Solve some math, ooooo fun

Answer:

  DE ≈ 14.91

Step-by-step explanation:

Make use of the relationships between sides and angles in a right triangle. These are summarized by the mnemonic SOH CAH TOA:

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

__

The side DE is opposite the angle 19°, so the sine or tangent relation will be involved. The sine relation requires you know hypotenuse EF. The tangent relation requires you know adjacent side DF.

The only common side between triangles CDF and DEF is side DF. That side is opposite the given 61° angle. The given side length (CF = 24) is adjacent to the 61° angle.

This means you have enough information to use these relations:

  tan(61°) = DF/CF = DF/24

  DF = 24·tan(61°)

and

  tan(19°) = DE/DF

  DE = DF·tan(19°) = (24·tan(61°))·tan(19°) . . . . . use DF from above

  DE ≈ 24(1.804048)(0.344328) ≈ 14.908

The length of DE is about 14.91.

Answer: 28

Step-by-step explanation:

3 to the power of 3 is 3x3= 9 x3 = 27

27 divided by 3 = 9

9-2 = 7 x 4 = 28

The amount of water that should be mixed with 18 liters of 14% bleach solution to form 10% bleach solution is 7.2 liters.

The amount of water should be mixed with 1 liter of 14% bleach solution,

we know that the water will have 0% bleach. thus, the amount of water we need to mix with the 14% bleach solution is (2/5) liters.

Therefore, the ratio of water and bleach solution can be written as,

[tex]\rm \dfrac{14\%\ solution}{Water} = \dfrac{5}{2}[/tex]

We know the ratio of water and bleach solution that should be mixed to form a 10% concentration bleach is (5/2), therefore, we will use the same ratio,

[tex]\rm \dfrac{14\%\ solution}{Water} = \dfrac{5}{2}[/tex]

[tex]\rm \dfrac{18}{Water} = \dfrac{5}{2}\\\\\rm {Water} = \dfrac{18\times 2}{5}\\\\\rm Water = 7.2\ liters[/tex]

Hence, the amount of water that should be mixed with 18 liters of 14% bleach solution to form 10% bleach solution is 7.2 liters.

Learn more about Ratio:

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Answer:

PQ = 37 Km

Step-by-step explanation:

let PQ = x , then

PR =  x + 15 and QR = 3(x + 15) = 3x + 45

sum the parts and equate to 245

x + x + 15 + 3x + 45 = 245 , that is

5x + 60 = 245 ( subtract 60 from both sides )

5x = 185 ( divide both sides by 5 )

x = 37

then

PQ = x = 37 Km

Answer:

The answer is 969.3 miles

Step-by-step explanation:

1560 kilometers = 969.3 miles

Step-by-step explanation:

63.5*0.088 =5.588 tax for your answer

Answer:

Step-by-step explanation:

You can square both the sides and then use the formula for finding the roots of the obtained quadratic equation to find the solution needed.

The statements describing the solutions to the given equations are

Let the quadratic equation be [tex]ax^2 + bx + c = 0[/tex]

Then the solution to this quadratic equation is given as

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Those values of the variables who come out behaving like solutions but when tested, doesn't get proved as solutions to the given equation are called extraneous solutions.

Solutions to an equation means those values of the unknown for which the equation is true.

The given equation is

[tex]\sqrt{x-2} -4 = x - 6[/tex]

Converting that equation to quadratic form, we get

[tex]\sqrt{x-2} -4 = x - 6\\\\\sqrt{x-2} = x - 2\\[/tex]

From the obtained equation, we can see that x-2 is such a number whose square root is it itself. It is true for 2 numbers only.

First 1, and second 0.

Putting these values, we get

[tex]x-2 = 1\\x = 2+1 = 3\\\\x-2 = 0\\x = 2[/tex]

Thus, there are two solutions to the given equation. They are x = 2, and x = 3

Testing both the solutions by putting them in the given equation.

Case 1: x = 2

[tex]\sqrt{x-2} -4 = x - 6\\\sqrt{2-2} - 4 = 2 - 6\\0-4 = -4\\-4 = -4[/tex]

This is correct equality, thus, x = 2 is a correct solution.

Case 2: x = 3

[tex]\sqrt{x-2} -4 = x - 6\\\\\sqrt{3-2} - 4 = 3 - 6\\1 - 4 = -3\\-3 = -3[/tex]

This is correct equality, thus, x = 3 is a correct solution.

