prove that 5^31–5^29 is divisible by 100.

Answer:

18

Step-by-step explanation:

The distance is 12 - (-6) = 12 + 6 = 18

-6+x=12 it’s obviously 18 units apart

The correct graph of the circle [tex]\rm x^2+y^2=9[/tex] is graph D, the corrcet option is D.

A circle can be represented as;

[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]

Where h and k are the centers of the circle and r is the radius of the circle.

The given equation of the circle is;

[tex]\rm x^2+y^2=9[/tex]

Here the center of the circle h = 0 and k = 0 so the circle passes through the origin.

The radius of the circle is;

[tex]\rm r^2=9\\\\r^2=3^2\\\\r=3[/tex]

Hence, the correct graph of the circle [tex]\rm x^2+y^2=9[/tex] is graph D, the correct option is D.

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Answer:

  105

Step-by-step explanation:

The numbers that can be used to form triangles are collectively called "triangle numbers." The n-th triangle number is the sum of all numbers less than or equal to n. It is ...

  n(n+1)/2

For n=14, the number is 14(15)/2 = 7·15 = 105.

The clerk used 105 oranges to make the arrangement.

The grocery clerk used 105 oranges to set up a triangular display. This is calculated with the formula for triangular numbers sequence (n*(n+1))/2 where n is the base of the triangle.

To solve the problem, we need to use the approach for calculating the number of items in a triangular number sequence. Triangular numbers are used to form equilateral triangles. The nth term of a triangular number sequence is given by the formula (n*(n+1))/2. In this case, the base of the triangle contains 14 oranges, so n=14.

Using the formula, the total number of oranges used to form triangle by the grocery clerk is (14*(14+1))/2 = 105 oranges. So, the clerk used 105 oranges to set up the display.

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Answer:

0.5 hour

Step-by-step explanation:

Given

Speed of Dina = 10 km/h

Distance = 20 km

So the time Dina taken to complete the track is:

[tex]Speed=\frac{distance}{time}\\10=\frac{20}{time}\\time=\frac{20}{10}\\ time=2\ hours[/tex]

The time taken by Dina is 2 hours. As masha started with dina but she was 4 km of the path left to cycle,

her distance covered in 2 hours was:

[tex]Distance\ covered\ by\ Masha\ in\ 2\ hours=20-4\\=16 km[/tex]

So we know the time and distance:

Now,

[tex]Speed\ of\ Masha=\frac{distance}{time}\\ =\frac{16}{2}\\ =8\ kilometer\ per\ hour[/tex]

We have to calculate the time that will be needed by MAsha to complete the track:

As we know the speed and remaining distance

[tex]Speed=\frac{distance}{time}\\8=\frac{4}{time}\\ time=\frac{4}{8}\\time=0.5\ hours[/tex]

Masha needs 0.5 hour to complete the track ..

Answer:

30 minutes

Step-by-step explanation:

Answer:

No. The ladder is too steep.

Step-by-step explanation:

Length of ladder = 17 feet.  This is the hypotenuse.

Side a of a right triangle = 16.6

To answer this, you need one of the trigonometric functions.  

Opposite = 16.5

hypotenuse = 17

The function you need is the sine function.

Sin(theta) = opposite / hypotenuse

sin(theta) = 16.5 / 17

Sin(theta) = 0.97059

theta = sin-1(0.07059)

theta = 76.07

No the ladder is too steep.

Answer:

The ladder will not be safe.

Step-by-step explanation:

The ladder is 17 ft long

The top of the ladder is 16.5 ft above the ground

The ladder makes a right triangle of height = 16.5 ft and hypotenuse = 17 ft

To find the angle the ladder makes with the ground,

Height ÷ hypotenuse = sin angle

i.e [tex]\frac{16.5}{17}[/tex] = sin angle

[tex]sin^{-1}[/tex] angle = 76.1°

So the ladder is not safe since the angle it makes with the ground is greater than 70°.

Answer:

The measure of angle A is 115°

Step-by-step explanation:

we know that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

∠C+∠A+∠B=180°

substitute values and solve for x

x°+(3x-35)°+(x-35)°=180°

5x°=180°+70°

x=250°/5=50°

Find the measure of angle A

∠A=(3x-35)°

substitute the value of x

∠A=(3(50)-35)=115°

Answer:

[tex]m\angle A=115\degree[/tex]

Step-by-step explanation:

The sum of angles in a triangle is 180 degrees.

