Problem 4 the measure of the largest angle of a triangle is 90◦ more than the measure of the smallest angle, and the measure of the remaining angle is 30◦ more than the measure of the smallest angle. find the measure of each angle. showyourwork in obtaining your answe

Answers

Answer 1

Answer: The measurements of the angles are: 110° ; 50° ; 20° .
_________________________________________________________
Explanation:
________________________________________________________
Note: There are 3 (three) angles in any triangle (by definition).

By definition, all the angles in any triangle add up to 180° .
________________________________________________________
The problems asks us to find the measure of EACH angle of the triangle.

We can set up an equation; given the information in the problem; to solve for the measure of EACH of the 3 (THREE) angles in the triangle:
________________________________________________________
→ " x + (x + 90) + (x + 30) = 180 " ;
_____________________________________________
in which: "x" is the measure of one of the angles;
(specifically, the smallest angle) in the triangle;
"(x + 90)" is the measure of another one of the angles in the triangle;
  "(x + 30)" is the measure of another one of the angles in the triangle;
___________________________________________________________
By solving for "x" in the equation; we can solve for the measures of all the angles in the triangle;
_________________________________________________
→ x + (x + 90) + (x + 30) = 180 ;

x + x + 90 + x + 30 = 180 ;

  → 3x + 120 = 180 ;
______________________________________
Subtract "120" from each side of the equation ;

3x + 120 − 120 = 180 − 120 ;

to get: 3x = 60 ;
________________________________
Now, divide EACH SIDE of the equation by "3" ; to isolate "x" on one side of the equation ; and to solve for "x" ;

3x = 60 ;

3x / 3 = 60 / 3 ;

x = 20 ;
_________________________________________
Now, we have the original equation:
__________________________________
x + (x + 90) + (x + 30) = 180 ;

in which: x = 20° {the smallest angle) ;
"(x + 90)" = "(20 + 90) = 110° ;
"(x + 30)" = "(20 + 30)" = 50° ;
__________________________________________________________
Answer: The measurements of the angles are: 110° ; 50° ; 20° .
__________________________________________________________
To check our work:

20 + 110 + 50 =? 180 ?? ;   → 130 + 50 =? 180 ?? ; → Yes!
_____________________________________________________

Related Questions

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Leena knits 10 rows in 12 min. At this pace, how long will it take her to knit the next 25 rows? Enter your answer in the box. min

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Answer would be 30 mins
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----- -----
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HELP PLZ!!
Solve for x: −3(x + 3) = −3(x + 1) − 5. (1 point)
6

−6

All real numbers

No solution

Answers

-3(x + 3) = -3(x+1) - 5

Multiply everything in the parenthesis by -3.

-3x - 9 = -3x - 3 - 5

Combine like terms.

-3x - 9 = -3x - 8

Add 9 to both sides.

-3x = -3x + 1

Add 3x to both sides.

0 = 1

This means that there is no solution.

Hope this helps!

What she said above

Can someone help me with this please? And can you explain why that answer is right

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i believe it's c. √21 because when you simplify the square root, you get 4.5825 and so forth and in the number line, it's almost close to 5.

hope that helps, God bless!

A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Describe how a sequence can be used to determine the height of the ball when it reaches its fourth peak.

Answers

Hey there!

A= value of the first term
n= the number of the term you want to find
r= common ratio
value of r is = 2/3 because 27 times 2/3 = 18 which is the second term
n = 4 since you want to find the 4th term in the sequence
Plug it in and results are
4th term = 27(2/3)^(4-1) = 8
The answer is 8

Hope this helps!

