A car will be traveling a total distance of 520 miles. The first part of the trip takes 2 hours, and the car’s average rate is 65 miles per hour. If the entire trip takes 8 hours, what is the car’s average rate, in miles per hour, during the second part of the trip?

49

57

50

65

Final answer:

The correct statement for a 45-45-90 triangle is that the legs are equal in length, and the hypotenuse is the length of a leg multiplied by √2, following from the Pythagorean Theorem.

Explanation:

The correct statement for 45-45-90 triangles is that they are special right triangles featuring two 45-degree angles and one 90-degree angle. In such triangles, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of a leg. This arises from the fact that in a 45-45-90 triangle, the two legs opposite the 45-degree angles are congruent, which also means that their corresponding sides are in a ratio of 1:1, and the hypotenuse can be found by multiplying one of the legs by √2.

This is a consequence of the Pythagorean Theorem where, for a right-angle triangle with sides 'a' and 'b' and hypotenuse 'c', the relationship is c^2 = a^2 + b^2. Since 'a' and 'b' are equal in a 45-45-90 triangle (let's call each side 's'), the equation simplifies to c^2 = 2s^2, implying c = s√2. This ratio is essential to understanding the properties of these triangles and is used frequently in various geometry and trigonometry problems.

Answer:

you must solve the question.

Step-by-step explanation:

it would be when we're solving a formula for himself a variable we must solve it.

Answer:

isolate

Step-by-step explanation:

For this case we have the following functions:

[tex]f (x) = 3x\\g (x) = x ^ 2 + 1[/tex]

We must find (f + g) (x). By definition of operations with functions we have to:

(f + g) (x) = f (x) + g (x)

So we have to:

[tex](f + g) (x) = 3x + (x ^ 2 + 1)\\(f + g) (x) = x ^ 2 + 3x + 1[/tex]

Answer:

[tex](f + g) (x) = x ^ 2 + 3x + 1[/tex]

Option B

Answer:

[tex]\boxed{\text{D. }3\sqrt{2}}[/tex]

Step-by-step explanation:

Multiply numerator and denominator by √2

[tex]\dfrac{6}{\sqrt{2}} = \dfrac{6}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}}\\\\= \dfrac{6\sqrt{2}}{2}\\\\= \boxed{3\sqrt{2}}[/tex]

Answer: D. [tex]3\sqrt{2}[/tex]

Step-by-step explanation:

The given fraction : [tex]\dfrac{6}{\sqrt{2}}[/tex]

Here, the denominator is in radical form which makes it not an simplified form.

So , we rationalize it by multiplying [tex]\sqrt{2}[/tex] to the numerator and the denominator , we get

[tex]\dfrac{6}{\sqrt{2}}\times\dfrac{\sqrt{2}}{\sqrt{2}=\dfrac{6\sqrt{2}}{2}}\\\\=\dfrac{2\times3\times\sqrt{2}}{2}\\\\=3\sqrt{2}[/tex]  [Cancel 2 from the numerator and the denominator.]

Hence, the choice is equivalent to the given fraction = [tex]3\sqrt{2}[/tex]

Hence, the correct option is D. [tex]3\sqrt{2}[/tex]

Answer:

15% apex confirmed

Step-by-step explanation:

The taxpayer and his spouse, with a combined taxable income of $27,900, will fall into the 15% tax bracket for a married couple filing jointly for the 2020 tax year.

The subject of this question is the United States Federal Income Tax Brackets. The taxpayer and his spouse have a combined taxable income of $14,200 + $13,700 = $27,900. For the 2020 tax year, a married couple filing jointly with taxable income between $0 and $19,750 fall in the 10% tax bracket, while those with taxable income between $19,751 to $80,250 are in the 15% tax bracket. So, the taxpayer and his spouse, with their combined taxable income, will fall into the 15% tax bracket. Their taxable income exceeds the threshold for the 10% tax bracket and does not reach the threshold for the 38% bracket. Please note, it's important to stay informed about tax brackets as they can change annually.

