PLEASE HELP DUE TODAY!!!!
while browsing in an antique store, cameron found this page that came from an old book of riddles
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Now that will mean that the sum of the angles that are listed as (8m - 18) and (5p + 2) will add up to 90. And since the angle (7m + 3) is opposite to the (5p + 2) angle, they're equal. Therefore (8m - 18) + (7m +3) = 90. Let's see what m is
(8m - 18) + (7m +3) = 90
8m - 18 + 7m + 3 = 90
15m - 15 = 90
15m = 105
m = 7
Since m = 7, you immediately know that (8m - 18) = 38, and (7m + 3) = 52.
And because of the opposite angles, you also know that (5p + 2) = 52, so p = 10, and (11t - 17) = 38, so t = 5
The line CE has been divided into 2 equal halves by point D, so
5a + 12 = 9a - 12
Solving for a, gets
5a + 12 = 9a - 12
12 = 4a - 12
24 = 4a
6 = a
So a = 6
The two angles off of point E are marked as congruent, so
48 = 21s + 6
42 = 21s
2 = s
So s = 2.
Now let's arrange the variables in numeric order.
s = 2
t = 5
a = 6
m = 7
p = 10
And upon doing so I see the word "stamp" as the answer to the riddle "What sits in a corner but travels around the world?"
Simultaneous equations can be solved if the number of unknown variables are equal to the number of equations. In the geometry question, the equations are given by the relationship between the lines and angles
Part A
m = 7°, p = 10°, t = 5°, a = 6, and s = 2°
Part B
Arranging the variables from least to greatest gives; stamp
A stamp sits at the corner of an envelope but travels around the world
Part A
From the diagram, we have;
H is a vertical angle to the 90° angle
(7·m + 3)° + 90° + (8·m - 18)° = 180° (linear angles)
∴ (7·m + 3)° + (8·m - 18)° = 180° - 90° = 90°
(15·m - 15)° = 90°
15·m = 90°+ 15° = 105°
m = 105°/15 = 7°
m = 7°
(7·m + 3)° = (5·p + 2)° (vertically opposite angle theorem)
∴ (5·p + 2)° = (7 × 7 + 3)° = 52°
p = (52° - 2°)/5 = 10°
p = 10°
(8·m - 18)° = (11·t - 17)° (vertically opposite angle theorem)
∴ (8 × 7 - 18)° = (11·t - 17)°
38° = (11·t - 17)°
11·t = 38° + 17° = 55°
t = 55°/11 = 5°
t = 5°
CD = 5·a + 12 and DE = 9·a - 12 are congruent segments
5·a + 12 = 9·a - 12 (Definition of congruent segments)
9·a - 5·a = 12 + 12 = 24
4·a = 24
a = 24/4 = 6
a = 6
(21·s + 6° and 48° are congruent congruent angles
21·s + 6° = 48° (Definition of congruent angles)
∴ s = (48° - 6°)/21 = 2°
s = 2°
Part B
Arranging the values of the variables from least to most gives;
s = 2°
t = 5°
a = 6
m = 7°
p = 10°
Which gives;
The answer to the riddle = s, t, a, m, p = Stamp
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Related Questions
Using altitude and hypotenuse to find the area of a right triangle
Answers
Then multiply the base with the altitude and divide that by 2 and you'll get the area
The graph of g(x)=(1/2)x is the graph of f(x)=2x reflected over the y-axis. Which graph represents g(x) please help!
Answers
Answer:
Step-by-step explanation:
What is the equation of the line in standard form? (-1,-4) (2,2)
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When you set it up, it should look something like this: (2-(-4))/(2-(-1)) which would simplify to 6/3 which would simplify to 2. This only finds your slope, however. Now that you know your slope, you can start by first setting up you equation in slope intercept form which should be in this format: y=mx+b
Since you already know the slope (m) and the x and y values (you can use either coordinate, I'm just using (2,2)) your equation would look something like this: 2=2(2)+b. After this, you solve for b which happens to be -2, making your slope intercept equation: y=2x-2.
