What is the distance between the two points? A. 4 units B. 5 units C. 6 units D. 7 units

Answer:

2 real solutions

Step-by-step explanation:

[tex]f(x)=(x+3)^2-8\\\\0=(x+3)^2-8\\\\8=(x+3)^2\\\\\pm\sqrt{8}=x+3\\\\x=-3\pm\sqrt{8}[/tex]

Therefore, the function set at [tex]f(x)=0[/tex] has two real solutions (x-intercepts).

You can also check the discriminant of the function by expanding it:

[tex](x+3)^2-8=x^2+6x+9-8=x^2+6x+1\\\\b^2-4ac=6^2-4(1)(1)=36-4=32 > 0[/tex]

Since it's greater than 0, there's two real solutions

15.3%

1) Lotte buys 50 cans for £17.

2) Sells 32 cans for 50 penny each.

3) Sells remaining for 20 penny each.

Total cost for 32 cans:

price of each can × total cans

50 penny × 32

1600 penny

Remaining Cans : 50 - 32 = 18 cans

Total cost of this 18 cans:

20 penny × 18

360 penny

[tex]\boxed{\bf 100 \ penny \ (p) = 1 \ pound \ ( \sf \£ )}[/tex]

Total Gained : 1600 + 360 = 1960 pence ≈ £19.6

Profit : selling price - cost price : 19.6 - 17 = £2.6

Profit In percentage:

[tex]\sf \dfrac{(selling \ price - cost \ price)\ x \ 100}{cost \ price}[/tex]

[tex]\rightarrow \sf \dfrac{2.6\ x \ 100}{17}[/tex]

[tex]\rightarrow \sf 15.294 \%[/tex]

[tex]\rightarrow \sf 15.3 \% \ \ (rounded \ to \ nearest \ three \ significant \ figure)[/tex]

Lottie's percentage profit based on the provided information is 15.29%

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per cent refers to one hundred percent.

The cost will be  £17 according to the question

Total  amount generated are;

32 cans * £0.50=£16

18 cans * £0.20=£3.60

Then the total will be £16 + £3.60 = £19.60

Profit =  amount generated- cost

=£19.60 - £17

= £2.60

The percentage profit:

[tex]= \frac{2.60}{17} * 100 \\\\=[/tex]

15.29%

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Answer:

3units squared

Step-by-step explanation:

1/2 the base times the height

1/2 * 2 * 3 = 3

Using the z-distribution, it is found that the margin of error for the 95% confidence interval is of 0.117.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The sample size and the estimate are given as follows:

[tex]n = 45, \pi = \frac{9}{45} = 0.2[/tex]

Hence the margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{0.2(0.8)}{45}}[/tex]

M = 0.117.

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Answer:

8

Step-by-step explanation:

Answer:

  260 cm

Step-by-step explanation:

Each 1/00 of a meter is 1 cm, so 65/100 meters is 65 cm. If that is the length of paper required for 1 kite, then 4 times that length will be required for 4 kites.

__

The paper required for 4 kites is ...

  (65 cm) × 4 = 260 cm

Answer:

4,771

Step-by-step explanation:

In the number 4771, the hundreds digit (7) is 10 times the tens digit (7).

Answer:

C. the amount the tomato plant grows each week

Step-by-step explanation:

its height is already 23 and it grows by 2.4 each week (x)

Have a nice day! :)

Answer:

8 quarts

Step-by-step explanation:

There are 4 quarts in 1 gallon

So in 2 gallons there would be 4 × 2 = 8 quarts

Its 2 Lquid gallons = 8 Liquid quart

Answer: 79.375

Step-by-step explanation:

Answer:

79.375

Step-by-step explanation:

hope i helped

Answer:

distributive

Step-by-step explanation:

(x+y) (z) = xz+ yz    is distributive

Answer:

we know that

Victoria has $125 to spend

[purchase price skateboard]=$139.99-0.15*$139.99-----> $139.99-$21

[purchase price skateboard]=$118.99

sales tax is 7%----------> 0.07*$118.99----------> $8.33

sales tax is $8.33

Victoria has to pay [$118.99]+[$8.33]=$127.32

$127.32 > $125

therefore

Victoria has not enough money to buy the skateboard

the answer is

Victoria has not enough money to buy the skateboard

Step-by-step explanation:

Answer:

7/8

Step-by-step explanation:

Understanding the situation

Parallel lines have the same slopes.

If line t is parallel to line u then the slope of line t is the same as the slope of line u.

