Answers
Answer:
∠RUS = 90°
Step-by-step explanation:
PT is a line. This means that it has a measure of 180°
This means that all of the angles that it is broken up into must add together to equal 180°.
In this case, ∠PUQ +∠QUR +∠RUS +∠SUT = 180°
As we have the measures for all of the angles aside from ∠RUS, we can solve for that
First, let us input each of the measures of the angles
39+23+∠RUS+28=180
Now all we need to do is isolate ∠RUS by subtracting everything to the other side
Once that is done, we get
∠RUS = 90°
Answer:
[tex]\large\boxed{m\angle RUS=90^o}[/tex]
Step-by-step explanation:
[tex]m\angle PUT=m\angle PUQ+m\angle QUR+m\angle RUS+m\angle SUT\\\\\text{We have:}\\\\m\angle PUT=180^o,\ m\angle PUQ=39^o,\ m\angle QUR=23^o,\ m\angle SUT=28^o\\\\\text{Substitute:}\\\\180^o=39^o+23^o+m\angle RUS+28^o\\\\180^o=90^o+m\angle RUS\qquad\text{subtract}\ 90^o\ \text{from both sides}\\\\90^o=m\angle RUS[/tex]
Related Questions
let (-3,-2) be a point on the terminal side of 0. find the exact values of cos0 csc0 and tan0
Answers
To find the exact values of cos(0), csc(0), and tan(0) given a point on the terminal side of 0, we can use the coordinates of the point to determine the values of the trigonometric functions.
Explanation:To find the exact values of cos(0), csc(0), and tan(0) given that (-3,-2) is a point on the terminal side of 0, we can use the coordinates of the point to determine the values of the trigonometric functions.
First, we can find the value of cos(0) by dividing the x-coordinate (-3) by the distance from the origin, which is sqrt((-3)^2+(-2)^2). Therefore, cos(0) = -3 / sqrt(13).
Next, we can find the value of csc(0) by dividing 1 by the y-coordinate (-2). Therefore, csc(0) = 1 / -2 = -1/2.
Finally, we can find the value of tan(0) by dividing the y-coordinate (-2) by the x-coordinate (-3). Therefore, tan(0) = -2 / -3 = 2/3.
Given that (-3,5) is on the graph of f(x), find the corresponding point for the function f(x) - 4.
Answers
Answer:
(- 3, 1 )
Step-by-step explanation:
Given f(x) then f(x) + c represents a vertical translation of f(x)
• if c > 0 then shift up by c units
• if c < 0 then shift down by c units
Thus for f(x) - 4
(- 3, 5 ) → (- 3, 5 - 4 ) → (- 3, 1 )
Max is buying bags of oranges each bag has 8 oranges when he opens the bag he finds that 12 of the total oranges are rotten what are the options for the number of bags he should buy in order to end up at least 40 good oranges
Answers
Answer: 7 bags
Step-by-step explanation:
Total no. of oranges rotten - 12
To buy no. of bags to get - at least 40 good oranges
No. of oranges in a bag - 8
40 + 12 = 52 oranges
As each bag contains 8 oranges and 52 is not divisible by 8 we end up taking the closest divisible number that is 54.
If we divide 54 by 8 we get 7.
Hence Max needs to buy 7 bags of oranges.
Note: As they have asked at least 40 good oranges
Which expression can be used to find the surface area of the following rectangular prism?
Answers
Answer
30+30+15+15+18+18
Step-by-step explanation:
The expression to calculate the surface area of the prism is 2 * (3 * 5 + 3 * 6 + 5* 6)
How to determine the expression of the surface area?The given parameters are:
Length = 3Width = 5Height = 6The surface area of a rectangular prism is:
Area = 2 * (Length * Width + Length * Height + Width * Height)
Substitute known values
Area = 2 * (3 * 5 + 3 * 6 + 5* 6)
Hence, the expression to calculate the surface area of the prism is 2 * (3 * 5 + 3 * 6 + 5* 6)
Read more about areas at:
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Explain how to find 3 × 5 × 2
Answers
Answer:
30
Step-by-step explanation:
3x5=15
15x2=30
Answer:
30
Step-by-step explanation:
Multiply 3 by 5 which is 15 and them multiply by 2 which is 30
The area of a circle is directly
proportional to the square of its
radius. A circle with a radius of 2
cm has an area of 12.566 cm^2.
