Write an equation of the line that passes through the points (3,6) and (4,9)

Step-by-step explanation:

a rectangle has two pairs of equally long sides and each of the 4 angles between the sides is 90 degrees.

given that ABCDEF is a regular hexagon, it means that all its sides are equally long, and therefore also all internal angles are the same size.

that means for ACDF that the sides DC and FA are equally long.

DEF and ABC are congruent triangles, as the sides DE = BC, EF = AB, and the angle E is congruent to angle B.

based on the SAS criteria this confirms that DF is congruent to AC.

the angles ACB, CAB, EDF and EFD have to be all the same, and therefore also the angles FDC, DCA, CAF and DFA.

so, all 4 angles of the parallelogram ACDF are the same, and the sum of all these angles has to be 360 degrees, we have

360 = 4×angle

angle = 90 degree.

so, all angles are 90 degrees and we have two pairs of equally long sides : this process that ACDF us a rectangle

Answer:

Step-by-step explanation:

In the standard form of a quadratic,

[tex]h(x)=-x^2+v_0x+h_0[/tex],

that last term, the h0, is the initial height off the ground that the object is. That means that for the first question, the irrigation system is initially 9.5 feet off the ground.

In order to answer the next question, we need to find the vertex of the parabola, because this is where the max height will occur and at how many feet away from the system. The max height is the k of the vertex and the horizontal distance away is the h of the vertex: (h, k). Thankfully, we have simple formulas to find those:

[tex]h=-\frac{b}{2a}[/tex]  and  [tex]k=c-\frac{b^2}{4a}[/tex]  where a, b, and c come from the coefficients in the equation. For us, a = -1, b = 10, and c = 9.5. Finding h first:

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

and now k:

[tex]k=9.5-(\frac{10^2}{4(-1)})=9.5-(\frac{100}{-4} )=9.5-(-25)=9.5+25=34.5[/tex]

Summing it up, the vertex is at (5, 34.5), The interpretation of that is that "The spray reaches a max height of 34.5 feet at a horizontal distance of 5 feet away from the sprinkler head."

Next we are asked how far away from the sprinkler head the water hits the ground. To do this we factor the expression to find the zeros. The zeros tell us where the water will hit the ground after it reaches its max height and then falls back down to earth.

I used my calculator to factor this for me to get that the water will hit the ground 10.87 feet away from the sprinkler head.

Answer:

D

Step-by-step explanation:

[tex]8x \sqrt{2} - 4 \sqrt{2} [/tex]

Answer:

7

Step-by-step explanation:

total mnm 16

group 1= 4 mnm

group 2= x mnm

group 3= x mnm

group 1+ group 2+ group 3= 16

4+ x+x=16

2x= 16-4

x= 14/2

x=7

Answer:

14

Step-by-step explanation:

The formula for the area of a triangle is: 1/2 times base times height.

1/2x8x3.5=14

Answer:

x = -3 or x = -5

Step-by-step explanation:

x (x -2 ) = -5

x = -5 or x = -5+2

x = -3

Answer:

P(black|coin fell tails) = ¼

Step-by-step explanation:

Since a coin has a head and a tail, then probability of landing tail is;

P(tail) = ½

Now, if it falls tails, a marble is drawn from Box 2, which contains two white and two black marbles.

Thus, probability of getting a black marble is; 2/4 = ½

Thus;

P(black|coin fell tails) = ½ × ½ = ¼

Step-by-step explanation:

Hey there!

Here;

f(x) = 2x²-x+1

g(X) = x²+3x-3

Since f(X) = g(X);

2x²-x+1 = x²+3x-3

2x²-x²-x-3x+1+3 = 0

x²-4x+4 = 0

(x-2)² = 0

Therefore, the value of X is 2.

Hope it helps!

Step-by-step explanation:

Explanation is in the attachment

Hope it helpful to you

Answer:

50^(2)

Step-by-step explanation:

(30+20)*50=50*50=50^(2)

Answer: -17, 17, -3, 3, -7, 7,

Step-by-step explanation:

Find all Factors of -18, (got -18 from multiplying 6 and -3)

Add the factors together. (+/- 6 and +/- 3), (+/-9 and +/-2), (+/-18 and +./-1)

Answer:

2020³-1/4041

Step-by-step explanation:

Answer:

74 degrees

.................

Answer:

74

Step-by-step explanation:

BEC and CED form a straight line so they add to 180

BEC+CED = 180

106+ CED = 180

CED = 180-106

CED = 74

E is halfway between A and C

coordinates are

-2a , -2b

you could basically see it in the picture.

the formula is alrdy given, so I just gave you the solution

Answer: C

Step-by-step explanation:

To solve for 12, we can use eliminate or substituion to solve our system of equations. Let's use elimination method.

[tex]\left \{ {{3f-2k=10} \atop {-3f-2k=14}} \right.[/tex]

Let's add the equations together. This way, 3f+(-3f)=0

[tex]-4k=24[/tex]                   [divide both sides by -4]

[tex]k=-6[/tex]

Now that we know k, we can plug it into either equation to find f.

[tex]3f-2(-6)=10[/tex]        [multiply]

[tex]3f+12=10[/tex]             [subtract both sides by 12]

[tex]3f=-2[/tex]                    [divide both sides by 3]

[tex]f=-\frac{2}{3}[/tex]

Now that we have f and k, we know that C is the correct answer.

