MATHEMATICS MIDDLE SCHOOL

Solve each equation by completing the square. If necessary, round to the nearest hundredth.19. X²-18x=19
20. 4 a²+8a-20=0

Answers

Answer 1
Answer: x^2-18x=19\n\nx^2-2x\cdot9+9^2-9^2=19\n\n(x-9)^2-81=19\n\n(x-9)^2=19+81\n\n(x-9)^2=100\iff x-9=\pm√(100)\n\nx-9=-10\ \vee\ x-9=10\n\nx=-10+9\ \vee\ x=10+9\n\nx=-1\ \vee\ x=19



4a^2+8a-20=0\ \ \ \ /:4\n\na^2+2a-5=0\n\na^2+2a\cdot1+1^2-1^2=5\n\n(a+1)^2-1=5\n\n(a+1)^2=5+1\n\n(a+1)^2=6\iff a+1=\pm\sqrt6\n\na=-\sqrt6-1\ \vee\ a=\sqrt6-1\n\na\approx-3.45\ \vee\ a=\approx1.45

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rita is make chili the recipe calls for 2 3/4 cups of tomatoes. How many cups of tomatoes,written as a fraction greater than one, are used in the recipe?

Answers

Given:
2 3/4 cups of tomatoes.

Number of cups of tomatoes written as a fraction greater than one.

2 3/4 is a mixed fraction. It is called such because it is a combination of a whole number and a fraction.

To find the number of cups of tomatoes written as fraction greater than 1, we need to convert the mixed fraction into an improper fraction.

Improper fraction is a fraction whose numerator is greater than its denominator.

2 3/4 ⇒ ((2*4)+3)/4 ⇒ (8+3)/4 ⇒ 11/4

11/4 is a fraction greater than one.

4/4 is a fraction that is equal to one.  So, any numerator that is greater than 4 is a fraction that is greater than one. In this case, it is 11/4.

Answer: 11/4

Step-by-step explanation:

4+4+3=11

11/4

How to solve 0.5(5-7x)=8-(4x+6)

Answers

\frac { 1 }{ 2 } \left( 5-7x \right) =8-\left( 4x+6 \right) \n \n \frac { 1 }{ 2 } \left( 5-7x \right) =8-4x-6

\n \n \frac { 1 }{ 2 } \left( 5-7x \right) =2-4x\n \n \frac { 1 }{ 2 } \left( 5-7x \right) =2\left( 1-2x \right) \n \n 2\cdot \frac { 1 }{ 2 } \left( 5-7x \right) =2\cdot 2\left( 1-2x \right)

\n \n 5-7x=4\left( 1-2x \right) \n \n 5-7x=4-8x\n \n -7x+8x=4-5\n \n x=-1

Hey! Just answering so the other guy can have brainiest! Hope this helped!

In a fraction, this is the number under the fraction bar.

Answers

The number under the fraction bar is referred to as the denominator. The number over the fraction bar is called the numerator.
Hope that helped =)
The number under the fraction is called the Denominator

More info: The number above the fraction is called the Numerator

What is the area of the figure?

Answers

I have already answered it

We first divide the big shape into smaller shapes

We get a trapezium and a triangle

We add the areas of the trapezium and the triangle together to get the total area of the big shape
It would be:

Area = area of trapezium + Area of triangle
         =(1)/(2) × 5 (14 + 18) + (1)/(2) × 12 × 18
         = 80  +  48  
         = 128 mm²

I need help with this!!! Which has a greater area, a triangle with a base of 100 feet and a height of 100 feet or a circle with diameter of 100 feet, please justify your selection.

Answers

I believe it is a Triangle with a base of 100 ft. and a height of 100 ft. 
Yet that's what I learned in class, my teacher isn't paying attention to much of our lessons, so forgive me if this is wrong. 

The Martin family's truck gets an average of 25 miles per gallon. Predict how many milrs they can drive using 7 gallons of gas.

Answers

If the Martin family's truck gets an average of 25 miles per gallon. The distance they can drive using 7 gallons of gas will be 175 miles.

What are arithmetic operations?

The study of numbers and their operations, which are relevant to all other fields of mathematics, is part of the discipline of arithmetic operations. Addition, subtraction, multiplication, and division are the basic operations that make up this system.

It is given that, the Martin family's truck gets an average of 25 miles per gallon.


We have to find the number of miles they can drive using 7 gallons of gas.

We'll apply division by Splitting into equalhalves or groups, the division may be used to decide how to distribute fuel evenly among a group.


The distance they can drive for the 7 gallons of gas will be,

=25 miles per gallon × 7 gallons

=175 miles

Thus, if the Martin family's truck gets an average of 25 miles per gallon. The distance they can drive using 7 gallons of gas will be 175 miles.

Learn more about the arithmeticoperations here,

brainly.com/question/25834626

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Okay so on average if they can go 25 miles per gallon that would mean you could just multiply 25 and 7 to get 175. So on average they could go 175 miles on 7 gallons of gas. Keep in mind that the answer can and will change depending on traffic, how fast or slow they are going, and if they are traveling behind a big-rig that moves more air that would normally be putting pressure on the car to push out of the way  but the big-rig helps save gas but it can also waste more gas if they are driving slower then normal.
Sorry for the extra information once I start it's hard to stop. Any way I hope this helps.
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