Answer:
30° and 60°
Step-by-step explanation:
Let the interior angles be ∠x₁ (smaller) and ∠x₂ (larger), and the exterior angle ∠X.
Making the statements into equations :
Size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles ⇒ ∠X + ∠x₁ + ∠x₂ = 180° [Equation 1]
Greater of the opposite interior angles exceeds smaller by 30° :
⇒ ∠x₂ = ∠x₁ + 30° [Equation 2]
By exterior angle property :
⇒ ∠x₁ + ∠x₂ = ∠X [Equation 3]
Substituting Equation 3 in Equation 1 :
⇒ ∠x₁ + ∠x₂ + ∠x₁ + ∠x₂ = 180°
⇒ 2 (∠x₁ + ∠x₂) = 180°
⇒ ∠x₁ + ∠x₂ = 90°
⇒ ∠x₂ = 90° - ∠x₁ [Equation 4]
Substituting Equation 4 in Equation 2 :
⇒ 90° - ∠x₁ = ∠x₁ + 30°
⇒ 2∠x₁ = 60°
⇒ ∠x₁ = 30°
Substituting the value of ∠x₁ in Equation 2 :
⇒ ∠x₂ = 30° + 30°
⇒ ∠x₂ = 60°
The measures of the interior angles are 30° and 60°
What are the phrase in a business cycle
Please help and thank you.
X=[?]
x = 6
Step-by-step explanation:Equilaterals are a type of triangle where all of the sides are congruent. The angles are also all equal.
Setting Up the Equation
As stated above, all of the sides are congruent. This means that the lines must be equal to which others. Since the sides are equal, we can set them equal to each other.
AB = ACNow, we can substitute the expressions in the equation.
22x - 33 = 7x +57Solving the Equation
After we set up the equation, we can solve for x using the properties of equality. There are different orders in which this can be solved. So if you prefer to work in a different order, the answer should still be the same.
First, rewrite the equation
22x - 33 = 7x +57Next, add 33 to both sides
22x = 7x + 90Then, subtract 7x from both sides
15x = 90Finally, divide both sides 15
x = 6This gives us our final answer of 6.
Checking the Answer
If you wanted to, you can check your answer by plugging 6 into the original equation.
22(6) - 33 = 7(6) + 57Then solve the equation
99 = 99Since both sides are equal, the answer must be correct.
Show what you know: work out the problems below and submit a photo of your work to receive full credit.
The Florida A&M Rattlers are decorating campus for homecoming weekend. Students use 3 rolls of orange streamers for every 2 rolls of green streamers for every dorm they decorate.
Draw a model that represents the ratio of different colored streamers.
Draw a model that shows the number of orange and green streamers needed to decorate 3 dorm rooms.
The model for representing the ratio of the number of orange and green rolls are [tex]\dfrac{3}{2}[/tex].
A model that shows the number of orange and green streamers needed to decorate 3 dorm rooms will be 3O=2G
What is ratio?The ratio is defined as the representation of the one number with respect to the other number. or one number is how many times to the other number.
A model that represents the ratio of different colored streamers.
[tex]\dfrac{O}{G}=\dfrac{3}{2}[/tex]
A model that shows the number of orange and green streamers needed to decorate 3 dorm rooms.
D=3O and D=2G
3O=2G
Hence the models are [tex]\dfrac{O}{G}=\dfrac{3}{2}[/tex] and 3O=2G.
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Victoria wants to purchase a tablet. She has $130 to spend. She finds one that regularly sells for $139.99 and is on sale of 15% off. Sales tax is 7%. How much will Victoria pay for the tablet? Show your work and record your answer in the red box.
Answer:
$127.32
Step-by-step explanation:
Selling price= $139.99
Sale discount= 15% = $139.99 * 0.15 = $21
Discounted price= $139.99 - $21 = $118.99
Sales tax added= 7% = $118.99 * 0.07 = $8.33
Victoria has to pay = $118.99 + $8.33 = $127.32 so she has enough money to buy it with $2.68 left
Byrn has a stack of photos measuring 12cm wide and 16cm high. He wants to display them on a large rectangular poster in such a way that all photos are equally spaced on each side, including at the edges of the poster, as illustrated (in the attached file)
Q1. Bryn wants to display 9 photos (with longer side vertical) in 3 rows of 3 photos each with 2cm spacing around each photo. What are the dimensions of the poster?
