What is the value of x?

In response to the supplied query, we may state that Ben's speed, equation rounded to one decimal place, is x + 0.8 = 2.5 mph.

Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.

Rate times distance

Let x represent Alan's speed in mph. Ben's speed will then be x + 0.8 mph.

They will have travelled 12.6 kilometres in total when they finally cross paths. The formula is as follows:

[tex]12.6 = (x + x + 0.8) × 3\\12.6 = 6x + 2.4 \s10.2 = 6x \sx = 1.7[/tex]

Alan is moving at a speed of 1.7 mph, decimal place included.

Ben's speed, rounded to one decimal place, is x + 0.8 = 2.5 mph.

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Answer:

​Alan's rate of speed is 1.7 mph.

​Ben's rate of speed is 2.5 mph.

Step-by-step explanation:

We can use the distance-rate-time formula to solve the given problem.

[tex]\boxed{\sf Distance=rate \times time}[/tex]

Create a distance equation for each of the hikers.

Therefore, the equation for Alan's distance in terms of r is:

[tex]\implies \sf d = 3r[/tex]

Therefore, the equation for Ben's distance in terms of r is:

[tex]\implies \sf d = 3(r+0.8)[/tex]

Alan and Ben are 12.6 miles apart and walking toward each other.  

Therefore, their combined distances will equal 12.6 miles.

Set the sum of the found expressions for distance equal to 12.6 and solve for r:

[tex]\implies \sf d_{Alan}+d_{Ben}=12.6[/tex]

[tex]\implies \sf 3r+3(r+0.8)=12.6[/tex]

[tex]\implies \sf 3r+3r+2.4=12.6[/tex]

[tex]\implies \sf 6r+2.4=12.6[/tex]

[tex]\implies \sf 6r=10.2[/tex]

[tex]\implies \sf r=1.7[/tex]

Therefore:

​Alan's rate of speed is 1.7 mph.

​Ben's rate of speed is 2.5 mph.

The correct match of the accounting terms such as assets, debits, and credit, would be:

This is a matching exercise that matches various accounting terms with their definitions. Here are the meanings of the terms:

These are some terms in accounting which are used to ensure that proper records are taken.

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Answer:

315

Step-by-step explanation:

The LCM for 45 and 7 is 315

One way to find the LCM of 7 and 45 is to start by comparing the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:

What are the Factors of 7?What are the Factors of 45?

Here is the prime factorization of 7:

7171

And this is the prime factorization of 45:

32×5132×51

When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 7, 3, 5

Answer:      a. 8.4 meters       b. 14 wreaths

Step-by-step explanation:

The following equation shows the problem, with x representing the number of wreaths made:

12 = 9(0.4) + 0.6x

To answer a, get 0.6x alone:

12 = 9(0.4) + 0.6x

12 = 3.6 + 0.6x

8.4 = 0.6x

There were 8.4 meters available to make wreaths

To answer b, get x alone

8.4 = 0.6x

14 = x

Diego could make 14 wreaths with the available ribbon

Hope this helps!

The answer is Start Fractiοn 2 οver 7 End Fractiοn.

Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.

Kyle's handful οf trail mix cοntains a tοtal οf 2 + 4 + 3 + 5 = 14 items.

The prοbability οf picking a peanut is the number οf peanuts in the handful divided by the tοtal number οf items in the handful:

prοbability οf picking a peanut = number οf peanuts / tοtal number οf items

prοbability οf picking a peanut = 4 / 14

Simplifying the fractiοn by dividing bοth the numeratοr and denοminatοr by 2, we get:

prοbability οf picking a peanut = 2 / 7

Therefοre, the answer is StartFractiοn 2 οver 7 EndFractiοn.

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The investment οf $1,000 will be wοrth $1,225.04 after 3 years.

Cοmpοund interest is interest οn the principal amοunt οr lοan which is calculated accοrding tο the number οf cοmpοunds in οne year.

In this, the interest earned in each periοd is based οn the tοtal amοunt, which includes bοth the principal and the accumulated interest.

The fοrmula used fοr cοmpοund interest is

Here we have

The principal amοunt is $ 1000

The annual interest rate here is 7.5%  

The interest is cοmpounded annually.

The time periοd is 3 years  

Using the fοrmula,

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

A = 1,000 (1 + 0.075/1)⁽¹⁽³⁾⁾

= 1,000 (1.075)³

= $1,225.04  

Therefοre,

The investment of $1,000 will be wοrth $1,225.04 after 3 years.

