Answers
Step-by-step explanation:
The Triangle Sum Theorem states that the interior angles of a triangle add up to 180 degrees. A square for an angle symbolizes that the angle is 90 °, as is the case with angle ∠ACB.
Therefore, as ∠CAB = 2x and ∠ABC = 3x, and angles ∠ACB, ∠CAB, and ∠ABC make up the interior angles of the triangle, we can say that ∠ACB + ∠CAB + ∠ABC = 180, so 90 + 2x + 3x = 180
90 + 2x + 3x = 180
90 + 5x = 180
subtract 90 from both sides to separate the x and its coefficient
5x = 90
divide both sides by 5 to separate the x
x = 18
(a) ∠CAB = 2x = 18(2) = 36
(b) ∠ABC = 3x = 18(3) = 54
(c) Any triangle with a 90° angle is called a right triangle. This has a 90° triangle, and is therefore a right triangle. Similarly, a 90° angle in a triangle is called a right angle.
Related Questions
5m - 3n = 19; m - 6n = -7 /pls. help me solve this linear equation with two variables.
Answers
Answer:
m = 5, n = 2
Step-by-step explanation:
[tex]5m - 3 n = 19\\m - 6n = - 7 \ => m = -7 + 6n\\\\Substitute \ m \ in \ 5m - 3n = 19\\\\5(-7 + 6n) - 3n = 19\\-35 + 30n -3n = 19\\27n = 19 + 35 \\27n = 54 \\n = 2\\\\Substitute \ n = 2 \ in \ m = -7 + 6n\\\\m = -7 + (6 \times 2) = -7 + 12 = 5[/tex]
Which input value produces the same output value for the two functions on the graph?
x = –3
x = –1
x = 1
x = 3
Answers
Answer:
X=3
Step-by-step explanation:
We have two linear functions which intersect at a point. Linear functions are lines which are made of points that satisfy the function or relationship. This means at the intersection, this point (3,-1), both functions have values. An input of x=3 produces y=-1 in both functions.
Jim writes 10^4 words every day how many words does he writes in 10^3 days?
Answers
10^4=10,000
10^3=1,000
The national park has a new kiosk which visitors pass through as they enter the park. The kiosk is in the shape of a cylinder with a diameter of 5 meters and a height of 3 meters and a conical roof that measures 2 meters in height. What is the volume of the kiosk? Round your answer to the nearest cubic meter
Answers
Answer:
The volume of the kiosk is 72 m³.
Step-by-step explanation:
The volume of the kiosk is given by the sum of the volume of a cylinder ([tex]V_{cy}[/tex]) and the volume of a cone ([tex]V_{c}[/tex]):
[tex] V = V_{cy} + V_{c} = \pi r^{2}h_{cy} + \frac{1}{3}\pi r^{2}h_{c} [/tex]
Where:
r: is the radius of the cylinder and the cone = d/2 = 5/2 = 2.5 m
d: is the diameter = 5 m
[tex]h_{cy}[/tex]: is the height of the cylinder = 3 m
[tex]h_{c}[/tex]: is the height of the cone = 2 m
Hence, the volume is:
[tex] V = \pi (2.5 m)^{2}(3 m + \frac{1}{3}*2 m) = 72 m^{3} [/tex]
Therefore, the volume of the kiosk is 72 m³.
I hope it helps you!
What is the solution set of the equation
x + 6 = 2(x + 3) - x?
Answers
Answer:
x = all real numbers
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
x + 6 = 2(x + 3) - x
Step 2: Solve for x
[Addition Property of Equality] Add x on both sides: 2x + 6 = 2(x + 3)[Distributive Property] Distribute 2: 2x + 6 = 2x + 6Here we see that both sides are identical.
∴ our solution is all real numbers.