The zeroes(also called solutions) of [tex]x^2 - 5x + 6 = 0[/tex] is found as:

[tex]x^2 - 5x + 6 = 0\\x^2 - 3x - 2x +6 = 0\\(x-2)(x-3) = 0\\x = 2, x = 3[/tex]

Thus, the The zeroes(also called solutions) of [tex]x^2 - 5x + 6 = 0[/tex]  are possible solutions to the radical equation given.

Thus,

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Answer:

C and E are the correct answers.

Step-by-step explanation:

It's correct on Edgen. (2022)

Answer:

x= 7 and -8

Step-by-step explanation:

hope this helps!

Answer:

25% discount

Step-by-step explanation:

40-30=10

10= 25% of 40

Check the picture below.

Make sure your calculator is in Degree mode.

Transformation of a function is shifting the function from its original place in the graph.

The functions have a maximum and are transformed to the left and down of the parent function are,

[tex]q(x) = -5(x +10)^2 -1[/tex]

[tex]t(x) = -2x^2 - 4x - 3[/tex]

Thus the option B and E is correct.

Transformation of a function is shifting the function from its original place in the graph.

Types of transformation-

Given information-

The given function in the problem is,

[tex]f(x)=x^2[/tex]

The functions have a maximum and are transformed to the left and down of the parent function.

In the option B the function is shifted 10 units left and 1 units down as,

[tex]q(x) = -5(x +10)^2 -1[/tex]

Thus the option B is the correct option.

In the option E the function is shifted 1 units left and 2 units down as,

[tex]t(x) = -2x^2 - 4x - 3\\t(x)=-2x^2 - 4x - 1-2\\t(x)=-2(x+1)^2-2[/tex]

Thus the option E is the correct option.

Hence, the functions have a maximum and are transformed to the left and down of the parent function are,

[tex]q(x) = -5(x +10)^2 -1[/tex]

[tex]t(x) = -2x^2 - 4x - 3[/tex]

Thus the option B and E is correct.

Learn more about the transformation of a function here;

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Answer:

(4 x 3) x 2=
=12 x 2

=24

Step-by-step explanation:

Step-by-step explanation:

(4 × 3) × 2

Always solve the one in the bracket first.

(4 × 3) ×2

(12) × 2

Now, you can multiply both numbers.

12 × 2

=> 24

Hope it helps you. Good night.

Answer:

x=-1, y=2

Step-by-step explanation:

Plug the y=-2x into the second equation in place of the y to get 4x+10(-2x)=16

Simplify this to 4x-20x=16 then to -16x=16

Divide both side by -16 to get x=-1

Plug x=-1 into the first equation to get -2(-1)=y

Simplify to get y=2

Using the perimeter of a rectangle, it is found that she can make a deck of 122 ft wide.

The perimeter of a rectangle of length l and width w is given by:

[tex]P = 2(l + w)[/tex]

In this problem:

Then:

[tex]P = 2(l + w)[/tex]

[tex]280 = 2(10 + 8 + w)[/tex]

[tex]36 + 2w = 280[/tex]

[tex]2w = 244[/tex]

[tex]w = \frac{144}{2}[/tex]

[tex]w = 122[/tex]

She can make a deck of 122 ft wide.

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I'm not sure what the answer is but I'll add subtract and multiply something. Remember PEMDAS for the order of operations

10 x 2 - 5

= 20 - 5

= 15

That's an example

Answer:

Step-by-step explanation:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2} \\=\sqrt{(-7-4)^2+(2-2)^2} \\=11[/tex]

Answer:

D) 11

Step-by-step explanation:

The points have in common the same value of the y-axis so the distance between them is the sum of the absolute values of x-axis.

Absolute values are always positive:

4 + 7 = 11

Hope this helps

Answer:

1 doller and 25 cents so easy

Step-by-step explanation:

Answer:

√104 in

Step-by-step explanation:

Well to start off we can use Pythagorean's theorem ~ A^2 + B^2 = C^2

in this case we will indirectly use this formula. Now we know this; A^2 + 11^2 = 15^2

Let's start using some algebra now B )

A^2 + 121 = 225 > A^2 = 225 - 121 > A^2 = 104 > A = √104

Which is the answer. ALso if you're the brainy type and want to know how to simplify this even further...

Can the Square Root of 104 Be Simplified?

104 can be simplified only if you can make 104 inside the radical symbol smaller. This is a process that is called simplifying the surd. In this example, the square root of 104 can be simplified.

√104 = 2√26.

