Find the area of a triangle when A=22 B=105 and B=14

assuming simple interest rate.

[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$300\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &1 \end{cases} \\\\\\ A=300[1+(0.06)(1)]\implies A=300(1.06)\implies A=318[/tex]

Answer:

$318

Step-by-step explanation:

I was just in a zoom class that used this as an example

you're answer would be two hundred eighty eight

Answer:

288

Explanation:

Hope this helps

The answer is: True.

A counterexample is a way that we can prove that something is not true about a mathematical equation or expression, it's also considered as an exception to a rule.

So:

[tex]sec^{2}x-1=\frac{cosx}{cscx}\\\\tg^{2}x=\frac{cosx}{\frac{1}{sinx}}\\\\\frac{1-cos2x}{1+cos2x}=cosxsinx[/tex]

Then, evaluating we have:

[tex]\frac{1-cos(2*45)}{1+cos(2*45)}=cos(45)*sin(45)\\\\\frac{1-0}{1+0}=\frac{\sqrt{2} }{2}*\frac{\sqrt{2}}{2}\\\\1=\frac{(\sqrt{2})^{2} }{4}\\\\1=\frac{2}{4}\\\\1=\frac{1}{2}[/tex]

Hence, we can see that the equation is not fulfilled, so, 45° is a counterexample for [tex]sec^{2}x-1=\frac{cosx}{cscx}[/tex] and the answer is true.

Have a nice day!

Answer:

Step-by-step explanation:

Use the sine law:

[tex]\dfrac{MO}{\sin(\angle N)}=\dfrac{NM}{\sin(\angle O)}[/tex]

We have:

[tex]MO=18\\\\NM=6\\\\m\angle O=17^o\to\sin17^o\approx0.2924[/tex]

Substitute:

[tex]\dfrac{18}{\sin(\angle N)}=\dfrac{6}{0.2924}[/tex]         cross multiply

[tex]6\sin(\angle N)=(18)(0.2924)[/tex]

[tex]6\sin(\angle N)=5.2632[/tex]          divide both sides by 6

[tex]\sin(\angle N)=0.8772\to m\angle N\approx61^o[/tex]

Answer:

hope this helps!

Step-by-step explanation:

The solution set of the given system of equations y = 3x + 10 and 2y = 6x – 4 is empty, indicating that the lines are parallel and do not intersect.

To find the solution set of the system of equations y = 3x + 10 and 2y = 6x – 4, we can solve the equations simultaneously by substitution or elimination method.

Using the substitution method:

Therefore, the solution set of the system of equations y = 3x + 10 and 2y = 6x – 4 is empty, indicating that the lines represented by the equations do not intersect and are parallel.

Answer:

the correct answer would be choice C

it went left 1/2 units and went down 4 1/2 units

Answer:

It's the third option.

Step-by-step explanation:

f(x) = |x| is shaped like a V with the vertex at the point (0, 0).

The translation is 1/2 unit to the left, 4 1/2 units down.

Answer:

The answer is C) -1 and -4

Step-by-step explanation:

Sorry i don't have the step by step explanation but that's the answer

Answer:

  Yes, the limit as x approaches 1 is 1.

Step-by-step explanation:

The function is defined at x=1 and to the left of there. The function approaches 1 as x approaches 1 from the right.

The limit is 1 from either direction, so the limit exists.

Answer: similar

Step-by-step explanation: apex

Answer:

The fill in the blank is the word similar.

Step-by-step explanation:

A pyramid has a cross-sectional shapes, taken parallel to its base, that are similar to one another.

When we do the cross-section of a pyramid parallel to its base, the cross-section formed will be in the same shape like the base.

Whenever a cross section is done parallel to the base of any pyramid, the resulting shape will be same like the base. As we move up in the pyramid and cross section it, the shape formed will be like the base but with smaller dimensions. But the shape will be the same as the base.

Answer:

-14.29422

Step-by-step explanation:

rounded to the nearest tenth = -14.3

are you trying to combine them?

if so, then when you multiply parenthesis stuffs, you should FOIL.

foil stands for first, outside, inside, and last.

when we combine (x -2)(3x-4)

1. we multiply the first parts together x & 3x to get 3x^2.

2. then we multiply the "outsides," x & -4 to get -4x.

3. insides would be -2 & 3x, so -6x.

