Lisa is asked to draw a triangle with the following specifications:

two angles are complementary
the side between the two complementary angles has a length of 12 centimeters

Which of the following statements about this triangle is true?

A.
Exactly one triangle exists with the given conditions, and it must be an isosceles triangle.

B.
More than one triangle exists with the given conditions, and all instances must be right triangles.

C.
More than one triangle exists with the given conditions, and all instances must be isosceles triangles.

D.
Exactly one triangle exists with the given conditions, and it must be a right triangle.

Answers

Answer 1

B is correct.

Since two of the angles are complementary, adding up to 90°, the third angle must be 180-90=90°.

However, this does not mean only one triangle exists. The only information we are given about the two angles is that they are complementary. This could be 30 and 60; 45 and 45; or multiple other combinations. This means there is more than one triangle that fits these criteria.

Answer 2

Final answer:

Triangles with two complementary angles must be right triangles. Since these angles add up to 90 degrees, the side between them is part of a right triangle. There can be many different right triangles that satisfy these conditions, but all must have a 90-degree angle. (Option D)

Explanation:

The question asks about the conditions that define a certain type of triangle. With two angles being complementary, they add up to 90 degrees. In geometry, a complementary pair of angles adds up to 90 degrees, which means that the two angles in question must be acute angles that add up to form a right angle. Therefore, the triangle with two complementary angles must be a right triangle.

Since the triangle can have many different dimensions for the other sides and angles while keeping the side between the complementary angles at 12 centimeters, we can infer that there are infinite variations of this triangle, each with different measures for the remaining side and angle. However, all those triangles must satisfy the condition of being right triangles.

Thus, the correct answer to this question is:

D. Exactly one triangle exists with the given conditions, and it must be a right triangle.

Related Questions

What is the equivalently non equivalent

Answers

Answer:
1/2 and 5/8 are not equivalent

Explanation:
The term equivalent means that a number or term has the same numerator-to-denominator (proportional) ratio as another number.

1/2 and 2/4 would be equivalent because if you divide the numerator and the denominator of the second fraction by 2, the result is the 1/2.

If you divide the denominator of 5/8 by 4, the result is a 2, matching the denominator of 1/2. However, if you divide the numerator by 5, the result is 1.25, which does not match the numerator of 1/2.

Therefore, these two numbers are not equivalent.

The perimeter of a rectangle is dependent on the length of each of its sides. Suppose the base of a rectangle is two more than its height. Complete an input/output table for at least three pairs of inputs and outputs. Make sure to use values that make sense within the context of this situation.

Answers

let
x---------> length of the base of a rectangle
y--------->height of the base of a rectangle

we know that
perimeter of a rectangle=2*[x+y]
and
x=y+2------> y=x-2

step 1
inputs
x=3
x=5
x=10

step 2
find the outputs

for x=3
y=x-2----> y=3-2-----> y=1
perimeter=2*[3+1]-----> 8

for x=5
y=x-2----> y=5-2-----> y=3
perimeter=2*[5+3]-----> 16

for x=10
y=x-2----> y=10-2-----> y=8
perimeter=2*[10+8]----->36

see the attached table

Donna wants to draw a right triangle. She wants the hypotenuse to be 1.5 inches long and one of the legs to be 1.2 inches long. Enter the length that she must use for the second leg to form a right triangle.

Answers

We will use the pythagorean theorem to answer this problem. a^2+b^2=c^2, where a and b are the legs of the right triangle, while c is the hypotenuse.
Since the measurements for one of the legs and the hypotenuse are already given, this leaves out only with one unknown, which we may say the "a" leg.

Substituting the given values, we have a^2 + (1.2)^2 = (1.5)^2. Simplying the exponents, we have a^2+1.44 sq.inches = 2.25 sq.inches. Now, isolating the unknown, a^2 = 2.25 - 1.44 sq.inches. Further, we have a^2 = 0.81 sq.inches. Therefore, a = √0.81 sq.inches or a = 0.9 inch.

In a circle,which ratio is equivalent to pi?

Answers

It is approximately equal to 3.14159. It can be simplified to 3.14

22/7 is the correct answer, hope this helps!:)

Evaluate square root of 24 - x when x = 6 . Write the answer in simplified radical form.?

Answers

So, first we input 6
24 - 6 = 18
So we now need to find the square root of 18
If you're allowed to use a calculator, the square root is 4.242

But if you don't, let's get as close as we can:
√(9 * 2)
Because the square root of 9 is 3:
3 * √2

solve the area of a triangle for b and use the resulting formula to find the base of a triangle with a height of 6 ft. and an area of 9 ft. ^2.

Answers

The formula of the area of a triangle:

[tex]A_\Delta=\dfrac{bh}{2}[/tex]

b - a base
h - a height

We have:
h = 6ft.and A=9 ft.²

substitute:

[tex]\dfrac{6b}{2}=9\\\\3b=9\ \ \ |:3\\\\b=3\ ft.[/tex]

Answer: b = 3ft.

HELP PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ!!!

Which of the following best describes the expression 9(x + 7)?

A. The sum of constant factors 9 and x + 7
B. The product of constant factors 9 and x + 7
C. The product of a constant factor 9 and a 2-term factor x + 7
D. The sum of a constant factor 9 and a 2-term factor x + 7

Answers

The product of constant factors 9 and x + 7

Answer:

THE ANSWER IS C NOT D

Step-by-step explanation:

The answer is C i got it correct on the test DON'T LISTEN TO THE PEOPLE THAT SAY D

can you solve x = 29 - 3(9 - 4)

Answers

The answer is 14. The first step is to subtract 4 from 9 (in PEMDAS you always do the equation in the parenthesis). Next, multiply (M= multiply, there are no exponents) -3 by 5 which gives you -15. Now, subtract 15 from 29 and the answer is 14.

The solution of expression is.

⇒ x = 14

We have to given that,

An expression,

⇒ x = 29 - 3 (9 - 4)

Now, We can solve the expression for value of x as,

⇒ x = 29 - 3 (9 - 4)

⇒ x = 29 - 3 × 5

⇒ x = 29 - 15

⇒ x = 14

Therefore, the solution of expression is.

⇒ x = 14

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ6

Only 6 of the 75 trees in a park are at least 30 feet tall. What percent of the trees are under 30 feet tall?

Answers

Percentage of tress under 30 = 6/75 x 100 = 8%

Answer: 8%

Answer:

Step-by-step explanation:

the rules of a contest say that there is a 5% chance of winning a prize. four hundred people enter the contest. predict how many people will win a prize

Answers

20 people.
400 times 0.05 is 20
20 times 20 is 400
5 times 20 is 100
therefore, 20 people

A percentage is a way to describe a part of a whole. The number of winners in the contest is 20.

What is the Percentage?

A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

As it is given that the chances of winning a prize are 5%, and 400 people enter the contest, therefore, the number of people who will be winning is 5% of the number of contestants.

[tex]\text{Number of Winner} = 5\%\ \text{of the Number of Contestants}\\\\\text{Number of Winner} = \dfrac{5}{100} \times 400 = 20[/tex]

Hence, the number of winners in the contest is 20.

Learn more about Percentages:

https://brainly.com/question/6972121

A computer store builds custom computers by allowing customers to choose 1 of 4 different CPUs, 1 of 8 hard drives, and 1 of 3 videos cards. How many different computers are possible?

Answers

There are 96 possible combinations.

The fundamental counting principle states that the number of total options is given by multiplying the number of possibilities for each option, or
Total choices = choices x choices x ...

4*3*8 = 96

WILL GIVE BRAINLIESTWhich of the following represents the ratio of the hypotenuse to the given side

Answers

The hypotenuse is 6√2 .
The 'given' side is the one with the length marked. That's 6 .
Their ratio is

6√2 / 6 .

In simplest form, that's √2 . (B)

The school's basketball team lost 4 times as many games as they won. They also tied 5 fewer games than they won.

If they played 43 games, how many did they lose?

Answers

If they played 43 games, the number of games that they lost is: 32

How to save algebra word problems?

Let

x represent number of games won

Let y represent number of lost games.

Thus;

y = 4x - - - - - equation (I)

Let z denote tied games.

