‍The length of a jogging trail is 3528 m. A jogger wants to complete the trail within 30 min. How many meters must the jogger travel each minute? 1174/15 m 1173/10 m 1171/3 m 1173/5 m

The correct answer is A. y = 2x +1

Explanation:

An equation is a statement that shows equality. In this context, the equation should lead to two equal numbers even if the values of y and x change. In this context, the correct equation is y= 2X + 1 because this is the only one, in which, the value of Y is always equivalent to 2x + 1. To prove this, let's replace y and x for the values of the table.

First  column

5 = 2 · 2 + 1

5 = 4 + 1

5 = 5

Second Column

9 = 2 · 4 + 1

9 = 8 + 1

9 = 9

Third column

13 = 6 · 2 + 1

13 = 12 + 1

13 =  13

Fourth column

17 = 8 · 2 + 1

17 = 16 + 1

17 = 17

Answer:

(3,-2)

Step-by-step explanation:

Given equations of line

3x-2y=13

2y+x+1=0​

=> x = -1 -2y

Point of intersection will coordinates where both equation have same value of (x,y)

top get that we have to solve the both equations by using method of substitution of simultaneous equation.

using this value of x in 3x-2y=13, we have

3(-1-2y) -2y = 13

=> -3 -6y-2y = 13

=> -8y = 13+3 = 16

=> y = 16/-8 = -2

x = -1 - 2y = -1 -2(-2) = -1+4= 3

Thus, point of intersection of line is (3,-2)

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Explanation:

The interval [tex]40 \le x < 50[/tex] has the midpoint (40+50)/2 = 90/2 = 45 which represents the average value from this interval. We don't know what the exact 21 values are from this interval, but the best guess we can make is each value is on average 45.

Similarly, the interval [tex]50 \le x < 60[/tex] has the midpoint (50+60)/2 = 110/2 = 55 which represents the average value in this interval.

The set of all midpoints is: {45, 55, 65, 75, 85}. You start at 45 and add 10 to each term to get the next term. Let's say x represents the midpoint. We'll multiply each x value with its corresponding frequency (f) to get a new column of values you see in the table below.

For example, in the first row, we have 45*21 = 945

Add up everything in the x*f column and we'll get this sum:

945+2145+2600+2550+2380 = 10,620

We'll divide this over the total frequency, which is the sum of the frequency column (21+39+40+34+28 = 162)

We then arrive at this estimated final answer: (10,620)/(162) = 65.55555... where the '5's go on forever. This rounds to 65.56

Answer:

The circumference is 50.24 in. and the area is 200.96 in².

Step-by-step explanation:

The circumference formula is C = 2πr where C = Circumference, π = pi and r = radius. We know that r = 8 and π = 3.14 and that we're solving for C, so we can substitute those values into the equation to get C = 2 * 3.14 * 8 = 50.24 in.

The area formula is A = πr² where A = Area, π = pi and r = radius. Again, we're solving for A and we know that r = 8 and π = 3.14 so A = 3.14 * 8² = 3.14 * 64 = 200.96 in².

Answer:

The circumference is 50.24 in. and the area is 200.96 in².

Step-by-step explanation:

MARK SNOG AS BRAINLIEST

Answer:

-3x - 7y = 36

Step-by-step explanation:

The given line -3x - 7y = 10 has an infinite number of parallel lines, all of the form -3x - 7y = C.

If we want the equation of a line parallel to -3x - 7y = 10 that passes through (-5, -3), we substitute -5 for x in -3x - 7y = 10 and substitute -3 for y in -3x - 7y = 10:

-3(-5) - 7(-3) = C, or

15  + 21 = C, or C = 36

Then the desired equation is -3x - 7y = 36.

Answer:

Step-by-step explanation:

The height on the side of the deck (h) can be found using the Pythagorean theorem. It tells you ...

  6^2 + h^2 = 10^2

  h = √(10^2 -6^2) = √64 = 8

The ladder touches the deck 8 feet above the ground. Tom is not afraid of that height.

