Radian measure of the central angle is 4 radian
Solution:
Given that,
A circle of radius 1.5 meter that intercepts an arc of length 600 centimeters
To find: Radian measure of the central angle
Let us find the circumference of circle
The circumference of circle is given as:
[tex]\text{ circumference of circle } = 2 \pi r[/tex]
Where "r" is the radius of circle
[tex]\text{ circumference of circle } = 2 \times \pi \times 1.5 = 3 \pi[/tex]
Therefore circumference of circle = [tex]3 \pi[/tex] meters , which subtends central angle of [tex]2 \pi[/tex] radian
Given that arc of length 600 centimeters. Let us convert 600 centimeter to meter
We know that, to convert centimeter to meter divide the length value by 100
[tex]\text{ 600 centimeter } = \frac{600}{100} \text{ meter } = 6 \text{ meter}[/tex]
Therefore arc of 6 meter will subtend a central angle of:
[tex]\rightarrow \frac{6}{3 \pi} \times 2 \pi = 4[/tex]
Therefore radian measure of the central angle is 4 radian
a relation is a function
a. there is exactly one input for each output
b. there is exactly one output for each input
c. there is more than one input for each output
d. there is more than one output for each input
A relation is a function if there is exactly one output for each input ⇒ b
Step-by-step explanation:
Let us revise the meaning of relation and function
A relation is a set of inputs and outputs that are related in some wayWhen each input in a relation has exactly one output, the relation is said to be a functionA function is a relation with one output for each inputExamples:
{(1 , 2) , (-2 , 3) , (1 , 5) , (2 , 4)}
∵ x is the input
∵ y is the output
∵ The input 1 has two output 2 and 5
∴ The set above is a relation
{(1 , 2) , (-2 , 3) , (-1 , 5) , (2 , 4)}
∵ x is the input
∵ y is the output
∵ Each input has only one output
∴ The set above is a function
A relation is a function if there is exactly one output for each input
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Triangles and angle bisectors? Can somebody please help me find x & y ?
Answer:
x = 12
y = 5
Step-by-step explanation:
a triangle's side is divided by an angle bisector that bisects the opposite angle. Their relative lengths equals to the relative lengths of the other two sides of the triangle
x / 8 = 9 / 6
x = 9/6 * 8 = 12
(y-3) / 3 = 4 / 6
y - 3 = 4/6 * 3 = 2
y = 5
graph quadrilateral ABCD with vertices A (-4,1) B (-3,3) C (0,1) D (-2,0) and its image after the translation (x,y) to (x-1,y-5)
Answer:
see attached
Step-by-step explanation:
The translation is 1 unit left and 5 units down. It is easy enough to count squares. It is just as easy to add (-1, -5) to each of the preimage coordinates.
a bucket hold b liters of water, but a jar holds 8fewr liters than the bucket. how many times more water can the bucket hold than the jar?
Final answer:
To find how many times more water the bucket can hold than the jar, divide the bucket's capacity by the jar's capacity.
Explanation:
The bucket holds b liters of water, and the jar holds 8 fewer liters than the bucket. To find out how many times more water the bucket can hold than the jar, we need to compare their capacities. \
The bucket's capacity is b liters, and the jar's capacity is b - 8 liters.
To find the ratio of the bucket's capacity to the jar's capacity, we divide the bucket's capacity by the jar's capacity:
b / (b - 8)This ratio represents how many times more water the bucket can hold than the jar.
Let f(x) = 5x3 + 3x2 – 3 and g(x) = x2 + X - 5, fin
4) f(x) + g(x)
Answer:
[tex]f(x)+g(x)=5x^{3} +4x^{2}+x-8[/tex]
Step-by-step explanation:
Given:
Two functions are given:
[tex]f(x)=5x^{3} +3x^{2} -3[/tex]
[tex]g(x)=x^{2} +x-5[/tex]
Find [tex]f(x)+g(x)[/tex]
Solution:
[tex]f(x)+g(x)=(5x^{3} +3x^{2} -3)+(x^{2} +x-5)[/tex]
[tex]f(x)+g(x)=5x^{3} +3x^{2} -3+x^{2} +x-5[/tex]
[tex]f(x)+g(x)=5x^{3} +(3x^{2} +x^{2})+x-3-5[/tex]
[tex]f(x)+g(x)=5x^{3} +4x^{2}+x-8[/tex]
Therefore, the function of [tex]f(x)+g(x)=5x^{3} +4x^{2}+x-8[/tex]
(f-g)(x)
f(x)= 1/x+2
g(x)= 3x
Answer:
f(x) - g(x) = (1/x) + 2 - 3x or (f - g)(x)
Step-by-step explanation:
f(x) = 1/x+2
-g(x) = 3x
can be summarized on line line as:
f(x) - g(x) = (1/x) + 2 - 3x or (f - g)(x)
what is What is the measure of XYZ ?
