An isosceles triangle’s altitude will bisect its base. Which expression could be used to find the area of the isosceles triangle above?

Answer:

X=30, Scalene

Step-by-step explanation:

A circle is 360, The triangle is in the circle.

Part A:3x+30+2x+20+5x+10=360

10x+60=360

-60=-60

10x=300

x=30

Part B:Side BA is 3(30)+30=120

Side BC is 2(30)+30=90

Side AC is 5(30)+10=160

All three sides are unequal

Answer:

3x^2+x-9

Step-by-step explanation:

f+g

means you are going to add whatever f equals to what g equals

so you have

(-3)+(3x^2+x-6)

Combine like terms

3x^2+x+(-3+-6)

3x^2+x+-9

or

3x^2+x-9

Answer:

A. 68°

Step-by-step explanation:

sum of angles inside a triangle = 180°

75 + 37 + x = 180

x = 180 - 75 - 37

= 68°

The sum of angles inside a triangle is 180°. so option is A. 68°.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

Given angles are; 75 and 37.

The sum of angles inside a triangle = 180°

75 + 37 + x = 180

x = 180 - 75 - 37

x = 68°

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Answer:

2x+5

because you are subtracting it is basically multiplying (5x-6) by negative one so you have to distribute it out so you are basically adding (7x-1) and (-5x+6) by adding like terms you get 7x-5x= 2x and -1+6=5

so the answer is 2x+5

Answer:

x ≅ 79.1

Step-by-step explanation:

10log(4x) = 25  

2log(4x) = 5  

log((4x)²) = 5  

(4x)² = 10⁵  

16x² = 100,000  

x² = 6,250  

x ≅ 79.1

(A) 79.06 is the correct answer!

Answer: Number of pizzas would be less than 5 but not more than 50.

Step-by-step explanation:

Since we have given that

Number of pizzas so far = 25

His principal asked him to make at least 30 pizzas but no more than 75.

According to question, we have

30 ≤ x + 25 ≤ 75

First we subtract 25 from both the sides:

[tex]30-25\leq x \leq 75-25\\\\=5\leq x\leq 50[/tex]

Hence, number of pizzas would be less than 5 but not more than 50.

The solution to the compound inequality is 5  x 50.

The compound inequality given is 30 x 25  75, where x represents the number of additional pizzas Billy needs to make to satisfy the principal's request. To solve for x, we need to isolate x in the inequality.

First, we subtract 25 from all parts of the compound inequality to shift the 25 pizzas already made to the other side of the inequality. This gives us:

30 - 25 x + 25 - 25 75 - 25

Simplifying the inequality, we get:

5  x  50

This means that Billy needs to make at least 5 more pizzas to reach the minimum requirement of 30 pizzas (since 25 + 5 = 30) and no more than 50 additional pizzas to not exceed the maximum allowed number of 75 pizzas (since 25 + 50 = 75).

Therefore, the number of additional pizzas Billy should make is any integer value between 5 and 50, inclusive. This ensures that the total number of pizzas made will be within the principal's specified range of 30 to 75 pizzas."

Answer:

option 3 is the answer

Step-by-step explanation:

A polynomial  in two variables is said to be in standard form if exponent of one variable is keep decreasing  and another variable keep increasing

only option 3 follows it

As here exponent of x start from 5 and decreases up to 0

and exponent of y start from 0 and keep increasing up to 5

rest of the option do not follow this rule

Answer:

c)5x^5 - 9x^2y^2 - 3xy^3 + 6y^5

Step-by-step explanation:

[tex]\bf (WY+4)-Y=6\implies \stackrel{\textit{nope}}{WY+4-Y=6}[/tex]

recall, a quadratic has a polynomial with a degree of 2.

Answer:

The answer is b.

Step-by-step explanation:

Have a great day!!

Answer:

The answer is 6.

