The ____ ____ of equality allows you to divide both sides of an equation by the same number.

Answer:  First option is correct.

Step-by-step explanation:

Since we have given that

If two sides of a triangle are not equal,

According to Relationship between the angle and side , we know that the angle opposite the shortest side is the larger angle,

And,

The angle opposite the longest side is the shortest angle

So, First option is correct.

The school will have to pay $60 for 50 dozen buttons, by using a proportional calculation based on the known cost of $18 for 15 dozen buttons.

The student's question involves calculating the cost of purchasing a larger quantity of buttons based on a known cost for a smaller quantity. To solve this, we will use proportional reasoning.

The school pays $18 for 15 dozen buttons. First, we find the cost for one dozen by dividing the total cost by the number of dozens:

$18 ÷ 15 dozen = $1.20 per dozen

Next, we calculate the cost for 50 dozen buttons by multiplying the cost per dozen by the number of dozens:

$1.20 per dozen × 50 dozen = $60

Therefore, the school will have to pay $60 for 50 dozen buttons.

Final answer:

Using the Law of Cosines, the length of the third side of the obtuse triangle is x = sqrt(52) or x = 2sqrt(13).

Explanation:

To find the length of the third side of an obtuse triangle with sides of lengths 4 and 10 and an area of 12, you can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the equation c^2 = a^2 + b^2 - 2ab * cos(C) can be used to find the length of side c.

In this case, let's assume that the third side of the triangle has length x. We can set up the equation as x^2 = 4^2 + 10^2 - 2*4*10 * cos(C), where C is the angle opposite side x.

Simplifying the equation, we get x^2 = 116 - 80*cos(C).

Since we know that the area of the triangle is 12, we can use the formula Area = 0.5 * a * b * sin(C) to find the value of sin(C). Plugging in the given values, we get 12 = 0.5 * 4 * 10 * sin(C). Solving for sin(C), we find sin(C) = 0.6.

Using this value of sin(C), we can then find the value of cos(C) by using the trigonometric identity sin^2(C) + cos^2(C) = 1. Substituting sin(C) = 0.6, we get 0.6^2 + cos^2(C) = 1. Solving for cos(C), we find cos(C) = 0.8.

Now, we can substitute the value of cos(C) into the equation x^2 = 116 - 80*cos(C), giving us x^2 = 116 - 80*0.8. Simplifying further, we get x^2 = 52, which means that the length of the third side is either x = sqrt(52) or x = -sqrt(52).

However, since we are dealing with the length of a side, it cannot be negative. Therefore, the length of the third side is x = sqrt(52), which simplifies to x = 2sqrt(13).

Answer:

KMD,MDK,DKM

Step-by-step explanation:

Answer:

tan P = 24/7 and tan Q = 7/24

Step-by-step explanation:

tangent of any angle in a right angle triangle is always represented by

tan x = opposite side/ adjacent side = height / base

from the question we have to write tangent of P and Q.

tan P = QR/PR = 24/7

tan Q = PR / RQ = 7/24

So the answers are tangent ratios for P and Q are 24/7 and 7/24.

Answer:  The correct option is (B) [tex]10x=7.[/tex]

Step-by-step explanation:  The given equations are :

[tex]3x+y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-3y=-2~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

We are to select the correct result if the first equation is multiplied by 3 and then added to the second equation.

Now, multiplying equation (i) by 3, we get

[tex]3(3x+y)=3\times 3\\\\\Rightarrow 9x+3y=9~~~~~~~~~~~~~~~~~~~~(iii)[/tex]

adding equation (iii) to equation (ii), we get

[tex](9x+3y)+(x-3y)=9+(-2)\\\\\Rightarrow 9x+3y+x-3y=9-2\\\\\Rightarrow 10x=7.[/tex]

Thus, the required result is [tex]10x=7.[/tex]

Option (B) is CORRECT.

Jamal's height can be converted to dekametres by dividing his height in centimeters (167 cm) by 1000, because there are 1000 centimeters in a dekametre.

To convert Jamal's height from centimeters to dekametres, we should recall that 1 dekametre equals 10 meters or 1000 centimeters. Since Jamal is 167 cm tall, we need to divide his height in centimeters by the number of centimeters in a dekametre to get his height in dekametres.

Therefore, the correct expression to find Jamal's height in dekametres is:

167 divided by 1000

This is option D: 167 / 1000.

The property being used when substituting x=4 into the expression 5x to get 5*4=20 is the Substitution Property.

When given the statement If x=4, then 5x=20, we are looking at a basic arithmetic operation, specifically multiplication. The property illustrated here is known as the Identity Property of Multiplication, which states that multiplying any number by 1 gives the number itself. However, in the context of this problem, the property being used is actually the Substitution Property, where the value of a variable (x=4) is substituted into an expression (5x) to find its value (5*4=20).

https://brainly.com/question/12053340

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the answer is d,,,,,,,,,,,,,,,,,

Answer:

Correct option is D.

Step-by-step explanation:

Given the quadratic equation

[tex](ax+b)^2=c[/tex]

we have to define the first step in solving a quadratic equation.

To find the value of x we have make the equation linear i.e taking the square root on both sides as c is any constant.

If c is 0 the we use the zero product rule.

Hence, our first step in solving a quadratic equation of the form

[tex](ax+b)^2=c[/tex]

is to take the square root of both sides.

Correct option is D.  

Answer:

First F, then D, then C

Answer:

no real solutions.

Step-by-step explanation:

-11[tex]x^{2}[/tex] = x+11. Put into standard form of a quadratic equation.

11[tex]x^{2}[/tex] + x + 11 = 0 Find a, b, and c.

a = 11, b =1, c = 11 Write and substitute into the quadratic equation[tex]\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}[/tex] .

[tex]\frac{-1 +/- \sqrt{1^{2} - 4(11)(11)} }{2(11)}[/tex] Simplify.

[tex]\frac{-1 +/- \sqrt{1-484} }{2(11)}[/tex]=

[tex]\frac{-1 +/-\sqrt{-483} }{22}[/tex] BUT because the [tex]b^{2} -4ac[/tex] part under the √ is less than 0, THERE IS NO SOLUTION!

Answer: 8 units

Step-by-step explanation:

Given: The formula for the circumference of a circle is [tex]C=2\pi r[/tex], where r is the radius and C is the circumference.

To solve equation for r , we divide [tex]2\pi[/tex] on both sides, we get

[tex]r=\dfrac{C}{2\pi}[/tex]

Now, the circumference of the circle = [tex]16\pi \text{units.}[/tex]

Then, [tex]r=\dfrac{16\pi}{2\pi}=8\ \text{units}[/tex]

Hence, Circumference of the circle = 8 units

Answer:

C

Step-by-step explanation:

Let the cost of a pack of gum 20 years ago = x cents

Given, present cost of a pack of gum = 75 cents

Given, present cost of a pack of gum is 3 cents less than three times what the pack costs 20 years ago.

So,

[tex]75 + 3 =3x[/tex]

[tex]75= 3x -3[/tex]

[tex]3x-3=75[/tex]

Therefore,

Equation , [tex]3x-3=75[/tex]  , can be used to find the cost of the gum 20 years ago.

Answer:

The correct answer is A. 10

4+6+8+20+12=50

50/5 =10

Step-by-step explanation:

Answer:

-4x⁴y⁶

Step-by-step explanation:

To divide -12x⁸y⁸ by 3x⁴y², we can apply the rules of division for exponents.

When dividing variables with the same base, we subtract the exponents:

x⁸ / x⁴ = x⁸-⁴ = x⁴

Similarly, y⁸ / y² = y⁸-² = y⁶

Now, let's divide the coefficients:

-12 / 3 = -4

Putting it all together, the result of dividing -12x⁸y⁸ by 3x⁴y² is:

-4x⁴y⁶