Answer:
(r o g)(2) = 4
(q o r)(2) = 14
Step-by-step explanation:
Given
[tex]g(x) = x^2 + 5[/tex]
[tex]r(x) = \sqrt{x + 7}[/tex]
Solving (a): (r o q)(2)
In function:
(r o g)(x) = r(g(x))
So, first we calculate g(2)
[tex]g(x) = x^2 + 5[/tex]
[tex]g(2) = 2^2 + 5[/tex]
[tex]g(2) = 4 + 5[/tex]
[tex]g(2) = 9[/tex]
Next, we calculate r(g(2))
Substitute 9 for g(2)in r(g(2))
r(q(2)) = r(9)
This gives:
[tex]r(x) = \sqrt{x + 7}[/tex]
[tex]r(9) = \sqrt{9 +7{[/tex]
[tex]r(9) = \sqrt{16}[/tex]{
[tex]r(9) = 4[/tex]
Hence:
(r o g)(2) = 4
Solving (b): (q o r)(2)
So, first we calculate r(2)
[tex]r(x) = \sqrt{x + 7}[/tex]
[tex]r(2) = \sqrt{2 + 7}[/tex]
[tex]r(2) = \sqrt{9}[/tex]
[tex]r(2) = 3[/tex]
Next, we calculate g(r(2))
Substitute 3 for r(2)in g(r(2))
g(r(2)) = g(3)
[tex]g(x) = x^2 + 5[/tex]
[tex]g(3) = 3^2 + 5[/tex]
[tex]g(3) = 9 + 5[/tex]
[tex]g(3) = 14[/tex]
Hence:
(q o r)(2) = 14
XZ is the perpendicular bisector of segment WY. Solve for k. Enter a NUMBER only.
Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 4.
What is the numerical value of K?A bisector divides an angle or segment into two equal halves.
Given the data in the question;
XZ is the perpendicular bisector of segment WYSegment WX = 6k + 8Segment XY = 11k - 12Value of k = ?Since XZ is a perpendicular bisector of segment WY,
Segment WX is equal to Segment XY
Segment WX = Segment XY
Plug in the given values and solve for k.
6k + 8 = 11k - 12
Collect like terms
6k - 11k = -12 - 8
-5k = -20
Divide both sides by the coefficient of k
-5k/-5 = -20/-5
k = 4
Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 4.
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What is the result of
36 over 9 + 6?
Answer: 10
Step-by-step explanation:
First you can re-order = 36/9 + 6
36/9=4
Then add 4+6
It equals 10
Find the greatest common factor of the expressions.
12y1329, -16y6z9
Answer:
2 and 3 and y
Step-by-step explanation:
2x2x4x y x 1x2x3x3x3
-2x7x y x 2x3x z x3x3
How can u do the 5th problem
Answer:
3/4 of 5. It equals 3 3/4.
Step-by-step explanation:
The question asks for 3/4 of 5 cups of milk.
How would this graph look please help
The inequality graph of the system of inequalities is graph (a)
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to determine how the inequality graph would look like?The system of inequalities is given as
-2x + 3y < 9
x^2 - y <= 10
4x + y > 3
In the above system of inequalities, there are two linear inequalities and a parabola inequality
The inequality symbols in the linear inequalities are opposite
This means that the region between both lines would be shaded
Also, for the parabola; the upper part would be shaded.
This is so because when y is made the subject of the formula, the symbol becomes >=
Using the above as a guide, the inequality graph of the system of inequalities is graph (a)
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Hello! I need help with #2 and #3 please!
The banker should invest $ 30,000 at 6 % interest rate to earn an interest of 3800 per year from both the investments.
Principal 1 = $ 50,000
Rate 1 = 4 %
Let principal 2 be x
Rate = 6 %
Time = 1 year
Interest = 3800
Using simple interest, we get that:
SI = p × r × t
3800 = ( 50,000 × 0.04 × 1) + ( x × 0.06 × 1)
3800 = 2000 + 0.06 x
0.06 x = 3800 - 2000
0.06 x = 1800
6 x = 180000
x = 180000 / 6
x = 30,000
Therefore, we get that, the banker should invest $ 30,000 at 6 % interest rate to earn an interest of 3800 per year from both the investments.
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A traffic cone with a height of 20 in. is ideal for traffic control. Find the lateral area of a cone with a height of 20 in. and a diameter of 12 in. Round the answer to the nearest whole number. (Hint: The height given is not the slant height.)
