All tangents to the circle are congruent and form a square. the perimeter of square aceg is 24 cm. a circle is inscribed in square a c e g. points f, h, b, and d of the circle are on the sides of the square. what is the length of line segment bc? 2 cm 3 cm 6 cm 8 cm

Answer:

Median

Order the data values from smallest to largest:

55, 57, 57, 57, 58, 58, 58, 59, 59, 60, 61, 61, 61, 62, 62, 62, 63, 63, 64, 64, 65, 65, 66, 67

As there is an even number of values, the median is the mean of the middle two values ⇒ Median = 61

Quartiles

55, 57, 57, 57, 58, 58, 58, 59, 59, 60, 61, 61 || 61, 62, 62, 62, 63, 63, 64, 64, 65, 65, 66, 67

The first quartile is the median of the data points to the left of the median  ⇒ first quartile = 58

The third quartile is the median of the data points to the right of the median  ⇒ first quartile = 63.5

Five-number summary

Draw a box from the first quartile (58) to the third quartile (63.5)

Add the median (61) as a the vertical line through the box.

The whiskers are horizontal lines from each quartile to the minimum (55) and maximum values (67).

Answer:

none of those are correct.

Step-by-step explanation:

5 red

7 blue

8 white

5 red + 7 blue= 12

5 red + 7 blue + 8 white= 20

=12/20

=6/10

Answer:(-8,0)

Step-by-step explanation:

Add (-1,-6) with translation move (-7,6)

-1 , -6

-7 , 6

____

-8 , 0

Step-by-step explanation:

in a parallelogram we have 2 equally large angles and 2 equally small angles.

the sum of all 4 angles must be 360°.

so let's first determine what angles are together 204°.

if it would be 2 neighboring angles, it would be the sum of a large and a small angle.

and the sum of the remaining 2 angles would be the same (again 204°).

but that that would together be 408°. too much.

so, it can only be that the 2 given angles are a pair of equal angles. and each would be

204/2 = 102°

as they are larger than 90°, they are the large angles in the parallelogram.

so, the other 2 angles are the pair of equally large small angles. together they have

360 - 204 = 156°

and each one is then

156/2 = 78°

There exists one real zero when the vertex lies on the x-axis, from that we conclude that the correct option is A.

The real zeros of a quadratic function are the values of x at which the graph of the quadratic function intercepts the x-axis.

If we want only one real zero, then we must have only one intercept. And this only can happen if the vertex of the quadratic function lies on the x-axis.

As you can see, the only graph where that happens is the one in option A, so we conclude that option A is the correct one.

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The results for the matching between function and its period are:

If a given function presents repetitions, you can define the period as the smallest part of this repetition. As an example of periodic functions, you have: sin(x) and cos(x).

[tex]\mathrm{Period\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}[/tex]

[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}[/tex]

The period of sin(x) and cos(x) is 2π.

For solving this question, you should analyze each option to find its period.

1) Option 1

[tex]\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}\\ \\ \mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{2\pi }{\frac{1}{2} }=4\pi[/tex]

Thus, the option 1 matches with the letter D.

2) Option 2

[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}\\ \\ \mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{4} =\frac{\pi }{2}[/tex]

Thus, the option 2 matches with the letter A.

3) Option 3

[tex]\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}\\ \\ \mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{2} =\pi[/tex]

Thus, the option 3 matches with the letter C.

4) Option 4

[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}\\ \\ \mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{8} =\frac{\pi }{4}[/tex]

Thus, the option 4 matches with the letter B.

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Answer:

  obtuse

Step-by-step explanation:

A "form factor" can be computed whose sign will tell you the classification of the triangle. For short sides a, b and long side c, the form factor is ...

  f = a² +b² -c²

And the interpretation is ...

__

For the given side lengths, the form factor is ...

  f = 11² +15² -20² = 121 +225 -400

  f = -54

The value is less than zero, signifying an obtuse triangle.

_____

Additional comment

The value f/(2ab) = -54/(2·11·15) = -9/55 is the cosine of the largest angle. Here, the largest angle is arccos(-9/55) ≈ 99.4°. This is greater than 90°, hence an obtuse angle.

This cosine relation comes from the Law of Cosines. The interpretation of the "form factor" can be developed by considering the Pythagorean theorem (f=0 ⇒ right triangle) and the relationship between sides and angles. If the longest side is longer than necessary for a right triangle, the largest angle will be greater than 90°.

Answer:

The answer is option A

Step-by-step explanation:

The solution is in the image

Answer:

D) x = 12

Step-by-step explanation:

Given:

[tex]\sf{\dfrac{5}{2}x-7=\dfrac{3}{4}x+14 \implies \dfrac{10}{4}x-7=\dfrac{3}{4}x+14}[/tex]

1. Multiply both sides by 4

[tex]\sf{4\left(\dfrac{10}{4}x-7\right)=4\left(\dfrac{3}{4}x+14\right)}\\\\\implies 10x-28=3x+56[/tex]

2. Subtract 3x from both sides

[tex]\sf{10x-3x-28=3x-3x+56}\\\\\implies 7x-28=56[/tex]

3. Add 28 to both sides

[tex]\sf{7x-28+28=56+28}\\\\\implies 7x=84[/tex]

4. Divide both sides by 7 to isolate the variable:

[tex]\sf{\dfrac{7x}{7}=\dfrac{84}{7}}\\\\\implies x=12[/tex]

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The height of the right cone is 10.68 unit

Volume is defined as the space occupied by a three dimensional object.

Volume of a right cone is given  by

V = π r²h/3

C = 2 π r

r = 247/2 π

3 * 17287 =  π  r²h

3 * 17287 =  π *(247/2 π )²h

h = 51861 *π *4/61009

h = 10.68 unit

Therefore the height of the right cone is 10.68 unit.

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Answer:

48 units²

Step-by-step explanation:

Lateral Surface Area :

Answer:

48 units²

Step-by-step explanation:

The lateral area of a square based pyramid comprises the four triangular sides.

Area of a triangle = 1/2 × base × height

                             = 1/2 × 8 × 3

                             = 1/2 × 24

                             = 12 units²

Lateral SA = 4 × area of triangle

                 = 4 × 12

                 = 48 units²

The first step that we must take before solving a problem is to understand what the problem statement is asking us to do and what is given to us to do so.  Looking at the problem they are asking what the slope of the line is. What is provided to us is an equation which was captured as [tex]y=-2x + 3[/tex].

The next step that we must take is to determine what the slope of the line is. Let us first define what slope is.

Slope-Intercept form is a form in which an equation can be expressed in and it follows the y = mx + b format.  M is equal to the slope while b displays the y-intercept of the expression.

The easiest way to determine the slope using slope-intercept form us by looking at the coefficient of the variable x (in this case) which is also known as m.  Looking at our equation, we can see that the coefficient in front of the variable x is -2.

Therefore, the option that would best match the details that we provided would be option B, -2.

Answer:

B. -2

General Formulas and Concepts:
Algebra I

Slope-Intercept Form:
[tex]\displaystyle y = mx + b[/tex]

Step-by-step explanation:

Step 1: Define

Identify given equation.

[tex]\displaystyle y = -2x + 3[/tex]

Step 2: Find Slope m

Let's compare our given equation to the general equation Slope-Intercept Form to identify our values for slope m and y-intercept b:

We can see that our y-intercept b is equal to 3 and that our slope m is equal to -2.

∴ the slope of the given line is equal to -2 and the answer choice that correlates with this is answer choice B.

___

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Topic: Algebra I

Answer:

a) v>4.5

b) w<6.5

a) 0.3 recurring

b) 5/11

The average rate of change of the function over the interval [-1, 2] is: C. 2.5.

The average rate of change over an interval of a function is: f(b) - f(a) / b - a.

Given the interval  [-1, 2]:

a = -1; f(a) = -5

b = 2; f(b) = 2.5

Average rate of change = (2.5 - (-5)) / (2 - (-1)) = 7.5/3

Average rate of change = 2.5 (option C).

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Answer: A= -5

Step-by-step explanation:

Answer: a = 5

Step-by-step explanation:

      To solve, we will isolate the variable a.

Given:

2а + 20 = -3а - 5

Add 3a to both sides of the equation:

5а + 20 = - 5

Subtract 20 from both sides of the equation:

5а = 25

Divide both sides of the equation by 5:

a = 5

Answer:

x=14

Step-by-step explanation:

The sum of a interior angle is 180°

(7x-11)+(2x-3)+(5x-2)°=180°

7x+2x+5x=180+11+3+2

14x/14=196/14

x= 14

Hope this answers your question!! :)

Answer:

[tex]y=\dfrac{1}{2}(x+5)^2-3[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

Parent function

[tex]y=-x^2[/tex]

Reflected in the x-axis

[tex]-f(x) \implies y=-(-x^2)\implies y=x^2[/tex]

Compressed vertically by a factor of 1/2

Multiply the whole function by the given scale factor:

[tex]\dfrac{1}{2}f(x)\implies y=\dfrac{1}{2}x^2[/tex]

Translated 3 units down

Subtract 3 from the whole function:

[tex]f(x)-3 \implies y=\dfrac{1}{2}x^2-3[/tex]

Translated 5 units left

Add 5 to the variable of the function:

[tex]f(x+5) \implies y=\dfrac{1}{2}(x+5)^2-3[/tex]

To sketch the parabola

Vertex = [tex](-5, -3)[/tex]

Axis of symmetry:  [tex]x = -5[/tex]

Plot points:

[tex]x=-9 \implies \dfrac{1}{2}(-9+5)^2-3=5 \implies (-9,5)[/tex]

[tex]x=-7 \implies \dfrac{1}{2}(-7+5)^2-3=-1 \implies (-7,-1)[/tex]

[tex]x=-3 \implies \dfrac{1}{2}(-3+5)^2-3=-1 \implies (-3,-1)[/tex]

[tex]x=-1 \implies \dfrac{1}{2}(-1+5)^2-3=5 \implies (-1,5)[/tex]

Answer:

x=0

Step-by-step explanation:

Expand the equation 4 + [tex]\sqrt{x}[/tex]+1=5

[tex]\sqrt{x} +5=5[/tex]

        -5   -5

subtract 5 from both sides

[tex]\sqrt{x} = 0[/tex]

x=0

square both sides

True= x=0

Answer:

the answer is x=0

Step-by-step explanation:

[tex]4+\sqrt{x} +1=5[/tex]

add "4 +1" which equals 5

[tex]\sqrt{x} +5=5[/tex]

now -5 on both sides :)

[tex]\sqrt{x}[/tex]

now you're left with a square root

[tex]\sqrt{x}=0[/tex]

The number of seeds in 2 ounce package is 6.7 × 10⁷ seeds

From the question, we are to determine the number of seeds in 2 ounce package

From the given information,

An orchid seed weighs 3.2 × 10⁻⁸ ounces

If an orchid seed weighs 3.2 × 10⁻⁸ ounces

Then,

2 ounce package will contain [tex]\frac{2}{3\times 10^{-8} }[/tex] seeds

= 0.67 × 10⁸

= 6.7 × 10⁷ seeds

Hence, the number of seeds in 2 ounce package is 6.7 × 10⁷ seeds

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Answer:

This assumes the question should read:

"The average of 5 girls is 16 [not 6] yrs. the average of 4 of them is 16½. what is d age of d fifth gal​

The age, d, is 14 years.

Step-by-step explanation:

When the girl with age d is not included, the average goes up to 16.5 years.   Let's define GroupA as the sum of the ages of the 4 girls whose average age is 16.5 years.  d is the age of the girl that is removed from the average.

We know that all the girls (GroupA + d) have an average age of 16 years:

(GroupA + d)/5 = 16 years  [Add the ages for all the girls (GroupA and d) and divide by 5 to obtain the average age for the larger group].

We know that when d is removed, the average for the 4 remaining girls (GroupA) is 16.5 years:

(GroupA)/4 = 16.5 years

This tells us the sum of the ages for GroupA:

GroupA = 4*(16.5)

GroupA total = 66 years

From above:       (GroupA + d)/5 = 16 years

Since GroupA = 66 years,    (66 years + d)/5 = 16 years

(66 years + d) = 90 years

d = 14 years

Answer: The answer is B.

Step-by-step explanation: An open circle means < or >. A closed circle means lesser or equal to or greater or equal to. The open circle is on 4 and the ray is going right. The closed circle is on 0 and the ray goes left. This is correct.

The perimeter of the sector = 47.905 cm

47.905 cm is greater than 47.5 cm.

Perimeter of a sector = Arc length + 2(radius).

Arc length = ∅/360 × 2πr

Given the following:

Perimeter = (∅/360 × 2πr) + 2(r) = (135/360 × 2×π×11) + 2(11)

Perimeter = 25.905 + 22

Perimeter = 47.905 cm

Thus, the perimeter of the sector (47.905 cm) is greater than 47.5 cm.

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Answer:

yes they do

Step-by-step explanation:

they share a ray

The value of m<3= 130

The correct option is (c)

Given:

m<1= 50

m<1+ m<2= 180  (Linear pair)

m<2= 180-50

m<2=130

Now, m<2 = m<3  [alternate interior angles]

m<3= 130

Hence, the measure of <3 is 130.

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Answer:

The person above me is correct

Step-by-step explanation:

Answer:

last option

Step-by-step explanation:

hope it helps

One way to determine the factors of x³ + 5x² - 6x - 30 by grouping is shown by option D. x² (x + 5) - 6(x + 5).

Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.

Given a cubic polynomial,

x³ + 5x² - 6x - 30

Taking the first two terms together and the other two terms together,

(x³ + 5x²) + (- 6x - 30)

Taking x² common from first and -6 common from second,

x² (x + 5) - 6(x + 5)

Hence the correct option is D.

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Step-by-step explanation:

5x – 2x + 7 – x = ?x + ?

I need the answer for "no solution" and "infinite solutions".

NO SOLUTION:

no solution because any value you give to x is not solvable, it remains +7

5x – 2x + 7 – x = ?x + ?

2x = 2x + 7

INFINITE SOLUTION

infinite solutions because any value you give to x is solvable

5x – 2x + 7 – x = ?x + ?

5x – 2x + 7 – x = 2x + 7

2x + 7 = 2x + 7

Answer:

-5/6

Step-by-step explanation:

A great way to divide fractions is to use the "leave it, change it, flip it" method.  You leave the first fraction as it is, change the division sign to a multiplication sign, and flip the second fraction so you get the reciprocal.  Like this:

-5/7 ÷ 6/7

-5/7 x 6/7

-5/7 x 7/6

Then you multiply through.  First -5 x 7, -35, and then 7 x 6, 42, to get -35/42.  Because both of these are divisible by 7, we can simplify to get -5/6.

Answer:

-5

6

Step-by-step explanation:

⇒ [tex]\frac{-5}{7}[/tex] ÷ [tex]\frac{6}{7}[/tex]

⇒ [tex]\frac{-5}{7}[/tex] × [tex]\frac{7}{6}[/tex]

(We do this because when dividing a fraction by another fraction we take the inverse of the second fraction and multiply it to the first fraction.)                                                                                                          

⇒ -5 × 7 = -35 (to simplify just divide both by 7) = -5

     7 × 6     42                                                             6

So the answer is -5

                            6

Step-by-step explanation:

x is less than or equal to 0.

so click x than the choose the third option then click 0

Since the polyhedron is about 78.5 m², the radius of the sphere is 2.5 m

Since the sum of the faces of the polyhefron equals the surface area of the sphere, we find its surface area.

The surface area of sphere is given by A = 4πr² where r = radius of sphere

Making r subject of the formula, we have

r = √(A/4π)

Given that he sum of all the faces of the polyhedron is about 78.5 square meters, this is equal to the surface area of the sphere.

So, A = 78.5 m²

Substituting this into the equation for r, we have

r = √(A/4π)

r = √(78.5 m²/4π)

r = √(19.625 m²/π)

= √(6.246 m²)

= 2.499 m

≅ 2.5 m

So, the radius of the sphere is 2.5 m

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