The measures of two complementary angles are in the ratio of 5:7. what is the measure of the smaller angle?

Answers

Answer 1

Final answer:

To find the measure of the smaller angle with a ratio of 5:7 in two complementary angles, set up an equation based on the sum of 90 degrees, leading to a solution where the smaller angle measures 37.5 degrees.

Explanation:

The question asks to find the measure of the smaller angle when two complementary angles have a ratio of 5:7. To solve this problem, we recall that complementary angles sum up to 90 degrees. Since the angles are in a ratio of 5:7, we can denote the measures of the smaller and larger angles as 5x and 7x, respectively.

By combining these ratios, we have 5x + 7x = 90 degrees, which simplifies to 12x = 90 degrees. Solving for x gives us x = 90 / 12 = 7.5. Therefore, the measure of the smaller angle is 5x = 5 × 7.5 = 37.5 degrees.

Related Questions

angle efg and angle gfh are a linear pair, the measure of angle efg equals 4n+20, and measure of angle gfh equals 3n+13. what are the measures of angle efg and angle gfh?

Answers

A linear pair of angles are defined to equal 180 degrees. This means that you can add both expressions together and set them equal to 180 degrees. Once, you've done this, isolate the variable n in the equation and plug in the value to determine each angle.

Answer:

∠EFG=104° and ∠GFH=76°

Step-by-step explanation:

Given information:∠EFG = (4n+20)°, ∠GFH = (3n+13)° and ∠EFG and ∠GFH are a linear pair.

If two angles are a linear pair, then the sum of those angles is 180°.

It is given that ∠EFG and ∠GFH are a linear pair.

[tex]\angle EFG+\angle GFH=180^{\circ}[/tex]

Substitute the given values.

[tex](4n+20)+(3n+13)=180[/tex]

Combined like terms.

[tex](4n+3n)+(20+13)=180[/tex]

[tex]7n+33=180[/tex]

Subtract 33 from both sides.

[tex]7n+33-33=180-33[/tex]

[tex]7n=147[/tex]

Divide both sides by 7.

[tex]n=21[/tex]

The value of n is 21.

[tex]\angle EFG=4n+20=4(21)+20=104^{\circ}[/tex]

[tex]\angle GFH=3n+13=3(21)+13=76^{\circ}[/tex]

Therefore, the measure of ∠EFG and ∠GFH are 104° and 76° respectively.

If 6 people in the United States each eat the average amount of popcorn for 5 years, how many quarts of popcorn will they eat.

Answers

The average American eats 68 quarts of popcorn each year.

68*5= 340.

340*6= 2,040 quarts of popcorn.

Hopefully this helps! :)

Help solve x for this

Answers

14+6x = 134
6x = 120
x = 20

<GOF = 180 - 134 = 46

134 = 14 +6x

subtract 14 from each side

120 = 6x

divide each side by 6

x = 120/6 = 20

x = 20

ANGLE GOF = (360 - (134+134)) /2 = 92/2 = 46 degrees

Find three consecutive integers such that the sum of the first and twice the second is equal to the third plus four.

Answers

Our three consecutive integers are

First: x
Second: x + 1
Third: x + 2

Here is the equation you need:

x + 2(x + 1) = (x + 2) + 4

Take it from here.

A car service charges a fixed fee of $3 plus $2 for each mile. Find the cost of a 7-mile ride. Let x=the number of miles.

Answers

3 + 2x = 17
3 + 2 times 7 miles (x) = 17
Hope this helps!!

geometry proof help please

Answers

check the picture below.

so, because those two triangles, have HF in common, they also would have the bisected angle in common, and the other side as well, therefore, those EHF and GHF triangles are congruent by [tex]\bf \boxed{S} ide\quad \boxed{A} ngle\quad \boxed{S} ide[/tex].

namely, one side, then the angle and the other side stemming from that angle.

now, if those two triangles are congruent by SAS, then the last side must also be congruent too.

If y varies directly as x and y is 18 when x is 5 which expression can be used to find the value of y when x is 11?

