If KL = x + 8
, LM = 12
, and KM = 3x − 14
, what is KL?

Answer:

Step-by-step explanation:

Given quadrilaterals JKLM and NPQR are similar with K=100°, M=85°, JK=12, LM=(5y+1), MJ=20, RN=10, NP=(x+4), PQ=7, QR=8, you want to identify the true statments.

Corresponding angles are congruent, so we have ...

  ∠K≅∠P = 100°

  ∠M≅∠R = 85°

Corresponding sides have the same ratio. The larger : smaller ratio here appears to be 2 : 1.

  JK : NP = 12 : (x+4)   ⇒   x+4 = 6   ⇒   x = 2

  KL : PQ = ? : 7   ⇒   KL = 14

  LM : QR = (5y+1) : 8   ⇒  5y+1 = 16   ⇒   y = 3

  MJ : RN = 20 : 10 . . . . . establishes the ratio for the others

The true statements are ...

__

Additional comment

It can be helpful to write a list of the specific correspondences (based on the similarity or congruence statement).

<95141404393>

The average speed of Sophie in miles per hour is 5.04 miles per hour.

The speed in feet per second is 7.39 feet per second.

Given that,

Sophie recently ran a marathon.

It took her 5.2 hours to run the 26.2 miles required to complete a marathon.

Total distance ran = 26.2 miles

Total time taken = 5.2 hours

Speed = Total distance / Total time

           = 26.2 / 5.2

           = 5.04 miles per hour

Speed in feet per second = (5.04 × 5280 feet) / 3600 seconds

                                           = 7.39 feet per second

Learn more about Speed here :

https://brainly.com/question/17661499

#SPJ1

We can see that the number multiplied by t is 50. Therefore, the simplified expression is -6t^2 + 50t + 56, and the number multiplied by t is 50.

To simplify the given expression (8t - 6t^2) + 14(3t + 4), we first need to apply the distributive property by multiplying 14 with both terms inside the parentheses. This gives us:
8t - 6t^2 + 42t + 56
Now, we can combine like terms by adding the coefficients of the t and t^2 terms. The t^2 term has a coefficient of -6, and there are no other t^2 terms in the expression, so we can just bring it down as it is. The t term has a coefficient of 8 + 42 = 50, so we can simplify the expression further as:
-6t^2 + 50t + 56
From this expression, we can see that the number multiplied by t is 50. Therefore, the simplified expression is -6t^2 + 50t + 56, and the number multiplied by t is 50.

For more such questions on multiplied

https://brainly.com/question/29793687

#SPJ8

A. The hypothesis is stated in a correlational form.

B. It does not specify whether it uses a directional or non-directional test.

C. The level of measurement for these variables is not specified.

D. The higher the level of anxiety among Staff Nurses, the lower their performance.

a. The hypothesis "The performance of the Staff Nurses is affected by their level of anxiety." is stated in a correlational form.

b) The given hypothesis does not specify whether it uses a directional or non-directional test.

c) The variables in this hypothesis are "performance of the Staff Nurses" and "level of anxiety." The level of measurement for these variables is not specified.

d) To convert the non-directional hypothesis into a directional one, we would need to specify the direction of the relationship between the variables. For example: "The higher the level of anxiety among Staff Nurses, the lower their performance."

learn more about hypothesis: https://brainly.com/question/606806

#SPJ9

Answer: Please See attached file for answers and work for problems 1-2.

1. a= 7

  b= 70 degrees

2. a= 6

  b= 19pi/20

Step-by-step explanation:

Use the rule(s):

[tex]z_{1} z_{2} =r_{1} r_{2} cis[/tex](θ[tex]_{1}[/tex]+θ[tex]_{2}[/tex])

[tex]\frac{z_{1} }{z_{2}} =\frac{r_{1} }{r_{2}}cis[/tex](θ[tex]_{1}[/tex]-θ[tex]_{2}[/tex])

and isolate it to standard form: a (cos b + i sin b)

you can also rewrite that as a (cis b)

Answer:

7.6

Step by step explanation

The equation in standard form for the circle with center (0, 9) passing through (15/2, 5) is x²+y²-18y-54.25=0.

