Each leg of a 45°-45°-90° triangle measures 14 cm. what is the length of the hypotenuse? 7 cm 7 startroot 2 endroot cm 14 cm 14 startroot 2 endroot cm

By using trigonometric relations, we will see that:

x = √3

In the image, we can see a right triangle, where the hypotenuse measures √6, and the two legs have the same measure.

Then this is a 45°, 45°, 90° right triangle.

Then we can use the relation:

cos(a) = (adjacent cathetus)/(hypotenuse).

Where a = 45°, adjacent cathetus = x, hypotenuse = √6

Replacing that, we get:

cos(45°) = x/√6

Remember that cos(45°) = 1/√2

Replacing that we get:

1/√2= x/√6

√6/√2 = x

√(6/2) = x

√3 = x

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Using a system of equations, it is found that £52 was originally shared.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

Angela and Michelle shared some money in the ratio 4: 9, hence, considering t as the total:

Angela gave Daniel half her share.Michelle gave Daniel a third of her share. Daniel was given a total of £20, hence:

[tex]\frac{x}{2} + \frac{y}{3} = 20[/tex]

[tex]\frac{4t}{26} + \frac{9t}{39} = 20[/tex]

[tex]\frac{12t + 18t}{78} = 20[/tex]

30t = 20 x 78

t = 20 x 78/30

t = £52.

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Answer: 9 m

Step-by-step explanation:

[tex]75=\frac{1}{3}(25)(h)\\\\h=\frac{75}{25/3}=9[/tex]

Answer:

First, do 15/12 then take that and divide by 500!

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{2(-5x + 4) + 4x - 5 = -3}[/tex]

[tex]\huge\textbf{Solving for it:}[/tex]

[tex]\mathbf{2(-5x) + 2(4) + 4x - 5 = -3}[/tex]

[tex]\mathbf{-10x + 4 + 4x - 5 = -3}[/tex]

[tex]\huge\textbf{Combine the like terms:}[/tex]

[tex]\mathbf{(-10x + 4x) + (8 - 5) = -3}[/tex]

[tex]\mathbf{-10x + 4x + 8 - 5 = -3}[/tex]

[tex]\mathbf{-6x + 3 = -3}[/tex]

[tex]\huge\textbf{Subtract \boxed{\bf 3} to both sides:}[/tex]

[tex]\mathbf{-6x + 3 - 3= -3 - 3}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{-6x = -3 - 3}[/tex]

[tex]\mathbf{-6x = -6}[/tex]

[tex]\huge\textbf{Divide \boxed{\bf -6} to both sides:}[/tex]

[tex]\mathbf{\dfrac{-6x}{-6} = \dfrac{-6}{-6}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{x = \dfrac{-6}{-6}}[/tex]

[tex]\mathbf{x = -6\div-6}[/tex]

[tex]\mathbf{x = 1}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf x =\frak{1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The line b is perpendicular to the line y, then the line a will also perpendicular to the line y.  Then the correct option is B.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

If the line a is parallel to the line b, then the slope of the line a and b will be same.

The line b is perpendicular to the line y, then the line a will also perpendicular to the line y.

Then the correct option is B.

The diagram is given below.

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The store manager would reach his goal of $20,000 if the sales team sold 80 tables and 10 laptops.

To calculate if the store manager achieves its goal, we must perform the following operations:

According to the above, sales do reach the goal if 80 tablets and 10 laptops are sold.

Note: This question is incomplete because there is some information missing. Here is the missing information:

A computer store sells both tablets and laptops. One brand of tablet costs $200. That same brand of laptop costs $400. The store manager wants to sell enough of this brand of tablets and laptops to reach the sales goal of $20,000.

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The height of the pole is 96 feet

In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the legs a, b and the hypotenuse c, often called the Pythagorean equation:[1]

[tex]a^{2}+b^{2}=c^{2},[/tex]

Create a diagram of the scenario first. You would have a right triangle with a hypotenuse (longest side) of h + 4, a longest leg of h - 68, and one leg of length h to represent the pole.

Set up the equation [tex]h^2 + (h - 68)^2 = (h + 4)^2[/tex] using the Pythagorean theorem ([tex]a^2 + b^2 = c^2[/tex]).

