He measures of the angles of a triangle are in the extended ratio 4 : 5 : 6. what is the measure of the smallest angle?

Answers

Answer 1
In a triangle, the three interior angles always add to 180°

4x + 5x + 6x = 180
15x = 180
x = 180/15
x = 12

the measure of the smallest angle = 4x = 4*12 = 48°

Related Questions

Which of the following statements is true?
The number 2 /3 is an irrational number.
The number -4 is a whole number.
The number 9 is a rational number.
The number 5/8 is a natural number.

Answers

the number -4 is a whole number

Given f(x) = x + 2 and g(x) = x2 – 4, find the function (g/f)(x).

Answers

hello : 
(g/f)(x) = g(x) /f(x) = (x²-4)/(x+2)= (x-2)(x+2) /(x+2)
if : x ≠ -2  so : (g/f)(x) = = x-2

Triangle FGH is a right triangle. Angle G is a right angle, m∠F = 9x – 1, and m∠H = 3x + 7. What is m∠F?

Answers

interior angles of a triangle add up to 90 degrees

< F + < G + < H = 180
9x - 1 + 90 + 3x + 7 = 180
12x + 96 = 180
12x = 180 - 96
12x = 84
x = 84/12
x = 7

so < F = 9x - 1 = 9(7) - 1 = 63 - 1 = 62 <=====
< G = 90
< H = 3x + 7 = 3(7) + 7 = 21 + 7 = 28
added : 62 + 90 + 28 = 180
the angles of a triangle must add up to 180 degrees.

G = 90 (because it's a right angle)
F = 9x - 1
H = 3x + 7

90 + (9x - 1) + (3x + 7) = 180
(9x - 1) + (3x + 7) = 90
12x + 6 = 90
12x = 84
x = 7

now that we have x, we can find out the measure of angle F.

9(7) - 1
63 - 1
62

angle F is 62 degrees

Find 2 consecutive positive even integers such that the product of the 1st and 2nd is 2 less than 5 times the 3rd. Use an algebraic solution.

Answers

Assume the smaller one is x, then the other ones will be x+2 and x+4

x(x+2) + 2 = 5(x+4)

x^2 + 2x - 5x - 18 = 0

-> x^2 - 3x - 18 = 0

-> (x-6)(x+3) = 0

-> x = 6 or -3, since x must be positive, then x = 6

So the numbers are: 6, 8, 10

(50 Points Please help)
Drag the expression that is the most reasonable measurement for each object.

Answers

Answer:

A. Length of a Tour Bus                       ↔     #2.      1.1 × 10¹ meters

B. Width of an apple                             ↔      #3.     4 × 10⁰ centimeters

C. Distance from Earth to a Satellite    ↔    #6.     8 × 10² kilometers

D. Thickness of a human hair               ↔     #5.      9 × 10¹ micrometers

Step-by-step explanation:

The length of a tour bus should be measured in meters. It sure is way less than 1 kilometer and way more than a few centimeters. It could be about some meters, more than 5 meters, may be between 10 meters and 15 meters.

The measurement in the box # 2. is 1.1 × 10¹ meters, which is equivalent to 1.1 × 10 meters = 11 meters. Thus, this is a reasonable length.

B. Width of an apple.  

The most appropriate unit to measure the width of an apple should be centimeter. It certainly is shorter than 1 meter and bigger than 1 mm.

The width of an apple could be, more or less, around 8 centimeters. The only measurement in the boxes that is in that order is that in the box #3., 4 × 10⁰ centimeters, because 10⁰ = 1, so 4 × 10⁰ = 4 × 1 = 4 centimeters.

C. Distance from Earth to a Satellite

The distance from Earth to a satellite should be measured in kilometers.

You can find in the internet that the distances of the satellites are between 700 kilometers and 36,000 kilometers.

The number in the box #1 is too big, in the order of ten trillions of kilometers, because one trillion is 10¹²; thus that is nonseasonal (too big).

The number in the box #6 is  8 × 10² kilometers, which is equal to 8 × 100 = 800 kilometers.

Thus,  8 × 10² kilometers (box #6) is the most reasonable measurement for the distance from Earth to a Satellite

D. Thickness of a human hair

Of course, kilometers, meters, centimeters and even millimeters are units too big to measure the thickness of a human hair.