Q2. Bryn wants to display 24 photos (with longer side vertical) with 2cm spacing around each photo. He wants more columns than rows of photos. Find the smallest poster area that is needed.
Q3. Bryn wants to display 18 photos in 3 rows of 6 photos each with 3cm spacing around each photo. The photos may all be displayed in portrait orientation (longer side vertical) or in landscape (longer side horizontal). Which orientation uses the lesser poster area?
Q4. Bryn wants to display 24 photos (with longer side vertical) in 6 rows of 4 photos each with equal spacing around each photo. He has a poster that is 62cm wide and 120cm high. He wants to use the full width of the poster but is prepared to trim some of its height to achieve the equal spacing. How much of the poster does he need to trim?
Please provide working out for all of the answers. Thanks.
The answers for the questions are:
1) The dimensions of poster are 44cm by 56cm
2) The smallest poster area needed is 5328 square centimeter
3) The orientation that uses the lesser poster area is portrait.
4) He needs to trim 4.4cm of the height of poster
What is a rectangle?A rectangle is a quadrilateral with opposite sides equal and all angles 90°
Analysis:
1) since there are 3 photos per row, the spacing for the three photos are 4. Also since there are 3 photos on the column, the spacing would be 4
width of poster = 2x4 + 3x12 = 8 + 36 = 44cm
Height of poster = 4x2 + 3x16 = 56cm
2) possible combinations, are 8 picture on a row and 3 picture on a column
width = 9spacing x 2cm + 8 pictures x 12 = 114cm
length = 4 spacing x 2 + 3pictures x 16 = 56cm
12 pictures on a row and 2 pictures on a column
width = 13 spacing x 2cm + 12 pictures x 12 = 170cm
length = 3 spacing x 2cm + 2 pictures x 16 = 38cm
6 pictures on a row and 4 pictures on a column
width = 7 spacing x 2cm + 6 pictures x 12 = 72cm
length = 5 spacing x 2cm + 4 pictures x 16 = 74cm
The smallest area is 74 x 72 = 5328 square centimeter
3. For portrait,
width = 6 photos x 12cm + 7 spacing x 2cm = 86cm
length = 3 pictures x 16cm + 4 spacing x 2cm = 56cm
For landscape,
width = 6 photos x 16cm + 7spacing x 2cm = 110cm
length = 3 pictures x 12cm + 4 spacing x 2 = 44cm
The lesser poster area is portrait orientation with 86 x 56 = 4816 square centimeter.
4. Let the equal spacing be P
for full width = 62cm
4pictures x 12cm + 5 spacing x P = 62
48 + 5p = 62
5P = 62-48
5P = 14
P = 14/5 = 2.8cm
length of poster using equal spacing of 2.8cm
length would take 6 photos
6 photos x 16 + 7 spacing x 2.8 = 115.6cm
original length of poster is 120cm
so he would need to trim (120-115.6) = 4.4cm
In conclusion, The answers to the questions are:
1) dimensions of poster are 44cm by 56cm
2) The smallest poster area needed is 5328 square centimeter
3) The orientation that uses the lesser poster area is portrait
4) He needs to trim 4.4cm of the height of poster
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Solve the following equation: 3t = 21
3t=21
[tex]t = \frac{21}{3} \\ t = \frac{ \cancel{{21}}{{}^{\:\:\:7}}}{\cancel3} \\ t = 7 \: \: answer[/tex]
5
5.2
4
Find the area of the parallelogram.
square units
Answer:
20 square units
Step-by-step explanation:
Area of a parallelogram is calculated with the following formula:
b*h (b: base, h: height)
5*4 = 20 square units
If you reflect point B(- 2, 5) over the y- axis, what is the reflected point ?
