Triangle ABC has vertices at A(-2, 3), B(-3,-6), and C(2,-
1). Is triangle ABC a right triangle? If so, which angle is the
right angle?
w Ano
A(-2,3)
O No, the triangle has no right angles.
O Yes, the right angle is angle A.
O Yes, the right angle is angle B.
O Yes, the right angle is angle C.
6
5
4 -3 3-2 -1,5
2
6
x
3 4 5
C (2,-1)
B(-3,-6)

Answer:

congrats

Step-by-step explanation:

Answer:

The test contains 10 three-point questions and 14 five-point questions

Step-by-step explanation:

Given equations are:

[tex]x+y = 24\\and\\3x+5y=100[/tex]

From 2nd equation we can deduce that x represents number of 3-point questions and y represents number of 5-point questions.

Using the substitution method:

From x+y = 24

y= 24-x

Putting this valu of y in 3x+5y=100

[tex]3x+5(24-x) = 100\\3x + 120 - 5x = 100\\-2x+120=100\\-2x = 100-120\\-2x = -20\\\frac{-2x}{-2} = \frac{-20}{-2}\\ x = 10\\Putting\ the\ value\ of\ x\ in\ x+y=24\\10+y=24\\y = 24-10\\y = 14[/tex]

Hence, the correct answer is:

The test contains 10 three-point questions and 14 five-point questions..

Answer: B is the answer

Step-by-step explanation:

Just subtract 1/6 from 11/18 to get the answer!

Answer:

x = 3.133

Step-by-step explanation:

I'm going to take a chance and assume that you meant "ln 11," not "in11."

If I'm right, then we have:

3x-5 = ln 11 + 2.

Adding 5 to both sides yields

3x = ln 11 + 2 + 5, or ln 11 + 7.  Since ln 11 = 2.398,

3x = 2.398 + 7, or    3x = 9.398, and so

x = 3.133.

If this is not what you expected, please ensure that you have copied down the original problem accurately.  Thank you.

Answer:

Option 4 (3)

Step-by-step explanation:

The first step involved in calculating the median it to list the observations in the ascending order. This gives:

12 15 33 45 46 51 52 57.

The second step is to identify the middle number (in case the observations are in odd numbers) or numbers (in case the observations are in even numbers) after the ascending order step has been done. It can be observed that the middle numbers in this data set are 45 and 46. Since there are two numbers, so their average will be the median of this data set. Therefore, the median is 45.5.

It can be observed that that there are 2 outliers in the data set: 12 and 15. Once removed, the data set will be:

33 45 46 51 52 57.

The middle numbers are 46 and 51 and the mean of the two middle numbers is 48.5.

Therefore, the difference between the median of the data, including the possible outliers and excluding the possible outliers is given by 48.5 - 45.5 = 3. Therefore, Option 4 is the correct answer!!!

Answer:

A, B, and D are the correct statements.

79+(-42/6)-(-24)

first use -42 divide by 6

79 + (-7) - (-24)

then open all the parentheses

79 - 7 + 24

and use 79 minus 7

72 +24

add them together

96

That's how to get it.

Answer:

Step-by-step explanation:

79+(-42 divide 6)- -24

The first step is division

79+(-7)- -24

Then we add and subtract from left to right

72 --24

72+24

96

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y-4=(4/3)(x-2)[/tex]

This is the equation of a line into point slope form

The point is (2.4)

The slope is m=4/3

To plot the line find the intercepts

The y-intercept is the value of y when the value of x is equal to zero

For x=0

y-4=(4/3)(0-2)

y=(-8/3)+4

y=4/3

The x-intercept is the value of x when the value of y is equal to zero

0-4=(4/3)(x-2)

-4=(4/3)x-(8/3)

Multiply by 3 both sides

-12=4x-8

4x=8-12

x=-1

we have the points

(2,4), (0,4/3),(-1,0)

Plot the line

Note With only two points it was necessary to draw the line. The third point was calculated for didactic purposes.

see the attached figure

The geometric mean of two numbers is the square root of their product.

sqrt{4 • 12}

sqrt{48}

sqrt{16} •sqrt{3}

4•sqrt{3}.

The geometric mean of 4 and 12 is

4•sqrt{3}.

