Quadrilateral EFGH is similar to quadrilateral IJKL. Find KL. Round your
answer to the nearest tenth if necessary. Figures are not drawn to scale.
59
H
13
E
27
F
G
I
L
X
K

The solution of the inequality 2b + 5 ≤ 30 is b ≤ 12.5

Inequalities refers to some type of equations where the relationship between the left hand side and the right hand side of an equation is expressed in terms of symbols other than equal to

The symbols include

In the problem given the symbol used is less than or equal to and the equation is solved by

2b + 5 ≤ 30

2b + 5 - 5 ≤ 30 - 5

2b ≤ 25

dividing through by 2

2b / 2 ≤ 30 / 2

b ≤ 12.5

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As corresponding angles ∠5 and ∠8 are equal. Hence line x is parallel to line z by converse of corresponding angles theorem.

What does converse of corresponding angles theorem states?

If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.

How can we show two lines are parallel to each other?

We can show lines are parallel by finding a pair of corresponding angles that are congruent.

Proving if two lines are parallel then third line is parallel too.

According to the given data:

       Therefore, ∠5 ≅ ∠7 (i.e. corresponding angles)

       ∠5 = ∠7

       ∠6 ≅ ∠8 (Corresponding angles are equal)

        ∴ Measure of angles is also equal ⇒ ∠6 = ∠8

       ∠5 = ∠8 (transitive property of equality of angles which says if

                               ∠a = ∠b and ∠b = ∠c then ∠a = ∠c)

       ∠5 ≅ ∠8 (If measure of angles is same then they are congruent)

Therefore, line x || line z

(Converse of the Corresponding Angles Theorem).

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The rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.

The distance covered in a unit of time is known as speed.

Given that, the airplane travels 7680 km in 8 hours flying against the wind, and 12420 km in 9 hours.

Therefore, the rate of the airplane against the wind is:

7680/8

= 960 km / hr

The rate of the airplane with the wind is:

12420/9

=1380 km / hr

Let the rate of the airplane in still air be a and the rate of the wind be w.

The net rate while flying against the air is:

a - w = 960       (1)

The net rate while flying with the wind is:

a + w = 1380      (2)

Add equations (1) and (2):

2a = 2340

a = 1170 km/hr

Substitute a = 1170 into equation (1):

1170 - w = 960

1170 - 960 = w

210 = w

Hence, the rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.

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For the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.

As given in the question,

Geometric mean GM = 30

Let us assume the first number is x

and second number i.e. 9 times of the first number is 9x

By the formula GM = [tex]\sqrt{x.y}[/tex]

Now putting the value

30 = [tex]\sqrt{x.9x}[/tex]

30 = [tex]\sqrt{9x^{2} }[/tex]

30 = 3x (∴ square root of 9 is 3 and sq root of x² is x)

10 = x  (by dividing both the side by 3)

Therefore, for the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.

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Answer:

x<6

Step-by-step explanation:

2x/3<4

2x<12

x<6

Answer:

x < 6

Step-by-step explanation:

[tex]\frac{2x}{3}[/tex] < 4 ( multiply both sides by 3 to clear the fraction )

2x < 12 ( divide both sides by 2 )

x < 6

Answer:

as shown in underline ^^

Step-by-step explanation:

Fill in the missing words:

When a solid mixes with a liquid and becomes part of the liquid it dissolves.

A solid that dissolves in a liquid is soluble.

A solid that does not dissolve in a liquid is insoluble.

Answer:

5 hours

Step-by-step explanation:

$65 - $15 = $50

$50/$10 = 5

Answer:

[tex]\frac{4+\sqrt{11} }{5}[/tex]

Step-by-step explanation:

to rationalise the denominator, multiply the numerator and denominator by the conjugate of the denominator.

the conjugate of 4 - [tex]\sqrt{11}[/tex] is 4 + [tex]\sqrt{11}[/tex] , then

[tex]\frac{1(4+\sqrt{11}) }{(4-\sqrt{11})(4+\sqrt{11}) }[/tex] ← expand denominator using FOIL

= [tex]\frac{4+\sqrt{11} }{16-11}[/tex]

= [tex]\frac{4+\sqrt{11} }{5}[/tex]

By using the vertex and the given point, we will see that the graphed quadratic equation is:

y = -(x - 2)^2 + 4

A quadratic equation with a leading coefficient a and a vertex (h, k) can be written as:

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

Here the vertex is (2, 4), replacing that we get:

y = a*(x - 2)^2 + 4

Now we also can see that the line passes through the point (0, -8), replacing these values we get:

-8 = a*(0 - 2)^2 - 4

-8 = 4a - 4

-8 + 4 = 4a

-4 = 4a

-4/4 = a

-1 = a

The quadratic equation is:

y = -(x - 2)^2 + 4

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Answer: See the image below for the table and graph

==========================================================

Explanation:

We replace x with the values mentioned. Do so one at a time to compute the corresponding y value.

For instance, if x = -2, then...

[tex]\text{y} = 2\text{x}^2\\\\\text{y} = 2(-2)^2\\\\\text{y} = 2(4)\\\\\text{y} = 8\\\\[/tex]

If x = -2, then y = 8. This produces the point (-2,8) which is on the parabola.

We'll write "8" without quotes into the box next to x = -2, as shown in the table diagram below.

Repeat for x values x = -1 through x = 2.

Once we determine those point coordinates, we then plot said points to form the parabola shown below. The more points, the better accurate picture you'll have of the curve. I used GeoGebra to make the graph and table. Desmos is another good option which I recommend.

Answer: x=18

Step-by-step explanation:

It just does ok

The correct answer to this question is d. the value of the 6 in 364 is 10 times the value of the 6 in 346.

The place value of the 6 in 346 is six because it is in the place of ones, whereas the place value of the sixth in 364 is 60 because it is in the place of tens. As a result, the value of 60 is ten times that of the value of 6.

The value of each digit in a number is known as place value. Every digit in a number has a distinct value depending on where it is located. The value of a digit depends on its position in the number, which can result in a number having two similar digits with different values.

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Answer:

y=1/4x+3

Step-by-step explanation:

To write an equation, let's infer we need to write it in slope-intercept form. We need the y-intercept. We can plug 1/4 and (-4,2) into y=mx+b, to solve for b. We have:

2=1/4*-4+b

2=-1+b

3=b

Since we have the slope, 1/4, we can create our equation:

y=1/4x+3

Solve for b in (y=mx+b):

b=y-mx

b=2-(1/4)(-4)

b=2+1

b=3

So the equation is y= (1/4)x + 3

Answer:

y= 38 + 0.20x

The equation will be y=38+0.20x where x is the number of texts and y is in dollars.

An equation is a relationship between the variables and constants representing how they are related to each other. It includes equal to "=" sign.

It is known that the fixed payment is of $38 and each text costs $0.20.

Assume Colette sends x texts in a month and y be the total cost.

Determine the monthly cost equation.

Total cost= Fixed cost+ x(cost of each text)

y=38+0.20x

So, the total monthly cost will be represented by the equation, y=38+0.20x.

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Answer:

answer. {-2187x}/{625}

There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.

In mathematics, the greatest common divisor of two or more nonzero integers is the largest positive integer that divides each integer

. The greatest common divisor (GCF) of a set of numbers is the greatest factor of division of all numbers.

GCF by listing factor method :-

Factors of 9: 1, 3, 9

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.

other two methods are attached below .

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A floor that is 3 3/4 yards wide and 5 1/2 yards long requires 20 5/8 square yards of hardwood flooring area.

length = 5 1/2 yd, breadth = 3 3/4 yd.

Make fractions out of both measurements first.

3 3/4 = 3 + 3/4

= 12/4 + 3/4

= 15/4

5 1/2 = 5 + ½

= 10/2 + ½

= 11/2

Area = (15 * 11)/(4 * 2) yd2

Area = 165/8 yd2

They essentially believed that 165/8 = 20 leftover 5 area = 20 5/8 yd2.

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Step-by-step explanation:

so, we have

6x² + 8xy + 8y²

and

5x² + 3xy + 16y²

we can combine only terms of the same kind (defined by the type and exponent of the used variables).

this is like adding fruit.

e.g. when we have a mixture of 3 apples, 4 oranges and 5 plums, and we add a mixture of 6 apples, 2 oranges and 3 plums - what do we get ?

we get a new mixture of

3+6 = 9 apples

4+2 = 6 oranges

5+3 = 8 plums

and exactly the same thing happens with mixing terms when adding them up.

so, we get

6+5 = 11x²

8+3 = 11xy

8+16 = 24y²

so, the result is

11x² + 11xy + 24y²

it is really that simple.

Answer:

25.5 feet because of some

Step-by-step explanation:

.,........

Answer:

Step-by-step explanation:

The price of one kilogram of jelly bean and gummy worms is $7 and $8 respectively.

Let the price of 1 kilogram of jelly bean cost be x

and the price of 1 kilograms of gummy worms be y

Dean bought 2 kilograms of jelly beans and 3 kilograms of gummy worms

for $38

2x + 3y = 38......equation 1

Sue bought 3 kilograms of jelly beans and 3 kilograms of gummy worms

for $45

3x + 3y = 45........equation 2

Subtracting equation 2 from equation 1

2x + 3y - (3x + 3y) = 38 - 45

2x - 3x + 3y - 3y = -7

-x = -7

x = 7

2(7) + 3y = 38

14 + 3y = 38

3y = 24

y = 8

Therefore, the price of one kilogram of jelly bean and gummy worms is $7 and $8 respectively.

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The homogeneity of variance is an assumption for the one-way between-subjects anova means each population from which the samples are drawn has the same level of variation.

Both t tests and F tests (also known as analyses of variance, or ANOVAs) are based on the premise that the population variances (i.e., the distribution, or "spread," of scores around the mean) of two or more samples are identical. The independent samples t-test and ANOVA employ the t and F statistics, which, provided that group sizes are equal, are often resistant to breaches of the assumption. A ratio of less than 1.5 between the largest and smallest group can be used to identify equal group sizes.

The independent samples t-test and ANOVA make the assumption of homogeneity of variance, which states that all comparison groups have the same variance. The homogeneity of variance is an assumption for the one-way between-subjects anova means each population from which the samples are drawn has the same level of variation.

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Betsie should buy the 250 envelopes from the shop Letter2go.

As, 250 envelopes will cost £31.9 in Shop Letter2go whereas will cost £33.17 in Shop Value World.

Given, that Betsie is going to buy 250 envelopes.

the cost of envelopes in two shops:

Value World:

Pack of 10 envelopes for £1.99

Buy 2 packs get 1 pack free

Letters2go:

Pack of 25 envelopes for £3.19

Now, if we see the cost of envelopes in shop 1 i.e. Value World

Cost of Pack of 10 envelopes = £1.99

Also, 1 pack is free for 2 packs

1 pack = £1.99

2 packs = 2×£1.99 = £3.98

Also, with 2 packs Betsie get 1 pack free

so, Betsie gets 3 packs for £3.98.

1 pack = 10 envelopes

3 packs = 30 envelopes.

Hence, In shop Value World:

30 envelopes = £3.98

1 envelope = £3.98/30

250 envelopes = (3.98/30)×250

So, 250 envelopes will cost £33.17 in Shop Value World.

And in shop Letter2go:

25 envelopes = £3.19

1 envelope = £3.19/25

250 envelopes = (3.19/25)×250

So, 250 envelopes will cost £31.9 in Shop Letter2go.

Hence, 250 envelopes will cost £33.17 in Shop Value World and £31.9 in Shop Letter2go.

So, Betsie should buy the 250 envelopes from the shop Letter2go.

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The area of the rectangle is increasing at the rate of 156 [tex]cm^{2}[/tex]/s .

Let the length (cm) be l , width (cm) be w , area be A ([tex]cm^{2}[/tex]) and time (s) be t .

Given : dl / dt = 6 cm/s and dw / dt = 8 cm/s

Area of rectangle = l * w

Differentiating wrt. t ,

dA / dt = ( l ) ( dw / dt ) + ( dl / dt ) ( w )

Therefore , dA / dt = 8l + 6w

Hence , when l = 12 cm and w = 10 cm

dA / dt = ( 8 * 12 ) + ( 6 * 10 )

dA / dt = 156 [tex]cm^{2}[/tex]/s .

The area of the rectangle is increasing at the rate of 156 [tex]cm^{2}[/tex]/s .

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The total amount of water Karla drank before and after the tennis practice is 5 cups and 9 fluid ounces.

The correct answer option is option C.

Convert fluid ounces to cups:

1 fluid ounces = 0.125 cups

15 fluid ounces = 1.875 cups

Total volume of water Kayla drank = Volume of water Karla drank before tennis practice + Volume of water Karla drank after tennis practice

= 1.875 cups + 4 cups

= 5.875 cups

Approximately,

5 cups and 9 fluid ounces

Therefore, the total volume of water Karla drank is approximately 5 cups and 9 fluid ounce

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The selling price of the the purse in a department store is cents.

For the given question-

A purse in such a department store costs $12.50 at wholesale.

The purse will be 140% more expensive at the store.

Then,

140% of 12.50 = 140 x 12.50 / 100

140% of 12.50 = 17.5

Selling price  = percent increase + cost price

Selling price  = 17.5 + 12.5

Selling price  = $30.0

Selling price  = 3000 cents

Thus, the selling price of the the purse in a department store is cents.

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The number -58 is a real number and it cannot be represented as a complex number

From the question, we have the following expression that can be used in our computation:

Expression = -58

The given expression above is a number

And also, it is a negative number

Negative numbers of this form are real numbers

This means that the such numbers cannot be represented as a complex number

Hence, the number -58 does not have a complex equivalent

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The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

The equation of the parabola

f(x) = [tex]7x^2[/tex]

The standard vertex form of a parabola is

y = [tex]a(x-h)^2[/tex] + k

The coordinates of the vertex of a parabola = (3, 5)

Where (h, k)  is the coordinates

From the given function of the parabola f(x) =  [tex]7x^2[/tex]

The value of a = 7

Substitute the values in the vertex form of a parabola

y = [tex]7(x-3)^2[/tex] + 5

Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

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Answer:zh  0 89 1 87.6

Step-by-step explanation: 0 89 1 87.6

Answer:

L=66 degrees

KL=3.5

LM=8.7

The sum of all angles in a triangle sum up to 180.

∠1 = x+37

∠2=x+67

∠3=90° (right triangle)

∠1+∠2+∠3 = 180°

(x+37)+(x+67)+90=180

2x+104+90=180

2x+194=180

2x=-14

x=-7

An angle can't be negative, but when plugged in it works!!

∠1 = -7+37=30

∠2=-7+67=60

30+60+90=180

Hope it helps!