Factoring polynomials maze

Answer: 19.3

Step-by-step explanation: To solve this we can find numbers whose squares are close to 372. We know 20x20 = 400 and 19x19 = 361 so it has to be between these two.372 is closer to 361 meaning the square root of it is less than 19.5. Now we can just test numbers. 19.4x19.4 = 376ish and 19.3x19.3 is 372.49. This number is close enough so 19.3 is our answer.

Answer: 93 [tex]\frac{1}{3}[/tex] yards³

Step-by-step explanation:

      We will find the volume in feet with this formula:

                               V = LWH

V = LWH

V = (140)(4)(0.5)

V = 280 feet³

      There are 3 feet in a yard, and the question asks for yards, so we will divide:

280 feet³ / 3 = 93 [tex]\frac{1}{3}[/tex] yards³

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The required value of y for the given segment AB is given as y = 16, -8.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

here,
A(0, 4), B(5, y), and AB = 13.

Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂- y₁]²]

Substitue the value in the above expression,
13 = √[[5 - 0]² + [y - 4]²]
169 = 25 + [y - 4]²
[y - 4]² = 144
y - 4 = ± 12

y = 16, -8

Thus, the required value of y for the given segment AB is given as y = 16, -8.

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The area of the rectangle will be equal to 11 square units.

Matrix is defined as the arrangement of the numbers variables and expressions in the table as rows and columns.

A matrix is a structured table with columns and rows for arranging numbers, expressions, and even symbols. If the two matrices have equal row and column sizes, they can be added to, subtracted from, and multiplied element by element.

The area of the rectangle is calculated by finding the determinant of the matrix as below,

[tex]A = \left[\begin{array}{cc}3&-1&\\5&2&\\\end{array}\right][/tex]

A = ( 6 - ( -5 )

A = 6 + 5

Area = 11 square units

Hence, the value of the area of the rectangle is 11 square units.

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The correlation coefficient may assume any value between -1 and 1. Correct answer: letter D.

This means that the coefficient may be negative, zero, or positive, with a value of -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation.

The correlation coefficient is a numerical measure of the degree of linear dependence between two variables. It is a statistic that measures the strength of the relationship between two variables. A correlation coefficient of 1 indicates a perfect positive correlation, a coefficient of -1 indicates a perfect negative correlation, and a coefficient of 0 indicates no correlation between the two variables.

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Answer: 70

Step-by-step explanation: To find this answer, we must use PEMDAS. So, we have parentheses (adding) and multiplying. The P is first, so we solve for parentheses first. So, 2 + 5 = 7. So, now we multiply. 10 * 7 = 70. Therefore 70 is our answer. I hope this helped!

Answer:

4/5

Step-by-step explanation:

Call our unknown variable ‘x’

X(1/4)=1/5

Therefor, x=4/5

Katie spent approximately $285.544 on fuel during her vacation in Australia.

The Average Cost is the per unit cost of the product received by dividing the total cost (TC) by the total output (Q). By per unit cost of production, we mean that all the fixed and variable costs are considered for calculating the average cost. Thus, it is also called Per Unit Total Cost.

Symbolically, the average cost is expressed as:

AC = TC/Q

To estimate how much Katie spent on fuel, you need to multiply the number of gallons of gas she used (56 gallons) by the average cost of gas per gallon ($5.099):

56 gallons × $5.099/gallon = $285.544

So, Katie spent approximately $285.544 on fuel during her vacation in Australia.

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P(X + Y < 4) = 0.53 rounded to the first decimal place.

To find the probability P(X + Y < 4),

we need to find the values of x1 and x2 that satisfy the condition

X + Y < 4, and then sum up the corresponding probabilities in the table.

We can start by plotting the points (x1, x2) on a graph and finding the region where X + Y < 4.

This region can be determined by shading in the portion of the graph that is below the line X + Y = 4.

Next, we need to find the values of x1 and x2 in the table that fall within this region and sum up their probabilities.

This gives us P(X + Y < 4) = 0.20 + 0.14 + 0.11 + 0.08 = 0.53.

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2 is the initial amount, growth rate is (3ˣ - 1) × 100% , domain of the function is all real numbers and  range of the function is all positive real numbers

A relation is a function if it has only One y-value for each x-value.

The given function is:

f(x) = 2(3)ˣ

To find the initial amount, we need to find f(0):

f(0) = 2(3)⁰ = 2(1) = 2

So the initial amount is 2.

To find the growth rate, we can use the formula:

growth rate = (f(x) - f(0)) / f(0) × 100%

= (2(3)ˣ - 2) / 2 × 100%

= (3ˣ - 1) × 100%

So the growth rate is (3ˣ - 1)×100%.

The domain of the function is all real numbers because the function is defined for all values of x.

The range of the function is all positive real numbers because the function is always positive for any value of x.

