The graph of the quadratic function
g(x) = x² + 4 is shown.
17
8
gix
2
Domain:
Range:
7
T
O
For

Answer:

C

Step-by-step explanation:

P = S1t - S2t ← factor out t from each term on the right side

P = t(S1 - S2) ← isolate t by dividing both sides by S1-S2

[tex]\frac{P}{S1-S2}[/tex] = t

Answer:

Step-by-step explanation:

Answer:

16/50 or 32% chance of getting a multiple of 3

Step-by-step explanation:

Starting at 0 and going to 50, there are 16 numbers in the range that are multiples of 3.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, and 48

Attached is a chart for reference!

So, 16 of the 50 numbers are multiples of 3, making your odds 16/50 (divide that to get .32 which = 32%!)

step by step explanation:

(multiples of 3)= 3 , 6 ,9, 12 ,15, 18 ,21 ,24, 27, 30, 33, 36 ,39 ,42, 45 and 48

probability (multiples of 3)= nó of required outcome/ nó of possible outcome

16 /50 = 8/25 ( you get this after dividing 16/50)

in percentage 8/ 25 would give you 32%

Answer:

Birds = 8

Mice = 6

Step-by-step explanation:

Conditions

Let the birds = x

Let the mice = y

Equations

x + y = 14

2x + 4y = 40

Solution

Using the top equation solve for x

x = 14 - y

Use this result to substitue for x

2(14 - y) + 4y = 40                      

Remove the brackets

28 - 2y + 4y = 40

Combine

28 + 2y = 40

Subtract 28 from both sides

28 - 28 + 2y = 40 - 28

2y = 12

Divide by 2 on both sides

2y/2 = 12/2

y = 6

Solve for x

x + y = 14

x + 6 = 14

Subtract 6 from both sides

x + 6 - 6 = 14 - 6

x = 8

Answer:

7 mice and 7 birds

Step-by-step explanation:

14 heads would mean there are 14 animals in total, as each animal has one head.

Birds have two legs, and mice have four.

2+4=6

40/6=6.67 (recurring)

6.67*2=13.3 (recurring)

6.67*4=26.67 (recurring)

Animal legs can't be in decimal numbers, so we can round the numbers.

13.3 becomes 13, 26.67 becomes 27.

13+27=40

Now we can see that there are 13 bird legs and 27 mice legs.

Divide the bird legs by 2 to get 6.5

Divide the mice legs by 4 to get 6.75

Again, we can't have a decimal of an animal, so we can round.

6.5 becomes 7, and 6.75 also becomes 7.

Therefore, there is 7 of each type of animal.

The value of ? and X are 24 and 32 respectively

A triangles is 2D shape with three sides and angles.

From the given diagram, the ratio of similar sides is equal to a constant as shown;

15/20 = 9+15/20+x

Cross multiply

15/9+15 = 20/20+x

15/24 = 20/20+x

Comparing with the given ratio

? = 24

X = 20+x

Find x

15(20+x) = 480

300 + 15x = 480

15x = 180

x =12

X = 20 +x

X= 32

Hence the value of ? and X are 24 and 32 respectively

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Answer:

Step-by-step explanation:

[tex]=(1 +tan\theta)^2 + (1 - tan\theta)^2\\=(1+2tan\theta+tan^2\theta)+(1-2tan\theta+tan^2\theta)\\=2(1+tan^2\theta)\\=2sec^2\theta.\\[/tex]

The irrational number that can be multiplied to produce 1 is - √41/41

Let the following expression

-√41 x = 1

We are to find the value of x that will make the expression true

√41 x = -1

Divide both sides by √41

√41 x/ √41 = -1/ √41

x = - √41/41

Hence the irrational number that can be multiplied to produce 1 is - √41/41

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Answer:

[tex]x = \frac{-7 +\sqrt{489} }{2}[/tex]

[tex]x = \frac{-7 - \sqrt{489} }{2}[/tex]

Step-by-step explanation:

2x² +21x-61 = (x+7)²

expand

2x² + 21x - 61 = x² + 14x +49

move everything to one side

x² + 7x - 12 = 0

use quadratic formula

[tex]x = \frac{-b +- \sqrt{b^{2}-4ac } }{2a}[/tex]

plug in the values

[tex]x = \frac{-7 +- \sqrt{7^{2}-4(1)(-110) } }{2(1)}[/tex]

solve

[tex]x = \frac{-7 +- \sqrt{49-4(1)(-110) } }{2}[/tex]

[tex]x = \frac{-7 +- \sqrt{49 + 440 } }{2}[/tex]

[tex]x = \frac{-7 +- \sqrt{489} }{2}[/tex]

Answer:

10u²

Step-by-step explanation:

The formula for area of a triangle is b*h/2. When you plug in the numbers, you get 10. Hope this helps!