Answer:
(2,5)
Step-by-step explanation:
Since it is reflected across the y-axis only the x point will change and vise-versa
The figure below shows three quadrilaterals on a coordinate grid: A coordinate grid is shown from positive 8 to negative 8 on the x axis and from positive 8 to negative 8 on the y axis. An image of a rectangle labeled M is shown on ordered pair negative 1, negative 1 and negative 3, negative 1 and negative 3, negative 2 and negative 1, negative 2. Another image of a rectangle labeled N is shown on ordered pair negative 2, negative 2 and negative 6, negative 2 and negative 6, negative 4 and negative 2, negative 4. Another image of a rectangle labeled O is shown on ordered pair 1, 1 and 1, 2, and 3 , 2 and 3, 1. Which of the following statements is true about the three quadrilaterals? N and O are similar and congruent. M and N are similar and congruent. M and O are similar but not congruent. M and N are similar but not congruent.
The quadrilateral A and quadrilateral B are similar but not congruent. Then the correct option is A.
What is a quadrilateral?Any closed figure made by 4 line segments joined end to end in a series is called a quadrilateral.
If a polygon is four-sided (a quadrilateral), the sum of its angles is 360°
The figure below shows three quadrilaterals A, B, and C on a coordinate grid.
Then the quadrilateral A and quadrilateral C are similar and congruent too.
The quadrilateral A and quadrilateral B are similar but not congruent.
Similarly, the quadrilateral C and quadrilateral B are similar but not congruent.
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What is the domain of the function graphed below?
O(-2, ∞) O(-3,4] and [7, ∞). O(-∞,4). O [-2,0] and (7, ∞)
Using it's concept, it is found that the domain of the function graphed below is given by:
[tex](-2,4][/tex] and [tex][7, \infty)[/tex].
What is the domain of a function?It is the set that contains all possible input values for the function. In a graph, it is given by the values of x.
In this problem, x assumes values greater than -2 and less or equal than 4, and then values of 7 or greater, hence the domain is given by:
[tex](-2,4][/tex] and [tex][7, \infty)[/tex].
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PLS HELP!!!
The coast guard is out to sea and gets notification that two ships need help. One ship is directly west of the coast guard, and the other is directly south, as shown in the image below. The two ships are 6 miles from each other. Which ship is currently closer to the coast guard?
PLEASE INCLUDE EXPLANATION!!!! THANK YOU!!!
So
cos47=Base/Hypotenusecos47=y/6y=6cos47And
sin47=x/6x=6sin47sin47=0.73
cos47=0.68
So meanwhile sin is greater so 6sin is also greater
x is greatership 2 is closerAnswer:
Ship 2
Step-by-step explanation:
From inspection of the diagram, the problem has been modeled as a right triangle. Therefore, to find [tex]x[/tex] and [tex]y[/tex], use trigonometric ratios then compare to determine which distance is the smallest.
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)To find [tex]x[/tex] use the sine trig ratio:
[tex]\implies \sf \sin(\theta)=\dfrac{O}{H}[/tex]
[tex]\implies \sin(47^{\circ})=\dfrac{x}{6}[/tex]
[tex]\implies x=6 \sin(47^{\circ})[/tex]
[tex]\implies x=4.39 \: \sf miles \:(2\:dp)[/tex]
To find [tex]y[/tex] use the cosine trig ratio:
[tex]\implies \sf \cos(\theta)=\dfrac{A}{H}[/tex]
[tex]\implies \cos(47^{\circ})=\dfrac{y}{6}[/tex]
[tex]\implies y=6 \cos(47^{\circ})[/tex]
[tex]\implies y=4.09 \: \sf miles \: (2 \: dp)[/tex]
As 4.09 < 4.39, ship 2 is currently closer to the coast guard.
In triangle HJK shown above what is the measure of ∠J in degrees
Angles in a triangle adds up to 180
180 - (25.5 +120.2) = 34.3
So, missing angle is 34.3 degrees
Hope this helps!
A ball is hit from the ground. When the ball has traveled a horizontal distance of d meters, its height, h, in
meters, can be modeled by the function h (d) = -
1 d + d.
What is the horizontal distance from the point where the ball is hit to the point where the ball lands on the
ground?
nour in the snaca nrovided
Answer:
125 meters
Step-by-step explanation:
The ball will hit the ground when its height is zero. Use that value for h in the equation, and solve for d.
__
h(d) = -d²/125 +d . . . . the given equation
0 = d(-d/125 +1) . . . . . use h=0, and factor out d
This equation is satisfied by values of d that make the factors zero:
d = 0 ⇒ d = 0
-d/125 +1 = 0 ⇒ d = 125
The horizontal distance to the landing point is 125 meters.