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Answer:

Step-by-step explanation:

Center

x = 5

y = - 3

r = 4

(x - 5)^2 + (y - - 3)^2 = 4^2

(x - 5)^2 + (y + 3)^2 = 16

Answer:

60 meters

Step-by-step explanation:

The standard form for parabolic motion is

[tex]h(x)=-5x^2+v_{0}x+h_{0}[/tex]

where [tex]v_{0}[/tex] is the initial upwards velocity and [tex]h_{0}[/tex] is the initial launching height.  If I am understanding your question, this is what you are looking for.  So the height AT the time of launch was 60 meters.

Answer:

The height of the object at the time of the launch is [tex]60m[/tex]

Step-by-step explanation:

We know that the height in meters, x seconds after the launch is modeled by the following function :

[tex]h(x)=-5x^{2}+20x+60[/tex]

For example, after [tex]x=3s[/tex] from the launch the height of the object is :

[tex]h(3s)=-5.(3^{2})+20.(3)+60=75[/tex]

[tex]h(3s)=75m[/tex]

If we want to know the height of the object at the time of the launch we will need to find the height of the object at [tex]x=0s[/tex] because that is the instant where the object is launched.

If we use [tex]x=0s[/tex] in [tex]h(x)[/tex] ⇒

[tex]h(0s)=-5.(0^{2})+20.(0)+60=60[/tex]

We find that the height of the object at the time of launch is [tex]60m[/tex]

Answer:

Option C. [tex]452.16\ cm^{2}[/tex]

Step-by-step explanation:

step 1

Find the circumference

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=3\ cm[/tex]

[tex]\pi=3.14[/tex]

substitute

[tex]C=2(3.14)(3)=18.84\ cm[/tex]

step 2

Find the area of the rectangle made by the circumference and height of the cylinder

The area of the rectangle is equal to

[tex]A=C*h[/tex]

substitute the values

[tex]A=(18.84)(24)=452.16\ cm^{2}[/tex]

Answer:

C

Step-by-step explanation:

Answer:

The answer is D.

Step-by-step explanation:

Each Monday, Luke spends $5 ($3 for the muffin, $2 for the juice). To figure out how much he spends in 6 weeks, you multiply $5 by 6. Hope this helps! :)

C. bc chickens have two legs each making it 12 chickens times 2 legs equal 24 plus the remaining 25 animals (pigs) would be 25x4=100+24 chicken legs = 124

For this case we have that the pigs have 4 legs while the hens have 2.

We propose a system of equations:

x: Variable representing the number of pigs

y: Variable representing the number of chickens

[tex]x + y = 37\\4x + 2y = 124[/tex]

We multiply by -4 the first equation:

[tex]-4x-4y = -148[/tex]

We add the equations:

[tex]-4x-4y = -148\\4x + 2y = 124\\-4y + 2y = -148 + 124\\-2y = -24\\y = \frac {24} {2}\\y = 12[/tex]

So, there are 12 chickens.

[tex]x + 12 = 37\\x = 37-12\\x = 25[/tex]

There are 25 pigs.

ANswer:

25 pigs

12 chickens

Option C

Answer:

162.4 in²

Step-by-step explanation:

The area (A) of a regular octagon is

A = [tex]\frac{1}{2}[/tex] perimeter × apothem

here perimeter = 8 × 5.8 = 46.4 in, hence

A = 0.5 × 46.4 × 7 = 162.4 in²

[tex](-\infty, +\infty)[/tex]

Hope this helps.

r3t40

Answer:

• The water bottle loses 0.5 an ounce of water per minute

Step-by-step explanation:

The definition of the variables tells you that m stands for minutes and that W stands for the water remaining in the bottle. So, the -0.5m in the equation has the effect of reducing the remaining water by 0.5 each time m increases by 1. That is, there are 0.5 fewer ounces of water after each additional minute: the bottle loses 0.5 ounces per minute.

There’s twenty over nine pounds

Answer:

2.22..

Step-by-step explanation:

First you divide four by nine to get 0.44..

then you multiply that by five to get your answer which is 2.22.. , Two Point Two repeating, 20/9, 2 2/9 or Two and Two Ninths.

Answer is y = 3sin2(x - pi/4).

