The vertices of an isosceles triangle are A(-4, 0), B(-10, -2) and C(-6, -6).

What is the equation of the triangle's line of symmetry?

y = - x - 4
y = x - 4
y = x + 4
y = - x + 4

Answer:

C) When an altitude is drawn from the right angle of a right triangle it creates three similar triangles.

Step-by-step explanation:

The Inscribed Similar Triangles Theorem states that if an altitude is drawn from the right angle of any right triangle, then the two triangles formed are similar to the original triangle and all three triangles are similar to each other.

Answer:

O 8 ^x/3

Step-by-step explanation:

Remember that :

[tex]\sqrt[n]{x} = x^\frac{1}{n}[/tex]

………………………………

Then

[tex]\sqrt[n]{8^x} = (8^{x})^{\frac{1}{3}}[/tex]

      [tex]= 8^{x\times\frac{1}{3}[/tex]

      [tex]=8^{\frac{x}{3}[/tex]

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:f < 0 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 33 + 6f < 33[/tex]

[ subtract 33 on both sides ]

[tex]\qquad \tt \rightarrow \: 33 - 33+ 6f < 33 - 33[/tex]

[tex]\qquad \tt \rightarrow \: 6f < 0[/tex]

[tex]\qquad \tt \rightarrow \: f < 0[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The square for the  equation:  [tex]y=2x^{2} + 12x +1[/tex] is [tex]y=2(x+3)x^{2} -17[/tex]

The square for the  equation:  [tex]y=4x^{2} +48x-10[/tex] is [tex]y=4(x+6)x^{2} -154[/tex]

a)

[tex]y=2x^{2} +12x +1[/tex]

[tex]y = 2[(x^{2} + 6x)] + 1[/tex] ( taking common)

[tex]y = 2[(x+3)^{2} - 9] + 1[/tex] ( adding and subtracting 9 to make a square term

[tex]y = 2(x+3)^{2} - 18 + 1[/tex] ( multiplying by 2)

[tex]y=2(x+3)x^{2} -17[/tex]

b)

[tex]y=4x^{2} +48x-10[/tex]

[tex]y = 4[(x^{2} + 12x)] - 10[/tex]  (taking 4 common)

[tex]y = 4[(x+6)^{2} - 36)] - 10[/tex] (adding and subtracting 36)

[tex]y = 4(x+6)^{2} - 144 - 10[/tex](multiplying by 4)

[tex]y=4(x+6)x^{2} -154[/tex]

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If the function is vertically stretched by a factor of 3, the resulting function will be g(x) = [tex]3(5^{x-2})[/tex]

Given the parent function f(x) = x, if the function is vertically stretched by k units, the resulting function will be g(x) = kx

Given the parent function

f(x) = [tex]5^{x-2}[/tex]

If the function is vertically stretched by a factor of 3, the resulting function will be g(x) = [tex]3(5^{x-2})[/tex]

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Answer:

A = -12

Step-by-step explanation:

A   put in -2 for 'x' in the equation to find value

       2(-2)  - y = 8       add 4 to both sides

              -y = 12

               y = -12              

        I think YOU can now find B and C  with this method !

Answer:

People surveyed: 79

a) p(s) = 46/79

b) p(snv) = 13/79

c) p(suv) = 96/79

hope this helps, and tell me if you get it right! It's prob wrong though, im bad at venn diagrams (×_×)⌒☆

Answer:

9,000 minutes (150 hours)

Step-by-step explanation:

You have 3,600 points total; you need to divide it by 2 points.
3,600 ÷ 2 = 1,800

So, now you need to multiply the 1,800 points by 5 minutes.

1,800 × 5 = 9,000

Another way:

You can figure out how long it takes to get 1 point. If 2 points takes 5 minutes, divide 5 by 2.

5 ÷ 2 = 2.5

Now you need to figure out how long it would take to get 3,600 points. If each point takes 2.5 minutes, just multiply.

3,600 × 2.5 = 9,000

It would take 9,000 minutes (which is equivalent to 150 hours) to get to 3,600 points.

La forma adecuada para saber el área requerida para conservar la separación de las sillas es multiplicar (7.5) (4.5) opción B.