Step-by-step explanation:

Plug in:  f(-5)=|-5+1|

Because this an absolute problem -5 is positive within |x|

so therefore f(-5)= |6|

Answer:

16%

Step-by-step explanation:

100% - 68% = 32%

32%/2 = 16%

its (8,6)

to get your x, you set what's in the absolute value to 0

so

x-8=0

then subtract 8 on both sides to get

x=8

then your y is just the number to the right of the absolute value so

y=6

Answer: Option B

(8, 6)

Step-by-step explanation:

By definition, for an absolute value function of the form

[tex]f (x) = | x-h | + k[/tex]

the vertex of f(x) will always be at the point

(h, k)

In this case we have the function of value ansoluto:

[tex]g(x) = |x - 8| + 6[/tex]

Therefore in this case

[tex]h=8\\k=6[/tex]

Finally the vertex of the function g(x) is: (8, 6)

The answer is the option B

An answer is

  [tex]\displaystyle f\left(x\right)=\frac{\left(x+1\right)^3}{\left(x+2\right)^2\left(x-1\right)}[/tex]

Explanation:

Template:

  [tex]\displaystyle f(x) = a \cdot \frac{(\cdots) \cdots (\cdots)}{( \cdots )\cdots( \cdots )}[/tex]

There is a nonzero horizontal asymptote which is the line y = 1. This means two things: (1) the numerator and degree of the rational function have the same degree, and (2) the ratio of the leading coefficients for the numerator and denominator is 1.

The only x-intercept is at x = -1, and around that x-intercept it looks like a cubic graph, a transformed graph of [tex]y = x^3[/tex]; that is, the zero looks like it has a multiplicty of 3. So we should probably put [tex](x+1)^3[/tex] in the numerator.

We want the constant to be a = 1 because the ratio of the leading coefficients for the numerator and denominator is 1. If a was different than 1, then the horizontal asymptote would not be y = 1.

So right now, the function should look something like

  [tex]\displaystyle f(x) = \frac{(x+1)^3}{( \cdots )\cdots( \cdots )}.[/tex]

Observe that there are vertical asymptotes at x = -2 and x = 1. So we need the factors [tex](x+2)(x-1)[/tex] in the denominator. But clearly those two alone is just a degree-2 polynomial.

We want the numerator and denominator to have the same degree. Our numerator already has degree 3; we would therefore want to put an exponent of 2 on one of those factors so that the degree of the denominator is also 3.

A look at how the function behaves near the vertical asympotes gives us a clue.

Observe for x = -2,

Observe for x = 1,

We should probably put the exponent of 2 on the [tex](x+2)[/tex] factor. This should help preserve the function's sign to the left and right of x = -2 since squaring any real number always results in a positive result.

So now the function looks something like

  [tex]\displaystyle f(x) = \frac{(x+1)^3}{(x+2 )^2(x-1)}.[/tex]

If you look at the graph, we see that [tex]f(-3) = 2[/tex]. Sure enough

  [tex]\displaystyle f(-3) = \frac{(-3+1)^3}{(-3+2 )^2(-3-1)} = \frac{-8}{(1)(-4)} = 2.[/tex]

And checking the y-intercept, f(0),

  [tex]\displaystyle f(0) = \frac{(0+1)^3}{(0+2 )^2(0-1)} = \frac{1}{4(-1)} = -1/4 = -0.25.[/tex]

and checking one more point, f(2),

  [tex]\displaystyle f(2) = \frac{(2+1)^3}{(2+2 )^2(2-1)} = \frac{27}{(16)(1)} \approx 1.7[/tex]

So this function does seem to match up with the graph. You could try more test points to verify.

======

If you're extra paranoid, you can test the general sign of the graph. That is, evaluate f at one point inside each of the key intervals; it should match up with where the graph is. The intervals are divided up by the factors:

So we need to see if -2 < x < -1 matches up with the graph. We can pick -1.5 as the test point, then

  [tex]\displaystyle f(-1.5) = \frac{\left(-1.5+1\right)^3}{\left(-1.5+2\right)^2\left(-1.5-1\right)} = \frac{(-0.5)^3}{(0.5)^2(-2.5)} \\= (-0.5)^3 \cdot \frac{1}{(0.5)^2} \cdot \frac{1}{-2.5}[/tex]

We don't care about the exact value, just the sign of the result.

Since [tex](-0.5)^3[/tex] is negative, [tex](0.5)^2[/tex] is positive, and [tex](-2.5)[/tex] is negative, we really have a negative times a positive times a negative. Doing the first two multiplications first, (-) * (+) = (-) so we are left with a negative times a negative, which is positive. Therefore, f(-1.5) is positive.

the answer is not 65 and not 4

[tex]\bf |x-6|<4\implies \begin{array}{llll} +(x-6)<4\\ -(x-6)<4 \end{array}\implies \begin{cases} x-6<4\implies &\boxed{x<10}\\ \cline{1-2} -(x-6)<4\\ \stackrel{notice}{x-6\stackrel{\downarrow }{>}-4}\implies &\boxed{x>2} \end{cases}[/tex]

Answer:

The correct answer is: 21x + 14 = 98; x = 4.

