Homework help
Consider the difference of squares identity

Answer:

To find the average speed in miles per hour, we need to divide the total distance by the time taken:

Average speed = Total distance / Time taken

Average speed = 234 miles / 6 hours

Average speed = 39 miles per hour

Therefore, Nathan's average speed was 39 miles per hour.

Step-by-step explanation:

Answer:

Nathan drove an average of 39mph

Step-by-step explanation:

r=d/t

rate=234/6

234+6=240

240/6=40

Because we added a six, we need to subtract one:

40-1=39

Nathan drove an average of 39mph

Answer:

x=9

Step-by-step explanation:

The value of x is 47 from the given figure.

An angle is formed when two straight lines or rays meet at a common endpoint.

The sum of angles is 180 degrees from the figure.

x-2+x-2+x-2+x-2=180

Add the like terms

4x-8=180

Add 8 on both sides

4x=188

Divide both sides by 4

x=188/4

x=47

Hence, the value of x is 47 from the given figure.

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This is not a fair game since P + Q is greater than 1. To make game fair, we can modify conditions for scoring points. One possible modification is to give Pietro a point if all three toss results match (HHH or TTT).

This gives Pietro an additional outcome to score a point, which makes the game fair. Another modification is to give Eva a point if any two toss results match (H-T-H, T-H-T, T-T-H, H-T-T, HHT, TTH, THT, HTT). This also makes the game fair since both players have 3 possible outcomes to score a point.

There are 2³ = 8 possible outcomes when a coin is tossed three times. We can list them as follows:

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

Let E be the event that no two consecutive toss results match and let P(E) be the probability of event E. We can count the number of outcomes that satisfy E as follows:

HTH

HTT

THT

TTH

THT

TTT

Therefore, there are 6 outcomes that satisfy E and P(E) = 6/8 = 0.75.

Let P be the probability that Pietro scores a point and let Q be the probability that Eva scores a point. We can count the number of outcomes that satisfy each player's condition as follows:

Pietro: HHT, HTH, THH (3 outcomes)

Eva: H-T-H, T-H-T, T-T-H, H-T-T (4 outcomes)

Therefore, P = 3/8 and Q = 4/8 = 1/2.

The game is not fair since P+Q is greater than 1. This means that the players have a greater than 50% chance of scoring a point on each turn, so the first player to reach 10 points will have an advantage.

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The value of the function f(-10), f(2) and f(3) is 20201, 17 and 142 respectively.

According to the remainder theorem, when a polynomial p(x) is divided by a linear polynomial q(x) whose zero is x = a, the remainder is given by r = p(a). The remainder theorem enables us to calculate the remainder of the division of any polynomial by a linear polynomial, without actually carrying out the steps of the long division.

Given that, f(x)=2x⁴+x²-10x+1.

Here, f(-10)

Substitute x=-10 in the given function, we get

f(-10)= 2(-10)⁴+(-10)²-10(-10)+1

= 20000+100+100+1

= 20201

Substitute x=2 in the given function, we get

f(2)= 2(2)⁴+(2)²-10(2)+1

= 32+4-20+1

= 17

Substitute x=3 in the given function, we get

f(3)= 2(3)⁴+(3)²-10(3)+1

= 162+9-30+1

= 142

Therefore, the value of the function for x=-10 is 20201.

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The amount of dressing required to serve 11 guests who still want salad is therefore around 11 ounces. The answer, when adjusted to the closest whole ounce, is 11 ounces.

Round the figure up if 5, 6, 7, 8, or 9 follow the amount you are rounding. For instance, 40 when rounded to a nearest ten is 38. Round the figure down if it is followed by the digits 0, 1, 2, 3, or 4. 33 becomes 30 if it is adjusted to the nearest ten.

Many variables, such as the salad's serving size, the type of sauce, and personal preferences, will affect how much dressing is needed for 11 dinner guests. But as a general rule, a salad with dressing serving size is roughly 2-3 teaspoons (1 ounce = 2 tablespoons).

Assuming that each visitor will consume 2 tablespoons of dressings, the necessary quantity of dressing would be:

11 guests x 2 tablespoons/guest = 22 tablespoons

Tablespoons to ounces conversion:

22 tablespoons / 2 tablespoons/ounce = 11 ounces

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The solution to the equation is 7.8075 or -12.8075

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

We have the Quadratic Equation: 0.02 x² + 0.1 x - 2 = 0

2x² + 10x - 200 = 0

Using Discriminant Method

D = √b² - 4ac

D = √10² - 4(2)(-200)

D = √100 + 1600

D = √1700

D = 41.23

So, x = -b± D/2a

x = -10 ± 41.23 / 4

x= -10 + 41.23/4  or x= -10 -41.23 /4

x= 31.23/4 or x= -51.23/4

x= 7.8075 or x = -12.8075

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Current yield = 4.51%

The price of a bond is equal to the future cash flows' present value, discounted at the appropriate discount rate—the yield to maturity.

The price of a bond is the amount that investors are willing to spend on an existing bond. Bond prices are stated as a percentage of face (par) value in the online offering table and statements you get.

Current Yield=Annual Cash Inflows/Market Price

Annual cash flow is 4.75% of 100 = $4.75

Market Price of Bond = $105.25

Current Yield = 4.75/105.25

=4.51%

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Answer:

16°

Step-by-step explanation:

10p+20=180

10p=120

p=16

Answer:

-21/5

Step-by-step explanation:

The given series is:-7(3/8)^1 - 7(3/8)^2 - 7(3/8)^3 - ...

We can see that this is a geometric series with first term a = -7(3/8)^1 = -21/8 and common ratio r = 3/8.

The sum of an infinite geometric series with first term a and common ratio r (where |r| < 1) is given by:

sum = a/(1-r)

Substituting the values for a and r, we get:sum = (-21/8)/(1-3/8) = (-21/8)/(5/8) = -21/5Therefore, the sum of the given series is -21/5.

Therefore, the correct solution for the expression 2/5 + 3/8 is:

2/5 + 3/8 = 31/40

Option B is the correct solution. Answer: B. 16/40 + 15/40 = 31/40

A number is an arithmetic value that is used to indicate quantity. Hence, a number is a mathematical construct that is utilised for counting, measuring, and labelling. As a result, mathematics is built on numbers. As an illustration, this is a single butterfly, and these are four.

We can simplify the expression 2/5 + 3/8 as follows:

First, we need to find a common denominator. The smallest number that both 5 and 8 divide into evenly is 40.

2/5 can be written as 16/40 (by multiplying the numerator and denominator by 8)

3/8 can be written as 15/40 (by multiplying the numerator and denominator by 5)

Now we can add the fractions:

16/40 + 15/40 = 31/40

Therefore, the correct solution for the expression 2/5 + 3/8 is:

2/5 + 3/8 = 31/40

Option B is the correct solution. Answer: B. 16/40 + 15/40 = 31/40

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The surface area of the pyramid, given the dimensions of the pyramid can be found to be 1, 188 m ²

The surface area of a pyramid can be found by the formula :

= Base area of pyramid + 12 x ( Perimeter of the base x Slant height )

The surface area of this pyramid is :

= ( 6 x 6 ) + 12 x ( ( 6 + 6 + 6 + 6 ) x 4 )

= 36 + 12 x ( 24 x 4 )

= 36 + 12 x 96

= 1, 188 m ²

In conclusion, the surface area of the pyramid is 1, 188 m ².

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The value of x, given the sides in the right - angled triangle, would be 31. 8 °.

We are given side that is opposite the angle, and we are also given the hypotenuse.

This means that we can use the operation of Sin which is :

Sin ( angle ) = Opposite / Hypotenuse

Opposite = 10 units

Hypotenuse = 19 units

The value of x is :

Sin ( x ) = 10 / 19

Sin ( x ) = 0. 5263

x = Sin ⁻ ⁵ ( 0. 5663 )

x = 31. 8 °

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In this case, the equation is 6/2 = x/3, so x = 6/2 * 3/1 = 9/2.Therefore, the two possible values of x are 11/6 and 9/2.

Corresponding angles are angles that have the same relative position when two parallel lines are cut by a transversal line. When two parallel lines are cut by a transversal, corresponding angles are the same size. Corresponding angles are also known as vertically opposite angles.

In order to determine the value of x, we must assume that the two triangles in the diagram are similar. This means that the corresponding angles are equal and the corresponding sides are proportional. We will also assume that the angles of the triangle are in degrees and the sides are in the same unit of length.

Using the properties of similar triangles, we can calculate the value of x. We start by looking at the given angles, which are both 60°. Since the sides are proportional, we can set up a proportion equation between the two sides. We will use the side lengths given in the diagram to solve the proportion equation.

The proportion equation is: 11/3 = x/2.

Solving this equation for x, we get x = 11/3 * 2/1, which simplifies to x = 11/6.

We can also use the same equation to solve for x using the second given side length, which is 6. In this case, the equation is 6/2 = x/3, so x = 6/2 * 3/1 = 9/2.

Therefore, the two possible values of x are 11/6 and 9/2.

* The assumptions that I made in my working are that the two triangles in the diagram are similar and that the angles are measured in degrees and the sides are measured in the same unit of length.

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The center of this circle is (3,0) and its radius is 3.

It is required to find the center and radius of the circle.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.

here, we have,

Given that: (X-3)^2+y^2=9

The equation of a circle in standard form is:

(x -a)² + (y-b)² = r²

The x-coordinate of the center is a the y-coordinate of the center is b

, and r is the radius.

In this case,

a=3

b=0

and

r=3.

Hence, the center of this circle is (3,0) and its radius is 3.

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The slide is approximately 12.2 meters away from the monkey bars.

What is Pythagoras Theorem?

You may determine the right angled triangle's missing length using Pythagoras' Theorem. The triangle has three sides: the adjacent, which doesn't touch the hypotenuse, the opposite, which is usually the longest, and the hypotenuse (which is between the opposite and the hypotenuse).

We can solve this problem by using the Pythagorean theorem, which states that for a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).

Let's label the distance between the slide and the monkey bars as "x". We can see that the distance between the slide and the tire swing, and the distance between the tire swing and the monkey bars form the two shorter sides of a right triangle, with the hypotenuse being the distance between the slide and the monkey bars.

Using the Pythagorean theorem, we have:

[tex]x^2 = 7^2 + 10^2\\\\x^2 = 49 + 100\\\\x^2 = 149\\\\x = \sqrt{(149)}[/tex]

x ≈ 12.2 meters (rounded to the nearest tenth)

Therefore, the slide is approximately 12.2 meters away from the monkey bars.

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The correct expIanation is B. When 7 3 8 is muItipIied by a number greater than 1, the product is Iess than 7 3 8.

A fraction is a way of representing a part of a whoIe or a ratio between two quantities. It consists of a numerator (top number) and a denominator (bottom number) separated by a horizontaI Iine.

To compare the two fractions, we can convert them to decimaIs.

7 3/8 is equaI to 7.375, and

4/5 is equaI to 0.8.

MuItipIying 7.375 by 0.8, we get:

7.375 × 0.8 = 5.9

This means that 7 3/8 muItipIied by 4/5 is Iess than 7 3/8, since the product is 5.9 which is Iess than 7.375.

Therefore, the correct expIanation is B. When 7 3 8 is muItipIied by a number greater than 1, the product is Iess than 7 3 8.

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Answer:

7.0094

Step-by-step explanation:

Equation of best fit line on scatter plot is y = 30x + 40

Correct option is D.

A straight line is an infinite one-dimensional shape with no width. An infinite combination of points connected on either side of the point. A straight line has no curves. It can be horizontal, vertical, or slanted. An angle drawn between any two points on a straight line is always 180 degrees.

Given,

Scatter plot of the data of studying time of students

By the graph, point on the line are (0, 40) and (2,70)

Equation of the line

y - y₁ = ((y₂-y₁)/(x₂-x₁))(x-x₁)

y - 40 = ((70-40)/(2-1))(x-0)

y - 40 = (30/1)x

y - 40 = 30x

y = 30x + 40

Hence, y = 30x + 40 is the equation of the best fit line in scatter plot.

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The measure of the angle x with its supplementary angle is 51.7°.

The difference between complementary and supplementary angles is that complementary angles add up to 90 degrees, whereas supplementary angles add up to 180 degrees. In other words, the total of two complimentary angles' measurements equals 90 degrees. The total of the measurements of two additional angles is 180 degrees.

Let us suppose the measure of angle = x.

The measure of its supplementary angle is 180° - x.

From the given statement we have:

x = (180° - x) - 76.6

2x = 103.4

x = 51.7

Hence, the measure of the angle x with its supplementary angle is 51.7°.

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Reason:

The graph starts off very steep at x = 0. As x increases, the steepness goes down. Meaning the tangent lines become more shallow as you move to the right.

This tells us that the person learning the new task learns a lot at first. Then as time wears on, they learn less and less, until leveling off at some plateau.

If your teacher has covered derivatives, then you'll find the derivative of y = 1-e^(-0.28x) is dy/dx = 0.28e^(-0.28x)

Graph this derivative function using something like GeoGebra. Notice how the derivative curve is always decreasing. Therefore, x = 0 is when the derivative is largest, which points to the original function having the steepest increase (aka largest instantaneous rate of change).

See the graph below.

The image of the quadrilateral is R' = (-2, -1), S' = (-4, -2), T' = (-5, -4) and U' = (-3, -3)

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

R = (1, -2)

S = (2, -4)

T = (4, -5)

U = (3, -3)

The transformation is given as

90 degrees rotation about the origin

This is represented as

(x, y) = (y, -x)

Using the above as a guide, we have the following:

R' = (-2, -1)

S' = (-4, -2)

T' = (-5, -4)

U' = (-3, -3)

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The coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin are;

M = (1, 2)

N = (2, 4)

P = (4, 5)

Q = (3, 3)

The coordinates of the quadrilateral RSTU is

R = (1, -2)

S =(2, -4)

T = (4, -5)

U = (3, -3)

When the quadrilateral RSTU is rotated 90 degrees about the origin, it forms the quadrilateral MNPQ which has the coordinates

M = (1, 2)

N = (2, 4)

P = (4, 5)

Q = (3, 3)

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The surface area of the rectangle will be 24 meters. The correct option is A.

The surface area of the rectangular plate is calculated by applying the formula for the area of the rectangle.

A rectangle is a type of quadrilateral with four sides and four right angles. The opposite sides of a rectangle are parallel and equal in length, and the opposite angles are congruent (equal). This means that a rectangle has two pairs of congruent sides and four right angles.

Surface area = Length x Width

Surface area = 6 x 4

Surface area = 24 square meters

Therefore, the surface area of the rectangle will be 24 square meters.

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The complete question is given below.

Find the area of the upper surface of the rectangular plate having a length of 6 meters and a width of 4 meters.

Answer:

77

Step-by-step explanation:

Bisects means that the angle is split in half perfectly thus if angle JKM is 154 then JKR is 154/2 = 77

The equation for the situation is f(x) = 40(1+1)^x, which simplifies to f(x) = 40(2)^x.

Exponential growth is a process where a quantity increases at a constant percentage rate per unit of time. It can be represented by:

The equation f(x) = a(1+r)^x,

where "a" is the initial value, "r" is the growth rate, and "x" is the number of time periods.

This is exponential growth because the growth rate is given as 100%, which means the value is doubling with each step.

The formula for exponential growth is f(x) = a(1+r)^x,

where

r is the growth rate expressed as a decimal.

In this case, r = 1, since the growth rate is 100%, or 1.00 as a decimal.

So, the equation for the situation is f(x) = 40(1+1)^x, which simplifies to f(x) = 40(2)^x.

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In response to the aforementioned query, we may say that The loan's interest future value is $8640 as a result.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.

Interest is calculated as follows: Principal x Interest Rate x Time

where Principle represents the loan amount, Rate is the interest rate, and Time represents the loan's term in years. We may enter the figures since the loan is for 9 months, or 0.75 years:

Interest: $540 ($8000 x 0.09 x 0.75);

As a result, the student is required to pay interest of $540.

b. The following formula can be used to determine the loan's future value:

Principle x (1 + Rate x Time) = Future Value

where the same values for Principle, Rate, and Time apply as in section a. When we enter the values, we obtain:

Future Value = $8000 x (1 + 0.09 x 0.75), which is $8640.

The loan's future value is $8640 as a result.

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Answer:

C. Simple interest involves interest calculated only on the principal. Compound interest is interest computed on the original principal as well as on any accumulated interest.

Step-by-step explanation:

y = 5x+1. ____equ(1)

4x + y = 10. ____equ (2)

substituting equ(1) into equ(2)

4x + y = 10

4x + 5x + 1 = 10

9x = 10 -1

9x = 9

x = 1

x = 1 into equ (1)

y = 5x + 1

y = (5 ×1) + 1

y = 5 + 1

y = 6

I hope this will help.

have a nice day dear :)

Answer:

Mean = 325.6

Range = 80

Median = 49

Step-by-step explanation:

Mean= All numbers added dividend by 10 (amount of digits)

Range= Highest number minus lowest number

Median= Middle number (process of cancellation)

Answer: Let x be the measure of the angle in degrees. Then, the measure of its supplementary angle is 180 - x degrees.

We are told that the angle measures 153.4 degrees more than its supplementary angle. Using this information, we can set up an equation:

x = (180 - x) + 153.4

Simplifying this equation, we get:

2x = 180 + 153.4

2x = 333.4

x = 166.7

Therefore, the angle measures 166.7 degrees, and its supplementary angle measures:

180 - x = 180 - 166.7 = 13.3 degrees

We can check that the angle and its supplementary angle add up to 180 degrees:

166.7 + 13.3 = 180

So our solution is correct.

Step-by-step explanation: