Rewrite 3/4x+2=9/10 so that it doesn’t have fractions

Answer:

The given equation is H = -16t^2 + 64t + 60, where t is the elapsed time in seconds. This equation represents the height, H, of an object thrown upward from the ground with an initial velocity of 64 ft/s.    

Step-by-step explanation:

1. The term -16t^2 represents the effect of gravity on the object. Since the coefficient is negative, it indicates that the object is moving upward against the force of gravity. The square of the time, t^2, shows that the effect of gravity increases as time passes.  2. The term 64t represents the initial velocity of the object. The coefficient 64 indicates that the object was thrown upward with an initial velocity of 64 ft/s. The time, t, shows the effect of the initial velocity on the height.  3. The constant term 60 represents any additional height above the ground at the start. It could be the height from which the object was thrown or any elevation from the ground.  By plugging different values of t into the equation, you can find the corresponding heights at different times. For example, if you substitute t = 0, the equation becomes H = -16(0)^2 + 64(0) + 60 = 60. This means that at the start (t = 0), the object is at a height of 60 feet above the ground.  To find the maximum height reached by the object, we need to determine the vertex of the parabolic equation. The vertex is given by the formula t = -b/(2a), where a and b are the coefficients of t^2 and t, respectively.  In this case, a = -16 and b = 64. Substituting these values into the formula, we get t = -64/(2(-16)) = 2 seconds. This means that the object reaches its maximum height after 2 seconds.  To find the maximum height, substitute t = 2 into the equation: H = -16(2)^2 + 64(2) + 60 = 64 feet. Therefore, the object reaches a maximum height of 64 feet above the ground after 2 seconds.  I hope this explanation helps you understand the meaning of the given equation and how to interpret it in the context of elapsed time and height. Let me know if this helped!

Answer:

Step-by-step explanation:

u had 11 and u spent 7

7/11 <=== the fraction of money u spent is 7 out of 11

Answer:

813 = 800 + 10 + 3 = (8 [tex]\times 10^{2}[/tex] ) + ( 1[tex]\times 10^1[/tex] ) + ( 3 [tex]\times 10^0[/tex] )  

Step-by-step explanation:

i) 813 = 800 + 10 + 3 = (8 [tex]\times 10^{2}[/tex] ) + ( 1[tex]\times 10^1[/tex] ) + ( 3 [tex]\times 10^0[/tex] )  

answer: 28: 4

21: 3

70: 10

step-by-step explanation:

divide 28 by 4, and of course, do to the bottom what you do to the top. 4 divided by 4 is 1, and 28 divided by 4 is 7.

7: 4.

then, multiply by the number of smoothies.

for 3, it's 21: 3.

for 10, it's 70: 10.

Answer:

n = 5

Step-by-step explanation:

Step  1  :

Step  2  :

Pulling out like terms :

2.1     Pull out like factors :

  -4n + 30  =   -2 • (2n - 15)

Equation at the end of step  2  :

 (0 -  -6 • (2n - 15)) -  -30  = 0

Step  3  :

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  12n - 60  =   12 • (n - 5)

Equation at the end of step  4  :

 12 • (n - 5)  = 0

Step  5  :

Equations which are never true :

5.1      Solve :    12   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

5.2      Solve  :    n-5 = 0

Add  5  to both sides of the equation :

                     n = 5

One solution was found :

                  n = 5

Processing ends successfully

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To solve this, you need to isolate/get the variable "n" by itself in the equation:

-3(-4n + 30) = -30        Divide -3 on both sides

[tex]\frac{-3(-4n+30)}{-3} =\frac{-30}{-3}[/tex]     [two negative signs cancel each other out and become positive]

-4n + 30 = 10       Subtract 30 on both sides

-4n + 30 - 30 = 10 - 30

-4n = -20          Divide -4 on both sides to get "n" by itself

[tex]\frac{-4n}{-4}=\frac{-20}{-4}[/tex]

n = 5

PROOF

-3(-4n + 30) = -30       Substitute/plug in 5 into "n"

-3(-4(5) + 30) = -30

-3(-20 + 30) = -30      Simplify what's inside the parentheses  [PEMDAS}

-3(10) = -30

-30 = -30

Answer:

45.7%

Step-by-step explanation:

16/14*40%=45.7%

The correct statement is that the profit is 60% if it had been sold for $16.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.Triangle?

Given

When an article was sold for $14 the profit was 40%.

When an article was sold for $14 the profit was 40%.

Then, the cost of the article will be $10.

If the article is sold for $16.

Then profit will be

[tex]\rm Profit = \dfrac{selling\ price \ - \ cost\ price}{cost\ price}*100\\\\\rm Profit = \dfrac{16-10}{10}*100\\\\\rm Profit = 60 \%[/tex]

Thus, the profit will be 60%.

More about the percentage link is given below.

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To complete the calculations, more data is needed. We only have the angle of elevation of the mother bird, we need one relevant data, as for example, the distance from Lisa to the tree. We'll assume it to be 20 feet.

Answer:

The mother bird is 47 feet above the ground

Step-by-step explanation:

Right Triangles

They are a special type of triangles that have an internal angle of 90°. In such conditions, the following trigonometric relationship is valid:

[tex]\displaystyle tan\theta=\frac{y}{x}[/tex]

Where [tex]\theta[/tex] is the angle of elevation, y is the height of the triangle and x is the horizontal distance to the vertical leg

We can easily find the height of the tree by solving for y

[tex]y=xtan\theta[/tex]

[tex]y=20tan67^o[/tex]

[tex]y=47\ feet[/tex]

The mother bird is 47 feet above the ground

The calculation of take home pay is the actual amount calculation of how much you will be credited on a job done well.

Step-by-step explanation:

Before calculation, things to be taken care of are -

Now knowing these much in exact form of amount, we may proceed to calculation -

Answer:

[tex]y=-1.5x[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In this problem we have

y=15/2 when x=-5

Find the constant of proportionality k

[tex]k=\frac{y}{x}[/tex]

substitute the given values

[tex]k=\frac{(15/2)}{-5}=-1.5[/tex]

therefore

The linear equation that relates x and y is equal to

[tex]y=-1.5x[/tex]

Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2)  [tex]y=100x+300[/tex]

Part 3) [tex]\$12,300[/tex]

Part 4) [tex]\$2,700[/tex]

Part 5) Is a exponential growth function

Part 6) [tex]A=6,000(1.07)^{t}[/tex]

Part 7) [tex]\$11,802.91[/tex]

Part 8)  [tex]\$6,869.40[/tex]

Part 9) Is a exponential growth function

Part 10) [tex]A=5,000(e)^{0.10t}[/tex]    or  [tex]A=5,000(1.1052)^{t}[/tex]

Part 11)  [tex]\$13,591.41[/tex]

Part 12) [tex]\$6,107.01[/tex]

Part 13)  Natalie has the most money after 10 years

Part 14)  Sally has the most money after 2 years

Step-by-step explanation:

Part 1) What type of equation models John’s situation?

Let

y ----> the total money saved in a jar

x ---> the time in months

The linear equation in slope intercept form

y=mx+b

The slope is equal to

[tex]m=\$100\ per\ month[/tex]

The y-intercept or initial value is

[tex]b=\$300[/tex]

so

[tex]y=100x+300[/tex]

therefore

John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

so

[tex]10\ years=10(12)=120 months[/tex]

For x=120 months

substitute in the linear equation

[tex]y=100(120)+300=\$12,300[/tex]

Part 4) How much money will John have after 2 years?

Remember that

1 year is equal to 12 months

so

[tex]2\ years=2(12)=24\ months[/tex]

For x=24 months

substitute in the linear equation

[tex]y=100(24)+300=\$2,700[/tex]

Part 5) What type of exponential model is Sally’s situation?

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex] 

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]P=\$6,000\\ r=7\%=0.07\\n=1[/tex]

substitute in the formula above

[tex]A=6,000(1+\frac{0.07}{1})^{1*t}\\ A=6,000(1.07)^{t}[/tex]

therefore

Is a exponential growth function

Part 6) Write the model equation for Sally’s situation

see the Part 5)

Part 7) How much money will Sally have after 10 years?

For t=10 years

substitute  the value of t in the exponential growth function

[tex]A=6,000(1.07)^{10}=\$11,802.91[/tex] 

Part 8) How much money will Sally have after 2 years?

For t=2 years

substitute  the value of t in the exponential growth function

[tex]A=6,000(1.07)^{2}=\$6,869.40[/tex]

Part 9) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex] 

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]P=\$5,000\\r=10\%=0.10[/tex]

substitute in the formula above

[tex]A=5,000(e)^{0.10t}[/tex]

Applying property of exponents

[tex]A=5,000(1.1052)^{t}[/tex]

 therefore

Is a exponential growth function

Part 10) Write the model equation for Natalie’s situation

[tex]A=5,000(e)^{0.10t}[/tex]    or  [tex]A=5,000(1.1052)^{t}[/tex]

see Part 9)

Part 11) How much money will Natalie have after 10 years?

For t=10 years

substitute

[tex]A=5,000(e)^{0.10*10}=\$13,591.41[/tex]

Part 12) How much money will Natalie have after 2 years?

For t=2 years

substitute

[tex]A=5,000(e)^{0.10*2}=\$6,107.01[/tex]

Part 13) Who will have the most money after 10 years?

Compare the final investment after 10 years of John, Sally, and Natalie

Natalie has the most money after 10 years

Part 14) Who will have the most money after 2 years?

Compare the final investment after 2 years of John, Sally, and Natalie

Sally has the most money after 2 years

Answer:

The answer is figure a :-)

The reason why is because all sides of figure A are equivalent.

Answer:

_____________________________________________

Step-by-step explanation:

Answer:

(identity has been verified)

Step-by-step explanation:

Verify the following identity:

tan(θ) (cot(θ)^2 + 1)/(tan(θ)^2 + 1) = cot(θ)

Multiply both sides by tan(θ)^2 + 1:

tan(θ) (cot(θ)^2 + 1) = ^?cot(θ) (tan(θ)^2 + 1)

(cot(θ)^2 + 1) tan(θ) = tan(θ) + cot(θ)^2 tan(θ):

tan(θ) + cot(θ)^2 tan(θ) = ^?cot(θ) (tan(θ)^2 + 1)

cot(θ) (tan(θ)^2 + 1) = cot(θ) + cot(θ) tan(θ)^2:

tan(θ) + cot(θ)^2 tan(θ) = ^?cot(θ) + cot(θ) tan(θ)^2

Write cotangent as cosine/sine and tangent as sine/cosine:

sin(θ)/cos(θ) + sin(θ)/cos(θ) (cos(θ)/sin(θ))^2 = ^?cos(θ)/sin(θ) + cos(θ)/sin(θ) (sin(θ)/cos(θ))^2

(sin(θ)/cos(θ)) + (cos(θ)/sin(θ))^2 (sin(θ)/cos(θ)) = cos(θ)/sin(θ) + sin(θ)/cos(θ):

cos(θ)/sin(θ) + sin(θ)/cos(θ) = ^?(cos(θ)/sin(θ)) + (cos(θ)/sin(θ)) (sin(θ)/cos(θ))^2

(cos(θ)/sin(θ)) + (cos(θ)/sin(θ)) (sin(θ)/cos(θ))^2 = cos(θ)/sin(θ) + sin(θ)/cos(θ):

cos(θ)/sin(θ) + sin(θ)/cos(θ) = ^?cos(θ)/sin(θ) + sin(θ)/cos(θ)

The left hand side and right hand side are identical:

Answer: (identity has been verified)

By using the Pythagorean trigonometric identities and substituting the expressions of tan θ, sec θ, and csc θ, we can simplify the given expression to prove that tan θ (1 + cot2 θ) / (1 + tan2 θ) equals cot θ.

To prove that tan θ ( 1 + cot2 θ ) / ( 1 + tan2 θ ) = cot θ, we can use trigonometric identities. Recall the Pythagorean identity which states that cot2 θ + 1 = csc2 θ and tan2 θ + 1 = sec2 θ. Using these identities, we can rewrite the expression on the left side of the equation:

tan θ ( 1 + cot2 θ ) / ( 1 + tan2 θ ) = tan θ * csc2 θ / sec2 θ

Since sec θ = 1/cos θ and csc θ = 1/sin θ, and remembering that tan θ = sin θ / cos θ, we substitute these into the expression:

tan θ * csc2 θ / sec2 θ = (sin θ / cos θ) * (1/sin2 θ) / (1/cos2 θ)

With simplification, the sin2 θ in the numerator and denominator cancel out, as do the cos2 θ terms, leaving us with:

cos θ / sin θ = cot θ

Thus, the original expression simplifies to cot θ.

Answer:

C(g) = 2.19g ; 2.5

Step-by-step explanation:

Question 1

Since the cost is $2.19 per gallon. For every gallon, the cost will increase by $2.19. Hence, the cost per gallon C(g) is 2.19g.

Question 2

f(1.5) = 3(1.5) - 2

= 4.5 - 2

= 2.5

Answer:

1. C(g) = 2.98g

2. 2.5

Step-by-step explanation:

1. 1 gallon cost $2.98

Therefore y gallon will cost = y2.98 ie C(g) = 2.98g

2. F(x) = 3x — 2

F(1.5) = 3x1.5 — 2 = 4.5 — 2 = 2.5

In this problem, we use the Triangle Inequality Theorem to find that the minimum value for x, which would yield a valid triangle, is 27.67.

In this Mathematics problem, we're given a triangle with sides 9cm, 3x-20cm, 72cm, and 56cm. According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. By doing this, we can set up an inequality to solve for x:

So, the minimum value for x that would yield a valid triangle is 27.67.

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Answer:

x= 1÷4

Step-by-step explanation:

2x - 6x + 1 =0

-4x + 1= 0

-4x = -1

Final answer:

Using the quadratic formula, the real solutions of the equation [tex]x^2 - 6x + 1 = 0[/tex]are x = 3 + 2√2 and x = 3 − 2√2 since the discriminant is positive, indicating two real solutions.

Explanation:

To find all real solutions of the quadratic equation  [tex]x^2 - 6x + 1 = 0[/tex], we can use the quadratic formula, which is x = −b ± √(b2 − 4ac) / (2a) where a, b, and c are coefficients from the equation in the form [tex]ax^2 + bx + c = 0[/tex]. For our equation, a = 1, b = −6, and c = 1. Let's apply these values into the formula:

Calculate the discriminant: (−6)2 − 4(1)(1) = 36 − 4 = 32.

Since the discriminant is positive, there are two real solutions.

Calculate the solutions: x = (6 ± √32) / (2 × 1) = (6 ± 4√2) / 2 = 3 ± 2√2.

The real solutions of the equation are x = 3 + 2√2 and x = 3 − 2√2.

Answer:

Option 2 (B) 2/3

Step-by-step explanation:

Got it correct

Answer:

[tex]f(3)=-60[/tex]

Step-by-step explanation:

[tex]f(3)=5(3)^2-7(4(3)+3)\\\\f(3)=5(3)^2-7(12+3)\\\\f(3)=5(3)^2-7(15)\\\\f(3)=5\times 9-7\times 15\\\\f(3)=45-105\\\\f(3)=-60[/tex]

Answer:

[tex]-16x^2[/tex]

Step-by-step explanation:

[tex](2x)^2 * -4\\=4x^2*-4\\=-16x^2[/tex]

Answer:

0

Step-by-step explanation:

An exponent multiply's that number by that amount of the exponent.

