A rectangular garden is 20 feet long and it measures 25 feet diagonal. What is the area in square feet

Distance: 19

Steps:

Distance (d) = √(16 - -3)2 + (8 - 8)2

= √(19)2 + (0)2

= √361

=          19

Answer:

700 + 50x ≥ 1200

where x represents the number of weeks needed to save.

Step-by-step explanation:

Check the picture below.

whatever those savings are on week "x", they have to be at least $1200

Time spent in class per week is 6 × 52 × 5 = 1560 minutes.

Time spent in class per day is 6 × 52 = 312 minutes.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Since Stephanie has 6 classes a day. Each class is 52 minutes. She goes to school 5 days a week.  The time she spend in class can written as:

time in class = 6 × 52 × 5 = 1560 minutes per week

The time can also be written in form of the time spent per day:

time in class = 6 × 52 = 312 minutes per day

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The point estimate of the population mean is 21.

The point estimate of the population mean is the midpoint of the confidence interval.

To find the midpoint, add the lower and upper bounds of the interval and divide by 2. In this case, the lower bound is 17 and the upper bound is 25, so the point estimate of the population mean is (17 + 25) / 2 = 21.

On the other hand, the margin of error is a measure of the precision of the estimate. It is the amount by which the estimate could be off and still be considered accurate. The margin of error is typically expressed as a percentage of the point estimate. In this case, the margin of error would depend on the level of confidence you have in the estimate and the size of the sample you used to generate the interval. Without more information, it is not possible to determine the margin of error.

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Answer:::

267 divided by 742

is

0.35983827493

rounded off to 0.36

This system of equations has been solved graphically and its solution is equal to the ordered pair (2, 2).

In Mathematics, a graph refers to a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.

In this scenario, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection of the lines on the graph;

y = 3x - 4     ........equation 1.

y = -1/2x + 3       ........equation 2.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which is given by the ordered pair (2, 2).

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The graph of the system of linear equation is attached below with solution of x, y as (2, 2)

A graph of a system of linear equations is a set of lines (or a line in case of a unique solution) on a coordinate plane that represent the solutions of the system. The graph of a system of linear equations can have different types of solutions depending on the number of lines and the relationship between them.

In this problem, we will use a graphing calculator to plot the equation and find the point of intersection which is the solution to the graph.

The point of intersection which shows the solution (x,y) of the system of linear equation is at (2, 2)

Kindly find the attached graph below as solution.

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Answer:

96

Step-by-step explanation:

2 x 6=12

12 x 4= 48

48 x 2=96

The solutions of the quadratic equation:

(x+ 2)*(x + 8) = 0

are:

x = -2

x = -8

Here we have the following quadratic equation:

(x + 2)*(x + 8) = 0

And we want to solve it for x.

Remember the zero property, for any real number A, the product with zero gives:

A*0 = 0

Then:

(x + 2)*(x + 8) = 0

If either (x + 2) = 0 or (x + 8) = 0

Solving these two we get:

x + 2 = 0

x = -2

x + 8 = 0

x = -8

The two solutions of the quadratic equation are x = -2 and x = -8

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Answer:

Option a) 6x+6 is correct.

Step-by-step explanation:

Option a) 6x+6 is correct.

The given expression 6x+6 represents a linear expression.

Step-by-step explanation:

Definition: Linear expression  is a mathematical statement defining an equality. It is usually a polynomial equation having degree 1. It can be written as linear relationship with variables and a constant.

6x+6 expression represents a linear expression

Because it has degree 1.

Therefore Option a) 6x+6 is correct.

The given expression 6x+6 represents a linear expression.

a) 6x+6

The given expression 6x+6 represents a linear expression.

Definition:

Linear expression is a mathematical statement defining equality. It is usually a polynomial equation having a degree of 1. It can be written as a linear relationship with variables and a constant.

6x+6 expression represents a linear expression.

Because it has degree 1.

Therefore, a) 6x+6 is correct.

The given expression 6x+6 represents a linear expression.

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Answer:

+5 + 3 = 8

Step-by-step explanation:

Answer:16/15

1 and 1/15

Step-by-step explanation:

4/5 x 4/3

The length of third side of the triangle will be A. x + 13.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

In this situation, triangle has a perimeter of 9x+6. The first side of the triangle has a length of 5 x and the second side has a length of 3x-7.

The length of third side of the triangle will be:

= 9x + 6 - (3x - 7 + 5x)

= x + 13

The correct option is A.

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The area and the perimeter of the figure are given as follows:

The figure is composed as follows:

Applying the Pythagorean Theorem, the diameter of the circle is given as follows:

d² = 2 x 12²

[tex]d = \sqrt{2 \times 12^2}[/tex]

d = 16.97 cm.

