Which angle is an acute angle?

Answer:

Step-by-step explanation:

As per diagram, the angles BGC and CGF are marked as congruent.

It gives us:

Solve it for x:

Find the angle measures:

To find the measure of ∠BGF consider the angle addition:

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:

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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First, any number multiplied by 1 yields the result of itself

Therefore, we can rewrite it as 5/3 x 3.

We do the multiplication : 5/3 x 3 = 5/3 x 3/1 = (5x3)/(3x1) = 15/3 = 5.

Rewrite 5 as 5/1 for a fraction result.

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:

Step-by-step explanation:

Answer:

figure out how to get 180% from those 3 points

Step-by-step explanation:

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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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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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]

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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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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By using the method subtraction,

1 quarter is 0.25

1 nickel is 0.05

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

Given that,

Isaac has 18 coins, all quarters and nickels.

The total value of the coins it $3.50.

Let the quarters be x and nickels be y

x+ y= 18

x= 18 - y... equation 1

1 quarter is 0.25

1 nickel is 0.05

So,

0.25x+ 0.05y= 3.50

substitute x value in above equation

0.25(18-y)+0.05 = 3.50

4.5-0.25y+ 0.05 = 3.50

4.55 - 3.50 = 0.25y

1.05= 0.25y

y= 4.2

y in equation 1

x= 18 - y

x= 18-4.2

x= 13.8

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Check the picture below.

Answer:

10^22

Step-by-step explanation:

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

= 10^22

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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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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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

The surface area of the cylinder is 1733.28 square inches

The area of a shape is the amount of space on the shape

For most regular quadrilaterals, you multiply the side lengths to determine the area

The shape is given as

Shape = cylinder

Also, we have

Radius, r = 12 inches/2

r = 6 inches

Height, h = 40 inches

The surface area of the cylinder is calculated as

SA = 2πr² + 2πrh

So, we have:

SA = 2 * 3.14 * 6² + 2 * 3.14 * 6 * 40

Evaluate

SA = 1733.28 square inches

Hence, the area is 1733.28 square inches

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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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Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

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:

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

Step-by-step explanation:

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