The given coordinate points are (0, 9) and (15/2, 5).

The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²

Here, (0-7.5)²+(9-5)²=r²

56.25+16=r²

r=8.5

Now, the equation is (x-0)²+(y-9)²=8.5²

x²+y²-18y+18=72.25

x²+y²-18y+18-72.25=0

x²+y²-18y-54.25=0

Therefore, the equation in standard form for the circle with center (0, 9) passing through (15/2, 5) is x²+y²-18y-54.25=0.

To learn more about an equation of a circle visit:

https://brainly.com/question/23799314.

#SPJ1

The image of the figure  after dilation is attached and the new dimensions are

A'B' = C'D' = 6 units

A'D' = B'C' = 2 units

To find the new dimensions after dilation, we need to know the dimension of the preimage.

Examining the attached figure, assuming each do represent 1 unit we have that

AB = CD = 18 units

AD = BC  6 units

Using the scale factor of 1/3 results to

A'B' = C'D' = 18 * 1/3 = 6 units

A'D' = B'C' =  6 * 1/3 = 2 units

Learn more about dilation at

https://brainly.com/question/30240987

#SPJ1

The value of the function f(-1) is 1/3. Option D

A function can be defined as a law, an expression or rule that is used to show the relationship between two variables.

These variables are listed as;

From the information given, we have the function written as;

f(x) = 3ˣ

To determine the function f(-1), we need to substitute the value of the variable x as -1 in the function f(x)

Substitute the values, we have;

f(-1) = 3⁻¹

Take the inverse of the value, we get;

f(-1) = 1/3

Learn more about functions at: https://brainly.com/question/11624077

#SPJ1

Answer:

To find the experimental probability of not spinning a 1, we need to determine the total number of spins and the number of spins that resulted in not landing on 1.

From the bar graph, we can see that the bar labeled "1" ends at 8, indicating that the spinner landed on 1 a total of 8 times.

To find the total number of spins, we sum up the values at the end of each bar:

Total number of spins = 8 + 6 + 9 + 11 + 9 + 7 = 50

The number of spins that did not result in landing on 1 is the sum of the values at the ends of the bars labeled 2, 3, 4, 5, and 6:

Number of spins not landing on 1 = 6 + 9 + 11 + 9 + 7 = 42

Now, we can calculate the experimental probability of not spinning a 1 by dividing the number of spins not landing on 1 by the total number of spins:

Experimental probability of not spinning a 1 = Number of spins not landing on 1 / Total number of spins

Experimental probability of not spinning a 1 = 42 / 50

Experimental probability of not spinning a 1 = 0.84 or 84%

Therefore, the experimental probability of not spinning a 1 is 84%.

Step-by-step explanation:

Answer: 21/25 or 0.84

Step-by-step explanation:

8+6+9+11+9+7=50

50-8=42

42/50=21/25=0.84

Answer:

Step-by-step explanation:

To determine the amount by which Norah’s taxable income and federal tax payable would increase, we need to calculate the following:

The amount of foreign source income that will be included in Norah’s taxable income.

The federal tax payable on the foreign source income.

For non-business income:

The amount of foreign source income that will be included in Norah’s taxable income is $30,000.

The federal tax payable on the foreign source income is $6,525.

For business income:

The amount of foreign source income that will be included in Norah’s taxable income is $30,000.

The federal tax payable on the foreign source income is $8,700.

The classification of the given polynomial is cubic polynomial, the correct option is C.

We are given that;

The equation=3x^3-x^2-x+4

Now,

Suppose the considered polynomial is of only one variable.

Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.

Degree of 3x^3=3

Degree of x^2=2

Degree of x=1

The heighest degree of the polynomial is three of 3x^3.

Therefore, by the polynomial the answer will be cubic polynomial.