What is 16x^4-100y^4 factored completly
Answer:
16x^(4)-y^(4)
Step-by-step explanation:
a. Lily paid $6 for 3/8 lb of nuts.
What is the unit rate as complex fraction (simplify)
Answer:
Ib = $16 per lb
Step-by-step explanation:
Juan leaned a 55-foot ladder against the side of a building. The base
of the ladder is 21 feet from the base of the building. The top of the
ladder is 11 feet from the top of the building. How tall is the building?
Provide an answer accurate to the nearest tenth of a foot.
11
55
21
tabel optional
PLEASE HELP ME PASS 8th GRADE
Answer:
61.8 feet to nearest tenth.
Step-by-step explanation:
USING THE PYTHAGORAS THEOREM:
55*2 = 21^2 + h^2 where h is the height of the top of the ladder from the ground.
h^2 = 55^2 - 21^2
= 2584
h = √2584
= 50.83 ft.
So the height of the building
= 11 + 50.83
= 61.83 feet.
Write an equation in standard form of the line
With slope 2/5 and going through (-3,6).
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad \qquad \stackrel{slope}{m}\implies \cfrac{2}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{\cfrac{2}{5}}(x-\stackrel{x_1}{(-3)})\implies y-6=\cfrac{2}{5}(x+3)[/tex]
[tex]y-6=\cfrac{2}{5}x+\cfrac{6}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y-6)~~ = ~~5\left( \cfrac{2}{5}x+\cfrac{6}{5} \right)}\implies 5y-30~~ = ~~2x+6 \\\\\\ -2x+5y-30=6\implies -2x+5y=36\implies 2x-5y=-36[/tex]
r= 8.4 in
Calculate the diameter of the
circle.
Answer:
The diameter is 16.8
Step-by-step explanation:
The diameter is double the radius.
- -- - - - - - - - - - - - - - - - - - - - - - -
[tex]\diamond\large\blue\textsf{\textbf{\underline{Question:-}}}[/tex]
r=8.4 in. What is the circle's diameter?
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
Since the radius is exactly one-half of the diameter, we multiply the radius times 2 in order to find the diameter, which results in:-
d(diameter)=16.8 in
Good luck with your studies.-- - - - - - - - - - - - -- -- - - - - - - - - - - -- - -
What is “y is __ times x”
Answer:
6
Step-by-step explanation:
How to multiply problem in photo?
_____
yStep-by-step explanation:
15. Chris can run at a constant speed of 12 km/h. How long will it take him to run from
his home to the park, a distance of 0.8 km?
Remember to check that your answer is reasonable.
Answer:
Step-by-step explanation
1= 12
.8 of 1 = 48
so it should only take him 48 minutes since hes not taking a full hour but 0.8 is two of from an hour
whats mean and median of 11, 18, 5, 20, 8, 124, 17?
Answer:
The mean would be 29 and the median would be 17
Step-by-step explanation:
Hope this helps! :)
What am I supposed to do here?
Answer:
here is your answer.
Step-by-step explanation:
total frequency is 24
Next → Post Test: The Pythagorean Theorem and Volume
1
Select the correct answer from each drop-down menu.
50⁰
Z
45⁰
529
Factor completely.
5x² - 20x + 20 =
Answer:
[tex]5(x-2)^2[/tex]
Step-by-step explanation:
[tex]5x^2-20x+20\\=5(x^2-4x+4)\\=5(x-2)(x-2)\\=5(x-2)^2[/tex]
Complete the table to show the area of each circle.
Answer: look at my work its 10 pi cm ^2
Step-by-step explanation:
Answer:
Below in bold.
Step-by-step explanation:
Area of:
The large circle = π r^2 = π * 10^2 = 100π
The small circle = π * 5^2 = 25π.
Which of the following describes how to calculate net pay? Subtract the total deductions from the net pay. Subtract the total deductions from the net pay. Subtract the total deductions from the gross pay. Subtract the total deductions from the gross pay. Add the total deductions to the gross pay. Add the total deductions to the gross pay. Subtract the total deductions from the take-home pay.