Now you can convert to standard form. In standard form, you have to have the equation in this format: ax+by=c where there cannot be decimals, fractions, and everything needs to already have the greatest common factor taken out. When you do this, you first need to subtract over 2x which makes the equation look like this: -2x+y=-2. However, ax cannot be negative, so you multiply your entire equation by -1. You then get your answer: 2x-y=2
Name a pair of vertical angles, a straight angle, and two scute angles other than
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Answer:
∠GEN and ∠FED, ∠GEF and ∠DEN are few of the vertical angles.
∠ENM and ∠NKP, ∠HKC and ∠ADE are few of the straight angles.
∠GEN and ∠FED, ∠JNM and ∠EHK are few of the acute angles.
Step-by-step explanation:
Vertical angles are the angles made by two intersecting lines and they are equal
So,
∠GEN and ∠FED, ∠GEF and ∠DEN are few of the vertical angles.
Straight angles are angles that are 180°
So,
∠ENM and ∠NKP, ∠HKC and ∠ADE are few of the straight angles.
The angles less than 90° are called acute angles
So,
∠GEN and ∠FED, ∠JNM and ∠EHK are few of the acute angles.
∠GEN and ∠FED, ∠GEF and ∠DEN are few of the vertical angles.
∠ENM and ∠NKP, ∠HKC and ∠ADE are few of the straight angles.
∠GEN and ∠FED, ∠JNM and ∠EHK are few of the acute angles.
How to explain the angleVertical angles are the angles made by two intersecting lines and they are equal, ∠GEN and ∠FED, ∠GEF and ∠DEN are few of the vertical angles.
Straight angles are angles that are 180° ∠ENM and ∠NKP, ∠HKC and ∠ADE are few of the straight angles.
The angles less than 90° are called acute angles∠GEN and ∠FED, ∠JNM and ∠EHK are few of the acute angles.
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To which graph does the point (−1, 4) belong?
y ≤ −x + 4
y ≤ −x − 2
y ≤ 2x − 3
y ≤ 4x + 1
Answers
4 <= -(-1) + 4 = 5
so this fits
Its A
Answer: First one
Step-by-step explanation:
Due to slope form which is y=mx + b.
-1 = x and y = 4.
It does not show the one because it would be equal to X, but it does show the negative
An exterior angle of an isosceles triangle has measure 130°. Find two possible sets of measures for the angles of the triangle.
If the exterior angle of the bases is 130°, then the measure of the angle of each base is
--------degrees° and the measure of the vertex is --------
I ALWAYS GIVE BRAINLIEST!! PLZ HELP
Answers
vertex is 50°: base=(180-50)/2=65°
base is 50°: vertex= 180-2*50=80°
vertex 50 base 65; vertex 80, base 50
(2)base=180-130=50°
vertex=180-2*50=80°
base 50 vertex 80
Given that an isosceles triangle has an exterior angle of its base angle that is 130°, the two possible sets of angles obtainable in the triangle are:
Base angles: [tex]\mathbf{30^{\circ}}[/tex]Vertex angle: [tex]\mathbf{80^{\circ}}[/tex]Recall:
An isosceles triangle has two equal base angles and two equal sides.Thus:
The isosceles triangle has been given in the image attached below to show the possible angle measures we can get.
In figure 1, we see that when the exterior angle of the bases is 130°, the measure of each of the base angles would be:
[tex]\mathbf{180 - 130 = 50^{\circ}}[/tex]
The vertex angle would be:
[tex]\mathbf{180 - (50 + 50) = 80^{\circ}}[/tex]
Therefore, given that an isosceles triangle has an exterior angle of its base angle that is 130°, the two possible sets of angles obtainable in the triangle are:
Base angles: [tex]\mathbf{30^{\circ}}[/tex]Vertex angle: [tex]\mathbf{80^{\circ}}[/tex]Learn more here:
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If l || m, what is the value of x?
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D. 27 should be your answer.
A triangle has angles that measure 120°, 39°, and 21°. what kind of triangle is it?