Answer:

4xy[2xy - x - 3]

Step-by-step explanation:

When finding the Greatest Common Factor [GCF], along with the coefficient, you have to factor out the least degree term possible, which in this case is 4xy. This is because although all terms have y and x, their degrees are not all similar, so we have to go with 4xy.

The graph of the equation y = x + 3 is a straight line with a slope of 1 and a y-intercept of 3. This means that for every increase of 1 in x, y increases by 1 and the line crosses the y-axis at y = 3.

The student is asking for the graph of the function g(x)=[x+3]. Please note, the symbol '[' and ']' is usually used to denote the greatest integer function or floor function, but since the context is not very clear, I'll assume that this is a simple linear function y = x + 3.

In such case, the graph of y = x + 3 is a **straight line** with a **slope** of 1 and a y-**intercept** of 3. Remember, the ^ slope is the change in y for every increase of 1 in x, and in this equation, for every increase of 1 in x, y increases by 1 . The intercept is simply where the line crosses the y-axis, and in this case it's at y = 3.

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Answer:

a(n) = -3(-1/5)^(n - 1)

Step-by-step explanation:

From the first term, -3, we get the second term, 3/5, by multiplying -3 by -1/5.

Thus, the common ratio is -1/5.

The general formula in this case is a(n)=(first term)(common ratio)^(n - 1), or

a(n) = -3(-1/5)^(n - 1)

Answer:

Step-by-step explanation:

Givens

Height = h = 4cm

b = ?

Area = 40 cm^2

Formula

Area = 1/2 * h * b

Solution

40 cm^2 = 1/2 * 4 * b      Combine the right

40 cm^2 = 2 * b              Divide by 2

40 cm^2 /2 = 2b/2         Do the division

20 cm = b

Answer D

Answer: There are no solutions to the system because the equations represent parallel lines.

The value 0 = -12 indicates an inconsistent system with no solution.

0 = -12 means that the system of equations is inconsistent, and there is no solution. In this case, the equations represent parallel lines that never intersect, hence no common solution exists.

Answer:

3.6 fl oz

Step- by-step explanation:

Well if one gallon equal 2.4 fl oz that would mean that half of a gallon would be half of that amount. Half of that amount would be 1.2 fl oz. we have now found how much a full gallon needs and how much half a gallon need. Now we add these 2 numbers. 2.4 fl oz + 1.2 fl oz = 3.6 fl oz.

Please give me Brainliest.

Final answer:

To get the correct oil mix for 1.5 gallons of gasoline at a ratio of 2.4 fl oz of oil per gallon, you should add 3.6 fl oz of oil.

Explanation:

To calculate the amount of oil needed for 1.5 gallons of gasoline with a mix ratio of 2.4 fl oz of oil per gallon, you follow these steps:

Determine the amount of oil needed for one gallon of gas, which is 2.4 fl oz.

Multiply this amount by the total gallons of gas. In this case, 2.4 fl oz x 1.5 gallons.

The calculation will be 2.4 fl oz/gallon x 1.5 gallons = 3.6 fl oz of oil.

Therefore, you should add 3.6 fl oz of oil to 1.5 gallons of gasoline to achieve the correct mix ratio.

Answer:

The turning point is (-2,10)

Step-by-step explanation:

we have

[tex]y=6-4x-x^{2}[/tex]

This is a quadratic equation (vertical parabola) open downward

we know that

The turning point of a quadratic equation is the vertex

so

Convert the quadratic equation into vertex form

[tex]y-6=-4x-x^{2}[/tex]

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

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

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

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

[tex]y=-(x+2)^{2}+10[/tex] ----> equation in vertex form

The vertex is the point (-2,10)

therefore

The turning point is (-2,10)

The turning point of the parabola described by the equation y=6-4x-x^2 is at the point (-2, 10), which is a maximum since the parabola opens downwards.

To find the turning point of the curve given by the equation y=6-4x-x^2, we first need to rewrite the equation in the form of the vertex of a parabola, which is given by y=a(x-h)^2+k, where (h,k) is the coordinate of the turning point or vertex. Noting that there is a mistake in the information provided since the second derivative would actually be y" = -2, and not 6x - 12, indicating that we have a concave down parabola with a maximum point, not a point of inflection. We can complete the square to rewrite the function in vertex form.