The lateral area of the cone is 394 square inches
How to determine the value
The formula for lateral area of a cone is expressed as;
Lateral area = πr √h² + r²
Given that;
height = 20 inDiameter = 12 in, radius = 12/ 2 = 6 inSubstitute the values into the formula
Lateral area = 3. 142(6) √20² + 6²
Lateral area = 18. 85 √436
Lateral area = 18. 85 × 20. 8
Lateral area = 394 square inches
Thus, the lateral area of the cone is 394 square inches
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Michael drove from point A to point B at 15 miles
per hour and immediately returned by the same
route at 30 miles per hour. What was his average
speed, in miles per hour, for the entire trip?
E. 20
F. 22.5
G. 24
H.25
Answer:
E
Step-by-step explanation:
Say the distance is 'd'
time for going = d/15
time for returning = d/30
average speed = total distance / ( total time)
= 2d / ( d/15 + d/30 )
solve for average speed = 20 mi/hr
Absolute value of 4 is
Answer: -4
Step-by-step explanation:
it is -4 because we are looking for like the opposite so the opposite of 4 is -4
Answer:
Absolute value of |4| = 4
Step-by-step explanation:
The absolute value of a number is always positive
Simplify the radical √54
Answer: 3√6
Step-by-step explanation:
√54=
√(9*6)=3√6
A group of people were asked if they had run a red light in the last year. The number of people that
responded yes is 397 and no is 159. Find the probability that if a person is chosen at random, he/she has
run a red light in the last year. Round to two decimal places.
Question Help:
If a person is chosen at random, there is a 71% probability that he or she has run a red light in the last year.
What do we mean by probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.So, to find the probability:
P = number of favorable terms/number of total termsFavorable terms = 397Total number of terms = 397 + 159 = 556Apply values in the formula:
P = 397/556P = 0.714028On rounding off, P = 71%.Therefore, if a person is chosen at random, there is a 71% probability that he or she has run a red light in the last year.
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true or false???????
Answer:
False
Step-by-step explanation:
3 x 1/3
3/1 x 1/3 = 1
Answer:false
Step-by-step explanation: i did the test
In the following triangle, what is the value of n?
Given that the triangle is a right triangle, the value of sin (n) is √5/5.
Hence, option D)√5/5 is the correct answer.
What is the value of sin(n) in the triangle?Trigonometry is simply a branch in mathematics that looks into the relationships between angles and side lengths of a triangle.
Given the data in the question;
Hypotenuse = 2√5Opposite of angle n = 2Adjacent of angle n = 4To determine the value of sine n, we will use one of six functions of an angle commonly used in trigonometry.
Sine of angle n = Opposite of angle n / Hypotenuse
sin(n) = Opposite / Hypotenuse
Plug in the given values and simplify
sin(n) = Opposite / Hypotenuse
sin (n) = 2 / 2√5
Next, rationalize the denominator.
Cancel out the common factor 2.
sin (n) = 2 / 2√5
sin (n) = 1 /√5
Multiply both the numerator and the denominator by √5.
sin (n) = (1×√5) / (√5 × √5)
sin (n) = √5/5
Given that the triangle is a right triangle, the value of sin (n) is √5/5.
Hence, option D)√5/5 is the correct answer.
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What is your average speed in miles per hour and in feet per second if you travel a mile in 21 minutes?
Answers:
2.857142 mph
4.190476 ft per second
Both values are approximate
=======================================================
Work Shown:
21 min = 21/60 = 0.35 hrs which is exact
distance = rate*time
rate = distance/time
rate = (1 mile)/(0.35 hrs)
rate = (1/0.35) mph
rate = 2.857142 mph which is approximate
------------------
21 min = 21*60 = 1260 seconds
1 mile = 5280 ft
rate = distance/time
rate = (5280 ft)/(1260 seconds)
rate = (5280/1260) ft per second
rate = 4.190476 ft per second approximately
Answer: 2.857 miles/hr
4.19 ft/sec
Step-by-step explanation:
60 min=1 hr.
1 mi/21 min*60 min=
60 min*1 mi/21 min=2.857 miles/hr
60 sec=1 min
60*60 sec=1 hr
1 hr=3600 sec
2.857 miles/hr=
2.857/3600 miles/sec=0.00079 miles/sec
1 mile=5280 ft
0.00079 miles/sec=
0.00079*5280 ft/sec=4.19 ft/sec
Are these fractions equivalent or
nonequivalent?
The two fractions are equivalent.
When two fractions have the same value, they are said to be equivalent, meaning that even though the numbers in the two fractions are different, their overall value is the same.
