What are the solutions to the system of equations? {y=2x2−8x+5y=x−2 (3.5, 0.5) and (1, −1) (7, 5) and (0.5, −1.5) (3.5, 1.5) and (1, −1) (3.5, 1.5) and (−1, −3)

Answer:

-3

Step-by-step explanation:

The length of a segment is

sqrt( ( y2-y1)^2 + (x2-x1) ^2) = 2 sqrt(10)

sqrt( ( a-4 - -1)^2 + (2a -4) ^2) = 2 sqrt(10)

sqrt( ( a-4 +1)^2 + (2a -4) ^2) = 2 sqrt(10)

Combine like terms

sqrt( ( a-3)^2 + (2a -4) ^2) = 2 sqrt(10)

Square each side

( a-3)^2 + (2a -4) ^2) = 4 *(10)

FOIL the left side

a^2 -6a +9   + 4a^2 -16a +16 = 40

Combine like terms

5a^2 -22a +25 = 40

Subtract 40 from each side

5a^2 -22a -15 =0

Factor

(a - 5) (5 a + 3) = 0

Using the zero product property

a-5 =0   5a +3 = 0

a = 5       5a = -3

a=5     a = -3/5

The product of the terms is

5 * -3/5 = -3

Answer:

2

Step-by-step explanation:

g(x) = 2x-1

g(-3)+5

2(-3)-1 +5

-6-1+5

-7+5

-2

Answer:

Step-by-step explanation:

Answer:

No, they aren't perpendicular

Step-by-step explanation:

Two lines are perpendicular if the product of their slope is - 1. The slope of line AB=(-1-10)/(0-(-1))=-11 and the slope of the line AC=(2-10)/(-3-(-1))=4. Since the product of their slope isn't - 1. They aren't perpendicular.

Answer:

16/3 hours  5 1/3

Step-by-step explanation:

Answer: 5 1/3

Step-by-step explanation:

Answer:

720 different ways.

Step-by-step explanation:

Permutation has to do with arrangement. For example, in order to arrange 'n' objects in any order, this can only be done in n! ways since there is no condition or restriction on how to arrange the objects.

n! = n(n-1)(n-2)... (n-r)!

If there are 3 statistics books, 2 math books, and 1 computer science book on your bookshelf, the total number of books altogether is 3 + 2 + 1 = 6 books.

The number of ways that 6 books can be arranged in any order is 6!.

6! = 6(6-1)(6-2)(6-3)(6-4)(6-5)

6! = 6*5*4*3*2*1

6! = 120*6

6!= 720 different ways.

Hence, the books on your shelf can be arranged in 720 different ways.

Answer:

[tex]\boxed{\frac{3}{5}}[/tex]

Step-by-step explanation:

The trigonometric functions are described as follows:

[tex]sin = \frac{opposite}{hypotenuse}\\\\cos = \frac{adjacent}{hypotenuse}\\\\tan = \frac{opposite}{adjacent}[/tex]

Using reference angle ∠A, use the sin trigonometric function. This will be the side opposite (cannot be the hypotenuse) of ∠A over the side adjacent (cannot be the hypotenuse).

The side opposite of ∠A is 3. The hypotenuse of the triangle is 5.

[tex]\boxed{\frac{3}{5}}[/tex]  is the final answer!

Answer:

$7,415.99

Step-by-step explanation:

Hello, please consider the following.

[tex]P\cdot (1+\dfrac{10.5\%\cdot 9}{12})=A = 8000 \\\\P = \dfrac{8000}{(1+\dfrac{31.5}{400})}=\dfrac{8000}{1.07875}\\\\=7415.990730...[/tex]

So it gives $7,415.99

Thank you.

Answer:

JK=12

KI=16

Step-by-step explanation:

[tex]K\in\ [JI]\ \Rightarrow\ |JK|+| KI |=|KI|\\\\x^2-4x+3x-2=28\\\\\Longleftrightarrow\ x^2-x-30=0\\\\\\\Longleftrightarrow\ x^2+5x-6x-30=0\\\\\\\Longleftrightarrow\ x(x+5)-6(x+5)=0\\\\\\\Longleftrightarrow\ (x+5)(x-6)=0\\\\x=-5\ (excluded)\ or\x=6\\\\\\\Longleftrightarrow\ \\|JK|=x^2-4x=6^2-4*6=36-24=12\\|KI|=3x-2=3*6-2=18-2=16\\\\Proof: 12+16=28\\[/tex]

9514 1404 393

Answer:

  210

Step-by-step explanation:

The number of combinations of 10 things taken 6 at a time is ...

  10!/(6!(10-6)!) = 210

210 bit strings of length 10 will have 6 1-bits.

