A man drove 14 mi directly east from his home, made a left turn at an intersection, and then traveled 9 mi north to his place of work. if a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?

Answer:

26 units

Step-by-step explanation:

By using the Pythagoras Theorem,

C^2 = A^2 + B^2

Substitute in given values for A and B.

C^2 = 10^2 + 24^2

= 100 + 576

= 676

[tex]c = \sqrt{676} \\ = 26[/tex]

Hope this helped! ^^

Sidenote: Pythagoras Theorem can only be used on right-angled triangles.

An isotope with z > 83, which lies close to the band of stability, will generally decay through decay.

Therefore, an isotope with z > 83, which lies close to the band of stability, will generally decay through decay.

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The standard deviation of the distribution of means is generally smaller than the standard deviation of the population of individuals.

The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation, which is also known as the square root of variance.

The population of individuals is always smaller than the entire population, therefore the possibilities for variances will be lower with the sample than with the population. The higher the population, the greater the chances for deviation from the mean.

Therefore, the standard deviation of the distribution of means is generally smaller than the standard deviation of the population of individuals.

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The equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]

To find the equation:

When we differentiate the function [tex]y=6 \sec (x)-12 \cos (x)[/tex], we get:

[tex]\begin{aligned}y^{\prime} &=\frac{d}{d x}(6 \sec (x)-12 \cos (x)) \\&=6 \frac{d}{d x}(\sec (x))-12 \frac{d}{d x}(\cos (x)) \\&=6 \sec (x) \tan (x)+12 \sin (x)\end{aligned}[/tex]

The slope of the tangent line is given by this derivative at the point [tex]x=\frac{\pi}{3}[/tex]:

As a result, this tangent line has the equation: [tex]y-6=18 \sqrt{3}\left(x-\frac{\pi}{3}\right)[/tex]

Therefore, the equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]

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The correct question is given below:

Find the equation of the tangent line to the curve y = 6 sec (x) at the point ([tex]\pi[/tex]/3, 6). Give your answer in the form y = mx + b where m is the slope and b is the y--intercept.

Answer:

The zeros are x =5, -7/2

Step-by-step explanation:

To find the zeros, set the expression equal to zero

(x-5)(2x+7) =0

Using the zero product property

(x-5)=0     (2x+7)=0

Solve each equation

x=5               2x = -7

x=5                  x = -7/2

The zeros are x =5, -7/2

Answer:

5, -7/2

Step-by-step explanation:

[tex]x - 5 = 0 = 5\\\\2x + 7 = 0\\2x + -7 = 0\\\frac{2x}{2} = \frac{-7}{2}\\ x = \frac{-7}{2}\\x = -\frac{7}{2}[/tex]

Thus,

x = 5

x = -7/2

I'm assuming the equation is

[tex]\frac{3}{4}y - \frac{2}{4}y+7 = \frac{2}{4}y-1[/tex]

Let me know if the equation is different so I can update the solution.

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

Fractions are a pain to deal with, so it's best to eliminate them whenever we can. In equations like this, we can multiply both sides by 4 since this is the LCD (which stands for "lowest common denominator").

If we multiply both sides by 4, then all the denominators of 4 will cancel.

We'll have these steps:

[tex]\frac{3}{4}y - \frac{2}{4}y+7 = \frac{2}{4}y-1\\\\4\left(\frac{3}{4}y - \frac{2}{4}y+7\right) = 4\left(\frac{2}{4}y-1\right)\\\\3y - 2y + 28 = 2y - 4 \ \ \text{ ... denominators cancel after distributing}\\\\y + 28 = 2y - 4\\\\y- 2y =- 4-28\\\\-y = -32\\\\y = \frac{-32}{-1}\\\\y = 32\\\\[/tex]

Answer:

[tex]y=32[/tex]

Step-by-step explanation:

Given the following question:

[tex]\frac{3}{4}y-\frac{2}{4}y+7=\frac{2}{4}y-1[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y+7-7=\frac{2}{4}y-1-7[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y=\frac{y}{2}-8[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y-\frac{y}{2}=\frac{y}{2}-8-\frac{y}{2}[/tex]
[tex]-\frac{y}{4}=-8[/tex]
[tex]4\left(-\frac{y}{4}\right)=4\left(-8\right)[/tex]
[tex]\frac{-y}{-1}=\frac{-32}{-1}[/tex]
[tex]y=32[/tex]

Therefore "y = 32."

Hope this helps.

Option D x+2y+10 .

A trinomial with a constant term will have three terms, and one of those terms will be a constant, which is a number.

we also know about the Constant

A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.

Some relatable terms are :

Monomial: Polynomial having a single term.

Binomial: Polynomial having two terms.

Trinomial: Polynomial having three terms.