PLEASE HELP ME WITH THIS ITS DUE TONIGHT
BE HONEST WITH YOU ANSWER AND EXPLAIN HOW YOU GOT IT PLEASE
THANK YOU
Answers
Answers:
Angle C = 95 degreesAngle D = 72 degreesAngle F = 108 degreesArc CFE = 216 degrees================================================
Explanations:
For any inscribed quadrilateral like this, the opposite angles are always supplementary. So that means C+E = 180. Plugging in E = 85 leads to C = 95.Angle D is an inscribed angle that subtends arc CFE. By the inscribed angle theorem, the inscribed angle is half that of the arc it cuts off, so angle D is half of 144 degrees at 144/2 = 72 degrees.Use the idea mentioned in problem 1. So we'll have F+D = 180. Plug in D = 72 to find that F = 108.Arcs CDE and CFE form a full circle. So the arc measures must add to 360 degrees. We simply subtract 144 from 360 to get the answer 216. As an alternative, you can use the idea mentioned in problem 2, but work in reverse.Find the area of the shaded region
Answers
Answer:
Area of the shades region = 244.6 ft²
Step-by-step explanation:
Area of the shaded region = Area of the rectangle ABCD- Area of the right angle triangle DEC
Area of the rectangle = Length × width
= 29.8 × 13
= 387.4 ft²
By applying Pythagoras theorem in the right triangle DEC,
(Hypotenuse)² = (leg 1)² + (leg 2)²
CD² = DE² + EC²
(29.8)² = DE² + (28)²
888.04 = DE² + 784
DE² = 888.04 - 784
DE = 10.2 ft
Area of ΔDEC = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(10.2)(28)[/tex]
= 142.8 ft²
Area of the shades region = 387.4 - 142.8
= 244.6 ft²
Sum of two numbers is 5/22. If one of the number is 2/11, then the other number is
Answers
Answer:
1/22
Step-by-step explanation:
2/11 = 4/22 therefore 4/22 + x = 5/22 and 5/22 - 4/22 = 1/22
[tex]\huge\bold{Given :}[/tex]
✎ Sum of two numbers = [tex] \frac{5}{22} [/tex]
✎ One of the number = [tex] \frac{2}{11} [/tex]
[tex]\huge\bold{To\:find :}[/tex]
✿ The other number.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\sf\blue{The \:other \:number \:is }[/tex] [tex] \frac{1}{22} [/tex]. ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
❥ Let the other number be [tex]x[/tex].
❥ As per the question, we have
[tex]sum \: of \: the \: two \: numbers = \frac{5}{22} \\ \\ ⇢ \frac{2}{11} + x = \frac{5}{22} \\ \\⇢ x = \frac{5}{22} - \frac{2}{11} \\ \\ ⇢ x = \frac{5}{22} - \frac{2 \times 2}{11 \times 2} \\ \\⇢ x = \frac{5 - 4}{22} \\ \\ ⇢ x = \frac{1}{22} [/tex]
[tex]\sf\purple{Therefore,\:the\:other\:number\:is}[/tex] [tex] \frac{1}{22} [/tex].
[tex]\huge\bold{To\:verify :}[/tex]
[tex] \frac{2}{11} + \frac{1}{22} = \frac{5}{22} \\ \\➪ \: \frac{2 \times 2}{11 \times 2} + \frac{1}{22} = \frac{5}{22} \\ \\ ➪ \: \frac{4 + 1}{22} = \frac{5}{22} \\ ➪ \: \frac{5}{22} = \frac{5}{22} \\ \\ ➪ \: L. H. S. = R. H. S[/tex]
Hence verified. ✔
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Please help ASAP!!!!!
Answers
Answer:
SHORT ANSWER IS B.
Angles in a triangle add up to equal 180 degrees
Hence, 40x - 27 + 25 - 2x + 26 + x = 180
( Note that we just created an equation that we can use to solve for x)
We now solve for x using the equation we created
40x - 27 + 25 - 2x + 26 + x = 180
Combine like terms
39x + 24 = 180
Subtract 24 from both sides
39x = 156
Divide both sides by 39
I need fast
How many pieces ,each of length 3 ¾ m can be cut from a rope of length 30m?
Answers
Answer:
8
Step-by-step explanation:
Divide 30 by 3.75 to get 8.
Hope that this helps!
2
Use the Pythagorean Theorem (a + b² = c) to find the missing side length.
Answers
Answer:
21.4
Step-by-step explanation:
[tex]a^{2} + b^{2} = c^{2} \\13^{2} + 17^{2} = c^{2} \\169+ 289 = \sqrt{c^{2} } \\\sqrt{458} = \sqrt{c^{2} } \\21.4 = c[/tex]
[tex]\huge\bold{Given:}[/tex]
Length of the base "b" = 17 yd.
Length of the perpendicular "a" = 13 yd. [tex]\huge\bold{To\:find:}[/tex]
The length of the missing side, hypotenuse ("c").
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\boxed{C.\:21.4\:yd}[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
Using Pythagoras theorem, we have
[tex]({perpendicular})^{2} + ({base})^{2} = ({hypotenuse})^{2} \\ \\⇢( {13 \: yd})^{2} + ( {17 \: yd})^{2} = {c}^{2} \\ \\⇢ {c}^{2} = 169 \: {yd}^{2} + 289 \: {yd}^{2} \\ \\⇢c = \sqrt{458 \: {yd}^{2} } \\ \\⇢c = 21.40 \: yd[/tex]
[tex]\sf\blue{Therefore,\:the\:length\:of\:the\:missing\:side\:"c"\:is\:21.4\:yd.}[/tex]
[tex]\huge\bold{To\:verify :}[/tex]
[tex]( {13 \: yd})^{2} + ( {17 \: yd})^{2} = {21.4 \: {yd}^{2} }\\ \\ ⇝169 \: {yd}^{2} + 289 \: {yd}^{2} = 457.96 \: {yd}^{2} \\ \\⇝458 \: {yd}^{2} = \: 458\: {yd}^{2} \\\\⇝ L.H.S.=R. H. S[/tex]
Hence verified. ✔
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
PLS HELP ME IM RLLY STUCK I WILL GIVE BRAINLIEST
Answers
Check the picture below.