Using combination

[tex]\\ \sf\longmapsto {}^{10}C_6[/tex]

We know

[tex]\boxed{\sf {}^nC_r=\dfrac{n!}{r!(n-r)!}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{10!}{6!(10-6)!}[/tex]

[tex]\\ \sf\longmapsto \dfrac{10!}{6!(4!)}[/tex]

[tex]\\ \sf\longmapsto 210[/tex]

Answer:

3/4

Step-by-step explanation:

First find the number that are not seniors

80 -20 = 60

60 are not seniors

The ratio of not seniors to total

60/80

Divide top and bottom by 20

3/4

Answer:

60 students

Step-by-step explanation:

80 -20 = 60

Answer:

Step-by-step explanation:

P = 2(3x-20) + 2(2x+4) = (6x-40) + (4x+8) = 10x-32

The required perimeter of the playground is 10x-32.

The length of the playground measures (3x-20) metres.
The width of the playground measures (2x+4) metres.

Perimeter, is the measure of the figure on its circumference.

The Required perimeter is for the playground is given by
= 2(3x-20) + 2(2x+4)

= 10x-32

Thus the required perimeter of the playground is 10x-32.

learn more about perimeter here:

brainly.com/question/6465134

#SPJ2

Answer: It's B

Step-by-step explanation:

The table that represents the double number line is (b)

On the double number line, we have the following points

x: 0    1

y: 0    25

This means that as x increases by 1, y increases by 25.

So, we have:

x: 0  1    2    3   4

y: 0 25  50 75 100

The above is represented by the second table

Hence, the table that represents the double number line is (b)

Read more about number lines at:

https://brainly.com/question/4727909

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Answer:

1048576

Step-by-step explanation:

Given the following :

Pizza order :

Size = small, medium, large, or extra large = 4 possible sizes

Toppings = any combination of 8 possible toppings (getting no toppings is allowed, as is getting all 8).

Combination of Toppings = 2^8

Four different sizes of pizza = 4

Number of possibilities in ordering for a single pizza :

(4 * 2^8) = 4 * 256 = 1024

Number of possibilities in ordering two pizzas :

(4 * 2^8)^2

(2^2 * 2^8)^2

From indices :

[2^(2+8)]^2

[2^(10)]^2

2^(10*2)

2^20

= 1048576

Answer:

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Answer:

$325.28

Step-by-step explanation:

152+152=304

304x1.07=325.28

Answer:

325.28

Step-by-step explanation:

increase the price by 100 %

152* 100%

152

Add this to the original price

152+152 = 304

Now find the sales tax

304 * 7%

304 * .07

21.28

Add this to the amount of the purchase price

304+21.28

325.28

Answer:

when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³

Step-by-step explanation:

Let the initial length of the sides of the cube = x unit

when the length of the cube = x ;  volume of the cube = length × breadth × height = x × x × x = x³ (unit)³

when the length increased by 1 unit,

new length = (x + 1) unit

New volume = (x + 1) × (x + 1) × (x + 1)

multiplying the first two brackets

New volume = (x² + 2x + 1 ) (x + 1)

espanding the brackets

New volume = x³ + 2x² + x + x² + 2x + 1

New volume = x³ + 3x² + 3x + 1 (unit)³

Change in volume:

(New volume) - (old volume)

(x³ + 3x² + 3x + 1) - (x³)

x³ + 3x² + 3x + 1 - x³

collecting like terms:

(x³ - x³) + 3x² + 3x + 1

0 + 3x² + 3x + 1

change in volume = 3x² + 3x + 1

Therefore, when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³

Answer:

option A is correct

4x.2x²+4x.(-2)+1.2x²+1.(-2)

hope this will help :)

Answer:

A.  4x * 2x² + 4x( -2) + 1 * 2x² + 1 * (-2)

Step-by-step explanation:

(4x + 1)(2x² – 2)

apply the FOIL method

= 4x * 2x² + 4x( -2) + 1 * 2x² + 1 * (-2)

Answer:

-4

Step-by-step explanation:

(f(a+h)-f(a))/h=(2-4(a+h)-2+4a))/h=-4h/h=-4

Answer:

x = 300 feet

Step-by-step explanation:

In the given right triangle,

Length of the string of the kite = 324 feet

Angle between the string and the ground = 68°

By applying law of Sines in the given right triangle,

[tex]\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{\text{SinC}}{c}[/tex]

Now we substitute the values of angles and sides in the formula,

[tex]\frac{\text{Sin68}}{x}=\frac{\text{Sin90}}{324}[/tex]

[tex]\frac{\text{Sin68}}{x}=\frac{1}{324}[/tex]

x = 324 × Sin(68)°

x = 300.41 feet

x ≈ 300 feet

Therefore, measure of side x = 300 feet will be the answer.

Answer:

2.5 meters

Step-by-step explanation:

Answer:

[tex]volume = 0.32 m^3[/tex]

Step-by-step explanation:

The object shown above consists of 5 cubes having side lengths of ⅖m each.