[tex]\implies (x-35)\degree+x+(3x-35)\degree=180\degree[/tex]

[tex]\implies 5x-70\degree=180\degree[/tex]

[tex]\implies 5x=180+70[/tex]

[tex]\implies 5x=250[/tex]

Divide both sides by 5.

[tex]\implies x=50[/tex]

We substitute the value of angle A to obtain:

[tex]m\angle A=3(50)-35[/tex]

[tex]m\angle A=115\degree[/tex]

Answer:

I think I could help you

Have fun and feel free to ask me something new.

Or we can prove some properities without calculating by details

Step-by-step explanation:

I think I could help you

Have fun and feel free to ask me something new.

Or we can prove some properities without calculating by details

Answer:  The perimeter of triangle ABC is (112√3 + 168) cm.

Step-by-step explanation:  Given that in isosceles triangle △ABC, AB = BC and CH is an altitude. Also,

CH = 84 cm   and  

[tex]m\angle HBC = m\angle BAC+m\angle BCH~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We are to find the perimeter of triangle ABC

Since AB = BC, so the angles opposite to them are congruent and have equal measures.

That is, [tex]m\angle BAC=m\angle ACB~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Now, since angle HBC is an exterior angle of triangle ABC and triangles BAC and ACB are remote interior angles.

So, we have

[tex]m\angle HBC=m\angle BAC+m\angle ACB\\\\\Rightarrow m\angle BAC+m\angle BCH=m\angle BAC+m\angle ACB\\\\\Rightarrow m\angle ACB=m\angle BCH.[/tex]      

Therefore, from equation (i) implies that

[tex]m\angle HBC = m\angle BAC+m\angle BCH\\\\\Rightarrow m\angle HBC=m\angle BCH+m\angle BCH~~~~~~~[\textup{applying equations (ii) and (iii)}]\\\\\Rightarrow m\angle HBC=2m\angle BCH.[/tex]

Now, from angle sum property in triangle BCH, we have

[tex]m\angle HBC+m\angle BCH+m\angle BHC=180^\circ\\\\\Rightarrow 3m\angle BCH+90^\circ=180^\circ\\\\\Rightarrow 3m\angle BCH=90^\circ\\\\\Rightarrow m\angle BCH=30^\circ.[/tex]

So, we get

[tex]m\angle BAC=m\angle ACB=m\angle BCH=30^\circ,\\\\m\angle HBC=2\times30^\circ=60^\circ.[/tex]

In right-angled triangle ACH, we have

[tex]\tan 30^\circ=\dfrac{CH}{AH}\\\\\\\Rightarrow \dfrac{1}{\sqrt3}=\dfrac{84}{AH}\\\\\\\Rightarrow AH=84\sqrt3.[/tex]

In right-angled triangle BCH, we have

[tex]\tan 60^\circ=\dfrac{CH}{BH}\\\\\\\Rightarrow \sqrt3=\dfrac{84}{BH}\\\\\\\Rightarrow BH=\dfrac{84}{\sqrt3}.[/tex]

And,

[tex]\sin 60^\circ=\dfrac{CH}{BC}\\\\\\\Rightarrow \dfrac{\sqrt3}{2}=\dfrac{84}{BC}\\\\\\\Rightarrow BC==\dfrac{168}{\sqrt3}=56\sqrt3.[/tex]

Therefore,

[tex]AB=AH-BH=84\sqrt3-\dfrac{84}{\sqrt3}=\sqrt3(84-28)=56\sqrt3.[/tex]

Now, in triangle ACH,

[tex]\sin 30^\circ=\dfrac{CH}{AC}\\\\\\\Rightarrow \dfrac{1}{2}=\dfrac{84}{AC}\\\\\Rightarrow AC=168.[/tex]

Thus, the perimeter of triangle ABC is given by

[tex]P=AB+BC+CA=56\sqrt3+56\sqrt3+168=112\sqrt3+168.[/tex]

The perimeter of triangle ABC is (112√3 + 168) cm.

you need to find the mean on these numbers that is step one in finding standard deviation. so this is 44.2. now you need to subtract the mean from each number and square the result. after that step you now have these numbers.... 3.24, 139.24, .64, .4,.64,282.24,116.64,77.44,27.04. now the next step is to find the mean of these numbers. you get 71.9 appx.. now all you do is square root this number you get 8.5 when you round to the nearest thenth

To work this out, you find out how many triangles can fit into the shape.