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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 magazine has a special offer of 18 issues for $28.44. How much does each issue cost?
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18x = 28.44
Divide 18 from both sides.
x = 1.58
Each issue costs $1.58
Hope this helps!
Answer:
A magazine has a special offer of 18 issues for $28.44. Each issue costs $1.58. Solution: 28.44 / 18 = 1.58.
Prove that the sum of three consecutive positive integers is divisible by 3
Answers
[tex]n+n+1+n+2=3n+3=3(n+1)[/tex]
Which statements are true about the ordered pair (−3, 1) and the system of equations?
{x−4y=6
3x+y=−8
Select each correct answer.
The ordered pair (−3, 1) is a solution to the first equation because it makes the first equation true.
The ordered pair (−3, 1) is a solution to the second equation because it makes the second equation true.
The ordered pair (−3, 1) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (−3, 1) is a solution to the system because it makes both equations true.
Answers
-3 - 4(1) = 6
-3 - 4 = 6
-7 = 6
so this in incorrect. the ordered pair is not a solution to the first equation.
3x + y = -8 (-3, 1)
3(-3) + 1 = -8
-9 + 1 = -8
-8 = -8
this is correct. the ordered pair is a solution to the second equation.
the answer is the ordered pair (-3, 1) is a solution to the second equation because it makes the second equation true.
hope this helped, God bless!
At 2:00 p.m. two cars start toward each other from towns 240 miles apart. If the rate of one car is 10 mph faster than the other, how fast does each car go if they meet at 5:00 p.m.? If 3x represents the distance that the slower car traveled, then which expression represents the distance the faster car traveled?
Answers
To find the speed of each car, we set up and solve an equation based on the given information. The slower car's speed is 35 mph and the faster car's speed is 45 mph.
Explanation:To solve this problem, we need to set up an equation based on the given information. Let's assume that the slower car's speed is x mph, so the faster car's speed would be (x + 10) mph. Since they meet at 5:00 p.m. and start at 2:00 p.m., they have been traveling for 3 hours.
Using the formula: speed = distance/time, we can write the equation:
x * 3 + (x + 10) * 3 = 240
Simplifying the equation, we get:
3x + 3(x + 10) = 240
6x + 30 = 240
6x = 210
x = 35
So, the slower car's speed is 35 mph and the faster car's speed is (35 + 10) = 45 mph.
What system of linear inequalities is shown in the graph?
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u have a solid line...it has a y int of 2...it has a slope of -2...it is shaded below the line...this inequality is : y < = -2x + 2
tony and sal drove in opposite direction from the same starting point. tony averaged 15 mpg faster then sal. after 5 hours they were 425 miles apart. how fast was each of them driving?
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distance = speed * time
distance = 425 miles
time = 5 hours
Sal's speed = s
Tony's speed = s + 15
Since they drove in opposite directions, the speed between them is the sum of the speeds.
distance = speed * time
425 = (s + s + 15) * 5
85 = 2s + 15
70 = 2s
s = 35
s is Sal's speed and is 35 mph.
Tony's speed is 15 mph faster, so Tony's speed = 35 mph + 15 mph = 50 mph
Answer:
Sal's speed was 35 mph
Tony's speed was 50 mph
Are the following figures similar?
yes or no?
Corresponding angles are congruent
Yes or no?
Corresponding sides are proportional
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Francesca typed 496 words in 8 minutes. Which of the following is a correct understanding of this rate?
a. at this rate, it takes 62 minutes for Francesca to type one word
b.at his rate, Fransesca can type 62 words in 8 minutes.
c. at this rate, Fransesca can type 62 words in one minute.
d. at this rate, Fransesca can type 8 words in one minute.
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HELP ME PLS!!!!!!!!!!!!!!!!!!!
Answers
the number inside the parenthesis includes the interest rate ( annual percentage
looking at the possible functions, if you raise the interest rate to the power of 12, you would need to divide the number of years (t) by 12 as well
so the function could be rewritten as A=1000(1.023^12)^t/12
since the annual percentage rate is 2.3% ( 0.023)
divide 0.023/12*100 = 0.19% per month interest
Mrs. Williams is deciding between two field trips for her class. The Science Center charges $80 plus $5 per student. The Dino Discovery Museum simply charges $7 per student. For how many students will the Science Center charge less than the Dino Discovery Museum charges?
fewer than 40 students
78 or fewer students
78 or more students
more than 40 students
HELP!!
Answers
Answer: More than 40 students
Step-by-step explanation:
Let x be the number of students .
Given : Mrs. Williams is deciding between two field trips for her class. The Science Center charges $80 plus $5 per student.
i.e. Total cost : [tex]80+5x[/tex] (1)
The Dino Discovery Museum simply charges $7 per student.
i.e. Total cost : [tex]7x[/tex] (2)
The inequality that shows Science Center charge less than the Dino Discovery Museum charges will be :-
[tex]80+5x<7x[/tex]
Subtract 5x on both sides , we get
[tex]80<2x[/tex]
Divide both sides by 2 , we get
[tex]40<x[/tex]
Hence, for more than 40 students the Science Center charge will less than the Dino Discovery Museum charges.
If it takes 5 machines 5 minutes to make 5 widgets, how many minutes does it take 500 machines to make 500 widgets?
Answers
You need to buy fertilizer for a circular flower bed with a diameter of 13 feet. If one bag will fertilize 10 square feet, how many bags do you need to buy?
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The area of the flower bed is approximately 132.73 square feet. Each bag of fertilizer covers 10 square feet, so we'd need 13.27 bags. Rounding up, we'll need to buy 14 bags.
Explanation:The question involves the calculation of the area of a circular flower bed and determining the amount of fertilizer needed for that area. The area of a circle can be calculated using the formula πr², where 'r' (radius) is half of the diameter. In this case, the diameter of the flower bed is 13 feet, so the radius is 13/2 = 6.5 feet. We then square the radius (6.5²) which gives us 42.25 and multiply by π (approximately 3.14), resulting in an area of approximately 132.73 square feet. Given that each bag of fertilizer covers 10 square feet, we would need 13.27 bags of fertilizer. Since we cannot buy a fraction of a bag, we would need to buy 14 bags to fully cover the flower bed.
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Timothy deposited $2,780.20 in a savings account that earns 4.3% simple interest. What will Timothy’s account balance be in 7 months?
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[tex]\bf \qquad \textit{Simple Interest Earned Amount}\\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \$2780.20\\ r=rate\to 4.3\%\to \frac{4.3}{100}\to &0.043\\ t=years\to &\frac{7}{12} \end{cases} \\\\\\ A=2780.20\left(1+0.043\cdot \frac{7}{12} \right)[/tex]
What is the solution to the equation 1.2m − 0.8 = −2.0m?
A.) m= 0.25
B.) m= 0.4
C.) m= 1
D.) m= 4
Answers
Simplify. 1/3(−32.48−14.02) Enter your answer, as a decimal to tenths, in the box.
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= 1/3(-46.5)
= -15.5
-15.5 is the answer.
Answer: After doing the order of operations and round the decimal to tenths the result is - 15.5
Solution:
1/3(-32.48-14.02)
1. Operations inside the parentheses: Add numbers with the same sign:
1/3(-46.50)
2. Multiplication:
1/3(-46.50/1)=[(1)(-46.50)] / [(3)(1)]=(-46.50)/(3)
3. Dividing:
(-46.50)/(3) = - 15.50
4. Rounding decimal to tenths:
- 15.50 = - 15.5
Televisions are on sale for 85% of the original price of $499. what is the sale price?
Answers
What are the real and imaginary parts of the complex number?
-6-i
Answers
imaginary part=-i
Answer:
Real part: -6
Imaginary part: -1
Step-by-step explanation:
A complex number is a number that has a real part and an imaginary part. These numbers usually are represented in the form a + bi where a and b are real numbers and b is the imaginary part (i is actually the solution to the equation [tex]x^{2} +1=0[/tex] or x²=-1 which has no roots in the real numbers and therefore we call the solution √-1=i)
Now, proceeding to the complex number you wrote, if we write it as a + bi we would have a = -6 b = -1
Therefore the real part is a = -6 and the imaginary part would be -1.