Step-by-step explanation:

She needs to type the notes she recorded in her 98-page workbook. If whe types x hours at a rate of 21 pages per hour, and 14 pages are already done. Then the equation is:

21x + 14 = 98;

Now, the number of hours she will take to complete the task can be found by solving for 'x':

21x = 98 - 14

21x = 84

x = 4.

Therefore, the correct option is: 21x + 14 = 98; x = 4.

Answer:

21x + 14 = 98; x = 4

Step-by-step explanation:

Camille has already typed notes from the first 14 pages of her workbook, and she types for x hours at a rate of 21 pages per hour. An expression for the one side of the equation needs to represent the total number of pages she has typed in terms of x. The number of pages Camille has typed after x hours is represented by the expression 21x + 14.

The workbook has a total of 98 pages. Thus, the other side of the equation which represents the number of pages Camille has typed after x hours is 98.

Hence, the equation that represents the number of pages she has typed after x hours is 21x + 14 = 98.

Solve the equation to determine how many hours it will take Camille to complete the task.

So, x = 4. Therefore, it takes Camille 4 hours to complete the task.

Answer:

A

Step-by-step explanation:

Answer:  5

Step-by-step explanation:

f(5) = 2 means that when x = 5, y = 2 --> (5, 2)

f⁻¹(2) is the inverse (when the x and y are swapped) --> when x = 2, y = 5

Answer:

c.1/3

Step-by-step explanation:

To check, multiply 1/3 each time to each number. Note that the first number is 27:

27 x 1/3 = 27/3 = 9

9 x 1/3 = 9/3 = 3

3 x 1/3 = 3/3 = 1

1 x 1/3 = 1/3

etc.

This means that the common ratio decreases by the common multiple of 1/3.

~

The answer is C.

Hope this helps.

r3t40

Answer:

512.4 miles

Step-by-step explanation:

The distance from city to beach town = 500 miles

Distance from airport to hotel = 20 kilometers

In order to find the total distance we have to convert the kilometers in miles to bring both quantities in same unit

So,

1 kilometer = 0.62 miles

20 kilometers = 20*0.62 =12.4 miles

As both the quantities are in same unit,

The total distance = Distance from city to beach town + distance from airport to hotel

= 500 + 12.4

= 512.4 miles

Hence, total distance covered by them is 512.4 miles ..

For this case we can make a change of variable, to obtain a quadratic equation of the form:

[tex]ax ^ 2 + bx + c = 0[/tex]

Making the change:[tex]u = 3x + 2[/tex]

Substituting the change we have:

[tex]u ^ 2 + 7u-8 = 0[/tex]

Thus, the correct option is:[tex]u ^ 2 + 7u-8 = 0[/tex]where [tex]u = 3x + 2[/tex]

Answer:

Option B

Answer:

second option: [tex]u^{2}+7u-8=0[/tex]

Step-by-step explanation:

We have the equation given:

[tex](3x+2)^{2}+7(3x+2)-8=0[/tex]

We can replace the variable in the quardatic equation.

So,

[tex]Putting\\u=3x+2[/tex]

Putting u in place of 3x+2 will give us:

[tex](u)^{2}+7(u)-8=0[/tex]

So the answer is:

[tex]u^{2}+7u-8=0[/tex]

So, the second option is correct ..

Let n be a number

2n - 3 = 55

Add 3 to both sides

2n + (-3 + 3) = 55 + 3

2n = 58

Divide 2 to both sides

2n/2 = 58/2

n = 29

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: Option b

[tex]f (1) = 0[/tex]

Step-by-step explanation:

For a function of the form

[tex]f (x) = ax ^ n + bx ^ {n-1} + ... + c[/tex]

Where n is the main exponent of the polynomial and a, b c are the coefficients of the variables then this polynomial can be written based on its factors as

[tex]f (x) = a (x-h) (x-k) (x-s)...[/tex]

Where [tex]x = h[/tex], [tex]x = k[/tex], [tex]x = s[/tex], ... are the points where [tex]f(x) = 0[/tex]

Therefore if for this case we know that

[tex](x-1)[/tex] is a factor of a polynomial function [tex]f (x)[/tex] then it is fulfilled that

[tex]f (1) = 0[/tex]

Answer:

The statement is True

Step-by-step explanation:

The Isosceles Triangle Theorem states that;

If two sides of a triangle are congruent, then the angles opposite those sides are also congruent. The converse of this statement is;

if two angles are congruent, then sides opposite those angles are congruent.

