Bobby hopes that he will someday be more than 70 inches tall he is currently 61 inches tall how many more inches, x,does Bobby need to grow to reach his desired height

Answer

Average speed of the train = 90 km/h and average speed of the airplane = 360 km/h.

Explanation:-

If speed of train = x then the  speed of airplane = 4x km/h and we have the 2 equations

x = 1440 / (t + 12)                               (t = time taken by the train)

4x = 1440 / t................................(1)       (t = time taken by train)

Multiply the first equation by 4:-

4x = 5760 / (t + 12).....................(2)  

Combining equations (1) and (2):-

1440 / t =  5760 / (t + 12)

Cross multiplying:-

5760t = 1440t + 17,280

4320t = 17,280

t = 17280/4320

t = 4 hours

speed of train = 1440/ (4 + 12) = 90 km/h and speed of plane = 4*90 = 360 km/h.

[tex]2)\\\\6+5k+2=18\\\\(6+2)+5k=18\\\\8+5k=18\qquad\text{subtract 8 from both sides}\\\\5k=10\qquad\text{divide both sides by 5}\\\\\boxed{k=2}\\\\4)\\\\-8(a-8)=96\qquad\text{divide both sides by (-8)}\\\\a-8=-12\qquad\text{add 8 to both sides}\\\\\boxed{a=-4}[/tex]

[tex]6)\\7m+35=7(5m-3)\qquad\text{divide both sides by 7}\\\\m+5=5m-3\qquad\text{subtract 5 from both sides}\\\\m=5m-8\qquad\text{subtract 5m from both sides}\\\\-4m=-8\qquad\text{divide both sides by (-4)}\\\\\boxed{m=2}[/tex]

Answer: D

Step-by-step explanation:

Inverse is when the x's and y's are swapped

x   |   y        Inverse

-3 |   5         (5, -3)

-2 |  -3         (-3, -2)

0 |   3          (3, 0)

1  |  -5         (-5, 1) ← this matches choice D

2  |   6          (6, 2)

3  |  10          (10, 3)

Answer:

14.4 yards

Step-by-step explanation:

Each shirt needs 0.8 yards so 18 shirts needs 18 * 0.8 = 14.4 yards of material.

14.4 yards of material will be needed to make 18 shirts.

Multiplication is when you take one number and add it together a number of times.

Given that, one shirt is of 0.8 yards of material,

18*0.8 = 14.4

Hence, 14.4 yards of material will be needed to make 18 shirts.

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Answer: [0, 6) ∪ (6, 15]

Step-by-step explanation:

The particle is moving to the right when the velocity is positive.

[tex]s(t)=\dfrac{t^3}{3} -\dfrac{12t^2}{2}+36t[/tex]

v(t) = s'(t)

     = t² - 12t + 36

First, find the zeros of v(t): ⇒ v(t) = 0

  0 = t² - 12t + 36

     = (t - 6)²

0 = t - 6

6 = t

The zero occurs when t = 6

Next, find when v(t) > 0

Choose a test point between 0 and 6:

v(5) = (5 - 6)²

     =     (-²)

     =      (+)

Since velocity is positive between 0 and 6, the particle is moving to the right during that interval.

Choose a test point between 6 and 15:

v(7) = (7 - 6)²

     =    (+)²  

     =    (+)

Since velocity is positive when t > 6, the particle is moving to the right.

Answer:

190 percentage of the weight limit is 114 pounds.

Step-by-step explanation:

Given: A rocking horse has a weight limit of 60 pounds.

We have to find what percentage of the weight limit is 114 pounds.

x percentage of the weight limit is 114 pounds.

⇒ x% of 60 = 114

[tex]\frac{x}{100} \times 60 = 114[/tex]

Solve for x;

[tex]\frac{6x}{10} = 114[/tex]

Multiply both sides by 10 we get;

[tex]\frac{6x}{10} \times 10 = 114 \times 10[/tex]

[tex]6x = 1140[/tex]

Divide both sides by 6 we get;

[tex]x = \frac{1140}{6}[/tex]

Simplify:

x = 190%

Therefore, 190 percentage of the weight limit is 114 pounds.

To find the percentage, divide the given weight by the weight limit and multiply by 100. 114 pounds is 190% of the weight limit of 60 pounds.