Connor needs to buy 430 orange balloons for a party. The orange balloons are sold in packs of 6. If he buys the smallest possible number of packs, how many balloons will be left over?
Answers
Answer:
2 balloons.
Step-by-step explanation:
6x = 430
x = 71.6
He has to buy 72 packs, there will be:
72 * 6 = 432 - 430 = 2 balloons left.
Find all the missing elements:
40°
120°
8
C = [?]º a = [ ] c = [ ]
Answers
Answer:
C=20° a=10.8 c= 4.3
Step-by-step explanation:
first we need to find the value of angle C by subtracting the sum of angle A and B from 180°.
to find c and a we need to use sin rule which states that sinB/b=sinA/a=sinC/c respectively
PLS HURRY!! Susan needs 228 ounces of fruit juice for a party. She is choosing between two brands of juice.
Two Brands of Juice
Brand A
Brand B
12 ounces
8 ounces
$2.55
$1.45
She finds the unit rate of each brand and rounds to the nearest cent. Which statement about the unit rates is true?
Brand A costs approximately $0.18 per ounce, and Brand B costs approximately $0.21 per ounce.
Brand A costs approximately $0.12 per ounce, and Brand B costs approximately $0.15 per ounce.
Brand A costs approximately $0.15 per ounce, and Brand B costs approximately $0.12 per ounce.
Brand A costs approximately $0.21 per ounce, and Brand B costs approximately $0.18 per ounce.
Answers
Answer:
Brand A costs approximately $0.21 per ounce, and Brand B costs approximately $0.18 per ounce
Step-by-step explanation:
divide the price by the the number of ounces.
2.55/12 = .21
1.45/8 = .18
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
220
27.5
110
15.8
Answers
Answer:
x = 27.5
Step-by-step explanation:
x/55 = 4/8 (ratio between the two polygons); cross multiply.
220 = 8x; divide 8 on both sides
x = 27.5
please help me help help help
Answers
xy+xb+ya+ab = 32
x(y+b) + a(y+b) = 32
(x+a) (y+b) = 32
4.(y+b) = 32
(y+b) =32/4
(y+b) = 8
OPTION C
which graphs represent functions
A. Graph D only
B. Graph B and Graph D
C. Graph C and Graph D
D. Graph A only
Answers
Answer: C i believe
Step-by-step explanation:
Answer:
the option answer is B
Step-by-step explanation:
the is the answer because it represents functions
in a survey of 100 cars,47 were white,23 were blue and 30 were red.express each of these numbers as a percentage of the total.
Answers
Answer:
white- 47% Blue-23% Red- 30%
Step-by-step explanation:
White cars- (47/100)*100= 47%
Blue cars- (23/100)*100=23%
Red cars- (30/100)*100=30%
Answer:
White 47 percent, 23 percent blue 30 percent red.
47+23+30=100 percent
Step-by-step explanation:
So to get the percentages you first have to get the numbers that you need in this case it is 47,30,and 23.
After that we have to first multiply the numbers(47,30,23)by 100 because
100 hundred is our total percent so 47x100=4700 30x100=3000
and 23x100=2300.And 47x100=4700 30x100=3000
and lastly 23x100=2300.So after we multiply the numbers by 100 hundred we have to divide so we see there's 100 cars so we divide by that because that is the total amount of cars and if we divide all our numbers by 100 we will get the answer,
4700/100=47 percent 3000/100=30 percent 2300/100=23 percent
and to check our answer is right we have to add all our number percentages up to see if all the numbers add up to 100.(percentage)so 47+30+23=100
So that means our answer is right.
angle I and N are complementary. If angle N has a meause of 48 degrees, find the measure of angle I
Answers
Answer:
42°
Step-by-step explanation:
Complementary angles are two angles that add up to 90°
1) 90-48 = 42
Hope this helps! :)
Answer:
angle I = 42 degree
Step-by-step explanation:
In complementary angles sum of two angles ia always 90 degree.
angle I +angle N=90 degree (since they are complementary)
substitute the value of angle N
angle I + 48 = 90
angle I = 90 -48
angle I =42 degree
So there’s two cell phones the length on first is 8.4 inches the width on the first cell phone is 5.6 inches. On the second cell phone the length is 9.21 inches. The length and width of the two cell phones are proportional. What is the width, inches of the larger of the cell phone?