Answer:

Step-by-step explanation:

A) The diagonals of a parallelogram are perpendicular

B) The diagonals of a kite bisect each other

C) A polygon is a quadrilateral

D) Thé diagonals of a rectangle are equal

E) Thé opposite angles of a parallelogram are equal

F) A rhombus is a rectangle

#1

Rhombus has diagonals perpendicular to each other.

#2

#3

#4

#5

#6

All sides of Rhombus are equal where as rectangle has opposite sides equal

The correct factor is (x - 2) and (x + 1).

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

Given

x² - x - 2 = 0 is a quadratic equation.

The factor of the given equation.

x² - x - 2 = 0 is a quadratic equation.

According to factorization,

            x² - x - 2 = 0

    x² - 2x + x - 2 = 0

x(x - 2) +1 (x - 2) = 0

  ( x - 2 ) ( x + 1 ) = 0

Thus the correct factor is (x - 2) and (x + 1).

More about the quadratic equation link is given below.

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Answer:

x=4+5yif sum is increased by 3 (x+y+3), result is 31x+y+3=31minus 3 both sidesx+y=28x=4+5y subsiutute4+5y+y=284+6y=28minus 4 both sides6y=24divide by 6y=4sub backx=4+5yx=4+5(4)x=4+20x=24the numbers are 24 and 4

Step-by-step explanation:

If I helped you

dolphinsproduction on insta

Answer:

29 and 5

Step-by-step explanation:

Given system of equations

[tex]\left \{ {{x=4+5y} \atop {x+y+1=35}} \right.[/tex]

Substitute top equation into bottom equation to determine y

[tex]x+y+1=35\\\\(4+5y)+y+1=35\\\\4+5y+y+1=35\\\\5+6y=35\\\\6y=30\\\\y=5[/tex]

Substitute y=5 into top equation to determine the x-value

[tex]x=4+5y\\\\x=4+5(5)\\\\x=4+25\\\\x=29[/tex]

Therefore, the two numbers are 29 and 5

Answer:

  660

Step-by-step explanation:

If n represents the number, we are told ...

  900% × n = 5940

We know that 900% = 900/100 = 9, so this is ...

  9n = 5940

Dividing by the coefficient of n gives ...

  n = 5940/9 = 660

The number is 660.

Notice that 72 hours is 12 times the half-life of 6 hours. So, the starting amount of 100 mg will decay to half, 12 times. In other words

• after 1 hour, 100 mg decays to 50 mg

• after a total 2 hours, 100 mg decays to 25 mg

• after a total 3 hours, 100 mg decays to 12.5 mg

and so on, so that after a total of 72 hours, the hospital is left with

[tex]\dfrac{100\,\rm mg}{2^{12}} = \boxed{0.0244140625 \, \mathrm{mg}}[/tex]

Answer:

23 , -6

Step-by-step explanation:

Let the unknown two numbers be x & y.

According to the question,

The sum of 2 numbers is 17 .

x + y = 17 ⇒ (1)

Their difference is 29 .

x - y = 29 ⇒ (2)

First let us find the value of x.

(1)  + (2)

x + y + ( x - y ) = 17 + 29

x + y + x -y = 46

2x = 46

Divide both sides by 2.

x = 23

And now let us find the values of y.

x + y = 17

23 + y = 17

y = 17 - 23

y = -6

There fore, the two numbers are 23 , (-6)

Hope this helps you  :-)

Let me know if you have any other questions :-)

Answer:

The answer is D.

Step-by-step explanation:

Angle two is not congruent to angle four in any way, they are not vertical angles, but they are adjacent, although this doesn't mean they are congruent, rather it means that if added, they will equal 180 degrees.

The lines are intersecting and the angles ∠2 ≅ ∠4 is not true

Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees.

Perpendicular lines are two straight lines that intersect and form right angles. When two perpendicular lines intersect, they form four right angles.

When lines intersect, two angle relationships are formed:

Opposite angles are congruent

Adjacent angles are supplementary

Given data ,

Let the first line be represented as a

Let the second line be represented as b

Now , the lines a and b intersect at point O

where ,

m∠2 + m∠3 = 180° ( angles on a straight line = 180° )

m∠2 + m∠4 = 180° ( angles on a straight line = 180° )

And , ∠3 and ∠4 are congruent ( vertical angles )

Hence , the incorrect statement about intersecting lines is ∠2 ≅ ∠4

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Answer:

8.40

Step-by-step explanation:

so I put 20x6.75/100 which = 1.35 and 4.5x6.75/100 which = .30 and I added .30 to 6.75 which = 7.05 and then I added 1.35 to that and got 8.40

so I got $8.40