence of transformations are reflection over the y-axis and then a rotation 90° clockwise about the origin.

Learn more about the rotation of 90° counterclockwise here:

brainly.com/question/1571997.

#SPJ6

Answer:

According to steps 2 and 4. The second-order polynomial must be added by [tex]-c[/tex] and [tex]b^{2}[/tex] to create a perfect square trinomial.

Step-by-step explanation:

Let consider a second-order polynomial of the form [tex]a\cdot x^{2} + b\cdot x + c = 0[/tex], [tex]\forall \,x \in\mathbb{R}[/tex]. The procedure is presented below:

1) [tex]a\cdot x^{2} + b\cdot x + c = 0[/tex] (Given)

2) [tex]a\cdot x^{2} + b \cdot x = -c[/tex] (Compatibility with addition/Existence of additive inverse/Modulative property)

3) [tex]4\cdot a^{2}\cdot x^{2} + 4\cdot a \cdot b \cdot x = -4\cdot a \cdot c[/tex] (Compatibility with multiplication)

4) [tex]4\cdot a^{2}\cdot x^{2} + 4\cdot a \cdot b \cdot x + b^{2} = b^{2}-4\cdot a \cdot c[/tex] (Compatibility with addition/Existence of additive inverse/Modulative property)

5) [tex](2\cdot a \cdot x + b)^{2} = b^{2}-4\cdot a \cdot c[/tex] (Perfect square trinomial)

According to steps 2 and 4. The second-order polynomial must be added by [tex]-c[/tex] and [tex]b^{2}[/tex] to create a perfect square trinomial.

Answer: D

Step-by-step explanation:

EDGE 2023

Answer:

C

Step-by-step explanation:

The dependent variable is always graphed on the y-axis and the independent variable is always graphed on the x-axis. Therefore, the dependent and independent variables are total price ($) and number of boxes respectively which makes the answer C.

Answer:

C. The total price depends on the number of boxes.

Step-by-step explanation:

In a graph, the x-variable is the independent variable; it is what you can change.

The y-variable is the dependent variable; its value depends on the value of the x-variable.

In this case, the y-variable is the total price of cupcakes, which depends on the x-variable, the number of boxes. C is your answer.

Hope this helps!

Answer:

The answer is 3.

Step-by-step explanation:

This is because f(-3) = -(-3) = 3.

Answer:

B) Reflection along y-axis; Translation: (x, y) → (x, y – 3)

Step-by-step explanation:

A transformation is the movement of a point from its initial position to a new position. If an object is transformed, all its points are also transformed. Types of transformation are dilatation, rotation, reflection and translation.

The point of triangle ABC are A(-4, 4), B(-7, 1) and C(-3, -2) while for triangle A'B'Ç' is at A'(4, 1), B'(7, -2) and C'(3, -5)

If a point C(x, y) is reflected along y axis, the y coordinates is the same and the x coordinate is opposite (negated), i.e C'(-x, y). If a point C(x, y) is translated 3 units down, the new point is (x, y - 3).

ΔABC transformation to ΔA'B'C', the x coordinate is opposite and the y coordinate is 3 units downward, therefore this is a Reflection along y-axis; Translation: (x, y) → (x, y – 3)

Answer: c

Step-by-step explanation:

The answer is c bc you reflect across the y axis and then translate

Answer:

20 miles

Step-by-step explanation:

Given that :

When the car traveling north 'N' had gone 15 miles, the distance between the cars was 5 miles more than the distance traveled by the car heading east

Let the distance moved by the east bound car be e,

therefore, distance between the cars when the northbound car had traveled a distance of 15 miles = e + 5

Using Pythagoras rule:

(Hypotenus)^2 = (adjacent)^2 + (Opposite)^2

(e+5)^2 = 15^2 + e^2

(e+5)(e+5) = 225 + e^2

e^2 + 5e + 5e + 25 = 225 + e^2

e^2 + 10e + 25 = 225 + e^2

e^2 - e^2 + 10e = 225 - 25

10e = 200

e = 200 / 10

e = 20 miles

Check attached picture for solution diagram

Answer:

2400months

Step-by-step explanation:

6/100*40,000

maybe

it is isosceles triangle as you see

so that 62 = other unknown angle

as it is a triangle interior angles sum = 180

124 + x = 180

x = 180 - 124

x = 56

Answer:

a) 8.8 square centimetres

b) 31.8 square centimetres

c) (3a + 12) square centimetres

d) Area = (2b + 2c + 4) square centimetres

Step-by-step explanation:

a) We have to split the diagram into three separate rectangles as shown below.

The area of A:

Area = 5.3 * 1 = 5.3 square centimetres

The area of B:

Area = 3.3 * 1 = 3.3 square centimetres

The area of C:

Area = 2 * 1 = 2 square centimetres

The area of the shape is the sum of the areas of the three shapes:

Area = 5.3 + 3.3 + 2 = 8.8 square centimetres

b) We have to split the diagram into two separate rectangles as shown below.

Note:(The diagram has conflicting values for 2.6 and 2.1 but I went with 2.6 as it seems more feasible in the diagram)

The area of A:

Area = 3 * 2.6 = 7.8 square centimetres

The area of B:

Area = 6 * 4 = 24 square centimetres

The area of the shape is the sum of the areas of the two shapes:

Area = 7.8 + 24 = 31.8 square centimetres

c) The shape is a rectangle and so its area is:

Area = 3 * (a + 4) = (3a + 12) square centimetres

d) The shape is a trapezium and so its area is:

Area = 0.5(A + B)H

where A =  c cm

B = b + 2 cm

H = 4 cm

The area of the shape is therefore:

Area = 0.5 * (c + b + 2) * 4

Area = 2 * (b + c + 2)

Area = (2b + 2c + 4) square centimetres

Answer:

Step-by-step explanation:

Hello,

For the step 1:

We multiply the first equation by 3 and the second equation by 2, so we are using the Multiplication Property of Equality.

For the step 2:

To eliminate the x we subtract the first equation to the second one, so we are using the Subtraction Property of Equality.

For the step 3:

We divide by -16 both parts of the equation, so we are using the Division Property of Equality.

For the step 4:

We replace y in the initial first equation, we we are using the Substitution Property of Equality.

For the step 5:

We just Simplify.

For the step 6:

We add 4 to both parts of the equation, so we are using the Addition Property of Equality.

For the step 7:

We divide by 2, so we are using the Division Property of Equality.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: 3 toys

Step-by-step explanation:

equation will be 60 - 5 x t = 45

solving it we get

5 x t = 60 - 45 = 15

=> t = 15/5 = 3

Answer:

0.4.84

Step-by-step explanation:

you divide the 40 by 100

Answer:

 3.0 mi/h < σ < 8.54 mi/h

Step-by-step explanation:

Given:

Sample data:  x: 65 62 62 55 62 55 60 59 60 70 61 68

Confidence = c = 98% = 0.98

To find:

Construct a 98​% confidence interval estimate of the population standard deviation.

Solution:

Compute Mean:

number of terms in data set = n = 12

Mean = Sum of all terms / number of terms

          = 65 + 62 + 62 + 55 + 62 + 55 + 60 + 59 + 60 + 70 + 61 + 68 / 12

          = 739/12

Mean  = 61.58

Compute standard deviation:

s = √∑(each term of data set - mean)/ sample size - 1

s = √∑([tex]_{x-} {\frac{}{x} }[/tex])²/n-1

  = √( 65 - 61.58)² + (62 - 61.58)² + (62 - 61.58)² + (55 - 61.58)² + (62 - 61.58)² + (55 - 61.58)² + (60 - 61.58)² + (59 - 61.58)² + (60 - 61.58)² + (70 - 61.58)² + (61 -61.58)² + (68 - 61.58)² / 12-1

  = √(11.6964 + 0.1764 + 0.1764 + 43.2964 + 0.1764 + 43.2964 + 2.4964 + 6.6564 + 2.4964 + 70.8964 + 0.3364 + 41.2164) / 11

  = √222.9168/11

  = √20.2652

  = 4.50168

  = 4.5017

s =  4.5017

Compute critical value using chi-square table:

For row:

degree of freedom = n-1 = 12 - 1 = 11

For Column:

(1 - c) / 2 = (1 - 0.98) / 2 = 0.02/2 = 0.01

1 - (1 - c) / 2 = 1 - (1-0.98) / 2 = 1 - 0.02 / 2 = 1 - 0.01 = 0.99

[tex]X^{2} _{1-\alpha/2}[/tex] = 3.053

[tex]X^{2} _{\alpha/2}[/tex] = 24.725

Compute 98​% confidence interval of standard deviation:

[tex]\sqrt{\frac{n-1}{X^{2} _{\alpha/2}} } s[/tex]  = [tex]\sqrt{\frac{12-1}{24.725} } ( 4.5017)[/tex] = [tex]\sqrt{\frac{11}{24.725} } ( 4.5017)[/tex] =  [tex]\sqrt{0.44489}(4.5017)[/tex]