To do this, you take the number of sides and subtract it by 2.

So in a polygon with 11 sides, there are:

9 triangles          (11 - 2 = 9)

Remember, the total number of angles in one triangle is 180 degrees.

So to work out the total number of angles in a polygon, you multiply the number of triangles in it by 180.

So the total sum of interior angles in a polygon with 11 sides is:

180 x 9  = 1620 degrees          (180 degrees times number of triangles)

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

Answer:

1620 degrees

Answer:

It has no horizontal asymptote

Step-by-step explanation:

It has no horizontal asymptote.  This is a cubic function which has the end behavior of the left tail down and the right tail up, so both the domain and the range are infinity.  That means that there is no horizontal asymptote to go through.  Because it is not a rational function, there are no vertical asymptotes that could make the denominator go to 0 since there is no denominator (not rational).

Answer:

C,

It crosses the horizontal asymptote at the origin.

Step-by-step explanation:

Plato

Answer:

$8/mile

Step-by-step explanation:

Total distance walked was 2  1/4 mi  +  5  1/2 mi = 7  3/4 mi.  Please note: you must use the " / " symbol to indicate division;  "2 1 4" is unclear.

                                           $62

Unit rate = $ per mile = --------------- = $8/mile

                                        7  3/4 mi

Answer:

46 craft sticks per student

Step-by-step explanation:

The simplest situation would be that in which the available 644 craft sticks are evenly divisible by the number of students receiving them.  If that's the case, all we have to do is to divide:

644 craft sticks

----------------------- = 46 craft sticks per student

     14 students

Answer:

[tex]f(g(x)) = 16x ^ 4-32x ^ 2 + 18[/tex]

Step-by-step explanation:

we have two functions

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

We wish to find the compound function f(g(x))

To find f(g(x)) you must introduce the function g(x) within the function f(x). This is change the variable x, in the function f(x), by g(x).

[tex]f (g (x)) = (4x ^ 2-3) ^ 2 - 2 (4x ^ 2-3) +3[/tex]

Now simplify the expression:

[tex]f (g (x)) = 16x ^ 4-24x ^ 2 + 9 - 8x ^ 2+6 +3\\\\f(g(x)) = 16x ^ 4-32x ^ 2 + 18[/tex]

ANSWER

[tex]f(g(x)) = 16 {x}^{4} -3 2{x}^{2} +18[/tex]

EXPLANATION

The given functions are:

[tex]f(x)={x}^{2} - 2x + 3[/tex]

and

[tex]g(x) = 4 {x}^{2} - 3[/tex]

We want to find

[tex]f(g(x)) = f(4 {x}^{2} - 3)[/tex]

This implies that;

[tex]f(g(x)) = ( 4 {x}^{2} - 3)^{2} - 2(4 {x}^{2} - 3) + 3[/tex]

We expand to get,

[tex]f(g(x)) = 16 {x}^{4} - 24 {x}^{2} + 9- 8 {x}^{2} + 6+ 3[/tex]

[tex]f(g(x)) = 16 {x}^{4} -3 2{x}^{2} +18[/tex]

Answer:

C C C C

Step-by-step explanation:

DONT LISTEN TO THE FIRST GUY ITS C THEY MADE A MATH ERRORRR

ANSWER

169.1m

EXPLANATION

From the diagram, the horizontal distance traveled is x meters.

This is the side adjacent to the 6° angle.

Since we know the hypotenuse to be 170m, we use the cosine ratio to find the value of x.

[tex]\cos(6 \degree) = \frac{opposite}{hypotenuse} [/tex]

[tex] \cos(6 \degree) = \frac{x}{170} [/tex]

.