Answer:
(b) Subtract the total deductions from the gross pay
Step-by-step explanation:
The term "net pay" is applied to the pay after deductions are subtracted. It is also called "take-home pay."
The pay computed based on earnings, commissions, credits, and bonuses, before any deductions, is called the "gross pay."
net pay = gross pay - deductions
Net pay is calculated by subtracting total deductions from gross pay.
Students in a school were asked to collect old bottles as part of a recycling drive. Some of the data recorded at the drive is shown in the histogram below:
A histogram is shown with title Recycle Drive Collection. On the horizontal axis the title is Number of bottles. The title on the vertical axis is Students. The range on the horizontal axis is 0 to 3, 4 to 7, and 8 to 11. The values on the vertical axis are from 0 to 10 at intervals of 1. The bar for the first range is till 3, the bar for the second range is till 6, the bar for the third range is till 1.
Which information is not provided in the histogram?
The total number of students who collected bottles
The number of students who collected exactly 9 bottles
The number of students who collected 3 or fewer bottles
The total number of students who collected 7 or fewer bottles
*will Mark Brainliest*
Answer:
I'm very sure it is B. The number of students who collected exactly 9 bottles.
Step-by-step explanation:
A is wrong because it does show the total amount of students.
C is wrong because it does show the amount of students that collected 3 or fewer bottles.
D is wrong because it does show the total number of students who collected 7 or fewer bottles.
So, B would be the only correct answers. Hope I helped!! Pls mark brainliest if I did help.
Answer:
The answer your looking for would be B. "The number of students who collected exactly 9 bottles"
Step-by-step explanation:
I took the FLVS test.
Aaron is designing a party game in which he needs exactly 24 possible outcomes. Which sets of actions can he use to have a statistically fair game?
Toss a coin twice, then roll a 6-sided number cube with the digits 1 to 6.
Select a card from a set of cards with the letters A through D, then spin this once.
Randomly select a number from 1 to 16, then roll an 8-sided number cube with the digits 1 to 8.
Spin this and roll an 8-sided number cube with the digits 1 to 8.
Randomly select an odd digit {1, 3, 5, 7, 9}, then flip a coin twice.
Select a card from a set of cards with the letters A through N, then spin this once.
The set of actions that should be used is: toss a coin twice, then roll a 6-sided number cube
Which sets of actions can he use to have a statistically fair game?
We know tath the game has 24 possible outcomes. Then we need to find a set of actions that gives 24 different outcomes all with the same probability.
Of the given options, the only one that has a sample space of 24 elements is the first one.
Toss a coin twice and then roll a D6.
For each coin toss, the outcomes are 2 (tails and heads).
For the D6 there are 6 outcomes (1, 2, 3, 4, 5, 6)
Then the total number of outcomes for two tosses and rolling the number cube is given by the product between the numbers of outcomes for each individual part:
C = 2*2*6 = 4*6 = 24.
From this, we conclude that this is the correct option.
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Answer:
the correct ones are
2, Select a card from a set of cards with the letters A through D, then spin this once.
5,Toss a coin twice, then roll a 6-sided number cube with the digits 1 to 6.
6, spin this and roll an 8-sided number cube with the digits 1 to 8.
Step-by-step explanation:
so basically both the colored wheel answers and the one with the coin and cube
plato 2022
Answer the Volume Based Question. I will make uh Brainliest + 50 points
Step-by-step explanation:
(i) For cuboid shaped container:[tex]l = 3a\: cm,\: b = 3a\:cm,\: h = x\:cm[/tex] (Given)Container is filled with water so the volume of water can be given by the following formula:[tex]V_{water} = lbh[/tex]Plugging the values of l, b and h in the above formula, we find:[tex]V_{water} = (3a)(3a)(x)[/tex][tex]\huge{\red{\boxed{V_{water} = 9a^2x\:cm^3}}}[/tex](ii) For solid right circular cylinder:radius (r) = a cm, h = a cmFormula for volume of cylinder is given as:[tex]V_{cylinder} =\pi r^2 h[/tex][tex]V_{cylinder} =\pi (a)^2 (a)[/tex][tex]\huge{\purple{\boxed{V_{cylinder} =\pi a^3 \:cm^3}}}[/tex]