find the gradient and y- intercept of the line with equation 2x+3y-7=0

Step-by-step explanation:

2 things to remember for problems like this :

the sum of all angles in a triangle is always 180 degrees.

the law of sines :

a/sin(A) = b/sin(B) = c/sin(C) or upside-down (whatever fuss the situation better), with the sides being always opposite of the angles.

so, now for the given problems :

4.

x/sin(90) = 12/sin(29)

x/1 = x = 12/sin(29) = 24.75198408...

rounded x = 24.8

5.

the opposite angle of x is

180 - 90 - 16 = 74 degrees.

x/sin(74) = 37/sin(90) = 37

x = 37×sin(74) = 35.56668275...

rounded x = 35.6

6.

the opposite angle of x is

180 - 90 - 58 = 32 degrees.

x/sin(32) = 22/sin(58)

x = 22×sin(32)/sin(58) = 13.74712574...

rounded x = 13.7

7.

the opposite angle of 15 is

180 - 90 - 51 = 39 degrees.

x/sin(51) = 15/sin(39)

x = 15×sin(51)/sin(39) = 18.52345735...

rounded x = 18.5

Answer:

29

Step-by-step explanation:

The formula for calculating degrees of freedom in a t-test is n-1 where n is the sample size. Therefore, there are 30-1=29 degrees of freedom if the sample size is n=30.

Use the Pythagorean Theorem  [tex]a^2 + b^2 = c^2[/tex].

Since we have 2 sides we can easily solve for the third.

[tex]c^2 = 10^2 + 14 ^2[/tex]

[tex]c = \sqrt{100 + 196}[/tex][tex]= \sqrt{296}[/tex] ≈[tex]17.205[/tex]

Answer:

y - 9 = m(x + 3)

Step-by-step explanation:

Given a line whose slope is m, the slope of a new line that is perpendicular to the given line is the negative reciprocal of m:  -1/m

Given y = 2x + 8, we see that the slope is 2 and figure that the negative reciprocal of that is -1/2.  This is the slope of the desired perpendicular line.

We can write the equation of this perpendicular line most easily by using the point-slope form y - k = m(x - h), where (h, k) represents the point:

y - 9 = m(x + 3)

The outline that that illustrate how k values change so that the solutions are the ones in the question are as follows

(a) The number line solution contains zero

Using algebra, we have;

The given quadratic inequality is; -x² + 4 ≥ x + k

The number line solution is the expression of the solution on the number line.

We have;

-x² + 4 ≥ x + k

-x²  - x + 4 - k ≥ 0

Dividing by (-1), we get;

x² + x - 4 + k ≤ 0

When - 4 + k = -2

k = 2, we get;

x² + x - 4 + 2 ≤ 0

x² + x - 2 ≤ 0

(x - 1)·(x + 2) ≤ 0

Given that the result of the product is less than zero, we have;

((-3) - 1)·((-3) + 2) > 0

Therefore, the solution are;

x ≤ 1, or x ≥ -2

Which gives

-2 ≤ x ≤ 1

The solution of the above inequality includes 0 as shown in the attached number line

The graph of the inequality is plotted using MS Excel, showing the solution set, of -2 ≤ x ≤ 1

(b) There are no solution to the inequality

In the present case, we have;

((-1)² - 4×(-1) × (4 - k) <  0

17 - 4·k < 0

[tex]k > \dfrac{17}{4}[/tex]

Let k = 5, we have;

-x² + 4 ≥ x + k

-x² - x + 4 - 5 ≥ 0

-x² - x  -1 ≥ 0

The discriminant, is (1² - 4×(-1)×(-1)) = -3 < 0, therefore, there are no real

roots to inequality, and -x² - x  -1 is not equal to zero.

Please find attached the graph of the function, which does not intersect with the x-axis, and therefore, has no values at which y = 0

(c) The solution is a single number

-x² + 4 ≥ x + k

When k = x + 5, we have;

0 ≥ x² + 2·x + 1

0 ≥ (x + 1)²

Therefore;

The only solution is; x = -1

Using diagrams:

Please find attached the solution of the function on the number line

The graph of the function showing only one intercept is attached

Learn more here:

https://brainly.com/question/11982012

Answer:

5^9

Step-by-step explanation:

I had this question before.