Answers

y = kx where k is a constant Thats direct variation.

plug in given values:-

18 = k * 5

k = 18/5 = 3.6

so the equation of variation is y = 3.6x

when x = 11, y = 3.6 * 11 = 39.6 Answer

Answer:

The value of y is [tex]\frac{198}{5}[/tex] or 39.6.

Step-by-step explanation:

It is given that y varies directly as x and y. It means y is directly proportional to x.

[tex]y\propto x[/tex]

[tex]y=kx[/tex] .... (1)

where, k is constant of proportionality.

It is given that y is 18 when x is 5.

Substitute y=18 and x=5 in equation (1).

[tex]18=k(5)[/tex]

Divide both sides by 5.

[tex]\frac{18}{5}=k[/tex]

The value of k is [tex]\frac{18}{5}[/tex]. So, the relation between x and y is

[tex]y=\frac{18}{5}x[/tex] .... (2)

We need to find the value of y when x=11.

[tex]y=\frac{18}{5}(11)[/tex]

[tex]y=\frac{198}{5}[/tex]

[tex]y=39.6[/tex]

Therefore the value of y is [tex]\frac{198}{5}[/tex] or 39.6.

HELP PLEASE!!!

A wheel makes 20 revolutions per minute. Find the angular velocity.

10π rad/min
20π rad/min
40π rad/min

Answers

Answer:

Angular velocity of a wheel which makes 20 revolutions per minute is 40π rad/min

Step-by-step explanation:

Angular velocity, ω = 2πf , where f is the frequency.

Here frequency, f = 20 revolutions per minute

Substituting frequency value in angular velocity equation,

Angular velocity, ω = 2πf = 2 x π x 20 = 40π rad/min

So angular velocity of a wheel which makes 20 revolutions per minute is 40π rad/min

f(x)=x+7
if you know the domain is {-9,-3} then the range must be?

Answers

Domain is the set of x-values and range is the set of images f(x).

x           F(x) = x + 7

-9         -9 + 7 = -2

-8         -8 + 7 = -1

-7          -7 + 7 = 0

-6           -6 + 7 = 1

-5           -5 + 7 = 2

-4           -4 + 7 = 3

-3           -3 + 7 = 4

So the range is {-2,4} <------ answer

The length of one base of a trapezoid is 19 less than five times the length of the other base. If the trapezoid has a height of 18 feet and an area of 477 ft squared, find the length of the longer base.

Answers

Area of a trapezoid: [(top +bottom)*height]/2
suppose the length of one base is x, then the other base is 5x-19
[(x+5x-19)*18]/2=477
[6x-19]*18=954
6x-19=53
6x=72
x=12
The longer base is 5*12-19=41

Final answer:

The length of the shorter base of the trapezoid is found by solving the equation generated by using the formula for the area of a trapezoid. After finding this length, it is substituted into the equation representing the length of the longer base to find its value, which is 76 feet.

Explanation:

To solve this problem, let's denote the length of the shorter base of the trapezoid as 'a'. According to the problem, the length of the longer base is then 5a - 19. We also know that the area of a trapezoid is given by the formula: (1/2) * (sum of lengths of bases) * height. So, by substituting the given trapezoid area (477 ft squared) and height (18 ft) into the this formula, we get: 477 = 1/2 * (a + (5a - 19)) * 18. Solving this equation will give us the value of 'a'. As calculating 'a' we find it to be 19. After that, we insert 'a' into the longer base equation: 5a - 19, we find the length of the longer base to be 76 ft.

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What is the equation of the line in slope-intercept form?

Answers

The equation of the line that passes through the points is y=3/5x+3

ANSWER

The equation of the line in slope-intercept form is

[tex]y = \frac{3}{5} x + 3[/tex]

EXPLANATION

The slope intercept form of a line is given by
[tex]y = mx + c[/tex]
Where [tex]m[/tex]is the slope and [tex]c[/tex]
is the y-intercept.

We can read any two points from the graph and use it to determine the slope of the line.

For instance, the graph passes through the points
[tex](-5,0)[/tex]and [tex](0,3)[/tex]

The slope can be found using the formula,

[tex]m= \frac{y_2-y_1}{x_2-x_1}[/tex]

This implies that,

[tex]m = \frac{ 3 - 0}{0 - - 5} [/tex]

[tex]m = \frac{ 3 - 0}{0 + 5} [/tex]

[tex]m = \frac{ 3 }{ 5} [/tex]

Also the y-intercept is

[tex](0,3)[/tex]

Therefore [tex]c = 3[/tex]

We substitute all these values in to the above equation to obtain,

[tex]y = \frac{3}{5} x + 3[/tex]

Help please!

Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years.

Enter an inequality that can be used to represent this situation in the box, where x represents Victoria's neighbor's age.

Answers

Since it is no more than 14 years, you would subtract 4 from 14 and get 10, the two numbers you would put the inequality symbol in between would be the 10 and the variable x. No more than 14 would mean that her neighbor's age must be 10 or under which would mean that x must be equal to or less than 10.

An item is regularly priced at $65 . it is on sale for 80% off the regular price. how much (in dollars) is discounted from the regular price?

Answers

$52 is discounted off of the regular price

Determine algebraically whether the function is even, odd, or neither even nor odd.

f(x)=x+ [tex] \frac{4}{x} [/tex]

a))Even
b))Neither
c))Odd

Answers

the function is odd just substitute f(x) for f(-x) and replace all the x's with -x's then go back to the original problem and substitute f(x) for -f(x) and multiply the original problem by -1 and since f(-x) and -f(x) are equal, it is odd. if the original problem, f(x) and f(-x) were equal it would be even and if none of the three are equal it would be neither. the answer to this question is odd because f(-x) and -f(x) are equal.

What is the solution to the system of equations?

y = x + 3

x = –2

Answers

x= -2

y= 1

Just plug in the x= -2 into the y system of equation. so y= (-2)+3

What is the value of c such that: x2 + 14x + c, is a perfect-square trinomial? A. 7 B. 98 C. 196 D. 49

Answers

I think b is your answere.

Your answer is d.49 because x²+14x+49
First list greatest common factors of 49 which is 7 and 7
Second your second addition sign is telling you that both numbers are going to be the same
Third your first sign is telling you that both numbers are positive
So your equation is (x+7)(x+7) if you do the box method or any other formula you will com out with x² +14x+49

If you need additional help from this topic I will gladly send you my notes your welcome

At a baseball game, a vender sold a combined total of 112 sodas and hot dogs. the number of sodas sold was three times the number of hot dogs sold. find the number of sodas and the number of hot dogs sold.

Answers

84 sodas and 28 hot dogs

Cards numbered 1 through 30 are shuffled in a bin one card is randomly selected what is the probability of selecting a number that is a multiple of 11 ? please help

Answers

the answer is 2:30 since the multiples are 11 and 22

Reaner Recycling shreds 7/8 ton of aluminum each day.The machines can shred 1/24 ton aluminum per cycle.How many cycles will be needed to shred the aluminum?

plz help I don't get it

Answers

7/8 divided by 1/24= 7/8(24)= 168/8

168/8= 21

21 cycles will be needed to shred the aluminum.

Hope this helps!

Answer:

21.

Step-by-step explanation:

We have been given that Reaner Recycling shreds 7/8 ton of aluminum each day.The machines can shred 1/24 ton aluminum per cycle.

To find the number of cycles needed to shred the aluminum, we will divide amount of aluminium by 1/24 as:

[tex]\text{Number of cycles}=\frac{7}{8}\div \frac{1}{24}[/tex]

Convert into multiplication problem by flipping the 2nd fraction:

[tex]\text{Number of cycles}=\frac{7}{8}\times \frac{24}{1}[/tex]

[tex]\text{Number of cycles}=\frac{7}{1}\times \frac{3}{1}[/tex]

[tex]\text{Number of cycles}=7\times 3[/tex]

[tex]\text{Number of cycles}=21[/tex]

Therefore, 21 cycles will be needed to shred the aluminum.

Which is an equivalent form of the equation 4x-y= 14

Answers

4x - y = 14
-y = 14 - 4x
y = -14 + 4x

Answer:

y = 4x - 14 is equivalent from of y = 4x - 14.

Step-by-step explanation:

Given : 4x-y= 14

To find : Which is an equivalent form of the equation.