Answer:

True.

Step-by-step explanation:

To start with , remember that congruent angles have the same degree of measurement. For example, in an isosceles triangle, the base angles are congruent angles because they both measure 45°

The base angles  theorem states that the sides next to congruent angles are equal.The statement is therefore True.If sides of the triangle are congruent, the opposite angles in the triangle are congruent .

Answer:

8

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 5, 2) and (x₂, y₂ ) = (- 9, 9)

d = [tex]\sqrt{(-9+5)^2+(9-2)^2}[/tex]

  = [tex]\sqrt{(-4)^2+7^2}[/tex]

  = [tex]\sqrt{16+49}[/tex] = [tex]\sqrt{65}[/tex] ≈ 8 ( nearest unit )

Answer:  The required distance between my house and the subway stop is 8 units.

Step-by-step explanation:  Given that a grid shows the positions of a subway stop and my house. The subway stop is located at (-5,2) and my house is located at (-9,9).

We are to find the distance, to the nearest unit, between my house and the subway stop.

We will be using the following formula :

Distance formula :  The distance between the points (a, b) and (c, d) is given by

[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]

Therefore, the distance between the points (-5, 2) and (-9, 9) is given by

[tex]D\\\\=\sqrt{(-9-(-5))^2+(9-2)^2}\\\\=\sqrt{(-9+5)^2+7^2}\\\\=\sqrt{4^2+49}\\\\=\sqrt{16+49}\\\\=\sqrt{65}\\\\=8.06.[/tex]

Rounding to the nearest units, we get

D = 8 units.

Thus, the required distance between my house and the subway stop is 8 units.

Answer:

Step-by-step explanation:

1 group = 10 students

x group = 240 students.

1/x = 10/240              Cross multiply

10x = 240                  Divide by 10

10x/10=240/10          Do the division

x = 24

units like radius, height, width, length or segments are single units, like meter or feet.

areas are double units, so they'd be in say meter² or feet².

volumes are triple units, namely like meter³ or feet³.

Answer:

The unit of measuring volume of the sphere is cubic meter.

Step-by-step explanation:

Given  :  Sphere with a  radius of 2 meters.

To find : Which unit of measure would be appropriate for the volume of sphere.

Solution : We have given Radius = 2 meter .

Volume = [tex]\frac{4}{3}\pi (radius)^{3}[/tex].

Volume  =  [tex]\frac{4}{3}\pi (2 meter)^{3}[/tex].

Volume of sphere =   [tex]\frac{32}{3}\pi[/tex] meter³ .

Therefore, The unit of measuring volume of the sphere is cubic meter.

Answer:

Step-by-step explanation:

By observation, you can see that the irregular polygon can be split into 4 triangles (see attached image). We know that the sum of the internal angles of 1 triangle is always 180 degrees. Hence the sum of all the internal angles of the polygon is,

180 degrees x 4 triangles = 720 degrees.

Therefore Angle B,  

= sum of internal angles - sum of all other known angles

= 720 - (133 +102+117+90+170)

= 108 degrees.

The measure of angle B is 108 degrees.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

We can divide the given polygon in split into 4 triangles.

Using, angle sum property,

The sum of the internal angles of triangle is always 180 degrees.

Hence the sum of all the internal angles of the polygon is,

=180 x 4 triangles

= 720 degrees.

Now, angle B

= 720 - (133 +102+117+90+170)

=720 -612

= 108 degrees.

Hence, angle B is 108 degrees.

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Answer:

-2x + 8y - 5z

Step-by-step explanation:

-1/2*4x = -2x

-1/2 * - 16y = 8y

-1/2 * 10z = - 5z

Combine

-2x + 8y - 5z

If you break the question apart like this, you will never get confused by what the signs do. What is left for signs is what you put in the answer.