One micrometer is 10⁻⁶ meters or 10⁻³ millimeters.

In the internet you can find that diameter of the human hair is in the range from 17 micrometers to 181 micrometers.

The measurement in the box #5. is 9 × 10¹ micrometers, which is equivalent to 9 × 10 = 90 micrometers.

Thus, 9 × 10¹ micrometers is the most reasonable measurement for the thickness of a human hair.

A. Length of a Tour Bus                       ↔       2.      1.1 × 10¹ meters

B. Width of an apple                             ↔      3.     4 × 10⁰ centimeters

C. Distance from Earth to a Satellite   ↔     6.     8 × 10² kilometers

D. Thickness of a human hair              ↔      5.      9 × 10¹ micrometers

What is Satellite?

A satellite is a moon, planet or machine that orbits a planet or star. For example, Earth is a satellite because it orbits the sun. Likewise, the moon is a satellite because it orbits Earth.

What is expression?

An act, process, or instance of representing in a medium (such as words) : utterance freedom of expression. Something that manifests, embodies, or symbolizes something else this gift is an expression of my admiration for you.  

According to question, we have to drag the expression that is the most reasonable measurement for each object.

Length of Tour Bus is generally between 1 meter to 2 meters.

So, Reasonable measurement for Length of a Tour Bus is [tex]1.1[/tex]× [tex]10^{1}[/tex] meters

Width of an apple is generally between [tex]2[/tex] centimeters to [tex]6[/tex] centimeters

So, Reasonable measurement for Width of an apple  is  [tex]4[/tex]×[tex]10^{0}[/tex]   centimeters .

Distance from Earth to a Satellite is generally between [tex]700[/tex]  kilometers to  [tex]3600[/tex] kilometers.

So, Reasonable measurement for   Distance from Earth to a Satellite is

[tex]8[/tex]×[tex]10^{2}[/tex] kilometers.

Thickness of a human hair  is generally between  17 micrometers to 181 micrometers.

So, Reasonable measurement for Thickness of a human hair is [tex]9[/tex]×[tex]10^{1}[/tex] micrometers.

Hence, we can conclude that the following expression  is the most reasonable measurement for each object.

A. Length of a Tour Bus                        ↔     2.      1.1 × 10¹ meters

B. Width of an apple                             ↔      3.     4 × 10⁰ centimeters

C. Distance from Earth to a Satellite   ↔     6.     8 × 10² kilometers

D. Thickness of a human hair              ↔      5.      9 × 10¹ micrometers

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In a right triangle angle C measures 40 degrees. The hypotenuse of the triangle is 10in long. What is the approximate length of the side adjacent to angle C?

Answers

https://us-static.z-dn.net/files/dc0/3fhttps://us-static.z-dn.net/files/dc0/3f8c9cbb3558907fd513c03e3db25ee1.jpg

I need to know how to find angle "H"

Answers

check the picture below.  Recall your SOH CAH TOA.

Someone please answer this for me

Answers

Each gallon costs $1.25
$15/$1.25 each= 12 gallons
Final answer: C
15/1.25 =C.12 that would be the answer

A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The carpenter knows that angle ADC is a right angle and that angle BDC is 32° greater than mangle ADB. Solve an equation to find angle BDC and angle ADB.

Answers

Answer:

m∠ADB = 29° and m∠BDC = 61°

Step-by-step explanation:

It is given that m∠ADC = 90°

Since m∠ADB + m∠BDC = 90° [∠ADB and ∠BDC are complimentary]

Since ∠BDC = ∠ADB + 32°

So, m∠ADB + m∠ADB + 32° = 90°

2(m∠ADB) + 32° = 90°

2(m∠ADB) = 90 - 32

2(m∠ADB) = 58°

m∠ADB = 29°

Since m∠ADB + m∠BDC = 90°

So, m∠BDC + 29° = 90°

m∠BDC = 90 - 29

             = 61°

Therefore, m∠ADB = 29° and m∠BDC = 61°

m∠ADB = 29° and m∠BDC = 61°

Solving this will just be based on some basic angle theorems in a triangle.

