MATHEMATICS HIGH SCHOOL

Find the area bounded by the curve y=x2 and the straight line y=2+xA.4 1/6
B. 4 1/2
C. 5 1/6
D. 5 1/2

Answers

Answer 1
Answer: x^2=2+x\n x^2-x-2=0\n x^2+x-2x-2=0\n x(x+1)-2(x+1)=0\n (x-2)(x+1)=0\n x=2 \vee =-1\n\n \displaystyle A=\int \limits_(-1)^22+x-x^2\, dx\n A=\left[2x+(x^2)/(2)-(x^3)/(3)\right]_(-1)^2\n A=2\cdot2+(2^2)/(2)-(2^3)/(3)-\left(2\cdot(-1)+((-1)^2)/(2)-((-1)^3)/(3)\right)\n A=4+2-(8)/(3)-\left(-2+(1)/(2)+(1)/(3)\right)\n A=6-(8)/(3)+2-(1)/(2)-(1)/(3)\right)\n A=8-(9)/(3)-(1)/(2)\n A=8-3-(1)/(2)\n A=5-(1)/(2)\n A=4(1)/(2)

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MARKIN BRAINIEST !!!

Answers

your answer is option D

A store is having a sale on walnuts and chocolate chips. For 4 pounds of walnuts and 8 pounds of chocolate chips, the total cost is $25. For 2 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $10. Find the cost for each pound of walnuts and each pound of chocolate chips.

Answers

Answer:

The cost of each pound of walnuts is $1.25 and each pound of chocolate chips is $2.50

Step-by-step explanation:

Let,

x be the price per pound of walnuts

y be the price per pound of chocolate chips

According to given statement,

4x+8y=25     Eqn 1

2x+3y=10      Eqn 2

Multiplying Eqn 2 by 2

2(2x+3y=10)

4x+6y=20    Eqn 3

Subtracting Eqn 3 from Eqn 1

(4x+8y)-(4x+6y)=25-20

4x+8y-4x-6y=5

2y=5

Dividing both sides by 2

(2y)/(2)=(5)/(2)\ny=2.50

Putting y=2.50 in Eqn 2

2x+3(2.50)=10

2x+7.50=10

2x=10-7.50

2x=2.50

Dividing both sides by 2

(2x)/(2)=(2.50)/(2)\nx=1.25

Hence,

The cost of each pound of walnuts is $1.25 and each pound of chocolate chips is $2.50

The point (–3, 5) has been reflected so that the image is at (5, –3). What is the line of reflection?

Answers

Hello,
the line is the  perpendicular bisector of A(-3,5) and B(5,-3)

Let M the middle of AB
M=((-3+5)/2,(5+(-3))/2)=(1,1)
Slope of AB= (-3-5)/(5+3)=-8/8=-1
Slope of the perpendicular : -1*?=-1=>?=1
Equation :y-1=1*(x-1)==>y=x

The sum of two consecutive integers is 183. What is the smaller integer?

Answers

91

Explanation: Since the ones digit ends in a 3, that means the the ones digits of the two consecutive integers must be 1 and 2 or 6 and 7. However, you see 18 in the number 183. 9 + 9 = 18. When you add 6 and 7, you have to carry over one. However, when you add 1 and 2, you do not. Therefore, the two consecutive numbers are 91 and 92. 91 is the smaller integer, so that is the answer.

Answer:

yes the answer is 91

Step-by-step explanation:

i took the test and i got that one correct

Diana usually drives at average rate of 30 mph.If Diana drives for two hours with the speed of x mph, what distance will she cover?
PLZZZZZZZZZZZZZ HELP QUICK I WILL MAKE BRAINLIST

Answers

The total distance would be 60 miles traveled by Diana drives for two hours with a speed of 30 mph.

What is Average speed?

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

We have been given that Diana usually drives at an average rate of 30 mph.

she drives for two hours with the speed of 30 mph,

To determine the distance will she cover

Average speed = total distance / total time

Here total time = two hours and the average speed = 30 mph

30 mph = total distance / two hours

total distance = 30 × 2

total distance = 60 miles

Therefore, the total distance would be 60 miles traveled by Diana drives for two hours with a speed of 30 mph.

Learn more about the average speed here :

brainly.com/question/12322912

#SPJ2

Answer: 2x

Step-by-step explanation

Its 2x because we  dont know the speed so we just put the x and the 2 is the hours so its 2x.

Determine the domain of the function.

Answers

\left\{\begin{array}{ccc}x+4\geq0&(1)\n(x+2)(x-5)\neq0&(2)\end{array}\right\n\n(1)\ x+4\geq0\ \ \ |-4\nx\geq-4\to x\in\left\ \textless \ -4;\ \infty\right)\n\n(2)\ (x+2)(x-5)\neq0\iff x+2\neq0\ \wedge\ x-5\neq0\n\nx\neq-2\ \wedge\ x\neq5\n\n\text{The domain:}\n\nx\geq-4\ \wedge\ x\neq-2\ \wedge\ x\neq5\n\nx\in\left\ \textless \ -4;\ -2\right)\ \cup\ (-2;\ 5)\ \cup\ (5;\ \infty)
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