In given option we'll define

in option A there is no constant .

option B there i sonly given x which is also not constant.

further in option c it is simply binomial in which only two terms are given without constant .

so at last conclusion is in option D there are three terms are given with one constant which is number 10 .

x+2y+10 is trinomial with a constant.

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Answer:

Sum of ages is 35

Since there are two persons and it says four years from now, each year 2 more years will be added on to the 35 so year 1: 2years Year 2:4years Year 3:6years Year 4 : 8years

35+8= 43

Remember that Melanie will be 5 years older ( which she should have already been)

so 43+5= 48 ( Melanie's age)

and 48-5 = 43 ( Her brother's age)

Deciles are 61.3 and 67.7

What are deciles?

Deciles are measures of position calculated on a set of data. The deciles are the values that separate a distribution into ten equal parts, where each part contains the same number of observations). The decile is a member of the wider family of quantiles.

Given:

Normal distribution =64.5 inches

Standard deviation=σ =2.5 inches

​

So, here the z- score for left decile= -1.28

and for right decile= +1.28

we know,

z= x-[tex]\mu[/tex]/σ

x= zσ + [tex]\mu[/tex]

x=-1.28*2.5 + 64.5

x= 61.3  and,

x= 1.28*2.5 + 64.5

x=67.7

hence, the deciles are 61.3 and 67.7

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Answer:

19

Step-by-step explanation:

5w+3°=98°

5w=98°-3°

5w=95°

therefore w=95/5=19

The dimensions of the rectangle are:

width = 10 units

length = 17 units

We are given to find the dimensions of a rectangle with an area equal to the parallelogram with vertices (6, 21), (14, 15), (6, 0), and (-2, 6).

If we have two points with coordinates as (a, b) and (c, d) The distance is given by the formula: √[(c - a )² + (d - b)²]

Now, of the coordinates are labelled as;

A(6, 21), B(14, 15), C(-2,6),  (6,0)

Thus;

AB = √(14 - 6)² + (15 - 21)² = √100 = 10 = CD

AC = √(-2 - 6)² + (6 - 21)² = 64 + 225 = √289 = 17 = BD

Thus the dimensions of the rectangle are:

AB = 10 = width

AC = 17 = length

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We get the surface area as 202 inches² and volume as 168 inches³.

The surface area of a cuboid is given by:

Surface area = 2xy + 2xz + 2yz

Here length = x = 7 inches

Breadth = y = 3 inches

Height = z = 8 inches.

Substituting the values in the formula, we get that:

Surface area = A = 2(7)(3) + 2(7)(8) + 2(3)(8) inches²

A = 42 + 112 + 48 inches²

A = 42 + 160 inches²

A = 202 inches²

Volume of a cuboid is given by :

Volume = xyz

Substituting the values, we get that:

Volume = (7) (3) (8) inches³

Volume = 21 × 8 inches³

Volume = 168 inches³.

Therefore, we get the surface area as 202 inches² and volume as 168 inches³.

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The method of altering a graph to produce a different version of the one that came before is known as graph transformation. The graphs are movable in the x-y plane and can be translated. Along with these modifications, they can also be stretched.

Horizontal stretching

Vertical stretching

Vertical translation

Horizontal translation

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The solution to the fraction expression -2 1/3 + (-1 3/4) is -4 1/12

The fraction expression is given as

-2 1/3 + (-1 3/4) =

Express the terms of the expression as an improper fraction

So, we have

-2 1/3 + (-1 3/4) = -7/3 + (-7/4)

Remove the bracket in the above expression.

So, we have

-2 1/3 + (-1 3/4) = -7/3 - 7/4

Take the LCM in the above expression.

So, we have

-2 1/3 + (-1 3/4) = (-7 * 4 - 7 * 3)/12

Evaluate the difference

-2 1/3 + (-1 3/4) = -49/12

Express the fraction as a mixed fraction

-2 1/3 + (-1 3/4) = -4 1/12

Hence, the solution to the fraction expression -2 1/3 + (-1 3/4) is -4 1/12

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The number of years to the nearest hundredth is t = 21 years and 3 months.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

It is given that:

A = $25,600

P = $29,00

r = 10.4 = 0.104

n = 4

[tex]\rm 25600 = 2900(1+\dfrac{0.104}{4})^{4t}[/tex]

After solving:

t = 21.212 years

Or

t = 21 years and 3 months

Thus, the number of years to the nearest hundredth is t = 21 years and 3 months.

The complete question is:

How long will it take for $2900 to grow to $25,600 at an interest rate of 10.4% if the interest is compounded quarterly round the number of years to the nearest hundredth?

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The required density of the given solid substance is 7.07 g/cm³.

What is the density of a substance?

The density of a substance is the property which is obtained by dividing the mass of the given substance by its volume. Its SI unit is kg/m³.