Answer:

The answer is B

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

y > 5x-4

This inequality is greater than, so it would be a dotted line

You would have a solid line when it is greater than or equal to ≥  or less than or equal to ≤

Hello!  

To find the mass of the liquid by itself, subtract the mass of the container from the mass of the liquid and container.

⇒ 1,300 - 250

⇒ 1,050 grams

∴ The mass of the liquid by itself is 1,050 grams.

Answer:

18

Step-by-step explanation:

Polygon A : Polygon B = x : 3x

4A = 24

A = 6

B = 18

B is the larger polygon so the perimeter is 18.

Answer:

1st = [tex]A. \sf \ y = 1[/tex]

2nd = [tex]D. \ \sf y - 5 = 3(x + 2)[/tex]

PART A

Given: y = -2

This equation has a slope of 0

Equation that pass (-1, 1)

y - 1 = 0(x -(-1))

y = 1

PART B

[tex]\sf Given : y = -\dfrac{1}{3} x + 2[/tex]

Here slope is -1/3 and y-intercept is 2

Perpendicular lines has negatively inverse slope.

→ per. slope = -(slope)⁻¹ = -(-1/3)⁻¹ = 3

Equation in point slope form:

[tex]\sf y - y_1 = m(x - x_1)[/tex]

[tex]\sf y - 5 = 3(x - (-2))[/tex]

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

Answer:

[tex]y = 1[/tex]

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

Step-by-step explanation:

The line [tex]y = -2[/tex] is a horizontal line.

Therefore, a line that is parallel to the given line and passes through point (-1, 1) is another horizontal line with the y-value of the point.

Therefore, the line is [tex]y = 1[/tex]

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

Slope-intercept form of a linear equation:

 [tex]y=mx+b[/tex]

where:

Given linear equation:

[tex]y=-\dfrac{1}{3}x+2[/tex]

Therefore, the slope of this equation is -1/3.

If two lines are perpendicular to each other, the product of their slopes will be -1.   Therefore, the slope (m) of the line perpendicular to the given line is:

[tex]\implies m \cdot -\dfrac{1}{3}=-1[/tex]

[tex]\implies m=3[/tex]

Use the point-slope form of a linear equation, with the found slope and the point (-2, 5) to create the equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-5=3(x-(-2))[/tex]

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

The family consumes 3 whole pizzas in total. They should order 3 whole pizzas to have enough for everyone.

To find out how many whole pizzas the Hayden family should order, we can calculate the total number of pizzas they need.

Since each person always eats 3/4 of a pizza, the total amount they eat can be calculated as follows:

3/4 + 3/4 + 3/4 + 3/4 = 4 × (3/4) = 3

So, the family consumes 3 whole pizzas in total. Therefore, they should order 3 whole pizzas to have enough for everyone.

As for the picture, imagine a circle representing a whole pizza. Divide it into four equal parts to represent each person's portion (3/4). Repeat this division three times to represent the three pizzas needed.

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The graph of a function f(x) = ∛x is shown in the picture, and the domain of the function will be all real numbers.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a function:

f(x) = ∛x

The domain of the function will be all real numbers.

x ∈(-∞, ∞)

The graph will be curved.

Plug x = 0, y = 0

x = 1, y = 1

The graph is shown in the attached picture.

Thus, the graph of a function f(x) = ∛x is shown in the picture, and the domain of the function will be all real numbers.

