2. Simplify 14 to the 15th power over 14 to the 5th power . 1) 13 2) 110 3) 143 4) 1410

Step-by-step explanation:

We have,

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function :

[tex]h=-16t^2 + 36t + 10[/tex] ......(1)

Part (a) :

The maximum height reached by the ball is given by :

[tex]\dfrac{dh}{dt}=0\\\\\dfrac{d(-16t^2 + 36t + 10)}{dt}=0\\\\-32t+36=0\\\\t=\dfrac{36}{32}\\\\t=1.125\ s[/tex]

Part (b) :

The maximum height of the ball is calculated by putting t = 1.125 in equation (1) such that :

[tex]h=-16(1.125)^2 + 36(1.125)+ 10\\\\h=30.25\ m[/tex]

Answer:

Step-by-step explanation:

correct one is b

Answer: $1.35

Step-by-step explanation:

1.29 * 5% = 1.29 * 0.05 = 0.0645

0.0645 rounds down to 0.06

1.29 + 0.06 = 1.35

Answer:

x = 360° - 132° - 54° - 90°

x = 84°

Step-by-step explanation:

total degree of a cirlce is 360°

Answer:

[tex]84 \: \: degrees[/tex]

Step-by-step explanation:

[tex]90 + 132 + 54 + x = 360 \\ 276 + x = 360 \\ x = 360 - 276 \\ x = 84 \: \: degrees[/tex]

Answer:

6 : 1

Step-by-step explanation:

Given the ratio

12 : 2 ( divide both parts by 2 )

= 6 : 1 ← in the form n : 1

Answer:

pls mark as brainliest

Step-by-step explanation:

let the ratio be= 2:1

let the boys be= 2x

let the girls be= 1x=x

x+24=2x

x-2x=-24

-x=-24

so the minus sign will cut

x=24

2x=2×24

Boys in the class are 48

hope it helps you

Answer:

48 boys

Step-by-step explanation:

girls: x, boys: 2x

x+24=2x

24=x

girls=24, boys=48

Answer:

The third option: 48 degrees.

Step-by-step explanation:

Angle GFH is congruent to angle CFE, which is congruent to ACB, therefore, all are congruent and equal to 48.

Answer:

x = 48

Step-by-step explanation:

∠x ≅ ∠C (vertical angles)

∠C ≅ ∠CFG (corresponding angles)

∠CFG ≅ ∠HFG ≅ 48° (vertical angle)

So

∠x ≅ 48 (Transitive property of equality)

Answer:

RQ=35.51 km

PR=34.62 km

Step-by-step explanation:

Bearing of Q from P = 72 degrees

Bearing of R from Q=320 degrees

320=270+50

Therefore, the second angle of Q is 50 degrees.

[tex]\angle P=72^\circ\\\angle Q=68^\circ\\\angle R=180^\circ-(72^\circ+68^\circ)=40^\circ[/tex]

Using Law of Sines

[tex]\dfrac{r}{\sin R} =\dfrac{p}{\sin P} \\\dfrac{24}{\sin 40} =\dfrac{p}{\sin 72} \\p=\sin 72 \times \dfrac{24}{\sin 40}\\\\p=RQ=35.51$ km[/tex]

Using Law of Sines

[tex]\dfrac{q}{\sin Q} =\dfrac{r}{\sin R} \\\dfrac{q}{\sin 68} =\dfrac{24}{\sin 40} \\q=\dfrac{24}{\sin 40}\times \sin 68\\\\q=PR=34.62$ km[/tex]

Answer:

Length = 7 cm

Width = 2 cm

Step-by-step explanation:

Perimeter of rectangle = 18 cm

Let length of rectangle = [tex]l[/tex] cm

Let width of rectangle =  [tex]w[/tex] cm

As per given statement, length is 3 cm more than the twice of its width:

Writing equation:

[tex]l = 2\times w +3 ....... (1)[/tex]

Formula for perimeter of a rectangle is given as:

[tex]P = 2 \times (Length + Width)[/tex]

OR

[tex]P = 2 \times (l + w)[/tex]

Putting values of P as given and [tex]l[/tex] by using equation (1):

[tex]18 = 2 \times (2w +3 + w)\\\Rightarrow \dfrac{18}2 = 3w +3 \\\Rightarrow 9 = 3w +3\\\Rightarrow 3w = 9 -3\\\Rightarrow w = \dfrac{6}{3}\\\Rightarrow w = 2\ cm[/tex]

Putting value of [tex]w[/tex] in equation (1):

[tex]l = 2\times 2 +3 \\\Rightarrow l = 4+3\\\Rightarrow l = 7\ cm[/tex]

So, the dimensions are:

Length = 7 cm

Width = 2 cm

Answer:

It moves 8 to the right

Step-by-step explanation:

This is in the y axis so it will move 8 on the x axis

The last 2 shapes.

When you rotate both of them 360 degrees only at 180 and back at 360 it looks same.

Answer:

46

Step-by-step explanation:

=> [tex]10+7^2-14+1[/tex]

=> 10+49-14+1

=> 59-14+1

=> 45+1

=> 46

Answer:

46

Step-by-step explanation:

10+7^2-14+1

10+49-14+1

59-14+1

45+1

46

Answer:

4.92*10^5

Step-by-step explanation

The annual flow of the Mississippi River would fit in the Atlantic Ocean approximately 4.92 x 10⁵ times.

The space occupied by an object in three-dimensional space is called the volume of an object. In simple words, space is taken by an object.

To find out how many times the annual flow of the Mississippi River would fit in the Atlantic Ocean, we need to divide the volume of the Atlantic Ocean by the annual flow of the Mississippi River:

number of times = (volume of Atlantic Ocean) / (annual flow of Mississippi River)

= (3.1 x 10¹⁷ cubic meters) / (6.3 x 10¹¹ cubic meters)

= 4.92 x 10⁵

Rounding to two decimal places, the final answer is approximately 4.92 x 10⁵. Therefore, the annual flow of the Mississippi River would fit in the Atlantic Ocean approximately 492,000 times.

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Answer:

d

Step-by-step explanation:

To construct an angle bisector with a compass  D. Place the compass needle on the vertex of the angle, and draw an arc across both legs of the angle.

An angle bisector is a line segment that divides angle into two equal parts.

According to the given statements to construct an angle bisector using a compass span any width of radius in a compass pace in onto the vertex of the angle cut the two arc on the two lines then without changing the radius draw two arcs where the previous arcs have intersected the two lines.

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Answer:

117, 118

Step-by-step explanation:

if 2 consecutive numbers have a sum of 235, then

Let the 2 numbers be n and n+1

Given That:

n + n+1 = 235

Simplify and solve:

2n + 1 - 235

2n = 234

n = 117.

If n = 117, then n +1 = 118. These are the 2 consecutive numbers.

Hope this helps.

Good Luck

Answer:

236 AND 237

Step-by-step explanation:

Two consecutive numbers means next two continuous numbers

Answer:

6, 8, 10

Step-by-step explanation:

x y and z are three consecutive even numbers

it means that you can write y = x + 2

and z = y + 2 = x + 4

so

  [tex]y^2-2=2x+5z\\ <=> (x+2)^2-2=2x+5(x+4)\\<=>x^2+4x+4-2=2x+5x+20[/tex]

  [tex]<=> x^2+4x+2=7x+20\\<=>x^2+4x+2-7x-20=0\\<=>x^2-3x-18=0\\<=>(x+3)(x-6)=0<=>(x=-3\ or \ x=6)[/tex]

so the solutions are

x = 6

y = 8

x = 10

Answer:

6, 8, 10

Step-by-step explanation:

x, y, z

y=x+2, z= x+4

Solving the quadratic equation we get:

Answer:

1060

Step-by-step explanation:

Given:

No. of boys = 870

No. of girls = 800

Probability that a boy chosen studies Spanish = [tex]\dfrac{2}{3}[/tex]

Probability that a girl chosen studies Spanish = [tex]\dfrac{3}{5}[/tex]

the number of boys in the school who study Spanish :

[tex]\dfrac{2}{3}\times 870=290\times 2=580[/tex]

the number of girls in the school who study Spanish :

[tex]\dfrac{3}{5}\times 800 \\=3\times 160\\\\=480[/tex]

Therefore, total number of students who study Spanish would be :

480+580=1060

Answer:

B. Pentagon

Step-by-step explanation:

A cross-section is basically the 2D figure created by slicing through a 3D shape.