Learn more about standard form of a polynomial here:

https://brainly.com/question/15313798

#SPJ1

The simplified form of (5m² - 3)² is 25m⁴ - 30m² + 9.

Given is an expression (5m² - 3)², we need to simplify the expression,

To multiply the expression (5m² - 3)², we can use the formula for squaring a binomial:

(a - b)² = a² - 2ab + b²

In this case, a = 5m² and b = 3.

Substituting these values into the formula, we get:

(5m² - 3)² = (5m²)² - 2(5m²)(3) + (3)²

= 25m⁴ - 30m² + 9

Therefore, the simplified form of (5m² - 3)² is 25m⁴ - 30m² + 9.

Learn more about expression click;

https://brainly.com/question/15994491

#SPJ1

Answer:

m = 5/4

Y-intercept: (0,0)

Step-by-step explanation:

The equation is in slope-intercept form y = mx + b

m = the slope

b = y-intercept

Our equation y = 5/4x

m = 5/4

Y-intercept is located at (0,0)

Answer:

the slope is 5/4 and the y-intercept is 0

Step-by-step explanation:

The slope is the number before x.

The y intercept is the constant term in the equation.

Info related to the question

The equation I just worked with was given in slope intercept form :

Where the slope is defined as m and the intercept is defined as b.

If the position of 5 m below sea level is expressed as -5, then the number that expresses the position of 7 m above sea level would be + 7.

In this particular instance, with the position residing 7 m above sea level, we articulate it as +7. This notation elegantly captures the notion of elevation, affirming the distance above the familiar sea level benchmark.

In the realm of vertical measurements, sea level occupies a crucial position as the reference point, embodying the zero mark on the vertical scale. It is from this fundamental reference point that we navigate the vast spectrum of altitudes.

Find out more on reference point at https://brainly.com/question/29358435

#SPJ9

The values of m and n are 15 and 19, respectively in the given data.

From the given values:

x: 1, 2, 7, 4, 9

y: 3, 5, 11, m, n

Looking at the x-values, we can observe that they are increasing by 1 each time.

Looking at the y-values, we can observe that they are increasing by 2 each time except for the last two values (m and n) which are unknown.

Based on this pattern, we can establish the following equation:

y = 2x + 1

Now, let's calculate the values of m and n using this equation:

For x = 7:

y = 2(7) + 1

y = 14 + 1

y = 15

Therefore, m = 15.

For x = 9:

y = 2(9) + 1

y = 18 + 1

y = 19

Therefore, n = 19.

Hence, the values of m and n are 15 and 19, respectively.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

The shepherd could put 7 sheep in the second pen and 49 sheep in the third pen.

We have,

Let's solve the problem step by step.

-Let's assume that the number of sheep in the second pen is 7x, where x is a positive integer representing the number of multiples of 7.

Similarly, let's assume that the number of sheep in the third pen is 7y, where y is a positive integer representing the number of multiples of 7.

According to the given information, the shepherd placed a total of 63 sheep in the pens:

7 + 7x + 7y = 63

We can simplify this equation by dividing both sides by 7:

1 + x + y = 9

Now we need to find positive integer values for x and y that satisfy this equation.

Since we know that there were more sheep in the third pen, y should be greater than x.

Let's try different values for x and y:

If x = 1, then y = 9 - (1 + 1) = 7

If x = 2, then y = 9 - (2 + 1) = 6

If x = 3, then y = 9 - (3 + 1) = 5

If x = 4, then y = 9 - (4 + 1) = 4

We can see that when x = 1, y = 7, which satisfies the condition that there were more sheep in the third pen.

Therefore, the number of sheep in the second pen (7x) is 7 x 1 = 7, and the number of sheep in the third pen (7y) is 7 x 7 = 49.

Thus,

The shepherd could put 7 sheep in the second pen and 49 sheep in the third pen.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

The complete question:

A shepherd put sheep in pens. In a corral he placed 7 sheep, in the

second and in the third pen he placed multiples of 7. If in total he placed 63

sheep, knowing that where more sheep, was in the third corral.

How many sheep could he put in pens 2 and 3?

The regression equation that correctly models the data is B. y = 2.87x + 11.85

The regression equation is calculated using the following formula:

y = a + bx

where:

y is the dependent variable (daily food costs)

x is the independent variable (number of children in attendance)

a is the y-intercept

b is the slope of the line

The slope of the line is calculated using the following formula:

b = (∑xy - ∑x ∑y / n) / (∑x2 - (∑x)² / n)

Using the data from the table, we can calculate the y-intercept and slope of the line as follows:

a = 411 / 5 = 82.2

b = (13,393 - (143)(411) / 5) / (4,573 - (143)² / 5) = 2.87

Substituting the y-intercept and slope into the regression equation, we get the following equation:

y = 11.85 + 2.87x

Simplifying, we get the following equation:

y = 2.87x + 11.85

Learn more about regression on

https://brainly.com/question/25987747

#SPJ1

[tex]3a-2b=13\\4a+b=21|\cdot2\\\\3a-2b=13\\\underline{8a+2b=42}\\11a=55\\a=5\\\\3\cdot5-2b=13\\2b=2\\b=1[/tex]

Answer:

a = 5, b = 1

Step-by-step explanation:

We need to realize that in a parallelogram, opposite sides are congruent. Therfore, the length of NO and MP must be the same if we assume that Quadrilateral MNOP is a parallelogram.

Length of NO = 21

Length of MP = 4a + b

Therfore, we can get this equation: 4a + b = 21

We can do the same with the other 2 sides to get: 3a - 2b = 13

As you can see, this is a systems of equations! Lets solve it!

To find the values of "a" and "b" in the given system of equations:

Equation 1: 4a + b = 21

Equation 2: 3a - 2b = 13

We can solve this system of equations using either the substitution method or the elimination method. Let's use the elimination method:

Multiply Equation 1 by 2:

2(4a + b) = 2(21)

8a + 2b = 42

Now, we can add Equation 2 and the modified Equation 1 to eliminate the "b" term:

(3a - 2b) + (8a + 2b) = 13 + 42

3a + 8a - 2b + 2b = 55

11a = 55

Divide both sides of the equation by 11:

a = 55 / 11

a = 5

Substitute the value of "a" into Equation 1 to find "b":

4(5) + b = 21

20 + b = 21

b = 21 - 20

b = 1

Therefore, the solution to the system of equations is a = 5 and b = 1.

Therfore, the answer is B, which is what you got as well! Good job!

~~~Harsha~~~

With f(1), we're being given an x-value of 1.

Since 1 < 3 (and not ≥3) we need to use the first formula that is used when x<3.

f(1) = 1 - 2 = -1

A

Step-by-step explanation:

The probability that either event A or B will occur is equal to 0.89 to the nearest hundredth

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 20 + 12 + 4 = 36

probability of A = P(A) = 20/36

probability of B = P(B) = 12/36

probability that either event A or B will occur = 20/36 + 12/36

probability that either event A or B will occur = (20 + 12)/36

probability that either event A or B will occur = 32/36

probability that either event A or B will occur = 0.89

Therefore, the probability that either event A or B will occur is equal to 0.89 to the nearest hundredth

Read more about probability here:https://brainly.com/question/251701

#SPJ1

The required first answer u = [tex]x^{2}[/tex] + 1 and du = 2x  and second answer u = tanx and du = [tex]sec^2 x[/tex] .

Given that if  [tex]\int\limits {f(g(x)) g'(x)} \, dx[/tex]  then u = g(x) and du = g'(x),

[tex]\int\limits {\frac{x}{\sqrt{x^2+1} } } \, dx[/tex]  and [tex]\int\limits {tan^2 x sec^2 x} \, dx[/tex]

To find u and du by using the integral property

[tex]\int\limits {f(g(x)) g'(x)} \, dx = f(g(x))[/tex].

Consider  [tex]\int\limits {\frac{x}{\sqrt{x^2+1} } } \, dx[/tex]

The above integral can be expressed as

[tex]\int\limits {\frac{x}{\sqrt{x^2+1} } } \, dx = \int\limits {\frac{1}{\sqrt{x^2+1} } } \,x dx[/tex]

That implies, u = g(x) = [tex]x^{2}[/tex] + 1.

Differentiating with respect to x gives,

du = g'(x)

du = d/dx( [tex]x^{2}[/tex] + 1 )

du = 2x + 0.

du = 2x.

Consider  [tex]\int\limits {tan^2 x sec^2 x} \, dx[/tex]

The above integral can be expressed as

[tex]\int\limits {tan^2 x sec^2 x} \, dx = \int\limits {(tanx)^2 sec^2 x} \, dx[/tex]

That implies, u = g(x) = tanx.

Differentiating with respect to x gives,

du = g'(x)

du = d/dx( tanx )

du = [tex]sec^2 x[/tex].

du = [tex]sec^2 x[/tex].

Hence, the required first answer u = [tex]x^{2}[/tex] + 1 and du = 2x  and second answer u = tanx and du = [tex]sec^2 x[/tex].

Learn more about integral click here:

https://brainly.com/question/30884486

#SPJ1

Answer:

$120

Step-by-step explanation:

Job1:

       To find the tax, multiply the payment per week ($70) by 0.1.

         Tax = payment * tax rate

                = 70 * 10%

                [tex]\sf = 70 * \dfrac{10}{100}\\\\ = \$7[/tex]

Now, to find his earning after deduction of tax, subtract 7 from 70.

Amount after deduction of tax = 70 - 7

                                                  = $ 63

Job2:

       Tax = 60 * 5%

              = 60 * 0.05

               = $3

  Amount after deduction = 60 - 3

                                           = $ 57

Total amount Byron takes home = 63 + 57

                                                      = $120

The number that belongs in the green box is 130.4 units.

In Mathematics and Geometry, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;

a + c + b = 180°

12° + 27° + b = 180°

39° + b = 180°

b = 180° - 39°

b = 141°

In Mathematics and Geometry, the law of sine is modeled or represented by this mathematical equation:

sinA/a = sinB/b

sin141/a = sin12/43

a = 43sin141/sin12

a = 27.108/0.2079

a = 130.4 units.

Read more on triangles here: https://brainly.com/question/29789248

#SPJ1

The number of new health units is 937, and the number of improved health units is 1,137.

The number of improved health units exceeds the new ones by 200. In other words, I = N + 200.

We also know that the total number of health units counted in the report is 2,074.

Therefore, we have the equation N + I = 2,074.

Substituting the value of I from the first equation into the second equation, we can solve for N:

N + N + 200 = 2,074

2N + 200 = 2,074

2N = 1,874

N = 937

Now, we can substitute the value of N back into the first equation to find I:

I = N + 200

I = 937 + 200

I = 1,137

Therefore, the number of new health units is 937, and the number of improved health units is 1,137.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

The numeric value of the expression in this problem is given as follows:

-77.

The expression in the context of this problem is defined as follows:

[tex]2^5[/tex] x (-2) - 4 x 5 + 7.

Considering the PEMDAS acronym, the power operation has the precedence over the remaining operations, hence:

[tex]2^5[/tex] x (-2) - 4 x 5 + 7 = 32 x (-2) - 4 x 5 + 7.

Then, following the same acronym, we have that the multiplication operation has precedence over the addition/subtraction operations, hence:

32 x (-2) - 4 x 5 + 7 = -64 - 20 + 7.

Finally, we can just subtract and add the numbers to obtain the numeric value of the expression as follows:

-64 - 20 + 7 = -77.

A similar problem, also featuring numeric values of a function, is given at brainly.com/question/28367050

#SPJ1

Answer:

Step-by-step explanation:

The expression x-3 is a factor of P(x)=x²-x2-2x-12 because the remainder is zero. P(x) written as a product of two factors is (x-3)(x²+2x+4).