4. finally last is -2 & -4 to make 8.

putting it all together we get 3x^2 - 4x - 6x + 8.

or simply 3x^2 - 10x + 8 by combing like terms.

for (x + 6)^2 keep in mind that squaring is multiplying something by itself. so (x+6)^2 is the same as (x+6)(x+6).

applying the same foil technique:

1. x * x = x^2

2. x * 6 = 6x

3. 6 * x = 6x

4. 6 * 6 = 36

so we get x^2 + 6x + 6x + 36.

simplified it's x^2 + 12x + 36

keep in mind also that FOILing is only really good for binomials. (something like (x+6)(6x^2+7x+6) wouldnt work).

also also remember that all were really doing is just distributing

Answer:

If it is [tex]p(x)=\frac{90}{(9+50e^{-x})}[/tex], then: [tex]p(3)=7.83[/tex]

If it is [tex]p(x)=\frac{90}{9}+50e^{-x}[/tex], then: [tex]p(3)=12.48[/tex]

Step-by-step explanation:

To solve this exercise you must substiute x=3 into the expression given in the problem.

1) If the expression is [tex]p(x)=\frac{90}{(9+50e^{-x})}[/tex], you obtain:

[tex]p(3)=\frac{90}{(9+50e^{-(3)})}[/tex]

[tex]p(3)=7.83[/tex]

2) If the expression is [tex]p(x)=\frac{90}{9}+50e^{-x}[/tex], you obtain:

[tex]p(3)=\frac{90}{9}+50e^{-(3)}\\p(3)=12.48[/tex]

Answer:

p (3) = 7.83

Step-by-step explanation:

We are given the following expression and we are to evaluate it given that the value of [tex] p = 3 [/tex]:

[tex] p ( x ) = \frac { 9 0 } { 9 + 5 0 e^ { - x } } [/tex]

Substituting the given value of [tex] p [/tex] to get:

[tex] p ( 3 ) = \frac { 9 0 } { 9 + 5 0 e^ { - 3 } } [/tex]

[tex] p ( 3 ) = \frac { 9 0 } { 11.489 } [/tex]

[tex] p ( 3 ) = 7.83 [/tex]

Answer:

The two numbers would be -51 and 51

Step-by-step explanation:

To find these, first set the equation for the first number as x. You can then set the second number as x + 102. Now, find their product.

x(x + 102) = x^2 + 102x

Now, to find the minimum, find the value of x in the vertex of this equation.

-b/2a = -102/2(1) = -102/2 = -51

So we know -51 is the first number. Now we find the second using the prewritten equation.

x + 102 = -51 + 102 = 51

The two numbers whose difference is 102 and whose product is a minimum are -51 and 51. This is obtained by differentiating and finding the minimum of the function that represents their product.

To find two numbers whose difference is 102 and whose product is a minimum, we initially express the two numbers as x and x + 102. The product of these two numbers can be denoted as f(x) = x(x + 102) = x² + 102x. To find the minimum product, we differentiate f(x) to find f'(x) = 2x + 102. Setting this equal to zero gives x = -51. We should note, f''(x) = 2, verifies that there is a minimum at x = -51. Hence, the two numbers are -51 and (-51 + 102) = 51.

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Answer:

the numbers are [tex]4,6[/tex]

Step-by-step explanation:

Let

x-------> the smaller even consecutive integer

x+2-------> the larger even consecutive integer

we know that

[tex]x^{2}=(x+2)+10[/tex]

solve for x

[tex]x^{2}-x-12=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2}-x-12=0[/tex]

so

[tex]a=1\\b=-1\\c=-12[/tex]

substitute in the formula

[tex]x=\frac{1(+/-)\sqrt{-1^{2}-4(1)(-12)}} {2(1)}[/tex]

[tex]x=\frac{1(+/-)\sqrt{49}} {2}[/tex]

[tex]x=\frac{1(+/-)7} {2}[/tex]

[tex]x=\frac{1(+)7} {2}=4[/tex]  ------> the solution (must be positive)

[tex]x=\frac{1(-)7} {2}=-3[/tex]

therefore

the numbers are [tex]4,6[/tex]

Two positive even consecutive numbers are [tex]4,6[/tex].

Let  [tex]x,\;x+2[/tex]  are two positive consecutive even number.