Answer:

$30

Step-by-step explanation:

$500 x 0.02 x 3 = 30

Answer:

$30   is the    answer  

Answer:

It is 12.5

Step-by-step explanation:

It is because the formula of finding the volume of a rectangular prism is area of the base x height.

So you do 200 divided by 16 (Which is the height) which equals 12.5

Answer:

The height of the prism is 12.5 units.

Step-by-step explanation:

Volume formula:  V = (length)(width)(height)

or                           V = (area of base)(height)

Here, we want to calculate the height.  The appropriate formula is

(height) = (volume) / (area of base) = (200 units³) / (16 units²) = 12.5 units

The height of the prism is 12.5 units.

Answer: Divide by 9 ------- APEX

Step-by-step explanation:

i got it wrong and that was the right answer eiahhh

To check her register for transposing errors, Lia needs to subtract the balances and divide the difference by 9. so. the correct option is A.

Suppose that there are k things which are to be divided in P parts, then

K÷ P will give the amount that each one of P parts would get from k, which will make equal distribution of k things in P parts.

Lia is comparing her check register to her bank statement, and the ending balances don't seem to match.

To balance her check register, Lia needs to subtract the balances and divide the difference by 9.

If entries in her bank statement do not appear in her check register or vice versa.

To check her register for transposing errors, Lia needs to subtract the balances and divide the difference by 9. so. the correct option is A.

Learn more about division here;

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Answer:

120 ways.

Step-by-step explanation:

We have been given that you have 6 reindeer, Prancer, Rudy, Balthazar, Quentin, Jebediah, and Lancer, and you want to have 3 fly your sleigh. You always have your reindeer fly in a single-file line.

We will use permutation formula to solve our given problem as:

[tex]_{r}^{n}\textrm{C}=\frac{n!}{(n-r)!}[/tex]

[tex]_{3}^{6}\textrm{C}=\frac{6!}{(6-3)!}[/tex]

[tex]_{3}^{6}\textrm{C}=\frac{6\cdot 5\cdot 4\cdot 3!}{3!}[/tex]

[tex]_{3}^{6}\textrm{C}=6\cdot 5\cdot 4[/tex]

[tex]_{3}^{6}\textrm{C}=120[/tex]

Therefore, you can arrange your reindeer in 120 different ways.

Hello there! The answer is B. (3, 21).

So you want to be able to substitute one of the equations into the other. We can't do this right now since both of the equations are y = something, so we need to change the second equation to x = something so we can plug it in to the value of x in the first equation.

y = x + 18 can translate to x = y - 18. Now, plug "y - 18" into x in the first equation.

y = 10(y-18) - 9 and solve.

y = 10y - 180 - 9

-9y = - 180 - 9

-9y = -189

y = 21.

Now we have our y value, but we need our x value. Well, remember that y = x + 18? So, since y is 21, what plus 18 is equal to 21? The answer is 3, making our x value 3.

If x = 3 and y = 21, the ordered pair is (3, 21) or option B. I hope this was helpful and have a great day! :)

Hello

10x-9=x+18

10x-x=18+9

9x=27

x=3

=30-9=21

(3,21)

Good Luck

Goodbye ♥

Answer:

A box of 50 stickers would cost $13

Explanation:

1- getting the equation representing the price:

We have two variables; the number of stickers and the price of the box

We can note that the price is the dependent variable (y) while the number of stickers is the independent one (x)

We are given that:

A box of 15 stickers cost $6..........> first point is (15,6)

A box of 25 stickers cost $8 ........> second point is (25,8)

The general equation of the linear line is:

y = mx + c

where m is the slope and c is the y-intercept

i. getting the slope:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-6}{25-15}=0.2[/tex]

The equation now became: y = 0.2x + c

ii. getting the y-intercept:

To get the y-intercept, use any of the given points and substitute in the equation we got in part i. I will use the point (15,6)

y = 0.2x + c

6 = 0.2(15) + c

c = 6 - 0.2(15) = 3

The final equation is:

y = 0.2x + 3

where y is the price of the box and x is the number of stickers it contains

2- getting the price of a box with 50 stickers:

To get the price of a box of 50 stickers, simply substitute with x = 50 in the equation we got from part 1

This is done as follows:

y = 0.2(50) + 3 = 13

Therefore, a box of 50 stickers will cost $13

Hope this helps :)

Answer:

Step-by-step explanation:

Area of a circle is ...

