Answer:
15°
Step-by-step explanation:
The exterior angle at vertex S is 360°/12 = 30°. That angle has a measure that is equal to the sum of the congruent angles at R and T of ΔRST. In other words, ...
∠T = 30°/2 = 15°
The size of angle STR is 15°.
The sides of a regular polygon are congruent.
The size of STR is 15 degrees
The polygon is 12-sided.
This means that:
[tex]\mathbf{n =12}[/tex]
The sum of angles in a regular hexagon is 360.
So, the angle at vertex S is:
[tex]\mathbf{\theta = \frac{360}{n}}[/tex]
This gives
[tex]\mathbf{\theta = \frac{360}{12}}[/tex]
[tex]\mathbf{\theta = 30^o}[/tex]
The external angle of a triangle equals the sum of the opposite internal angles.
This means that:
[tex]\mathbf{\theta = \angle STR + \angle SRT}[/tex]
Where:
[tex]\mathbf{ \angle STR = \angle SRT}[/tex]
So, we have:
[tex]\mathbf{\theta = \angle STR + \angle STR}[/tex]
[tex]\mathbf{\theta = 2\angle STR}[/tex]
Substitute [tex]\mathbf{\theta = 30^o}[/tex]
[tex]\mathbf{30^o = 2\angle STR}[/tex]
Divide both sides by 2
[tex]\mathbf{15^o = \angle STR}[/tex]
Rewrite as:
[tex]\mathbf{\angle STR = 15^o }[/tex]
Hence, the size of STR is 15 degrees
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A rectangular window in a door is 30 inches tall. If the area of the window is 300 square inches, how wide is the window?
10 inches
(300 square inches devided by 30 inches)
it is 10 inches wide!
explanation:
300/30=10
#15 You earned 89 out of
100 points on your math
quiz. What percent of the
points did you earn?
#16 Outc
are in bar
of studen
Answer:
89%
Step-by-step explanation:
Percent is a number out of 100.
If you got 89 out of 100, you got 89%
Find the quotient 7/8 divided 3/8
Step-by-step explanation:
Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.
Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes
7/8 x 8/3 = ?
For fraction multiplication, multiply the numerators and then multiply the denominators to get
7 x 8
8x3
56/24
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 56 and 24 using
GCF(56,24) = 8
56/8 = 7
24/8 = 3
The fraction 7/3 is the same as 7 divided by 3
Convert to a mixed number using long division for 7 ÷ 3 = 2R1, so
Therefore:
7/3 = 2 1/3
2 1/3
The required quotient is 7/3 when 7/8 is divided by 3/8.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.
The division operation is given in the question following as:
⇒ 7/8 ÷ 3/8
We have to determine the quotient when 7/8 is divided by 3/8
As per the given question, we have
⇒ 7/8 ÷ 3/8
⇒ (7/8) / (3/8)
Reciprocal the terms in the numerator, and we get
⇒ (7/8) × (8/3)
Apply the multiplication operation,
⇒ 56/24
Reduce the above fraction to the simplest form
⇒ 7/3
Therefore, the required quotient is 7/3 when 7/8 is divided by 3/8.
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To the nearest millimeter, a cell phone is 82 mm long and 36 mm wide. What is the ratio of the width to the length?
Please I need the answer
Step-by-step explanation:
Given,
The length of a cell phone(l) = 82 mm and
The width of a cell phone(b) = 36 mm
Find, the ratio of the width to the length of a cell phone = ?
∴ The ratio of the width to the length of a cell phone
= 36 mm : 82 mm
= 36 : 82
Divided by 2, we get
= [tex]\dfrac{36}{2}[/tex] : [tex]\dfrac{82}{2}[/tex]
= 18 : 41
Thus, the ratio of the width to the length of a cell phone is 18 : 41.
What is the answer to (7+4)2+(14/7)
Answer:
24
Step-by-step explanation:
What is the measure of angle X? 56° 41°
Question:
What is the measure of angle X?
The image of the measurements is attached below:
Answer:
The measure of angle x is 83°
Explanation:
Since, Vertical angles have equal measure,
Let us consider that the angle opposite to 41° is ∠y and they are equal.
i.e, ∠y = 41°
Since, the angles in a straight line add up to 180°, we have,
∠x + ∠y + 56° = 180°
Substituting the value ∠y = 41°, we have,
∠x + 41° + 56° = 180°
Adding the terms, we get,
∠x + 97° = 180°
Subtracting both sides by 97°, we get,
∠x = 83°
Thus, the measure of ∠x is 83°
Answer:
83 degrees
Step-by-step explanation:
I took the test
Which number has the smallest number? -5 or -15?
Answer:
-15
Step-by-step explanation:
this is the negative scale, so the bigger the smaller
Answer:-15
Step-by-step explanation:
-15 is 15 away from 0 while -5 is only 5 away from 0
Casey has a collection of 39 amusement park pins. The pins are from an amusement park in Florida and an amusement park in Virginia. There are twice as many pins from the amusement park in Florida. How many pins are from the amusement park in Virginia?
Answer:
13 pins
Step-by-step explanation:
2x=Florida
x=Virginia
39=2x+x
39=3x
÷3 ÷3
13=x
26 pins are from city V.
Let,
x = number of pins from city F.
y = number of pins from city V.
According to the question:
[tex]x+y=39\\y = 2x[/tex]
Solving them, [tex]x = 13, y=26[/tex]
So 26 pins are from city V.
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Which of the following has a solution set of {x | x = 0}?
(x + 1 < -1) ∩ (x + 1 < 1)
(x + 1 ≤ 1) ∩ (x + 1 ≥ 1)
(x + 1 < 1) ∩ (x + 1 > 1)
Answer:
(b) (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = {x | x = 0}
Step-by-step explanation:
Here, the given expression is : {x | x = 0}
So, the ONLY element in the given set = {0}
Now, take each option and solve the given expression:
(a) x + 1 < -1
Adding -1 BOTH sides, we get:
x + 1 -1 < -1 -1
or, x < - 2 ⇒ x = { -∞ , .... , -4,-3}
Also, x + 1 < 1
Adding -1 BOTH sides, we get:
x + 1 -1 < 1 -1
or, x <0 ⇒ x = { -∞ , .... , -4,-3,-2,-1}
So, (x + 1 < -1) ∩ (x + 1 < 1) = { -∞ , .... , -4,-3}∩ { -∞ , .... , -4,-3,-2,-1}
= { -∞ , .... , -4,-3}
⇒ (x + 1 < -1) ∩ (x + 1 < 1) ≠ {0}
Similarly, solving
(b) (x + 1 ≤ 1) ∩ (x + 1 ≥ 1)
(x + 1 ≤ 1) = x≤ 0 = { -∞ , .... , -4,-3,-2,-1, 0}
(x + 1 ≥ 1) = x ≥ 0 = {0,1,2,3,... ∞}
⇒ (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = {0}
(b)(x + 1 < 1) ∩ (x + 1 > 1)
(x + 1 < 1) = x < 0 = { -∞ , .... , -4,-3,-2,-1}
(x + 1 > 1) = x > 0 = { 1,2,3,... ∞}
⇒ (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = Ф
Hence, (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = {x | x = 0}
(x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = {x | x = 0}
Explain how to use the distributive property to find an
expression that is equivalent to 20 + 16.
Answer:
4(5+4)
Step-by-step explanation:
Answer:
Sample Response: First, I would find that the GCF of 20 and 16 is 4. Then, I would divide both 20 and 16 by 4. Last, I would use the distributive property to write the sum as 4(5 + 4).
Step-by-step explanation:
Given that ABCD is a rhombus, what is the value of x?
(3x - 26)
Answer:its 29
Step-by-step explanation:
Answer:
29
Step-by-step explanation:
Kim says that multiply 1/4×12 is the same as dividing 12 x 4 do you agree with him explain your answer
Answer: No
Step-by-step explanation: 12 x 4 is 48. 12 x 1/4 is the same as dividing 12 by 4, which gives you 3. 3 is not equal to 48.
The correct statement is that the number 3 is not equal to 48.
I do not agree with him.
What is simplification?Simplification is to make something easier to do or understand and to make something less complicated.
Given
Kim says that multiplying 1/4×12 is the same as dividing 12 x 4
How to find the solution?The multiplication of 12×4 = 48.
1/4×12 is the same as dividing 12 by 4, which gives you 3.
Therefore, 3 is not equal to 48.
I do not agree with him.
More about the simplification link is given below.