What is the radius of a circle with
an area of 78.54 cm^2?
[?] cm
Round to the nearest whole number.
Answers
Answer:
[tex]radius=5\ cm[/tex]
Step-by-step explanation:
Let r be the radius of the circle and A be the area of the circle.
Given:
[tex]r_{1} = 2\ cm, A_{1}=12.566\ cm^{2}[/tex]
And [tex]r_{2} = ?, A_{2}=78.54\ cm^{2}[/tex]
The area of a circle is directly proportional to the square of its radius.
A ∝ [tex]r^{2}[/tex]
[tex]A = kr^{2}[/tex]-----------(1)
Where k is the constant of proportionality
Find constant value by substituting [tex]r_{1} = 2\ cm, A_{1}=12.566\ cm^{2}[/tex]
in equation 1.
[tex]A = kr^{2}[/tex]
[tex]A_{1}=k(r_{1})^{2}[/tex]
[tex]12.566=k\times 2^{2}[/tex]
[tex]12.566=k\times 4[/tex]
[tex]k=\frac{12.566}{4}[/tex]
[tex]k=3.141[/tex]
Find [tex]r_{2}[/tex] by substituting k and [tex]A_{2}[/tex] value in equation 1.
[tex]A = kr^{2}[/tex]
[tex]A_{2}=k(r_{2})^{2}[/tex]
[tex]12.566=3.141\times (r_{2})^{2}[/tex]
[tex](r_{2})^{2}=\frac{78.54}{3.141}[/tex]
[tex](r_{2})^{2}=25.004[/tex]
where: 25.004 ≅ 25
[tex](r_{2})^{2}=25[/tex]
[tex]r_{2}=\sqrt{25}[/tex]
[tex]r_{2}=5\ cm[/tex]
Therefore; the radius of the circle is 5 cm.
Final answer:
The radius of a circle with an area of 78.54 cm² is approximately 4 cm, after setting up a proportion with a known circle area and solving for the unknown radius.
Explanation:
The area of a circle is given by the formula A = πr², where A is the area and r is the radius of the circle. Given that a circle with a radius of 2 cm has an area of 12.566 cm², we set up a proportion to find the radius of a circle with an area of 78.54 cm²:
(12.566 cm²) / (2 cm)² = (78.54 cm²) / r².
Solving for r, we find r² = (78.54 cm²) × (2 cm)² / (12.566 cm²).
After calculation, we get r approximately equal to 4 cm, rounding to the nearest whole number.
(Easy Points, Will mark Brainliest) What number is point A on the number line?
Answers
Answer:
1/4
Step-by-step explanation:
There are 7 points from 0 to 7/4. This means each point represents 1/4. Therefore A is 1/4
Answer:
1/4
Step-by-step explanation:
If you count back from the 7/4, A will be at the 1/4 point.
Hope this helps :)
Rafael is on his way home in his car. His drive is 22 miles long. He has finished one-half of the drive so far, how far has he driven
Answers
Answe
Step-by-step explanation:
he has drive 11 miles of his drive
if you divide 22 by 2 it equals 11
(PLEASE ANSWER ASAP; WILL MARK BRAINIEST)
The table shows y as a function of x. Suppose a point is added to this table. Which choice gives a point that preserves the function?
A) (9, 8)
B) (−6, 3)
C) (−5, −2)
D) (−3, −8)
Answers
Good evening ,
Answer:
D.Step-by-step explanation:
______________________________________________________
Note:
if f is a function then each number of the domain has an unique image.
______________________________________________________
since (regarding the table) the image of 9 is 6 then the answer A is wrong
The same apply on answers B and C .
then the right answer is D(-3,-8).
:)
Answer:
dddddddddddddddddd
A line passes though the points (7, 10) and (7, 20). Which statement is true about the line? It has a slope of zero because x2-x1 in the formula m=
Answers
Answer:
It has no slope because (x2-x1) in the formula [tex]m=\frac{y2-y1}{x2-x1}[/tex] is equal to zero, and the denominator of a fraction cannot be zero
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
the points (7, 10) and (7, 20)
substitute the values
[tex]m=\frac{20-10}{7-7}[/tex]
[tex]m=\frac{10}{0}[/tex] ----> is undefined
The line has a slope undefined ---> is a vertical line (parallel to the y-axis)
Which of the following options is an equivalent function to f(x) = 4(3)2X?
f(x) = 36
f(x) = 4(9)
f(x) = 144
f(x) = 4(6x)
Answers
Answer:
[tex]f(x)=4(6x)[/tex]
Step-by-step explanation:
Given:
the given expression is.
[tex]f(x)=4(3)2x[/tex]
Simplify the given expression.
[tex]f(x)=4(3)2x[/tex]
[tex]f(x)=4(3\times 2x)[/tex]
[tex]f(x)=4(6x)[/tex]
Therefore, the option [tex]f(x)=4(6x)[/tex] is an equivalent function to [tex]f(x)=4(3)2x[/tex].
Please help I will mark previous
Answers
Answer:
[tex] \frac{5}{16}, \: 31.25\%[/tex]
A flower shop has 11 red roses, 7 pink roses, 9 white he roses , and 3 yellow roses in stock . One type of rose is randomly selected for a flower arrangement. What is the probability they the selected rose is red or yellow.
Answers
Answer:
7/15
Step-by-step explanation:
11+7+9+3= 30
11= red
3=yellow
11+3=14
=14/30
=7/15
Answer:
7/15
Step-by-step explanation:
Probability of an event is the number of possible outcome divided by the total outcome. It is a ratio. The probability that an event will or will not happen is 1 as those are the only two possibilities.
Given that the flower shop has 11 red roses, 7 pink roses, 9 white he roses , and 3 yellow roses in stock , the total number of flower available
= 11 + 7 + 9 + 3
= 30 flowers
The probability that a rose selected is ;
red = 11/30
yellow = 3/30
the probability they the selected rose is red or yellow
= 11/30 + 3/30
= 14/30
= 7/15
Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the
expression
17. 8(5 - 1)
a. 8 x 5 - 8x1 = 48
b. 85-8x1 - 32
c. 8 x 5-1 - 39
d. 8 % (5 - 1) *8 - 256
Answers
To use the Distributive Property on the expression 8(5 - 1), you would multiply 8 by each term inside the parentheses, simplify, and perform the subtraction. The final evaluated result is 32.
Explanation:The problem is asking to use the Distributive Property to simplify the mathematical expression and then evaluate it. The Distributive Property, in basic terms, indicates that multiplication distributes over addition or subtraction. So, for the expression 8(5 - 1), you would apply the Distributive Property as follows:
You multiply 8 by each of the terms inside the parentheses:
8 * 5 - 8 * 1
Then, simplify that expression:
40 - 8
And finally, perform the subtraction:
= 32
So, the equivalent expression is 40 - 8, and the evaluated result is 32.
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Type the correct answer in each box. Use numerals instead of words.
Consider this quadratic equation.
x^2 + 2x + 7 = 21
The number of positive solutions to this equation is____.
The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is____.
Answers
Answer:
1 positive solution
2.87.
Step-by-step explanation:
x^2 + 2x + 7 = 21
x^2 + 2x - 14 = 0
The product of its roots = c/a = -14 so it will have 1 positive solution.
x = -2 +/- sqrt (2^2 - 4*-14) / 2
x = -1 +/- sqrt60/2
= -1 +/- 3.873
GreATest solution is 2.87
Reggie Means invested part of $31,000 in municipal bonds that earn 7.5% annual simple interest and the remainder of the money in 8.5% corporate bonds. How much is invested in each account if the total annual interest earned is $2,475?