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Answer:

4√5

Step-by-step explanation:

To simplify √20+√45-√5, we need to look for factors that can be simplified under the square root. We can simplify 20 and 45 by factoring out perfect squares:

√20 + √45 - √5 = √(4×5) + √(9×5) - √5

= 2√5 + 3√5 - √5

= 4√5

Therefore, the simplest form of the expression is 4√5

The equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3)

The equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3).

The commutative property of addition states that the order of the numbers does not matter when adding them together.

In this equation, the numbers are rearranged but the result is still the same. This is because the commutative property of addition allows for the numbers to be added in any order and still have the same result.

Here is the step-by-step explanation:

Identify the commutative property of addition, which states that a+b=b+a.

Look at the given equations and see which one follows the commutative property of addition.

The equation (1+2)+3=1+(2+3) follows the commutative property of addition because the numbers are rearranged but the result is still the same.

Therefore, the equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3).

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Answer:

<HDG = 39°

Step-by-step explanation:

Red square is a right angle which mean its a 90°

Those two angle <CDG and <HDG are complementary angle which mean they both add up to 90°

<CDG + <HDG = 90°

51° + (3t+15)° = 90°

Solve for t.

3t + 51 + 15 = 90°

3t + 66 = 90°

3t = 24

t = 8

Plug t = 8 into <HDG to find the measurement.

<HDG = 3t + 15

<HDG = 3*8 + 15

<HDG = 24 + 15

<HDG = 39°

The shape of the distribution of the sample mean for all possible simple random samples of size 5 from this population is approximately Normal

If the amount of orange juice that can be obtained from a single orange is Normally distributed, then the distribution of the sample mean of orange juice obtained from a sample of size 5 from this population will also be Normally distributed.

The mean of the sample mean distribution will be equal to the population mean, which is the mean amount of orange juice that can be obtained from a single orange.

The standard deviation of the sample mean distribution, also known as the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size.

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The given question is incomplete, the complete question is:

The amount of orange juice that can be obtained from a single orange is Normally distributed. A manufacturing company selects an SRS of size n = 5 from the population of all oranges in their inventory and calculates the sample mean amount of orange juice that is obtained. What is the shape of the distribution of the sample mean for all possible simple random samples of size 5 from this population?

Using dilation, the scale factor here is 2,

X' = (2,2)

Y' = (4,4)

Z' = (6,0)

A thing must be scaled down or altered during the dilation process. It is a transformation that reduces or enlarges the objects using the supplied scale factor. The pre-image is the original figure, while the image is the new figure that emerges via dilatation. Two types of dilation exist:

Expansion describes an increase in an object's size.

Reduction in size is referred to as contraction.

In the given question,

The scale factor here is 2.

So, the new dilated triangle will be:

X' = (2,2)

Y' = (4,4)

Z' = (6,0)

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The answers are (a) (fog)(4) = 6√2, (b) (gof)(2) = 6√2, (c) (f of)(1) = 3√3, and (d) (gog)(0) = 0.

The given expressions are f(x) = 3√x and g(x) = 2x. We need to find the following expressions: (a) (fog)(4) (b) (gof)(2) (c) (f of)(1) (d) (gog)(0)

(a) (fog)(4) = f(g(4)) = f(2(4)) = f(8) = 3√8 = 3√(4*2) = 3√4 * √2 = 3*2*√2 = 6√2

(b) (gof)(2) = g(f(2)) = g(3√2) = 2(3√2) = 6√2

(c) (f of)(1) = f(f(1)) = f(3√1) = f(3) = 3√3

(d) (gog)(0) = g(g(0)) = g(2(0)) = g(0) = 2(0) = 0

Therefore, the answers are (a) (fog)(4) = 6√2, (b) (gof)(2) = 6√2, (c) (f of)(1) = 3√3, and (d) (gog)(0) = 0.

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Answer:

dddiejehehegeheheheh

Answer:

Proof:

Using the given information, we know that PQ is approximately equal to QS and QS is exactly equal to ST.

Since a value that is approximately equal to another value can be treated as equal in many cases, we can say that PQ is roughly equal to ST.

To prove that PQ is exactly equal to ST, we must use the transitive property of equality.

Transitive Property of Equality: If a = b and b = c, then a = c.

Using the transitive property, we can say:

PQ ≈ QS and QS = ST → PQ ≈ ST

Since PQ is approximately equal to ST and they have the same units of measurement, we can round the values to the same number of decimal places and say:

PQ ≈ ST ≈ rounded value

Therefore, PQ is exactly equal to ST because they have the same rounded value.