Specifically, the range of the function is (0, infinity).

Hence, 2 is the initial amount, growth rate is (3ˣ - 1) × 100% , domain of the function is all real numbers and  range of the function is all positive real numbers

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The probability that the proportion of a sample is higher than 0.30 can be estimated using the Central Limit Theorem (CLT) which states that the distribution of the sample means approaches a normal distribution as the sample size increases. With a large sample size (n >= 30), we can use the normal distribution to approximate the distribution of the sample means.

Assuming the sample size is large, the standard error (SE) of the sample mean is given by

SE = sqrt(p * (1 - p) / n), where p is the population proportion (0.27) and n is the sample size.

With this information, we can find the Z-score corresponding to 0.30 using the formula: Z = (0.30 - 0.27) / SE

Since we don't know the sample size, we'll assume a conservative sample size of 30.

With a sample size of 30, the SE is approximately 0.039, and the Z-score is approximately 0.77.

Using a standard normal table, we can find the probability of a Z-score being greater than 0.77 is approximately 0.22.

Therefore, the approximate probability that the proportion who exercise at least five days per week is higher than 0.30 is 0.22.

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1)

The axis of symmetry is x = -6.

2)

Vertex is (-6, 26).

3)

f(x) has a maximum value.

4)

f(x) is concave down.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

f(x) = -x² - 12x - 10

This is in the form of ax² + bx + c.

a = -1, b = -12, c = -10

The axis of symmetry is x = -b/2a

x = 12/(-2)

x = -6

Now,

f(x) = -x² - 12x - 10

f(x) = -(x² + 12x + 10)

f(x) = - { (x² + 12x + 36) - 36 + 10}

f(x) = -(x + 6)² + 26

This is in the form of f(x) = a (x - h)² + k

a = -1, h = -6, k = 26

Vertex = (h, k) = (-6, 26)

Now,

f(x) = -x² - 12x - 10

f'(x) = -2x - 12

f''(x) = -2

It is a negative value.

This means f(x) has a maximum value.

Now,

From the graph, we see that f(x) is concave down.

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Answer:

Yes because there all the same shape the size dosent effect the shape of it.

Step-by-step explanation:

Answer:

101.  ΔABC congruent to ΔDEF

102. ΔJKL not congruent to ΔMNO

Step-by-step explanation:

Q 101

Triangle ABC has 3 sides equal  to each of the three sides of DEF

The corresponding two angles of ABC and DEF are also equal

So the third angle of ABC ∠B must be equal to the third angle of DEF so we have three sides equal, three angles equal, hence congruent

ΔABC congruent to ΔDEF

Q 102

We have JL = MP = 1.9

m∠J = m∠M = 24°

The other two angles are not correspondingly equal

This only makes one side equal and one angle equal. Not sufficient to make it congruent

Hence ΔJKL not congruent to ΔMNO

The time taken to fill a 275-gallon hot​ tub is 69 minutes.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

A hose fills a hot tub at a rate of 3.99 gallons per minute.

This means,

3.99 gallons = 1 minute

Multiply 275/3.99 on both sides.

275 gallons = 275/3.99 x 1 minute

275 gallons = 69 minutes

Thus,

It will take 69 minutes to fill a 275-gallon hot​ tub

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The center of mass coordinates of the given plane is -

COM{X, Y} = { [tex]$\int\limits^4_0 {\rho (x,y)/x} \, \;dx[/tex],  [tex]$\int\limits^2_0 {\rho (x,y)/y} \, \;dy[/tex]}

The center of mass is the point at which the whole mass of the body or system can be considered to be concentrated.

Given is the plane with the equation -

ρ(x, y) = (1 + x/2)

We can write the center of mass as -

X{C.M.} = [tex]$\int\limits^4_0 {\rho (x,y)/x} \, \;dx[/tex]

Y{C.M.} = [tex]$\int\limits^2_0 {\rho (x,y)/y} \, \;dy[/tex]

Therefore, the center of mass coordinates of the given plane is -

COM{X, Y} = { [tex]$\int\limits^4_0 {\rho (x,y)/x} \, \;dx[/tex],  [tex]$\int\limits^2_0 {\rho (x,y)/y} \, \;dy[/tex]}

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Answer:

$ 481.50

Step-by-step explanation:

Discount:

    Discount = 25% of retail price of TV

                    = 0.25 * 600

                    = $ 150

   Price after discount = Retail price - discount

                                     = 600 - 150

                                     = $ 450

Tax:

Tax = 7% of 450

        = 0.07 * 450

        = $ 31.50

Amount to be paid:

Amount needs to be paid = price after discount +  tax

                                           = 450 + 31.50

                                            = $ 481.50

Answer: -1/x-17        -1-17x

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

that is 3×3×3×3×3×3....×3 21 times and the other is 50 times,so u have to multiply 3²¹ with more 3s so u ger 3⁵⁰

Answer:

%6, 1/2, 0.6, 6/5

Step-by-step explanation:

Answer:

Bottom left option

Step-by-step explanation:

The four numbers present in this order are:

[tex]\frac{1}{2} = 0.5[/tex]

0.6

[tex]\frac{6}{5} = 1.2[/tex]

[tex]6 percent = \frac{6}{100}[/tex] = 0.06

The order of the numbers from least to greatest are:

6%, [tex]\frac{1}{2}[/tex], 0.6, [tex]\frac{6}{5}[/tex]

Answer:

x = 40/3

Step-by-step explanation:

x+5/3=15

x + 5/3 = 45/3

x = 40/3

Let's check

40/3 + 5/3 = 15

45/3 = 15

15 = 15

SO, x = 40/3 is the correct answer.

Answer:

Yes

Step-by-step explanation:

Yes, they do since if you multiply the y by 2.5 it will give you all the answers you entered

Radius of Circle B = 6 cm + 3 cm = 9 cm

Radius of Circle C = 9 cm + 3 cm = 12 cm

Radius of Circle D = 12 cm - 2 cm = 10 cm

What is a circle's straightforward definition?

Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed.

The area of a circle is given by the formula: A = πr^2, where A is the area and r is the radius.

The area of Circle A is A = π(6 cm)^2 = 36π cm^2

The area of Circle B is A = π(9 cm)^2 = 81π cm^2

The area of Circle C is A = π(12 cm)^2 = 144π cm^2

The area of Circle D is A = π(10 cm)^2 = 100π cm^2

To find how many times greater than the area of Circle A is the area of Circle D, we can divide the area of Circle D by the area of Circle A:

100π cm^2 / 36π cm^2 = 2.78

The area of Circle D is 2.78 times greater than the area of Circle A.

Note: since π is a constant, we can ignore it for the purposes of comparing the areas of the circles. It will always be the same value and it will cancel out when dividing.

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Answer:

Step-by-step explanation: First, do the multiplication inside the parenthesizes so 8x5 is 40, and 40+2 is 42. 120-42=78

8n=78

n=9.75

Basically, there are two different types of geometric shapes such as: Two – Dimensional Shapes.

Define area of geometrical shape?

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Basically, there are two different types of geometric shapes such as: Two – Dimensional Shapes. Total area under graph = 15 + 12.56 + 3 + 20 = 50.56 sq. units

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

The area of shape is the space enclosed within the perimeter or the boundary of a given shape. We can calculate the area of shape for different geometrical shapes using specific mathematical formulae.

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

Area is measured in square units such as square inches, square feet or square meters. To find the area of a rectangle, multiply the length by the width. The formula is: A = L * W where A is the area, L is the length, W is the width, and * means multiply.

The area under the graph will be -

area of rectangle = length × breadth

= 5 × 3 = 15 sq. unit

area of circle = πr²

= 3.14 × 2 × 2

= 12.56 sq units

area of triangle = 1/2 × base × height

= 1/2 × 3 ×2

= 3 sq. units

area of trapezium = a + b / 2 . h

= 5 + 3 / 2 . 5

= 20 sq. units

area of triangle = 1/2 × 2 × 5 = 5 sq. units

Total area under graph = 15 + 12.56 + 3 + 20 = 50.56 sq. units

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Ans:-

[tex] \: [/tex]

[tex] \: [/tex]

Int b nd c can be divide by 12

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

The Sum In The Form a( b + c ):-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)

Answer:

[tex]f(x) = {x}^{2} + 7 \\ \dashrightarrow \: f(a + 5) = {(a + 5)}^{2} + 7 \\ \dashrightarrow \: f(a + 5) = {a}^{2} + 25 + 10a + 7 \\ \dashrightarrow \: \: \boxed{ f(a + 5) = {a}^{2} + 10a + 32}[/tex]

hope helpful! :)

An equation of the function graphed above include the following: f(x) = 2∛x - 4.

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.

Additionally, a geometric figure that is translated downward simply means subtracting a digit from the value on the y-coordinate of the pre-image or parent function.

By critically observing the graph of the function shown above, we can logically deduce that it is a cube root function that has been vertically shifted by a scale factor of 2 units and then translated downward by 4 units. Therefore, this can be modeled by this equation as follows;

f(x) = 2∛x - 4.

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The total value of the account after 18 years, deposit of $100,000 with monthly compounding and a rate of 5%, is given as follows:

$245,501.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]P = 100000, r = 0.05, n = 12, t = 18[/tex]

Hence the balance is given as follows:

A(18) = 100000 x (1 + 0.05/12)^(12 x 18)

A(18) = $245,501.

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Answer:

b = 8 cm

Step-by-step explanation:

Area: 1/2*base*height

1/2*base*3=12

3*base=24

base=24/3

base=8 cm