Finding the slope of line t

Slope formula = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

where the x and y values are derived from points on the line

here, we are given that line to goes through (2,2) and (10,9)

Given that we can assign variables

we have (x1,y1) = (2,2) so x1 = 2 and y1 = 2

we also have (x2,y2) = (10,9) so x2 = 10 and y2 = 9

Now that we have assigned variables we plug them into the formula

Recall formula : [tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

==> plug in x1 = 2 , y1 = 2, x2 = 10 and y2 = 9

[tex]slope =\frac{9-2}{10-2}[/tex]

==> simplify top and bottom

[tex]slope =\frac{7}{8}[/tex]

The slope of line t is 7/8

Finding the slope of line u

Because line t and line u are parallel line u also has a slope of 7/8

Two or more angles whose sum is 180° are called supplementary angles. The measure of the ∠y is 120°.

Two or more angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

Given the puck strikes the wall at an angle of 30°, it goes away at the same angle of 30°. Therefore, the measure of angle y can be found using the sum of the angle as a supplementary angle. Thus, we can write,

30° + ∠y + 30° = 180°

60° + ∠y = 180°

∠y = 180° - 60° = 120°

Hence, the measure of the ∠y is 120°.

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Answer:

no mode, median=8.5  mean 13

Step-by-step explanation:

5, 9, 13, 14, 17, 20

If the two prisms are stacked on top of each other then the height of the prism is 30 inches. Then the volume of the prism will be 1080 in³.

A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.

A toy store is building a display with two rectangular prisms.

The base of each prism is a square with an edge length of 6 inches.

One prism is 10 inches tall and the other is twice as tall.

The two prisms are stacked on top of each other.

Then the total volume of the display will be

The volume of the prism will be

Volume = Base area × Height

Then the height of the second prism will be

h₂ = 2 × 10 = 20 inches

Then the volume of the prism will be

Volume = 6 × 6 × 10 + 6 × 6 × 20

Volume = 360 + 720

Volume = 1080 cubic inches

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Answer: 7cm

Step-by-step explanation:

Use pythagorean theorum:

Variables:

Let the edge = A

Face diagonal (F) = 10cm

Inner diagonal (I) = sqrt(150) cm

A^2 = I^2 - F^2

A^2 = [sqrt(150)]^2 - 10^2

A^2 = 150 - 100

A^2 = 50

A = sqrt(50)

A = 7.0710678 cm

A = 7cm (to the nearest tenth)

so, length of an edge = 7cm

Answer:

i think the answer is c

Step-by-step explanation:

Answer:

the first one is 3

second. is -5/2

third is 5/-2

fourth is -1/3

fifth is 3

sixth is 0/-5

Answer:

Square Root of 10: (3, 4) and (2,1)

(-4,-2) and (-3, 1)

(-2, 3) and (1,2)

Square Root of 29:

(3,7) and (5,2)

(5, -2) and (3,3)

(4,-1) and (-1,1)

Step-by-step explanation: Just took the test

Answer:

Start at (0,1) and then go up 4 spaces over 1 to the left and repeat going up 4 over 1. To complete the graph by getting it to go behind the y intercept of (0,1) you go from the y intercept down 4 over 1 to the right and repeat going down 4 over 1.

For plotting a line, we need to plot points [tex](0,1)[/tex] and [tex](\frac{-1}{4},0)[/tex] on the cartesian plane and join them to form a line.

For plotting a line, we only need two points to graph a line. With that idea, we take advantage of the two “convenient” points which can easily be solved algebraically from the equation of the line; namely, the x-intercept (x,0) and y-intercept (0,y).

[tex]y = 4x + 1\\\\Put\ x = 0 \\y = 1\\we\ get\ (0,1)\ as\ a\ point\ lying\ on\ the\ line. \\\\Put\ y = 0 \\x = \frac{-1}{4} \\we\ get\ (\frac{-1}{4} ,0)\ as\ a\ point\ lying\ on\ the\ line. \\[/tex]

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Answer:

Question 3: 1/15   Question 4: 50

Step-by-step explanation:

Just divide the fractions by the numbers.

Answer:

Enough to cover the seat

Step-by-step explanation: If this is a question dealing with the area of said object (seat) simply make an equation to find the area of your object.  So let's say we got a seat that is 4 feet wide and 6 feet tall.

We will multiply 4 feet times 6 feet and that's where we get 24 feet.

So we know how many inches are in a feet right, there are 12 inches per foot. So 12 time 24 is our problem 12 x 24 = 288 inches. So we would need enough stain to cover 288 inches .