Start by completing the square: y = -x^2 - 4x + 6 can be rewritten as y = -(x^2 + 4x) + 6. Adding and subtracting 4 inside the parenthesis (which is the square of half the coefficient of x), we get y = -(x^2 + 4x + 4 - 4) + 6, which simplifies to y = -(x + 2)^2 + 10. Thus, the vertex or turning point is at (-2, 10).

This shows the turning point of the parabola is at the point (-2, 10), which is a maximum since the parabola opens downwards as reflected by the negative coefficient of the x^2 term. This can be visualized on the graph of the function as the highest point on the curve. Remember that a quadratic equation represents a parabola in a Cartesian coordinate system.

Answer:

Step-by-step explanation:

U-4.5=6.46

   +4.5   +4.5

U=10.96

Suppose [tex]x=3.1\overline6[/tex]. Then [tex]10x=31.\overline6[/tex], and [tex]100x=316.\overline6[/tex].

Now,

[tex]100x-10x=316.\overline6-31.\overline6=316-31[/tex]

[tex]\implies90x=285[/tex]

[tex]\implies x=\dfrac{285}{90}=\boxed{\dfrac{19}6}[/tex]

ANSWER

[tex]y = 4x - 2[/tex]

EXPLANATION

The equation of a straight line can be found using the formula

[tex]y =mx + b[/tex]

We have that,the y-value increases by 4 for every x that increases by 1.

This implies that, the slope is

[tex]m = \frac{4}{1} = 4[/tex]

The line also crosses the y-axis at –2.

Hence the y-intercept is b=-2.

Therefore the equation is

[tex]y = 4x - 2[/tex]

The correct answer is A

Answer:

[tex]\frac{4x^3-3x^2+5x+6}{x+6}=4x^2-27x+167-\frac{996}{x+6}[/tex]

Step-by-step explanation:

The division problem given to us is [tex](4x^3-3x^2+5x+6)\div (x+6)[/tex].

To perform the synthetic division, we write out the coefficient of the polynomial. We set the linear factor to zero and solve for x, this becomes our divisor. That is [tex]x+6=0\implies x=-6[/tex].

We carry out the synthetic division as shown in the attachment.

The result of the synthetic division is 4   -27   167   -996

The first three terms are the coefficients of the quotient and the last term is the remainder.

Therefore the quotient is [tex]q(x)=4x^2-27x+167[/tex] and the remainder is [tex]r(x)=-996[/tex].

The dividend, the quotient and the divisor are written as

[tex]\frac{4x^3-3x^2+5x+6}{x+6}=4x^2-27x+167-\frac{996}{x+6}[/tex]

The correct answer is A

Answer:

Yes

Every straight line can be represented by an equation: y = mx + b.

m=slope

b=y-intercept

(www.math.com/school/subject2/lessons/S2U4L2GL.html)

Answer:

A) Obtuse

Step-by-step explanation:

It is Obtuse due to the angle 115° being in the Triangle. This rules out Acute since the middle angle is not less than 90°. It is not Equiangular since all three angles are not equal. Furthermore it is not a right triangle either since there is no 90° angles. Making it Obtuse.

To classify a triangle based on angle measures, we need to know the specific angles. Triangles can be obtuse, acute, right, or equiangular, and each type has its own unique properties used in various applications across different fields.

To classify the following triangle based on its angle measures, we must first understand the definitions of different types of triangles. A triangle can be classified as:

Considering these definitions, the seeking student must provide the angle measures of their specific triangle to accurately classify it.

Making distinctions between different types of triangles is crucial because each classification has unique properties that are important in various fields such as mathematics, engineering, architecture, and physics. These properties assist in solving problems and understanding the world around us.

For instance, an obtuse triangle may be used in special construction scenarios, while right triangles are essential in trigonometry and geometry, appearing frequently in real-life applications like building and navigation.