Take a look at this figure: it's a pentagonal prism. One note to remember is that for all prisms, their cross-sectional shapes are the same shapes as the shape of their bases.

Here, the two bases are pentagons, so we know the cross-section will be a pentagon.

Thus, the answer is B.

~ an aesthetics lover

Answer:

8 x^6  y^3

Step-by-step explanation:

(2x^2y)^3

(ab)^c = a^c  * b^c

2^3  * x^2^3  * y^3

8  * x^2^3  * y^3

We know that a^b^c = a^(b*c)

8  * x^(2*3)  * y^3

8  * x^(6)  * y^3

8 x^6  y^3

Answer:

t ≤ 4.24

Step-by-step explanation:

P(t) ≥ 40000 implies

500t/(2t²+9) ≥ 40000

Multiplying through by t², we have

500t ≥ 40000(2t²+9)

500t/40000 ≥ 2t²+9

Collecting like terms

0.0125t  ≥ 2t²+9

0  ≥ 2t²+ 9 - 0.0125t

2t²+ 9 - 0.0125t  ≤ 0

2t²- 0.0125t + 9 ≤ 0

Using the quadratic formula,

[tex]t = \frac{-(-0.0125) +/-\sqrt{(-.0125)^{2} - 4 X 2 X 9} }{2 X 2} \\= \frac{0.0125 +/-\sqrt{(0.00015625 - 288} }{4}\\= \frac{0.0125 +/-\sqrt{-287.9998} }{4}\\= \frac{0.0125 +/-16.97i }{4}\\=0.00313 + 4.24i or 0.00313 - 4.24i[/tex]

The factors of the equation are (t - 0.00313 -4.24i) and (t - 0.00313 + 4.24i)

So, (t - 0.00313 -4.24i)(t - 0.00313 + 4.24i) ≤ 0

(t - 0.00313)² - 4.24² ≤ 0

(t - 0.00313)² ≤ 4.24²

taking square-root of both sides,

√(t - 0.00313)² ≤ √4.24²  

t - 0.00313 ≤ 4.24

t ≤ 4.24 + 0.00313

t ≤ 4.24313 ≅ 4.24

t ≤ 4.24

Answer:

Step-by-step explanation:

This is an exponential function. In order to find the answer to the question, we need to first determine what the equation is that models this information. The standard form for an exponential function is

[tex]y=a(b)^x[/tex] where a is the initial value and b is the growth/decay rate. If the starting population is 5000, then

a = 5000

If the population is growing, that means that it retains 100% of the initial population and is added to by another 3.5%. So in a sense the population grows 100% + 3.5% = 103.5% or, in decimal form, 1.035. So

b = 1.035

Our function is

[tex]y=5000(1.035)^x[/tex] where y is the ending population and x is the number of years it takes to get to that ending population. We want to know how long, x, it will be til the population reaches 7300, y.

[tex]7300=5000(1.035)^x[/tex] and we need to solve for x. The only way to do that is by using logs. I'll use natural logs for this.

Begin by dividing both sides by 5000 to get

[tex]1.46=1.035^x[/tex] and take the natural log of both sides:

[tex]ln(1.46)=ln(1.035)^x[/tex]

The power rule for natural logs is that we can now bring the exponent down in front of the ln to get:

[tex]ln(1.46)=xln(1.035)[/tex] To solve for x, we now divide both sides by ln(1.035):

[tex]\frac{ln(1.46)}{ln(1.035)}=x[/tex]

Do that division on your calculator and get that

x = 11.0 years.

That means that 11 years after the population was 5000 it will be expected to reach 7300 (as long as the growth rate remains 3.5%)

Answer:

-x^2+3x+3;  5

Step-by-step explanation:

polynomial is -x^2+3x+3

when x=2 then -2^2+3*2+3=-4+6+3=5

The solution is Option B.