Answers
Answer:
Principal Invested in Municipal Bonds is $16,000
Principal Invested in Corporate Bonds is $15,000
Step-by-step explanation:
If;
Principal Invested in municipal bonds = a
Principal Invested in corporate bonds = b
then we have;
a + b = $31,000 --------------------------------Equation 1
0.075a + 0.085b = $2,475 ---------------Equation 2
From equation 1 we have;
a = 31,000 - b
By putting the values of a in Equation 2 we get;
0.075 (31,000 - b) + 0.085b = 2,475
2,325 - 0.075b + 0.085b = 2,475
0.01b = 150
b = $15,000
By putting the values of b in equation 1 we get;
a = $16,000
Final answer:
Reggie Means invested $16,000 in municipal bonds at 7.5% interest and $15,000 in corporate bonds at 8.5% interest to earn a total annual interest of $2,475.
Explanation:
Let the amount invested in municipal bonds be $x. Thus, the amount invested in corporate bonds will be $(31,000 - x). The municipal bonds earn 7.5% annual interest and the corporate bonds earn 8.5% interest. The total annual interest from both investments is $2,475.
To calculate the interest from municipal bonds, use the formula Interest = Principal × Rate × Time. The interest from municipal bonds is 0.075x (since 7.5% is the same as 0.075).
Similarly, for corporate bonds, the interest will be 0.085(31,000 - x). The sum of these interests equals $2,475:
0.075x + 0.085(31,000 - x) = 2,475
Solving this equation:
Multiply through by 100 to clear decimals: 7.5x + 8.5(31,000 - x) = 247,500Distribute the 8.5 and combine like terms: 7.5x + 263,500 - 8.5x = 247,500Simplify and solve for x: x = (247,500 - 263,500) / (7.5 - 8.5)Calculate x to find the amount invested in municipal bonds: x = $16,000. Therefore, the amount in corporate bonds is $16,000.What is 12001 ➗ 4180
Answers
Answer:
2.871052631578947
Step-by-step explanation:
this is exactly the answer.
How I did it:
which system of inequalities is represented by the graph?
Answers
Answer:
[tex]y\leq 2x+4[/tex]
[tex]y\geq -x-6[/tex]
Step-by-step explanation:
step 1
Find the equation of the solid line with positive slope
we have the points
(0,4) and (-2,0)
Find the slope
[tex]m=(0-4)/(-2-0)=2[/tex]
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=2\\b=4[/tex]
substitute
[tex]y=2x+4[/tex]
step 2
Find the equation of the inequality with positive slope
we know that
The solution of the inequality, is the shaded area below the solid line
so
The equation of the inequality is
[tex]y\leq 2x+4[/tex] ----> inequality A
step 3
Find the equation of the line with negative slope
we have the points
(-6,0) and (-4,-2)
Find the slope
[tex]m=(-2-0)/(-4+6)=-1[/tex]
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=2\\point\ (-6,0)[/tex]
substitute
[tex]0=-(-6)+b[/tex]
solve for b
[tex]0=6+b[/tex]
[tex]b=-6[/tex]
so
The linear equation is
[tex]y=-x-6[/tex]
step 4
Find the equation of the inequality with negative slope
we know that
The solution of the inequality, is the shaded area above the solid line
so
The equation of the inequality is
[tex]y\geq -x-6[/tex] ----> inequality B
therefore
The system of inequalities is
[tex]y\leq 2x+4[/tex] ----> inequality A
[tex]y\geq -x-6[/tex] ----> inequality B
PLEASE HELP!!!
Acar depreciates at a rate kf 13% per year. the car was originally purchased for 28,000.
1. what is the decay factor of the car?
