MATHEMATICS HIGH SCHOOL

Carly will enter two baking competitions. The first competition requires her to make 2x + 4 cupcakes. The second competition requires her to make 3x + 2 cupcakes.Complete the expression to represent the total number of cupcakes.

x +

Answers

Answer 1
Answer: First, we combine the 2 problems, So 2x+4+3x+2. Then we combine like terms. that means that we can add the x's together, then add the normal numbers. That equals 5x+6. Is this what you're looking for?
Answer 2
Answer: Well what we need to do here is first combine the two equations, like this 5x+6 and thats about it, Enjoy! (just add them together)

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If (9x − 4)(9x + 4) = ax2 − b, what is the value of a?

The value of a is _____________.

Answers

(9x - 4) (9x + 4) 
9x (9x + 4 ) -4 (9x + 4)
81x^2 + 36x - 36x - 16
81x^2 - 16

ax2 - b

therefore the value of a is equal to 81

Answer:

value of a is, 81

Step-by-step explanation:

Using the identity rule:

(a+b)(a-b)=a^2-b^2

Given the equation:

(9x-4)(9x+4)=ax^2-b

Apply the identity rule:

(9x)^2-(4)^2=ax^2-b

⇒81x^2-16=ax^2-b

On comparing both sides we have;

a = 81 and b = 16

Therefore, the value of a is, 81

Given the equations y = x2 - 4x - 5 and y + x = -1, one point that satisfies both equations is

Answers

\left \{ {{y=x^2-4x-5} \atop {y+x=-1}} \right. \n \n \left \{ {{y=x^2-4x-5} \atop {y=-1-x}} \right. \n\n \n x^2-4x-5=-1-x\n \n x^2-3x-4=0\n \n \Delta=(-3)^2-4.1.(-4)=9+15=25\n \n x=(3 \pm5)/(2)\n \n x_1=-1 \rightarrow y=-1+1=0\n \n x_2=4 \rightarrow y=-1-4=-5

We found 2 points that satisfies both equations  (4,-5) and (-1,0)

Carol and Jan leave from the same place and travel on the same road going the same direction. Carol walks at a rate of 2 miles per hour. Carol left 5 hours earlier than Jan, but Jan rides a bike at a rate of 6 miles per hour. How far did the travel when Jan caught up to Carol?

Answers

Let, the time when Jan cough up to Carol = x

We know, Distance = Speed * Time.

So, Equation would be: 2x + 5*2 = 6x

2x + 10 = 6x

6x - 2x = 10

4x = 10

x = 10/4 = 2.5

Distance traveled in that time = 2.5 * 6 = 15 miles

In short, Your Answer would be: 15 miles

Hope this helps!

Simplify the expression. 7(3x + 5y) + 4y

Answers

=21x + 35y + 4y
= 21x + 39y

A spinner with 10 equally sized slices has 2 red slices, 4 yellow slices, and 4 blue slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a red slice?

Answers

The probability that the dial stops on a red slice, when it is spun and stops on a slice at random is 1/5.

How to get probability of an event?

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

A spinner with 10 equally sized slices has 2 red slices, 4 yellow slices, and 4 blue slices.

The total number of slices is 10 and the total number of favorable outcome to get a red slice is 2. Thus, the probability that the dial stops on a red slice is,

P=(2)/(10)\nP=(1)/(5)

Thus, the probability that the dial stops on a red slice, when it is spun and stops on a slice at random is 1/5.

Learn more about the probability here;

brainly.com/question/24756209

#SPJ2

Answer: 5

Step-by-step explanation: with these problems you're supposed to add all the numbers and then you divide it by the number you're asking to find the probability of so 10/2=5

What is the cosine of 135 degrees?

Answers

cos135^o=cos(90^o+45^o)=-sin45^o=-(\sqrt2)/(2)\n\nreduction\ formulas:\ cos(90^o+\alpha)=-sin\alpha
cos(180^0- \alpha )=-cos \alpha \n \n cos135^0=cos(180^0-45^0)=-cos45^0=- ( √(2) )/(2)
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