Answers
Answer:
The width, in inches of the larger cell phone is 6.14 inches.
Step-by-step explanation:
To solve we must set up a ratio.
[tex]\frac{8.4}{5.6} = \frac{9.21}{y}[/tex]
After setting this ratio up, we can cross multiply to solve for y.
8.4(y) = 5.6(9.21)
8.4(y) = 51. 576
To get y alone we divide by 8.4 on both sides.
y = 6.14
The width, in inches of the larger cell phone is 6.14 inches.
Which of the following is not a possible value for a probability? (A p e x)
A. 0.001
B. 1/16
C. 0.82
D. 5/4
Answers
Explanation: step by step process
It's urgent I need help quick pls help me
Answers
Answer:
11
Step-by-step explanation:
16 - 4[tex]\sqrt{5}[/tex] + 4[tex]\sqrt{5}[/tex] - 5
= 16 - 5
= 11
simplify ,without using a calculator(2 1/2)2 + (0.5)2
Answers
Answer:
22
Step-by-step explanation:
Step-by-step explanation:
2 1/2 × 2
=5/2 × 2
=5
(0.5)2
=0.5×2
=1
5+1
=6
The solution is n=-2 verified as a solution to the equation 1.4n + 2 = 2n + 3.2. What is the last line of the justification?
Answers
Answer:
- 0.8 = - 0.8
n = - 2 is a solution.
Step-by-step explanation:
1.4n + 2 = 2n + 3.2
1.4(- 2) + 2 = 2(- 2) + 3.2
- 2.8 + 2 = - 4 + 3.2
- 0.8 = - 0.8
How to solve
1.4n + 2 = 2n + 3.2
1.4n + 2 - 2 = 2n + 3.2 - 2
1.4n = 2n + 1.2
1.4n - 2n = 2n - 2n + 1.2
- 0.6n = 1.2
- 0.6n ÷ - 0.6 = 1.2 ÷ - 0.6
n = - 2
Please, help!! Those are the steps that I have so far.
Answers
2sin^2x+7sin x.cosx-cos^2x=4
Answers
Step-by-step explanation:
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help asap will mark brainliest !!!!!!
Question 12(Multiple Choice Worth 1 points)
(01.03 MC)
What is the simplified expression for 4 power 4 multiplied by 4 power 3 over 4 power 5?
40
41
42
43
Answers
Answer:
4²
Step-by-step explanation:
simplified expression of 4 power 4 multiplied by 4 power 3 over 4 power 5.
Answer:
4^2
Step-by-step explanation:
(4^4*4^3)/4^5
4^4 * 4^3 = 4^7 because of an exponent multiplication property, when exponents of the same number multiply, they can just add
4^7/4^5
4^7-5
= 4^2 Because..
another exponent property is that if the exponents of the same number divide, they can subtract! The opposite of the other property!
Please help me with this asap.
Answers
Answer:
80
Step-by-step explanation:
10*8=80
Answer:
Step-by-step explanation:
to find height use pythagoras theorem
height be x
a^2+b^2=c^2
x^2+8^2=10^2
x^2+64=100
xx^2=100-64
x^2=36
x=[tex]\sqrt{36[/tex]
x=6
area of the triangle =base*height/2
=8*6/2
=48/2
=24 square units.
David gasta el 20% de su salario en el pago de los servicios básicos de su casa del resto gasta el 50% en alimentación si al final se queda con 2000 Córdoba cuanto gana David
Answers
Answer:
Gana 6666,67 Córdoba de los cuales
gasta 3333,33 en alimentos y 1333,33 en servicios.
Step-by-step explanation:
Se queda 2000 Córdoba
Gasta el 20% de su salario para pagar los servicios básicos de su casa.
Gasta el 50% de su salario en comida.
Suponga que gana x cantidad
luego
x = 0,2x + 0,5x + 2000
x = 0,7x + 2000
x-0,7x = 2000
0,3 veces = 2000
x = 2000 / 0,3
x = 6666,67
Gana 6666,67 Córdoba de los cuales
gasta 3333,33 en alimentos y 1333,33 en servicios.
He keeps 2000 Córdoba
He spends 20% of his salary to pay for the basic services of his hous.
He spends 50% of his salary to pay on food.
Suppose he earns x amount
then
x= 0.2x+0.5x+2000
x= 0.7x+2000
x-0.7x=2000
0.3x= 2000
x= 2000/0.3
x= 6666.67
English
He earns 6666.67 Córdoba out of which
he spends 3333.33 on food and 1333.33 on services .