Solve The System Of Equations

Answer:

The answer is the slope of XV is 1.

The slope of UW is -1

The slopes of the diagonals are negative reciprocals

The diagonals of kite UVWX are perpendicular

Step-by-step explanation:

Negative reciprocals in a kite create a perpendicular bisector. So the two lines share a midpoint so they are perpendicular.

One of the diagonal of a kite has a slope that is equal to the inverse

multiplied by (-1)  of the other, therefore the diagonals are perpendicular

Reasons:

The proof that the diagonals of a kite are perpendicular is as follows;

The properties of a kite are;

The lengths of adjacent sides are equal

Therefore, taking the vertex at , U, as the origin, we have;

Coordinates of U = (0, 0)

Coordinates of V = (-a, b)

Coordinates of W = (0, c)

Coordinates of X = (a, b)

Step 1:

[tex]\displaystyle The \ slope \ of \ XV = \mathbf{ \frac{b - b}{x - (-x)} }=0[/tex]

The slope of XV is 0; XV is a horizontal line.

Step 2:

[tex]\displaystyle The \ slope \ of \ UW = \mathbf{\frac{c - 0}{0 - 0}} =\infty[/tex]

The slope of UW is infinity; UW is a vertical line.

Step 3:

The slope of the diagonals are; m₁ = 0, and m₂ = ∞

The above values satisfy the equation, [tex]\displaystyle m_2 = \mathbf{-\frac{1}{m_1}}[/tex]

Therefore;

Learn more about the characteristics of a kite here:

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Answer:

y = 10, x = 10sqrt3

Step-by-step explanation:

30-60-90 right triangles follow the ratio of x:xsqrt3:2x

In this case, 2x = 20, so y = x = 10, and x = xsqrt3 = 10sqrt3

If you are curious as to how to find these ratios, I suggest noticing that the 30-60-90 triangle is really just half of an equilateral triangle.

Answer:

x = 10sqrt(3) = 17.3

y = 10

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

short leg : long leg : hypotenuse

1 : sqrt(3) : 2

The short leg is half the hypotenuse.

hypotenuse = 20

short leg = y = 20/2 = 10

The long leg is sqrt(3) times the short leg.

long leg = x = 10sqrt(3) = 17.3

This is an isosceles trapezoid, because the two angles are supplementary on the right side.

y is 25 based on the Pythagorean theorem

w is sqrt (850)=29.15

z must be 15

Making a right triangle to look at the altitude

cos 59=a/15, so a is 7.73 between the right corner and the edge of x

That means x is 29.15-2(7.73)=13.69

=============

The median should be half way between 13.69 and 29.15

That is half their sum, or half of 42.84 or 21.42

That doesn't change the answer above

Once I know the trapezoid is isosceles, the angles at the base have to be 59d and the angles at the top 121d.

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Answer:

Step-by-step explanation:

Answer:

8x+7

Step-by-step explanation:

Use the given functions to set up and simplify  

(f+g)(x)

Answer:

8x + 7

Step-by-step explanation:

(f+g)(x)= f(x) +g(x) = 3x + 10 + 5x - 3 = 8x + 7

Answer:

the smallest prime factor of 52 is 2

Step-by-step explanation:

What is the smallest prime that is a factor of 52?

52 = 4*13, or 52 = 2*2*13.  So the smallest prime factor of 52 is 2.

Answer:

17.5

Step-by-step explanation:

The ratio of "pure drug" to liquid is 35:150

Therefore to evaluate for 75 mls we get the ratio 75/2150 or simply 1/2

we can then multiply 35 by the ratio 1/2

35/2=17.5

State the answer

In 75 mls there are 17.5 grams of pure drug

The amount of the pure drug in 75 ml will be 17.5 grams.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

The ratio of the two proportional items will remain the same.

The amount of the drug is directly proportional to the contained liquid.

If 35 gms of the pure drug are contained in 150 ml.

Then the amount of the pure drug in 1 ml will be

⇒ 35 / 150

⇒ 0.2333 grams per ml

Then the amount of the pure drug in 75 ml will be

⇒ 0.2333 x 75

⇒ 17.5 grams

The amount of the pure drug in 75 ml will be 17.5 grams.

More about the ratio and the proportion link is given below.