A.
278
B.
196
C.
98
D.
164
Answer:
The arc length, radius and the included angle are related as
r\theta=\widehat {XYZ} where \theta is in radians.
The radius r is given by
r=\frac{\widehat {XYZ} }{\theta} \\ r=\frac{10.8}{1.8} \\ r=6\;units
Correct choice is (B).
Step-by-step explanation:
How many ways can we choose a 5 digit code out of 10 digits (includes ) if no numbers can be repeated?
simplify -2/5 + 4/3
Answer:
14/15
Step-by-step explanation:
find common denomerator 15
giving you -6/15 + 20/15
add
Rita is hiking along a trail that is 13.8 miles long. So far she has hiked along one-tenth of the trail.
How far has Rita hiked?
Rita has hiked
miles.
Rita has hiked 1.38 miles so far.
Step-by-step explanation:
Given,
Total length of the hiking trail = 13.8 miles
Distance covered by Rita so far = [tex]\frac{1}{10}\ of\ the\ trail[/tex]
Distance covered in miles = [tex]\frac{1}{10}*13.8[/tex]
Distance covered in miles = 1.38 miles
Rita has hiked 1.38 miles so far.
Keywords: fraction, division
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write the fact family for 1,4,and 4
Answer:
For 1 is 1
For 4 is 1,2,4
Step-by-step explanation:
A fact family for 1, 4, and 4 can be created using addition and subtraction. The addition equations are 1 + 4 = 5 and 4 + 1 = 5. The subtraction equations are 4 - 1 = 3 and 4 - 3 = 1.
Explanation:In mathematics, a fact family is a set of three numbers that can be used to create four different addition and subtraction equations. In this case, the numbers given are 1, 4, and 4. To create the fact family, we can use the numbers and their corresponding operations.
The addition equations would be: 1 + 4 = 5 and 4 + 1 = 5.
The subtraction equations would be: 4 - 1 = 3 and 4 - 3 = 1.
Therefore, the fact family for 1, 4, and 4 is: 1, 4, and 5 (addition) and 4, 1, and 3 (subtraction).
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simplify 3^-6 × (3^4 ÷ 3^0)^2
Answer:
Step-by-step explanation:
3^-6 × (3^4 ÷ 3^0)^2 = 3^-6 × (3^4 ÷ 1 )^2 {any number raise to zero = 1}
= 3^-6 × (3^4 )^2
= 3^-6 × (3^8) [ (a^m)^n = a^ m*n ]
= 3^ -6 + 8 = 3^2 = 3 * 3 = 9
Katie Made a scale drawing of a restaurant in real life the restaurant kitchen is 12 m wide it is 36 mm wide in the drawing what scale katie use for the drawing?
Answer:
Scale : 1 mm = [tex]\frac{1}{3}\ m[/tex]
Or
Scale : 3 mm = 1 m
Step-by-step explanation:
Let the scale used be 1 mm = 'x' m
Given:
Actual width of kitchen is 12 m.
Length used by Kate in drawing is 36 mm.
So, 36 mm in drawing is equivalent to 12 m in actual.
Therefore, 1 mm in drawing is equivalent to 'x' m in actual.
Taking proportions and solving by cross multiplication, we get
[tex]\frac{36}{12}=\frac{1}{x}\\36x=12\\x=\frac{12}{36}\\x=\frac{1}{3}\ m[/tex]
Therefore, 1 mm in drawing is equal to [tex]\frac{1}{3}\ m[/tex] in actual.
Scale : 1 mm = [tex]\frac{1}{3}\ m[/tex]
Or
Scale : 3 mm = 1 m
A researcher conducted a study investigating the effect of computer screen time on a person’s amount of REM sleep. The researcher randomly assigned 100 people into four groups. The first group was given 2 hours of computer screen time each day, the second group was given 4 hours each day, the third group was given 6 hours each day, and the fourth group was given 8 hours each day. The study was conducted for one week, and the amount of REM sleep for each person was measured. What is the explanatory variable in the study?
Answer:
Amount of screen time
Step-by-step explanation:
Explanatory variables are those variables that are not totally independent and are used to predict or explain differences in the response variable.
Having pointed what an explanatory variable is, we'll list the explanatory variable(s) in the question, using the definition above.
The Variable used to predict results here is the amount of screen time.
In that case, it is the explanatory variable.
And it's of numerical type.
In the described study, the explanatory or independent variable is the amount of computer screen time each day, as it is the variable that is being manipulated by the researcher in order to examine its effect on REM sleep.
Explanation:In this particular research study, the explanatory variable, or the independent variable, is the amount of computer screen time each day. This is because the explanatory variable is the factor manipulated by the researcher to observe any potential effects on the outcome variable, which in this case, is the amount of REM sleep.
The participants were divided into four different groups, each exposed to a different amount of screen time: 2 hours, 4 hours, 6 hours, and 8 hours. These varying hours of exposure were purposely manipulated by the researcher to observe and measure any differences in the REM sleep duration. Therefore, the computer screen time is the explanatory variable or cause, and the observed alterations to the REM sleep will be the response, or the dependent variable.
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What are four points that can line slope=5 and y-intercept=-1
Answer:
see the explanation
Step-by-step explanation:
step 1
Identify the equation of the given line
we know that
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
we have
[tex]m=5\\b=-1[/tex]
substitute
[tex]y=5x-1[/tex]
step 2
Identify the coordinates of four points on the line
First point
The given y-intercept
point (0,-1)
Second point
The x-intercept
For y=0
[tex]0=5x-1[/tex]
[tex]x=\frac{1}{5}=0.20[/tex]
point (0.20,0)
Third point
For x=1
[tex]y=5(1)-1=4[/tex]
point (1,4)
Fourth point
For x=2
[tex]y=5(2)-1=9[/tex]
point (2,9)
HELP WORTH 20 POINTS!!! I have attached the answer chooses.
Which linear function has the steepest slope?
Answer:
The 3rd one
Step-by-step explanation:
The steepest slope is basically the slope with the greatest absolute value. You can find slope by finding rise over run when given the graphs and finding change in y/change in x in the tables.
Function 1: -3
Function 2: (13-10)/(6-3) = 3/3 = 1
Function 3: 2
Function 4: (-4-(-12))/(2-4) = 8/-2 = -4
Function 4's slope has the greatest absolute value.
answer: the fourth one
Every minute, there are two Christmas trees sold at the tree farm. At this rate, how many trees will be sold in three and a half hours?
420 trees
210 minutes in 3 1/2 hours
x2 per minute
=420 trees in 3 1/2 hours
There are 420 trees will be sold in three and a half hours.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Every minute, there are two Christmas trees sold at the tree farm.
Now,
Since, Every minute, there are two Christmas trees sold at the tree farm.
Hence, Number of sold Christmas tree in 1 hour = 2 × 60
= 120
So, Number of sold Christmas tree in 3 1/2 hour = 120 × 3 1/2
= 120 × 7/2
= 420
Thus, There are 420 sold Christmas tree in 3 1/2 hour.
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Mr Logan needs to buy snacks for his daughter soccer team. He decides to buy crackers and granola bars at a local store. The price of the crackers is $9 for 3 boxes, and the price of the granola bars is $6 for 3 boxes. Mr Logan ends up buying $20 worth of crackers and granola bars. Which equation represents the relationship between the number of boxes of crackers, x, and the number of boxes of granola bars, y, that Mr Logan bought at the grocery store.
Answer:
20 = 3x+2y
Step-by-step explanation:
one box of crackers is $3 (3x)
one box of granola bars is $2 (2y)
Sofia's parents gave her an allowance for summer camp of $125.if she is going to be at camp for 6 weeks,what is the most she can spend each week while she is at camp? Inequality
Sofia can spend at most $20.83 each week.
Step-by-step explanation:
Given,
Amount of given by Sofia's parent = $125
Number of weeks = 6
Let,
x represent the amount that Sofia can spend each week.
As Sofia has $125, therefore, she can spend maximum $125 or less than that.
[tex]6x\leq 125[/tex]
Dividing both sides by 6
[tex]\frac{6x}{6}\leq \frac{125}{6}\\x\leq 20.83[/tex]
Sofia can spend at most $20.83 each week.
Keywords: inequality, division
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if x+3/3 = y+2/2, then x/3 = ?
A. Y + 1
B. Y / 3
C. Y / 2
D. Y - 1
Answer:
C
Step-by-step explanation:
(x+3)/3 =(y+2)/2
x/3 +3/3 = y/2 +2/2
x/3 +1 = y/2 +1
x/3 = y/2
30 points - Find x please!
First find m<HGC.
m<HGC=14 degrees (through vertical angles)
So...
m<HGE=14+78=92 degrees (through adjacent angles)
Now we have two parallel line cut by a transversal. And so... <HGE and <CEG are same side interior angles which means they are supplements (sum to 180 degrees)
m<HGE+m<CEG=180
92+m<CEG=180
m<CEG=88 degrees
<CEG and <CEB make a linear pair and are thus are supplements as well.
So...
m<CEG+m<CEB=180
88+m<CEB=180
m<CEB=92 degrees
m<CEB=4x=92
x=92/4=23 degrees
answer: 23 degrees
Can you also help with this one? Thank you!
Answer:
97
Step-by-step explanation:
9+7*9=72
9+18+10=37
10+10+7=27
7+9*10=97
2x=(360÷4) solve for x.
Answer:
Step-by-step explanation:
2x=(360÷4)
2x = 90
Dividing by 2
x = 90/2
x = 45
By following the steps of simplifying, isolating, and solving for x, we find that x = 45 is the value that satisfies the given equation.
To solve the equation 2x = (360 ÷ 4) for x, we need to isolate x on one side of the equation. Follow these steps to find the value of x:
Step 1: Simplify the expression on the right side of the equation.
360 ÷ 4 = 90
Step 2: Replace the right side of the equation with its simplified value.
2x = 90
Step 3: To isolate x, divide both sides of the equation by 2.
(2x) ÷ 2 = 90 ÷ 2
This simplifies to:
x = 45
The solution to the equation is x = 45. To verify, you can substitute x = 45 back into the original equation:
2(45) = 90
90 = 90
Since both sides of the equation are equal, x = 45 is indeed the correct solution.
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Olive Oil costs $8.70 per liter. A restaurant owner buys 5.6 liter of olive oil. How much does the owner pay?
Answer:
$48.72
Step-by-step explanation:
5.6 liters x $8.70 per liter= $48.72 total cost
Final answer:
To determine the total cost of the olive oil, multiply the quantity of 5.6 liters by the price per liter, which is $8.70. The total cost for the restaurant owner is $48.72.
Explanation:
The question asks us to calculate the total cost for a restaurant owner who buys 5.6 liters of olive oil at a price of $8.70 per liter. To find the total cost, we multiply the quantity of olive oil by the price per liter.
Calculation: Total cost = Quantity x Price per liter
Total cost = 5.6 liters x $8.70 per liter
Total cost = $48.72
Therefore, the restaurant owner will pay $48.72 for 5.6 liters of olive oil.
Jacob deposited $4,010 in his bank account at an interest rate of 7%. The following function represents his balance after t years.
Please help, giving brainliest!
Continue the sequence:
1, 3, 7, 15, 31, 63, __
Answer:
127, 255 are the next 2 terms.
Step-by-step explanation:
The difference in terms are 2,4,8,16,32 and so on.
What is the equation of the following graph
Answer:I believe it's y=log(x-3)
Step-by-step explanation:
Tim's phone service charges $25.08 plus an additional $0.22 for each text message sent per month. If Tim's phone bill was $30.58, which equation could be used to find how many text messages, x, Tim sent last month?
Final answer:
To find how many text messages, x, Tim sent last month, use the equation: Total cost = fixed cost + variable cost. Given that Tim's phone bill was $30.58, the equation is $30.58 = $25.08 + $0.22x. Solving the equation gives x ≈ 25, so Tim sent approximately 25 text messages last month.
Explanation:
To find the number of text messages, x, Tim sent last month, we can use the equation:
Total cost = fixed cost + variable cost
Given that Tim's phone bill was $30.58, the fixed cost is $25.08. The variable cost is $0.22 per text message sent. Let's represent the number of text messages sent by x.
So, the equation becomes:
$30.58 = $25.08 + $0.22x
To solve for x, we need to isolate x. Subtract $25.08 from both sides of the equation:
$30.58 - $25.08 = $0.22x
Simplify:
$5.50 = $0.22x
Divide both sides of the equation by $0.22:
x = $5.50 / $0.22
x ≈ 25
Therefore, Tim sent approximately 25 text messages last month.
how to use the rational root theorem
Here are the steps:
1. Arrange the polynomial in descending order.
2. Write down all the factors of the constant term. These are all the possible values of p.
3. Write down all the factors of the leading coefficient. ...
4. Write down all the possible values of . ...
5. Use synthetic division to determine the values of for which P( ) = 0.
Answer:
Step-by-step explanation:
Arrange the polynomial in descending order.
Write down all the factors of the constant term. These are all the possible values of p.
Write down all the factors of the leading coefficient.
Michael and Alexandra left their home at 8:00am to drive to new york. Michael drove at 55 miles an hour and arrived at 5:00 pm. Alexandra drpvw at 45 miles an hour and arrived at the same place as Michael. At what time did Alexandra arrive?
Answer:
7:00 pm
Step-by-step explanation:
You want to know Alexandra's arrival time if she started at the same time as Michael (8:00 am) and drove at 45 mph, while Michael drove at 55 mph and arrived at 5:00 pm.
TimeTravel time is inversely proportional to speed, so the time it takes Alexandra to make the trip is 55/45 = 11/9 times what it take for Michael to make the trip.
Michael's travel time from 8 am to 5 pm is 9 hours, so Alexandra's travel time is ...
(11/9)(9 h) = 11 h
She will arrive 2 hours after Michael does.
Alexandra arrives at 7:00 pm.