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can you solve this equation for me?
simplify the expression 6-2x+5+4x
Answer:
11 + 2x
Step-by-step explanation:
First you will want to separate like variables, so (6, 5) and then (-2x, 4x)
Then you will use the signs to do the math. You can move everything to help visualize the solution easier.
6+5+4x-2x
6+5 = 11
4x-2x = 2x
Because you cannot add or subtract a variable with a non variable, and both numbers are positive you end up with
11 + 2x
The expression 6-2x+5+4x simplifies to 11 + 2x by combining like terms: the constants (6+5=11) and the variables (-2x+4x=2x).
To simplify the expression 6-2x+5+4x, we start by combining like terms. Combining the constant terms (6 and 5) and the variable terms (-2x and 4x), we get:
Constant terms: 6 + 5 = 11
Variable terms: -2x + 4x = 2x
Thus, the simplified expression is 11 + 2x.
Renna pushes the elevator button, but the elevator does not move. The mass limit for the elevator is
450 kilograms (\text{kg}kgstart text, k, g, end text), but Renna and her load of identical packages mass a total of 620\,\text{kg}620kg620, start text, k, g, end text. Each package has a mass of 37.4\,\text{kg}37.4kg37, point, 4, start text, k, g, end text.
Answer:
Whats the full question ?
Step-by-step explanation:
Answer:
37.4p ≥ 170
5 packages
Step-by-step explanation:
The inequality is:
37.4p ≥ 170
Renna needs to remove a minimum of 555 packages from the elevator to meet the mass requirement.
Also the answer above is not ok to do.
Saying random things just for the points is wrong.
Instead you can say it where it says comment under the question
Hope this helps ;)
there were 20 members in thr running club in september. the membership increased to 25 in october. the membership decreased back to 20 in november. what was the percent decrease from october to november?
There was a decrease of 20% in membership from October to November.
Step-by-step explanation:
Step 1; To find the percent by which the running clubs membership decreased we must find the difference between the number of members in October and the number of members in November. The number of members in the club in October was 25 whereas it reduced to 20 in the month of November.
Difference in members = Number of members in October -Number of members in November = 25 - 20 = 5
Step 2; To find the percent decrease in number of members in the running club, we divide the difference in number of members by the number of members in November . We multiply this value by 100 to get it in terms of percentage.
Percent decrease in number of members =(Difference in members / number of members in November) *100
= (5/25) * 100 = 0.20 * 100 = 20%
So number of members in the club decreased by 20% from October to November.
What is the slope of the line that passes through the points (3,3) and (-3,-1).
Answer:
2/3
Step-by-step explanation:
-1 - 3 = - 4
-3 - 3 = - 6
-4/-6 = 2/3
[tex]\text{Use the slope formula:}\\\\\frac{y2-y1}{x2-x1}\\\\\text{Plug in your coordinates:}\\\\\frac{-1-3}{-3-3}\\\\\text{Solve:}\\\\\frac{-1-3}{-6}\\\\\frac{-4}{-6}\\\\\boxed{\frac{4}{6}}[/tex]
Please help me calculate the proper number of significant figures, I would like to check my answers to see if this is correct based on the significant figure rules
A.) 320.80−(6101.3/1.8)320.80−(6101.3/1.8)=
B.) [(286.4×105)−(1.300×103)]×2.8951=
C.) (0.0041×26000.0)+(2811×15)=
D.) 863×[1251−(3.11×109)]=
Final answer:
To determine the proper number of significant figures in a calculation, follow the rules for addition/subtraction and multiplication/division, and round the final answer to the proper number of significant figures.
Explanation:
To determine the proper number of significant figures in a calculation, follow these rules:
Addition and subtraction: The result should have the same number of decimal places as the number with the fewest decimal places.Multiplication and division: The result should have the same number of significant figures as the number with the fewest significant figures.Rounding: Round the final answer to the proper number of significant figures.Using these rules, the proper number of significant figures for the given calculations are:
A.) 320.80 - (6101.3 / 1.8) = 300
B.) [(286.4 x 105) - (1.300 x 103)] x 2.8951 = 839000
C.) (0.0041 x 26000.0) + (2811 x 15) = 40000
D.) 863 x [1251 - (3.11 x 109)] = -1.7742e12
The perimeter of the rectangle is 14x + 4, the length of the rectangle is 2x. What is the width of the rectangle?
Answer:
5x+2
Step-by-step explanation:
P=2L+2W
14x+4=2(2x)+2W
14x+4=4x+2W
14x+4-4x=2W
14x-4x+4=2W
10x+4=2W
(10x+4)/2=W
5x+2=W
I Need Help With This Question!
I Need To Draw A Plot Line
Answer:
A line plot graph will show the repetition or frequency of information or value in a number line.
This line plot graph can be used to compare numbers over a certain limit. It is a simple and quick way to order data.
Steps to draw plot graph:-
Write the number sequence in ascending order. Mark the distinct numbers in the sequence.Draw a line and mark points with that distinct numbers. Now look at the sequence and check with the diagram. When a number in the sequence matches the number in the diagram. Then mark a point above that line corresponding to that value.Ascending order: [tex]1\frac{1}{2}, 2\frac{1}{2} ,2\frac{3}{4} ,3,3\frac{1}{2}, 3\frac{3}{4}.\\[/tex]
refer the diagram below for the answer.
Share £40 in the ratio 1:4
Answer:
8:32
Step-by-step explanation:
1x+4x=40
5x=40
x=8
1*8:4*8
8:32
A concert hall has three sections: the main floor, the balcony, and the gallery. For a recent concert, 1020 tickets were sold. There were twice as many balcony tickets sold as gallery tickets, and 225 more main floor tickets than balcony tickets. If g represents the number of gallery tickets sold, which expressions represents this situation?
Answer:
Let the number of balcony seats be b
Let the number of gallery tickets be g
Let the number of main floor tickets be m
b + g + m = 1020
b = 2g
m = b + 225
The number of balcony tickets = 318
The number of gallery tickets = 159
The number of main floor tickets = 543
Step-by-step explanation:
Let the number of balcony seats be b
Let the number of gallery tickets be g
Let the number of main floor tickets be m
i) Therefore we can write b + g + m = 1020
ii) there were twice as many balcony tickets sold as gallery tickets
therefore b = 2g [tex]\Rightarrow[/tex] g = 0.5b
iii) there were 225 more main floor tickets than balcony tickets
therefore m = b + 225
iv) using equation ii) and equation iii) in equation i) we can write
b + g + m = b + 0.5b + b + 225 = 1020 [tex]\Rightarrow[/tex] 2.5b = 795 [tex]\Rightarrow[/tex] b = 318
v) g = 0.5 b = 0.5 [tex]\times[/tex] 318 = 159
vi) m = b + 225 = 318 + 225 = 543
Answer:
D. Gallery: g
Balcony: 2g
Main Floor: 2g+225
Step-by-step explanation:
Gallery is g
Balcony had 2 times as many tickets than Gallery so 2•g (2•gallery)
Main floor had 225 more tickets than Balcony so Balcony’s equation plus 225 tickets. 2g + 225
doug has 45 coins worth $9.00. The coins are all quarters or dimes. How many of each type of coin dose doug have?
Doug have 30 quarters and 15 dimes.
Step-by-step explanation:
Given,
Number of coins = 45
Worth of coins = $9.00 = 9.00*100 = 900 cents
Each quarter = 25 cents
Each dime = 10 cents
Let,
x be the number of quarters
y be the number of dimes
According to given statement;
x+y=45 Eqn 1
25x+10y=900 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=45)\\10x+10y=450\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](25x+10y)-(10x+10y)=900-450\\25x+10y-10x-10y=450\\15x=450[/tex]
Dividing both sides by 15
[tex]\frac{15x}{15}=\frac{450}{15}\\x=30[/tex]
Putting x=30 in Eqn 1
[tex]30+y=45\\y=45-30\\y=15[/tex]
Doug have 30 quarters and 15 dimes.
Keywords: linear equation, elimination method
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Doug has 30 quarters and 15 dimes.
Let
x = number of quarters
y = number of dimes
The total number of coins is 45. Therefore,
Total number of coins:x + y = 45Total amount of the coins is $9. Therefore,
Total cost of the coins:0.25x + 0.1y = 9Therefore,
x + y = 45
0.25x + 0.1y = 9
0.1x + 0.1y = 4.5
0.25x + 0.1y = 9
0.15x = 4.5
x = 4.5 / 0.15
x = 30
y = 45 - 30
y = 15
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44 decreased by twice a number
use the variable "n" to represent an unknown number
Answer:
44-2n
Step-by-step explanation:
Hope it helps!
Final answer:
The expression '44 decreased by twice a number' can be represented as 44 - 2n, where n is the unknown number.
Explanation:
The question involves expressing a given mathematical relationship using a variable. Here, the relationship is '44 decreased by twice a number.' To represent this situation with the variable n, we use the expression 44 - 2n. To simplify further, just substitute the variable 'n' with the unknown number. This represents the original number 44 being reduced by two times the value of some unknown number n.
Arthur earned $136 in three weeks. He goes back to school in one more week. He needs at least $189 to buy the coat that he wants for school. How much must Arthur earn in the next week?
Solve for the intersection point
2x+3y=-6
-2x+3y=-18
Answer:
(3,-4)
Step-by-step explanation:
Write the expression "N is the same as 6 reduced by 2" as a number sentence.
Answer:
N = 6 - 2
Step-by-step explanation:
Take each part of the word expression and translate it:
"N" => N ("N" is a variable that represents a number you don't know)
"is the same as" => = ("the same" means equals)
"6 reduced by 2" => 6 - 2 ("reduced" means use subtraction "-")
Put the sentence back together in the same order.
N = 6 - 2
If you wanted to find "N", you can simplify by doing 6 - 2.
N = 4
urgent please be my saint VX is a midsegment of △WYZ. If YZ=t+95 and VX=10t, what is the value of t?
Answer:
[tex]t = 5[/tex]
Step-by-step explanation:
By the mid-segment theorem of triangles,
[tex]VX= \frac{1}{2} YZ[/tex]
We substitute the expressions in terms of t.
[tex]10t = \frac{1}{2} (t + 95)[/tex]
We multiply through by 2 to get:
[tex]20t = t + 95[/tex]
Subtract t from both sides:
[tex]20t - t = 95[/tex]
[tex]19t = 95[/tex]
Divide both sides by 19:
[tex]t = \frac{95}{19} [/tex]
[tex]t = 5[/tex]
Find the area of shaded region. Round the answer to 2 decimal places if necessary
[tex]\boxed{A=50units^2}[/tex]
Explanation:Hello! Remember you have to write complete questions in order to get good and exact answers. Here you haven't provided any regions so I'll help you assuming a system of inequalities that leads to a shaded region that is a right triangle as shown in the figure below. The system is the following:
[tex]\left\{ \begin{array}{c}x>0\\y>0\\y<-x+10\end{array}\right.[/tex]
From the figure below, the shaded region is a right triangle with base 10 units and height 10 units. So:
[tex]A=\frac{b\times h}{2} \\ \\ \\ A:Area \ of \ the \ triangle \\ \\ b:base \ of \ the \ triangle \\ \\ h:height \ of \ the \ triangle[/tex]
So:
[tex]A=\frac{10\times 10}{2} \\ \\ A=\frac{100}{2} \\ \\ \boxed{A=50units^2}[/tex]
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I need help it with this it also has three parts to it. Wayne another painter is mixing paint. He makes six quarts of brown paint by mixing equal quantities of yellow paint and violet paint. The violet paint is made from one-third red paint and two-thirds blue paint
1.How much red paint does he use?
2. How much blue paint does he use?
3. What percentage of the brown paint is made from blue paint?
Answer:
a) 1 quart
b) 2 quarts
c) 33.33 % of the brown paint is made of blue paint
Step-by-step explanation:
6 quarts brown paint = 1/2 of yellow paint and 1/2 violet paint
violet paint = 1/3 red paint 2/3 blue paint
then
6 quarts brown paint = 1/2 of yellow paint and 1/2 (1/3 red paint and 2/3 blue paint)
or
6 quarts brown paint = 1/2 of yellow paint , (1/2*1/3) red paint and (1/2*2/3) blue paint
6 quarts brown paint = 1/2 of yellow paint , 1/6 red paint and 1/3 blue paint
then
a) he uses 1/6 of 6 quarts to make red paint = 1/6*6 = 1 quart
b) he uses 1/3 of 6 quarts to make red paint = 1/3*6 = 2 quarts
c) brown paint is made with 1/3 of blue paint = 33.33 % of the brown paint is made of blue paint
make g the subject of x=3g+2
Answer:
look at picture shown.