According to question,

[tex]x^2=(x+2)+10[/tex]

[tex]x^2-x-12=0[/tex]

Solve the quadratic equation,

[tex]x^2-4x+3x-12=0\\x(x-4)-3(x-4)=0\\(x-4)(x-3)=0\\\; x-4=0\\ \; x-3=0\\[/tex]

So [tex]x=3 , 4[/tex].

Positive even number is the requirement so [tex]3[/tex] is not a even number so eliminate.

Hence value of [tex]x[/tex] is [tex]4[/tex].

Two positive even consecutive numbers are [tex]4,6[/tex].

Learn more about quadratic equation here:

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The dimensions of the box that minimize the amount of material used are approximately 39 cm by 39 cm by 39 cm.

To minimize the amount of material used, we need to minimize the surface area of the box.

Let's denote the dimensions of the box as x,y, and z, where x and y are the dimensions of the base (length and width), and z is the height.

The volume V of the box is given by:

[tex]\[ V = xyz \][/tex]

We're given that  V = 62500  cubic cm.

The surface area A of the box (excluding the top) is given by:

[tex]\[ A = xy + 2xz + 2yz \][/tex]

To minimize the amount of material used, we need to minimize A subject to the constraint  V = 62500 .

We can solve this problem using the method of Lagrange multipliers. First, let's define the Lagrangian function L as follows:

[tex]\[ L(x, y, z, \lambda) = xy + 2xz + 2yz + \lambda(62500 - xyz) \][/tex]

Now, we take partial derivatives of L with respect to x,y,z, and [tex]\( \lambda \),[/tex] and set them equal to zero:

[tex]\[ \frac{\partial L}{\partial x} = y + 2z - \lambda yz = 0 \]\[ \frac{\partial L}{\partial y} = x + 2z - \lambda xz = 0 \]\[ \frac{\partial L}{\partial z} = 2x + 2y - \lambda xy = 0 \]\[ \frac{\partial L}{\partial \lambda} = 62500 - xyz = 0 \][/tex]

Solving these equations will give us the dimensions that minimize the amount of material used.

However, this system of equations is quite complex to solve manually. Let's simplify the problem by recognizing that the dimensions that minimize the amount of material used will likely be those where the box is as close to a cube as possible. This means x=y to minimize the perimeter, and x=y=z to minimize the surface area.

So, let's find the cube root of 62500 :

[tex]\[ \sqrt[3]{62500} \approx 38.99 \][/tex]

Since [tex]\( 38^3 = 54872 \)[/tex] and [tex]\( 39^3 = 59319 \)[/tex], the closest perfect cube to 62500 is [tex]\( 39^3 \)[/tex]. Therefore, the dimensions of the box that minimize the amount of material used are approximately 39 cm by 39 cm by 39 cm.

Answer:

37

Step-by-step explanation:

w=(180-69)/3

Answer:

C = π(6)

C = 6π

C = 18.84

Step-by-step explanation:

The circumference is the distance around the circle. It relates the number of times the diameter will encircle the circumference as 3.14 or π. As a result, the formulas for the circumference of a circle are C = 2πr or C = πd. The information given is the diameter so use C = πd by substituting d = 6.

C = π(6)

C = 6π

C = 18.84

Answer:

A 3.14x6

Step-by-step explanation:

Answer:

sample response He added instead of multiplying 20 and 6. The correct answer is 120 cubic inches.

Answer:

He added instead of multiplying 20 and 6. The correct answer is 120 cubic inches.

That is the correct answer

Step-by-step explanation:

Answer:

A = 53.13 degrees

Step-by-step explanation:

sin theta = opposite side/ hypotenuse

sin A = 4/5

Take the inverse of each side

sin ^-1 sin A = sin ^-1 (4/5)

A = 53.13010

To the nearest hundredth

A = 53.13 degrees

Answer:

Option C. [tex]2.5[/tex]

Step-by-step explanation:

we know that

In the rectangle of the figure

[tex]\frac{H}{W}=\frac{25}{10}=2.5[/tex]

so

[tex]H(W)=2.5W[/tex]

The constant is equal to [tex]2.5[/tex]

Answer:

2.5

Step-by-step explanation:

Answer:

wouldn't it be 6/5 or 5/6 or 1.2

Step-by-step explanation:

Answer:

450

Step-by-step explanation:

5% of 300 = 15

300+10(15)=450

Using the compound interest formula, if you deposit $300 in an account earning 5% interest compounded annually, you would have approximately $488.85 in the account after 10 years.

