Round 241,639 to the nearest thousand

Answers

Answer 1

Hi!

The thousandths place is the fourth digit to the left of the decimal.

241,639

Look to the right of the 1.
Since 6 is greater than 4, we round up.

242,000

The answer is 242,000

Hope this helps! :)

Related Questions

Evaluate the surface integral. ∫∫s (x2 + y2 + z2) ds s is the part of the cylinder x2 + y2 = 16 that lies between the planes z = 0 and z = 5, together with its top and bottom disks.

Answers

Decompose the surface into three components, [tex]\mathbf r_1,\mathbf r_2,\mathbf r_3[/tex], corresponding respectively to the cylindrical region and the top and bottom disks:

[tex]\mathbf r_1(u,v)=\begin{cases}x(u,v)=4\cos u\\y(u,v)=4\sin u\\z(u,v)=v\end{cases}[/tex]
where [tex]0\le u\le2\pi[/tex] and [tex]0\le v\le5[/tex],

[tex]\mathbf r_2(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=0\end{cases}[/tex]
where [tex]0\le u\le4[/tex] and [tex]0\le v\le2\pi[/tex], and

[tex]\mathbf r_3(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=5\end{cases}[/tex]
where [tex]0\le u\le4[/tex] and [tex]0\le v\le2\pi[/tex].

For the cylinder, we have

[tex]\dfrac{\partial\mathbf r_1}{\partial u}\times\dfrac{\partial\mathbf r_1}{\partial v}=\langle4\cos u,4\sin u,0\rangle\implies\left\|\dfrac{\partial\mathbf r_1}{\partial u}\times\dfrac{\partial\mathbf r_1}{\partial v}\right\|=4[/tex]

and the integral over this surface is

[tex]\displaystyle\iint_{\text{cyl}}(x^2+y^2+z^2)\,\mathrm dS=4\int_{v=0}^{v=5}\int_{u=0}^{u=2\pi}((4\cos u)^2+(4\sin u)^2+v^2)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle320\int_{u=0}^{u=2\pi}\mathrm du+8\pi\int_{v=0}^{v=5}v^2\,\mathrm dv[/tex]
[tex]=640\pi+\dfrac83\pi(125)[/tex]
[tex]=\dfrac{2920\pi}3[/tex]

Bottom disk:

[tex]\dfrac{\partial\mathbf r_2}{\partial u}\times\dfrac{\partial\mathbf r_2}{\partial v}=\langle0,0,u\rangle\implies\left\|\dfrac{\partial\mathbf r_2}{\partial u}\times\dfrac{\partial\mathbf r_2}{\partial v}\right\|=u[/tex]

and the integral over the bottom disk is

[tex]\displaystyle\iint_{z=0}(x^2+y^2+z^2)\,\mathrm dS=\int_{v=0}^{v=2\pi}\int_{u=0}^{u=4}u((u\cos v)^2+(u\sin v)^2)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle2\pi\int_{u=0}^{u=4}u^3\,\mathrm du[/tex]
[tex]=128\pi[/tex]

The setup for the integral along the top disk is similar to that for the bottom disk, except that [tex]z=5[/tex]:

[tex]\displaystyle\iint_{z=5}(x^2+y^2+z^2)\,\mathrm dS=\int_{v=0}^{v=2\pi}\int_{u=0}^{u=4}u((u\cos v)^2+(u\sin v)^2+5^2)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle2\pi\int_{u=0}^{u=4}(u^3+25u)\,\mathrm du[/tex]
[tex]=528\pi[/tex]

Finally, the value of the integral over the entire surface is the sum of the integrals over the component surfaces:

[tex]\displaystyle\iint_S(x^2+y^2+z^2)\,\mathrm dS=\frac{2920\pi}3+128\pi+528\pi=\dfrac{4888\pi}3[/tex]

Final answer:

Evaluate the given surface integral by parameterizing the surface and computing the integral on each surface separately. Take the antiderivatives of both dimensions defining the area, from the bounds of the integral for an accurate solution.

Explanation:

The problem you've presented is a surface integral in the field of calculus, specifically relating to multivariable calculus. To solve this, we need to evaluate the integral over the specified parts of the cylinder and the top and bottom disks. We start by parameterizing the surface. Given that our cylinder is x² + y² = 16 between z = 0 and z = 5, we can use cylindrical coordinates with the parameterization: r(θ, z) = <4cos(θ), 4sin(θ), z> for 0 ≤ θ ≤ 2π and 0 ≤ z ≤ 5. With this parameterization, you can derive the equation for the surface integral and solve it.