The value of the equation is A = -x² + 3x + 3 , and when x = 2 , A = 5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = x + 3x² + 2x - 3 - 4x² + 6   be equation (1)

On simplifying the equation , we get

A = 3x² - 4x² + x + 2x - 3 + 6

A = -x² + 3x + 3

Now , when x = 2

Substitute the value of x = 2 in the equation , we get

A = - ( 2 )² + 3 ( 2 ) + 3

A = -4 + 6 + 3

A = 9 - 4

A = 5

Therefore , the value of A is 5

Hence , the equation is A = -x² + 3x + 3

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Answer:

Do it your self

Step-by-step explanation:

Answer:

35 cm

Step-by-step explanation:

As shown in the image attached, the A large rectangle is made by joining three identical small rectangles,

The width of one small rectangle is x cm and the length of one small rectangle is 2x cm. Therefore the perimeter of the small rectangle is given as:

2(length + width) = Perimeter

2(2x + x) = 21

2(3x) = 21

6x = 21

x = 21/6 = 3.5 cm

x = 3.5 cm

From the image attached, the width of the large rectangle is 2x (x + x) and the length is 3x (2x + x). Therefore, the perimeter of the large rectangle is:

2(length + width) = Perimeter

2(3x + 2x) = Perimeter

Perimeter = 2(5x)

Perimeter = 10x

Perimeter = 10(3.5)

Perimeter = 35 cm

Answer:

0.08 minutes for a kilometer.

Step-by-step explanation:

If the track is 25 kilometers, and he runs 25 kilometers in 2 minutes, he runs a kilometer in 2÷25 minutes or 0.08 minutes which is 4.8 seconds.

I'm pretty sure the track isn't 25 kilometer or he can't run a lap in 2 minutes. But if so, the answer is 0.08 minutes.

Answer: 0.5

Step-by-step explanation:

Total bags (U) = 140

Number of bags with both button and zip:

(48 + 47 + x + 22) = 140

117 + x = 140

x = 140 - 117

x = 23

Therefore, probability that bag has button :

Total Number of bags with button:

(Bags with button alone + bags with both button and zip)

(47 + 23) = 70

Probability = (required outcome / Total possible outcomes)

P(bag has button) = (number of bags with button / total number of bags)

P(bag has button) = 70/140 = 0.5

P(bag has button) = 0.5

Answer:

[tex]\frac{8}{27}[/tex] is the probability that a player draws out two tiles of the same color assuming they are drawing one tile from each bag.

Step-by-step explanation:

In each bag there are red, green, and blue tiles, meaning that no matter which color is pulled out first there is always some probability that the second tile will be the same color. So, we can set up three possible outcomes:

Red: The player pulls out a red tile first. This has a [tex]\frac{1}{9}[/tex] probability of happening. Then in order to succeed for the problem, the next tile also needs to be red which has a [tex]\frac{6}{12}[/tex] probability attached to it. [tex]\frac{1}{9}[/tex] × [tex]\frac{6}{12}[/tex]=[tex]\frac{1}{18}[/tex] probability of happening.

Green: There is a [tex]\frac{5}{9}[/tex] probability of the player pulling out a green tile first. In this case we want to calculate the probability of the second tile being green, which would be [tex]\frac{4}{12}[/tex]. [tex]\frac{5}{9}[/tex]×[tex]\frac{4}{12}[/tex]=[tex]\frac{5}{27}[/tex].

Blue: There is a [tex]\frac{3}{9}[/tex] probability of the first tile being blue in which case we are hoping for the second tile to be blue as well. The probability of the second tile being blue is [tex]\frac{2}{12}[/tex] on its own, and them both being blue is  [tex]\frac{3}{9}[/tex]×[tex]\frac{2}{12}[/tex]=[tex]\frac{1}{18}[/tex]

Adding [tex]\frac{1}{18}[/tex]+[tex]\frac{1}{18}[/tex]+[tex]\frac{5}{27}[/tex] we get the answer [tex]\frac{8}{27}[/tex].

Answer:

x^2-6x+9

Step-by-step explanation:

(x-3)^2

(x-3)(x-3)

x^2-3x-3x+9

x^2-6x+9

Answer:

12.5%

Step-by-step explanation:

8 / 64*100 =

(8 * 100) / 64 =

800 / 64 = 12.5

Hope this helped buddy! :D

Answer:

total memory = 8 GB + 64 GB

= 72 GB

extra memory = 64 GB

so percentage increase of memory

= ( 64 GB / 72 GB ) × 100

= 88.89 %