A sequence can be used to illustrate the difference in heights of each jump and develop a pattern from them. In this case, we have 27, 18, 12,... Assuming the pattern continues, we have the previous height divided by 3 and then subtracted from itself:
[tex]a_n=a_{n-1}-\frac{a_{n-1}}{3}[/tex]

Here:
[tex]a_4=a_3-\frac{a_3}{3}=12-\frac{12}{3}=12-4=8[/tex]

Solve for x. 5x−2(x+1)=1/4

Answers

5x - 2(x+1) = 0.25

5x - 2x + 2 = 0.25

3x = 0.25 - 2

3x/3 = -1.75/3

x = - 0.583

hope this helps

5x - 2(x+1) = 0.25

5x - 2x + 2 = 0.25

3x = 0.25 - 2

3x/3 = -1.75/3

x = - 0.583
yes ik i copied but points are worth more than integrity

A Chef buys 9 cucumbers, 18 peppers and 21 tomatos at the farmers market. Cucumbers ae 6 for $2, pEPPERS ARE 12 for $9 and tomatoes are 6 for $4

Answers

In this question, you are given 3 separate vegetables without single price. If you want to solve it step by step, it will be easier to count each vegetable price before hand. The price would be:
Cucumber: 2$/6 pieces= $0.33 /piece
Pepper: $9/12 pieces= $0.75/piece
Tomatoes: 4$/6 pieces= $0.66/piece

Then the total cost for the chef shopping item would be: 9 * $0.33 + 18 * $0.75 + 21* $0.66= $3 + $13.5+ $14= $30.5

PLEASE HELP QUICK!!!!!
WILL GIVE BRAINIEST TO FIRST ANSWER

Solve the inequality below for t.
9 - 7t > -9 - 4t

A. t is greater than or equal to 0
B. t is less than or equal to 0
C. t is grater than or equal to 6
D. t is less than or equal to 6

Answers

The answer is D
Solve for " t " by simplifying both sides of the inequality, then Isolating the variable.

Hoped this helped.

Find f(x) and g(x) so that the function can be described as y = f(g(x)).

y = eight divided by x squared + 2

Answers

The first thing to notice in this problem is that the math solution PEMDAS will be in effect. You will have y = 8/ (x^2 + 2) Since x isn't clarified, then there is no way to complete the solution or simplify it. This problem was worded and showed weird.

At a point on the ground 24ft from the base of a tree, the distance to the top of the tree is 4ft more than 3times the height of the tree. find the height of the tree.

Answers

78ft ------------------------------ 24+24+24+4 or 24*3+4

Please help, this is due in 5 minutes

Answers

notice, "x" is a variable, so it varies, it will take on many values.

usually car dealers will say, you need to pay some processing fee, a flat-fee, and after that, you get charged for the "wear and tear" of the car, so by the mileage you drive, the more miles you drive, the more wear and tear, therefore, the more you pay, the less you drive, the less you pay.

0.15x <---- 15 cents for every "x", miles

if you drive 200 miles you owe 0.15(200)
300 miles the 0.15(300) and so on.

the 22, is never changing in that equation, is a constant, just like the flat-fee.

[tex]\bf \stackrel{cost}{y}=\stackrel{\textit{15c per mile}}{0.15x}+\stackrel{flat-fee}{22}[/tex]

A rectangular prism has a length of 3/4 cubic inch and a width of 1/2 inch. The volume is 21/32 cubic inch. Find the height of the prism. Write your answer as a mixed number in simplest form.

Answers

21 / 32 = (3/4) * (1/2) * height

21 / 32 = (3 / 8) * height

21 / 32 * (3 / 8) = height =

63 / 256 inches

Answer:

[tex]\texttt{Height of the prism}=1\frac{3}{4}[/tex]

Step-by-step explanation:

Volume of rectangular prism = Length x Width x Height

[tex]\texttt{Volume of rectangular prism =}\frac{21}{32}\\\\\texttt{Length =}\frac{3}{4}\\\\\texttt{Breadth =}\frac{1}{2}[/tex]

Substituting

[tex]\frac{21}{32}=\frac{3}{4}\times \frac{1}{2}\times h\\\\h=\frac{7}{4}=\frac{4+3}{4}=1\frac{3}{4}[/tex]

[tex]\texttt{Height of the prism}=1\frac{3}{4}[/tex]

The greatest common factor of 4a(2) b and 6ab(3)

Answers

4a^2b and 6ab^3

first, find the greatest common factor of ur coefficients 4 and 6.....and that is gonna be 2

as for ur variables and exponents....take the lowest ones

so both have an " a " and a " b " variable....the lowest a term is just " a "...and the lowest " b " term is b

so the GCF of these 2 terms are : 2ab

The greatest common factor of the expressions 4a^2b and 6ab^3 is 2ab.