             = 0.6670 (4.5017) = 3.0026

[tex]\sqrt{\frac{n-1}{X^{2} _{\alpha/2}} } s[/tex]  =  3.0026

[tex]\sqrt{\frac{n-1}{X^{2} _{1-\alpha/2}} } s[/tex] =  [tex]\sqrt{\frac{12-1}{3.053} } ( 4.5017)[/tex] =  [tex]\sqrt{\frac{11}{3.053} } ( 4.5017)[/tex] =  [tex]\sqrt{3.6030} (4.5017)[/tex]

               =  1.8982 ( 4.5017) = 8.5449

[tex]\sqrt{\frac{n-1}{X^{2} _{1-\alpha/2}} } s[/tex]  = 8.5449

3.0026 mi/h < σ < 8.5449 mi/h

Answer:

Alternate interior angles theorem

Step-by-step explanation:

DG // EF   and GE is the transversal. So, alternate interior angles are congruent

Therefore, ∠HGD ≅ ∠HEF

DG // EF   and DF is the transversal. So, alternate interior angles are congruent

Therefore, ∠HDG ≅ ∠HFE

Answer:

what does ; resemble

Step-by-step

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

         Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

A) Let's solve for x. [tex]y^2-7=2xy[/tex]

Step 1: Flip the equation.

[tex]2xy = y^2 - 7[/tex]

Step 2: Divide both sides by 2y.

[tex]\frac{2xy}{2y} = \frac{y^2- 7}{2y}[/tex]

[tex]x = \frac{y^2- 7}{2y}[/tex]