I hope this helps, when you ask for an awswer on brainly. I would highly recommend providing as much relevant context as you can. Have a nice day, and don't over think things ;)

Answer:

So we must determine the distance between our two given points and that can be found using the distance formula [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].

Plugging the values into the equation and solve

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]d=\sqrt{(-9-5)^2+(-2-6)^2}[/tex]

[tex]d=\sqrt{(-14)^2+(-8)^2}[/tex]

[tex]d=\sqrt{196+64}[/tex]

[tex]d=\sqrt{260}[/tex]

[tex]d=16.125\ units[/tex]

Therefore, our final answer is that the distance is 16.125 units

Hope this helps!  Let me know if you have any questions

Based on the calculations, the two (2) statements which are true are:

Mathematically, range can be calculated by using this formula;

Range = Highest number - Lowest number

Range 1 = 71 - 32

Range 1 = 39.

Range 2 = 71 - 3

Range 2 = 68.

Therefore, the range of Data Set 2 is not smaller than the range of Data Set 1.

Mathematically, the mean for these data sets would be calculated by using this formula:

Mean = [F(x)]/n

For the total number of Data Set 1, we have:

F(x) = 32 + 41 + 51 + 63 + 66 + 71

F(x) = 324.

Substituting the parameters into the formula, we have:

Mean = [F(x)]/n

Mean 1 = [324]/6

Mean 1 = 54.

For the total number of Data Set 2, we have:

F(x) = 32 + 41 + 51 + 3 + 66 + 71

F(x) = 324.

Substituting the parameters into the formula, we have:

Mean 2 = [264]/6

Mean 2 = 44.

Difference = Mean 1 - Mean 2

Difference = 54 - 44

Difference = 10.

Therefore, the mean of Data Set 2 is exactly 10 less than the mean of Data Set 1.

For the standard deviation of Data Set 1, we have:

SD₁ = √(1/n × ∑(xi - u₁)²)

SD₁ = √(1/5 × ∑(32 - 54)² + 1/5 × ∑(41 - 54)² + 1/5 × ∑(51 - 54)² + 1/5 × ∑(63 - 54)² + 1/5 × ∑(66 - 54)² + 1/5 × ∑(71 - 54)²)

SD₁ = 15.34.

For the standard deviation of Data Set 2, we have:

SD₂ = √(1/n × ∑(xi - u₂)²)

SD₂ = √(1/5 × ∑(32 - 44)² + 1/5 × ∑(41 - 44)² + 1/5 × ∑(51 - 44)² + 1/5 × ∑(3 - 44)² + 1/5 × ∑(66 - 44)² + 1/5 × ∑(71 - 44)²)

SD₂ = 24.88.

Therefore, the standard deviation of Data Set 2 is larger than the standard deviation of Data Set 1.

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Answer:

5 strawberries

Step-by-step explanation:

$21.25÷$4.25=5

Answer:

700π m ~ 2199 m

Step-by-step explanation:

diameter = d = 200 m

2 min 20s = 140 s

1 round / 40 s

140 = 40 * 3 + 20

so the athlete will cover 3 round and half

1 round = d * π

covered = c = 3 * 200 * π + 200/2 * π = 700 * π

Answer: -21 + -18t

Step-by-step explanation:

-3(7+6t)

-3 x 7= -21

-3 x 6t= 18t

Answer:

680

Step-by-step explanation:

Use the binomial coefficient where you choose [tex]k=3[/tex] numbers out of [tex]n=17[/tex] possible numbers and find the total amount of combinations since order does not matter:

[tex]\displaystyle \binom{n}{k}=\frac{n!}{k!(n-k)!}\\ \\\binom{17}{3}=\frac{17!}{3!(17-3)!}\\\\\binom{17}{3}=\frac{17!}{3!(14)!}\\\\\binom{17}{3}=\frac{17*16*15}{3*2*1}\\\\\binom{17}{3}=680[/tex]

Thus, you can make 680 three-non-repeating-number codes

Answer:

C

Step-by-step explanation:

I took the test.

The additional point could be added to the graph to show Amber that the equation does not represent a function will be (8, -4). Then the correct option is C.

A statement, principle, or policy that creates the link between two variables is known as a function.

The equation is given below.

x = (1/2)y²

For the single value of x, the value of y is not single.

Thus, it is not a function.

The additional point could be added to the graph to show Amber that the equation does not represent a function will be (8, -4).

Then the correct option is C.

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Answer:

Step-by-step explanation:

2(2 + 1)^2 = 2(3)^2 = 2(9)= 18