This implies that

x=170cos(6°)

x=169.0687222

To the nearest tenth, the horizontal disance travelled is 169.1m

Answer:

you mulitple the two bottomz by the other number

example 3/4 and 2/8

8 is a common mulitple so 3/4 becomes 6/8 and now they have common denominators

Step-by-step explanation:

example 3/4 and 2/8

8 is a common mulitple so 3/4 becomes 6/8 and now they have common denominators

and the numerator gets multipled with the same number as the denominator

d = 92+6 = 98

an = a1 + 98 (n-1)

a1=a19-98 (n-1)

a1=-92 -98 * 18

=-1856

It’s A ( an = -1856+98(n-1) )

Answer:

  see below

Step-by-step explanation:

The functions for these tables are, respectively, ...

  f(x) = 5 - x

  f(x) = 3x

  f(x) = (x -1)² . . . . . a quadratic relation

  f(x) = 4x² . . . . . . a quadratic relation

We assume the intention is that the terminology "quadratic variation" mean "proportional to the square of x". In that case, only the last function has such variation.

use pythagorean theorem

Answer:

x = 3.6

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan20° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{10}[/tex]

Multiply both sides by 10

10 × tan20° = x, hence

x ≈ 3.6

Answer:

The parent function y = 0.5x is DECREASING  across its domain because its base, b, is such that 0<b<1.

The function, f, shifts the parent function 8 units UP .

The function, f, shifts the parent function 5 units RIGHT .

Translation involves moving a function vertically or horizontally.

The function [tex]\mathbf{y = 0.5^{x- 5} + 8}[/tex] shifts the parent function 5 units right, and 8 units up.

The parent function is given as:

[tex]\mathbf{y = 0.5^x}[/tex]

Move the function right, by 5 units

[tex]\mathbf{y = 0.5^{x- 5}}[/tex]

Move the function up by 8 units

[tex]\mathbf{y = 0.5^{x- 5} + 8}[/tex]

So, the function [tex]\mathbf{y = 0.5^{x- 5} + 8}[/tex] shifts the parent function 5 units right, and 8 units up.

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Answer:

135

Step-by-step explanation:

Angles 1 and 3 are vertical angles, so they are congruent.

Since angle 1 measures 135 deg, angle 3 also measures 135 deg.

Angles 3 and 7 are corresponding angles of parallel lines cut by a transversal, so they are congruent.

Since angle 3 measures 135 deg, angle 7 also measures 135 deg.

Answer: m<7 = 135 deg

congruence, in mathematics, the term employed in several senses, each connoting harmonious relation, or agreement, and correspondence. so 2 triangles are congruent if 2 sides and their included angle in the 1 are = to 2 sides and their included angle in the other.

Angles one and three are vertical angles, so they are congruent.

Since angle one measures 135 degree, angle three also measures 135 degree.

Angles 3 or 7 are corresponding angles to the parallel lines cut by the transversal, so they are congruent.

Since angle 3 measures 135 deg, angle 7 also measures 135 deg.

Answer: m<7 = 135 degree

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Answer:  The point is (-2, 7)

Step-by-step explanation:

If we have a function f(x) and we apply the transformation

[tex]y = f (x + h)[/tex] then ::

If [tex]h <0[/tex] the graph of f(x) moves horizontally h units to the right

If [tex]h> 0[/tex] the grace of f(x) moves horizontally h units to the left

In this case we have the function f(x) and the point (0,7) and the transformation [tex]y = f (x + 2)[/tex]

Then [tex]h = 2> 0[/tex]. Therefore the graph of f(x) moves 2 units towards the left.

Therefore the point (0,7) moves 2 units to the left and we have the point (-2, 7) in the transformed function

Answer:

30th percentile:109

90th percentile: 188

Step-by-step explanation:

The given data set is:

129, 113, 200, 100, 105, 132, 100, 176, 146, 152

We arrange the data set in ascending order to obtain;

Array= [tex]100,100,105,113,129,132,146,176,200[/tex]

The 30th percentile is located at

[tex](\frac{30}{100}\times 10 )}[/tex] -th position, where n=10 is the number of items in the data set

This implies that the 30th percentile is at the 3rd position.

Since 3 is an integer, the 30th percentile is the average of the 3rd and 4th occurrence in the array;

This implies that the 30th percentile = [tex]\frac{105+113}{2}=\frac{218}{2}=109[/tex]

The 90th percentile is located at

[tex](\frac{90}{100}\times 10 )}[/tex] -th position, where n=10 is the number of items in the data set

This implies that the 90th percentile is at the 9th position.

