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3 years ago

A line passes through the point (-3, -3) and has a slope of 1/2 What is the equation of the line?

1 answer:

3 0

Y-y1=m(x-x1)
(x1,y1) is a given point
m=slope
y-(-3)=1/2(x-(-3))
y+3=1/2(x+3) is an equation

2x+3y=6
x+y=4
multiply second equation by -2 and add to first

2x+3y=6
-2x-2y=-8 +
0x+1y=-2

y=-2
sub back

x+y=4
x-2=4
add 2
x=6

x=6
y=-2
(6,-2)

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Maci and I are making a small kite. Two sides are 10". Two sides are 5". The shorter diagonal is 6". Round all your answers to t

Art [367]

Answer:

A. 4".

B. Approximately 9.54".

C. Approximately 13.54".

Step-by-step explanation:

Please find the attachment.

Let x be the distance from the peak of the kite to the intersection of the diagonals and y be the distance from the peak of the kite to the intersection of the diagonals.

We have been given that two sides of a kite are 10 inches and two sides are 5 inches. The shorter diagonal is 6 inches.

A. Since we know that the diagonals of a kite are perpendicular and one diagonal (the main diagonal) is the perpendicular bisector of the shorter diagonal.

We can see from our attachment that point O is the intersection of both diagonals. In triangle AOD the side length AD will be hypotenuse and side length DO will be one leg.

We can find the value of x using Pythagorean theorem as:

$(AO)^2=(AD)^2-(DO)^2$

$x^{2}=5^2-3^2$

$x^{2}=25-9$

$x^{2}=16$

Upon taking square root of both sides of our equation we will get,

$x=\sqrt{16}$

$x=\pm 4$

Since distance can not be negative, therefore, the distance from the peak of the kite to the intersection of the diagonals is 4 inches.

B. We can see from our attachment that point O is the intersection of both diagonals. In triangle DOC the side length DC will be hypotenuse and side length DO will be one leg.

We can find the value of y using Pythagorean theorem as:

$(OC)^2=(DC)^2-(DO)^2$

Upon substituting our given values we will get,

$y^2=10^2-3^2$

$y^2=100-9$

$y^2=91$

Upon taking square root of both sides of our equation we will get,

$y=\sqrt{91}$

$y\pm 9.539392$

$y\pm\approx 9.54$

Since distance can not be negative, therefore, the distance from intersection of the diagonals to the top of the tail is approximately 9.54 inches.

C. We can see from our diagram that the length of longer diagram will be the sum of x and y.

$\text{The length of the longer diagonal}=x+y$

$\text{The length of the longer diagonal}=4+9.54$

$\text{The length of the longer diagonal}=13.54$

Therefore, the length of longer diagonal is approximately 13.54 inches.

3 0

3 years ago

Is a percent a number?

mars1129 [50]

Yes, percent is a number.

7 0

3 years ago

Read 2 more answers

How can you tell if the solution is one value,all real numbers,or no solutions

zysi [14]

One value: would be a single valued function, or just one answer.

Real numbers would be: natural numbers, whole numbers, integers, rational numbers (fractions and repeating or terminating decimals), and irrational numbers.

No solution: there is no answer to the question.

8 0

3 years ago

Identify two composite numbers that each have 8 as a factor.

Dima020 [189]

A composite number, we remember, is a whole number (no decimals or fractions) that can evenly divide (again, into no fractions or decimals) into two numbers other than itself and 1 (sort of the opposite of a prime number). So, 8 needs to be one of the two numbers. Pick another number--any whole number--and multiply it by 8. The result will be your composite number. Two examples: 8 times 6 equals 48. This works as 48 divided by 8 equals 6, both of which are whole numbers other than 48. Another is 72, the product of 8 times 9.

5 0

3 years ago

Resuelve el siguiente problema un buzo en una laguna decendio 8m en una hora.Si cada hora bojo la misma cantidad de metros, ¿cua

S_A_V [24]

Answer:

X = 32 meters.

Step-by-step explanation:

Let the unknown distance be X.

Given the following data;

Distance = 8 meters per hour
Time = 4 hours

To find how many meters he would cover in four hours;

1 hour = 8 meters

4 hours = X meters

Cross-multiplying, we have;

X = 8 * 4

X = 32 meters.

7 0

3 years ago