To find the percentage of the weight limit, we need to divide the given weight (114 pounds) by the weight limit (60 pounds) and then multiply the result by 100. So, the calculation would be:

Percentage = (114 pounds / 60 pounds) * 100

Simplifying this equation, we get:

Percentage = 190%

Therefore, 114 pounds is 190% of the weight limit of 60 pounds.

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Answer: 6.3093

Step-by-step explanation:

[tex]3^{\frac{x}{5}} = 4[/tex]

[tex]ln3^{\frac{x}{5}} = ln4[/tex]

[tex]\frac{x}{5} ln3 = ln4[/tex]

xln3 = 5ln4

[tex]x = \frac{5ln4}{ln3}[/tex]

x = 6.3093

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Answer: 5, 3, [tex]\frac{1}{5}[/tex], D

Step-by-step explanation:

a) x ≤ 0 so, f(-5) = | -5 | = 5

   x ≤ 0 so, f(-3) = | -3 | = 3

   x > 0 so, f(5) = [tex]\frac{1}{5}[/tex]

b) graph D

************************************************************

Answer: [tex]\frac{\pi}{12}[/tex]

Step-by-step explanation:

 [tex]\frac{25\pi}{12} - \frac{2\pi}{}[/tex]

=  [tex]\frac{25\pi}{12} - \frac{24\pi}{12}[/tex]

=  [tex]\frac{\pi}{12}[/tex]

The roots of the polynomial function F(x)=x^3-3x^2+2 can be found by reducing the function to zero and solving for x, likely by applying synthetic division or the Rational Root Theorem, as the polynomial is of third order.

In Mathematics, especially in algebra, we often encounter the concept of finding the roots of polynomial functions. The roots of the function F(x)=x^3-3x^2+2 can be found by setting the function equal to zero and solving for the variable x:

Note: This explanation suggests general approaches. The actual solution would require longer calculations.

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The only root of the polynomial function F(x) = x³ - 3x² + x + 5 is 2 + i.

Let's go through the possible roots of this polynomial function one by one and see which of them will make the function equal to zero. Recall that if a number p is a root of a polynomial, then when we substitute p into the polynomial, the resulting value will be zero.

A. First, let's consider 2+i as a possible root.

We would evaluate F(2+i) = (2+i)³ - 3(2+i)² +(2+i) + 5 = 0.

Upon evaluation, it turns out that F(2+i) does indeed equal 0.

B. Now let's see if -2+i is a root.

We evaluate F(-2+i) = ((-2+i)³ - 3(-2+i)² + (-2+i) + 5. This happens not to equal 0. Therefore, -2+i is not a root.

C. Then, we check if 1 is a root by computing

F(1) = 1³ - 3×1² +1 +5. Upon computing, we find that this doesn't result in 0 either. So, 1 is not a root

D. Finally, let's check if 2 is a root.

We compute F(2)= 2³ - 3×2² +2 +5. This computation also doesn't result in 0, therefore 2 is not a root of the polynomial function.

In conclusion, the only given number that is a root of the function is 2 + i.

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Which of the following are roots of the polynomial function below?

F(x)=x³-3x²+x+5

A. 2+i

B. -2+i

C. 1

D. 2

Answer:

When f(x) is 0, then x is -1.8.

Step-by-step explanation:

To find this, you simply have to look for the place where the line crosses the x axis. This is where y (or f(x)) is equal to 0. Since this graph only crosses that axis at x = -1.8, that is the number we are looking for.

well, we don't have to use the pythagorean theorem per se, only the distance formula, since the distance formula is really the pythagorean theorem in disguise.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ M(\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\qquad N(\stackrel{x_2}{4}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ MN=\sqrt{[4-5]^2+[-8-(-3)]^2}\implies MN=\sqrt{(4-5)^2+(-8+3)^2} \\\\\\ MN=\sqrt{(-1)^2+(-5)^2}\implies MN=\sqrt{26}[/tex]

Answer:

B

Step-by-step explanation:

We have perpendicular bisector through a chord of the circle. We know the length, so either side of the chord is 11 due to the bisector cutting it directly in half. Since the radius is a fixed distance from the center to any point on the edge of the circle, we can draw the radius x from the circle to the end of the chord to form a right triangle.

We can use Pythagorean Theorem [tex]a^{2} +b^{2} =c^{2}[/tex] to find the missing side length x. a=6, b=11 and c=x.