Solution : We have given 4x - y = 14.

We can write it in slope intercept form y = mx + b

Where, m = slope , b = y intercept.

4x - y = 14.

On subtracting both sides by 4x

- y= -4x + 14.

On dividing both sides by -1.

y = 4x - 14.

Therefore, y = 4x - 14 is equivalent from of y = 4x - 14.

What is the reference angle for a 240° angle

Answers

A 240-degree angle is between 180 and 270 degrees, so its terminal side is in QIII. Subtract 180 from 240. You find that 240 – 180 = 60, so the reference angle is 60 degrees. hope this helps :)

The reference angle for a 240° angle is 60 degree.

What is a Reference Angle?

Reference Angle is the acute angle between the terminal side and the x axis. The value of reference angle is always positive and less than 90 degree.

The angle is 240 degree, for which the reference angle has to be determined.

The angle 240 degree lies in the third quadrant between 180 and 270 degree.

To determine the reference angle, the given angle will be subtracted by 180 degree.

=> 240 - 180

=> 60 degree

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18 POINTS PLUS BRAINLIEST FOR CORRECT ANSWER

Find the equation of the line perpendicular to y=−2 that passes through the point (4, −2).

Answers

The line y = -2 is a horizontal line through -2 on the y axis.

Anything perpendicular to this horizontal line will be a vertical line. All vertical lines are of the form x = k where k is some fixed value.

In this case, the answer is x = 4 because want the vertical line to go through (4,-2). In other words, we want all points on the vertical line to have x coordinate of 4.

Side Note: the slope of y = -2 is 0 while the slope of x = 4 is undefined.

5(x+2)7x+4 plz help idk what to do

Answers

5x + 10 * 7x + 4

70x + 5x = 75x

75x + 4

hope this helps

This may make me look dumb but idk what to do. I need answers please

Answers

Angle 1: 36 degrees - It is opposite to angle 4, and is therefore equal. To solve for angle 4, you have to do 90 - angle 3 (because it is a right angle and totals 90)
Angle 2: 90 degrees - It is a right angle
Angle 4: 36 degrees (explained above)
Angle 5: 90 degrees - It is a right angle. It is also an opposite angle to angle 2, and is therefore equal to it.

Since the two diagonal lines are parallel, the angles will relate to each other.

Angle 7: 126 - It will be 180 - angle 10 (because a straight line = 180)
Angle 8: 54 - It is opposite to angle 10, and is therefore equal
Angle 9: 126 - It will be 180 - angle 8 (because a straight line = 180). It is also an opposite angle 7, and is therefore equal
Angle 10: You already figured this one out! :)
Angle 11: 36 degrees - A triangle is 180, and angles 11, 5, and 8 all make up a triangle. Therefore, 180 - angle 5 - angle 8 = angle 11
Angle 12: 144 degrees - It will be 180 - angle 13 (because a straight line = 180).
Angle 13: 36 degrees - it is opposite to angle 11, and is therefore equal
Angle 14: 144 degrees - it is opposite to angle 12, and is therefore equal

I hope this helps!

Jan scored 539,178 points in a video game what is Jans score rounded to the nearest ten thousand?

Answers

600,000 is the answer ok

15 coins worth $3.15. if the coins are all quarters and dimes, how many quarters and dimes does she have?

Answers

11 quarters and 4 dimes

if you cross multiply 10 over 2.4=15 over x

Answers

IO/2.4 = I5/x
IOx = 36
x = 3.6

A rectangular room is three times as long as it is wide, and its perimeter is 48 meters. Find the length of the room.

Answers

y=6 x=18 i think that is the answer is 54.

x,y dimensions
x=3y and perimeter equation is 2x+ 2y = 48
2*3y + 2y = 48
6y + 2y = 48
8y= 48

y= 6 and x = 18

There are 2 4/5 pounds of bricks in a bag. each brick weighs 2/5 of a pound. how many bricks are in the bag?

Answers

I think there are 7 bricks in the bag

Is the value a an improper fraction less than 1 or greater than 1

Answers

The value of an improper fraction is greater than 1 since it can be simplified into a mixed number unless the improper fraction is negative.

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