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[tex]f(x) =4 x {}^{3} - 4x {}^{2} - 16x + 16[/tex]

[tex]divide \: by \: x - 2[/tex]

[tex]4x {}^{2} \: into \: (x - 2) = 4x {}^{3} - 8x {}^{2} [/tex]

[tex]g(x) = 4x {}^{2} - 16x + 16[/tex]

[tex]4x \: into \: (x - 2) = 4x {}^{2} - 8x[/tex]

[tex]z(x) = - 8x + 16[/tex]

[tex] - 8 \: into \: (x - 2) = - 8x + 16 \\ no \: remainder[/tex]

[tex]f(x) = (x - 2)(4x {}^{2} + 4x - 8)[/tex]

[tex]f(x) = 0 \\ x - 2 = 0 \: \: \: \: \: \: \: \: \: 4x {}^{2} + 4x - 8 = 0 \\ [/tex]

[tex]x = \frac{ - 4 + \sqrt{4 {}^{2} - 4(4)( - 8) } }{2(4)} = \frac{ - 4 + \sqrt{144} }{8} = \frac{ - 4 + 12}{8} = 1[/tex]

[tex]x = 2[/tex]

[tex]x = \frac{ - 4 - 12}{8} = \frac{ - 16}{8} = - 2[/tex]

Answer: B

Step-by-step explanation:

Edge 2023

(3(1) + 9)² - 64

(3 + 9)² - 64

(12)² - 64

= 144 - 64

= 80

Going by the rules of the game to pick a random card and then multiply it by a roll of a number cube, we can find that:

If the die is rolled, it will land on a number between 1 and 6 while there are only four cards that can be picked.

The sample space is:

                  Dice             Card            Product        

                      1                 5                         5

                      1                 6                         6

                      1                 7                         7

                      1                 8                         8

                      2                 5                         10

                      2                 6                         12

                      2                 7                         14

                      2                 8                         16  

                      3                 5                         15

                      3                 6                         18

                      3                 7                         21

                      3                 8                         24

                      4                 5                         20

                      4                 6                         24

                      4                 7                         28

                      4                 8                         32

                      5                 5                         25

                      5                 6                         30

                      5                  7                         35

                      5                  8                         40

                      6                 5                         30                        

                      6                 6                         36

                      6                 7                         42

                      6                 8                         48

Based on the products, we can come up with the following frequency table:

                                 Frequency table

                          Product                     Frequency

                              5                                      1

                              6                                      1

                              7                                      1

                              8                                      1

                              10                                      1

                              12                                      1

                              14                                      1

                              16                                      1

                              15                                      1

                              18                                      1

                              21                                      1

                              24                                      2

                              20                                      1

                              28                                      1

                              30                                      2

                              32                                      1

                              25                                      1

                              35                                      1

                              40                                      1

                              36                                      1

                              42                                      1

                              48                                      1

                              Total                                24

The frequency table shows that to get 28 or more, a person will have a relative frequency of:

= 1 + 2 + 1 + 1 + 1 + 1 + 1 + 1

= 9

Probability is:

= 9 / 24

= 3/8

= 37.5%

The number of products required to win 25% of the time is:

= 25% x 24

= 6

To find the winning number, count down from the highest product 6 times to get 32.

The probability of getting 36 or higher is:

= ∑(Probabability of picking 36 and above numbers)

= 1 / 24 + 1/24 + 1/24 + 1/24

= 1 / 6

The probability of repeating this 4 consecutive times is:

= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6

= 1 / 1,296

= 0.0007716

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The speed of skaters was 10 km per hr.

Mathematically, the speed of an object is directly proportional to the distance traveled and inversely proportional to the time taken. In simple words, the more the speed, the distance traveled is more in a short period and vice-versa.

Let the speed of the skater be x

We know, speed = [tex]\frac{Distance}{Time}[/tex]

According to the question:

[tex]\frac{20}{x} = \frac{40}{x + 10}[/tex]

Cross multiplying both sides,

20(x+10) = 40x

20x + 200 = 40x

20x = 200

x = 10

Thus, the speed of skaters was 10 km per hr.

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Answer: 5.22

Step-by-step explanation:

The apothem = 87 cm = 0.87 m.

Using the formula [tex]A=\frac{1}{2}ap[/tex] to find the area of the base, where a is the apothem and p is the perimeter, we get [tex]A=\frac{1}{2}(0.87)(6)=2.61[/tex]

So, using the formula [tex]V=Bh[/tex], we get the volume to be [tex]2.61(2)=5.22 \text{ m}^{3}[/tex]

The mean is the best central tendency to measure the expected number of strokes required for the ninth hole.