We are given; m∠ADB = 29° and m∠BDC = 61°  We are told that m∠ADC is a right angle. This means that; m∠ADC = 90°

Now, since m∠ADC = 90°, it means that;

m∠ADB + m∠BDC = 90° (because m∠ADB and m∠BDC are complimentary angles due to the fact that angle at point D is 90°)

We are also told that;

m∠BDC is 32° greater than angle m∠ADB

This means that we can write as;

m∠BDC = m∠ADB + 32°

From earlier, we saw that;

m∠ADB + m∠BDC = 90°

Thus, putting m∠ADB + 32° for m∠BDC, we will have;

m∠ADB + m∠ADB + 32° = 90°

2(m∠ADB) + 32° = 90°

     Subtract 32° from both sides to get;

2(m∠ADB) = 90° - 32°

2(m∠ADB) = 58°

m∠ADB = 58°/2

m∠ADB = 29°

Puttting 29° for m∠ADB into; m∠ADB + m∠BDC = 90° gives us;

29° + m∠BDC= 90°

       Subtract 29° from both sides to get;

m∠BDC = 90° - 29°

m∠BDC = 61°

In conclusion, m∠ADB = 29° and m∠BDC = 61°

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Four girls and three boys volunteer to represent their class at a school assembly.the teacher selects one name and then another from a bag containing the seven students names.what is the probability that both representatives will be girls

Answers

4/7*3/6
the answer is 2/7
A basket contains 13 pieces of fruit:5 apples,5 oranges,and three bananas.jonas takes a piece of fruit at random from the basket and then Beth takes a piece at random.what is the probability that Jonas will get an orange and Beth will get an apple ?

In EFG, mE = 30, mF = 60, and mG = 90. Which of the following statements about EFG are true?

Answers

[tex]FG=cos60^o * EF = \frac{1}{2} * EF \\ \\ EG = cos30^o * EF = \frac{ \sqrt{3} }{2} * EF \ \ \ \text{[B is true]} \\ \\EG=tan60^o*FG= \sqrt{3}*FG \ \ \ \text{[C is true]} \\ \\ EF= \frac{FG}{cos60^o}= \frac{FG}{ \frac{ 1 }{2} } = 2*FG \ \ \ \text{[F is true]}[/tex]

Statements B, C, and F are all true based on the given angle measures in triangle EFG.

Let's reevaluate the statements with the given angle measures in triangle EFG:

m∠E = 30°

m∠F = 60°

m∠G = 90°

A. FG = √3/2 EF

FG = (EF * √3) / 2

This statement is true. FG is indeed equal to √3/2 EF.

B. EG = √3/2 EF

EG = (EF * √3) / 2

This statement is true. EG is equal to √3/2 EF.

C. EG = -√3 FG

EG = -√3 * FG

This statement is true. EG is equal to -√3 FG.

D. EF = -√3 FG

EF = -√3 * FG

This statement is true. EF is equal to -√3 FG.

E. EG = 2 FG

EG = 2 * FG

This statement is true. EG is equal to 2 FG.

F. EF = 2 FG

EF = 2 * FG

This statement is true. EF is equal to 2 FG.

Statements B, C, and F are all true based on the given angle measures in triangle EFG.

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The perimeter of a triangle is 86 inches. The largest side is four inches less than twice the smallest side. The third side is 10 inches longer than the smallest side. What is the length of each side?

Answers

Hello,
Assume x the smallest side.
y the third side
z the largest side
z=2x-4
y=10+x
x+y+z=86
==>x+(10+x)+(2x-4)=86
==>4x=86-10+4
==>x=20, y=30 and z=36

Which number is greatest?

a. 3.4 × 10-2

b. 4.3 × 10-3

c. 5.2 × 10-4

d. 6.1 × 10-4

Answers

a) =27.2
b) = 30.1
c) =31.2
d) =36.6

answer = D

Answer:

the answer is d 6.1x 10-4

Step-by-step explanation:

Sarah is y years old now. How could you represent her age 5 years ago?


y + 5
5 y
y - 5
y ÷ 5

Answers

you would have to subtract 5 from her age so the equation would by y-5

y-5..................................................


The size of a bicycle is determined by the diameter of the wheel. You want a 24-in bicycle for Christmas. What is the circumference of one of the wheels? A 75.4 in B 75.3 in C 37.7 in D 37.6 in

Answers

Answer:

The circumference of one of the wheels is:  

                     Option: A    75.4 in.