[tex]h^2 + (h - 68)^2 = (h + 4)^2[/tex]

On simplifying we get

[tex]h^2+h^2-136h+4624 = h^2+8h+16[/tex]

[tex]2h^2-136h+4624=h^2+8h+16[/tex]

[tex]h^2-144h+4608=0[/tex]

Solving using quadratic formula

[tex]h_{1,\:2}=\frac{-\left(-144\right)\pm \sqrt{\left(-144\right)^2-4\cdot \:1\cdot \:4608}}{2\cdot \:1}[/tex]  

[tex]h_1=\frac{-\left(-144\right)+48}{2\cdot \:1},\:h_2=\frac{-\left(-144\right)-48}{2\cdot \:1}[/tex]

h1 = 96 feet , h2 = 48 feet

If height would have been 48 feet then the other side would have a negative value as as 48 - 68 = -20 .

Hence the height of the pole is 96 feet

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Answer:

Divide the number of events by the number of possible outcomes. After determining the probability event and its corresponding outcomes, divide the total number of ways the event can occur by the total number of possible outcomes. For instance, rolling a die once and landing on a three can be considered one event.

Step-by-step explanation:

for more information check the above attachment

Answer:

x = 40

Step-by-step explanation:

All angles in a triangle add up to 180

(3x-10) + 30 + x = 180

4x = 160

x = 40

Answer: x = 40

Step-by-step explanation:

All the interior angles of a triangle add up to 180°

Therefore,

30 + 3x - 10 + x = 180

30 + 4x - 10 = 180

20 + 4x = 180

4x = 160

x = 40

Answer: 4:9

Step-by-step explanation:

The ratio of the surface areas is the square of the ratio of the edge lengths.

Step-by-step explanation:

if the area of each face of a cubical solid is 1764 CM square find its length

[tex]\angle EHF=90^{\circ}[/tex] (an angle inscribed in a semicircle is a right angle)

[tex]\angle HEF=38^{\circ}[/tex] (alternate segment theorem)

[tex]a=52^{\circ}[/tex] (angles in a triangle add to 180 degrees)

Answer:

(a) 1416

(b) 2 × 2 × 2 × 3 × 59

Step-by-step explanation:

The prime numbers between 0 and 10 are 2, 3, 5,7 (1 is not considered prime)
Therefore m = 2357

The square numbers between 0 and 10 are  1, 4, 9 and in descending order 9,4.1so n = 941

m - n = 2357 - 941 = 1416

Unique prime factors of 1416 are 2,3,59

1416 as a product of prime factors = 2 × 2 × 2 × 3 × 59

The following statements are true:

A negative number in mathematics is any number that is less than zero i.e. x < 0.

This means that zero is greater than any negative number.

However, the higher the digit of a negative number, the smaller that number becomes. It is opposite of positive numbers or integers.

Therefore, the following statements are true:

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[tex]\displaystyle\lim_{t\to \infty}(20+100(0.3)^{0.2t})=20+100\lim_{t\to \infty}0.3^{0.2t}=20+100\cdot 0=20[/tex]

Answer:

z = 30

Step-by-step explanation:

→ 360 ÷ z = 12

→ 360/z = 12

→ 12z = 360

→ z = 360/12

→ [ z = 30 ]

Hence, the value of z is 30.

Answer:you have to isolate z,make z the subject.

Step-by-step explanation: z=360 multiply by 12,

giving us 4320.z=4320,i mean thisis the answer you have to stick with if u want to find a value for z.

step by step;z/360=12

z=360 into 12

z=4320

Step-by-step explanation:

I assume that DF and DQ are tangents to the circle.

angle FGQ = 268°

therefore, angle FQ = 360 - 268 = 92°

b = 1/2 × (angle FGQ - angle FQ) = 1/2×(268 - 92) =

= 1/2 × 176 = 88°

Answer:

mode: number that appears most

mode=4 and 7

mean: =3+4+5+6+7+8+9+10+11÷9=7

so mean is 7

Answer:

5x/2

Step-by-step explanation:

Say the mystery number is "x"

5 times that = 5 * x = 5x

Then the quotient (that means the result of division, so divide!) of that and 2 would give you: 5x/2

Answer:

The answer might be C.(x=0)

Answer: P(A)=4/425≈0,0094.

Step-by-step explanation:

[tex]P(A)=\frac{C_4^1*C_3^1}{C_{51}^2} .[/tex]

The desk has 4 kings.

First card is drawn from a well shuffled deck is a card of king.     ⇒

[tex]C_4^1=\frac{4!}{(4-1)!*1!} =\frac{3!*4}{3!*1}=4.[/tex]

Second card is drawn from a well shuffled deck is a card of king too.    ⇒

[tex]C_{4-1}^1=C_3^1=\frac{3!}{(3-1)!*1!}=\frac{2!*3}{2!*1}=3.\\ The \ desk\ has\ 51\ card.\ \ \ \ \Rightarrow\\C_{51}^2=\frac{51!}{(51-2)*2!}=\frac{49!*50*51}{49!*1*2} =51*25=1275.\\ P(A)=\frac{4*3}{1275} =\frac{4}{425} \approx0,0094.[/tex]

The rule for the reflection of the pre-image M(-5, 4), L(-4, 2), N(-2, 3), to form the image M'(-5, -4), L'(-4, -2), N'(-2, -3) is the option;

The given pre-image points are;

Possible third point; N(-2, 3)

The image points are;

The difference (change) between the pre-image and the image is a change in the sign of the y-value, which is equivalent to a reflection across the x-axis.

Therefore;

The rule for the reflection is therefore;

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Answer: 6

Step-by-step explanation:

This is a direct application of the exponent rule [tex](a^b)^c=a^{bc}[/tex].

The equivalent expressions are 3(6x - 3) = 72 and 18x - 9 = 72

Given the equation below as shown;

3/5(30x - 15) = 72

Expand

3/5(30x) - 3/5(15) = 72

90x/5 - 15/5 = 72

3(6x - 3) = 72

Expand

18x - 9 = 72

Hence the equivalent expressions are 3(6x - 3) = 72 and 18x - 9 = 72

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The x intercept of the given line is (10, 0)

The x intercept of a line is the point where the line crosses the x-axis

It is the point where the value of y is zero

Given the equation of a line -2x+5y = -20

Substitute y = 0 into the equation

-2x +5(0) = -20

-2x = -20

x = 10

Hence the x intercept of the given line is (10, 0)

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Answer:

3

Step-by-step explanation:

Irregular pentagon since it has 5 sides

Answer:

irregular pentagon

(first option listed)

Step-by-step explanation:

This shape still has five sides--making it a pentagon. Because the angles are not exactly the same, and so the side lengths are also not equal, we name it an "irregular" pentagon.

hope this helps! have a lovely day :)

First, 0.0004853 is < 1, so we need to multiply the number by 10 to a negative power if it's greater than 1 (if that makes sense i cant describe it better)

So, b and c is incorrect.

10 to the power of negative 4 = 0.0001, and 4.853 x 0.0001 = 0.0004853 (true), so answer is a

Answer:

a

Step-by-step explanation:

a number expressed in standard form is

a × [tex]10^{n}[/tex]

where 1 ≤ a < 10 and n is an integer

given

0.0004853 ( place the decimal point after the 4 )

= 4.853 × [tex]10^{n}[/tex]

to place the decimal point in its original position we require to shift it 4 places left , denoted by - 4 on the exponent , that is

0.0004853 = 4.853 × [tex]10^{-4}[/tex]

The rational number, 5/7 converted to a decimal is 0.714.

A rational number is a number that can be expressed as a fraction of two integers.

A decimal is a non-integer in which the integers are separated from the non integers by a point. In order to convert the fraction to a decimal, divide the numerator by the denominator.

5/7 = 0.714

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The value on the table above will be $30.6. Then the correct option is D.

The quantity of anything is stated as though it were a fraction of a hundred.

Raj was friends with his waitress, so he left her a 90 percent tip.

If his tip was $27.54.

Then the value in the table above will be

⇒ $27.54 / 0.90

⇒ $30.6

Then the correct option is D.

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