Solve for the long leg and for the hypotenuse of the 30-60-90 triangle.

Answer:

35

Step-by-step explanation:

Answer:

9/11, 8/9, 0.79, 81%

Step-by-step explanation:

i don't know how to explain but this is pretty much how you'd do it

Answer:

m∠Y  = 40°

Step-by-step explanation:

The sum of the three angles of a triangle must equal 180°

Thus

m∠W + m∠X + m∠y = 180°

→   (10x + 17) +  (2x - 9) + (3x + 7) = 180

→   10X + 17 + 2X + 9 + 3X + 7 = 180

Collecting like terms
→  10X + 2X + 3X + 17 - 9  + 7  = 180°

→ 15x + 15 = 180

Subtract constant 15 from both ssides:

→ 15x + 15 - 15 = 180 - 15

→ 15x = 165

Divide both sides by 15

→ 15x/15 = 165/15

→ x = 11

m∠Y = 3x + 7

m∠Y = 3 x 11 + 7

m∠Y  = 33 + 7

m∠Y  = 40°

Answer:

Step-by-step explanation:

The total cost of the meal is 66.045

Given,

The cost of the meal = 64.75

The discount given on that day = 15%

The tip given by Zurn family = 20%

We have to find the total cost of the meal.

First we have to find the total cost including tip before discount is added.

That is,

120% of 64.75

= 64.75 × 120/100

= 6.475 × 12

= 77.7

Here, the total cost including tips before discount is 77.7

Now, we have to deduct the discount.

100 - 15 = 85

That is,

85% of 77.7 will be the total cost of the meal

= 77.7 × 85/100

= 6604.5 / 100

= 66.045

Therefore, the total cost of the meal is 66.045

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Check the picture below.

The number of hours it would take Ganymede to complete a full rotation is 171.25 hours.

The first step is to convert days to hours. A day is equivalent to 24 hours. In order to convert days to hours, multiply 7 by 24.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

1 day = 24 hours

24 x 7 = 168 hours

The second step is to convert minutes to hours, In order to do this, divide 15 by 60. Division is the process that is used to determine the quotient of two or more numbers.

60 minutes = 1 hour

15 / 60 = 0.25 hours

Now, add all the converted hours together. Addition is the mathematical operation that is used to determine the sum of two or more numbers.

Total hours = 168 hours + 3 hours + 0.25 hours = 171.25 hours

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The change in Oliver's score due to the incorrect questions will be -63.

It should be noted that the table shows the number of questions answered incorrectly by each player on a game show.

It should be noted that based on the information, every question missed is worth -7 points.

Therefore, the change in Oliver's score due to the incorrect questions will be:

= 9 ×-7

= -63

The change is -63.

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Answer:

[tex]\frac{2}{25}[/tex]

Step-by-step explanation:

There are a total of 15 pieces of fruit.  For the first selection, we want a apple (6) and the second pick we want and orange (3).

[tex]\frac{6}{15}[/tex] x [tex]\frac{3}{15}[/tex] =

Which is the same as

[tex]\frac{2}{5}[/tex] x [tex]\frac{1}{5}[/tex]  if I simplify both fractions which is [tex]\frac{2}{25}[/tex]

Answer: A

180-130= <D

50=<D

50+70= 120

180-120=<B

60=<B

m<BCD= 70

m<DBC= 60

70-60=10

Answer:

О A = 10°

Step-by-step explanation:

∡ DBC = 180 - 130 = 50°

∡ DBC + ∡ CBD + ∡ BCD = 180°

50° + 70° + ∡BCD = 180°

∡BCD = 180° - (50°+70°)

∡BCD = 180° - 120°

∡BCD = 60°

Then:

∡BCD - ∡DBC = 60° - 50° = 10°

Answer:

Proved.

Step-by-step explanation:

l // m and p is transversal.

    ∠1 ≅ ∠3   ----------(I)   {Corresponding angles}

p // q and l is transversal.

   ∠3 ≅ ∠2   -------(II) {Corresponding angles}

From (I) & (II),

      ∠1 ≅ ∠2

Hence proved.

To prove ∠1 = ∠2

In a plane, parallel lines are those whose distances between them are constant. Lines that are parallel never cross. Lines that cross at a straight angle (90 degrees) are said to be perpendicular.

Given: l II m and p II q

According to the properties of parallel lines

∠1 and ∠ 3 are equal because l II m therefore ∠1 and ∠ 3 are corresponding angles.

Since  p II q therefore ∠3 = ∠2 { angles present on the same sides of the parallel lines called corresponding angles are equal }.

Thus since ∠1= ∠3 and ∠3=∠2 therefore we can say that ∠1 = ∠2.

Hence proved.

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Answer: v = 8, 5; The sum of these values would be 13.

∣2v − 13∣ + 6 = 9

Combine like terms, utilizing the properties of equality. Do not forget to follow the order of operations!

∣2v − 13∣ + 6 = 9

Subtract 6 from both sides of the equation.

∣2v − 13∣ = 3

Consider the definition of absolute value (distance from the number zero); the absolute value of x and -x would both be x.

2v − 13 = 3

2v − 13 = −3

Add 13 to both sides of the equation.

2v = 16

2v = 10

Divide both sides of the equation by 2.

v = 8

v = 5

Add the sum of the values.

8 + 5 = 13

Answer:

x = -3 and y = 6

Step-by-step explanation:

by plugging the function (y = 3x + 15) into the y value in the function (3x + 3y = 9), you can then solve to find that x = -3

After solving for the x-value, plug -3 into the easiest equation to solve for the y-value (y = 3x + 15) to then find that y = 6

This is method of solving is called substitution

Answer:

option (e) 8

Step-by-step explanation:

using identity

==>1/(a^(-x))=a^x()

=(1/2)^(-3)

=(2)^3

=2*2*2=8

option (e)

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Answer:

y=139

Step-by-step explanation:

add 59 to 80

Answer:

10 popcorn orders

Step-by-step explanation:

[tex]10 + 4.55 x = 8 + 4.75x \\ 4.55x - 4.75x = 8 - 10 \\ - 0.2x = 8 - 10 \\ - 0.2x = - 2 \\ x = \frac{ - 2}{ - 0.2} \\ x = 10[/tex]

The average change in the temperature per hour is -1.5°F.

Average:

Average means a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.

Given,

On a cold day, the temperature in a certain city changed −14.4°F over 9.6 hours.

Here we need to find the average change in temperature per hour.

To find the average temperature we have to divide the given two temperature.

Temperature change in 9.6 hour = -14.4°F

So, the average change is calculated as,

=> temperature / hour

=> -14.4 / 9.6

=> -1.5°F

Therefore, the average change in temperature is -1.5°F per hour.

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The average change in the temperature per hour is -1.5°F.

Average:

Average means a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.

Given,

On a cold day, the temperature in a certain city changed −14.4°F over 9.6 hours.

Here we need to find the average change in temperature per hour.

To find the average temperature we have to divide the given two temperature.

Temperature change in 9.6 hour = -14.4°F

So, the average change is calculated as,

=> temperature / hour

=> -14.4 / 9.6

=> -1.5°F

Therefore, the average change in temperature is -1.5°F per hour.

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Answer: the number of teachers are 14.4 and the amount of students that don’t own laptops of 5400

Step-by-step explanation:

Taking into account the definition of vertex form, the quadratic function y=x² +2x-12 in vertex form is f(x) = 1(x - +1)² -13

The function f(x) = ax²+ bx + c with a, b, c real numbers and a ≠ 0, is a quadratic function expressed in its polynomial form.

The graph of a quadratic function is a curve called a parabola.

Every quadratic function can be expressed by f(x) = a(x - h)² + k

where

The value of -b÷(2a) indicates the value of x or h and replacing this value into the function, you get the value of y or k of the vertex of the function.

In this case, the quadratic equation y=x² +2x-12, where:

The value of x or h of the vertex is calculated as -2÷(2×1)

Solving: -2÷2= -1

The value of y or k of the vertex of the function is calculated as y=(-1)²+2×(-1) -12

Solving y= -13

Finally, the quadratic function can be expressed in vertex form by f(x) = 1(x - +1)² -13

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The value of the trigonometric ratio sin C of the given right angle triangle is; A: a/b

We know that the three trigonometric ratios of a right angle triangle are given as;

sin θ = opposite/hypotenuse

cos θ = Adjacent/hypotenuse

tan θ = Opposite/Adjacent

Now, from the right angle triangle given to us, if we want to consider the angle C, then we will have the trigonometric ratios as;

sin C = a/b

cos C = c/b

tan C = a/c

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Answer:

A = 73°

Step-by-step explanation:

angle A + angle B = 180°

[tex](6x-35)+(3x+53) = 180[/tex]

[tex]6x+3x-35+53=180[/tex]

[tex]9x+18=180[/tex]

[tex]x=\frac{180-18}{9}[/tex]

[tex]x=18[/tex]

Angle A = 6(18) - 35 = 108 - 35 = 73°

Angle B = 3(18) + 53 = 54 + 53 = 107°

73 + 107 = 180

Hope this helps

Answer:

10^22

Step-by-step explanation:

= (10^11)(10^11) -> the bases are the same, add the exponents

= 10^22

Answer:

figure out how to get 180% from those 3 points

Step-by-step explanation:

The size of the angle marked t is 60 degrees.

We are given an isosceles triangle with one angle as 30 degrees.

We have to find the angle marked t.

Let us name the triangle.

Let the vertex formed by the intersection of two equal sides be A and,

The vertex with 30 degree angle be B and the third vertex be C.

We know that,

AB = AC

Hence,

∠ ABC = ∠ ACB = 30 degrees.

Hence, ∠ BAC =  180 - 30 - 30 = 120 degrees

We know that,

t + ∠ BAC = 180 degrees (supplementary angles)

Hence,

t + 120 = 180

t = 180 - 120

t = 60 degrees

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The cost for making the container if steel costs $2.95/m and aluminum costs $1.57/m is  $28. 27

Based on the information given, we have that;

We also have the following deductions;

The properties of a square prism include;

The cost for aluminum = 10($1.57)

Multiply the values by expanding the

The cost for aluminum = $10. 57

The cost for steel = 6($2.95)

Multiply through, we have;

The cost for steel = $17. 7

Total cost for the container = Cost of steel + cost of aluminum

Total cost for the container = $10. 57 +  $17. 7

Total cost for the container = $28. 27

Thus, the value of the cost is $28. 27

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