EX : 2^3 where ^ represents exponent

You would write it out like :2*2*2=8

Your problem asks us to multiply the number 2 by itself twice, equaling 4

and 4 subtracted by 4 is zero .

Answer:

364 inches cubed

Step-by-step explanation:

Answer:

364 inches cubed

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ

Well, the formula for volume is L*H*W

L=4 in, H=13 in, W=7 in

4*13*7=364

(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥

Answer:

Step-by-step explanation:

0.79 x 8 =

6.72

15.21 - 6.72 =

Answer =

8.49

Question:

In the right triangle shown, ∠B=60° and BC = 2√3

How long is AB?

Answer exactly, using a radical if needed.

The image of the triangle is attached below:

Answer:

The length of AB is [tex]4\sqrt{3}[/tex]

Explanation:

It is given that ∠B = 60° and BC = [tex]2\sqrt{3}[/tex]

To determine the length of AB, we shall use the cosine formula.

Because the value of the angle and its adjacent side is given and AB is the hypotenuse, we shall substitute the value of angle and adjacent side in the formula to find the value of AB.

Thus, the formula for [tex]\cos \theta[/tex] is given by

[tex]\cos \theta=\frac{a d j}{h y p}[/tex]

Where [tex]\theta=60[/tex] and [tex]adj= 2\sqrt{3}[/tex] and [tex]hyp=x[/tex]

Substituting these values in the formula, we get,

[tex]\cos 60=\frac{2 \sqrt{3}}{x}[/tex]

Interchanging, we get,

[tex]x=\frac{2 \sqrt{3}}{\cos 60}[/tex]

The value of [tex]cos 60 =\frac{1}{2}[/tex]

Substituting, we get,

[tex]x=\frac{2 \sqrt{3}}{\frac{1}{2} }[/tex]

[tex]x=4\sqrt{3}[/tex]

Thus, the value of x is [tex]4\sqrt{3}[/tex]

Hence, the length of the hypotenuse AB is [tex]4\sqrt{3}[/tex]

Answer:

b

Step-by-step explanation:

Answer:

x=-1/3, y=-13/3. (-1/3, -13/3).

Step-by-step explanation:

y=x-4

4x-y=3

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

4x-(x-4)=3

4x-x+4=3

3x+4=3

3x=3-4

3x=-1

x=-1/3

y=-1/3-4

y=-1/3-12/3=-13/3

Answer: ([tex]-\frac{1}{3},-\frac{13}{3}[/tex]

Step-by-step explanation:

Substitut (x-4) into the equation of 4x-y=3

(Substitute what y equals into the equation

Make sure to keep parentheses!

That becomes 4x-(x-4)=3

Than you must distribute the negative to x and to -4

When you do it creates the equation of 4x-x+4=3

When combining like terms you get: 3x+4=3

Then solve                                                -4   -4

3x=-1

3    3               x=-1    

                           3

Than substitute the x in for the equation of y=x-4 to find what y equals! since you know that x equals -1/3 than subtract -1/3 - 4 to get

y= -13          

     3        

Answer:5/8

Step-by-step explanation:

Answer:

We also know that If two angles are complementary then  their sum is equal to 90°. So, two angles ∠1 & ∠2 are complementary.

Step-by-step explanation:

As BA is perpendicular to BC. So, angle ∠ABC is 90°.

We also know that If two angles are complementary then  their sum is equal to 90°. As ∠ABC is the sum of the ∠1 & ∠2. In other words, ∠1 & ∠2 are complementary. So, two angles ∠1 & ∠2 are complementary.

Lets prove this.

Given: BA ⊥ BC

Prove: ∠1 & ∠2 are complementary.