Answer:

212

Step-by-step explanation:

106 x 2= 212

Answer:

ok so when there is 106 bags of brownies there is two ways that u can do this that i can think of so u can do 106 + 106 which= 212 or 106 x 2 = 212 this one was pretty easy u got this feel free to ask more questions!

Step-by-step explanation:

Answer:

560 is your answer... I hope it helps

Answer:

50% is 0.5

10% is 0.1

75% is 0.75

Step-by-step explanation:

When multiplying to find the percent of a number, you make it a decimal by dividing it by 100.

Answer:

38.30

Step-by-step explanation:

because 230 -6x=0

Answer:

70°

Step-by-step explanation:

Since  PTS shape is equal to QTR

and  PTQ shape is equal to STR

and Since QTP = 10

and Since  PTS = 60

Add both up 70

Therefore PQR = 70°

Answer:

NEED TRANSLATOR

Step-by-step explanation:

ENGLISH PLEASE

Answer:

Step-by-step explanation:

Minimum number of regions

You may have 100 parallel lines. This will give us 101 regions

Use following formula to find the maximum possible number of regions:

Answer:

Add 6x to both sides.

y + 6x = -5

Reorder the left side so that the x term is first.

6x + y = -5

:)

Answer:

A football is a sphere, so the formula for calculating its surface area is 4πr²

Hope it helps:)

Ashley is incorrect, they’re traveling at the same rate. hope this helped

Answer:

8 feet

Step-by-step explanation:

5 + 3 = 8

Answer:

Step-by-step explanation: The school of salmon are now 8 feet below the surface. They start at -5 feet and then you subtract 3 more feet which gives you -8 feet. -5-3=8

Answer:

30

Step-by-step explanation:

d=√(24²+18²)=6√(4²+3²)=6√(16+9)=6√(25)=6×5=30

Answer: C

Step-by-step explanation:

Answer:

x= -2

Step-by-step explanation:

y=x+4

y=2

2=x+4

-4+2=x

-2=x

x=-2

Answer:

x= -2

Step-by-step explanation:

Answer:

Roughly £2

Step-by-step explanation:

multiply the echange rate by 2 , its 378Yen

Answer:

1. C.

2. A.

3. B.

i just know those im sorry-

Answer:

1 - c 6.4 ×10^6

2 - a 6.4 ×10

3- b 6.04 ×10^5

4) 5.21× 10^8 × 1.6km

=8.33×10^8 km

5) 10,000,000,000 = 1 ×10^10

BRAINLIST PLS

Step-by-step explanation:

You have to go to Y axis first then to X. For example : (4,5) go up 4 and go to x axis and when u get to 5 you put a dot. The same thing if is (-4,-5) go down 4 and to the left 5 and mark a dot. When you mark the dot put (_,_).

Hope you understand. Let me know if you don't.

Speed of car

Answer:

-5

Step-by-step explanation:

Answer:

the answer is £300.

..........

Answer:

383.07

Step-by-step explanation:

All the info

£1 = €1.13 What are we trying to do? Turn €339 into £.

Therefore 339 X 0.13=44.07 So 44.07+339=£383.07 making £383.07 the exchanged sum

Answer:

30

Step-by-step explanation:

Answer:

Step-by-step explanation:

For every 30 minutes she dances, Nell stretches for 10 minutes

Ratio:

Answer:

y + 2 = [tex]\frac{1}{5}[/tex] (x - 10)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{5}[/tex] x - 4 ← is in slope- intercept form

with slope m = [tex]\frac{1}{5}[/tex]

Parallel lines have equal slopes

The equation of a line in point- slope form is

y - b = m(x - a)

Here (a, b ) = (10, - 2 ) , then

y - (- 2) = [tex]\frac{1}{5}[/tex](x - 10) , that is

y + 2 = [tex]\frac{1}{5}[/tex](x - 10) ← in point- slope form