How do I solve for x within a triangle?

The third side of the isosceles triangle with the given sides of 2 and 12 is 12 units.

To find the length of the third side of an isosceles triangle where two sides are given as 2 and 12, we must consider two cases.

In an isosceles triangle, two sides are equal in length and the two angles opposite these sides are also equal. This means either the two given sides are the equal sides, which is not possible since they are different lengths, or one of the given lengths will be the base and the equal sides are yet to be determined.

Case 1: If the side of length 2 is the base, the length of the equal longer sides will both be 12.

Case 2: If the side of length 12 is the base, then the length of the two equal sides must both be 2.

However, we must recognize that the first case is incorrect because it does not form a triangle (a triangle cannot have two sides of length 12 and one side of length 2, as the two longer sides would be parallel and never meet to form a triangle).

Therefore, the correct answer is given by Case 2: the third side of the triangle, which is the base, is 12 units long, and the two equal sides are 2 units long each.

The equation of the line in slope-intercept form would be; y=1/2x+5.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

(a) The slope of line passing through two points is given by;

[tex]m = \dfrac{y-q}{x-p}[/tex]

Here m = 4 - 9/ -2 - 8

m = 5/10

m = 1/2

(b) The equation of line passing through a point and having slope is given by ;

y-y₁ = m(x-x₁)

Here, y-4 = 1/2(x+2)

(c) The slope intercept form;

y-4=1/2(x+2)

y-4=1/2x+1

y=1/2x+5

Hence, the equation of the line in slope-intercept form would be; y=1/2x+5.

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The Calvin has a total of 252 utility coming from Oranges and Starfruit.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that oranges cost $2 per pound and starfruit costs $5 per pound.

The utility coming from Oranges and Starfruit, therefore he needs to spend his $26 on buying the oranges and starfruit

Since all in all he also spend $23 on it, and still has remaining $3 in his pocket,

Thus his total utility is 252.

Hence, The Calvin has a total of 252 utility coming from Oranges and Starfruit.

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The complete question is

The oranges cost $2 per pound and starfruit costs $5 per pound. calvin has $26 to spend. if calvin buys 4 pounds of starfruit and 3 pounds of oranges, how much is his total utility?

The probability we see at least one club and at least one ace would be 0.019225

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

The Total number of cards in a deck = 52

Number of aces in a standard deck = 4

Number of clubs in a standard deck = 13

The Probability = required outcome / Total possible outcomes

P(ace) = 4 / 52 = 0.0769

P(club) = 13 / 52 = 1/4 = 0.25

Therefore, the probability we see at least one club and at least one ace

0.0769 x 0.25

= 0.019225

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Answer:

The correct option is B.

Step-by-step explanation:

The given quadratic function is

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

We have to find the value of the function y at x=6.

Substitute x=6 in the given function.

[tex]y=2(6)^2-2(6)-2[/tex]

[tex]y=2(36)-12-2[/tex]

[tex]y=72-14[/tex]

[tex]y=58[/tex]

The value of the function is 58 at x=6 is 58.

Therefore the correct option is B.

The correct answer is:

5 tons = 10,000 lb

10,000 lb − 570 lb = 9,430 lb = 4 tons and 1,430 lb

This answer is if you want it in tons and pounds.

Answer:x <= -2 and 2x >= 6 is the smae as

x <= -2 and x >= 3

Step-by-step explanation:

Final answer:

To solve the problem, we defined two variables for the larger (x) and smaller (y) numbers. Using the provided information, we set up two equations and solved them to find the numbers: x (the larger number) is 40, and y (the smaller number) is 28.

Explanation:

Step-by-Step Solution to Find the Two Numbers

Let's denote the larger number as x and the smaller number as y. We are given two pieces of information:

The sum of the two numbers is 68.

The smaller number is 12 less than the larger number.

These two statements can be turned into two equations:

x + y = 68 (Equation 1)

y = x - 12 (Equation 2)

Now, we can substitute Equation 2 into Equation 1 to find x:

x + (x - 12) = 68

2x - 12 = 68

Add 12 to both sides:

2x = 80

Divide both sides by 2:

x = 40

Now that we know the larger number, x, we can find y using Equation 2:

y = 40 - 12

y = 28

So, the two numbers are 40 and 28

The value of [tex]\int\limits^._R {xy^2} \, dA[/tex]  is 16.

The calculation of an integral is called integration. In math, many useful quantities like areas, volumes, displacement, and so on can be found using integrals. When we discuss integrals, we typically refer to definite integrals. Antiderivatives make use of the indefinite integrals. Apart from differentiation, one of the two major calculus topics in mathematics is integration.