[tex](6)^{2} +(11)^{2} =x^{2}[/tex]

[tex]36+121=x^2\\157=x^2\\\sqrt{157}=x\\ 12.5=x[/tex]

Answer:

125 candy bars

Step-by-step explanation:

[tex]\text{Let the number of candy bars sold by Carley is }x\\\text{Then since Beth has sold one less than twice the number of candy bars}\\\text{that Carley has sold, so number of candy bars sold by Beth}=2x-1\\\\\text{also given that they have sold 188 candy bars in all, so we have}\\\\\text{Candy bars sold by Carley + Candy bars sold by Beth}=188\\\\\Rightarrow (x)+(2x-1)=188\\\\\Rightarrow 3x-1=188\\\\\Rightarrow 3x=189\\\\\Rightarrow x=\frac{189}{3}=63[/tex]

[tex]\text{Hence the candy bars sold by Beth are:}\\=2x-1\\\\=2(63)-1\\\\=126-1\\\\=125\\\\\text{Hence, Beth sold 125 candy bars.}[/tex]

Answer:

100 yards

Step-by-step explanation:

It takes 4 yards of fabric to make a costume for one student.  She needs to make costumes for every student in chorus, so you just multiply this number by 25 and get 100 yards.

Answer:

100 yards.

Step-by-step explanation:

We have been given that a seamstress uses 12 yards of fabric to make 3 costumes for students in the chorus.

We will use proportions to solve the given problem.

[tex]\frac{\text{Yards of fabric}}{\text{Costumes}}=\frac{12}{3}[/tex]

[tex]\frac{\text{Yards of fabric}}{25}=\frac{12}{3}[/tex]

[tex]\frac{\text{Yards of fabric}}{25}*25=\frac{12}{3}*25[/tex]

[tex]\text{Yards of fabric}=4*25[/tex]

[tex]\text{Yards of fabric}=100[/tex]

Therefore, 100 yards of fabric is needed to make costumes for 25 students.

Answer: The meaning y-intercept is the initial value of a rare coin is 6.

Step-by-step explanation:

Given : The graph of [tex]f(t) = 6\times 2^t[/tex] shows the value of a rare coin in year t.

The y- intercept is the point on Cartesian plane when the graph intersects y axis. It given the initial value of the function by substituting the value of independent variable as zero.

i.e. , we need to put t=0, we get

[tex]f(0) = 6\times 2^0=6[/tex]

The meaning y-intercept is the initial value of a rare coin is 6.

Answer:

This team can lose 6 games and still achieve this goal.

Step-by-step explanation:

In order to find this, we can create a proportion and solve by cross multiplying. The proportion should compare amount of losses to total games.

Ratio = Total  

2/5 = x/15

Now cross multiply

15*2 = 5x

30 = 5x

6 = x

This means the team can lose 6 games and still keep the necessary ratio.

Answer:

8

Step-by-step explanation:

Change mixed number to decimal                    6 2/5 = 6.4

Change needed fraction to decimal                  4/5 = 0.8

Divide yogurt by yogurt needed                         6.4 / 0.8 = 8

Working the problem like this will help you with any same type of problem.

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Answer: He can make 8 smoothies.

Step-by-step explanation:

Given : The total amount of yogurt Dean has = [tex]6\dfrac{2}{5}[/tex] cups

In Improper fraction , it will be :

[tex]6\dfrac{2}{5}=\dfrac{6\times5+2}{5}=\dfrac{32}{5}[/tex]

Also, the amount of yogurt required for a fruit smoothie = [tex]\dfrac{4}{5}[/tex]

Now , The number of smoothies he can make = (Total amount of yogurt Dean has) ÷ (amount of yogurt required for a fruit smoothie )

[tex]=\dfrac{32}{5}\div\dfrac{4}{5}\\\\=\dfrac{32}{5}\times\dfrac{5}{4}=8[/tex]

Hence, he can make 8 smoothies.

Answer:

f^-1(x) = (x +7)/5

Step-by-step explanation:

Set x = f(y) and solve for y.

... x = 5y -7

... x+7 = 5y

... (x+7)/5 = y . . . . this is the inverse function

f^-1(x) = (x +7)/5

We know that : In a Triangle, If Two Angles are Equal then Corresponding Sides with Respect to those Two Angles Should be Equal.