When working with surface integrals, it's essential to remember that you are totaling up the quantity across the entire surface of an object. In such a situation, we could handle this problem by separating it into three parts: the side of the cylinder, the top disk, and the bottom disk, and compute the integral on each surface separately.

The integral can be solved by taking the antiderivatives of both dimensions defining the area, with the edges of the surface in question being the bounds of the integral. You can apply this approach to all the separate parts of this question.

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How many degrees would the hour hand move in 4hrs?

Answers

a complete circle is 360 degrees, there are 12 numbers on a clock

360/12 = 30 degrees between each number

30 * 4 = 120 degrees in 4 hours

John has taken out a loan for college. He started paying off the loan with the first payment of $100. Each month he pays, he wants to pay back 1.1 times the amount he payed the month before. Explain to John how to represent his first 20 payments in sequence notation. Then explain how to find the sum of the first 20 payments using complete sentences.

Answers

John's payments are
month 1: $100
month 2: $100*(1.1)
month 3: $100*(1.1)²
month 4: $100*(1.1)³

...

The payments form the geometric sequence
a, ar, ar², ..., arⁿ
where
a = $100
r = 1.1

The sum of the first n terms is
[tex]S_{n} = \frac{a(1-r^{n})}{1-r} [/tex]

Therefore the sum of the first 20 payments is
S₂₀ = [$100(1 - 1.1²⁰)]/(1 - 1.1)
= $5727.50

John makes a total of $5727.50 in the first 20 payments.

The infinite sequence –1, –2, –3, –4, –5, ... can be generated with which explicit formula?

Answers

Answer:

An = (-1)* n

Step-by-step explanation:

An = ( -1) * n

A2 = (-1 ) * 2 = -2

A3= ( -1 ) * 3 = -3

A4= ( -1 ) * 4 = -4

A5= ( -1 ) * 5 = -5

An explicit formula also known as an exact formula is a mathematical formula used to find the nth term in a series or sequence . hence the explicit formula used to find the nth term of this sequence can be represented as

An = ( -1 ) * n where n = number of the next term

Answer:

Step-by-step explanation:

i got it right

For an analysis of variance, the term “one-way” refers to

Answers

In statistics, you have statistical tests called ANOVA or Analysis of Variance. There is One-Way ANOVA and Two-Way ANOVA. You can only use One-Way ANOVA when you are testing only one dependent variable against at least two independent variables. For example, you want to find the statistics of the adsorption capacity with respect to two of its factors: pH and temperature. In this test, you only get the variance once and it is based on the F table of distibution. The other name for this, is actually the F-test.

Lily is standing at horizontal ground level with the base of the Sears Tower. The angle formed by the ground and the line segment from her position to the top of the building is 15.7°. The Sears Tower is 1450 feet tall. Find Lily's distance from the Sears Tower to the nearest foot.

Answers

This is the concept of trigonometry, the distance of Lily from the tower will be given by:
tan theta=[opposite]/[adjacent]
opposite=1450 ft
adjacent=x ft
theta=15.7
thus;
1450/x=tan15.7
hence;
x=1450/tan15.7
x=5,158.54 ft
x=5,159 (to the nearest foot)

Factor 2x^2-128 completely

Answers

2x² - 128

2(x² - 64), but (x² - 64) = x² - 8² (difference of 2 squares),[a²-b²=(a-b)(a+b)]

2(x² - 64) = 2(x² - 8²) = 2(x-8)(x+8)

If sin θ = 2 over 7 and tan θ > 0, what is the value of cos θ?

Answers

[tex]\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad cos(\theta)=\cfrac{adjacent}{hypotenuse} \quad % tangent tan(\theta)=\cfrac{opposite}{adjacent}\\\\ -------------------------------\\\\[/tex]

[tex]\bf sin(\theta )=\cfrac{2}{7}\cfrac{\leftarrow opposite}{\leftarrow hypotenuse}\qquad \textit{let's find the adjacent side} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{7^2-2^2}=a\implies \pm\sqrt{45}=a\implies \pm 3\sqrt{5}=a[/tex]

but.... which is it? the + or the -? well, we know that tan(θ) > 0, is another way to say that the tangent of the angle is positive, now, for the tangent to be positive, since it's opposite/adjacent both opposite and adjacent have to be the same exact sign, now, we know the opposite is +2, so that means the adjacent has to be the same sign, thus is the positive version 3√(5)

thus [tex]\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\qquad \qquad cos(\theta )=\cfrac{3\sqrt{5}}{7}[/tex]

A given line has the equation 2x + 12y = −1.