This problem involves compound interest, which appeal to financial maths. The formula for compound interest is A = P*(1 + r/n)^(nt), where:

For this problem, P = $300, r = 5% or 0.05, n = 1 (because it's compounded annually), and t = 10 years. Substituting these values into the formula, you have A = 300*(1 + 0.05/1)^(1*10).

Doing the math, A = $300 * (1.05)^10 ≈ $488.85. So after 10 years, you would have approximately $488.85 in the account.

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The graph of the data set will help you to understand if the data is displayed in the form of an exponential model. Example: if the data (when graphed) is similar in shape and growth to that of the graph of f(x)=e^x, then it could be deemed helpful.

Answer:

The correct answer option is 231 / 703

Step-by-step explanation:

We are given that a jar has 38 marbles, out of which 10 are red, 22 are black and 6 are green. Two marbles are drawn and the first marble is not returned when the second one is drawn.

We are to find the probability that both marbles are black.

1st draw: P (black) = [tex]\frac{22}{38} =\frac{11}{19}[/tex]

2nd draw: P (black) = [tex]\frac{21}{37} [/tex]

P (Both Black) = [tex]\frac{11}{19} \times \frac{21}{37}[/tex] = 231 / 703

Answer 2 she bought 3 gallons of lemonade

4x2.50=10

2x7.50=15

10+15=25

34-25=9

9 divided by 3=3

Answer:

Answer 2 is right.

Step-by-step explanation:

Given that Lisa purchased groceries worth $34 for a party.

A gallon of milk costs $2.50

No of gallons bought - 4

Cost of milk = [tex]2.50*4 =10[/tex]

a gallon of ice cream costs $7.50

Cost of ice creams = [tex]2*7.50 = 15[/tex]

, and a gallon of lemonade costs $3.00

Let lemonade purchased be x

Then total cost = [tex]10+15+3x[/tex]

This equals 34

[tex]25+3x =34\\3x=9\\x=3[/tex]

No of gallons of lemonade purchased =3

Answer 2 is right

Answer:

4 over sixteen, or 4/16 is your answer.

Step-by-step explanation:

There are 2 pizzas, each of which contain 8 pieces. So, in all, there were 8 pieces. Eric ate two pieces from each pizza. So, 2+2=4. Thus, he ate four out of the 16 pieces. That brings us to our answer, 4/16.

I hope this helps you, have a wonderful day!

Final answer:

The ratio of the total number of pieces Eric ate to the total number of pieces eaten by his family when they bought 2 pizzas, is 1:4, meaning Eric eats 1 out of every 4 pieces.

Explanation:

For every pizza Eric's family ate, Eric ate 2 of the 8 pieces. If Eric's family bought 2 pizzas, to find the ratio of the total number of pieces Eric ate to the total number of pieces the family ate, we start by calculating the total pieces in 2 pizzas and the pieces Eric ate.

Each pizza has 8 pieces, so 2 pizzas have 8 * 2 = 16 pieces in total.

Since Eric eats 2 pieces per pizza, for 2 pizzas, he would eat 2 * 2 = 4 pieces in total.

Therefore, the ratio of the pieces Eric ate to the total pieces is:

4 (pieces Eric ate) : 16 (total pieces), which simplifies to 1:4.

This ratio means that for every piece of pizza Eric eats, there are 4 pieces total, indicating Eric eats 1 out of every 4 pieces.

Answer:

Random Sample

Step-by-step explanation:

The scenario involves differentiating a proportional relationship between the woman's distance from a streetlight and the length of her shadow to determine the rate of change of the shadow's length and the speed of the shadow's tip.

The question involves finding the rates of change in the scenario where a woman walks toward a streetlight and the effects on her shadow's length and speed. Let's denote the distance between the woman and the streetlight as x, the length of her shadow as y, and her height as h. The streetlight's height is given as H. Using similar triangles, we can establish the relationship (H - h) / y = H / (x + y). Differentiating both sides with respect to time, t, allows us to calculate the rates of change we're interested in.

To find the rate of change of her shadow's length when she is 16 feet from the streetlight, we can take dh/dt as 0 since her height is constant, dx/dt as -4 ft/s because she is walking towards the light and substitute into the derived equation after differentiating. Similarly, we calculate the rate at which the tip of the shadow is moving by adding the rate of the woman's movement to the rate of change of the shadow's length.