2. Wrtie a function for this situation with the value if the car as a function of the age of the car in years
3. How much will the car be worth in 6 years?
4. Rewrite the function for question 2 so it is an equivalent function with a negative exponent.
Answers
Complete the equation of the line through
(-8,8) and (1,-10).
use exact numbers
Y=
Answers
Answer:
Step-by-step explanation:
Find the equation of the line thru the points (2,1) and (3,5)
---------------------
This is a 2 step process. First find the slope of the line thru the points.
slope, m = diffy/diffx
m = (5-1)/(3-2)
m = 4
---------
Now use y = mx + b with either point to find b, the y-intercept.
y = mx + b
5 = 4*3 + b
b = -7
-------
Answer:
Step-by-step explanation:
Formula for calculating the equation of a line is expressed as shown below;
y = mx+c OR y-y1 = m(x-x1) where
m is the slope or gradient
c is the intercept (the point where the line cuts the y axis)
m = ∆y/∆x
m = y2-y1/x2-x1
Given the points (-8,8) and (1,-10).
x1 = -8, y1 = 8, x2 = 1, y2 = -10
m = -10-8/1-(-8)
m = -18/9
m = -2
The equation of a line can also be written as a point slope:
y-y1 = m(x-x1)
Substituting the value of x1, y1 and m into the equation we have;
y-8 = -2(x-(-8))
y-8 = -2(x+8)
y-8 = -2x-16
y= -2x-16+8
y = -2x-8
The equation of the line is y = -2x-8
Each box contains 10 to the power of 2 pencils. The school store has 15 boxes of pencils. How many pencil does the school store have
Answers
Answer:
1500
Step-by-step explanation:
10×10=100
100×15=1500
Which number line represents the solution of 5x + 3 ≤ -7? A) A B) B C) C D) D
Answers
Answer: x≤-2
Step-by-step explanation: Solve for x. (NUMBER LINE ATTACHED)
Hope this helps you out.
The solution of the inequality is shown in figure.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ 5x + 3 ≤ - 7
Now,
Solve the inequality as;
⇒ 5x + 3 ≤ - 7
⇒ 5x + 3 - 3 ≤ - 7 - 3
⇒ 5x ≤ - 10
⇒ 5x/5 ≤ - 10/5
⇒ x ≤ - 2
Thus, The solution of the inequality is;
⇒ x ≤ - 2
Therefore, The solution of the inequality is shown in figure.
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The cost of cleaning a rectangular ground is $120 per square m. Calculate the price to be paid if theatre length of ground is 145m and breadth is 85m
Answers
Answer:
it will cost $ 14,79,000
Step-by-step explanation:
Area of the rectangular theatre ground=L*B= 145*85= 12,325 m²
Cost of cleaning per square metre = $ 120
Total cost of cleaning = $120* 12,325= $ 14,79,000
Victor buys some six-packs of soda for a party. He buys 42 cans in all. How many six-packs of soda did Victor buy?
Answers
Divide the total number of cans by 6.
42 / 6 = 7
He bought 7 six packs.
Final answer:
Victor bought 7 six-packs of soda.
Explanation:
To find the number of six-packs of soda Victor bought, divide the total number of cans by 6. In this case, Victor bought 42 cans in total, so dividing 42 by 6 gives us 7. This means Victor bought 7 six-packs of soda.
40% of the children in a sports club play badminton. 25% of the children who play badminton also play squash. There are 11 children in the club who play both badminton and squash.
How many children are there in the sports club altogether?
Answers
Answer:
There are 110 children total in the sports club
Step-by-step explanation:
To get this answer, its actually easier than it seems. You might need a calculator however.
First you start with the 11 children who play both badminton and squash, then, you divide that by 0.25 (25%) to get 44.
Next you take 44 and divide it by 0.4 (40%) to get 110.
And there you go! If you want to make sure you got it right simply start with 110 and multiply it by 0.4 then multiply the number/decimal you get by 0.25. You should get 11 to confirm your answer :)
An exterior angle of a triangle is 140 degrees. If the non-adjacent angles are congruent, then what are the measures of all of the interior angles of the triangle?