Thus;

z = x - 5 - - - - - equation(II)

Total games played is 43.

Thus;

x + y + z = 43 (III) equation

substitute (I) and (II) in (III)

therefore

x+(4x)+(x-5)=43

6x-5=43

x=48/6

x=8

y = 4x

= 4*8 =32

The answer is 32 lost games

Need help with 2 3 4 5 6

Answers

Answer:

all answers are shown and pictured

Find three consecutive integers such that three times the sum of the first two is eight more than 5 times the third.

Answers

Consecutive integers are numbers one after the other on the number one (ie. 1,2,3,4,5 or 203,204,205).

times= multiplication
sum= addition
more than= addition
is= equal sign

x= first integer
x+2= second integer
x+3= third integer

3(x + (x + 2))= 5(x + 3) + 8
add inside parentheses

3(2x + 2)= 5(x + 3) + 8
multiply 3 and 5 by their parentheses

(3*2x) + (3*2)= (5*x) + (5*3) + 8
multiply in parentheses

6x + 6= 5x + 15 + 8

6x + 6= 5x + 23
subtract 5x from both sides

x + 6= 23
subtract 6 from both sides

x= 17 first integer

x + 1= 17 + 1= 18 second integer

x + 2= 17 + 2= 19 third integer

CHECK:
3(x + (x + 2))= 5(x + 3) + 8
3(17 + (17 + 2))= 5(17 + 3) + 8
3(17 + 19)= 5(20) + 8
3(36)= 100 + 8
108= 108

ANSWER: The three consecutive integers are 17, 18 and 19.

Hope this helps! :)

A rectangular jewelry box costs $125 to gold plate. Calculate the cost of gold plating a box which is similar in shape and that holds 8 times as much.

The answer is not $1,000 or $8,000 or $64,000

Answers

To determine the amount of gold plating necessary for the similar box, you will use the fact that it is 8 times larger in volume to determine how many times larger the area is. This would be what you will multiply $125 by.

Volume is a three dimensional measurement, so the fact that it is 8 times larger tells us each dimension was 2 times larger (2 x 2 x 2=8).

Area is a two dimensional measurement, so the area would have been 2 x 2 or 4 times larger. This means the price would be 4 times as much.
$125 x 4 = $500.

It will cost $500 to gold plate the similar jewelry box.

Asher pays 156 every 6 weeks for piano lessons what is the price per year for piano lessons

Answers

356 days in a year / 7 days in a week = 50.8 weeks in a year

50.8 weeks in a year / 6 weeks = 8.48 payments

$156 x 8.48 payments = $1322.88 per year

The endpoints of GE are located at G(-6,-4) , and E(4,8). Using slope-intercept form, write the equation of GE.

Answers

Answer:

The line would be y = 6/5x + 26/5

Step-by-step explanation:

To find the equation, we first need to find the slope. We can do this by using the slope formula.

m(slope) = (y2 - y1)/(x2 - x1)

m = (8 - -4)/(4 - -6)

m = 12/10

m = 6/5

Now that we have the slope, we can use that and either point in point-slope form to get the equation.

y - y1 = m(x - x1)

y - 8 = 6/5(x - 4)

y - 8 = 6/5x - 24/5

y = 6/5x + 26/5

LMN≅PQR

What is the value of x in degrees?

Enter your answer in the box.

x = °

Answers

LMN≅PQR means that point L is equal to P, point M is equal to Q, and point N is equal to R. All lines are the same.

Point Q has an angle of 72, which means that point M also has an angle of 72.

Now you have two angles to find x. All interior angles of a triangle add up to 180, so you can set up the following equation to find x:

72 + 36 + x = 180

Subtract 36 from both sides.

72 + x = 144

Subtract 72 from both sides.

x = 72

The angle of point L, x, is 72.

Answer:

Step-by-step explanation:

The length of a rectangle is 5/2 units greater than twice its width. If its width is w, which expression gives the perimeter of the rectangle in terms of w?

Answers

Answer:
perimeter = 6w + 5 units

Explanation:
Perimeter of a rectangle can be calculated as follows:
Perimeter = 2(width + length)

We are given that:
width = w units
length is 5/2 units greater than twice the width. This means that:
length = 2w + 5/2

Now, substitute in the above equation to get the expression for the perimeter as follows:
Perimeter = 2(width + length)
Perimeter = 2(w + 2w + 5/2)
Perimeter = 2(3w + 5/2)
Perimeter = 2(3w) + 2(5/2)
Perimeter = 6w + 5

Hope this helps :)

Answer:

D: 6w + 5

Step-by-step explanation:

The perimeter of a rectangle can be calculated as follows:

Perimeter = 2(width + length)

We are given that:

width = w units

length is 5/2 units greater than twice the width. This means that:

length = 2w + 5/2

Now, substitute in the above equation to get the expression for the perimeter as follows:

Perimeter = 2(width + length)

Perimeter = 2(w + 2w + 5/2)

Perimeter = 2(3w + 5/2)

Perimeter = 2(3w) + 2(5/2)

Perimeter = 6w + 5

120e^(2x)=75e^(3x)
Please solve with steps

Answers

Step 1. Take natural logarithm to both sides of the equation:
[tex]120e^{2x}=75e^{3x}[/tex]
[tex]ln(120e^{2x})=ln(75e^{3x})[/tex]

Step 2. Apply product rule of logarithms [tex]ln(ab)=ln(a)+ln(b)[/tex]:
[tex]ln(120)+ln(e^{2x})=ln(75)+ln(e^{3x})[/tex]

Step 3. Apply the rule [tex]ln(e^x)=x[/tex]:
[tex]ln(120)+2x=ln(75)+3x[/tex]

Step 4. Solve for [tex]x[/tex]:
[tex]ln(120)+2x=ln(75)+3x[/tex]
[tex]ln(120)-ln(75)=3x-2x[/tex]
[tex]x=ln(120)-ln(75)[/tex]
Apply the quotient rule of logarithms [tex]ln(a)-ln(b)= ln(\frac{a}{b} )[/tex]:
[tex]x=ln( \frac{120}{75} )[/tex]
[tex]x=ln( \frac{8}{5} )[/tex]

We can conclude that the solution of our equation is [tex]x=ln( \frac{8}{5} )[/tex], which is approximately [tex]x=0.47[/tex].

|-7 + 5| +6
________
4

Answers

The answer should be 2.

2 is the answer because -7+5=2+6=8➗4=2. Hope it helps

Factor the quadratic expression Completely; -8x^2-15x+2

Answers

Answer:
(x + 2)(-8x + 1) or,
(-8x + 1)(x + 2)

Explanation:
To factor quadratic equations in the form ax² + bx + c that cannot be factored in your head, the first step is to find factors for the product of coefficient a and constant c whose sum equates to coefficient b. This may sound confusing, but it is easier in practice.

So, we find the product of -8 and 2 which is -16.
Now we list the factors of -16. I like to list them as factor pairs. These are:
1, -16, 2, -8, 4, -4, 8, -2, 16, -1

Next, we examine which combination of factor pairs has a sum of -15. These are -16 and 1. To check: -16 + 1 = -15

Then, we place these values as coefficients into the original equation as substitutes for -15x and find factor out the greatest common factor (GCF) of the equation terms:
-8x² - 16x + x + 2
(-8x² - 16x) + (x + 2)

The GCF between -8x² and -16x is -8x. The GCF between x and 2 is 1.
-8x(x + 2) + 1(x + 2)

If these binomials within the parenthesis match, then you have found the factors. The binomial within the parenthesis is one factor and the GCFs outside of each binomial are is the other factor. Thus, the factors of the original quadratic expression are:
(-8x + 1)(x + 2)

To check these factors for accuracy, we can use the FOIL method to expand the expression, combine like terms, and observe if it matches the original equation. FOIL stands for Firsts, Outsides, Insides, and Lasts, instructing which terms of each binomial are multiplied together.
Firsts: -8x(x) = -8x²
Outsides: -8x(2) = -16x
Insides: 1(x) = x
Lasts: 1(2) = 2

In an equation: -8x² - 16x + x + 2 → -8x² - 15x + 2
This is the original equation, therefore (-8x + 1)(x + 2) are accurate factors.