In the Given Right Angled Triangle, There are Two Angles which are Equal to 45°. It means The Lengths of the Sides Corresponding to those Equal 45° Angles should be Equal.

It Means The Given Right Angled Triangle is also an Isosceles Triangle

⇒ The Other Side of the Triangle is [tex]3\sqrt{2}[/tex]

As it is a Right Angled Triangle :

[tex]\mathsf{\implies (Hypotenuse)^2 = (3\sqrt{2})^2 + (3\sqrt{2})^2}[/tex]

[tex]\mathsf{\implies (Hypotenuse)^2 = 18 + 18}[/tex]

[tex]\mathsf{\implies (Hypotenuse)^2 = 36}[/tex]

[tex]\mathsf{\implies (Hypotenuse) = 6}[/tex]

The Length of Hypotenuse is 6

Answer:

a

Step-by-step explanation:

104 is the only number inside the box

The value of ∠1  is 38 degree , Option B is the correct answer.

Parallelogram is a polygon with four sides , Opposite sides are parallel and equal.

From the figure given

One of the angle is 104 degree

when two lines are parallel and intersected by a transversal

then the sum of the consecutive interior angles is 180 degree

∠1  +  ∠2 =  180 -104 = 76 degree

similarly the other two lines are parallel with each other

so  ∠1  =  ∠4

∠3 =   ∠2

Therefore the diagonals are bisecting the angle and so

the value of ∠1   = 76 / 2 = 38 degree

Therefore , The value of ∠1  is 38 degree , Option B is the correct answer.

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Answer:

3 brownies

Step-by-step explanation:

To find this answer we need to divide the 0.81 by 0.27 to find out how many brownies total 0.81:

0.81 ÷ 0.27 = 3

So he needs to sell 3 brownies.

Answer: [tex]\bold{\dfrac{1}{36}}[/tex]

Step-by-step explanation:

The first die can be any number:  [tex]P = (\dfrac{6}{6}) = 1[/tex]

The second die must match the first die: [tex]P = \dfrac{1}{6}[/tex]

The third die must also match the first die: [tex]P = \dfrac{1}{6}[/tex]

1st die   and   2nd die   and    3rd die  =  Probability of success

   1          x          [tex]\dfrac{1}{6}[/tex]             x          [tex]\dfrac{1}{6}[/tex]         =               [tex]\dfrac{1}{36}[/tex]

25 friends because 7*5=35

The volume of the cube would be S^3, where S is the length of the side.

Volume = (5a + 4b)^3

Which becomes:

(5a+4b)(5a+4b)(5a+4b)  

Multiply the first two sets of parenthesis by each other:

(25a^2+40ab+16b^2)(5a+4b)  

Now multiply that by the 3rd set of parenthesis to get:

125a^3+300a^2b + 240ab^2 + b^3

Answer:

x = 32

Step-by-step explanation:

This is an equilateral triangle, all three sides equal.  Since all three sides are equal, all three angle are equal.  180/3 = 60.  That means each angle is equal to 60 degrees.

2x-4 = 60

Add 4 to each side

2x-4+4 = 60+4

2x =64

Divide each side  by 2.

2x/2 = 64/2

x = 32

Answer:

2l + 3 = 39

Step-by-step explanation:

the equation is 3 + 2L = C, where L is Lindsay's age and C is Carol's age

3 + 2L = 39

Answer:

hello :

the graph passes by ( -4; 7/128)  : f(-4) = 7/128

a/ (-4)^4 = 7/128

a / 256 = 7/128

a/2 = 7

a = 14

We have the point:

[tex]\left(-4,\ \dfrac{7}{128}\right)[/tex]

Put the coordinates of the point to the equation of the function f:

[tex]f(x)=\dfrac{a}{x^4}\to y=\dfrac{a}{x^4}\\\\\left(-4,\ \dfrac{7}{128}\right)\to x=-4,\ y=\dfrac{7}{128}\\\\\dfrac{a}{(-4)^4}=\dfrac{7}{128}\\\\\dfrac{a}{256}=\dfrac{7}{128}\qquad\text{multiply both sides by 256}\\\\a=\dfrac{7}{128}\cdot256\\\\\boxed{a=14}[/tex]