Given: ΔABC is isosceles; AB ≅ AC
Prove: ∠B ≅ ∠C
Triangle A B C is shown. Sides B A and A C are congruent.
We are given that ΔABC is isosceles with AB ≅ AC. Using the definition of congruent line segments, we know that .
Let’s assume that angles B and C are not congruent. Then one angle measure must be greater than the other. If m∠B is greater than m∠C, then AC is greater than AB by the .
However, this contradicts the given information that . Therefore, , which is what we wished to prove.
Similarly, if m∠B is less than m∠C, we would reach the contradiction that AB > AC. Therefore, the angles must be congruent.

Answer:

3 < x < 13

Step-by-step explanation:

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let x be the length of the unknown side.

Therefore, x will either be the longest side or one of the shorter sides.

Therefore:

   x < 5 + 8

⇒ x < 13

And:

   8 < 5 + x

⇒ 3 < x

So the range of possible values of the third side is greater than 3 and less than 13:   3 < x < 13

Answer:

4 radians

Step-by-step explanation:

Arc Length (Radians) = rθ

Given Arc Length XY  = 40cm and radius, r = 10cm,

we will substitute these 2 values into the formula to find θ.

(10)θ  = 40

θ = 40 / 10

= 4 radians

Answer:

A

Step-by-step explanation:

the length of arc XY is calculated as

arc = circumference of circle × fraction of circle

      = 2πr × [tex]\frac{0}{2\pi }[/tex] ( r is radius and Θ is central angle )

here arc = 40 and r = 10 , then

2π × 10 ×[tex]\frac{0}{2\pi }[/tex] = 40

20π × [tex]\frac{0}{2\pi }[/tex] = 40 ( cancel 20π and 2π by 2π )

10Θ = 40 ( divide both sides by 10 )

Θ = 4 radians

Answer:

Step-by-step explanation:

The formula for circumference is 2πr

First, lets find the radius

3.14 * 2 = 6.28

56.52 / 6.28 = 9

The diameter = 2r

2 * 9 = 18

The diameter is 18 feet

Hope this helps!

Answer:

Hence, 87,50,000 can be expressed as [tex]$8.75 \times 10^{6}$[/tex].

Step-by-step explanation:

- Given 87,50,000

- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .

- Then count n and write in scientific notation.

Step 1 of 1

Consider 87,50,000.

8.75

So, 8.75 lies between 1 & 10 .

Now, Decimal moved to 6 places at left.

[tex]$8.75 \times 10^{6}$[/tex]

So, [tex]$87,50,000=8.75 \times 10^{6}$[/tex].

Answer:

√12×(-1)+√12×√5

-√12+√12×5

= -2√3+2√15

Answer:

13

Step-by-step explanation:

Since triangles CBA and DBA are equal, their lengths would also be equal, thus, DB = 13 as CA = 13

Answer:

CAB = DAB

CA is equivalent to BD

Answer:

15/50...may be/may not be......,,

The volume of a cylinder changes when you adjust the height or radius as the volume either increases or reduces.

Let's assume that the height and radius are 14cm and 7cm. The volume will be:

= πr²h

= 3.14 × 7² × 14

= 2154.04cm³

When the radius and height are reduced to 5cm and 9cm, the volume will be:

= πr²h

= 3.14 × 5² × 9

= 706.5cm³

This illustrates that the volume reduces when the height and radius reduces.

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We will use a combination formula to determine how many ways the prizes could be given out.

In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

The combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.

The formulas nCk is popularly known as counting formula.

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Answer:

Step-by-step explanation:

plus 18 and subtract 4

An expression is defined as a set of numbers, variables, and mathematical operations. The value of b for which the expression x² + bx + 18 can be factored is 9.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value of b for which the given expression x² + bx + 18 can be factored is 9. This will make the expression factored as (x+3) and (x+6).

Thus, the value of b for which the expression x² + bx + 18 can be factored is 9.

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The value of x is 126.87° and the value of y is 53°.

An obtuse angle is an angle that is greater than 90° but lesser than 180° while an acute angle is an angle between 0-90°.