Volume of a cube = [tex] a^3 [/tex]

Where, a = side length = ⅖ m

Volume of the object = [tex]5* (\frac{2}{5})^3[/tex]

[tex]volume = 5*\frac{8}{125} = 5*0.064 = 0.32 m^3[/tex]

Answer:

Sample size n [tex]\simeq[/tex] 1269.15

Step-by-step explanation:

From the information given ,

At 99% of confidence interval,

the level of significance ∝ = 1 - 0.99

the level of significance ∝ =  0.01

the critical value for 99% of confidence interval is:

[tex]\mathtt{\dfrac{\alpha }{2} = \dfrac{0.01}{2}}[/tex]

= 0.005

[tex]\mathtt {z_{\alpha/2} = z_{0.005/2} }[/tex]

The value for z from the standard normal tables

= 2.58

The Margin of error E= 3% = 0.03

The formula to  determine the sample size n used can be expressed as follows:

[tex]\mathtt { n = (\dfrac{z_{\alpha/2}}{E})^2 \ \hat p (1 - \hat p) }[/tex]

where;

[tex]\mathtt{\hat p }[/tex] = 22% = 0.22

Then:

[tex]\mathtt { n = (\dfrac{2.58}{0.03})^2 \ \times 0.22 \times (1 - 0.22) }[/tex]

[tex]\mathtt { n = (86)^2 \ \times 0.22 \times (0.78) }[/tex]

[tex]\mathtt { n = 7396 \ \times 0.22 \times (0.78) }[/tex]

n = 1269.1536

Sample size n [tex]\simeq[/tex] 1269.15

Answer:

Slope of the tangent line (m) = 1 / 2

Step-by-step explanation:

Given:

Point A = (4,2)

Origin point = (0,0)

Find:

Slope of the tangent line (m)

Computation:

Slope of the tangent line (m) = (y2-y1) / (x2-x1)

Slope of the tangent line (m) = (2-0) / (4-0)

Slope of the tangent line (m) = 2 / 4

Slope of the tangent line (m) = 1 / 2

Answer:

A 6 Packages of buns and 5 packages of wieners.

Step-by-step explanation:

Because if you multiply 6x10 you get 60 and if you multiply 5x12 you get 60 exactly 1 wieners per bun

Complete question is;

Students at the Akademia Podlaka conducted an experiment to determine whether the Belgium-minted Euro coin was equally likely to land heads up or tails up. Coins were spun on a smooth surface, and in 350 spins, 163 landed with the heads side up. Should the students interpret this result as convincing evidence that the proportion of the time the coin would land heads is not 0.5?

Test the relevant hypotheses using α = 0.01

Answer:

The Test result doesn't support the claim that proportion of the time the coin would land heads is not 0.5. Rather it supports the the probability to be 0.5. So the students shouldn't interpret this result as convincing evidence that the proportion of the time the coin would land heads is not 0.5

Step-by-step explanation:

The hypotheses would be;

Null hypothesis; H0: p = 0.5

Alternative hypothesis; Ha: p ≠ 0.5

We are given, X = 163 and n = 350

Thus; p^ = X/n = 163/350 = 0.4657

Since we are not given standard deviation, we will use test statistic formula;

Z = (p^ - p)/(√(p(1 - p)/n)

Z = (0.4657 - 0.5)/(√(0.5(1 - 0.5)/350)

Z = -1.28

From online P-value from T-score calculator as attached, we have;

p-value = 0.201395.

Since the p-value is > 0.01, it's not significant and so we will fail to reject the null hypothesis H0.

We will conclude that the Test result supports the conclusion that p = 0.5

Answer:

x = 34° and y = 62°

Step-by-step explanation:

Complementary angles sum to 90°, therefore 90 = 56 + x which means that x = 34°. The angles formed by an angle bisector are congruent and so are vertical angles; this means that ∠SOR = ∠POU = 56° and ∠POQ = ∠QOR = y. Since POS is a straight line, straight lines have a measure of 180° and because ∠POS = ∠POQ + ∠QOR + ∠SOR, we know that 180 = y + y + 56 → 180 = 2y + 56 → 180 → 2y = 124 → y = 62°.

Step-by-step explanation:

Tan² theta = sec² theta - 1

Cot² theta = cosec² theta - 1

Tan²+Cot² = sec²-1+cosec²-1

= sec²+cosec²-2

Please find attached herewith the solution of your question.

If you have any doubt, please comment.

Answer:

7200ft/per Hour divide it by mile ( 5280) makes 1.363 so maybe 1.4 Miles

Step-by-step explanation:

Work Shown:

1 mile = 5280 feet

1 hour = 3600 seconds (since 60*60 = 3600)

[tex]2 \text{ ft per sec} = \frac{2 \text{ ft}}{1 \text{ sec}}\\\\2 \text{ ft per sec} = \frac{2 \text{ ft}}{1 \text{ sec}}*\frac{1 \text{ mi}}{5280 \text{ ft}}*\frac{3600 \text{ sec}}{1 \text{ hr}}\\\\2 \text{ ft per sec} = \frac{2*1*3600}{1*5280*1} \text{ mph}\\\\2 \text{ ft per sec} = \frac{7200}{5280} \text{ mph}\\\\2 \text{ ft per sec} \approx 1.363636 \text{ mph}\\\\[/tex]

The result is approximate and the "36" portion repeats forever.