What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?

Answers

2x + 12y = -1
12y = -2x - 1
y = - 1/6x - 1/12...slope here is -1/6. A perpendicular line will have a negative reciprocal slope. All that means is flip the slope and change the sign. So our perpendicular line will need a slope of 6.

y = mx + b
slope(m) = 6
(0,9)...x = 0 and y = 9
sub and find b, the y int
9 = 6(0) + b
9 = b

so ur perpendicular equation is : y = 6x + 9 <==

Answer

the answer is d

Step-by-step explanation:

Complete the pattern ___, ___, ___, 0, 2, 4, 6

Answers

-6, -4, -2, 0, 2, 4, 6. They continue in increments of +2.

Answer:-6, -4, -2, 0, 2, 4, 6. They continue in increments of +2.

Step-by-step explanation:

A population of flies grows according to the function p(x) = 2(4)x, where x is measured in weeks. A local spider has set up shop and consumes flies according to the function s(x) = 2x + 5. What is the population of flies after two weeks with the introduced spider?

Answers

well, the spider is "consuming flies", so we'd have to subtract those flies the spider is picking up, that is 2x + 5, x = weeks.

now, after two weeks, x = 2

[tex]\bf P(x)-s(x)\implies 2(4)^2-[2(2)+5]\implies 32-9[/tex]

Answer:

answer is 23

Step-by-step explanation:

Let c be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. find the exact length of c from the origin to the point 4, 8, 32 3 .

Answers

Let [tex]x=t[/tex], so that

[tex]x^2=2y\implies t^2=2y\implies y=\dfrac{t^2}2[/tex]

[tex]3z=xy\implies3z=\dfrac{t^3}2\impiles z=\dfrac{t^3}6[/tex]

Then the length of the path is

[tex]\displaystyle\int_{t=0}^{t=4}\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2+\left(\frac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^4\sqrt{1+t^2+\frac{t^4}4}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^4\sqrt{4+4t^2+t^4}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^4\sqrt{(t^2+2)^2}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^4(t^2+2)\,\mathrm dt[/tex]
[tex]=\dfrac{44}3[/tex]

Final answer:

To find the exact length of the curve c from the origin to a given point, we can parameterize the curve and use the formula for arc length. In this case, we need to solve for x, y, and z in terms of a parameter t. Then, we can integrate the arc length formula to obtain the exact length.

Explanation:

To find the exact length of the curve c from the origin to the point (4, 8, 32/3), we need to first parameterize the curve. Given that x2 = 2y and 3z = xy, we can solve for x, y, and z in terms of a parameter t. Then, we can use the formula for arc length to calculate the length of the curve using integration.

Let's begin by solving for x, y, and z in terms of t:

From x2 = 2y, we have x = √(2t) and y = t2/2.Substituting these values into 3z = xy, we get 3z = √(2t) * (t2/2) or z = (t3√2)/6.

Now, we can calculate the arc length using the formula:

L = ∫ sqrt((dx/dt)2 + (dy/dt)2 + (dz/dt)2) dt

Plugging in the values of x, y, and z in terms of t, we can evaluate the integral to find the exact length of curve c.

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Whats the quotient of 2 1/4 and 5/8

Answers

[tex]\bf 2\frac{1}{4}\implies \cfrac{2\cdot 4+1}{4}\implies \cfrac{9}{4}\\\\ -------------------------------\\\\ \cfrac{9}{4}\div \cfrac{5}{8}\implies \cfrac{9}{4}\cdot \cfrac{8}{5}\implies \cfrac{9\cdot 8}{4\cdot 5}\implies \cfrac{72}{20}\implies \cfrac{18}{5}\implies 3\frac{3}{5}[/tex]

The law of cosines is a2+b2 - 2abcosC = c^2 find the value of 2abcosC .... A. 40 B. -40 C. 37 D. 20

(The sides are 2,4, and 5; A to B is 2, B to C is 4, and A to C is 5.)