Answer:

not a function

Step-by-step explanation:

Answer:

not a function

Step-by-step explanation:

Answer:

  100°

Step-by-step explanation:

You want the missing arc measure in the geometry where two chords cross at 85° and they intercept one arc of measure 70°.

The angle where chords cross is the average of the two arcs that they intercept. Here, that means ...

  85° = (AE +BC)/2

Solving for BC, we get ...

  2(85°) = AE +BC

  BC = 170° -AE = 100°

The missing arc measure is 100°.

shirt by sza and fav singer ariana grande!

thanks so much!

Answer:

Love The Way You Lie - Eminem

In linear equation, 2000 pupils are there in the school.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                            Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Ax+By=C is the typical form for linear equations involving two variables. Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.

= 540/27%

= 54000/27

= 2000

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The future value of the investment after 6 years is $14,370.88; while the effective annual interest rate is 2.56%.

To calculate the future value of the investment, we can use the formula: FV = PV (1 + r/n)^(nt), where FV is the future value, PV is the present value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, PV = $12,000, r = 0.025, n = 12 (compounded monthly), and t = 6.

Plugging these values into the formula, we get:

FV = $12,000 (1 + 0.025/12)^(12*6)

FV = $12,000 (1.002083333)^72

FV = $14,370.88

Therefore, the future value of the investment after 6 years is $14,370.88.

To calculate the effective annual interest rate, we can use the formula: EAR = (1 + r/n)^(n) - 1, where r is the annual interest rate and n is the number of times the interest is compounded per year.

In this case, r = 0.025 and n = 12 (compounded monthly).

Plugging these values into the formula, we get:

EAR = (1 + 0.025/12)^(12) - 1

EAR = (1.002083333)^12 - 1

EAR = 0.02568245

Therefore, the effective annual interest rate is 2.568245%.

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Answer:

5.5, 6, and 7.25

Step-by-step explanation:

3 numbers equal 18.75 tells us:

a + b + c = 18.75, where a, b, and c are the 3 unknown numbers respectively.

Next, we know that the range is 1.75. Let us consider that c is the greatest value and a is the smallest value. Thus, we can write

c - a = 1.75

Lastly, we know that there is a median of 6. This tells us that the "middle" number (which in this case would be b if c is greatest and a is smallest) should be 6.

b = 6.

Substituting we can write,

a + c + 6 = 18.75

a + c = 12.75

Also,

c - a = 1.75

c = a + 1.75

Substituting back into the other equation we get,

a + ( a + 1.75) = 12.75

2a + 1.75 = 12.75

2a = 11

a = 5.5

Now, we can find the last number.

c = (5.5) + 1.75

c = 7.25

Plug all 3 numbers back into the original equation to verify if our numbers are correct:

5.5 + 6 + 7.25 = 18.75

Thus, we know we are correct.

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The value of x would be equal to 20 degrees.

Linear pairs of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.

We are given the parameters as;

7x and (x + 20)

The sum of angle is equal to 180.

7x + (x + 20) = 180

8x + 20 = 180

8x = 180 - 20

8x = 160

x = 160/8

x = 20

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The vertical asymptote(s) for R(x) is x=1 and x=-2. The horizontal asymptote(s) is y=0.

To find the vertical asymptotes, we look at each factor and look for any x-values that would make the factor equal to zero.

The factors are (2x+6), (x-1), (4-x), and (x+2).

So, x=1 would make (x-1) equal to zero and x=-2 would make (x+2) equal to zero.

To find the horizontal asymptote, we look at the degree of the highest exponent and divide it into the coefficient of the term with the highest degree.

Since the highest exponent is 1 and there is no coefficient, the answer is y=0.

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The number of lbs in 15. oz is 9 3/8 lb

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

lb and oz are both units of weight of a substance.

1 oz = 0.0625 lb

therefore 1 oz = 625/1000

= 25/40 lb

15 oz = 25/40 × 15

= 75/8 lb

= 9 3/8 lb

therefore the number of lbs in 15 oz is 9 3/8 lb

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Therefore, the height (in feet) of the lighthouse is 88 feet.

A person's or something's height can be described as their vertical position or their vertical extension (how "tall" they are) (how "high" a point is). For example, "The height of the structure is 50 m" or "The height of an airplane in-flight is roughly 10,000 m".

Let's use proportions to solve the problem. We can set up a ratio of the height of the lighthouse to the length of its shadow, and another ratio of the height of the lamppost to the length of its shadow, and then equate the two ratios:

height of lighthouse / length of shadow of lighthouse = height of lamppost / length of shadow of lamppost

Let's plug in the given values:

h / 144 = 5.5 / 9

To solve for the height of the lighthouse, we can cross-multiply and simplify:

9h = 144 × 5.5

9h = 792

h = 88

Therefore, the height of the lighthouse is 88 feet.

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Yes, a line / is said to be tangent to a circle at a point P if and only if it meets the circle at P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line / passing through P, we can show that / is tangent to the circle at P if and only if it is perpendicular to the line OP.

To show this, first consider a line / that is perpendicular to the line OP. Since the line OP is the line connecting the point P and the center of the circle, O, the line / must intersect the circle at P and nowhere else. This means that / is tangent to the circle at P.

Now, consider a line / that is not perpendicular to the line OP. Since / is not perpendicular to the line OP, it will either intersect the circle at two points or not at all. Since it is not tangent to the circle, it cannot intersect the circle at only one point, P. Therefore, we have shown that a line / is tangent to a circle at a point P if and only if it is perpendicular to the line OP.

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The two real roots of the polynomial function S(r) = r^(5) + 5r^(4) - 7r^(3) - 43r^(2) - 8r - 48 are r = -8 and r = 3.

The two real roots of the polynomial function S(r) = r^(5) + 5r^(4) - 7r^(3) - 43r^(2) - 8r - 48 can be found by factoring the polynomial and finding the values of r that make the function equal to zero.

First, we can factor the polynomial using the Rational Root Theorem, which states that if a polynomial has rational roots, they must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

In this case, the constant term is -48 and the leading coefficient is 1, so the possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, and ±48.

We can use synthetic division to test these possible roots and find the ones that make the function equal to zero. After testing the possible roots, we find that the two real roots are r = -8 and r = 3.

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The response is A.

Option A's median value is 9, and its range is 13, therefore the smallest value is 9-6, which equals 3, and the greatest value is 9+6, which equals 15. This information is accurately represented by the box-and-whisker plot in option A.

The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.

As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.

from the question:

According to the information provided, the number of pupils in each class might range from 9+6 = 15 to 9+6 = 3. Because the maximum value exceeds 15, options C and D cannot accurately represent the number of students in the classes.

Option A's median value is 9, and its range is 13, therefore the smallest value is 9-6, which equals 3, and the greatest value is 9+6, which equals 15. This information is accurately represented by the box-and-whisker plot in option A.

Option B's median value is 9, but its range (from 9-5 = 4 to 9+5 = 14) is only 11, which is less than the range that could be achieved by the number of students. As a result, option B cannot accurately reflect the number of students enrolled in each class.

Thus, the response is A.

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The base and height of the parallelogram is B = 16 cm and H = 48 cm

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the area of the parallelogram be represented as A

Now , area of parallelogram A = bh

And , base of a parallelogram is one third its height

So , B = ( 1/3 )H

And , area of parallelogram is A = 768 cm²

On simplifying , we get

768 = ( 1/3 )H²

Multiply by 3 on both sides , we get

H² = 2304

Taking square roots on both sides , we get

H = 48 cm

So , the height of the parallelogram is 48 cm

And , the base of the parallelogram is 16 cm

Hence , the base and height of the parallelogram are 16 cm and 48 cm respectively

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The techniques of shifting, compressing, stretching, and reflecting can be used to transform the function g(x)=-x^(3)+7.

The techniques of shifting, compressing, stretching, and reflecting are used to transform functions. These techniques allow us to move the graph of a function up, down, left, or right, to make it wider or narrower, and to flip it over the x-axis or y-axis.

The function g(x)=-x^(3)+7 can be transformed using these techniques. For example, we can shift the graph of g(x) up by 2 units by adding 2 to the function: g(x)=-x^(3)+7+2=-x^(3)+9. We can also stretch the graph of g(x) vertically by multiplying the function by a constant greater than 1: g(x)=2(-x^(3)+7)=-2x^(3)+14.

Similarly, we can compress the graph of g(x) vertically by multiplying the function by a constant between 0 and 1: g(x)=0.5(-x^(3)+7)=-0.5x^(3)+3.5. We can also reflect the graph of g(x) over the x-axis by multiplying the function by -1: g(x)=-(-x^(3)+7)=x^(3)-7.

These are just a few examples of how the techniques of shifting, compressing, stretching, and reflecting can be used to transform the function g(x)=-x^(3)+7.

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