The question seeks to determine the greatest common factor of the expressions 4a2b and 6ab3. To find this, one must look at the common factors of the numerical coefficients (4 and 6) and the variables raised to their respective powers (a2 and a, b and b3). The numerical common factor of 4 and 6 is 2. The lowest power of 'a' common to both terms is a1 and for 'b' is b1. On doing this we get 2ab.

The slope of the line below is –. Write a point-slope equation of the line using the coordinates of the labeled point.

A. y + 4 = 8/7 –(x + 4)
B. y – 4 = 8/7–(x – 4)
C. y – 4 = 8/7(x – 4)
D. y + 4 = 8/7(x + 4)

Answers

y - 4 = -8/7(x - 4) is the answer

Find the value of y for a given value of x, if y varies directly with x. If y = –96 when x = 32, what is y when x = 58?

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Attached the solution and work.

True or False: Is the number 2 a solution to 7≥−3k

I'm not sure about this. Please explain

Answers

It is true. If you substitute 2 in for k, then 7 is greater than or equal to -6. this statement is true because 7 is indeed greater than 6.

t is true. If you substitute 2 in for k, then 7 is greater than or equal to -6. this statement is true because 7 is indeed greater than 6.

3m + 7/2 = −2m + 5/2 the / means there fractions

Answers

3m +7/2 = -2m +5/2

subtract 5/2 from each side

3m +2/2 = -2m

2/2 = 1

3m+1 =-2m

subtract 3m from each side

1=-5m

divide both sides by -5

m = 1/-5 = -1/5

m = -1/5

If a parent function is y=2x which is the function of the graph

Answers

not seeing the graph, y = 2x goes through the origin with a slope of +2.

if the line is on the positive side then your answer is "y=2^x+1 +2"

if the line is on the negative side your answer is "y=2^x-1 +2"

Positive always goes with positive

What is the slope of this graph?

Answers

Since the slope is falling, instead of rising, it would be negative.

Now, on the line, I plotted (0, 2) and (-2, 10).

You would now plug this into the rise/run formula.
The formula is [tex] \frac{y2 - y1}{x2 - x1} [/tex]

The equation would become,
[tex] \frac{10 - 2}{-2 - 0} [/tex] = [tex] \frac{8}{-2} [/tex] = -4

I believe the answer would be -4.

I hope this helps!

Compute the mean, variance, and standard deviation for the following data set. Round all answers to the nearest tenth. {85,95,90,70,75,95,85,85,95,90,70,75}

Answers

Mean: 84.1
You add all the numbers together and divide by the amount of numbers

What is 334.54 + 198 grams

Answers

334.54 + 198 = 532.54 grams total

hope this helps

ANSWER without rounding: 532.54 grams

Question: Is this a significant figures question?

ANSWER round to the significant figures: 533 grams

When you do addition you use the number with the least number of decimals places to determine how many decimal places will be in your answer. There are no decimal places in 198 so you would round before the decimal place in the answer (ones place).

If 3^2x+1=81, what is the value of x?

x=1/4
x=1/2
x=3/2
x=2/3

Answers

3^(2x+1)=81

3^(something)=81
3^4=81. I know this because 3X3X3X3=81
If I know 3^4=81, then I need to find a solution to get 4 for my exponent.
Let's solve.
2x+1=4
2x=3
x=3/2

Write an equation of the line that passes through the points (−3,12) and (0,6)

An equation of the line is y=

Answers

slope = (6 - 12)/(0 +3) = -6/3 = -2

b = 6
so

An equation of the line is
y = -2x + 6

Graph f(x)=−0.25x+4.

Answers

Hey. Hope this helps!

Answer:

Point, (0,4) and (-4,5), just took the test

How many 1/3 pound paperback books together weigh 25 pounds?

Answers

75 I think since 75 divided by 3 equals 25

Final answer:

We can find the quantity of 1/3 pound paperback books that weigh a total of 25 pounds by performing the calculation, 25 ÷ 1/3 or equivalently, 25 x 3, which equals 75. Therefore, we would need 75 of these books to total 25 pounds.

Explanation:

To find out how many 1/3

pound

paperback

books weigh a total of 25 pounds, we use division. Since each book weighs 1/3 of a pound, we divide the total weight we want (25 pounds) by the weight of each individual book (1/3 pound). So, our calculation would look like this:

25 ÷ 1/3

. In mathematics, dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of 1/3 is 3/1, or just 3. So, our calculation is now:

25 x 3

. Multiplying 25 by 3 gives us 75. So, we would need

of these paperback books to

weigh

a total of 25 pounds.

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Simplify 4x2(2x2− 8x + 6). 8x2− 32x + 24 6x2− 32x + 24 6 − 32x + 24x2 8x4− 32x3+ 24x2

Answers

4x^2(3x^2-8x+6)
(4*3)(x^(2+2))+(4*-8)(x^(2+1))+(4*6)(x^(2+0))
12x^4-32x^3+24x^2

Without graphing, find the slope of each line described below.

A) A line that goes through the points (4,1) and (2,5)

B) A line that goes through the origin and the point (10,5)

C) A vertical line that goes through the point (6,-5)

D) A line that goes through the points (1,6) and (10,6)

Answers

A) m= (5-1)/(2-4)= -2
B) m= (5-0)/(10-0) = 1/2
C) m= undefined
D) m= 0

A) The slope of line that goes through the points (4, 1) and (2, 5) is -2.

B) The slope of line that goes through the origin and the point (10, 5) is

1 / 2.

C) Vertical lines has undefined slope.

D) The slope of line that goes through the points (1, 6) and (10, 6) is 0.

What is Slope?

Slope is defined as the steepness of the line.

Since, Slope of line passes through points (x₁ , x₂) and (y₁ , y₂) is;

m = (y₂ - y₁) / (x₂ - x₁)

Now,

A) The slope of line that goes through the points (4, 1) and (2, 5) is;

m = 5 - 1 / 2 - 4

m = 4 / -2

m = - 2

B) The slope of line that goes through the (0, 0) and the point (10, 5) is;

m = 5 - 0 / 10 - 0

m = 5 / 10

m = 1 / 2

C) A vertical line that goes through the point (6,-5) has undefined slope.

Because the horizontal change is 0 and we cannot divide a number by 0.

D) The slope of line that goes through the points (1, 6) and (10, 6) is;

m = 6 - 6 / 10 - 1

m = 0 / 9

m = 0

Thus,

A) The slope of line that goes through the points (4, 1) and (2, 5) is -2.

B) The slope of line that goes through the origin and the point (10, 5) is

1 / 2.

C) Vertical lines has undefined slope.

D) The slope of line that goes through the points (1, 6) and (10, 6) is 0.

Learn more about the slope of line visit:

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The question that says " a school has 1200 pupils "

Answers

how many girls like sports? well, what's 2/5 of 1200? well, is just their product, 2/5 * 1200.

how many boys like sports? well, what's 3/5 of 1200? 3/5 * 1200.

[tex]\bf \cfrac{2}{5}\cdot 1200\implies \cfrac{2\cdot 1200}{5}\implies \cfrac{2400}{5}\implies \stackrel{girls}{480} \\\\\\ \cfrac{3}{5}\cdot 1200\implies \cfrac{3\cdot 1200}{5}\implies \cfrac{3600}{5}\implies \stackrel{boys}{720} \\\\\\ \textit{how many }\stackrel{students}{pupils}\textit{ like sports?}\qquad 480 + 720[/tex]

Arthur is treating his friends to a meal at Chez Rich. The meals added up to $152.30. If he tips the waiter 15%, what is the amount of the tip.
a. $20.80
b. $15.24
c. $22.85
d. $13.37

Answers

152.30(0.15)= 22.845

22.845 rounded to the nearest cent is $22.85.

Therefore, the answer is C. Hope this helps!

Answer:

Option C. $22.85

Step-by-step explanation:

Arthur is treating his friends to a meal at Chez Rich.

The meals added up to = $152.30

He tips the waiter = 15% of the bill

The amount of the tip = 15% × 152.30

= 0.15 × 152.30

= 22.845 ≈ $22.85

The amount of the tip would be $22.85.

Option C. $22.85

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