Since 9 is an integer, the 90th percentile is the average of the 9th and 10th occurrence in the array;

This implies that the 90th percentile = [tex]\frac{176+200}{2}=\frac{376}{2}=188[/tex]

Answer:

The probability of missing both two-point conversion attempts is 7.5%

Step-by-step explanation:

We are informed that the probability of missing the first attempt is 50% of the time. Furthermore, the probability of missing on the second attempt given that he missed the first attempt is 15% of the time

Now,the probability of missing on both the two-point conversion attempts will simply be given by the product of these two probabilities since the events are independent;

50%*15% = 0.5 * 0.15 = 7.5%

Therefore, the probability of missing both two-point conversion attempts is 7.5%

Answer:

The probability of missing both two-point conversion attempts is 7.5%

Step-by-step explanation:

^^

For this case we have that by definition, the volume of a parallelepiped is given by:

[tex]V = l * w * h[/tex]

Where:

l: It's the long

w: It is the width

h: It's the height

From the figure we have the following data:

[tex]V = 975 \ ft ^ 3\\h = 9 \ ft\\w = 4ft\\x =?[/tex]

We must find the value of the length of the parallelepiped:

[tex]975 = x * 4 * 9\\975 = 36x\\x = \frac {975} {36}\\x = 27.083[/tex]

Answer:

[tex]x = 27.1 \ ft[/tex]

In any cyclic quadrilateral, angles opposite one another are supplementary, meaning

[tex]m\angle K+m\angle I=m\angle L+m\angle J=180^\circ[/tex]

and given that [tex]\boxed{m\angle K=64^\circ}[/tex], we have [tex]\boxed{m\angle I=116^\circ}[/tex].

By the inscribed angle theorem,

[tex]m\angle JLK=\dfrac12m\widehat{KJ}[/tex]

[tex]m\angle ILJ=\dfrac12m\widehat{IJ}[/tex]

and since

[tex]m\angle L=m\angle JLK+m\angle ILJ[/tex]

we have

[tex]m\angle L=\dfrac{97^\circ+59^\circ}2\implies\boxed{m\angle L=78^\circ}[/tex]

and it follows that

[tex]m\angle J=180^\circ-m\angle L\implies\boxed{m\angle J=102^\circ}[/tex]

Answer:

Step-by-step explanation:

This is right triangle trig.  The reference angle is 12 in one case and 60 in the other, but the horizontal distance doesn't change in either one, and neither does what you are looking for, which is the height of the balloon in both cases of the angle differences.  And if you're looking for the difference in the height, you'll find both and subtract the smaller from the larger.  

The height is across from the reference angle and the horizontal distance is adjacent to the reference angle, so the trig identity you want is tangent.  Set up according to the angle measure of 12 degrees:

[tex]tan(12)=\frac{x}{280}[/tex] and

280 tan(12) = x

x = 59.5 ft

Now for the angle measuring 60 degrees:

[tex]tan(60)=\frac{x}{280}[/tex] and

280 tan(60) = x

x = 484.9

The difference between the two heights is 425.5 feet.

Answer:

x=12.5

Step-by-step explanation:

The given triangle is a right angle triangle.

We cannot use the Pythagoras theorem as the lengths of all sides are not known. We will use triangular ratios here to solve the given problem.  

As it is clear from the diagram that x is the hypotenuse of the triangle and 11 is the length of the base. We will use a ratio in which base and hypotenuse are used.

So,

cos ⁡θ= base/hypotenuse

cos⁡ 28=11/x

x=11/cos⁡28  

x=11/0.8829

x=12.45

Rounding off to nearest 10

x=12.5

In every right triangle, a leg is given by the multiplication between the hypothenuse and the sine of the opposite angle, or the cosine of the adjacent one.

So, in this case, we have

[tex]11 = x\cos(28)[/tex]

Solving for x, we have

[tex]x = \dfrac{11}{\cos(28)}\approx 12.5[/tex]

Answer:

6 hours.

Step-by-step explanation:

She has already travelled 45 miles so there's another 393-45 = 348 miles to travel. So  if she continues at 58 mph she will take 348 / 58 = 6 hours.

A is the correct answer