Ian's friend drove him from Toledo to Indianapolis. The distance is 220 miles and the trip took 4 hours. How fast was Ian's friend driving?

Thus, the picture frame with the side length of 5 in. 12 in. 13 in.  is right angled at the corner shown by point B.

Triangles with a single 90° angle are known as right-angled triangles.

Right angles are what this is. It is customary for the correct angle to be located in one of the bottom corners, however this is not required.

They are available in scalene and isosceles versions.

Given dimensions are-

5 in. 12 in. 13 in.

For the triangle to be right angled, it must satisfy the Pythagorean theorem.

H² = B² + P²

In which,

Put the values:

H² = B² + P²

13² = 12² + 5²

169 = 144 + 25

169 = 169

Since LHS = RHS, this proves that, the sides of the picture frame right angles.

Thus, the picture frame with the side length of 5 in. 12 in. 13 in.  is right angled at the corner shown by point B.

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Correct question:

A picture frame is shown in the diagram. Are the corners of the picture frame right angles? Three side of the frame are- 5 in. 12 in. 13 in.

Answer:

a-25

b-243

5^3 = 125/3 = 25

3^6 = 729/3 = 243

Answer:

Number 4. A

Number 5. B

Number 6. B

Step-by-step explanation: On god

Can You write me a three-paragraph reflection about how the first trimester went. Since I helped you plz

It will take 27 containers of 1/3 liter to fill the tank.

Since you need 3 containers of 1/3 to have a full liter, and 9 liters for the tank, 9*3=27.

Answer:

27

Step-by-step explanation:

1= 1/3x3

3x9=27

According to the information, the office purchased 8 computers and 4 printers.

To identify the number of computers and printers purchased for the office, we must take into account the total number of items purchased and the value of each of them. In this case the computers were worth $1,225 and the printers were worth $1,550. Therefore, we must raise the following expression and replace the values of C and P.

In this case, the office purchased 8 computers and 4 printers for a total expense of $16,000.

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To rewrite equation \(x^2 + 5x + 6\) as\(x^2 + rx + sx + 6\), we need to choose suitable values for r and s that satisfy r + s = 5.

To rewrite the quadratic expression\(x^2 + 5x + 6\) as equivalent to\(x^2 + rx + sx + 6\) , we need to find the values of r and s that satisfy the equation.

Let's start by expanding \(x^2 + rx + sx + 6:\)

\(x^2 + rx + sx + 6 = x^2 + (r + s)x + 6\)

We can see that the coefficient of x in the original expression is 5, and in the rewritten expression, it is (r + s). Therefore, we want to find values for r and s such that r + s = 5.

Next, we need to consider the constant term. In the original expression, the constant term is 6, and in the rewritten expression, it is also 6. Therefore, we want r, s, and 6 to satisfy the equation.

Since r + s = 5, we can solve for one variable in terms of the other. For example, if we choose r = 3, then s = 2 to satisfy the equation. Alternatively, we could choose r = 4 and s = 1, or any other combination that adds up to 5.

So, rewriting \(x^2 + 5x + 6\) as \(x^2 + rx + sx + 6\)can be achieved by choosing suitable values for r and s that satisfy r + s = 5.

For example, if we choose r = 3 and s = 2, the equivalent expression would be \(x^2 + 3x + 2x + 6.\)

In summary, to rewrite\(x^2 + 5x + 6\)as \(x^2 + rx + sx + 6\), we need to choose suitable values for r and s that satisfy r + s = 5.

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Answer:

57.75-(57.75*0.7)=17,325

Or 100-70=30

So 57.75*0.3=17.325

Answer:

$40.425

Step-by-step explanation:

hope it helps good luck

Answer:

D.

Step-by-step explanation:

To  find the mean you add all the numbers together then divide by the total of number so 5

Answer:

The answer is d

Step-by-step explanation:

Answer:

m<D = 105

Step-by-step explanation:

So, Triangle STU and DEF are similar triangles, because their corresponding side lengths have the same ratio.

For example FD can be multiplied by 2.5 to get SU, and EF can be multiplied by 2.5 to get TU, and ED can me multiplied by 2.5 to get 15.

Anyways, since the two triangles are similar, they have the same angle measures, meaning that angle D can be found by subtracting 46 and 25 from 180 degrees to find the missing angle, which is 105 degrees. I hope that helps.

Answer:

m∠D = 29°

Step-by-step explanation:

First, notice that ΔSTU and ΔDEF are similar triangles.

For instance, for side ST and DE, the scale factor is:

\(\displaystyle k=\frac{6}{15}=\frac{2}{3}\)

Likewise, for TU and EF and SU and DF, the scale factor reamins that same:

\(\displaystyle \frac{10}{4}=\frac{2}{5}\text{ and } \frac{8}{20}=\frac{2}{5}\)

By SSS Similarity, ΔSTU ~ ΔDEF.

Note that our similarity statement states that ∠S corresponds to ∠D.

So, ∠S = ∠D.

Since the angles remain the same in a scaled factor and ∠S measures 29°, ∠D is also 29°.

Answer:

Step-by-step explanation:

Area of triangle = 1/2 (base × height)

Given, area of a triangle is 192 sq ins. and its height is 8 ins less than its base.

Then, let base = b, height = b-8

Hence, 1/2 (b)*(b-8) = 192

Above equation; “times 2”,

(b)*(b-8) = 384

b^2 - 8b - 384 = 0

(b+16)(b-24)=0

The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters

What is measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.

Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.

Since we have 30 meters of fencing available, the total length of wire fencing used is:

L + 2W = 30 - W

Simplifying this equation, we get:

L = 30 - 3W

The area of the garden is:

A = LW

Substituting the expression for L from the previous equation, we get:

A = W(30 - 3W)

Expanding the expression, we get:

A = 30W - 3W²

To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:

dA/dW = 30 - 6W = 0

Solving for W, we get:

W = 5

Substituting this value back into the expression for L, we get:

L = 15

Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:

A = 5(15) = 75 square meters

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The  equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1

To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.

Alternatively, we can use PF = PM to find the equation of the parabola.

vertex is half way between the focus and directrix

It's a downward opening parabola, general form

y= a(x-h)^2 + k

where (h,k) = vertex= (-3,-1)

plug in another point on the parabola to solve for a which gives

am answer with either x coefficient = -1'/4 or =4 Check the math.

one or the other is right another point is the y intercept = 9a-1

Another point is directly to the right of the focus  (-1, -2)  It's 2 down from the directrix and 2 to the right of the focus, equidistant.   plug that point into y= a(x+3)^2 -1 and solve for "a"  

-2 = a((-1+3)^2 -1

-2 = 4a -1

4a = -

a = -1/4

The parabola is y = (-1/4)(x+3)^2 -1

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Answer:

a. 50 turns

b. 0.0114 A

c. 0.25 A, 10 V

Step-by-step explanation:

Given:-

- The required current ( Is ) = 0.5 A

- The required voltage ( Vs ) = 5 V

- Transformer is 100% efficient ( ideal )

- The number of turns in the primary coil, ( Np ) = 2200

- The Voltage generated by power station, ( Vp ) = 220 V

Find:-

a. The number of turns in the secondary coil of the transformer

b. The current supplied by the power station

c. The effect on output current and voltage when the number of turns of secondary coil are doubled.

Solution:-

- For ideal transformers that consists of a ferromagnetic core with two ends wounded by a conductive wire i.e primary and secondary.

- The power generated at the stations is sent to home via power lines and step-down before the enter our homes.

- A household receives a voltage of 220 V at one of it outlets. We are to charge a phone that requires 0.5 A and 5V for the process.

- The outlet and any electronic device is in junction with a smaller transformer.

- All transformers have two transformation ratios for current ( I ) and voltage ( V ) that is related to the ratio of number of turns in the primary and secondary.

                     Voltage Transformation = \(\frac{N_p}{N_s} = \frac{V_p}{V_s}\)

Where,

                 Ns : The number of turns in secondary winding

- Plug in the values and evaluate ( Ns ):

                           \(N_s = N_p*\frac{V_s}{V_p} \\\\N_s = 2200*\frac{5}{220} \\\\N_s = 50\)

Answer a: The number of turns in the secondary coil should be Ns = 50 turns.

- Similarly, the current transformation is related to the inverse relation to the number of turns in the respective coil.

                  Current Transformation = \(\frac{N_p}{N_s} = \frac{I_s}{I_p}\)

Where,

                 Ip : The current in primary coil

- Plug in the values and evaluate ( Ip ):

                        \(I_p = \frac{N_s}{N_p}*I_s\\\\I_p = \frac{50}{2200}*0.5\\\\I_p = 0.0114\)  

Answer b: The current in the primary coil should be Ip = 0.0114 Amp.

- The number of turns in the secondary coil are doubled . From the transformation ratios we know that that voltage is proportional to the number of turns in the respective coils. So if the turns in the secondary are doubled then the output voltage is also doubled ( assuming all other design parameters remains the same ). Hence, the output voltage is = 2*5V = 10 V

- Similary, current transformation ratio suggests that the current is inversely proportional to the number of turns in the respective coils. So if the turns in the secondary are doubled then the output current is half of the required ( assuming all other design parameters remains the same ). Hence, the output current is = 0.5*0.5 A = 0.25 A

Answer:

1) 7/8     8/7

2) 4.4

3) 3.7

4) 2.8

Step-by-step explanation:

Length of bottom side of Figure A: 8 cm

Length of bottom side of Figure B: 7 cm

From Figure A to Figure B, the scale factor is 7/8.

7/8

8/7

5 × 7/8 = 35/8 = 4.375

4.4

3.2 × 8/7 = 3.657...

3.7

3.2 × 7/8 = 2.8

2.8

Answer:

second option.

Step-by-step explanation:

Square (D)

PLS GIVE BRAINLIEST THANKS

GL WITH THE REST OF UR WORK

The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

Let \(S_n = \sum\limits_{k=0}^n x^k\). Then

\(S_n = 1 + x + x^2 + \cdots + x^n\)

\(xS_n = x + x^2 + x^3 + \cdots + x^{n+1}\)

\(\implies (1 - x) S_n = 1 - x^{n+1}\)

\(\implies S_n = \dfrac{1 - x^{n+1}}{1 - x}\)

\(\implies \displaystyle \sum_{k=0}^{2019} x^k = S_{2019} = \frac{1 - x^{2020}}{1 - x}\)

Let \(S_n' = \sum\limits_{k=1}^n k x^k\). (Starting the sum at k = 0 doesn't change its value.) Then

\(\displaystyle S_n' = \sum_{k=1}^n k x^k\)

\(\displaystyle S_n' = x \sum_{k=1}^n k x^{k-1}\)

\(\displaystyle S_n' = x \sum_{k=0}^{n-1} (k+1) x^k\)

\(\displaystyle S_n' = x \left(\sum_{k=0}^{n-1} kx^k + \sum_{k=0}^{n-1} x^k\right)\)

\(\displaystyle S_n' = x (S_{n-1}' + S_{n-1})\)

\(\displaystyle S_n' = x (S_n' - nx^n) + xS_{n-1}\)

\(\implies S_n' = \dfrac{x - (n+1)x^{n+1} + nx^{n+2}}{(1-x)^2}\)

\(\implies \displaystyle \sum_{k=1}^{2018} kx^k = S_{2018}' = \dfrac{x - 2019x^{2019} + 2018x^{2020}}{(1-x)^2}\)

So, the integrand reduces considerably to

\(\dfrac1{x-1} + \dfrac{S_{2018}' + S_{2018}}{S_{2019}} = \dfrac{2020 x^{2019}}{x^{2020}-1}\)

and its integral is trivial; by substitution,

\(\displaystyle \int \frac{2020x^{2019}}{x^{2020}-1} \, dx = \int \frac{d(x^{2020}-1)}{x^{2020}-1} = \boxed{\ln\left|x^{2020}-1\right| + C}\)

The equivalent expression to  4√3 is  √48 or 6.928.

An equivalent expression is an expression that has equal value to the original given expression.

From the given expression, we can determine its equivalent expression as follows;

The given expression = 4√3

We can square 4 and multiply it by 3 and enclose all with the square root.

4√3 = √(4² x 3 )

= √ ( 16 x 3 )

= √ ( 48 )

= 6.928

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The area of the triangle shown is 51.96 unit²

An equation is a expression that shows the relationship between numbers and variables.

The area of a triangle can be found given two adjacent sides and an angle between the two sides. It is given as:

Area = (1/2) * product of adjacent sides * sin(angle)

Hence:

Area of triangle shown = (1/2) * 10 * 12 * sin(60) = 51.96

The area is 51.96

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Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

The first hour there will be 18 costumers that will order Turkey sandwiches

Probability

First, we want to find the probability of having a costumer who choose Turkey sandwich.

In order to find it, we calculate the ratio of turkey sandwiches over the total number of orders.

Turkey sandwiches: 180

Total number of orders: 160 + 100 + 180 + 60 = 500

Ratio = turkey / total

Ratio = 180 / 500 = 0.36

Then, the probability of having a costumer who choose Turkey sanwich is

P(T) = 0.36 = 36%

Secondly, in order to find the 36% of 50, we just multiply 0.36 by 50:

Hence , the first hour there will be 18 costumers that will order Turkey sandwiches

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Answer:

The entry of net income of (100) would be entered in option D, in the operating cash flow section of the cash flow statement.

Step-by-step explanation:

The operating cash flow section of the cash flow statement reports cash inflows and outflows that result from the company's operating activities, such as revenues and expenses. Net income is an important component of operating cash flow, as it represents the profit earned by the company during a period after deducting all the expenses. When net income is negative, it is referred to as a net loss and would be entered as a negative number in the operating cash flow section of the cash flow statement.

Answer:

Total score → (9p + m - 1)

Step-by-step explanation:

Points scored by the football team in quarter 1 = 3p

Score in quarter 2 = (5p + 2)

Points scored in quarter 3 = (p - 4)

Score of quarter 4 = (m + 1)

Total points scored in entire game = 3p + (5p + 2) + (p - 4) + (m + 1)

                                                          = (3p + 5p + p) + m + (2 - 4 + 1)

                                                          = 9p + m - 1

Expression representing the total score by the team in entire game will be,

(9p + m - 1)

Answer:

Hope this helps you

Answer:

B

Step-by-step explanation:

The statement "Economists and accountants usually disagree in the inclusion of implicit costs into the cost analysis of a firm " is true

Accountants are the peoples who track the flow of money for the individuals and the business activities. But the Economist track the largest trends that use the money and resources of the company

So the view of the Economist and accountant on cost is different, because both of them are seeing the cost analysis of the company in different ways.  So it possible that the Economists and accountants disagree in the inclusion of implicit cost

Therefore, the given statements is true

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