Answer:

A) ( -8, -32 )

Step-by-step explanation:

Given function : f (x,y) = 21 - 4x^2 - 16y^2

point p( 1,1,1 ) on surface

Gradient of F

attached below is the detailed solution

Answer:

x=50 and y=80

Step-by-step explanation:

ATQ, x+50+y=180 and y+2x=180. x=50 and y=80

Answer:

(- 1, 4 )

Step-by-step explanation:

The line x + 2 = 0 can be expressed as

x + 2 = 0 ( subtract 2 from both sides )

x = - 2

This is the equation of a vertical line parallel to the y- axis and passing through all points with an x- coordinate of - 2

Thus (- 3, 4 ) is 1 unit to the left of - 2

Under a reflection in the line x = - 2

The x- coordinate will be the same distance from x = - 2 but on the other side while the y- coordinate remains unchanged.

Thus

(- 3, 4 ) → (- 1, 4 )

Answer:

[tex]\boxed{50}[/tex]

Step-by-step explanation:

Because the initial temperature is 40 degrees and it increases by 10, add the two values together to get the final temperature.

40 + 10 = 50

Therefore, the final answer is 50 degrees.

Answer:

50

Step-by-step explanation:

If it starts at 40 degrees and increases 10 degrees, it is going to be 50 degrees.  Increases means adding, so it is asking you to add 10 to 40 which is 50.  If it asks decreases in the future you will have to subtract.

Answer:

C  -3 < x ≤ 4

Step-by-step explanation:

-9 < 4x + 3 ≤ 19.

Subtract 3 from all sides

-9-3 < 4x + 3-3 ≤ 19-3

-12 < 4x  ≤ 16

Divide by 4

-12/4 < 4x/4 ≤ 16/4

-3 < x ≤ 4

Answer:

Mean; 762,143

Median; 800,000

Step-by-step explanation:

Mean;

Add all of the numbers together, then divide by how many there are.

There are seven home prices in total, add them together then divide by 7.

5,335,000 divided by 7 = 762,142.85714285; simplified to 762,143.

Median;

Organize the numbers from least to greatest

455,000, 780,000, 795,000, 800,000, 810,000, 840,000, 855,000

Then find the number in the middle

800,000

Answer:

The balance in two separate bank accounts grows each month at different rates. the growth rates for both accounts are represented by the functions f(x) = 2x and g(x) = 4x 12. in what month is the f(x) balance greater than the g(x) balance?

Answer:

6 months

A function is a relationship between inputs where each input is related to exactly one output.

x = 5,

f(5) = [tex]2^5\\[/tex] = 32

g(5) = 4 x 5 + 12 = 20 + 12 = 32

x = 6,

f(6) = [tex]2^6[/tex] = 64

g(6) = 4 x 6 + 12 = 24 + 12 = 36

At month 6 the funds in the f(x) bank account exceed those in the g(x) bank account.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = [tex]2^{x}[/tex]

g(x) = 4x + 12

x = number of months

Now,

x = 3,

f(3) = 2³ = 8

g(3) = 4 x 3 + 12 = 12 + 12 = 24

x = 4,

f(4) = [tex]2^4[/tex] = 16

g(4) = 4 x 4 + 12 = 16 + 12 = 28

x = 5,

f(5) = [tex]2^5\\[/tex] = 32

g(5) = 4 x 5 + 12 = 20 + 12 = 32

x = 6,

f(6) = [tex]2^6[/tex] = 64

g(6) = 4 x 6 + 12 = 24 + 12 = 36

We see that,

At x = 6,

f(5) = 64

g(5) = 36

Thus,

At month 6 the funds in the f(x) bank account exceed those in the g(x) bank account.

Learn more about functions here:

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Answer:

7

Step-by-step explanation:

First plug in the variable amounts so the expression now looks like this:

(3 × 4 - 12) + 1/2(4 × 6 - 10)

Now, start by solving the multiplication parts first, so it now looks like this:

(12 - 12) + 1/2(24 - 10)

Now, apply the rules of order of operation, so start by solving what's in parenthesis. It should now look like this: (0) + 1/2(14)

Next, solve the multiplication part, so it now looks like this: 0 + 7

Solve that and the answer is 7.

Answer:

12* 12 = 144

thus 4*12 = 48 feet of fence

Step-by-step explanation:

Answer:

6.034

Step-by-step explanation:

6 is a whole number.

.034 because it is 34 thousandths, not 34 hundredths.

Answer:

q > 27/61

Step-by-step explanation:

50q + 43 > −11q + 70

Add 11 q to each side

50q+11q + 43 > −11q+11q + 70

61q+43> 70

Subtract 43 from each side

61q> 27

Divide each side by 61

61q/61> 27/61

q > 27/61

Answer:

Step-by-step explanation:

The congruence correspondence between the two given triangles is HL as one leg and hypotenuse are given equal.

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OAmalOHopeO

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9514 1404 393

Answer:

  x = (√6)/10^0.7 ≈ 0.488737

Step-by-step explanation:

It can work reasonably well to take antilogs first.

  [tex]\log(6)-2\log(x)=1.4\\\\\dfrac{6}{x^2}=10^{1.4}\\\\\dfrac{6}{10^{1.4}}=x^2\\\\x=\dfrac{\sqrt{6}}{10^{0.7}}\approx0.488737[/tex]

Answer:

A.23

maaf kalosalah !(!)!(!)!(!)!(!)!(!)!(!)!(!)!(!)!

Considering you have four initial conditions (the last of which should probably read [tex]y'''(0)=0[/tex]), I'm assuming the ODE is

[tex]y^{(4)}(t)+2y''(t)+y(t)=\sin t[/tex]

with [tex]y(0)=1[/tex], [tex]y'(0)=-2[/tex], [tex]y''(0)=3[/tex], and [tex]y'''(0)=0[/tex].

Take the Laplace transform of both sides, denoting the transform of [tex]y(t)[/tex] by [tex]Y(s)[/tex]:

[tex](s^4Y(s)-s^3y(0)-s^2y'(0)-sy''(0)-y'''(0))+2(s^2Y(s)-sy(0)-y'(0))+Y(s)=\dfrac1{s^2+1}[/tex]

Solve for [tex]Y(s)[/tex]:

[tex](s^4+2s^2+1)Y(s)-s^3+2s^2-5s+4=\dfrac1{s^2+1}[/tex]

[tex]Y(s)=\dfrac{1+(s^3-2s^2+5s-4)(s^2+1)}{(s^2+1)(s^4+2s^2+1)}[/tex]

Notice that

[tex]s^4+2s^2+1=(s^2+1)^2[/tex]

[tex]\implies Y(s)=\dfrac{1+(s^3-2s^2+5-4)(s^2+1)}{(s^2+1)^3}[/tex]

and simplify a bit to get

[tex]Y(s)=\dfrac{s^5-2s^4+6s^3-6s^2+5s-3}{(s^2+1)^3}[/tex]

Decompose [tex]Y(s)[/tex] into partial fractions:

[tex]\dfrac{s^5-2s^4+6s^3-6s^2+5s-3}{(s^2+1)^3}=\dfrac{a_0+a_1s}{s^2+1}+\dfrac{b_0+b_1s}{(s^2+1)^2}+\dfrac{c_0+c_1s}{(s^2+1)^3}[/tex]

[tex]s^5-2s^4+6s^3-6s^2+5s-3=(a_0+a_1s)(s^2+1)^2+(b_0+b_1s)(s^2+1)+(c_0+c_1s)[/tex]

[tex]s^5-2s^4+6s^3-6s^2+5s-3=a_1s^5+a_0s^4+(2a_1+b_1)s^3+(2a_0+b_0)s^2+(a_1+b_1+c_1)s+(a_0+b_0+c_0)[/tex]

[tex]\implies\begin{cases}a_1=1\\a_0=-2\\2a_1+b_1=6\\2a_0+b_0=-6\\a_1+b_1+c_1=5\\a_0+b_0+c_0=-3\end{cases}[/tex]

[tex]\implies a_0=-2,a_1=1,b_0=-2,b_1=4,c_0=1,c_1=0[/tex]

So we have

[tex]Y(s)=\dfrac{s-2}{s^2+1}+\dfrac{4s-2}{(s^2+1)^2}+\dfrac1{(s^2+1)^3}[/tex]

Split up the first term to get two easy inverse transforms:

[tex]L^{-1}\left[\dfrac s{s^2+1}\right]=\cos t[/tex]

[tex]L^{-1}\left[-\dfrac2{s^2+1}\right]=-2\sin t[/tex]

Also split up the second term, but use the convolution theorem, which says

[tex]L\left[(\alpha \ast \beta)(t)\right]=A(s)\cdot B(s)[/tex]

where [tex]A(s)[/tex] and [tex]B(s)[/tex] are the Laplace transforms of [tex]\alpha(t)[/tex] and [tex]\beta(t)[/tex], respectively, and the convolution is defined by

[tex](\alpha \ast \beta)(t)=\displaystyle\int_0^t\alpha(\tau)\beta(t-\tau)\,\mathrm d\tau[/tex]

Take

[tex]A(s)=\dfrac{4s}{s^2+1}\text{ and }B(s)=\dfrac1{s^2+1}[/tex]

so that

[tex]\alpha(t)=4\cos t\text{ and }\beta(t)=\sin t[/tex]

and their convolution is

[tex]L^{-1}\left[\dfrac{4s}{(s^2+1)^2}\right]=(\alpha \ast \beta)(t)=2t\sin t[/tex]

Next, take

[tex]A(s)=-\dfrac2{s^2+1}\text{ and }B(s)=\dfrac1{s^2+1}[/tex]

[tex]\implies \alpha(t)=-2\sin t\text{ and }\beta(t)=\sin t[/tex]

[tex]\implies L^{-1}\left[-\dfrac2{(s^2+1)^2}\right]=t\cos t-\sin t[/tex]

You can treat the third term similarly, but with an extra step. First compute

[tex]L^{-1}\left[\dfrac1{(s^2+1)^2}\right][/tex]

by taking

[tex]A(s)=B(s)=\dfrac1{s^2+1}[/tex]

[tex]\implies \alpha(t)=\beta(t)=\sin t[/tex]

Then

[tex]L^{-1}\left[\dfrac1{(s^2+1)^2}\right]=\dfrac{\sin t-t\cos t}2[/tex]

Next, take

[tex]A(s)=\dfrac1{(s^2+1)^2}\text{ and }B(s)=\dfrac1{s^2+1}[/tex]

[tex]\implies \alpha(t)=\dfrac{\sin t-t\cos t}2\text{ and }\beta(t)=\sin t[/tex]

[tex]\implies L^{-1}\left[\dfrac1{(s^2+1)^3}\right]=\dfrac{(3-t^2)\sin t-3t\cos t}8[/tex]

Thus we end up with the solution,

[tex]y(t)=(\cos t-2\sin t)+(2t\sin t+t\cos t-\sin t)+\dfrac{(3-t^2)\sin t-3t\cos t}8[/tex]

[tex]\boxed{y(t)=\dfrac{(8+5t)\cos t+(-21+16t-t^2)\sin t}8}[/tex]

Answer:

10

Step-by-step explanation:

-3 = 7 - 10

-3 = -3

Answer:

Three points are (0,-5.5), (-1,-3), (-2.2,0) and graph is shown below.

Step-by-step explanation:

The given equation is

[tex]-2y=5x+11[/tex]

We need to find three points that solve the equation.