Answers
The measures of all of the interior angles of the triangle are 70 degrees, 70 degrees and 40 degrees
Solution:
Given that exterior angle of triangle is 140 degrees
The exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles
Given that adjacent angles are congruent
Let one of the non adjacent interior angles be "x"
x + x = 140
2x = 140
x = 70
So the two interior angles are 70 degrees and 70 degrees
Let us find the third interior angle
The angle sum property of a triangle states that the interior angles of a triangle always add up to 180 degrees
70 + 70 + third angle = 180
third angle = 180 - 70 - 70
third angle = 180 - 140
third angle = 40 degrees
Thus the measures of all of the interior angles of the triangle are 70 degrees, 70 degrees and 40 degrees
Only answer 28 ( I added this parentheses so that the thing would accept my question)
Answers
Answer:
(a). Number of protons in a chlorine atom = 17
(b). Atomic number of sodium = 11
Step-by-step explanation:
Let the number of protons in a sodium atom = x
Then, the number of protons in a chlorine atom = x + 6
Now, it is given that the atomic number of an element is equal to the number of protons per atom.
So, atomic number of sodium (Na) = x
Atomic number of chlorine (Cl) = x + 6
It is given that the atomic number of chlorine is 5 less than twice the atomic number of sodium.
∴ atomic number of chlorine (Cl) = 2 × atomic number of sodium (Na) - 5
⇒ x + 6 = 2x - 5
⇒ x - 2x = -5 - 6
⇒ -x = -11
Cancelling the minus sign from both sides, we get
x = 11
(a). Number of protons in a chlorine atom = x + 6
= 11 + 6 (∵ x = 11)
= 17
(b). Atomic number of sodium = x = 11
Everyone in a class of 30 students takes math and history. Seven students received an A in history and 13 received an A in math, including four that received an A in both courses. How many students did not receive an A in any of these two courses?
Answers
Answer:14
Step-by-step explanation:
30 students total.
7 received an a in history.
13 received an a in math.
4 received an a in both courses.
how many students did not receive an a in either course.
20 total received an a in history or math.
of these, 4 received an a in history and math.
those 4 are being counted twice.
once in history and once in math.
you need to subtract 4 from the number who got an a in history or an a in math to get a total of 16 students who got an a in history or in math.
this leaves 30 - 16 = 14 students who did not get an a in either course.
here's the breakdown.
14 students did not get an a in either course.
3 students got an a in history only.
9 students got an a in math only.
4 students got an a in both history and math.
total is 30 students.
Final answer:
To find how many students did not receive an A in either math or history, subtract the sum of students with As in both subjects (after adjusting for 4 students who received an A in both) from the total class size. It is found that 14 students did not receive an A in either subject.
Explanation:
To determine how many students didn't receive an A in either math or history, we can use the principle of inclusion-exclusion. Firstly, we have 30 students in total. We're told that 7 received an A in history and 13 in math, including four students who received an A in both subjects.
To avoid double-counting those four students, we add the number of students who received an A in history to the number who received an A in math, and then subtract the number who received an A in both:
Number of students with A in either subject: 7 (history) + 13 (math) - 4 (both) = 16 students
Then, we calculate the students who did not receive an A in either subject by subtracting those who received an A in at least one subject from the total class size:
Number of students without an A in any course: 30 (total students) - 16 (A in at least one subject) = 14 students
Therefore, 14 students did not receive an A in either math or history.
The population of a city is modeled by
P ( t ) = 78 , 300 ( 1.023 ) t
P ( t ) represents the number of people and t is the number of years since 2014.
Approximate the population of the city in the year 2035, rounded to the nearest whole number.
Answers
Answer:
the population of the city in the year 2035 is 126,226
Step-by-step explanation:
The population of a city is modeled by
[tex]P(t)= 78300(1.023 )^t[/tex]
P ( t ) represents the number of people and t is the number of years since 2014.
in the year 2014, the year t=0
we need to find the population in the year 2035
2035-2015= 21
so find population when t=21
[tex]P(t)= 78300(1.023 )^t[/tex]
[tex]P(21)= 78300(1.023 )^{21}=126226.36[/tex]
On a coordinate plane, a line goes through (negative 3, 2) and (2, negative 1). A point is at (3, 0). What is the equation of the line that is perpendicular to the given line and passes through the point (3, 0)
Answers
Answer:
y=\frac{5}{3}x-5
Step-by-step explanation: