A triangle with angles that measure 120°, 39°, and 21° is an obtuse triangle.
The student has asked about the classification of a triangle with angles that measure 120°, 39°, and 21°. Based on Euclidean geometry, the sum of the angles in any plane triangle is 180°. A triangle with one angle that measures more than 90° is an obtuse triangle, as it has one obtuse angle. Therefore, this triangle, with a 120° angle, is classified as an obtuse triangle.
a 12000-gallon pool is being filled at a rate of 40 gallons per minute. at this rate, how many minutes will it take to fill this pool 3/4 full?
The number of minutes taken to fill the pool in three-fourths full is 225.
Given that,
There is a 12,000-gallon pool filled at the rate of 40 gallons per minute.And, there is three-fourths full.Based on the above information, the calculation is as follows:
[tex]= (12000 \times \frac{3}{4}) \div 40[/tex]
= 225 minutes
Therefore we can conclude that the number of minutes taken to fill the pool in three-fourths full is 225.
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Write a number that is greater than 1 in scientific notation. explain how you know it is greater than 1
The positive power of 10 shows that the number is greater than 1.
What is scientific notation?A given number, equation, or expression is written in a format known as a scientific notation, which adheres to a set of principles. Large numbers like 8.6 billion are difficult to write in their numerical form since they are not only unclear but also time-consuming, and there is a potential that we may write a few zeros more or less.
Given:
number that is greater than 1 in scientific notation.
So, to get know the number is greater than 1 we can tell it by seeing the power of 10.
If the powers of 10 is positive then the number is also greater than 10.
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The ratio of the angle measures of the acute angles in a right triangle is 1:2 . What is the measures of these angles a. 30 and 60 b. 45 and 90 c. 60 and 120 d. 10 and 20
Answer:
30 & 60
Step-by-step explanation:
The tutor is correct, besides the fact that the interior angles would equal 180, not 190. Typos happen.
Arliss has two pieces of carpet runner. One is2/13 yards long and the other3/13
is yards long. She needs 10 yards of carpet runner altogether. How much more does she need to buy?
Answer:
5 2/3
Step-by-step explanation:i thought this problem was literally impossible to do and its stopped me from progressing but i finally found out the answer and here it is
A group of friends share slices of pizza.If each person gets 5 slices there will be 4 slices short.How many slices of pizza are there to share?
What is the value of the expression? ( 5/2 ) ^2 +3/4 ^3
5/2 ^2 = 6 1/4 = 6.25
3/4^3 = 27/64 = 0.4201875
6 1/4 + 27/64 = 6 43/64 (mixed number)
6.25 +0.421875 = 6.671875 (decimal)
not sure what format you need, since the question was in fraction form, I think you need to answer using a mixed number though.
The measure of an angle is 1/4 the measure of its complement. Find the measure of each angle
The two angles are 18 degrees and 72 degrees. The smaller angle is one-fourth of the larger, and they add up to 90 degrees because they are complementary.
Explanation:In mathematics, complementary angles are two angles whose measures add up to 90 degrees. Based on the question, let's denote the smaller angle as x and the larger angle (its complement) as y.
Given that x is 1/4 of y, we can write the equation x = y/4.
Also, since they're complementary, their measures add to 90 degrees, giving the equation x + y = 90.
From x = y/4, it can be inferred that y = 4x. Substituting y in the second equation we get x + 4x = 90, which simplifies to 5x = 90. Dividing both sides by 5, we have x = 18.
To find y, substitute x = 18 into the equation y = 4x, giving y = 4*18 = 72. Therefore, the measures of the two angles are 18 and 72 respectively.
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A cyclist rides her bike at a speed of 12 kilometers per hour. What is this speed in kilometers per minute? How many kilometers will the cyclist travel in 5 minutes? Do not round your answers.
Suppose g(x) = f(x + 2) – 3. Which statement best compares the graph of g(x) with the graph of f(x)?
Answer:
B. the graph of g(x) is shifted 2 units right and 3 units up
Step-by-step explanation:
just got it right
We conclude that g(x) = f(x – 2) + 3 means the graph of g(x) is shifted 2 units right and 3 units down. Option D is the correct answer.
The given function is g(x) = f(x + 2) – 3.
What is a function?A function is a relation for which each value from the set of the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.
To shift a function right:
Subtract inside the function's argument. For example, f(x)-b is basically f(x) shifted b units to the right.
Subtracting inside the function's argument moves you to the right.
So, g(x) = f(x – 2) means f(x) is shifted two units to the right.
To move a function down:
Subtract outside the function. For example, f(x)-b is basically f(x) moved down 3 units.
So, g(x) = f(x – 2) + 3 means, f(x) is moved 3 units down.
Therefore, we conclude that g(x) = f(x – 2) + 3 means the graph of g(x) is shifted 2 units right and 3 units down. So, option D is the correct answer.
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What is the approximate value of x? Round to the nearest tenth.