  A = πr² . . . r is the radius

Area of a sphere is ...

  A = 4πr²

Lateral area of a cylinder is ...

  A = πdh = 2πrh . . . h is the height

Volume of a cylinder is ...

  V = πr²h

Volume of a sphere is ...

  V = (4/3)πr³

___

The area of the composite figure is the sum of the areas ...

  total area = base circle area + cylinder lateral area + 1/2 sphere area

  = πr² + 2πrh + (1/2)4πr² = (πr)(r +2h +2r)

  = πr(3r +2h)

For the given dimensions, r=3 in, h = 13 in, this is ...

  total area = π(3 in)((3·3 +2·13) in) = 105π in²

___

The volume of the composite figure is the sum of the volumes ...

  total volume = cylinder volume + 1/2 sphere volume

  = πr²h + (1/2)(4/3)πr³ = πr²(h + 2/3r)

  = π(3 in)²((13 +2/3·3) in) = 135π in³

Answer:

is b

Step-by-step explanation:

Answer:

B.  16 hrs

Step-by-step explanation:

Distance = rate × time

The best way to do this is to make a table with the info.  We are concerned with the trip There and the Return trip.  Set it up accordingly:

                    d     =     r     ×     t

There    

Return

The train made a trip from A to B and then back to A again, so the distances are both the same.  We don't know what the distance is, but it doesn't matter.  Just go with it for now.  It'll be important later.

               d     =     r     ×     t

There      d    

Return     d

We are also told the rates.  There is 70 km/hr and return is 80 km/hr

               d     =     r     ×     t

There      d     =    70

Return     d     =    80

All that's left is the time column now.  We don't know how long it took to get there or back, but if it took 2 hours longer to get There than on the Return, the Return trip took t and the There trip took t + 2:

                      d     =     r     ×     t

There             d     =    70   ×    t+2

Return            d     =    80   ×     t

The distances, remember, are the same for both trips, so that means that by the transitive property of equality, their equations can be set equal to each other:

70(t + 2) = 80t

70t + 140 = 80t

140 = 10t

14 = t

That t represents the Return trip's time.  Add 2 hours to it since the There trip's time is t+2.  So 14 + 2 = 16.  

B.  16 hours

Number 3 is the correct answer

Tell me if you want further explanation

Answer:

f(x) = –2(x – 2)(x – 4)

Step-by-step explanation:

In the first two possible answer choices we have a 2 and a 4, whose product is 8, whereas we need a y-intercept of -16.  So omit the first two choices.

If the x-intercepts are at (2, 0) and (4, 0), the corresponding factors must be (x - 2)(x - 4), so the third answer, f(x) = –2(x – 2)(x – 4), must be the correct one.

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

The value of x is 12.5 in the triangle by using cosine function, option B is correct.

We need to find the value of x in the triangle.

The given triangle is a right angles triangle.

We find value of x by using cosine function.

Cosine function is a ratio of Adjacent side and hypotenuse.

Cosθ = Adj side/hypotenuse.

Here θ = 28 degrees.

Adjacent side = 11.

Hypotenuse = x.

Plug in these values in above formula:

Cos28 degrees = 11/x

x=11/cos28

x=11/0.882

x=12.47

x=12.5

Hence, the value of x is 12.5.

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1. First two pictures below.

2.Both of them have large clusters that are a couple spaces away. The range is greater with June 2013.  

3. Second two pictures below. The third pic is June 1985 and fourth is June 2013.

4. The spread is smaller for June 1985. The boxes are seem to have the same proximity to each other which shows a tight center between the two box plots.

May be to late, but I'll post my answers to your questions anyway :)

Final answer:

Without specific temperature data, we cannot create the comparative dot plots and box plots requested by the student. Instructions have been provided on how to create and analyze them once the data is available.