Then the radius of the circle is given as follows:

r = 0.5d

r = 0.5 x 16.97

r = 8.485 cm.

The area of a circle of radius r is given by the multiplication of π and the square of the radius, as follows:

A = πr².

Hence, considering that the figure is a semi circle, we have that:

Ac = 0.5 x π x (8.485)²

Ac = 36π

The area of the right triangle is of:

At = 0.5 x 12 x 12

At = 72 cm².

Meaning that the area of the shape is given as follows:

A = Ac + At.

A = 36π + 72

A = 36(π + 2) cm².

The perimeter of the shape is obtained by the sum of 2 times 12 cm and the circumference of the semi circle.

The circumference of a semicircle of diameter d is given as follows:

C = 0.5πd.

Hence:

C = 0.5π x 8.485

C =  4.2425π.

Meaning that the perimeter of the shape is given as follows:

P = (24 + 4.2425π) cm.

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The equation of the proportional relationship is y = 2x.

Proportional relationships are relationships between two variables where their ratios are equivalent. A proportional relationship is one in which two quantities vary directly with each other.

Therefore, the proportional relationship can be represented as follows:

y ∝ x

y = kx

where

using (2, 4)

y = kx

4 = 2k

k = 4 / 2

k = 2

Therefore, the equation is y = 2x.

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By writing and evaluating an exponential equation, we can see that the value of the car now is $9,216.

We know that the initial value of the car is $18.000, and the value depreciates at a rate of 20% per year.

If we define x as the number of years since the car was bought, we can write the value equation as:

V(x) = $18,000*(1 - 20%/100%)^x

V(x) = $18,000*(1 - 0.2)^x

V(x) = $18,000*(0.8)^x

The value of the car after 3 years is what we get if we evaluate the exponential equation in x = 3.

V(3) = $18,000*(0.8)^3

V(3) = $9,216

That is the value of the car now.

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Answer: y int is 8 the slope of the line is -1/2 and the equation of the line is y=-1/2x +8

Step-by-step explanation:

you can get slope by using the the points (6,5) and (8,4) to use y2-y1/x2-x1 and your y int is just where the line intersects the y axis which is 8. 8 then equals b in the equation y=mx+ b and you get m by using the first equation.

The  time that the rocket will hit the ground to the nearest tenth of a foot is 17 secs.

We were given the equation as y=-16x^2+261x+130 , thene we can equate this to zero. as

0=-16x^2+261x+130

from this we can see that this is a quadratic equation, where a= -16, b=261, c =130

Then input into the quadratic formular we have:

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

Then if we input the values we have [tex]x=\frac{-261+-\sqrt{261^{2}-4*-16*130} }{2*-16}[/tex]

Then the value of x are: -0.49 and 16.79

The positive value is the time that the rocket will hit the ground. Therefore, the rocket will hit the ground after 16.79 secs.

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The statements which are correct about the inequalities in each case as required are as follows;

It follows from the task content that the statement which is correct about each of the inequalities is to be matched accordingly.

It is noteworthy to know that the underlying perspective is such that;

If the coefficient of a variable upon isolation on one side of the inequality is negative, it follows that the inequality sign must be flipped while multiplying or dividing both sides of the inequality by a negative number.

On the other hand, if the coefficient of the variable is positive, the inequality sign is not to be flipped.

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The type of function that is shown in the given graph image is called a; Cubic Function

The vertical line test is a tool in graph functions that is very important when we are trying to determine the function that a specific graph represents. Now, we can further say that the vertical line is typically one that includes all points alongside a specific x-value with the y-value of a point that a vertical line will intersect a graph to represent an output for that particular input x value.

Now, there are different types of graphs and they all depend on the particular type of function that is being graphed. The eight most popular graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal. Each of the types of graphs are usually unique which means that is easy to visually differentiate from the rest.

In this given graph, we can see that the graph shows an image that corresponds to a cubic function because of the classical infinite branches, then the three real roots and then the two extrema values

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The distance of the straight line is √17 miles and the angle formed is

75.96°.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, A bus drives 1 mile west and 4 miles north.

Let, The distance the bus travels along the west be adjacent and the distance traveled in the north be the height.

So, By Pythagoras' theorem,

The straight line distance = √(1² + 4²).

= √(1 + 16) miles.

= √17 miles.

Now, We know tan = opposite/adjacent.

tan = 4/1.

tan⁻¹(4/1) = Ф.

Ф = 75.96°.