A) 3.1 cm
B) 3.9 cm
C) 4.6 cm
D) 5.4 cm
x = 6cm * sin(50) = 4.59
rounded to 4.6
Answer is C
Answer:
option C is correct
The approximate value of x is, 4.6 cm(nearest to tenth)
Step-by-step explanation:
In the given figure; the triangle is right angle triangle:
Label the figure:
then, the triangle XYZ is right angle triangle.
Using trigonometric ratio:
The ratio of the opposite side of a right triangle to the hypotenuse is called the sine. i.e,
[tex]Sine=\frac{opposite}{Hypotenuse}[/tex]
using sine ratio in triangle XYZ:
[tex]\sin 50^{\circ} = \frac{XY}{XZ}[/tex]
Substitute the value of XY = x cm and XZ = 6 cm in above ratio:
[tex]\sin 50^{\circ} = \frac{x}{6}[/tex] or
[tex]0.76604444247801 = \frac{x}{6}[/tex]
Simplify:
[tex]x= 4.59626665[/tex] cm
Therefore, the approximate value of x nearest to tenth is, 4.6 cm
Jack's overtime wage is $3 per hour more than his regular hourly wage. He worked for 5 hours at his regular wage and 4 hours at the overtime wage. He earned $66. Find his regular
What is the reason for each step in the solution of the equation? −5(x−6)=10x Drag and drop the reasons into the boxes to correctly complete the table.
Answer:
Step-by-step explanation:
-5(x -6) = 10x . . . . . given
-5x +30 = 10x . . . . distributive property of multiplication over addition
30 = 15x . . . . . . . . addition property of equality (5x was added to both sides)
2 = x . . . . . . . . . . . division property of equality (both sides were divided by 15)
hope this helped
Julio's father is 4 times as old as Julio. The sum of their ages is no less than 55.
What is the youngest age Julio can be?
Enter your answer in the box.
years
Please check and correct the following answers:
What decimal is equivalent to 72/100?
Is the answer 0.72?
Express 0.72 as a fraction in simplest form.
Is the answer 18/25?
What makes the statement true? 9^-2 = ?
Is the answer 1/81
assume that y varies inversely with x. if y=27 when x=12, find x when y=-12.
What is the common difference for the sequence shown below? coordinate plane showing the points 1, 5; 2, 2; and 3, negative 1?
Answer:
the common difference of the sequence (d) = -3
Step-by-step explanation:
Given sequence is 1st term, 2nd term, 3rd term
= 5, 2, -1
It is an arithmetic sequence.
The common difference (d) = second term - first term
d = 2 - 5
d = -3
Therefore, the common difference of the sequence (d) = -3
Hope this will helpful.
Thank you.
Choose the product. 4p^3 3(p 2^ + 8p - 3)
4p^5 + 12p^4 + 7p^3
4p^6 + 44p^3
4p^3 - 12p^2 +32p^4
4p^5 + 32p^4 -12p^3
Answer: The correct option is
(D) [tex]4p^5+32p^4-12p^3.[/tex]
Step-by-step explanation: We are given to choose the correct expression for the following product :
[tex]P=4p^3(p^2+8p-3)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the above product, we need to multiply 4p³ with every term within the bracket.
The required product (i) is
[tex]P\\\\=4p^3(p^2+8p-3)\\\\=4p^{3+2}+32p^{3+1}-12p^3\\\\=4p^5+32p^4-12p^3.[/tex]
Thus, the required product is [tex]4p^5+32p^4-12p^3.[/tex]
Option (D) is CORRECT.
The sum of two integers is 9 their difference is 5 what are the two integers
The values of the two integers are 7 and 2 respectively.
Let the two integers be a and b respectively.In this exercise, you're required to determine two integers from the given word problem.
Thus, we would write a mathematical (algebraic expression) for the sentence.
Translating the word problem into an algebraic expression, we have;
The sum of two integers is 9;
[tex]a + b =9[/tex] ....equation 1.
The difference between the two integers is 5;
[tex]a - b = 5[/tex] equation 2.
Solving the systems of linear equations by using the elimination method, we have:
[tex]2a = 14[/tex]
Dividing both sides by 2, we have:
[tex]a = \frac{14}{2}[/tex]
a = 7
To find the value of y:
[tex]a + b =9\\\\7 +b=9\\\\b =9-7[/tex]
b = 2
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The stores below each have the same snowboard for an original price of $189.59. At which store can you get the snowboard for the lowest price?
Answer:
D. You can get the lowest price at Store C.
Step-by-step explanation:
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How can you find a unit rate when given a rate?
Is the sequence geometric? If so, identify the common ratio.
2, -4, -16, -36, ...
A. Yes; -2
B. Yes; 2
C. Yes; -3
D. No
Answer:
No this is not the sequence geometric.
Step-by-step explanation:
Given : 2, -4, -16, -36, ...
To find : Is the sequence geometric? If so, identify the common ratio.
Solution : We have given that 2, -4, -16, -36, ...
In a Geometric Sequence each term is found by multiplying the previous term by a constant.