Step-by-step explanation:

The 24-in bicycle means that the diameter of the wheel of the bicycle isL 24 in.

We know that the wheel of the bicycle is in the shape of a circle.

This means that the diameter of circle is: 24 in.

Hence, the radius(r) of circle is: 12 in.

( since we know that the radius(r) of the circle is half the diameter(d) of the circle)

Now, we are asked to find the circumference of the circle.

The circumference(C) of the circle is given by:

C=2πr

i.e.

C=2×3.14×12

i.e.

C=75.36 in.

which to the nearest tenth is: C=75.4 in.

Segment DE is midsegment of triangle ABC. What is the length of segment DE?
A) 5
B) 10
C) 15
D) 20

Answers

(X+5)2=X+15
2X+10=X+15
X=5
A) 5 :)

Answer:

B) 10

Step-by-step explanation:

If DE is midsegment of the triangle, we know that AC measures twice as DE.

In the problem we have that AC = x + 15 and DE = x + 5

Writing this as an equation we have:

[tex]x + 15 = 2(x+5)\\x+15=2x +10\\15-10=2x-x\\5=x[/tex]

Therefore x = 5 and the length of segment DE is:

x + 5 = 5 + 5 = 10

Therefore the correct answer is B) 10

Sarah decides to take her six-year-old son to the circus the price for the child ticket is $4.75 dollars Less in the price for the adult ticket if we represent the price for the child ticket using the variable X how would you write the algebraic expression for the adult ticket price

Answers

Since the child ticket is y-4.75 (saying y is the adult ticket), we need to solve for y in y-4.75=x. Adding 4.75 to both sides, we get y=x+4.75

One-on-one mapping from one plane to the same plane is called:
congruency.
transformation.
isometry.
None of the choices are correct.

Answers

One-on-one mapping from one plane to the same plane is called transformation.

Transformation of a point either in form of translation, reflection, rotation or enlargement will map each coordinate of [tex]x[/tex] and [tex]y[/tex] onto a new coordinate [tex] x_{1} [/tex] and [tex] y_{1} [/tex]

Final answer:

Isometry is the term used for a one-on-one mapping from one plane to the same plane. It is key in transformations and geometry studies.

Explanation:

Isometry is the term for a one-on-one mapping from one plane to the same plane. In mathematics, this concept is crucial in the study of transformations and geometry. An isometry preserves distances, angles, and areas in a mapping, making it a significant concept in mathematical modeling.

If ABCDE is translated 2 units to the right and 4 units up, what will happen to the polygon?

Answers

The answer is A. it will move but wont change shape or size.

Answer:

A polygon will move but won't change shape or size

Step-by-step explanation:

Given the figure

If ABCDE is translated 2 units to the right and 4 units up, then we have to choose the correct option.

A translation is a geometric transformation that moves every coordinate point of a figure by the same distance.

The result of translation transformation implies

The size, the shape and the orientation of the image after translation are same as that of the original object.

Hence, a polygon will move but won't change shape or size

Option A is correct

WILL PICK BEST ANSWER IF ITS CORRECT TO ANSWER THESE FEW PROBLEMS
YOU MUST EXPLAIN WHY YOU KNOW

1)Which system of linear inequalities is represented by the graph?
(goes with pic 1)
y > 2/3x + 3 and y < -1/3x + 2
y > 2/3x + 3 and y < -1/3x + 2
y > 2/3x + 3 and y > -1/3x + 2
y > 2/3x + 3 and y >-1/3 x + 2

2)
Which system of linear inequalities is represented by the graph?
(goes with pic 2)
y > 2x – 1 and y < 2x + 2
y > 2x + 2 and y < 2x – 1
y < 2x + 2 and y > 2x – 1
y < 2x + 1 and y > 2x – 2

3)Which linear inequality is represented by the graph?
(goes with pic 3)
y > 2x + 2
y ≥ 1/2x + 1
y > 2x + 1
y ≥ 1/2x + 2

4)
What is the solution to the system of linear equations?
(goes with pic 4)
(–3, 0)
(–3, 3)
(0, 2)
(3, 1)

Answers

Part 1)

In this problem we have two lines

The equation of the fist line is

[tex]y=\frac{2}{3}x+3[/tex]

The solution is the shaded area above the dashed line

so

the inequality is

[tex]y>\frac{2}{3}x+3[/tex]

The equation of the second line is

[tex]y=-\frac{1}{3}x+2[/tex]

The solution is the shaded area below the full line

so

the inequality is

[tex]y\leq -\frac{1}{3}x+2[/tex]

therefore

the answer Part 1) is

[tex]y>\frac{2}{3}x+3[/tex] and [tex]y\leq -\frac{1}{3}x+2[/tex]

Part 2)

In this problem we have two lines

The equation of the fist line is

[tex]y=2x+2[/tex]

The solution is the shaded area above the full line

so

the inequality is

[tex]y\geq 2x+2[/tex]

The equation of the second line is

[tex]y=2x-1[/tex]

The solution is the shaded area below the full line

so

the inequality is

[tex]y\leq 2x-1[/tex]

therefore

the answer Part 2) is

[tex]y\geq 2x+2[/tex] and [tex]y\leq 2x-1[/tex]

Part 3)

In this problem we have only one line

The equation of the line is

[tex]y=2x+1[/tex]

The solution is the shaded area above the dashed line

so

the inequality is

[tex]y>2x+1[/tex]

therefore

the answer Part 3) is

[tex]y>2x+1[/tex]

Part 4)

we know that

the solution of the system of linear equations is the intersection both graphs

so

see the graph

the solution point is [tex](0,2)[/tex]

therefore

the answer part 4) is the option

[tex](0,2)[/tex]

The volume of a sphere with radius r is 4 3 πr 3 . what is the volume of a sphere with radius 5

Answers

Final answer:

To find the volume of a sphere with a radius of 5, plug the value into the formula V = (4/3)πr³. The result is approximately 523.6 cm³.

Explanation:

The question asks for the volume of a sphere with a given radius. The formula to calculate the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius of the sphere.

To find the volume of a sphere with radius 5, we substitute r with 5 in the formula:

V = (4/3)π(5)³

V = (4/3)π(125)

V = (4/3)π(125) = 500/3π cm³

The volume of a sphere with radius 5 is therefore 500/3π cubic centimeters, which is approximately 523.6 cm³ when rounded to one decimal place.

12 POINTS PLZ HELP ONLY HAVE 3 MINUTES LEFT

Which statement about histograms is true?

Data is organized in categories.

Data appears as bars that are all about the same height.

Data is organized in equal intervals.

Data appears as bars that do not touch.

Answers

Answer:

c

Step-by-step explanation:

The correct statement about Histogram is Data is organized in equal intervals.

What is Histogram?

A histogram is a graphical representation of discrete or continuous data. The area of a bar in a histogram is equal to the frequency. The y -axis is plotted by frequency density (which is proportional to the frequency) and the x -axis is plotted with the range of values divided into intervals.

Given:

Equal in breadth and corresponding to equal class intervals are the bars. However, they can occasionally be displayed as a wider variety within their groups, such as in size classes.

The width and data being achieved, for instance, forces a true event of varying class sizes in education upon the base of the graph.

and, for the purpose of displaying evenly spaced-out numerical data. The bars should be in close proximity to one another but not overlap. You can view the frequency distribution of the data or the number of pieces of data contained in each interval using these intervals.

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. In the algebraic expression mc034-1.jpg 7, 17, and –10 are _____ terms. operations. coefficients. variables.

Answers

Answer:

Coefficient

Step-by-step explanation:

The correct option is A.

In the algebraic expression 7a+17b-10c, 7, 17 , and −10 are coefficients.

A. Coefficients. The numbers 7, 17, and -10 are coefficients in the expression 7a + 17b - 10c because they are the constants that multiply the variables a, b, and c respectively.

B. Incorrect. Operations are mathematical actions like addition, subtraction, multiplication, or division, not the constants themselves.

C. Incorrect. Variables, denoted by a, b, and c, are letters or symbols representing unknown or changing quantities, not the constants.

D. Incorrect. Terms are the individual parts of an expression separated by addition or subtraction, consisting of a coefficient and possibly a variable or variables multiplied together. The numbers 7, 17, and -10 are coefficients within the terms of the expression but are not terms themselves.

So, the correct option is A. Coefficients.

