Find the missing lengths in the triangle above
ER=
IE=

Using the definition of congruent triangles, the missing measurements are:

23. m = 7; LO = 14; NO = 14

24. x = 15; m∠QTS = 90°

25. p = 3; IJ = 15; KJ = 15

26. r = 3; UW = 48

27. y = 7; m∠DEF = 50°

28. m = 5; p = 10

If two triangles are congruent, then all its corresponding sides and angles are equal.

23. The two triangles are congruent by SAS, therefore:

LO = NO

m + 7 = 2m

7 = 2m - m

7 = m

m = 7

LO = NO = m + 7 = 7 + 7 = 14

LO = 14

NO = 14

24. But triangles are congruent by SSS, therefore:

3x = 5x - 30

3x - 5x = -30

-2x = -30

x = 15

m∠QTS = 2(3x) = 6x = 6(15)

m∠QTS = 90°

25. Both triangles are congruent by ASA, therefore:

4p + 3 = 3p + 6

4p - 3p = -3 + 6

p = 3

IJ = KJ = 4p + 3 = 4(3) + 3 = 15

IJ = 15

KJ = 15

26. The two triangles are congruent by SAS, therefore:

5r + 9 = 8r

9 = 8r - 5r

9 = 3r

9/3 = r

r = 3

UW = 2(8r) = 16r = 16(3)

UW = 48

27. Both triangles are congruent by SSS, therefore:

3y + 4 = 5y - 10

3y - 5y = -4 - 10

-2y = -14

y = 7

m∠DEF = 2(3y + 4) = 6y + 8 = 6(7) + 8

m∠DEF = 50°

28. Both triangles are congruent by SSS, therefore:

2m = 10

m = 10/2

m = 5

2p - 5 = p + 5

2p - p = 5 + 5

p = 10

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Answer:

4.341 or 369÷85

Step-by-step explanation:

The table is

x | 4 | 8 | 12
y |  1 | 2 | 3

The question is not understandable. The well-formatted question is

Complete the table for the given rule

Rule:

[tex]y=\dfrac{1}{4}x[/tex]

Table:

x | 4 | 8 | 12
y |  ? | ? | ?

Evaluation of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the provided number to replace the expression's variable before applying the sequence of operations to simplify the expression.

For instance

On evaluation of y= x+7  when x=3, and x=12

we get y(3) = 3 + 7 = 10 and y(12) = 12 + 7 = 19

The given equation is

[tex]y=\dfrac{1}{4}x[/tex]

So, the table is

x | 4 | 8 | 12
y |  1 | 2 | 3

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Answer:

0

12/4

1.75

in that order

Answer:

146

Step-by-step explanation:

substitute x = 2, y = 3 into the expression

4(2)³ + 2(2)(3) - 2(3) + 3(2)²(3)²

= 4(8) + 12 - 6 + 3(4)(9)

= 32 + 12 - 6 + 108

= 38 + 108

= 146

Work Shown:

PR*RT = QR*RS

4*15 = 5*RS

60 = 5*RS

RS = 60/5

RS = 12

For more information, check out the intersecting chords theorem. This is the idea where multiplying pieces of two chords leads to the same product.  A chord is any segment where both endpoints are on the edge of the circle.

RS is equal to 12.

In a circle, two chords that intersect inside of a circle is given by this formula: PR * RT = QR * RS

Since these two chords are equal, we can set up this equation by putting what we know so far. Since PR * RT = 15 * 14 = 60, and QR * RS = 5 * RS, we get 5 * RS = 60. This is just a simple algebraic expression now.

Dividing by 5 from both sides, we get [tex]\frac{RS}{5}[/tex] = [tex]\frac{60}{5}[/tex].

We then get RS = 12. This wasn't so bad, right?

Hope this helped!

The team can be formed in 420 different ways

This is a combination problem since we are to select a set of people from a group. Combination has to do with selection.

if r number of objects is to be selected from a pool of n objects, this can be done in nCr number of ways.

[tex]nCr=\frac{n!}{r!(n-r)!}[/tex]

Now If A company has 8 male and 6 female employees, and needs to nominate 2 men and 2 women for the company bowling team, then this can be done in the following way;

[tex]_{8} C_{2}=\frac{8!}{2!6!} =28\\_{6} C_{2}=\frac{6!}{2!4!} =15[/tex]

[tex]_{8} C_{2}*_{6} C_{2}=28*15[/tex]

[tex]=420[/tex] teams

Hence, The team can be formed in 420 different ways

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Answer:

a.) 1003

Step-by-step explanation:

The formula to find the sum of an arithmetic sequence: Sn = n/2[2a + (n - 1)d], where a is the first term, n is the number of terms and d is the common difference.

1) Let's substitute the values into the formula.

S17 = 17/2[2(11) + (17 - 1)6]

S17 = 17/2[22 + (16)6]

S17 = 17/2[22 + 96]

S17 = 17/2[118]

S17 = 17/2 × 118

S17 = 1003

Therefore, the sum of the first 17 terms of this arithmetic sequence is 1003 (a).

Answer:

D

Step-by-step explanation:

Lets look at all of the answer choices:

Choice A:  9%

= 0.09

Choice B: 0.125

= 0.125

Choice C = 7.8*10^-2

= 0.078

Choice D = 7/16

= 0.4375(THE ONLY ANSWER ABOVE 0.4)

Answer:

D, 0.4375

Step-by-step explanation:

A, 9% = 0.09

B, 0.125 = 0.125

C, 7.8 * 10^-2 = 0.078

D, 7/16 = 0.375

Your answer will be D, 0.4375 because the other values are less the 0.4.

Answer:

9.62 cm²

Step-by-step explanation:

 diameter = 7 cm

              r = 7 ÷2 = 3.5 cm

             Ф = 45°

  [tex]\sf \boxed{\text{\bf Area of sector = $\dfrac{\theta}{360}*\pi r^2$}}[/tex]  

                              [tex]\sf =\dfrac{45}{360}*3.14*3.5*3.5\\\\ = 4.81 \ cm^2[/tex]

Area of the given sectors = 2 *4.81

                                           = 9.62 cm²

Hello!

Let's solve this in step

Let's find the circular region to the left of the center:

  [tex]Area = \frac{45}{360}*Area_.formuka_.of_.Circle =\\ Area = \frac{45}{360}*\pi (radius)^2\\ Area = \frac{45}{360} *\pi (3.5)^2\\Area=4.81[/tex]

Now let's find the circular region to the right of the center

 ⇒ the angle 45° by the vertical angle theorem is equal to the angle  

      opposite it in the other circular region

     ⇒ has the same area as the left region

Total Area = 4.81 + 4.81 = 9.62 cm²

Answer: 9.62 square centimeters

Hopefully that helps!

If the salesman chooses highway route 1 he will arrive in the shortest time because the distance in route 1 is less than the distance in route 2.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

Route 1:

The distance between A and D

Distance of AB:

[tex]\rm AB=\sqrt{(400-0)^2+(300-0)^2}[/tex]

AB = 500 mi

Distance between BD:

[tex]\rm BD=\sqrt{(1300-400)^2+(1500-300)^2}[/tex]

BD = 1500 mi

In route 1 the distance traveled by salesman:

AD = 500 + 1500 = 2000 mi

Route 2:

[tex]\rm AC=\sqrt{(800-0)^2+(1500-0)^2}[/tex]

AC = 1700 mi

[tex]\rm CD=\sqrt{(1300-800)^2+(1500-1500)^2}[/tex]

CD = 500 mi

AD(through C) = 1700 + 500 = 2200 mi

Thus, if the salesman chooses highway route 1 he will arrive in the shortest time because the distance in route 1 is less than the distance in route 2.

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In the equation, the value of x is 4 and y is 1.

From the information given,

2x - y = 7. ...... i

x + 2y = 6 ....... ii

Multiply equation i by 1

Multiply equation ii by 2

2x - y = 7.

2x + 4y = 12

Subtract both equations

-5y = -5

y = -5/-5

y = 1

From equation i

2x - y = 7.

2x - 1 = 7

2x = 7 + 1

2x = 8

x = 8/2

x = 4

Therefore, x = 4 and y = 1

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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

How do the graphs f(x) and f^-1(x) relate?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

These two functions are inverses of each other.

That's the way these two are related to each other.

f^-1(x) is the inverse function of f(x), and f(x) is the inverse function of f^-1(x).

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

            [tex]\bf{=They\;are\:inverses}[/tex]

[tex]\boxed{\bf{\space aesthetic \space \not101}}[/tex]

Answer: They are reflections of each other.

Step-by-step explanation:

Answer:

24 pounds of garlic

Step-by-step explanation:

if she spends 3$ per pound, you divide 72 by 3. the answer to that is 24, so if she spends 72 dollars on only garlic, she can buy 24 pounds.

Jennifer can buy 24 pounds of garlic

we see here, that if she spends 3$ per pound, you divide 72 by 3.

The answer would be 24, so if she spends 72 dollars on only garlic,

she can buy 24 pounds.

1: any of various units of mass and weight specifically: a unit now in general use among English-speaking peoples equal to 16 avoirdupois ounces or 7000 grains or 0.4536 kilogram — see Weights and Measures Table

2: the basic monetary unit of the United Kingdom.

In maths, a division is a process of splitting a specific amount into equal parts. For example, we can divide a group of 20 members into 4 groups of 5 members each or 5 groups of 4 members each

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Answer:

(x+9) and (x-4)

Step-by-step explanation:

Type of statistical characteristics of variables found in a sample and describes summarizes and synthesizes collected data is a. Descriptive.

Descriptive statistics are used to describe or summarize the characteristics of a sample or data set, such as a variable's mean, standard deviation, or frequency.

Descriptive statistics can be used to describe a single variable (univariate analysis) or more than one variable (bivariate/multivariate analysis). In the case of more than one variable, descriptive statistics can help summarize relationships between variables using tools such as scatter plots.

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Answer:

It must be probably √29

Step-by-step explanation:

[tex]distance = \sqrt{ { (- 4)}^{2} + {(5)}^{2} } [/tex]

hope it to be the correct...

Answer:

B

Step-by-step explanation:

[] means the endpoints are inclusive. Therefore [2,7] is equivalent to 2 <= x <= 7. So [2,7] represents graph B.

Answer:

Ratio is 11 : 13

Step-by-step explanation:

We are given;

Time to develop estimate = 30 minutes

Time to do the job = 2 hours 45 minutes = (2 * 60) + 45 = 165 minutes

Total time to develop and do job = 165 + 30 = 195 minutes

Thus;

Ratio of time spent on job to total time = 165 : 195

Whrn this is broken further, we have; 11 : 13

The solutions for the given equation [tex]4x^2+x-3=0[/tex] are x = -1 and x = 3/4. Using the quadratic formula, the solutions for the given equation are calculated.

The formula which is used to calculate the roots(solutions) of the quadratic equation in the form [tex]ax^2+bx+c=0[/tex] is

x = [- b ± [tex]\sqrt{b^2-4ac}[/tex]]/2a

The given equation is [tex]4x^2+x-3=0[/tex]

In comparison with the standard form of quadratic equation [tex]ax^2+bx+c=0[/tex],

we get, a = 4, b = 1 and c = -3

So, solving the given equation using the quadratic formula,

x = [- b ± [tex]\sqrt{b^2-4ac}[/tex]]/2a

  = [- 1 ± [tex]\sqrt{1-4(4)(-3)}[/tex]]/2(4)

  = [-1 ± [tex]\sqrt{49}[/tex]]/8

  = (-1 ± 7)/8

Thus, x =  (-1 + 7)/8 = 3/4 and x = (-1-7)/8 = -8/8 = -1

Therefore, the solutions of the given equation are x = -1 and x = 3/4.

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The false statement include:

This relationship between two variables involves them having a positive slope. This means that as volume increases, temperature also increases which isn't the case.

This cause and effect pattern also means that the volume doesn't have explanatory variables.

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Answer:

Volume is the explanatory variable

Step-by-step explanation:

because vanilla is better than chocolate

Answer:

C

Step-by-step explanation:

.........................

Answer:

c

Step-by-step explanation:I think the answer might be C. because they have asked for the area and the formulae is side multiply by side.

The equation in rectangular coordinates. (x - 1)² + y² = 1

There are many types of coordinate system depending upon the usage and ease of working , Spherical , Rectangular , Cylindrical , Polar are the examples of Coordinate System.

It is given that the equation in polar coordinates is  r = 2 cosθ

To change in rectangular coordinates

The relation between polar and rectangular coordinate is

x = r cosθ and y = r sinθ

x² + y² = r²

r = 2 cosθ

r² = 2r cosθ

r² = x

so the equation in rectangular coordinate system becomes

x² + y² = 2x

x² - 2x + y² = 0

x² - 2x + 1 + y² - 1 = 0

(x - 1)² + y² = 1

This represents the equation in rectangular coordinates.

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Answer:

t=1/2u

Step-by-step explanation:

Since t=tens digit and u=units digit, as given in the equation that means that t+u=9. Since the tens digit is one-half the units digit that means: [tex]t=\frac{1}{2}u[/tex] since it's one half the units digit.

Answer:

  1

Step-by-step explanation:

The probability that a random variable has a particular value or a range of values is the sum of the probabilities associated with each of the values.

All of the x-values in the table are less than or equal to 20, so p(x≤20) is the sum of all of the probabilities in the table.

  p(x≤20) = 0.20 +0.15 +0.05 +0.1 +0.25 +0.1 +0.15 = 1.00

The probability is 1 that x ≤ 20.

Answer:

It will take 1 hour and 24 minutes.

Step-by-step explanation:

Given that:

Eastbound train travels at a rate of 65 miles per hour and Westbound train travels at a rate of 85 miles per hour

So speed = 65 + 85 = 150 miles per hour

Total distance = 210 miles

We have to find the time, we know that

Distance = time * speed

OR

Time = distance / speed

Time = 210/150

Time = 1.4 hours

Or it can be written as:

Time = 1 hour 24 minutes

Hope this helped :D

Answer:

19912/76000=0.262.000000

Answer:

Step-by-step explanation:

 19912 76000  

-152000 0.262  

  471200

 -456000

    152000

   -152000

         0

Your question is incomplete. Please read below to find the missing content.

Using the exponential distribution, it is found that:

a) There is a 0.0952 = 9.52% probability that a television set fails in less than 10,000 hours.

b) There is a 0.3012 = 30.12% probability that a television set lasts more than 120,000 hours.

c) There is a 0.1809 = 18.09% probability that a television set fails between 60,000 and 100,000 hours of use.

d) The 90th percentile is of 230,259 hours.

In probability theory and records, the exponential distribution is a non-stop possibility distribution that frequently issues the quantity of time till a few specific events happen. It is a method wherein activities show up continuously and independently at a regular common rate.

As an instance, the amount of time (starting now) until an earthquake occurs has an exponential distribution. Different examples consist of the duration, in mins, of long-distance enterprise phone calls, and the quantity of time, in months, a car battery lasts.

The lifetime of LCD TV sets follows an exponential distribution with a mean of 100,000 hours. Compute the probability a television set:

a. Fails in less than 10,000 hours.

b. Lasts more than 120,000 hours.

c. Fails between 60,000 and 100,000 hours of use.

d. Find the 90th percentile. So 10 percent of the TV sets last more than what length of time?

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Solution :

0.9

0.3012

0.1809

230258.

Given that:

μ = 100,000

λ = 1/μ = 1 / 100000 = 0.00001

a. Fails in less than 10,000 hours.

P(X < 10,000) = 1 - e^-λx

x = 10,000

P(X < 10,000) = 1 - e^-(0.00001 * 10000)

= 1 - e^-0.1

= 1 - 0.1

= 0.9

b. Lasts more than 120,000 hours.

X more than 120000

P(X > 120,000) = e^-λx

P(X > 120,000) = e^-(0.00001 * 120000)

P(X > 120,000) = e^-1.2

= 0.3011942 = 0.3012

c. Fails between 60,000 and 100,000 hours of use.

P(X < 60000) = 1 - e^-λx

x = 60000

P(X < 60,000) = 1 - e^-(0.00001 * 60000)

= 1 - e-^-0.6

= 1 - 0.5488116

= 0.4511883

P(X < 100000) = 1 - e^-λx

x = 100000

P(X < 60,000) = 1 - e^-(0.00001 * 100000)

= 1 - e^-1

= 1 - 0.3678794

= 0.6321205

Hence,

0.6321205 - 0.4511883 = 0.1809322

d. Find the 90th percentile. So 10 percent of the TV sets last more than what length of time?

P(x > x) = 10% = 0.1

P(x > x) = e^-λx

0.1 = e^-0.00001 * x

Take the In

−2.302585 = - 0.00001x

2.302585 / 0.00001

= 230258.5

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Answer:

True, False, False, False

Step-by-step explanation:

I'll find the lengths of all sides of the drawing before answering individual answers so that it's less confusing.

1) The question says that QR is a perpendicular bisector of TS. This means that the length of TQ and QS is the same. Also, since both triangles TRQ and SRQ share the same side RQ, and the angle between the two segments is 90 degrees, the two triangles are congruent (RTQ and RSQ) using SAS.

2) Side RT and TS will have the same length since the two triangles are congruent. (2x+1) = (4x-3) --> -2x = -4 --> x = 2. We can conclude that x = 2.

3) Now that we know that x = 2, we can find the length of side RS by replacing the x with 2. 4(2)-3 is 5, so RS = 5.

4) We can use the Pythagorean theorem to find RQ (Hypotenuse^2 = Other two sides added after being squared individually). Since the hypotenuse of triangle RSQ is RS which is 5, and one side is 4, we can input those into our equation. (5)^2 = (4)^2 + (RQ)^2. --> 25 = 16 + (RQ)^2 --> 9 = (RQ)^2 --> RQ = 3.

5) Since the two triangles RTQ and RSQ are congruent, side TQ and SQ also have the same length, since CPCTC (Corresponding parts of congruent triangles are congruent). QS is 4, so TQ will also be 4. This means that ST will be 8 (4+4). ST = 8

Now that we have all the clues, all we need to do is choose True or False.

RS = 5 is TRUE

RS = 4 is FALSE

ST = 10 is FALSE

QR = 4 is FALSE