Triangle ABC is similar to triangle PQR, as shown below: Two similar triangles ABC and PQR are shown. Triangle ABC has sides AB = c, BC = a, and AC = b. Triangle PQR has sides PQ = r, QR = p, and PR = q. Angle CAB is congruent to angle RPQ. Angle ABC is congruent to angle RQP. Angle ACB is congruent to angle QRP. Which ratio is equal to r:c? c:p p:a r:a q:c

Answer:

The solution is (-2,-11)

Step-by-step explanation:

The given system is

[tex]-5x+y=-1[/tex]

and

[tex]y-4x=-3[/tex]

Make y the subject in the first equation to get;

[tex]y=5x-1[/tex]

Put [tex]y=5x-1[/tex] into the second equation.

[tex]5x-1-4x=-3[/tex]

Group similar terms;

[tex]5x-4x=-3+1[/tex]

[tex]x=-2[/tex]

Put [tex]x=-2[/tex] into [tex]y=5x-1[/tex].

This implies that;

[tex]y=5(-2)-1[/tex]

[tex]y=-10-1[/tex]

[tex]y=-11[/tex]

The solution is (-2,-11)

Answer:

(-2, -11)

Step-by-step explanation:

We are given the following two equations:

[tex]-5x + y = -1[/tex] --- (1)

[tex]y - 4x = -3[/tex] --- (2)

From equation (2):

[tex]y=4x-3[/tex]

Substituting this value of y in equation (1) to get:

[tex]-5x + y = -1[/tex]

[tex]-5x + (4x-3) = -1[/tex]

[tex]-5x+4x=-1+3[/tex]

[tex]x=-2[/tex]

Now substituting the value of x in equation (2) to get:

[tex]y - 4(-2) = -3[/tex]

[tex]y+8=-3[/tex]

[tex]y=-8-3[/tex]

[tex]y=-11[/tex]

Therefore, the solution of the equations as an ordered pair is (-2, -11).

Answer:

The ball will hit the ground in 2 seconds

Step-by-step explanation:

The formula for throwing a baseball in the air is represented by :

h = -16t² + 12t + 40

where h is the height of the ball and t is the time in seconds

Now we need to find after how many seconds will the ball hit the ground

When the ball hits the ground the height of the ball is 0

⇒ -16t² + 12t + 40 = 0

⇒ 4t - 3t - 10 = 0

⇒ 4t² - 8t + 5t - 10 = 0

⇒  4t(t - 2) + 5(t - 2) = 0

⇒ t cannot be negative so t = 2

Hence, The ball will hit the ground in 2 seconds

The ball will hit the ground after 2 seconds.

The formula for the height of a thrown baseball is given by:

h = -16[tex]t^{2}[/tex] + 12t + 40

where h is the height (in feet) and t is the time (in seconds).

To find the time when the ball hits the ground, we need to determine when the height h is equal to zero:

0 = -16[tex]t^{2}[/tex] + 12t + 40

Solving this quadratic equation using the quadratic formula:

The quadratic formula is: t = (-b ± √(b² - 4ac)) / 2a

For our equation, a = -16, b = 12, and c = 40. Plugging these values in:

Thus, the ball will hit the ground at t = 2 seconds.

Note that we ignore the negative time value as it doesn’t represent a meaningful physical solution.

Answer:

3 miles

Step-by-step explanation:

Answer:

35 7/8.

Step-by-step explanation:

The total length of the wood before any cutting was done = 4 * the mean

= 4* 36 5/8 =  4* 293/8

= 146 1/2 feet.

So the length of the fourth piece = 146 1/2 - (36 3/4 + 36 3/8 + 37 1/2)

= 146 1/2 - 110 5/8

= 36 + 1/2 - 5/8

=  35 7/8  answer.

Turn the mean into an improper fraction.

36 5/8 = 293/8

Multiply the mean by four.

293/8 * 4/1 = 1172/8 or 146 1/2

Add all the sides together.

36 3/4 + 36 + 3/8 + 37 1/2 = 110 5/8 or 885/8

Subtract.

1172/8 - 885/8 = 287/8 or 35 7/8

Best of Luck!

Answer:

27

Step-by-step explanation:

The point estimates for the mean and standard deviation of the given data is respectively; 68 and 17.6

A) To find the point estimate of the mean, we add all up all the data and divide by the number of values.

Thus;

∑x = 57 + 61 + 86 + 87 + 72 + 73 + 19 + 56 + 81 + 79 + 83 + 75 = 816

n = 12 numbers

Thus;

mean = ∑x/n = 816/12

Mean = 68

B) To find the estimate of the standard deviation, we would get it from the formula;

s = √[(n*(∑x²) - (∑x)²)/n(n - 1)]

∑x² = 572 + 612 + 862 + ... + 742 = 59,010

s = √[ (12*(59,010) - (816)²)/(12)(11)]

s = 17.6

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The   Answer    is     frequency

= (pi)/(2pi)

= 1/2 freq  

Answer:

Step-by-step explanation:

The easiest way to do this is to get the period correct first.

If the function f(x) = cos(B * x) then the period is

P =  2*pi/B  In this case B = 5

P = 2* pi/5

The frequency is the reciprocal of the period

f = 1/p

f = 1/(2pi/5) Now all you do is turn 2p/5 upside down.

f = 5/2*pi <<<< Answer

I don't know how simple your marker considers this, but it is the answer.

Answer:

4 and -21

Step-by-step explanation:

When you factor it (x-4)(x+21)

You get 4 and -21

Answer:

The two triangles may be congruent, but additional information is needed about the sides of each triangle.

Step-by-step explanation:

Given that Samantha measured two of the angles in PQR and found that they had measures of 65° and 70°. Then, she measured two of the angles in XYZ and found that they had measures of 65° and 45°.

We have by using properties of sum of angles of triangles, angles of PQR are 65, 70, 45 and also same for XYZ

Hence there is a chance that these triangles may be congruent depending on the sides.  We are sure that the angles are congruent hence triangles are similar.  But to prove congruence we must have additional information about sides.

The two triangles may be congruent, but additional information is needed about the sides of each triangle.

Answer:The two triangles may be congruent, but additional information is needed about the sides of each triangle

Step-by-step explanation:

Answer:

im not 100% sure but to me it looks like it could be 225

Answer:

The correct option is 3.

Step-by-step explanation:

From the given figure it is clear that the vertices of preimage are A(-4,-2), B(-2,1) and C(-2,-2).

Center of rotation is origin, i.e., (0,0).

Triangle ABC is rotated counterclockwise about the origin.

We need to find the angle of rotation.

Draw line segments OC and OC'. From the below figure it is clear that the angle of rotation counterclockwise about origin is

[tex]45^{\circ}+90^{\circ}+90^{\circ}=225^{\circ}[/tex]

Therefore the correct option is 3.

Answer:

Correct choice is D). -4.

Step-by-step explanation:

Given the following relation is a function where the relation is :

{(6,3),(-4,1),(8,-5),(x,1)}

Now we need to decide about which of the following cannot be a value for x.

Where given choices are:

A). 3

B). 1

C). -5

D). -4

E). 4

We know that a relation is called function if doesn't contains repeated values in domain or doesn't have repeated x-values.

In given relation, {(6,3),(-4,1),(8,-5),(x,1)}, we see that x-values are 6, -4 and 8.

So to prevent repetition, x can't be any of 6, -4 and 8.

Hence correct choice is D). -4.

Answer:

Option d.

Step-by-step explanation:

For this problem we have 2 sides of a triangle (a and b) and the angle between them C = 160 °.

We have a triangle of type SAS.

We have:

a=25

b=30

C= 160°

Then we use the law of cosine.

[tex]c = \sqrt{a^2 +b^2 - 2abcos(C)[/tex]

Now we substitute the values in the formula to find c

[tex]c = \sqrt{25^2 +30^2 - 2(25)(30)cos(160\°)}\\\\c = 54.2[/tex]

Now we use the cosine theorem to find B. (You can also use the sine)

[tex]b = \sqrt{a^2 +c^2 - 2accos(B)}\\\\b^ 2 = a^2 +c^2 - 2accos(B)\\\\b^ 2 -a^2 -c^2 =- 2accos(B)\\\\\frac{a^2 +c^2 -b^2}{2ac} =cos(B)\\\\B = arcos(\frac{a^2 +c^2 -b^2}{2ac})\\\\B = arcos(\frac{25^2 +54.2^2 -30^2}{2(25)(54.2)})\\\\B = 10.9\°[/tex]

Finally:

[tex]A=180\° - B- C\\\\A = 180\° - 10.9\° - 160\°\\\\A = 9.1\°[/tex]

B. R>2 because to win the game they must have had more runs than the losing team

Final answer:

The inequality that represents the number of runs the winning baseball team could have scored is r > 2, since the winning team must score more than the losing team, which scored 2 runs.

Explanation:

The student is asking for the inequality that represents the number of runs, r, that the winning team could have scored in a baseball game, given that the losing team scored 2 runs. The condition to win a game is that the winning team must score more runs than the losing team. Therefore, if the losing team scored 2 runs, the inequality that represents the number of runs the winning team scored is r > 2. This is because the winning team must have scored more than 2 runs to win.

Answer:

8.28 units

Step-by-step explanation:

The formula for the circumference of a circle is [tex]C=\pi d[/tex]

where

[tex]C[/tex] is the circumference of the circle

[tex]d[/tex] is the diameter of the circle

We know form our problem that the circumference of our circle is 26.28 units, so [tex]C=28.26[/tex]. Let's replace that value in our formula and find [tex]d[/tex]:

[tex]C=\pi d[/tex]

[tex]26=\pi d[/tex]

Divide both sides of the equation by [tex]\pi[/tex]

[tex]\frac{26}{\pi } =\frac{\pi d }{\pi }[/tex]

[tex]\frac{26}{\pi } =d[/tex]

[tex]d=\frac{26}{\pi }[/tex]

[tex]d=8.28[/tex]

The diameter of the circle that has a circumference of 28.26 units is 8.28 units.

Answer:

The diameter of a circle is 9 units

Step-by-step explanation:

A circle has a circumference of 28.26

Let diameter of a circle be d unit.

Formula:

[tex]C=\pi d[/tex]

where, C=28.26

[tex]28.26=\pi d[/tex]

[tex]d=\dfrac{28.26}{\pi}[/tex]

[tex]d=8.995\approx 9[/tex]

Hence, The diameter of a circle is 9 units

Answer:

P(A') = 0.65

Step-by-step explanation:

We are given that the probability P(A) = 0.35 and we are to determine the probability of the complement of A.

According to the Complement Rule of any probability, the sum of the probabilities of an event and its complement must be equal to 1.

So for for the event A,

P(A) + P(A') = 1

0.35 + P(A') = 1

P(A') = 1 - 0.35

P(A') = 0.65

The probability of the complement of A is 0.65

The probability of A is given as:

P(A) = 0.35

To calculate the probability of the complement of A, we make use of the following complement formula

P'(A) = 1 - P(A)

So, we have:

P'(A) = 1 - 0.35

Evaluate

P'(A) = 0.65

Hence, the probability of the complement of A is 0.65

Read more about probabiilty at:

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Total discount will be of $14.85.

To calculate the total discount Jennifer received on her purchase of music CDs, each original price must be multiplied by the discount rate of 33 percent (or 0.33 in decimal form).

Let's calculate the discount for each CD first:

For the $9.99 CD: $9.99 × 0.33 = $3.30

For the $14.99 CD: $14.99 × 0.33 = $4.95

For the $19.99 CD: $19.99 × 0.33 = $6.60

Next, add up the discounts to find the total discount:

$3.30 + $4.95 + $6.60

= $14.85

Look at the attached figure. We define the unit circle as a circle with center [tex]A[/tex] in the origin (0,0) and radius 1.

Then, we consider a point P on the circumference. We call [tex]\alpha[/tex] the angle between the positive half of the x axis and the radius AP.

We define

[tex]\cos(\alpha) = \overline{AD},\quad \sin(\alpha) = \overline{AC}[/tex]

As you can see, ACD is a right triangle, and so we have

[tex]\overline{AD}^2+\overline{AC}^2=\overline{AP}^2[/tex]

But since we know that AD is the cosine, AC is the sine, and AP is the radius (which is 1, and remains 1 when squared), we have just found out that

[tex]\cos(\alpha)^2+\sin(\alpha)^2=1[/tex]

Answer:

[tex]S_3=39[/tex]

Step-by-step explanation:

The nth term of the sequence is

[tex]a_n=3(3)^{n-1}[/tex]

To get the first term, substitute n=1,

[tex]a_1=3(3)^{1-1}=3[/tex]

To get the second term, substitute n=2,

[tex]a_2=3(3)^{2-1}=9[/tex]

To get the third term, substitute n=3,

[tex]a_3=3(3)^{3-1}=27[/tex]

The sum of the first three terms is

[tex]S_3=3+9+27=39[/tex]

We could also use the formula

[tex]S_n=\frac{a_1(r^n-1)}{r-1}[/tex] to get the same result.

Answer:

The correct answer is last option   39

Step-by-step explanation:

It is given that,

aₙ = 3(3)ⁿ⁻¹

To find a₁

a₁ = 3(3)¹⁻¹ = 3(3)°

= 3 * 1 = 3

To find a₂

a₂ = 3(3)²⁻¹ = 3(3)¹

= 3 * 3 = 9

To find a₃

a₃ = 3(3)³⁻¹ = 3(3)²

= 3 * 9 = 27

To find the value of S₃

S₃ = a₁ + a₂ + a₃

 = 3 + 9 + 27 = 39

Therefore the correct answer is last option   39

Answer:

Step-by-step explanation:

Graphs of quadratics are symmetrical about the vertex (minimum or maximum point).  

The x value of the point (-3, 11) is 3 units to the left of the vertex (0, 2), the x value that is 3 units to the right of the vertex will have the same y value, so the point

(3, 11) is also on the graph

The quadratic function has a minimum at (0, 2) and includes the point (-3, 11). Solving for the function's equation, we find y = x² + 2, and another point on the graph is (1, 3).

Since the quadratic function has a minimum at (0, 2), it means the vertex form of the quadratic function is y = a(x - 0)² + 2, or simply y = ax² + 2. We know another point on the graph is (-3, 11), so we can use this point to find the value of 'a'.

So, the equation of the quadratic function is y = x² + 2. To find another point on the graph, choose any x-value and compute the corresponding y-value. For example, let x = 1:

Thus, another point on the graph is (1, 3).

Answer:

A mere 15 years back, navigators would have scoffed at the idea of Paperless Navigation on big ocean going ships. After all, since centuries, navigational paper charts had been the heart and soul of ship navigation. Imagining that a day would come where we’d no longer have them onboard was nothing short of blasphemy.

Step-by-step explanation:

The advantages of technology versus old-school methods for determining the position at sea include ease of navigation and safety.

The ECDIS is the abbreviated form Electronic Chart Display and Information System. It is a modern technology used for navigation through waters.

With ECDIS as the dominant source of sailing, the Navigating Officer can plan and summarise the transition much more speedily than on Paper Charts.

This is the background that will sound an alarm if the ship is inside the limit stated.

This scene displays the non-traversable field and marks the confine save that the container can harmlessly cross.

Therefore, we have found that the advantages of technology versus old-school methods for determining the position at sea include ease of navigation and safety.

Learn more about navigational technologies here: https://brainly.com/question/24839581

#SPJ2

Answer:

The center is (2 ,-3)

The radius is 3

The diameter is twice the radius = 2(3) = 6

Step-by-step explanation:

The equation of a circle is given by

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

where (h,k) is the center and r is the radius

(x - 2)² + (y+3)² = 9

(x - 2)² + (y- -3)² = 3^2

The center is (2 ,-3)

The radius is 3

The diameter is twice the radius = 2(3) = 6

The center of the circle is at (2, -3), the radius is 3 units, and the diameter is 6 units. To graph the circle, plot the center point (2, -3) and draw a circle with a radius of 3 units around it.

(a) The coordinates of the center of the circle are (2, -3). The equation of the circle is in the form (x - h)² + (y - k)² = r², where (h, k) are the coordinates of the center and r is the radius. In this case, (h, k) = (2, -3).

(b) The radius of the circle is 3 units. The diameter is twice the radius, so the diameter of the circle is 6 units.

(c) To graph the circle, plot the center point (2, -3) and draw a circle with a radius of 3 units around it.

Answer:

D & E

Step-by-step explanation:

1/ they're the only ones in the right format

2/ they're both highlighted on the graph

(im not completely confident in my answer, so don't drag me if im wrong.)

Answer:

it is a and b

Step-by-step explanation:

Answer:

D) Over $4,000,000

Step-by-step explanation:

On the last day, the worker is paid $0.07*2²⁵ (it's by the power of 25 because it's 0 on the first day), which is $2,348,810.24. That means that the amount of money earned on all other days are $2,348,810.37, since 2⁰ + 2¹ + 2² + 2³... + 2ⁿ⁻² + 2ⁿ⁻¹ = 2ⁿ + 1.

That totals to approximately $4.6 million dollars, which is larger than $4 million.

To find the worker's total pay over 26 days, the pay is calculated as a geometric series with a first term of $0.07 and a common ratio of 2, using the geometric series sum formula.

The worker's pay is doubling each day. This pattern represents a geometric sequence where the first term a is $0.07 and the common ratio r is 2. To find the total pay after 26 days, we need to calculate the sum of the first 26 terms of the sequence.

The formula for the sum S of a geometric series is S = a(1 - r^n) / (1 - r), where n is the number of terms. Plugging in our values, we get S = 0.07(1 - 2^26) / (1 - 2).

Performing the calculation yields a sum that we can evaluate to determine the worker's pay over the 26-day period. This result would fall into one of the ranges provided in the original question.

Answer:

Negative 8 plus negative 6 equals negative fourteen.

Answer:

Negative eight plus negative six equals negative fourteen

360°=18

120°=x

x=120*18/360=6

Answer:

6/11

Step-by-step explanation:

We are not told which number cube shows a 4; it can be the first one or the second one.

If the first number cube is a 4, this gives us the options of:

4 and 1; 4 and 2; 4 and 3; 4 and 4; 4 and 5; 4 and 6.

However if the second number cube is a 4, this gives us

1 and 4; 2 and 4; 3 and 4; 4 and 4; 5 and 4; 6 and 4.

We cannot count "4 and 4" twice; this leaves us with 11 total possibilities.

Out of these 11, only the sum of 4 and an odd number will be odd:

1 and 4; 3 and 4; 5 and 4; 4 and 1; 4 and 3; 4 and 5.

There are 6 ways to have an odd sum out of 11 total possibilities; this gives us a probability of 6/11.

Answer:

Option A. 10

Step-by-step explanation:

we know that

Applying the Intersecting Secants Theorem

[tex]QS*RS=CS*TS[/tex]

substitute the values

[tex](11x-1+8)*(8)=(9+7)*(9)[/tex]

solve for x

[tex](11x+7)*(8)=(16)*(9)[/tex]

[tex]88x+56=144[/tex]

[tex]88x=144-56[/tex]

[tex]88x=88[/tex]

[tex]x=1[/tex]

Find the measure of QR

[tex]QR=11x-1=11(1)-1=10[/tex]

23/8 for the most part I think

Here is your answer

[tex]\bold{x=12}[/tex]

REASON:

[tex]<font color="blue" size=5>Concept used</font>[/tex]: The opposite sides of a parallelogram are equal.

So, in above given figure

[tex] 3x+7=5x-17 [/tex] (measures of opposite sides)

[tex] 5x-3x= 17+7 [/tex]

[tex] 2x= 24 [/tex]

[tex] x= 24/2 [/tex]

[tex] x= 12 [/tex]

HOPE IT IS USEFUL