What is mean?

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.

The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.

Why mean is the best choice in this case?

Since it considers all of the data in relation to one another, the mean is an effective indicator of central tendency. When there are outliers (extreme values) in the data, for example, the mean is a poor measurement; in this situation, the median is preferable.

The data set is roughly symmetrical in the scenario described in the question, so the mean is the most-suited central tendency measure to employ here.

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Answer:

The mean is the best choice because the data is nearly symmetrical.

Answer:

30 or 120 /4

Step-by-step explanation:

a^p/q here p denotes power raised and q denotes inverse power or root. So, 60^1/2 denotes square root of 60 raised to power 1.

The probability that he got at least 2 questions correct is 0.756.

Probability is simply how probably something is to appear. every time we're uncertain approximately the final results of an occasion, we can communicate approximately the possibilities of positive outcomes and how in all likelihood they may be. The analysis of occasions ruled through chance is called data.

Basic Probability Rules

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Answer:

Its a right isosceles triangle

Answer:

right isosceles

Step-by-step explanation:

it has the right at the top

Answer:

option b is the answer

Step-by-step explanation:

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

Answer:  [tex]\textsf{(1, 1) is NOT a solution of the inequality}[/tex]

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

Given:  [tex]y \le-3x + 1[/tex]

Find:  [tex]\textsf{Determine if (1, 1) is a solution of the inequality}[/tex]

Solution:  In order to determine if (1, 1) is a solution we need to plug in 1 for the x values and 1 for the y values and see if the equation evaluated to true.

Plug in the values

Simplify

As we can see the expression states that 1 is less than or equal to -2 which is false therefore (1, 1) is NOT a solution of the inequality.

Hey there!

Algebra I

Inequality

Ordered pair

y ≤ -3x+1

1 ≤ -3(1) + 1

1 ≤ -3 + 1

1 ≤ -2

The statement is NOT true as 1 is not less than or equal to -2.

Therefore, the ordered pair is not a solution of the inequality.

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Using an exponential function, the inequality is given as follows:

[tex]9400(0.857)^t < 6000[/tex]

The solution is t > 2.9, hence the tax status will change within the next 3 years.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

For this problem, the parameters are given as follows:

A(0) = 9400, r = 0.143.

The population after t years is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 9400(1 - 0.143)^t[/tex]

[tex]A(t) = 9400(0.857)^t[/tex]

The tax status will change when:

[tex]A(t) < 6000[/tex]

Hence the inequality is:

[tex]9400(0.857)^t < 6000[/tex]

Then:

[tex](0.857)^t < \frac{6000}{9400}[/tex]

[tex]\log{(0.857)^t} < \log{\left(\frac{6000}{9400}\right)}[/tex]

[tex]t\log{0.857} < \log{\left(\frac{6000}{9400}\right)}[/tex]

Since both logs are negative:

[tex]t > \frac{\log{\left(\frac{6000}{9400}\right)}}{\log{0.857}}[/tex]

t > 2.9.

The solution is t > 2.9, hence the tax status will change within the next 3 years.

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Part (i)

1. ABCD is a quadrilateral in which AD=BC and ∠DAB=∠CBA (given)

2. AB = AB (reflexive property)

3. Triangles ABD and BAC are congruent (SAS)

Part (ii)

4. BD=AC (corresponding sides of congruent triangles are equal)

Part (iii)

5. ∠ABD = ∠BAC (corresponding angles of congruent triangles are equal)

Answer:

Hey!

In △ABD and△BAC,

AD = BC (it's given)

∠DAB = ∠CBA (it's given)

AB = BA (Common)

By SAS congruence rule,

∴△ABD≅△BAC

=> BD = AC (By C.P.C.T) (ii)

And, ∠ABD = ∠BAC (By C.P.C.T) (iii)

Hope it helps, any confusions you may ask.

Answer:

B

Step-by-step explanation:

given f(x) then f(x ± a ) is a horizontal translation of f(x)

• if + a , then a shift left of a units

• if - a then a shift right of a units

here g(x) is the graph of f(x) moved 2 units right , then

g(x) = (x - 2)²