Please help on the fraction question

Answers

Im pretty sure the answer is 10. Hope this helped.

10 4/5 is the answer

What is the value of x. Enter your answer in the box.
A triangle with 3 sides that's a right triangle the longest one is 24 then 7 then x. What is x
X=___

Answers

Use the Pythagorean theorem to find the missing side:

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

We already know two sides, so plug those into the equation. The longest side will be c:

[tex]a = 7, c = 24[/tex]

[tex]7^{2} + b^{2} = 24^{2}[/tex]

[tex]49 + b^{2} = 576[/tex]

Subtract 49 from both sides.

[tex]b^{2} = 527[/tex]

Square root both sides to get b by itself:

[tex] \sqrt{527} = 22.9564[/tex]

[tex]b = 22.9564[/tex]

The value of x is 22.9564.

Use the Pythagorean Theorem: a² + b² = c².
a and b are the legs, c is the hypotenuse.

Refer to the picture :) I just drew a standard right triangle, *not to scale*.
The hypotenuse is always the longest side of a right triangle, so I plugged in 24 for c. I plugged in x and 7 for a and b.

x² + 7² = 24²
Square 7 and 24.

x² + 49 = 576
Subtract 49 from both sides.

x² = 527
Square root both sides to isolate and find x.

x = 23

if a hot air balloon descends at a rate of 320 feet per min for 3 mins what is its total change in altitude

Answers

You're told that the hot air balloon lowers itself (descends) by 320 feet a minute. That means for each minute that passes, the altitude changes by 320 feet.

Since you want to find the total change in altitude in 3 minutes, you would need to multiply 320 feet/min by 3 minutes. (Remember multiplication is the same thing as repeated addition, and you're repeatedly adding a change in 320 feet for every minute that passes):
[tex]320 \: ft/min \times 3 \: minutes = 960 \: ft[/tex]

-------

Answer: The total change in altitude is 960 feet.

On a map, 0.25 inches represents 1 mile. What is the area of a rectangle on the map that is 3.75 inches long and 2.25 inches wide?

Answers

Hi,
First we need to find 3.75/0.25, then multiply that with 1(same number),since 0.25 inch =1 mile
3.75/0.25=15
That means length=15 miles
Find width in the same way.
2.25/0.25=9
Width=9 miles
a=l*b
a=15*9
a=135 sq. miles
Hope this helps you.

Answer:

135 Square Miles

Step-by-step explanation:

On a map, 0.25 inches represents 1 mile. What is the area of a rectangle on the map that is 3.75 inches long and 2.25 inches wide?

270 square miles

135 square miles

48 square miles

24 square miles

Odyssey

7.68 cal/sec to Kcal/min

Answers

1 minute = 60 seconds

first covert cal/sect o cal/min

7.68 cal/sec x 60 seconds = 460.8 cal/min

1 Kcal = 1000 cal

divide cal by 1000 to get Kcal

460.8 cal/min / 1000 = 0.4608 Kcal/min
round answer as needed

you are dealt one card from a standard 52-card deck. Find the probability of being dealt a 3.

Answers

[tex]|\Omega|=52\\ |A|=4\\\\ P(A)=\dfrac{4}{52}=\dfrac{1}{13}\approx7.7\% [/tex]

PLZ HELP ASAP Using the frequency table below, find how many students received a score of 70 or better on a mathematics test.
A.19
B.12**
C.17
D.14
Score Interval Frequency

50 – 59 [2]

60 – 69 [5]

70 – 79 [5]

80 – 89 [7]

90 – 99 [2]

Answers

Okay this one is pretty easy.

Here are the steps:
1. we know that 70 - 79 = 5 students 80 - 89 = 7 students 90 - 99 = 2 students.
2. ADD
3. 5 + 7 + 2= 14
4. ANSWER

A: D there are 14 students scored 70 and above!
Hope this helped! (tell me if i'm wrong or right please!!!)

Answer:

D.14

Step-by-step explanation:

To find out the answer, we need to add up all the student s that a 70 or above. 5 got 70-79, 7 got 80-89, and 2 got 90-99.Add these up and we get 14. The answer is D.14

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