Explanation:

To answer the student's question about comparing the high temperatures for Dallas, Texas in June 1985 and June 2013 using comparative dot plots and comparative box plots, we first need the individual temperature data for each June to create these graphs. Unfortunately, without the specific data, we are unable to create the plots.

However, we can discuss how to approach this problem. To create a comparative dot plot, you would list the temperatures for each data set on a horizontal line, each set represented by dots. Then, assess the degree of overlap by visually inspecting where the dots from both data sets lie in relation to each other. Compare their shapes, centers, and spreads by observing the clustering of the dots, the location of the “middle” of the dots, and how far the dots extend out from the center.

For the comparative box plot, you would draw two box plots on the same axis. A box plot displays the minimum, first quartile, median (or second quartile), third quartile, and maximum. Assess the degree of overlap by comparing where the boxes and whiskers of the plots are positioned in relation to each other, again paying attention to the centers (medians), spreads (interquartile ranges), as well as the overall range of data. Both types of plots can help ascertain whether the high temperature in June of each year was significantly different from the other, and how each year's temperatures compare to the historical average.

It’s a frequency table, you find the middle number from the prices of mail received and you would multiply it. Not sure what with but if you search on Google Frequency tables there should be a good explanation.

Hope this helped you!

Answer:

6

Step-by-step explanation:

Arc length = radius * central angle

s = rθ

A circle is 2π radians, so 1/3 of that is 2/3 π.

Given that s = 12 and θ = 2/3 π:

12 = r (2/3 π)

r = 18/π

r ≈ 6

QUESTION 5

The given equation is:

[tex] \frac{5}{a + 3} = \frac{3}{a - 2} [/tex]

Cross multiply;

[tex]5(a - 2) = 3(a + 3)[/tex]

Expand:

5a-10=3a+9

Group similar terms:

5a-3a=9+10

2a=19

Divide both sides by 2

[tex]a = \frac{19}{2} [/tex]

[tex]a = 9\frac{1}{2} [/tex]

The correct answer is C.

QUESTION 7

The given equation is:

[tex] \frac{3}{y - 2}= 8[/tex]

There is an invisible 1 in the denominator on the RHS.

[tex] \frac{3}{y - 2}= \frac{8}{1} [/tex]

Cross multiply:

[tex] 3\times 1 = 8(y - 2)[/tex]

Expand:

[tex]3= 8y - 16[/tex]

Group similar terms,

[tex]3 + 16 = 8y[/tex]

[tex]19 = 8y[/tex]

Divide both sides by 8.

[tex]y = \frac{19}{8} [/tex]

[tex]y = 2 \frac{3}{8} [/tex]

The correct answer is C.

QUESTION 8

The given fraction is:

[tex] \frac{ {w}^{2} + 5w + 6}{ {w}^{2} - w - 12 } [/tex]

Factor both the numerator and the denominator to obtain:

[tex] \frac{(w + 3)(w + 2)}{(w + 3)(w - 4)} [/tex]

Cancel the common factors;

[tex]\frac{w + 2}{w - 4} [/tex]

The correct answer is B.

QUESTION 9

The given expression is;

[tex] \frac{3m}{m - 6} \times \frac{5 {m}^{3} - 30 {m}^{2} }{5 {m}^{2} } [/tex]

Factor the numerator of the second fraction.

[tex]\frac{3m}{m - 6} \times \frac{5 {m}^{2}(m - 6)}{5 {m}^{2} }[/tex]

Cancel the common factors,

[tex] \frac{3m}{1} [/tex]

[tex] = 3m[/tex]

The correct answer is D.

QUESTION 10

The given expression is:

[tex] \frac{7x + 21}{ {x}^{2} + 5x + 6} \div \frac{x + 6}{x + 2} [/tex]

Multiply by the reciprocal of the second fraction.

[tex]\frac{7x + 21}{ {x}^{2} + 5x + 6} \times \frac{x + 2}{x + 6} [/tex]

Factor the first fraction to get:

[tex]\frac{7(x + 3)}{ (x + 2)(x + 3)} \times \frac{x + 2}{x + 6} [/tex]

Cancel the common factors:

[tex] \frac{7}{x + 6} [/tex]

The correct answer is A.