Put x=0,

[tex]-2y=5(0)+11[/tex]

[tex]-2y=11[/tex]

[tex]y=-5.5[/tex]

Put x=-1,

[tex]-2y=5(-1)+11[/tex]

[tex]-2y=6[/tex]

[tex]y=-3[/tex]

Put y=0,

[tex]-2(0)=5x+11[/tex]

[tex]5x=-11[/tex]

[tex]x=-2.2[/tex]

So, three points (0,-5.5), (-1,-3) and (-2.2,0) are the solutions of the given equation.

Plot these points on a coordinate plane and connect them by a straight line as shown below.

9514 1404 393

Answer:

  108 cm²

Step-by-step explanation:

The area of a triangle is given by the formula ...

  A = 1/2bh

where b represents the base length, and h represents the height--the perpendicular distance from the base to the opposite vertex. The area of this triangle is ...

  A = 1/2(12 cm)(18 cm) = 108 cm²

Answer:

The error is the use of wrong trigonometric ratio formula.

Sine was used instead of tangent.

It should be: [tex] tan(A) = \frac{36}{84} [/tex]

Step-by-step explanation:

Side length, 36, is opposite to <A. Side length, 84, is the adjacent side. Therefore, the right trigonometric ratio formula to use is:

[tex] tan(A) = \frac{opposite}{adjacent} [/tex]

[tex] tan(A) = \frac{36}{84} [/tex]

[tex] A = tan^{-1}(\frac{36}{84}) [/tex]

m<A ≈ 23°

The error made was the use of wrong trigonometric ratio formula.

In functions; transformations are used to move lines, points, curves or shapes across the graph (i.e. up, down, right or left). After the transformation of [tex]f(x) = \log\ x[/tex], the resulting function is [tex]g(x) = 2\log\ (-x + 4) - 6[/tex]

Given that:

[tex]f(x) = \log\ x[/tex]

When translated 4 units left, the rule of translation is:

[tex](x,y) \to (x + 4,y)[/tex]

So, we have:

[tex]f'(x) = \log\ (x + 4)[/tex]

When translated 3 units down, the rule of translation is:

[tex](x,y) \to (x,y-3)[/tex]

So, we have:

[tex]f"(x) = \log\ (x + 4) - 3[/tex]

When reflected about the y-axis, the rule of reflection is:

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex]f'"(x) = \log\ (-x + 4) - 3\\[/tex]

Lastly, when it is vertically stretched by 2; the rule is:

[tex](x,y) \to (x,2y)[/tex]

So, we have:

[tex]g(x) = 2[\log\ (-x + 4) - 3][/tex]

Open bracket

[tex]g(x) = 2\log\ (-x + 4) - 6[/tex]

See attachment for the graph of function f(x) and the new function g(x)

Read more about function transformations at:

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Greetings from Brasil...

If  domain is (a,b] and the range is [c,d), so:

f(a) = c

f(b) = d

so

g(x) = m × f(x) + n

g(a) = m × f(a) + n       how f(a) = c, then

g(a) = mc + n

g(b) = m × f(b) + n

g(b) = md + n

So

Answer: see below

Step-by-step explanation:

A) y has the smaller radius so this is the Minor Axis

B) y has the smaller radius so these are the CoVertices

C) x has the bigger radius so these are the Vertices

D) This is the Center of the ellipse.

F & G) These are the Foci (plural for Focus)

H) x has the bigger radius so this is the Major Axis

Answer:

The answer is D)90

Hope I helped

Answer:

[tex]\huge\boxed{7^{\frac{2}{15}}}[/tex]

Step-by-step explanation:

[tex]\dfrac{\sqrt[3]7}{\sqrt[5]7}\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\=\dfrac{7^\frac{1}{3}}{7^\frac{1}{5}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=7^{\frac{1}{3}-\frac{1}{5}}\qquad\text{find the common denominator (15)}\\\\=7^{\frac{(1)(5)}{(3)(5)}-\frac{(1)(3)}{(5)(3)}}=7^{\frac{5-3}{15}}=7^{\frac{2}{15}}[/tex]

Answer:

D. 7 to the power of two fifteenths

Step-by-step explanation: