Type the correct answer in the box. round off your answer to the nearest integer. two right triangles d a b and b c d form a parallelogram. right angles are at a and c. side d a equals 6, side a b equals 5, and side d c equals 4. an acute angle p is at b d c. triangle d a b is shaded. ∠a and ∠c are right angles. m∠p = degrees.

Answer:

3/4x=12

3=4x*12

3=48x

3/48x=1/16

x=1/16

Statement is true because the corresponding sides are congruent. The answer is: BA = LN.

What is Triangle?

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many areas of mathematics, science, and engineering.

Since triangle ABC and triangle LMN have congruent corresponding sides, we know that they are similar triangles. This means that their corresponding angles are also congruent.

We are given that angle BAC is 58 degrees and angle MLN is 78 degrees. Since corresponding angles are congruent, this means that angle BAC is congruent to angle MLN.

Therefore, triangle ABC and triangle LMN are similar triangles with two pairs of corresponding congruent angles. This means that all corresponding sides are proportional.

Since AC = LN and BA = ML, we know that the ratio of the lengths of corresponding sides is:

AC / LN = BA / ML

Substituting the given values, we get:

1 = 1

This statement is true because the corresponding sides are congruent.

Therefore, the answer is: BA = LN.

Learn more about Triangle

https://brainly.com/question/17335144

#SPJ1

Answer:

4

Step-by-step explanation:

24 - 4x = 8

-4x = 8 - 24

-4x = -16

x = 4

To fence a rectangular garden, we need to fence the length 2 times, and the width 2 times.

So, it will take 120 : 2 = 60 meters of fence to fence 1 length and 1 width

-> The length = 60 : (3+1)x3 = 45 (meters)
-> The width = 60 - 45 = 15 (meters)

Recheck : (45+15) x 2 = 120 and 45:15 = 3


(If it's wrong you can tell me, I don't really know what do you mean by how wide is the fence)

The width of the rectangular garden, for which Gabriella needs 120 meters of fence to surround it is 15 units long.

The measure of the boundary of the sides of a rectangle is called its perimeter. The perimeter of a rectangle is twice the sum of its length and width.

\(P=2(l+w)\)

Here, (l) is the length of the rectangle and (w) is the width of the rectangle.

Let suppose the length of the garden is l units long. The length of the garden is three times its width, w. Thus,

\(l=3w\)

Gabriella needs 120 meters of fence to surround a rectangular garden. This fencing is equal to the perimeter of the rectangular garden. Thus,

\(P=2(l+ w)\\120=2(l+ w)\)

Put the value of length from equation 1 to this equation,

\(120=2(3w+ w)\\3w+w=\dfrac{120}{2}\\4w=60\\w=\dfrac{60}{4}\\w=15\rm\; units\)

Thus, the width of the rectangular garden, for which Gabriella needs 120 meters of fence to surround it is 15 units long.

Learn more about the perimeter of the rectangle here;

https://brainly.com/question/19819849

Answer:

SA = 360π in²

Step-by-step explanation:

The slant height l is the hypotenuse of the right triangle inside the cone.

Using Pythagoras' identity to find l

l² = 24² + 10² = 576 + 100 = 676 ( take the square root of both sides )

l = \(\sqrt{676}\) = 26

Then

SA = πrl + πr²

      = (π × 10 × 26) + (π × 10²)

      = 260π + 100π

      = 360π in²

Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

Answer:

0.15N

Step-by-step explanation:

Given data

Mass= 0.0056kg

distance=  4.85m

Velocity= 11.4m/s

The expression for the force is

F= mv^2/r

substitute

F=  0.0056* 11.4^2/4.85

F=  0.0056*129.96/4.85

F= 0.727776/4.85

F= 0.15N

Hence the force is 0.15N

To determine the common ratio for the sequence 64, 112, 196, 343, ... we need to find the ratio between any two consecutive terms.

The ratio between the second and first terms is:

112/64 = 1.75

The ratio between the third and second terms is:

196/112 = 1.75

The ratio between the fourth and third terms is:

343/196 = 1.75

Since the ratios between all consecutive terms are the same, we can conclude that the common ratio for this sequence is 1.75.

Therefore, the answer is (b) 1.75.

To learn more about explicit formula refer below:

https://brainly.com/question/13877261

#SPJ11

Answer: 360

Step-by-step explanation:

done

a) The initial amount of flyers is given as follows: 62 flyers.

b) The statement that best describes the relation is given as follows:

As time increases, the number of flyers that Andre has increases at a rate of 3 flyers per minute.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, when x increases by 5, y increases by 15, hence the slope m is given as follows:

m = 15/5

m = 3.

Hence:

y = 3x + b.

When x = 10,  y = 92, hence the intercept b, representing the initial amount, is obtained as follows:

92 = 30 + b

b = 62.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

The lines that best represent perpendicular lines are: D. FI and JH.

Perpendicular lines are lines that meet at a right angle, that is, the point of their intersection forms a right angle.

From the image given, lines FI and JH intersect at point I, and also appears to form a right angle.

Therefore, the lines that are perpendicular in the image are: D. FI and JH.

Learn more about perpendicular lines on:

https://brainly.com/question/1202004

#SPJ1

Answer:

see explanation

Step-by-step explanation:

sum the parts of the ratio, 1 + 2 + 3 = 6 parts

Divide 180° ( sum of angles in a triangle ) by 6

180° ÷ 6 = 30° ← value of 1 part of the ratio , then

2 parts = 2 × 30° = 60°

3 parts = 3 × 30° = 90°

The angles in the triangle are 30°, 60°, 90°

Then the triangle is right angled

Answer:

Step-by-step explanation:

Let missing angles be \(x\), \(2x\).

As the triangle is right-angled triangle.

\(x + 2x + {90}^{o} = {180}^{o} \)

\(3x = {180}^{o} - {90}^{o} \)

\(3x = {90}^{o} \)

\(x = {30}^{o} \)

\(2x = 30 \times 2 \\ = {60 }^{o} \)

Answer:

I believe c is correct

Answer: 1,004.8 cubic meters (choice D)

Work Shown:

V = (1/3)*pi*r^2*h

V = (1/3)*3.14*8^2*15

V = 1,004.8

Answer:

m=-3/5

Step-by-step explanation:

Answer:

$2205

Step-by-step explanation:

The formula is (2000*1.05^2) which is 2205

Answer:

\( \frac{63}{65} \)

Step-by-step explanation:

Please see the attached picture.

Let's find the value of the opposite side, XZ.

Applying Pythagoras' Theorem,

(XZ)² +(XY)²= (ZY)²

(XZ)² +16²= 65²

(XZ)²= 4225 -256 (bring constant to 1 side)

(XZ)²= 3969 (simplify)

Square root both sides,

XZ= \( \sqrt{3969} \)

XZ= 63 (simplify)

sinY

= XZ/ ZY

\( = \frac{63}{65} \)

Answer:

63/65

Step-by-step explanation:

Answer:

-11

Step-by-step explanation:

y2-y1/x2-x1

Take the y-value from the second pair of coordinates and subtract it from the first y-value, then do the same for the x-coordinates. Take the result from subtracting the y-values and put it over the result from subtracting the x-values. I got 11/-1, which is -11.

I hope this helps :)

Answer:

try -7

Step-by-step explanation:

Answer:

The velocity of the upper end P when Q is 4 m from the wall is -0.8 m/s

Step-by-step explanation:

Let's denote the distance of the lower end Q from the wall as x and the distance of the upper end P from the ground as y. We are given that the ladder has a length of 5 m, and thus by the Pythagorean theorem, we have:

x^2 + y^2 = 5^2 = 25

Now, we're given that the lower end Q is sliding away from the wall at a constant rate of 0.6 m/s. This means that the rate of change of x with respect to time (dx/dt) is 0.6 m/s. We need to find the rate of change of y with respect to time (dy/dt) when x = 4 m.

Differentiate both sides of the Pythagorean equation with respect to time (t):

d(x^2)/dt + d(y^2)/dt = d(25)/dt

2x(dx/dt) + 2y(dy/dt) = 0

We can plug in the known values and solve for dy/dt when x = 4 m:

2(4)(0.6) + 2y(dy/dt) = 0

To find the value of y when x = 4 m, we can use the Pythagorean equation:

4^2 + y^2 = 25

16 + y^2 = 25

y^2 = 9

y = 3 (since the height must be positive)

Now, we can substitute y = 3 into the equation we derived earlier:

2(4)(0.6) + 2(3)(dy/dt) = 0

4.8 + 6(dy/dt) = 0

Now, solve for dy/dt:

6(dy/dt) = -4.8

(dy/dt) = -4.8 / 6

(dy/dt) = -0.8 m/s

Thus, the velocity of the upper end P when Q is 4 m from the wall is -0.8 m/s. The negative sign indicates that the upper end P is moving downward.

The completed relationship is:

0.001 grams = 0.0000000551 µg

To complete the relationship, we need to convert the units of the left-hand side and simplify the right-hand side.

Starting with the left-hand side:

1 mg = 1 milligram = 0.001 grams

Now, we can substitute this into the relationship:

For the right-hand side:

1100 in binary is equal to\(12^3 + 12^2 + 02^1 + 02^0 = 8 + 4 = 12\)

10001000 in binary is equal to \(12^7 + 02^6 + 02^5 + 02^4 + 12^3 + 02^2 + 02^1 + 02^0 = 128 + 8 = 136\)

100 in binary is equal to \(12^2 + 02^1 + 0*2^0 = 4\)

Now, we can substitute these values into the relationship:

0.001 grams = 12 µg / 136 / 4

Simplifying the right-hand side:

12 µg / 136 / 4 = 12 * (1/1000000) * (1/136) * (1/4) = 0.00000005514706...

Rounding this to a reasonable number of significant digits, we get:

0.0000000551

Therefore, the completed relationship is:

0.001 grams = 0.0000000551 µg

Learn more about conversion factor

brainly.com/question/30166433

#SPJ11

Answer:

c

Step-by-step explanation:

The expected value of the amount of coins that come up heads is 2 coins.

The expected value of the amount of coins that come up heads when a penny, nickel, dime, and quarter are flipped simultaneously is given by the formula: E(X) = 1/2p + 1/2n + 1/2d + 1/2q where p, n, d, and q are the probabilities of getting heads when the penny, nickel, dime, and quarter are flipped. The probability of getting heads when a fair coin is flipped is 1/2.

Therefore, the probability of getting heads for each coin is 1/2.The expected value of the amount of coins that come up heads is: E(X) = 1/2 + 1/2 + 1/2 + 1/2= 2 coins. Therefore, the expected value of the amount of coins that come up heads is 2 coins.

To know more about expected value visit:-

https://brainly.com/question/13749480

#SPJ11

Answer:

cos F is 15/28

Step-by-step explanation:

Use SOH CAH TOA

CAH is for cosine and it's Adjacent over Hypotenuse

the adjacent side of F is 15 and the hypotenuse is 28

So 15/28 which does not simplify

Hope this helped! :)

The solution to the system of simultaneous equations is x = 34/7, y = -13/7, z = -9/7.

To solve the system of simultaneous equations:

i. x + 2y + 3z = -5

ii. 3x + y - 3z = 4

iii. -3x + 4y + 7z = -7

We can use the matrix method or the augmented matrix to solve the equations. Let's use the augmented matrix method:

1 2 3 | -5

3 1 -3 | 4

-3 4 7 | -7

We'll perform row operations to transform the matrix into row-echelon form:

R2 = R2 - 3R1

R3 = R3 + 3R1

1 2 3 | -5

0 -5 -12 | 19

0 10 16 | 4

R2 = -R2/5

R3 = R3 + 2R2

1 2 3 | -5

0 1 12/5 | -19/5

0 0 56/5 | -36/5

R3 = (5/56)R3

1 2 3 | -5

0 1 12/5 | -19/5

0 0 1 | -9/7

R2 = R2 - (12/5)R3

R1 = R1 - 3R3

1 2 0 | 8/7

0 1 0 | -13/7

0 0 1 | -9/7

R1 = R1 - 2R2

1 0 0 | 34/7

0 1 0 | -13/7

0 0 1 | -9/7

The row-echelon form of the augmented matrix is obtained. Now, we can read off the solution to the system of equations:

x = 34/7

y = -13/7

z = -9/7

Therefore, the solution to the system of simultaneous equations is x = 34/7, y = -13/7, z = -9/7.

Read more about matrices here:

brainly.com/question/1279486

#SPJ11

Answer:

(x + 1)(x + 2) is divisible by 3.

Step-by-step explanation:

Assume that x is not divisible by 3. This means that x can be expressed as x = 3k + r, where k is an integer and r is the remainder when x is divided by 3. Since x is not divisible by 3, the remainder r must be either 1 or 2.

Case 1: r = 1

If r = 1, then x = 3k + 1. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 1 + 1)(3k + 1 + 2)

= (3k + 2)(3k + 3)

= 3(3k^2 + 5k + 2)

We can see that (x + 1)(x + 2) is divisible by 3.

Case 2: r = 2

If r = 2, then x = 3k + 2. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 2 + 1)(3k + 2 + 2)

= (3k + 3)(3k + 4)

= 3(3k^2 + 7k + 4)

We can see that (x + 1)(x + 2) is divisible by 3.

Hence, the statement is proven.

Read more about integers,

brainly.com/question/12540626

brainly.com/question/26376738

Answer:

36

Step-by-step explanation:

8 * 4.5 = 36

James will earn 252 dollars if he work in a month from his part-time job. when his per hour pay is 8 dollars and assuming 4.5 weeks.

Whenever an employee work for a company he recieves a salary for his work now james is working as a part-time employee so he is getting 8 dollars for per hour working.

Suppose james is working one hour every day as a part timer so his income in one month or in 4.5 weeks will be

\(\rm James\ income =8\times 4.5\times 7\)

\(\rm James\ Income= 252\)

Hence James will earn 252 dollars if he work in a month from his part-time job. when his per hour pay is 8 dollars and assuming 4.5 weeks.

To know more about income follow

https://brainly.com/question/25745683