Answers

a² + b² - 2abcosC = c²

Аngle C lies opposite to the side AB, so "c" in the formula it is AB in your triangle

4² + 5² - 2abcosC = 2²
16 + 25 - 2abcosC = 4
41 - 4 = 2abcosC
2abcosC = 37

Given the Law of Cosines, the value of 2abcosC after plugging in the values of a, b, and c is: [tex]\mathbf{2abcosC = 37}[/tex]

Law of Cosines is given as: [tex]a^2+b^2 - 2abcosC = c^2[/tex]

Given also are the sides of a triangle:

a = 4 (side B to C)b = 5 (side A to C)c = 2 (side A to B)

Plug in the values into the Law of Cosines, [tex]a^2+b^2 - 2abcosC = c^2[/tex] to find [tex]\mathbf{2abcosC}[/tex]

Thus:

[tex]4^2+5^2 - 2abcosC = 2^2\\\\16 + 25 - 2abcosC = 4\\\\41 - 2abcosC = 4[/tex]

Subtract 41 from both sides

[tex]41 - 2abcosC - 41 = 4-41\\\\-2abcosC = -37[/tex]

Divide both sides by -1

[tex]\mathbf{2abcosC = 37}[/tex]

Therefore, given the Law of Cosines, the value of 2abcosC after plugging in the values of a, b, and c is: [tex]\mathbf{2abcosC = 37}[/tex]

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Which of the following is not one of the three ways to express a ratio A 3/4 B 3:4 C 3 of 4 D 3 to 4

Answers

3 of 4 is the wrong answer

3 of 4 is the incorrect way to express a ratio.

Which are the roots of the quadratic function f(q) = q2 – 125? Check all that apply. q = 5 q = –5 q = 3 q = –3 q = 25 q = –25

Answers

Answer:

q=5 sqrt 5 and q=-5 sqrt 5

Step-by-step explanation:

got it right on edge :)

Final answer:

The roots of the quadratic function f(q) = q^2 − 125 are q = -5 and q = 5. Other options listed do not satisfy the function. The roots are found by factoring the equation as a difference of squares.

Explanation:

The roots of the quadratic function f(q) = q2 − 125 can be found by solving the equation q2 − 125 = 0. To find the roots, we need to factor the quadratic or use the square root property since the equation is already set to zero.

We can see that this is a difference of squares equation, so it factors to (q + 5)(q - 5) = 0. Setting each factor equal to zero gives us q = -5 and q = 5.

So, the roots of the quadratic function are q = -5 and q = 5. The other options given (q = 3, q = -3, q = 25, q = -25) do not satisfy the equation f(q) = q2 − 125 = 0, hence they are not roots of this function.

If a new car is valued at $13,200 and 6 years later it is valued at $3000, then what is the average rate of change of its value during those six years?

Answers

I'm not in college so take what I say with a grain of salt but to figure that out first I found the range of 13,200 and 3,000 or basically subtracted 3,000 from 13,200 to get 10,200 so it's value went down 10,200 dollars worth of value in six years, next I divided 10,200 by six because it was six years. To get a rate of change of 1,700 dollars worth of value each year. So the answer is an average rate of 1,700 dollars during those six years or 1.28%

A deposit of $1,295 at 7% for 180 days what is the interest earned

Answers

Final answer:

To find the simple interest on a deposit of $1,295 at a 7% rate for 180 days, we use the formula I = P × r × t. With 180 days being roughly 0.5 years, the interest earned is approximately $45.33.

Explanation:

Calculating Simple Interest for a Deposit

To calculate the simple interest earned on a deposit, we can use the simple interest formula which is Interest (I) = Principal (P) × Rate (r) × Time (t).

In this case, a student wants to know the interest earned on a deposit of $1,295 at 7% for 180 days. Since simple interest is usually calculated on an annual basis, we need to adjust the time to reflect a portion of the year. 180 days is equivalent to ½ year (since 180/365 ≈ 0.493). Now we can plug in the values into the formula:

I = P × r × t

I = $1,295 × 0.07 × 0.5

So, the interest earned would be:

I = $1,295 × 0.07 × 0.5I = $45.325

The student will earn approximately $45.33 in interest (rounded to the nearest cent).

Write out the form of the partial fraction decomposition of the function (see example). do not determine the numerical values of the coefficients. (a) x4 + 5 / x5 + 2x3

Answers

[tex]\dfrac{x^4+5}{x^5+2x^3}=\dfrac{x^4+5}{x^3(x^2+2)}=\dfrac ax+\dfrac b{x^2}+\dfrac c{x^3}+\dfrac{dx+e}{x^2+2}[/tex]

A kitchen assistant knocked over a cooling rack and spilled 12% of the cookies onto the floor Francesca had
to bake 36 more cookies to replace them.
how many cookies were ordered in total

Answers

300 cookies because 36/.12=300.

the quadratic formula gives which roots for the equation 2x^2+x-6=0

Answers

2x^2 + x - 6 = 0
a=2, b=1, c=-6
x = -b+_ /(b^2 - 4ac) ÷ 2a
+_ (plus minus) / ( square root)
X = -1 +_ /1^2 - 4(2)(-6) ÷ 2(2)
= -1 +_ /49 ÷ 4
= -1 +_ 7 ÷ 4
= 6/4 or -8/4
= 3/2 or -2

Hope it helped!

Final answer:

The quadratic formula gives two roots for a quadratic equation. The roots of the equation 2x²+x-6=0 are 1.5 and -2.

Explanation:

The quadratic formula gives the roots of a quadratic equation of the form ax²+bx+c=0. For the equation 2x²+x-6=0, the values of a, b, and c are 2, 1, and -6, respectively.

Using the quadratic formula, we can calculate the roots:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values of a, b, and c into the formula:

x = (-1 ± √(1² - 4*2*(-6))) / (2*2)

Simplifying the expression:

x = (-1 ± √(1 + 48)) / 4

x = (-1 ± √49) / 4

x = (-1 ± 7) / 4

Therefore, the roots of the equation 2x²+x-6=0 are:

x = (-1 + 7) / 4 = 3/2 = 1.5

x = (-1 - 7) / 4 = -8/4 = -2

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Paula has 3 bananas. She wants to divide each of them into sections. How many 's are there in 3 bananas?

Answers

Answer:

B IS 21

Step-by-step explanation:

Andrew estimated the weight of his dog to be 60 lb. The dog’s actual weight was 68 lb. What was the percent error in Andrew’s estimate? Round your answer to the nearest tenth of a percent. __________ %

Answers

well, the error value is 8, he was off by 8 units... so, if we take 68 to be the 100%, what is 8 in percentage off of it?

[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 68&100\\ 8&x \end{array}\implies \cfrac{68}{8}=\cfrac{100}{x}[/tex]

The rounding rule for the correlation coefficient requires three decimal places true or false

Answers

Answer:

Round the value of r to three decimal places.

Step-by-step explanation:

The rounding rule for the correlation coefficient requires three decimal places

this statement is true.

The correlation coefficient in statistics is a parameter which measures the degree of strength of relation between two variables .

Its value lies between -1 to +1 .

The closer the correlation coefficient will be near to 1 the stronger the correlation will be.

The correlation between two variables can be positive or negative

Correlation coefficients are helpful in determining the functional relationships among the variables

So higher magnitude of correlation coefficients lead to accurate functional relation among variables.

The rounding rule for the correlation coefficient requires three decimal places

this statement is true.

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Ohm’s Law states that the electrical current, I in amperes, through a resistor is given by the formula 644-14-04-00-00_files/i0210000.jpg where V is the voltage in volts and R is the resistance in ohms. If the current is 6 amperes and the resistance is 18 ohms, what is the voltage?

Answers

if im am correct its V=I * R sooo 108 = 6 * 18

Your Answer is 108 volts

Answer:

The correct answer is D., or "108 volts".

whats the value of the equation

Answers

13x-2(x+4) = 8x+1 =

13x-2x-8 = 8x+1=

11x-8 = 8x+1

-8 =-3x+1=

-9 = -3x

x = -9/-3 = 3

x = 3

If (h, •) and (k, •) are subgroups of (g, •), prove that (h n k, •) is a subgroup of (g, •). can the same be said for the union, hu k? prove or give a counterexample.

Answers

Let [tex]\eta\in H\cap K[/tex]. Since both [tex]H[/tex] and [tex]K[/tex] are subgroups of [tex]G[/tex], we have

[tex]\eta\in H\cap K\implies\begin{cases}\eta\in H\\\eta\in K\end{cases}\implies\eta\in G[/tex]

Because both [tex]H,K[/tex] are subgroups of [tex]G[/tex], then [tex](H\cap K,\bullet)[/tex] contains the identity element [tex]e[/tex]. Furthermore, there must be some element [tex]\eta^{-1}\in H[/tex] and [tex]\eta^{-1}\in K[/tex], i.e. [tex]\eta^{-1}\in H\cap K[/tex], such that [tex]\eta\bullet\eta^{-1}=e[/tex].