Para identificar la operación necesaria para calcular el área requerida para ubicar las sillas con su respectiva separación de 1.5 metros es:

Esta expresión nos va a permitir calcular el área necesaria debido a que la separación entre sillas es 1.5 metros y tenemos 6 sillas a lo largo y 4 sillas a lo ancho, es decir:

Nota: Esta pregunta está incompleta porque falta la imagen y las opciones. Aquí está la información faltante:

Opciones:

A. Multiplicar (6)(4)

B. Multiplicar (7.5)(4.5)

C. Multiplicar (9)(6)

D. Multiplicar (9.5)(4.5)

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Answer:

Step-by-step explanation:

calculated the cost of numbers of units usex

Answer:

282.743 yd²

Step-by-step explanation:

Surface Area of the Cylinder: Top Base + Bottom Base + Side

Area of Top Base (Circle): πr² = π(5 yd)² = 25π yd²

Area of Bottom Base (Circle): same as top base = 25π yd²

Area of Side (Rectangle): Circumference*Height = (2πr)*(4 yd) =

2π(5 yd)*(4 yd) = 40π yd²

Total Surface Area = 25π yd² + 25π yd² + 40π yd² = 90π yd² = 282.743 yd²

Answer:

Shirts are 6

Hats are 5

Step-by-step explanation:

This is a system of equations. Set up the equations first.

7s + h = 47

5s + h = 35    

-----------------------      Subtract the equations to eliminate the h variable

2s = 12                      Divide by 2 to solve

s = 6                          Each hat is 6

Plug the 6 in for s in either of the original equations

7(6) + h = 47

42 + h = 47          Subtract 42 from both sides

h = 5

Answer:

7

Step-by-step explanation:

5x-3 = 3x+1

2x=4

x=2

plug in

5(2)-3

10-3

7

answer: 7

In terms of l?

TSA

LSA

Answer:

[tex]\sf SA=54\pi\:\:\:cm^2[/tex]

Step-by-step explanation:

Surface Area of a Cone

[tex]\sf SA=\pi r l+\pi r^2[/tex]

where:

Given:

Substitute the given values into the formula and solve for SA:

[tex]\implies \sf SA=\pi (3)(15)+\pi (3)^2[/tex]

[tex]\implies \sf SA=45\pi+ 9 \pi[/tex]

[tex]\implies \sf SA=54\pi\:\:cm^2[/tex]

Therefore, the surface area of the cone in terms of pi is:

[tex]\sf SA=54 \pi\:\:\:cm^2[/tex]

The answer is g(x) = 3x - 6

The value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.

We are given the logarithmic functions:

log₄3 = 0.792 ,,, (i), and log₄21 = 2.196 ... (ii),

and we are asked to find the value of the logarithmic function log₄7.

On subtracting (i) from (ii), we get:

log₄21 - log₄3 = 2.196 - 0.792.

Using the quotient law of logarithms, according to which:

logₓa - logₓb = logₓ(a/b), we can write the above equation as:

log₄(21/3) = 1.404,

or, log₄7 = 1.404.

Therefore, the value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.

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Answer:

A.

1.404

Step-by-step explanation:

Answer:

√72

Decimal Form:

1.32287565…

Step-by-step explanation:

To subtract fractions, find the LCD and then combine.

Answer:

BODMAS

[tex] {6}^{3 } + 5(4 - 2) = 216 + 5(2) \\ = 216 + 10 \\ = 226[/tex]

Answer: Answer is 226

Step-by-step explanation: Do math

The table that could be used to model his climb will consist of 125 ft/h for the first two hours and 87.5 ft/h for the next 4 hours.

The equation that can be used to model the motion of the climber is calculated as follows;

(1, 150)

(2, 275)

(4, 525)

(6, 700)

m = (275 - 150)/(2 - 1) = 125 ft per hour

m = (700 - 525)/(4 - 2) = 87.5 ft/hr

Thus, the table that could be used to model his climb will consist of 125 ft/h for the first two hours and 87.5 ft/h for the next 4 hours.

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Answer:

75

Step-by-step explanation:

Answer:

Group A, because seven children have a forearm length longer than 10 inches

Step-by-step explanation:

Create the dot plots based on the given information (please see attached images).

Group A = blue dots

Group B = red dots

From inspection of the attached dot plots, we can see that Group A appears to have the longer average forearm length.  This is because 7 children have a forearm length of longer than 10 inches.