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Answer:

(x+2)(3x+8)

Step-by-step explanation:

Answer:

6 x(6x)+6x*-1+1(6x)+1*-1  SIMPLIFIED: 36x^2-1

Step-by-step explanation:

Use foil and distributive property

Answer:

The answer is A (97.5)

Step-by-step explanation:

Formula Using the Diagonals

That means the two diagonals form two sides of a square that is twice the size of the rhombus. You can find the area in square units of the rhombus by multiplying the lengths of the two diagonals (d1 and d2 ) and dividing by two.

(13)(15) /2 = 195 /2

(Decimal: 97.5)

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Answer:

96%

Step-by-step explanation:

Take the amount spent of fruit and divide by the total

48/50

Percent means out of 100 so multiply the top and bottom by 2

96/100

96%

Answer:

If Joe has a total of 50 dollars and uses only 48 dollars and you are trying find the percentage of how much he spent, all you need to do is take the amount of money he use dives it by how much money he had in the beginning. Then multiply the number by 100 to get the percentage.

48/50=.96

.96*100=96%

In total he spent 96% of his money.

Answer:

[tex]\frac{2}{7}+\sqrt{121}[/tex]

Step-by-step explanation:

Given: expressions

To find: expression that denotes a rational number

Solution:

A number of the form [tex]\frac{p}{q}[/tex] where p and q are integers and [tex]q\neq 0[/tex] is said to be a rational number.

Sum of a rational and irrational number is irrational.

In [tex]\frac{5}{9}+\sqrt{18}[/tex], [tex]\frac{5}{9}[/tex] is a rational number and [tex]\sqrt{18}[/tex] is an irrational number

So, [tex]\frac{5}{9}+\sqrt{18}[/tex] is not a rational number.

In [tex]\pi+\sqrt{16}=\pi+4[/tex], [tex]\pi[/tex] is an irrational number and 4 is a rational number

So, [tex]\pi+\sqrt{16}[/tex]  is not a rational number.

In [tex]\frac{2}{7}+\sqrt{121}=\frac{2}{7}+11=\frac{2+77}{7}=\frac{79}{7}[/tex], [tex]\frac{79}{7}[/tex] is a rational number

So, [tex]\frac{2}{7}+\sqrt{121}[/tex]  is a rational number

In [tex]\frac{3}{10}+\sqrt{11}[/tex], [tex]\frac{3}{10}[/tex] is a rational number and [tex]\sqrt{11}[/tex] is an irrational number

So, [tex]\frac{3}{10}+\sqrt{11}[/tex] is not a rational number.

Answer:

2 / 7 + 12

Step-by-step explanation:

he is right i  just took the test i just wanna help more ..

Answer:

120°

Step-by-step explanation:

you can divide the shape into 4 triangles

each triangle is 180°

180 x 4 = 720

720 divided by the number of angles (6) is 120

Answer:

120

Step-by-step explanation:

360/3=120

Answer:

Try this solution, it consists of two parts (MN=8).

Step-by-step explanation:

Answer:

Step-by-step explanation:

The rectangle in the middle has an area of 30 because it is a 3x10.  

The triangles each have an area of 6 because they are a 3x4 and the forumla to find it is .5(bh) which is .5(12)=6.  There are 2 of them so the total area of the triangles add up to 12.  

Add the area and get 42.  30+12=42

[tex]\text{First, simplify the equation into slope intercept form:}\\\\2y+3x=1\\\\2y=-3x+1\\\\\text{Divide by 2}\\\\y=-\frac{3}{2}x+1\\\\\text{Now, the perpendicular line is the opposite of the slope, and the opposite}\\\text{value}\\\\\text{Since our original equation is negative, the perpendicular lien will be positive}\\\\\text{And then you would just flip the fraction}\\\\\text{Your perpendicular line should be:}\\\\\boxed{y=\frac{2}{3}x+1}[/tex]

Answer:

AAA would be the answer

Step-by-step explanation:

The answer would be AAA because they both have equal angles. 90 and 45. Because they are vertical angles, where they intersect at S is also an congruent angle. Angle U is congruent to angle Q and so on.

Answer:

AAA

Step-by-step explanation:

Answer:

Step-by-step explanation:

Give jamila's Mean earning = $24

let her ninth earning be x

we know that mean= (∑sumation of earnings)/number of earnings

[tex]24= \frac{15+20+ 10+ 12+ 20+ 16+ 18+ 25+x}{9}[/tex]

[tex]24= \frac{136+x}{9} \\24*9=136+x\\216=136+x\\x=136-216\\x=80[/tex]

Her ninth earning is $80

Answer:

a

Step-by-step explanation:

2x +7= 19

2x= 19 -7 (-7 on both sides)

2x= 12 (simplify)

x= 12 ÷2

x= 6

Answer:

a

Step-by-step explanation:

Given

2x + 7 = 19 ( subtract 7 from both sides )

2x = 12 ( divide both sides by 2 )

x = 6

Answer:

Total weight of blades = ~134gm

Step-by-step explanation:

Radius of circle, [tex]r[/tex] = 4 inches

Central angle of sector = [tex]20^\circ[/tex]

For finding the weight of blades, we need to find the area of blades.

Area of circle, A = [tex]\pi r^{2}[/tex]

We know that circle has a central angle of [tex]360^\circ[/tex].

We can use unitary method to find the area of sector with angle [tex]20^\circ[/tex].

Area of [tex]360^\circ[/tex] central angle = [tex]\pi r^{2}[/tex]

Area of [tex]1^\circ[/tex] central angle = [tex]\dfrac{\pi}{360} r^{2}[/tex]

Area of [tex]20^\circ[/tex] central angle = [tex]\dfrac{\pi}{360} r^{2} \times 20[/tex]

Putting value of r = 4 inches

Area of blade:

[tex]\dfrac{\pi}{360} \times 4^{2} \times 20\\\Rightarrow 2.79\ in^{2}[/tex]

We have 3 blades here, so area of 3 blades =

[tex]2.79 \times 3\\\Rightarrow 8.38\ in^{2}[/tex]

Weight of steel = 16 grams per square inch

Total weight of all 3 blades = 16 [tex]\times[/tex] 8.38 = ~ 134gm

Answer:

X< -1.26

Step-by-step explanation:

Combine like terms and solve like any other two step equations

Answer:

X< -1.26

Step-by-step explanation:

Answer:

the answer

is b

i hope that helps

Answer:

Step-by-step explanation:

If a ball thrown downward from a window in a tall building is modeled by the equation, s = 16t² + 32t where s in feet, in order to know the time it will take to fall a distance of 276, we will substitute s = 276feet into the equation and calculate for the value of t as shown;

276 = 16t² + 32t

16t² + 32t = 276

Dividing through by 4

4t² + 8t = 69

4t² + 8t - 69 = 0

Using the general formula to find t

t = -b±√b²-4ac/2a

a = 4, b = 8 and c = -69

t = -8±√8²-4(4)(-69)/2(4)

t = -8±√64+1104/8

t = -8±√1168/8

t = -8±34.176/8

t = -8+34.176/8 or -8-34.176/8

t = 3.272 or -5.272

neglecting the negative time, t = 3secs to the nearest seconds

It will take the all 3secs to fall 276 feets

Answer:

-5

Step-by-step explanation:

Answer:

228 ft^2

Step-by-step explanation:

1/10 of the given dimensions are 9.5 ft by 8 ft by 3 ft.

The volume of the model is thus (9.5 ft)(8 ft)(3 ft) = 228 ft^2

Answer:

7 ft

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

153.86 = 3.14 r^2

Divide each side by 3.14

153.86 / 3.14 = r^2

49 = r^2

Take the square root of each side

sqrt(49) = sqrt(r^2)

7 = r

Answer:

m∠HLI = m∠ILM

Step-by-step explanation:

Answer:

[tex]4x^2 + 12x + 8[/tex]

Step-by-step explanation:

Area of rectangle

= height * width

[tex]=4(x^2 +3x +2)\\= 4x^2 + 12x + 8[/tex]

Answer:

add 2 and 4

Step-by-step explanation:

x²+3x+6

Answer:

[tex] \boxed{f = -6} [/tex]

Step-by-step explanation:

[tex] = > - 7f - 9 = 9 - 4f \\ \\ = > - 7f + 4f - 9 = 9 \\ \\ = > - 3f = 9 + 9 \\ \\ = > - 3f = 18 \\ \\ = > 3f = - 18 \\ \\ = > f = - \frac{18}{3} \\ \\ = > f = - 6[/tex]