Fractions that are not equal to one another are referred to as nonequivalent fractions. The same cross multiplication procedure must be used to determine whether two fractions are comparable or not.
Consider these two fractions,
x = ( m / 4n ) and y = ( 2m / 8n )
Now when the fraction x is multiplying and dividing by 2.
We get,
x = ( m / 4n ) × ( 2 / 2 )
x = 2m / 8n
Therefore, x = y
Hence, the fractions are equivalent.
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A square field has an area of 22,500 square feet. To the nearest foot, what is the diagonal distance across the field?
A.150 feet
B.178 feet
C. 191 feet
D.212 feet
A square field has an area of 22,500 square feet, then the diagonal distance across the field in nearest foot is equal to 212 foot (approximately).
As given in the question,
Area of the square field = 22,500square feet
Let 'a' be the side and 'd' be the diagonal length of the square
a² =22,500
⇒a =150 foot
Using Pythagoras theorem
d² =a² +a²
⇒d² = 2(150)²
⇒d² =45000
⇒d =212.13
≈ 212 nearest foot (approximately)
Therefore, the diagonal distance across the field in nearest foot is 212 foot (approximately) with area of 22,500 square feet as given.
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Which is a solution of 2x+6>12? x>0 x>3 x>−1 x>5
Answer:
x>3
Step-by-step explanation:
2x+6-6 > 12-6 ditch the 6
2x/2 > 6/2 divide by 2
x>3
The graph below defines a function f (x). Find f (2).
3
N
7
s
4
m
14
-2 +
771 ?
1
2345
The perimeter of the figure below is 110 cm. Find the length of the missing side.
Answer:
6.1 cm
Step-by-step explanation:
You want to know the remaining side of the irregular figure such that the perimeter is 110 cm.
PerimeterThe perimeter of a plane figure is the sum of the lengths of the sides. Working clockwise from the upper left corner, we have ...
34.6 +8.6 +17.3 +11.6 +? +11.6 +11.6 +8.6 = 110
103.9 +? = 110 . . . . collect terms
? = 6.1 . . . . . . . . . subtract 103.9
The length of the missing side is 6.1 cm.
__
Additional comment
If the angles that appear to be right angles actually were right angles, the perimeter would be 109.6 cm. The perimeter is longer than this, so at least three of the angles are not right angles.
Express 55 mph in kilometers per hour. Round to the nearest hundredth.
Find the quotient. Do not round your answer 58.543/10,000
Answer:
0.0058543
Step-by-step explanation:
58.543/10,000 = 58.543 divide 10,000
(Scientific Notation LC)
WILL MARK BRAINLEIST ONLY IF CORECCT!
!Rewrite 2,290,000 in scientific notation.
2.29 x 10−6
2.29 x 10−4
2.29 x 104
2.29 x 106
2,290,000 in scientific notation is 2.29 x 10⁶.
What is scientific notation?Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations.
Converting a number in these cases means to either convert the number into scientific notation form, convert it back into decimal form or to change the exponent part of the equation.
Now the given number is,
2,290,000
To convert 2,290,000 into scientific notation, 2,290,000 must be converted into into decimal and multiples of 10.
So, factorizing 2,290,000 we get,
2,290,000 = 229 x 10,000
Now converting 10,000 into multiples of 10
Since, 10,000 = 10 x 10 x 10 x 10
So, 2,290,000 can be written as,
2,290,000 = 229 x 10 x 10 x 10 x 10
Multiplying and divide 229 by 100 we get,
2,290,000 = (229 x 100 x 10 x 10 x 10 x 10) / 100
Rearranging we get,
2,290,000 = (229 x 100) / 100 x (10 x 10 x 10 x 10)
Since, (229 x 100) / 100 = 2.29 x 100
2,290,000 = (2.29 x 100) x (10 x 10 x 10 x 10)
And 100 = 10 x 10
Therefore we get,
2,290,000 = 2.29 x 10 x 10 x 10 x 10 x 10 x 10
Since 10 x 10 x 10 x 10 x 10 x 10 = 10⁶
Therefore we get,
⇒ 2,290,000 = 2.29 x 10⁶
this is the required scientific notation of 2,290,000 .
Thus, 2,290,000 in scientific notation is 2.29 x 10⁶.
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P₁ 1:23:55 AM
Jatch help video
an is preheating his oven before using it to bake. Fabian wants to predict the final
perature after a minutes. He wrote the equation y 50x+78, where y
resents the final temperature in degrees Fahrenheit. What could the number 50 in
bian's equation represent?