From the given information:

sin x° = 0.8

x = sin⁻¹ (0.8)

x = 53.13°

x + 53.1° = 180°

x = 180° -53.13°

x = 126.87°

If cos 127° = -cos y°,

-cos y = -0.6018

cos y = 0.6018

y = cos⁻¹ (0.6018)

y = 53°

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Answer:

43°

Step-by-step explanation:

Calculating for the measure of angle C using

[tex] \frac{sin18}{9} = \frac{sinc}{20} \\ sinc = \frac{sin18 \times 20}{9} \\ sinc = 0.6867 \\ c = \csc(0.6867) \\ c = 43.3869 \\ c = 43 \: degrees[/tex]

The area of the given composite figure is 74.24cm^2

The figure is made up of semi circle and rectangle

Area = area of semicircle + Area of rectangle

Area = 3.14(4)^2 + 3(8)

Area = 50.24 + 24

Area. = 74.24cm^2

Hence the area of the given composite figure is 74.24cm^2

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Answer:

Generally x means times so the best and not dummest option is 2 times

2x and 2 x is the same the 2 x is spaced out a little

Step-by-step explanation:

[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{z^{2}-8 }-\sqrt{6z-17}=0 \end{gathered}$}[/tex]

Simplify the left side. Yes n is a positive integer greater than x and a is a real number or a factor, then [tex]\bf{\sqrt[n]{a^{x} }=a^{\frac{x}{n} }. }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{(z^{2}-8)^{\frac{1}{2} }-\sqrt{6z-17}=0 } \end{gathered}$}[/tex]

If n is a positive integer greater than x and a is a real number or a factor, then [tex]\bf{\sqrt[n]{a^{x} }=a^{\frac{x}{n} }. }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{(z^{2}-8)^{\frac{1}{2} }-(6z-17)^{\frac{1}{2}} =0 } \end{gathered}$}[/tex]

Draw each side of the equation. The solution is the x value of the point of intersection.

[tex]\red{\underbrace{\overbrace{\boxed{\boldsymbol{\sf{\green{z=3}}}}} \ \ \to \ \ \ Answer}}[/tex]

Answer:

Step-by-step explanation:

[tex]\sqrt{z^2-8} -\sqrt{6z-17} =0\\\sqrt{z^2-8} =\sqrt{6z-17} \\6z > 17\\z > \frac{17}{6} \\z^2-8=0\\z^2 > 8\\so \\z < -\sqrt{8} \\or\\z > \sqrt{8} \\combining\\z > \frac{17}{6} \\again\\z^2-8=6z-17\\z^2-6z-8+17=0\\z^2-6z+9=0\\z^2-3z-3z+9=0\\z(z-3)-3(z-3)=0\\(z-3)(z-3)=0\\z=3[/tex]

The x-coordinate of the point which divide the line segment is 3.

Given the coordinates in the figure are J(1,-10) and K(9,2) and the 1:3 is the ratio in which the line segment is divided.

When the ratio of the length of a point from both line segments is m:n, the Sectional Formula can be used to get the coordinate of a point that is outside the line.

To find the x-coordinate we will use the formula x=(m/(m+n))(x₂-x₁)+x₁.

Here, m:n=1:3 and x₁=1 from the point J(1,-10) and x₂=9 from the point K(9,2).

Now, we will substitute these values in the formula, we get

x=(1/(1+3))(9-1)+1

x=(1/4)(8)+(1)

x=8/4+1

x=3

Hence, the x-coordinate of the point that divides the directed line segment from k to j into a ratio of 1:3 is 3 units.

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Answer:

b. 3

Step-by-step explanation:

got it correct

The correct options regarding the circle with endpoints of the longest chord at (4, 5.5) and (4, 10.5) are:

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The center is the midpoint of the chords, hence:

The radius is half the distance between the chords, hence:

[tex]r = 0.5\sqrt{(4-4)^2 + (10.5 - 5.5)^2} = 0.5 = 2.5[/tex].

Hence the equation is:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

[tex](x - 4)^2 + (y - 8)^2 = 2.5^2[/tex]

[tex](x - 4)^2 + (y - 8)^2 = 6.25[/tex]

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Answer:

7.5 ft

Step-by-step explanation:

1st drop = 60 ft

2nd drop = 60/2 = 30 ft

3rd drop = 30/2 = 15 ft

4th drop = 15/2 = 7.5 ft

Answer:

She needs the starting amount of money to create an equation.

Step-by-step explanation:

The formula that she can use when she has the starting amount or the y-intercept is this one: f(t)=P(1+b)^t.

t=time

b=percent

P=starting value

The formula with the information given is: f(6)=P(1+3.75)^6

Hope this helps!

If not, I am sorry.

Answer:

Principal

Step-by-step explanation:

Since, the amount in the simple interest is,

Where, P is the principal amount,

r is the annual rate,

t is the time ( in years ),

Here, r = 3.75 %, t = 6 years,

Thus, By the above explanation,

It is clear that, we need the value of P, that is, principal to find the amount.

See attached plots.

The top one shows all three pieces plotted simultaneously, independent of their domains.

The bottom plot takes into account the domains and removes parts of each piece (the dashed gray parts) outside their respective domains.

Answer:

Choices for the measure of center that is best are: C. Rome data center is best described by the mean while that of New York data is best described by the median.

The measures of center include the mean and the median. Mean is best for a symmetrical data distribution while median is good for a skewed data distribution with an outlier.

The data for New work has an outlier, while that of Rome does not. Therefore, the best choices for the measure of center is: C. Rome data center is best described by the mean while that of New York data is best described by the median.

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The first few terms of a geometric sequence with first term [tex]a[/tex] and common ratio [tex]r[/tex] look like

[tex]a, ar , ar^2, ar^3, \ldots[/tex]

and so on. Notice that the [tex]n[/tex]-th term (where [tex]n[/tex] is a natural number) is [tex]ar^{n-1}[/tex].

For this particular sequence, the first term is

[tex]a=3[/tex]

and the fourth term is

[tex]ar^{4-1} = ar^3 = 1029[/tex]

Substitute [tex]a=3[/tex] into the second equation and solve for [tex]r[/tex].

[tex]3r^3 = 1029 \implies r^3 = 343 \implies r = \sqrt[3]{343} = \sqrt[3]{7^3} = 7[/tex]

Then the two terms between the 1st and 4th - i.e. the 2nd and 3rd terms - are

[tex]ar = 3\times7 = \boxed{21}[/tex]

and

[tex]ar^2 = 3\times7^2 = \boxed{147}[/tex]

Answer:

Term 2 is 21, and term 3 is 147.

Step-by-step explanation:

The geometric sequence is 3, 3r, 3r^2, 1029.

[tex]r = \sqrt[3]{ \frac{1029}{3} } [/tex]

[tex]r = \sqrt[3]{343} = 7[/tex]

So we have 3, 21, 147, 1029.

Answer:

64 girls

Step-by-step explanation:

Number of boys in a classroom: 4

Total no. of students in the classroom: 12

Number of girls in 1 classroom: 12-4 = 8

Number of girls in 8 such classrooms: 8 × 8 = 64

The x-coordinate of the altitude on EF is the same as the point D(4, 5) and by calculation, the height from D (1, 5) is also median from D (1, 5)

The height from D is perpendicular to EF

The slope of EF = (8 - 2)/(1 - 1) = ∞

Therefore, the side EF is parallel to the y-axis.

Therefore, the coordinates of the point of intersection of the altitude from D and the line EF is (1, 5)

The median is the midpoint of the side EF

The coordinates of the midpoint is found as follows;

[tex] \mathbf{ \left(1 + \frac{1 - 1}{2}, \: 1 + \frac{8 - 2}{2}\right)} = (1 ,5)[/tex]

Therefore;

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Hello,

[tex]$$\sum_{n=0}^4$$(\frac{1}{2})^{n} =(-\frac{1}{2})^{0}+(-\frac{1}{2})^{1}+(-\frac{1}{2})^{2}+(-\frac{1}{2})^{3}+(-\frac{1}{2})^{4}=1-\frac{1}{2} +\frac{1}{4} -\frac{1}{8}+\frac{1}{16}[/tex]

Answer:

x =7

Step-by-step explanation:

2x+6 = 20

To solve this equation, you first need to subtract 6 from each side

2x+6-6 = 20-6

2x = 14

Then divide each side by 2

2x/2 = 14/2

x = 7