Answer : [tex]x = \frac{y^2- 7}{2y}[/tex]

~~~~~~~~~~~~~

B) Let's solve for y. [tex]2x^2+3=xy[/tex]

Step 1: Flip the equation.

[tex]xy = 2x^2 + 3[/tex]

Step 2: Divide both sides by x.

[tex]xy = \frac{2x^2 + 3}{x}[/tex]

[tex]y = \frac{2x^2 + 3}{x}[/tex]

Answer : [tex]y = \frac{2x^2 + 3}{x}[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

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

Explanation:

Each cube has a side length of 4. Placed together like this, the total horizontal side combines to 4+8 = 8. This is the segment HP as shown in the diagram below. I've also added point Q to form triangle HPQ. This is a right triangle so we can find the hypotenuse QH

Use the pythagorean theorem to find QH

a^2 + b^2 = c^2

(HP)^2 + (PQ)^2 = (QH)^2

8^2 + 4^2 = (QH)^2

(QH)^2 = 64 + 16

(QH)^2 = 80

QH = sqrt(80)

Now we use segment QH to find the length of segment EH. Focus on triangle HQE, which is also a right triangle (right angle at point Q). Use the pythagorean theorem again

a^2 + b^2 = c^2

(QH)^2 + (QE)^2 = (EH)^2

(EH)^2 = (QH)^2 + (QE)^2

(EH)^2 = (sqrt(80))^2 + (4)^2

(EH)^2 = 80 + 16

(EH)^2 = 96

EH = sqrt(96)

EH = sqrt(16*6)

EH = sqrt(16)*sqrt(6)

EH = 4*sqrt(6), showing the answer is choice C

-------------------------

A shortcut is to use the space diagonal formula. As the name suggests, a space diagonal is one that goes through the solid space (rather than stay entirely on a single face; which you could possibly refer to as a planar diagonal or face diagonal).

The space diagonal formula is

d = sqrt(a^2+b^2+c^2)

which is effectively the 3D version of the pythagorean theorem, or a variant of such.

We have a = HP = 8, b = PQ = 4, and c = QE = 4 which leads to...

d = sqrt(a^2+b^2+c^2)

d = sqrt(8^2+4^2+4^2)

d = sqrt(96)

d = sqrt(16*6)

d = sqrt(16)*sqrt(6)

d = 4*sqrt(6), we get the same answer as before

The space diagonal formula being "pythagorean" in nature isn't a coincidence. Repeated uses of the pythagorean theorem is exactly why this is.

Answer:

2nd option

Step-by-step explanation:

plugging the values of x as 0,1,2,3,4,5 will help to find the exact equation

x= 0 , 199

x=1, 199* 1.25 =248.75 (approximately)

x=2, 199* (1.25)^2 = 310.9 (approximately)

x=3, 199* (1.25)^3 = 388.67 (approximately)

x=4, 199* (1.25)^4 = 485.83 (approximately)

x=5, 199* (1.25)^5 = 607.29 (approximately)

Answer:  f(x) ≈ 199(1.25)^x

Step-by-step explanation:

Answer:

Option C. 3√3

Step-by-step explanation:

Please see attached photo for brief explanation.

In the attached photo, we obtained the following:

Opposite = a

Adjacent = 3

Hypothenus = 6

Angle θ = 60°

We can obtain the value of 'a' as follow:

Tan θ = Opposite /Adjacent

Tan 60° = a/3

Cross multiply

a = 3 x Tan 60°

But: Tan 60° = √3

a = 3 x Tan 60°

a = 3 x √3

a = 3√3

Therefore, the length of the altitude of the equilateral triangle is 3√3.

Answer: 1/10

Step-by-step explanation:

given:

numbers contained in the i.d

1,4,3,7,6

1. permutations of 5 possible outcome

T = 5

= 5 * 4 * 3 * 2 *1

= 120 times.

2. permutations  of  3 odd numbers

( 1,3 and 7 )

T = 3

= 3 * 2 * 1 * 2 * 1

= 12

probability of of first three digits being odd numbers

P = 12 / 120

= 1 / 10

Answer: The probability is 0.10

Step-by-step explanation:

The ID number has five digits, and the digits can be 1, 4, 3, 7 and 6, and I will assume that each digit appears only once.

Then if we want to calculate the probability that the first 3 digits will be odd is:

Suppose that we have 5 slots, we want that in the first two slots to have odd numbers.

In our set, we have only 3 odd numbers {1, 3 and 7}

Then if we want an odd number in the first digit, we have 3 options

If we want an odd number in the second digit, we have two options (because we already selected one in the first selection)

If we want an odd number in the first digit, we have only one option.

For the fourth digit we have one of the two remaining even options, so we have 2 options.

For the fifth digit, we have only one digit.

The number of combinations is equal to the product of the number of options in each selection:

c = 3*2*1*2*1 = 12

Now, the total number of combinations is:

For the first digit we have 5 options

for the second digit we have 4 options.

for the third digit we have 3 options.

for the fourth digit we have 2 options.

for the fifth digit we have 1 options.

The number of combinations is:

C = 5*4*3*2*1 = 120.

Then the probability that the first 3 digits are odd numbers, is equal to the quotient between number of combination that start with 3 odd digits and the total number of combinations:

P = c/C = 12/120 = 0.10

Answer: $60

Step-by-step explanation:

Given the following :

Total cost of renting a personal water craft = $64.20

Sales tax charged = 7%

Let the pretax cost = y

Therefore,

total cost = pretax cost + tax

$64.20 = y + 7% of y

$64.20 = y + 0.07y

$64.20 = 1.07y

y = $64.20 / 1.07

y = $60

Therefore, the rental cost of a personal watercraft for half an hour before tax is $60

Answer:

subtract 3 from both sides

Step-by-step explanation:

Given

- 4.5x + 3 = 2 - 8.5x ( add 8.5x to both sides )

4x + 3 = 2 ( subtract 3 from both sides )

4x = - 1 ( divide both sides by 4 )

x = - [tex]\frac{1}{4}[/tex]

Answer:

subtract 3 from both sides

Step-by-step explanation:

D, the last one

Answer:

1.) Zero ( 0 )

2.) 55.47 feet , 8.6 feet

3.) 17.2 feet

Step-by-step explanation:

The height, in feet, of the ball is given by the equation h(x)=−.25x2+4.3x, where x is the number of feet away from the golf club (along the ground) the ball is.

1.) Since the equation has no intercept,

The ball will start zero feet above the ground.

2.) The distance of the ball at the maximum height will be achieved by using the formula

X = -b/2a

Where b = 4.3, a = -0.25

Substitutes both into the formula

X = -4.3 / 2( - 0.25 )

X = - 4.3 / - 0.5

X = 8.6 feet

Substitute X into the function to get the maximum height

h(x) = −.25(8.6)^2 + 4.3(8.6)

h(x) = 18.49 + 36.98

h(x) = 55.47 feet

3) As the ball returns to the ground, the height will be equal to zero, therefore,

0 = -0.25x^2 + 4.3x

0.25x^2 = 4.3x

X = 4.3/0.25

X = 17.2 feet

The ball returns to the ground at about 17.2 feet away

Answer:  D) 9, 15, 21, 27, ...

Step-by-step explanation:

Notice that the difference (d) for each option is 6.

Divide 2019 by 6 to see what the REMAINDER is (this is the first term).

2019 ÷ 6 = 336 r.3

None of the options start with 3 so the next option would be 3 + 6 = 9.

The only option that starts with 9 is option D.

Answer:

Option B. x = 13

Step-by-step explanation:

In this question, we shall give a separate diagram which will help us to further understand the question.

Please see attached photo for further details.

To find the value of x we shall use the pythagoras theory as illustrated below:

x is the longest side Therefore,

x² = 12² + 5²

x² = 144 + 25

x² = 169

Take the square root of both side

x = √169

x = 13

Therefore, the value of x 13.