-
Number 50 in the Jack's equation represents the rate of change in the oven's temperature over time (per minute) or with respect to time by using the slope form concept.
As per the question statement, Jack is preheating his oven before using it to bake. He wants to predict the final temperature after [tex]x[/tex] minutes.
He wrote the equation [tex]y =50x+78[/tex] , where [tex]y[/tex] represents the final temperature in [tex]fahrenheit[/tex]. We are supposed to tell the significance of number 50 in the given equation.
As we know that the equation which is in the form of [tex]y=mx+c[/tex], or the slop form equation, m is called the slope or the rate of change of value of [tex]y[/tex] with respect to value of [tex]x[/tex].
And the given equation [tex]y =50x+78[/tex] is also of the form of [tex]y=mx+c[/tex] hence we conclude that 50 is the slope or the rate of change of value of [tex]y[/tex] with respect to value of [tex]x[/tex].
As y is the temperature in Fahrenheit therefore x is the time hence "50 Degrees Fahrenheit change of temperature per unit minute" is the significance of 50.
Slop Form Equation: [tex]y=mx+c[/tex] where m is the slope and c is called as the intercept of the lineTo learn more about Slop Form Equation, click on the link given below:
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Steve and Jenna go door-to-door selling chocolate bars. Steve sells 23 chocolate
bars and Jenna sells 12 chocolate bars. Together they collect $210. How should
they divide the money so that each person gets a fair share?
Answer:
Steve: $138.00
Jenna: $72.00
Step-by-step explanation:
Steve:
[tex]\frac{23}{35}[/tex] x 210 = 138
Jenna:
[tex]\frac{12}{35}[/tex] x 210 = 72
I'm not really sure what this means, but i'll do what i think is right!
Answer:
Steve: $138
Jenna: $72
Step-by-step explanation:
If you're doing it so they each get what they sold, you would have to first add the total number of chocolate bars, giving you 35. To see how much each bar costs, you just have to divide $210 ÷ 35, giving you $6 per chocolate bar.
To give each what they gained, you multiply $6 by whichever amount you chose, 23 or 12, which will give you that person's amount. Steve will get $138 and Jenna will get $72.
hope this helps!
1-7: MathXL for School: Practice & Problem Solving
Challenge You buy 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears. What is your total bill?
Grocery Store Prices
Item
Apples
Peaches
Pears
Cost
$0.99 per pound
$1.09 per pound
$1.19 per pound
Your total bill is:
(Round to the nearest cent as needed.)
The total bill for 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears is $6.78 .
In the given question
The price of 1 pound apple = $0.99
The price of 1 pound Peaches = $1.09
The price of 1 pound Pears = $1.19
Total pounds of apples bought = 3.18 pounds
price of 3.18 pounds of apple = ( pounds of apple bought)*(price of 1 pound apple)
=3.18*0.99
=$3.15 ...(i)
Total pounds of Peaches bought = 1.45 pounds
price of 1.45 pounds of peaches = 1.45*1.09
= $1.59 ...(ii)
Total pounds of Pears bought = 1.71 pounds
price of 1.71 pounds of pears = 1.71*1.19
= $2.04 ...(iii)
Total bill = price of 3.18 pounds of apple + price of 1.45 pounds of peaches + price of 1.71 pounds of pears.
Substituting the values from equation (i),(ii)and (iii) we get ,
Total bill = $3.15 + $1.59 + $2.04
= $6.78
Therefore , the total bill for 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears is $6.78 .
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help with 5,6,&7 please!! will mark as brailylist
mous this mobail phonffyuuyy
the quotient of 10 and a number in math terms
Solve
31320= x + (.08x)
Answer:
Step-by-step explanation:
31320=x+0.08x
31320=1.08x
swap the sides
1.08x=31320
Divide by 1.08
x=29000
2 m - 54 cm equals????????
Answer:
146 centimeters or 1.46 meters.
Step-by-step explanation:
1m = 100cm
2m = 200cm
200 - 54 =146
Hope this helps!
You are having a dinner catered. You pay a rental fee of $150 for the dining hall, and you pay the caterer $10 for each person who attends the dinner. How much should you charge per ticket if you expect 50 people to attend? (Round your answer to the nearest cent.)
Answer:
$13
Step-by-step explanation:
For 50 people it will cost you 150 + 50(10) or 500
150 +500 = 650 Divide that among 50 people and you get a cost of $13 a person.