The complete question is here:

In the algebraic expression 7a+17b-10c, 7, 17 , and −10 are ______

A. coefficients.

B. operations.

C. variables.

D. terms.

What is the reason for the third step in this proof? Corresponding sides of congruent triangles are equal in length. The diagonals of a rectangle bisect each other. SSS criterion for congruence Opposite sides of a parallelogram are congruent.

Answers

Answer: D Opposite sides of a parallelogram are congruent.

Step-by-step explanation:

The correct answer is the Opposite sides of a parallelogram are congruent.

What is a parallelogram?

A parallelogram is a quadrilateral having four sides and the two opposite sides are equal and parallel to each other.

Consider a parallelogram with diagonals that are congruent and perpendicular.

In triangles Δ AOB and Δ AOD,

OA = OA (common)

OB = OD (Since the diagonals of a parallelogram bisect each other)

∠ AOB = ∠ AOD = 90° (diagonals are perpendicular)

Therefore, Δ AOB ≅ Δ AOD (By SAS postulate)

Since, corresponding parts of congruent triangles are equal,

AB = AD

Similarly, we can prove

BC = CD and CD = DA

So, AB = BC = CD = DA.

Also, it is given that AC = BD.

Therefore the correct answer is the Opposite sides of a parallelogram are congruent.

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2x^3+2x^2-19x+20=0 find the roots of the polynomial equation

Answers

the answer is   x=-4, (3±i)/2

Answer:

[tex]\frac{3+i}{2} , \frac{3-i}{2} , -4[/tex]

Step-by-step explanation:

PLEASE HELP!

Cynthia is constructing a circle inscribed in a triangle.She has partially completed the construction as shown below.What should her next step be in the construction (worth 50 points)

A. Connect vertex B to the arc markings to complete the angle bisector

B.use a straightedge to find the angle bisectors for angles A and B

C. Connect three arc markings together to form the triangle

D.use the arc markings to determine the radius to construct the circle

Please explain!

Answers

The correct next step that Cynthia should do is to:

D. use the arc markings to determine the radius to construct the circle

The arc markings are actually used as the baseline in determining the center and the radius of the circle. The arc markings are created with the use of a compass. All other choices are completely irrelevant because what we need is the arc and not the angles. The angles do not create the circle. Letter C is also wrong because what we are trying to form is the circle and not the triangle. The triangle is already created.

Meghan works at an ice cream shop and makes $8.25 per hour Lucas works at a landscaper and makes $6.50 per hour how much more does Meghan makes each hour ?

Answers

Find the difference of the two numbers.

8.25-6.5= 1.75

Final answer: $1.75

How do I find the perimeter and area?

Answers

To find the perimeter, just add up all the sides. 3+4+5=12m. The perimeter is 12 meters.

To find the area, multiply the base times height and multiply by 1/2. 3x4=12. 12*1/2=6. The area of this right triangle is 6m^2. (The ^2 is squared or to the second power).
I hope this helps! :)

A business’s assets are valued at $600,000, and the value depreciates 20% per year. Using the formula V(t) = V0(b)t, what is V0, what is (b), and what is the value of the assets after 5 (t) years? Show your work.
t = 5
V0 =
(b) =
Value after 5 years:

Answers

The formula is
V (t)=V0(b)^t
V (t) the value of the assets after 5 (t) years ?
V0 current value of assets 600000
B=1-0.20=0.8
T 5 years

So the value of assets after 5 years is
V (5)=600,000×0.8^(5)=196,608

You want to buy a new bike, and your parents will contribute $32.50 toward the cost of the bike. If the most expensive bike is $50.00, how much will you have to spend on the bike? Solve the following inequality 50.00 > 32.50 + x and graph its solution.

Answers

you will have to spend $17.50 on the bike. 17.50 > x

as for the graph, I assume it would be asking you to graph on a number line. So all you would have to do is go out to 17.50 on the line and make the graph going to the left, because it is saying that x is less than 17.50. If you think about it, X is less than 17.50 because the $50.00 bike is said to be the MOST expensive. So anything less would cause the $17.50 to go down, thus bringing the graph to the left. 
Let's think of this inequality for a second.

32.50 + x < 50.

The most expensive bike costs $50, meaning that the most you could spend on the purchase is (50 - 32.50).

50 - 32.50 = 17.5

The most you can spend on the purchase is $17.50

17.50 > x
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