MATHEMATICS MIDDLE SCHOOL

Find the equation of the line that is a vertical line that passes through(-6, -1)

Answers

Answer 1

Answer:

Answer:

$x = - 6$

Step-by-step explanation:

The equation of a vertical line through an ordered pair is given by:

$x = x - value$

The given ordered pair is (-6,-1).

The x-value of this ordered pair is -6.

Therefore the equation of the line that is a vertical line that passes through(-6, -1) is

$x = - 6$

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A triangle is shown. What is the length, in inches, of side a?

Answers

Using trigonometric ratios, the length in inches of the given triangle is 22 inches.

Given a right angled triangle.

The length of the hypotenuse is also given.

We can find the length of "a" using the sine trigonometric ratio.

We know that,

Sine of any angle is defined as the ratio of the opposite side to the hypotenuse of a right angled triangle.

Using the sine function here for the angle 30°,

sin (30°) = opposite side / adjacent side

sin (30°) = a / 44

Or,

a / 44 = sin (30°)

We know that sin (30°) = 1/2.

So,

a / 44 = 1/2

Multiplying both sides by 44, we get,

a = 44 / 2

a = 22 inches

Hence the length is 22 inches.

To learn more about Trigonometric Ratios, click on the linkhere :

brainly.com/question/29156330

#SPJ1

Answer:

Step-by-step explanation:

Write a problem that can be solved using a flowchart and working backward. Then draw the flowchart and solve the problem.

Answers

I'm sorry but do you ha e a picture of a flowchart

list the following rational numbers in order from least to greatest. -0.4 , 0.48, 4/8, -4/8. Someone plssssssss help me I need it for today.

Answers

For a problem like this, it is best to convert all numbers to a similar form making them easier to compare. I am going to convert them all to decimals, although converting them all to fractions can also work.
-0.4 is already a decimal, so it needs no conversion; the same goes for 0.48.
4/8 is equal to 1/2, which equals 0.5 as a decimal. -4/8 is the same as -1/2, which is -0.5.
Therefore, we are left with the following converted numbers:
-0.4; 0.48; 0.5; -0.5

Now to simply order them from least to greatest, we will start with the two negative numbers because they are both below zero. When comparing negative numbers, the "bigger" one is actually smaller because it is farther below zero. Therefore, -0.5 is the smallest, followed by -0.4.

Now for the last two, 0.5, or 0.50, is 0.02 bigger than 0.48. Therefore, 0.48 is the second largest number and 0.5 is the largest.

This is the order now:
-0.5 (smallest)
-0.4 (2nd smallest)
0.48 (2nd largest)
0.5 (largest)

Now they simply need to be converted back to their original form (if applicable):
-0.5 = -4/8
-0.4 = -0.4
0.48 = 0.48
0.5 = 4/8

This leaves us with the answer:
-4/8; -0.4; 0.48; 4/8

What is the scientific notation of 8,795,000

Answers

$8,\underbrace{795,000}_(\leftarrow6)=8.795\cdot10^6$

$boxed{8,795,000=8.795*10^(6)}$

DIRECTIONS: Draw a picture to represent each problem. Then, usethe Pythagorean Theorem to answer the question. Answer each
question in a complete sentence.

1. Your family wants to purchase a new laptop with a 17” widescreen. Since the 17
inches represents the diagonal measurement of the screen (upper corner to lower
corner), you want to find out the actual dimensions of the laptop. When you
measured the laptop at the store, the height was 10 inches, but you don’t
remember the width. Calculate and describe how you could figure out the width of
the laptop to the nearest tenth inch.

2. The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a
wall. When the top of the ladder is leaned against the wall, what is the distance
above the ground it will reach?

Answers

Pythagorean theorem is: a^2+b^2=c^2

1. 10^2+b^2=17^2
So 100+b^2=289
b^2=189
b= $√(189)$
b=13 3/4
The dimensions are 10 by 13 3/4

2. 5^2+b^2=13^2
So 25+b^2=169
b^2=144
b=12
The ladder reaches 12 feet off the ground

Find all possible value of the given variable 1.h²+5h=0
2.z²-z=0
3.m²+13m+40=0
4.z²-3z=0
5.q²+7q=0
6.k²+2k=0
7.x²-3x-70=0
8.q²+7q-60=0
9.z²+9z-36=0
10.d²-13d+22=0

Answers

$1.\n \n h^2+5h=0 \n \nh(x+5)=0\n \nx=0 \ \ \ or \ \ \ x+5 =0\ \ |-5\n \nx+5-5=0-5\n \nx=0 \ \ \ or \ \ \ x=-5$

$2.\n \n z^2-z=0\n \nz(x-1)=0\n \nz=0 \ \ \ or \ \ \ z-1 =0 \ \ | +1\n \nz-1+1 =0 +1 \n \nx=0 \ \ \ or \ \ \ z=1$

$3.\n \nm^2+13m+40=0 \n \na=1 ,\ b=13, \ c=40 \n \n\Delta =b^2-4ac =13^2-4\cdot 1\cdot 40=169 - 1600=-1431 \n \nand \ we \ know \ when \ \Delta \ is \ negative, \ theres \ no \solution$

$4.\n \nz^2-3z=0 \n \n (z-3)=0\n \nz=0 \ \ \ or \ \ \ z-3 =0\ \ |+3\n \n z-3+3=0+3\n \nz=0 \ \ \ or \ \ \ z=3$

$5.\n \nq^2+7q=0 \n \nq(q+7)=0\n \nq=0 \ \ \ or \ \ \ q+7 =0\ \ |-7\n \nq+7-7=0-7\n \nq=0 \ \ \ or \ \ \ q=-7$

$6.\n \nk^2+2k=0\n \nk(k+2)=0\n \nk=0 \ \ \ or \ \ \ k+2 =0\ \ |-2\n \nk+2-2=0-2\n \nk=0 \ \ \ or \ \ \ k=-2$

$7. \n \n x^2-3x-70=0 \n \na=1,\ b=-3, \ c=-70 \n \n\Delta =b^2-4ac = (-3)^2-4\cdot 1\cdot (-70)= 9+280=289\n \n x_(1)=(-b-√(\Delta) )/(2a)=(3-√(289))/(2 )=( 3-17)/(2)=(-14)/(2)=-7$

$x_(2)=(-b+√(\Delta) )/(2a)=(3+√(289))/(2 )=( 3+17)/(2)=(20)/(2)=10\n \n(x+7)(x-10)=0$

$8.\n \nq^2+7q-60=0 \n \na=1,\ b=7, \ q=-60 \n \n\Delta =b^2-4ac = 7^2-4\cdot 1\cdot (-60)=49+240=289 \n \n x_(1)=(-b-√(\Delta) )/(2a)=(-7-√(289))/(2 )=( -7-17)/(2)=(-24)/(2)=-12$

$x_(2)=(-b+√(\Delta) )/(2a)=(-7+√(289))/(2 )=( -7+17)/(2)=( 10)/(2)= 5\n \n(x+12)(x-5)=0$

$9.\n \nz^2+9z-36=0 \n \na=1,\ b=9, \ q=-36 \n \n\Delta =b^2-4ac = 9^2-4\cdot 1\cdot (-36)= 81+144=225\n \n x_(1)=(-b-√(\Delta) )/(2a)=(-9-√(225))/(2 )=( -9-15)/(2)=(-24)/(2)=-12$

$x_(2)=(-b+√(\Delta) )/(2a)=(-9+√(225))/(2 )=( -9+15)/(2)=(6)/(2)=3\n \n(x+11)(x-3)=0$

$10.\n \nd^2-13d+22=0 \n \na=1,\ b=-13, \ q=22 \n \n\Delta =b^2-4ac = (-13)^2-4\cdot 1\cdot 22= 169-88=81\n \n d_(1)=(-b-√(\Delta) )/(2a)=(13-√(81))/(2 )=( 13-9)/(2)=(4)/(2)=2$

$d_(2)=(-b+√(\Delta) )/(2a)=(13+√(81))/(2 )=( 13+9)/(2)=(22)/(2)=11\n \n(d-2)(d-11)=0$

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