The simplification of the expression is  [tex]\frac{15\sqrt{2} }{4}[/tex]

First, find the factors of the number that ahs square root

Given,

= [tex]\frac{5}{\sqrt{2} } + \frac{9}{\sqrt{6} } - \frac{2}{\sqrt{50} } + \sqrt{32}[/tex]

Multiply the numerators by the surd of the denominators

= [tex]\frac{5 *\sqrt{2} }{\sqrt{2}*\sqrt{2 } } + \frac{9 *\sqrt{8} }{\sqrt{8}* \sqrt{8} } - \frac{2 *\sqrt{50} }{\sqrt{50 * \sqrt{50} } } + \sqrt{32}[/tex]

Multiply through and find their square root

= [tex]\frac{5\sqrt{2} }{2} + \frac{18\sqrt{2} }{8 } - \frac{10\sqrt{2} }{50} + 16\sqrt{2}[/tex]

To simply, we have

= [tex]\frac{5\sqrt{2} }{2}+ \frac{9\sqrt{2} }{4} + \frac{1\sqrt{2} }{5} + 16\sqrt{2}[/tex]

Find the LCM

= [tex]\frac{10\sqrt{2} + 45\sqrt{2}+ 4\sqrt{2} + 16\sqrt{2} }{20}[/tex]

Add through

= [tex]\frac{75\sqrt{2} }{20}[/tex]

= [tex]\frac{15\sqrt{2} }{4}[/tex]

Thus, the simplification of the expression is  [tex]\frac{15\sqrt{2} }{4}[/tex]

Learn more about surds here:

https://brainly.in/question/4594146

#SPJ1

Answer:

Step-by-step explanation:

draw a parallel line to x at a distance of 23 cutting the quadrilateral in two points.

A right angle is formrd at the bottom.

Hypotenuse=59

one side=45-23=22

x= other side=√(59²-22²)=√(59-22)(59+22)=√((37)(81))=9√(37)≈54.74

Answer:

20 big bottles

14000 ml

Step-by-step explanation:

Let :

Small bottles = x ; big bottles = y

Capacity of small bottle = 400ml

Capacity of big bottle = 600 ml

Edwina :

Number of small bottles = 5

Georgi :

Number of big bottles = 16

Since Numbe of bottles are siad to be the same :

5 + y = 16 + x

y - x = 16 - 5

y - x = 11

y = 11 + x - - - (1)

Total capacity of Edwina's bottle is 800 ml more Than Georgi's total :

Edwina :

5(400) + 600y

Georgi :

400x + 16(600)

2000 + 600y = 800 + 400x + 9600

2000 + 600y = 10400 + 400x

600y - 400x = 10400 - 2000

600y - 400x = 8400 - - - (2)

Substitute y = 11+x for y in (2)

600(11+x) - 400x = 8400

6600 + 600x - 400x = 8400

200x = 8400 - 6600

200x = 1800

x = 1800 / 200

x = 9

Number of big bottles Edwina has :

y = 11 + x

y = 11 + 9

y = 20

Total capacity of Edwina's bottles :

5(400) + 600y

2000 + 600(20) = 2000 + 12000 = 14000 ml

The shape is an irregular pentagon

Answer:

x

[tex]x \leqslant - y + 1[/tex]

Steps are show in the picture above.

Answer:

i cannot understand

Step-by-step explanation:

Answer:

X=0

Step-by-step explanation:

5(6-X)-3=5+4(X+3)

30-5x=5+4x+12

30-5-12=4x+5x

13=9x

13/9=x

Answer:

Use BODMAS rule

1st:B- solve bracket

2nd-O- open bracket

3rd;D:divide

4th:M- multiply

5th:A- Addition

6th :Subtract

Solution given;

5 (6 - x) - 3 = 5 + 4 (x + 3)

open bracket

30-5x-3=5+4x+12

30-3-5-12=5x+4x

10=9x

x=10/9

x=10/9

Answer:

see explanation

Step-by-step explanation:

Given (x - m) is a factor of both then x = m make both expressions equal to zero.

m² - am + b = 0

m² - cm + d = 0

Then

m² - am + b = m² - cm + d ( subtract m² - cm from both sides )

cm - am + b = d ( subtract b from both sides )

cm - am = d - b ← factor out m from each term on the left side

m(c - a) = d - b ← divide both sides by (c - a)

m = [tex]\frac{d-b}{c-a}[/tex] ← as required

Answer:  2/1  (Choice D)

Explanation:

He flipped the coin 39 times, of which 26 heads came up. That must mean 39-26 = 13 tails came up.

The ratio of heads to tails is 26/13 = 2/1

We can write that as 2:1 to mean similar notation. The key is that we list heads first since the phrasing is "ratio of heads to tails", where heads is listed first. If you had tails first, then it would flip to 1/2 aka 1:2

Answer:

Step-by-step explanation:

first we need to calculate the area of isosceles triangle having sides 48cm, 48cm and 30cm

a = 48

b= 30

Area of isosceles triangle using only sides = ½[√(a^2 − b^2 /4) × b]

= 1/2*30√( 48² - 1/4×30²)

=1/2*30√ (2304 -225)

=684sq cm

cost required to make umbrella= 10*684*5

= 34200

9514 1404 393

Answer:

Step-by-step explanation:

Arc DV is 100°, so any inscribed angle that intercepts that arc will have a measure that is half of 100°, or 50°.

Inscribed angles DCV and VBD both intercept arc DV, so both are 50°.