Now let [tex]\eta_1,\eta_2,\eta_3\in H\cap K[/tex]. By the same reasoning as above it follows that each of these belong in [tex]G[/tex], and since [tex](G,\bullet)[/tex] is a group, we have [tex]\eta_1\bullet(\eta_2\bullet\eta_3)=(\eta_1\bullet\eta_2)\bullet\eta_3[/tex], so [tex]H\cap K[/tex] is associative under [tex]\bullet[/tex].

So [tex]H\cap K[/tex] contains the identity, is closed with respect to inverses, and is associative under [tex]\bullet[/tex]. Therefore [tex]H\cap K[/tex] must be a subgroup of [tex]G[/tex].

In the case of union, this is not always the case. Consider the group [tex](\mathbb Z,+)[/tex] with subgroups [tex](H,+)[/tex] and [tex](K,+)[/tex] where [tex]H[/tex] is the set of all integer multiples of 2 and [tex]K[/tex] is the set of all integer multiples of 3.

It's easy to show that [tex]H[/tex] and [tex]K[/tex] are indeed subgroups, but this is not the case for [tex]H\cup K[/tex]. We have

[tex]H\cup K=\{0,\pm2,\pm4,\ldots\}\cup\{0,\pm3,\pm6,\ldots\}[/tex]

Take the elements [tex]2\in H[/tex] and [tex]3\in K[/tex]. Addition yields [tex]2+3=5[/tex], but [tex]5\not\in H\cup K[/tex], so [tex]H\cup K[/tex] is not closed under [tex]+[/tex].

Simplify: 4x^2+36/4x•1/5x

Answers

[tex] \frac{4x^2+36}{4x}* \frac{1}{5x} = \frac{4(x^2+9)}{20x^2} = \frac{x^2+9}{5x^2} [/tex]

Answer:

Step-by-step explanation:

The given equation is:

[tex]\frac{4x^2+36}{4x}{\times}\frac{1}{5x}[/tex]

On solving the above equation, we get

=[tex]\frac{4x^2+36}{(4x)(5x)}[/tex]

=[tex]\frac{4(x^2+9)}{(4x)(5x)}[/tex]

=[tex]\frac{x^2+9}{(x)(5x)}[/tex]

=[tex]\frac{x^2+9}{(5x^2)}[/tex]

which is the required simplified form.

Thus, the simplified form of the given equation [tex]\frac{4x^2+36}{4x}{\times}\frac{1}{5x}[/tex] is [tex]\frac{x^2+9}{(5x^2)}[/tex].

How many minutes does it take an athlete to run a 10.0 kilometer race? assume the athlete's pace is 6.50 minutes per mile. (1 mi = 1.609 km)?

Answers

Final answer:

To find out how many minutes it takes an athlete to run a 10.0 kilometer race using a pace of 6.50 minutes per mile, we can set up a proportion and solve for x. The athlete takes approximately 40.33 minutes to run the race.

Explanation:

To convert the athlete's pace from minutes per mile to minutes per kilometer, we will use the conversion factor 1 mile = 1.609 kilometers. Therefore, the athlete's pace is 6.50 minutes per 1.609 kilometers. To find out how many minutes it takes the athlete to run a 10.0 kilometer race, we can set up a proportion:

6.50 minutes / 1.609 kilometers = x minutes / 10.0 kilometers

Using cross multiplication, we can solve for x:

x = (6.50 minutes × 10.0 kilometers) / 1.609 kilometers

x = 40.33 minutes (rounded to two decimal places)

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In the figure below, segment AC is congruent to segment AB:

Triangle ABC with a segment joining vertex A to point D on side BC. Side AB is congruent to side AC

Which statement is used to prove that angle ABD is congruent to angle ACD?

Answers

the answer is A. segment AD bisects angle CAB. I just took the exam and I got it right. hope this helps!

Answer: Isosceles triangle theorem

Step-by-step explanation:

In the given picture, there a triangle whose two sides are equal AB=AC.

Therefore it is an isosceles triangle.

Now, the isosceles theorem says that the angles opposite to the equal sides of a triangle are equal.

Therefore by isosceles triangle theorem in ΔABC we have

[tex]\angle{B}=\angle{C}[/tex]

Since [tex]\angle{ACD}=\angle{C}[/tex] [Reflexive]

[tex]\angle{ABD}=\angle{B}[/tex] [Reflexive]

Therefore, [tex]\angle{ACD}=\angle{ABD}=[/tex]

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