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Answer:

D. [tex]g(x)=\frac{1}{5}x^2[/tex]

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

Write the ratio this way

Pip: Sara: Total

5    : 4 :      9

We multiply each by 10 to get Pip to 50  (5*10 = 50)

5*10: 4*10: 9*10

50  : 40 :  90

Answer:

$90

Step-by-step explanation:

Given that the ratio of Pip: Sara is 5:4

This means :

Pip gets 5 parts

Sara gets 4 parts

Together they have 5 + 4 parts = 9 parts

Also given that Pip's 5 parts is equivalent to $50

Hence each 1 part is $50/5 = $10

if 1 part = $10

The total 9 parts = 9 x $10 = $90

For this case we have by definition, that the area of a rectangular prism is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex] is the area of the base

h: It's the height

Before finding[tex]A_ {b}[/tex]we convert the mixed numbers to fractions:

length: [tex]2 \frac {1} {4} = \frac {4 * 2 + 1} {4} = \frac {9} {4}[/tex]

width: 6

Height:[tex]3 \frac {1} {2} = \frac {2 * 3 + 1} {2} = \frac {7} {2}[/tex]

So, we have to:[tex]A_ {b} = \frac {9} {4} * 6 = \frac {54} {4} = 13.5[/tex]

Finally, the volume is given by:

[tex]V = 13.5 * \frac {7} {2} =47.25\ ft ^ 3[/tex]

Answer:

[tex]47.25 \ ft ^ 3[/tex]

ANSWER

[tex]Volume = 47\frac{1}{4} {ft}^{3} [/tex]

EXPLANATION

The formula for calculating the volume of a rectangular prism is

[tex]Volume = l \times b \times h[/tex]

Where

[tex]l = 2 \frac{1}{4} ft[/tex]

is the length of the rectangular box,

[tex]w = 6ft[/tex]

is the width and

[tex]h = 3 \frac{1}{2} ft[/tex]

is the height of the rectangular prism.

We plug in the given dimensions into the formula to get:

[tex]Volume = 2 \frac{1}{4} \times 6 \times 3 \frac{1}{2} [/tex]

Convert the mixed numbers to improper fraction to get:

[tex]Volume = \frac{9}{4} \times 6 \times \frac{7}{2} [/tex]

Multiply out to get

[tex]Volume = \frac{189}{4} {ft}^{3} [/tex]

Or

[tex]Volume = 47\frac{1}{4} {ft}^{3} [/tex]

Answer:

g(x)=4

Step-by-step explanation:

5.23(0)+4=4

Hope this helps!

Answer:

12 sqrt(2)

Step-by-step explanation:

Givens

a = 12 cm

b = 12 cm

c = ??

The triangle is isosceles with 1 right angle and 2 45 degree angles.

Formula

c^2 = a^2 + b^2

c^2 = 12^2 + 12^2

c^2 = 144 + 144

c^2 = 288

c^2 = 144 * 2

c = sqrt(144) * sqrt(2)

c = 12 * sqrt(2)

The answer isn't there. 12*sqrt(2) is the correct answer, 12sqrt(3).

Was this just a typo of some kind.

Answer: C)46 ft

Step-by-step explanation:

We know that the circumference of a circle can be calculated with this formula:

[tex]C=2\pi r[/tex]

Where "r" is the radius of the circle.

Since John is putting a fence around his garden that is shaped like a half circle and a rectangle, then we can find how much fencing he needs by making this addition:

[tex]Fencing=\frac{2\pi r}{2}+2l+w[/tex]

Where "l" is the lenght of the rectangle and "w" is the width of the rectangle.

Since we know that the radius of the circle is half its diameter, we can find "r". This is:

[tex]r=\frac{7ft}{2}=3.5ft[/tex]

Then, substituting values (and using [tex]\pi=\frac{22}{7}[/tex]), we get:

[tex]Fencing=\frac{2(\frac{22}{7})(3.5ft)}{2}+2(14ft)+7ft=46ft[/tex]

The answer is C) 46ft

Answer:

C.

Step-by-step explanation:

Add up the number of minutes Evan played.  you can ignore the number of minutes Josh played, the number of players in the team and the number of times Evan was substituted.

Answer:

The number of minutes Evan played.

Step-by-step explanation:

The most important variable is :  The number of minutes Evan played.

As at the end we have to find out how long did Evan play. And to get the answer, we have to consider Evan's play time in each quarter.

By adding all those numbers, we will get the answer.

Hence, option C is correct.

For this case we must find an expression equivalent to:

[tex]\sqrt [5] {13 ^ 3}[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, rewriting the expression:

[tex]13 ^ {\frac {3} {5}}[/tex]

Answer:

Option D

[tex]13 ^ {\frac {3} {5}}[/tex]