Geometric Sequence like this:
{a, ar, ar², ar³, ... }
On comparing
2, -4, -16, -36, ...
{ 2 , 2 ×-2, 2×(-2)², 2×(-2)³..
So we get { 2, -4, -8, -16...
Therefore , No this is not the sequence geometric.
Since the quotient between consecutive terms is different, the sequence is not geometric, and the correct option is:
D. No Geometric sequence:In a geometric sequence, the quotient between consecutive terms is always the same, and it is called common ratio.
In this problem, the sequence is: {2, -4, -16, -36, ...}
[tex]-\frac{4}{2} = -2[/tex]
[tex]\frac{-16}{-4} = 4[/tex]
Different quotients, hence not geometric, and option D is correct.
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The sum of two numbers is 28. one number is 14 more. find the numbers
The polynomial function y = x3 -3x2 + 16x - 48 has only one non-repeated x-intercept. What do you know about the complex zeros of the function?
A) The function has one imaginary zero.
B) The function has one real zero and two imaginary zeros.
C) The function has one real zero and one imaginary zero.
D) The function has one imaginary zero and two real zeros.
The correct answer is
D) The function has one imaginary zero and two real zeros.
x = 3, 4i, -4i
A building that is 15 meters tall casts a shadow that is 6 meters long. at the same time, a tree casts a shadow that is 9 meters long. how tall is the tree
Final answer:
To determine the height of the tree, we use proportions based on the shadow lengths. Since the building is 15 meters tall with a 6-meter shadow and the tree's shadow is 9 meters, the height of the tree is found to be 22.5 meters.
Explanation:
You're asking how to find the height of a tree based on its shadow's length using similar triangles. The building is 15 meters tall and casts a 6-meter-long shadow. We can set up a proportion since the tree and the building have the same sun angle, thus their heights and shadows are in proportion. We will compare the building's height to its shadow, and then set this ratio equal to the tree's height to its shadow.
Using the formula for proportions:
Building height / Building shadow = Tree height / Tree shadow
Which translates to:
15 meters / 6 meters = Tree height / 9 meters
Now we solve for the Tree height:
Tree height = (15 meters / 6 meters) * 9 meters = 22.5 meters
The height of the tree is 22.5 meters.
karen has 12 apples. she gives 3 to john, 4 to lennard, and 2 to tracy. she then takes away 2 from john, 1 from lennard, and 1 from tracy. how many apples does she have now?
Solve for the variable: 12.9 = x + 7.1 5.8 -5.8 20 -20
How do I write the interval(s) for which f(x) is greater than or equal to 0 (interval notation)
To write intervals where f(x) is greater than or equal to 0, solve the equation f(x) >= 0 for x. The solutions are then expressed in interval notation. For instance, x >= 3 is written as [3, infinity).
To write the interval for which f(x) is greater than or equal to 0 in interval notation, you first need to establish where the function is above or touching the x-axis. With algebraic functions, you simply solve the equation f(x) >= 0 for x to find where the function is non-negative. You then write these solutions in interval notation. For example, if your solution was x >= 3, you would write this in interval notation as [3, infinity). Also, keep in mind that round brackets ( ) are used when the number is not included in the interval while square brackets [ ] are used when the number is included.
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To rent a certain meeting room, a college charges a reservation fee of $37 and an additional fee of $6.70 per hour. the chemistry club wants to spend less than $90.60 on renting the meeting room. what are the possible amounts of time for which they could rent the meeting room? use t for the number of hours the meeting room is rented, and solve your inequality for t .
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
A coat hanger is in the shape of isosceles triangle ABC shown in the figure. Sides AB and BC are congruent.
if m<BAC=22, then m<ABC= ?
Answer: m∠ABC=136°
Step-by-step explanation:
In the given figure we have a coat hanger is in the shape of isosceles triangle ABC.
Sides AB and BC are congruent.
The isosceles theorem says that the angles opposite to the equal sides of a triangle are equal.
Therefore, in ΔABC, we have
m∠BAC=m∠BCA
If m∠BAC=22°, then m∠BCA= 22°
By angle sum property , we have
m∠BAC+m∠BCA+m∠ABC=180°
⇒22°+22°+m∠ABC=180°
⇒m∠ABC+44°=180°
⇒m∠ABC=180°-44°=136°
⇒m∠ABC=136°
Therefore, If m∠BAC=22°, then m∠ABC=136°
A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth. Area of a triangle = bh 68.7 cm2 161.7 cm2 381.3 cm2 450.0 cm2
Answer:
Option B is the correct answer.
Step-by-step explanation:
We have one side = 27.6 cm
Hypotenuse = 30 cm
Length of remaining side [tex]=\sqrt{30^2-27.6^2}=11.76cm[/tex]
Area of right angled triangle [tex]=\frac{1}{2}\times \texttt{Product of lengths of 2 sides other than hypotenuse}[/tex]
Area [tex]=\frac{1}{2}\times 27.6\times 11.76=161.7cm^2[/tex]
Option B is the correct answer.