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The value of the function P(8) given that P(x) = 3.5(1.4)ˣ is (c) 51.65 million

From the question, we have the following parameters that can be used in our computation:

An exponential function

The equation of the exponential function is then given as

P=3.5(1.4)x

Express properly

So, we have

P(x) = 3.5(1.4)ˣ

where x represents the amount of decades since 1800

From the question, we have

x = 8

Substitute the known values in the above equation, so, we have the following representation

P(8) = 3.5(1.4)⁸

Evaluate the expression

P(8) = 51.65261696

Approximate

P(8) = 51.65

Hence, the value of P(8) is (c) 51.65 million

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The limit lim x → ∞ (2/3)ˣ = ∞

A limit is the value of a function as the independent variable tends to a particular value.

Since we have lim x → ∞ (2/3)ˣ, to find this limit, using the fact that lim x → a ㏑f(x) = ㏑[lim x → a ㏑f(x) ]

So, since  lim x → ∞ (2/3)ˣ, taking natural logarithm of both sides, we have that

lim x → ∞ (2/3)ˣ

㏑[lim x → ∞ (2/3)ˣ] = lim x → ∞ ㏑(2/3)ˣ

= lim x → ∞ x㏑(2/3)

So, substituting x = ∞ into the equation, we have that

lim x → ∞ x㏑(2/3) = ∞㏑(2/3)

= ∞

So, lim x → ∞ (2/3)ˣ = ∞

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The  Distance between B to C = 58 km,

distance between C to D = 30 km

Average speed between B to C = 59.79 km/h

The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other terms, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined.

Given  A commuter train moves from station A to D via B and C,

distance from A to C via B = 70 km

distance from B to D via C = 88 km

av. speed of the train from A to B = 48 km/h

av. speed of the train from C to D = 45 km/h

time taken by train to reach B = 15 min = 15/60  = 0.25 hour

distance between A to B = speed x time from A to B

distance between A to B = 48 x 0.25

distance between A to B = 12 km

A. Distance between B to C = distance from A to C - distance between A to B

Distance between B to C = 70 - 12 = 58 km

B. distance between C to D = distance from B to D -  Distance between B to C  

distance between C to D = 88 - 58 = 30 km

C. let av. speed from B to C is x

total distance covered by train  = 12 + 58 + 30 = 100 km

av. speed for journey = 50 km/h

time taken to complete journey = 100/50 = 2 hours

time is taken from A to  B = 0.25 hour

time is taken from B to C = 58/x

Time is taken from C to D = 30/45 = 0.66 hour

halt at b = 3 minute and halt at C = 4 minute

total halt = 3 + 4 = 7 minute = 7/60 = 0.12 hour

Total time  = time taken from(A to B + B to C + C to D) + total hault

2 = 0.25 + 58/x + 0.66 + 0.12

58/x = 0.97

x = 59.79 km/h

Hence The  Distance between B to C = 58 km,

distance between C to D = 30 km

Average speed between B to C = 59.79 km/h

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All the mathematical expressions are,

1) 11 - k

2) p + 9

3) 16h

4) f < 12

5) 16 < m

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

All the algebraic expression are,

1. Eleven decreased by k

2. p increased by 9

3. Sixteen multiplied by a number h

4. f less than twelve

5. Sixteen less than m

Now,

We can write all the expression as,

1. Eleven decreased by k

⇒ k - 11

2. p increased by 9

⇒ 9 + p

3. Sixteen multiplied by a number h

⇒ 16 × h

⇒ 16h

4. f less than twelve

⇒ f < 12

5. Sixteen less than m

⇒ 16 < m

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The linear function in the table is given as follows:

g(x) = 4x - 1/2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

When x increases by 0.5, y increases by 2, hence the slope m is obtained as follows:

m = 2/0.5

m = 4.

When x = 0, y = -0.5, hence the intercept b is given as follows:

b = -1/2.

The function is then defined as follows:

g(x) = 4x - 1/2.

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(37.5, 42, 43.5} is the set of numbers that makes the inequality true

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given that:

Amanda uses the inequality below to calculate how many minutes, m, it takes her to swim at least 1,500 meters.

40m ≥ 1, 500

To determine which set of numbers makes the inequality true, solve for m and check the pick that contains the values greater than or equal to m:

40m ≥ 1, 500

m  ≥ 1, 500/40

m  ≥ 37.5

Thus, the set of numbers that makes the inequality true is (37.5, 42, 43.5}

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The statement "5 subtract from 9" as an expression is 9 - 5

From the question, we have the following parameters that can be used in our computation:

A mathematical statement

The mathematical statement is given as

5 subtract from 9

Subtraction means minus

So, we have the following representation

5 subtract from 9 = 9 - 5

The question does not require that we solve the expression

So, we leave it at 9 - 5

Hence, the required expression is 9- 5

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Answer:

False

Step-by-step explanation:

$1.45 * 8= $11.6.

The right unit price would be $1.50

I think  

Answer:

false 1.5 is correct

Step-by-step explanation:

so the answer is 8 divided by 12.00 and it is false the answer is 1.5