Statement                                                       Reasons

1. ∠1 & ∠2 are complementary                      1. Given

2. ∠1 + ∠2 = 90°                                             2. Def. of complementary angles

Answer:

1*56 8*7 ECT

Step-by-step explanation:

56 one time=56. 7 8 times = 56

The circumference of a circle is the distance around the Outside of the circle.

The circumference of found by multiplying PI by the diameter of the circle.

Answer:

The total number of fliers the volunteers gave out is 1,368: 756 in the first neighborhood and 612 in the second.

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Amount of fliers the volunteers gave for a political campaign = 21/38

Remaining 612 were given out in another neighborhood

2. What is the total number of fliers they gave out?

x = Total of fliers

21x/38 = Fliers given out in the first neighborhood

612 = Fliers given out in the second neighborhood

Let's solve for x, this way:

x - 21x/38 = 612

38x - 21x = 612 * 38 (38 is the Lowest Common Denominator)

17x = 23,256

x = 23,256/17

x = 1,368

The total number of fliers the volunteers gave out is 1,368: 756 in the first neighborhood and 612 in the second.

Answer:

Proof in the explanation

Step-by-step explanation:

Trigonometric Equalities

Those are expressions involving trigonometric functions which must be proven, generally working on only one side of the equality

For this particular equality, we'll use the following equation

[tex]\displaystyle cos(x-y)=cos\ x\ cos\ y+sin\ x\ sin\ y[/tex]

The equality we want to prove is  

[tex]\displaystyle arccos\ \sqrt{\frac{2}{3}}-arccos\left(\frac{1+\sqrt{6}}{2\sqrt{3}}\right)=\frac{\pi}{6}[/tex]  

Let's set the following variables:

[tex]\displaystyle x=arccos\ \sqrt{\frac{2}{3}},\ y=arccos(\frac{1+\sqrt{6}}{2\sqrt{3}})[/tex]

And modify the first variable:

[tex]\displaystyle x=arccos\ \frac{\sqrt{6}}{3}}=>\ cos\ x= \frac{\sqrt{6}}{3}}[/tex]

Now with the second variable

[tex]\displaystyle y=arccos\ \frac{1+\sqrt{6}}{2\sqrt{3}}=>cos\ y=\frac{1+\sqrt{6}}{2\sqrt{3}}=\frac{\sqrt{3}+3\sqrt{2}}{6}[/tex]

Knowing that

[tex]sin^2x+cos^2x=1[/tex]

We compute the other two trigonometric functions of X and Y

[tex]\displaystyle sin \ x=\sqrt{1-cos^2\ x}=\sqrt{1-(\frac{\sqrt{6}}{3})^2}=\sqrt{1-\frac{6}{9}}=\frac{\sqrt{3}}{3}[/tex]

[tex]\displaystyle sin\ y=\sqrt{1-cos^2y}=\sqrt{1-\frac{(\sqrt{3}+3\sqrt{2})^2}{36}}}[/tex]

[tex]\displaystyle sin\ y=\sqrt{\frac{36-(3+6\sqrt{6}+18)}{36}}=\sqrt{\frac{15-6\sqrt{6}}{36}}[/tex]

Computing

[tex]15-6\sqrt{6}=(3-\sqrt{6})^2[/tex]

Then

[tex]\displaystyle sin\ y=\frac{3-\sqrt{6}}{6}[/tex]

Now we replace all in the first equality:

[tex]\displaystyle cos(x-y)=\frac{\sqrt{6}}{3}.\frac{\sqrt{3}+3\sqrt{2}}{6}+\frac{\sqrt{3}}{3}.\frac{3-\sqrt{6}}{6}[/tex]

[tex]\displaystyle cos(x-y)=\frac{3\sqrt{2}+6\sqrt{3}}{18}+\frac{3\sqrt{3}-3\sqrt{2}}{18}[/tex]

[tex]\displaystyle cos(x-y)=\frac{9\sqrt{3}}{18}=\frac{\sqrt{3}}{2}=cos\ \pi/6[/tex]

Thus, proven