Given xy =3, xy = 7,

xy² = 3, xy² = 7

s = xy and t = xy²

dividing t by s we get

t/s = xy²/xy

y = t/s

and x = s/y = s²/t

now differentiate x and y partially with respect to s and t

∂x/∂s = 2s/t

∂x/∂t = -s²/t²

∂y/∂s = -t/s²

∂y/∂t = 1/s

The Jacobian is

∂(x, y)/∂(s, t) = [tex]\left|\begin{array}{ccc}dx/ds&dx/dt\\dy/ds&dy/dt\end{array}\right|[/tex]

∂(x, y)/∂(s, t) =[tex]\left|\begin{array}{ccc}2s/t&-s^{2}/t^{2} \\-t/s^{2} &1/s\end{array}\right|[/tex]

∂(x, y)/∂(s, t) =2/t - 1/t

∂(x, y)/∂(s, t) = 1/t

so for  [tex]\int\limits^._R {xy^2} \, dA[/tex] = [tex]\int\limits^a_b \int\limits^a_b {t}\frac{d(x, y)}{d(s, t) } \, dsdt[/tex]

for (s, t) (3 ≤ s ≤7, 3 ≤ t  ≤ 7)

= [tex]\int\limits^7_3 \int\limits^7_3 {t}*1/t } \, dsdt[/tex]

= [tex]\int\limits^7_3ds \int\limits^7_3 dt[/tex]

=[s]₃⁷ [t]₃⁷

= (7 - 3)(7 - 3)

= 16

Hence the value is 16.

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(7x+3) x (4x-5)

7x*4x = 28x^2

7x*-5 = -35x

3+4x = 12x

3*-5 = -15

so you get 28x^2 -23x -15

Answer:  The required multiplied expression is [tex]28x^2-23x-15.[/tex]

Step-by-step explanation:  We are given to multiply the following linear factors and write the answer is standard form :

[tex]M=(7x+3)(4x-5)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be using the following distributive property :

[tex](a+b)(c+d)=a(c+d)+b(c+d).[/tex]

From (i), we get

[tex]M\\\\=(7x+3)(4x-5)\\\\=7x(4x-5)+3(4x-5)\\\\=28x^2-35x+12x-15\\\\=28x^2-23x-15.[/tex]

Thus, the required multiplied expression is [tex]28x^2-23x-15.[/tex]

Answer:

option B

Step-by-step explanation:

A. [tex]3x^2 - 11x + 4 = 0[/tex]

3*4 = 12

We find out two factors whose sum is -11 and product is 12

1 times 12 = 12

To get sum -11 , then one factor should be negative. So, factoring is not possible.

B .  [tex]3x^2 - 11x - 4 = 0[/tex]

3*(-4) = -12

We find out two factors whose sum is -11 and product is -12

1 times (-12) = -12

1 + (-12) = -11

So two factors are 1  and -12

Split the middle term -11x using factors 1  and -12

So equation becomes

[tex]3x^2 + 1x - 12x - 4 = 0[/tex]

Now group first two terms and last two terms

[tex](3x^2 + 1x)+ (- 12x - 4) = 0[/tex]

[tex]x(3x+ 1)-4(3x +1)=0[/tex]

(3x+1)(x-4)=0

Now we set each parenthesis =0  and solve for x

3x+1 =0  , subtract 1 on both sides

3x = -1 ( divide both sides by 3)

x= -1/3

Now we set x-4=0

add 4 on both sides

so x=4

Option B is correct

The required simplified form of the expression 12x⁵/6x² is 2x³.

Exponential expressions, as the name indicates, involve exponents. We already know that the exponent of a number (base) specifies how many times the number (base) has been multiplied. To answer the exponential expressions, we may need to apply the relationship between exponents and logarithms.

The exponential expression is given in the question as:

12x⁵/6x²

To simplify the expression 12x⁵/6x², we can start by dividing 12 by 6 to get:

12x⁵/6x² = (12/6)x⁵/x² = 2x⁵/x²

Then, we can use the quotient of powers rule, which states that when we divide two powers with the same base, we can subtract the exponents to get:

2x⁵/x² = 2x⁵⁻² = 2x³

Therefore, the expression is 2x³ equivalent to the given expression 12x⁵/6x².

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Given ray OJ bisects angle IOK, we can set an equation for angles IOJ and JOK, solve for x and substitute x into the given measure of angle IOJ: 2*(16)-5 equals 27 degrees.

Since ray OJ bisects angle IOK, it means that angle IOJ and angle JOK are equal in measurement. Given in the problem, angle IOJ= 2x-5 and angle JOK= x+11. Because they are equal, we can set up the equation 2x-5 = x+11.

To solve for x, we subtract x from both sides of the equation, resulting in x-5 =11. And then, if we add 5 to both sides of the equation, the end result is x = 16.

Substituting x into the given measurement for angle IOJ, which is 2x-5, we would get the measure of angle IOJ as 2*(16)-5 = 27 degrees.

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Answer:

Pretty sure its the Transitive Property

Step-by-step explanation:

It's a dropdown on Edge so there's no A B C or D

To prove that point C is the midpoint of segment AB, we apply the segment addition property and the definition of congruent segments.

To prove that point C is the midpoint of segment AB, we can use the segment addition property. We are given that AB = 12 and AC = 6. By applying the segment addition property, we get AC + CB = AB. Substituting the given values, we have 6 + CB = 12. Solving for CB using the subtraction property, we find that CB = 6.

Now, by using the symmetric property, we can see that 6 = AC. Since CB = 6 and 6 = AC, we can conclude that AC is congruent to CB by the definition of congruent segments. This implies that C is the midpoint of AB, as it divides AB into two congruent segments.