50 POINTS
Mei draws three pairs of parallel lines that are each intersected by a third line. In each figure, she measures a pair of angles.
What is a reasonable conjecture for Mei to make by recognizing a pattern and using inductive reasoning?
Answers
when a pair of parallel lines are intersected by a third line, the alternate interior angles are congruent
A reasonable conjecture for Mei is the Alternate Interior Angles Theorem, which states if a transversal intersects parallel lines, the alternate interior angles are equal.
Explanation:Based on the scenario, a reasonable conjecture for Mei to make would be, if a transversal intersects parallel lines, then the alternate interior angles are congruent. This statement is known as the Alternate Interior Angles Theorem. In other words, in each of Mei's figures, if the angles she measured are alternate interior angles, they should have the same measurement.
For example, if three pairs of parallel lines are intersected by a third line (called a transversal), a pattern that consistently appears is the equality of the alternate interior angles (angles that are on opposite sides of the transversal and inside the parallel lines). This implies, if the two lines are parallel, then any alternate pair of interior angles are equal.
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There are 50 cards numbered from 1 to 50. two different cards are chosen at random. what is the probability that one number is twice the other number?
Answers
The probability that one number is twice the other number when two different cards are chosen at random is 1/49.
Explanation:To find the probability that one number is twice the other number when two different cards are chosen at random from a set of 50 cards numbered from 1 to 50, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The favorable outcomes occur when one card is twice the value of the other card. Let's consider the smaller number as 'x'. In that case, the larger number would be '2x'. We can see that 'x' can take any value from 1 to 25, since the larger number '2x' should be less than or equal to 50.
So, the number of favorable outcomes is 25. The total number of possible outcomes is the number of ways to choose 2 cards out of 50, which is given by the combination formula: C(50, 2) = 50! / (2! * (50-2)!), which simplifies to 50 * 49 / 2 = 1225.
Therefore, the probability is given by the ratio of the favorable outcomes to the total number of possible outcomes: 25/1225 = 1/49.
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The height of a right circular cone is multiplied by 3, but its radius remains fixed. By what factor will the volume of the cone be multiplied?
Answers
The volume of the cone will be multiplied by a factor of [tex]\(3^1 = 3\).[/tex]
The volume of a right circular cone is given by the formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cone.
Given that the height of the cone is multiplied by 3, the new height [tex](\( h' \))[/tex] becomes 3 times the original height [tex](\( h \))[/tex]:
[tex]\[ h' = 3h \][/tex]
Now, let's find the volume of the new cone with the updated height:
[tex]\[ V' = \frac{1}{3} \pi r^2 (3h) \][/tex]
[tex]\[ V' = \pi r^2 (h) \times 3 \][/tex]
So, the volume of the new cone is three times the original volume.
Now, let's dive into the explanation:
When the height of a cone is multiplied by a factor, the volume of the cone is directly proportional to the cube of that factor. This is because the volume formula contains the height term raised to the power of 3. So, if the height is tripled, the volume will be multiplied by[tex]\(3^3 = 27\).[/tex]
Alternatively, we can calculate it directly:
Original Volume: [tex]\(V = \frac{1}{3} \pi r^2 h\)[/tex]
New Volume:[tex]\(V' = \frac{1}{3} \pi r^2 (3h) = \pi r^2 h \times 3\)[/tex]
Therefore, the volume of the cone will be multiplied by a factor of [tex]\(3^1 = 3\).[/tex]
Complete question:
The height of a right circular cone is multiplied by 3, but its radius remains fixed. By what factor will the volume of the cone be multiplied?
Simplify the expression 2.1(4.5x)
Answers
I WILL GIVE YOU BRAINLIEST JUST HURRY PLZ
Does 1/1 count as 1 in fractions
Answers
if you have 1/2, it counts as 0.5, because 1 divided by 2 is 0.5
hope this helps