Calculation for the density of a solid substance

Mass of the given substance = 120 g

Side of cube, a = 2.57 cm

The volume of the given substance = a³

= 2.57³

= 16.97 cm³

The density of the given substance is given by the mass of the substance/volume of the substance

= 120 / 16.97

= 7.07 g/cm³

Hence, the density of the given solid substance is 7.07 g/cm³.

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Answer:

I think it's C but I'm not 100% sure

Answer:

Answer:

0.5

Step-by-step explanation:

12/24 = 0.5

6/12 = 0.5

3/6 = 0.5

1.5/3 = 0.5

Answer: 0.5

Now, it is not a function, same domain has different ranges

Answer:

31/35

Step-by-step explanation:

3/5 + 2/7 = (3 × 7) / (5 × 7)  + (2 × 5) / (7 × 5)

= 21/35 + 10/35

= 31/35.

The real distance between Hooperville and Michael's home town is 116.667 miles.

Scales are ratios commonly used to contain great extensions of land in images and maps and offer a quick though efficient manner to estimate distances. The real distance between Hoopersville and Michael's home town can be found thorugh this formula:

d' = d / r      

Where:

If we know that d = 3.5 in and r = 1.5 in / 50 mi, then the real distance between Hooperville and Michael's hown town is:

d' = 3.5 in / (1.5 in / 50 mi)

d' = 116.667 mi

The real distance between Hooperville and Michael's home town is 116.667 miles.

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Answer:

11

Step-by-step explanation:

Plug 4 into the x, 6(4) = 24

24 - 13 = 11

The coordinates of the other endpoint U are found to be (Xu, Yu) = (10, 5).

The coordinates are a pair of numbers which characterize the exact location of a point on a cartesian plane through using horizontal and vertical lines.

Now, as per the question.

To find the coordinates of U, use the midpoint formula with the coordinates of points u and v (Xv, Yv) and (Xm, Ym) respectively.

Let's refer to them as (Xu, Yu)

Midpoint formula {(Xv + Xu)/2, (Yv + Yu)/2)}

Fill in the recognized coordinates as needed.

Point V at (10, 7) =  (Xv, Yv)

Midpoint, point M at (10, 6) = (Xm, Ym)

For the x coordinates;

(10 + Xu)/2 = 10

Xu = 10.

Similarly for the y coordinate;

(7 + Yu)/2 = 6

7 + Yu = 12

Yu = 5

We can test this by plugging U's coordinates into the midpoint formula.

(10 + 10)/2 = 20/2 = 10

(5 + 7)/2 = 12/2 = 6

Therefore, the coordinates of the are (Xu, Yu) = (10, 5).

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The mistake done by Noah in his construction is that; length of the line segment AB and AC should be equal.

The steps in bisecting an angle say PQR is as follows;

Start with angle PQR that we will bisect.

1.  Place the compasses' point on the angle's vertex Q.

2.  Adjust the compasses to a medium wide setting. The exact width is not important.

3.  Without changing the compasses' width, draw an arc across each leg of the angle.

4.  The compasses' width can be changed here if desired. Recommended: leave it the same.

5.  Place the compasses on the point where one arc crosses a leg and draw an arc in the interior of the angle.

6.  Without changing the compasses setting repeat for the other leg so that the two arcs cross.

7.  Using a straightedge or ruler, draw a line from the vertex to the point where the arcs cross.

8. This is the bisector of the angle ∠PQR.

Therefore, the mistake done by Noah is that length of the line segment AB and AC should be equal in order to bisect it.

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Answer:

4

Step-by-step explanation:

After multiplying 0.7 by 0.003 there are two zero to right of the decimal point in the product.

Here,

Samuya is multiplying 0.7 by 0.003.

We have to find, zeros will be to the right of the decimal point in the product.

What is Product?

The product of two numbers is the result you get when you multiply them together.

Now,

Product of 0.7 and 0.003 we get;

0.7 x 0.003 = 0.0021

Clearly, there are two zero to the right of the decimal point in the product.

So, After multiplying 0.7 by 0.003 there are two zero to right of the decimal point in the product.

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Given that Point E is the midpoint of line segment YT, the numerical value of x is 2.

A midpoint is simply a point that divides a segment into two equal halves.

Given the data in the question;

Point E is the midpoint of line segment YT, YT is divided into two equal halves. Hence, Two times Line segment YE equals to YT.

2( Line segment YE ) = Line segment YT

Plug in the given values and solve for x.

2( Line segment YE ) = Line segment YT

2( 3x + 1 ) = 14

Expand using distributive property

2 × 3x + 2 × 1 = 14

6x + 2 = 14

Collect like terms

6x = 14 - 2

6x = 12

6x/6 = 12/6

x = 12/6

x = 2

Given that Point E is the midpoint of line segment YT, the numerical value of x is 2.

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