To calculate the average forearm length, sum all data values and divide by the total number of data values.

[tex]\textsf{Average of Group A}=\dfrac{ 3 \times 10 + 4 \times 11 + 3 \times 12}{10}=11[/tex]

[tex]\textsf{Average of Group B}=\dfrac{ 3 \times 9 + 5\times 10+ 2\times 11}{10}=9.9[/tex]

Thus proving that Group A has the longer average former length.

According to given text data

Average of both groups

A:-

B:-

Group A has bigger average

Answer:

18.1cm

Step-by-step explanation:

Please refer to the attached photo for a better understanding. Apologies for the terrible drawing.

First we will find the length of BE by using pythagoras' Theorem.

[tex]c^{2} =a^{2} +b^{2} \\AB^{2} =BE^{2} +EA^{2} \\16^{2} =BE^{2} +7^{2} \\256=BE^{2} +49\\BE^{2} =256-49\\BE=\sqrt{207} cm[/tex]

We will leave BE as it is as it is not the final answer.

Since we know CD = BE,

CD = [tex]\sqrt{207} cm[/tex]

Now from the photo, draw a line from C to A or A to C, you will see another triangle.

Now we will use Pythagora's Theorem again to find AC.

[tex]AC^{2} =AD^{2} +DC^{2} \\AC^{2} =11^{2} +(\sqrt{207}) ^{2} \\AC^{2} = 121+207\\AC^{2} =328\\AC=\sqrt{328} \\=18.1cm (1dp)[/tex]

Delete the commas if necessary.

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

Explanation:

There are 6 freshmen total and we want to pick 2 of them, where order doesn't matter. The reason it doesn't matter is because each seat on the committee is the same. No member outranks any other. If the positions were labeled "president", "vice president", "secretary", etc, then the order would matter.

Plug n = 6 and r = 2 into the nCr combination formula below

[tex]n C r = \frac{n!}{r!(n-r)!}\\\\6 C 2 = \frac{6!}{2!*(6-2)!}\\\\6 C 2 = \frac{6!}{2!*4!}\\\\6 C 2 = \frac{6*5*4!}{2!*4!}\\\\ 6 C 2 = \frac{6*5}{2!}\\\\ 6 C 2 = \frac{6*5}{2*1}\\\\ 6 C 2 = \frac{30}{2}\\\\ 6 C 2 = 15\\\\[/tex]

This tells us there are 15 ways to pick the 2 freshmen from a pool of 6 total.

Repeat those steps for the other grade levels.

n = 13 sophomores, r = 5 selections leads to nCr = 13C5 = 1287. This is the number of ways to pick the sophomores.

You would follow the same type of steps shown above to get 1287. Let me know if you need to see these steps.

Similarly, 8C4 = 70 is the number of ways to pick the juniors.

Lastly, 14C3 = 364 is the number of ways to pick the seniors.

-----------------------------

To recap, we have...

Multiply out those values to get to the final answer.

15*1287*70*364 = 491,891,400

This massive number is a little under 492 million.

Answer: 6.71

Step-by-step explanation:

[tex]AB=\sqrt{(-1-5)^{2}+(6-3)^{2}} \approx \boxed{6.71}[/tex]

Answer:

  4/3

Step-by-step explanation:

The tangent of any angle (θ) in standard position that has point (x, y) on its terminal ray is ...

  tan(θ) = y/x

__

For the given point on the terminal side, the tangent is ...

  tan(θ) = (-4)/(-3) = 4/3

_____

Additional comment

There are several ways this can be explained. One of them makes use of the relation between rectangular and polar coordinates:

  (x, y) = (r·cos(θ), r·sin(θ))

Then the ratio y/x is ...

  y/x = (r·sin(θ))/(r·cos(θ)) = sin(θ)/cos(θ) = tan(θ)

Answer:

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

here ,

base = 120 ft

height = 25 ft

Area = 1/2* 120*25

= 60 * 25

= 1500 ft²

Answer 2

Answer:

1/2 * base * height

so 1/2 * 25 * 120

= 1500

Answer:

[tex]28{cm}^{2} [/tex]

Step-by-step explanation:

we know

area of rectangle=l*b=(7*4)sq cm=28sq cm