Answer:
Step-by-step explanation:
which statement must be true?
Answer:
DF=FE
Step-by-step explanation:
first to make it easier we can find the angles to each side
the sum of all angles of a triangle equal 180 degrees so to find x we set all the angles equal to 180
(3x+5)+(4x-15)+(2x+10)=180
9x+0=180
/9. /9
x=20
now we can find each angle
3(20)+5
60+5
D=65 degrees
4(20)-15
80-15
E= 65 degrees
2(20)+10
40+10
F=50 degrees
Angle D and E are the only angles equal to each other so answer C and d ARE INCORRECT
Since there are 2 of the same angles this is an isosceles triangle
the 2 of the same angles are the base so the side going up are connecting to the top angle F so the sides will be DF and FE and these are equal
hopes this helps
cory has $3$ apples, $2$ oranges and $2$ bananas. if cory eats one piece of his fruit per day for a week and the pieces of fruit within each category are indistinguishable, in how many orders can cory eat the fruit? one such order is $aaaoobb.$
Then the orders can Cory eat the fruit is = 25
Given that,
If Cory has eat apples = 3$
If Cory has eat oranges = 2$
If Cory has eat bananas = 2$
Total eat fruits = 3 + 2 + 2
Total eat fruits = 7$
We have to express the amount of total fruits as an equation.
The amount of apples will be x,
The amount of oranges will be y,
The amount of bananas will be z
The amount of apples multiplied by 7 because they ate each day of the week.
7*(x) + y + z = now we have to replace the values of x, y and z with the ones that gave us the problem
Then,
x = 3
y = 2
z = 2
So,
We can write,
7*(x) + y + z = 7 *(3) + 2 + 2
= 21 + 2 + 2
= 25
Therefore,
Then the orders can Cory eat the fruit is = 25
To learn more about Indistinguishable problems visit :
brainly.com/question/29058084
#SPJ4
Estimate the values to the nearest hundredth to complete the table.
angleadjacent leg ++ hypotenuse
A= 0.31
C= (blank)
opposite leg ++ hypotenuse
A= 0.95
C= (blank)
opposite leg ++ adjacent leg
A= 3.06
C= (blank)
The required trigonometric ratios of angle C in the given table are
(a) adjacent leg ÷ hypotenuse (cos C) = 0.95
(b) opposite leg ÷ hypotenuse (sin C) = 0.31
(c) opposite leg ÷ adjacent leg (tan C) = 0.33
What are required trigonometric ratios?The three important trigonometric ratios are:
sin θ = opposite leg ÷ hypotenuse
cos θ = adjacent leg ÷ hypotenuse
tan θ = opposite leg ÷ adjacent leg
Calculation:In the given right-angle triangle, the ratios are given as
cos A = adjacent leg ÷ hypotenuse = 0.31
sin A = opposite leg ÷ hypotenuse = 0.95
tan A = opposite leg ÷ adjacent leg = 3.06
These ratios are w.r.t the angle A.
Since we know that, in the right angle triangle,
∠A + ∠B + ∠C = 180°
⇒ ∠A + 90° + ∠C = 180°
⇒ ∠A = 180° - 90° - ∠C
∴ ∠A = 90° - ∠C
So, the trigonometric ratios w.r.t the angle C are:
(a) cos A = cos (90° - ∠C) = sin C
But we have cos A = 0.31
∴ sin C = 0.31
(b) sin A = sin (90° - ∠C) = cos C
But we have sin A = 0.95
∴ cos C = 0.95
(c) Then, tan C = sin C/cos C
Here we got sin C = 0.31 and cos C = 0.95
So, tan C = 0.31/0.95 = 0.33
Thus, the table is as follows:
angle adj ÷ hyp opp ÷ hyp opp ÷ adj
A 0.31 0.95 3.06
B 0.95 0.31 0.33
Learn more about trigonometric ratios here:
https://brainly.com/question/24349828
#SPJ1
what is the value of 18 to the third power
Answer:
5832
Step-by-step explanation:
the interior angles of a regular polygon each measures 165 degrees. how many sides does the polygon have
Yujin Pon has a principal of $900 in her savings Iccount on October 1. The money earns interest at a rate of 6.5% compounded quarterly until July 1 of the following year. What is the amount in the account on July 1?
а.$914.63
b. $943.75
c.$943.87
d. $944.59
Answer: The correct answer is c. $943.87.
Step-by-step explanation: To solve this problem, we need to first determine the length of time between October 1 and July 1 of the following year. This is a period of 9 months, or 3 quarters. We can then use this information to calculate the amount of interest earned over this time period.
The principal in Yujin Pon's account is $900, and the interest rate is 6.5% compounded quarterly. This means that for each quarter, the account will earn 6.5/4 = 1.625% in interest. Over the 3 quarters between October 1 and July 1 of the following year, the account will earn a total of 1.625% * 3 = 4.875% in interest.
To calculate the amount of interest earned, we can multiply the principal by the interest rate:
Interest = Principal * Interest Rate
= $900 * 0.04875
= $43.87
The total amount in the account on July 1 will be the original principal plus the amount of interest earned over the 3 quarters:
Total = Principal + Interest
= $900 + $43.87
= $943.87
Therefore, the correct answer is c. $943.87.
A beetle is moving along a straight line at a constant rate. It moves 23 of a foot in 15 of a minute.
What is the average speed of the beetle?
The average speed of the beetle is 1.53 feet per minute.
What is the average speed?Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.
Given that, it moves 23 of a foot in 15 of a minute.
Here, the average speed
= 23/15
= 1.53 feet per minute
Therefore, the average speed of the beetle is 1.53 feet per minute.
Learn more about the average speed here:
https://brainly.com/question/9834403.
#SPJ1
will mark brainliest pls
-photo is attached ! :)
The figures are similar, and the ratio of the perimeters is 2: 5. Find x.
Answer: x=3.2
Ste by Step
We have that for the Question "The figures are similar, and the ratio of the perimeters is 2 : 5. Find x." it can be said that the perimeters of x is
x=3.2
From the question we are told
The figures are similar, and the ratio of the perimeters is 2 : 5. Find x.
Generally the equation for the the ratio is mathematically given as
2=x
and
5=8
Therefore
x=3.2
Therefore
the perimeters of x is
x=3.2
f(x) = x^2 + 1. g(x) =. 5 - x
(F+ g)(x)
We will aggregate terms with the same degree.
[tex](f+g)(x)=(x^2+1)+(5-x)=x^2-x+6[/tex]Therefore, the answer to the question should be Option 3 or Option C) from the beginning.
Let f(x) = e ^ (6x) and g(x) = 8in(x) Find and simplify g(f(- 2)) -96 -48 48 C B A
Answer: g(f(-2))=-96
Step-by-step explanation:
[tex]Given: \ f(x)=e^{6x}\ \ \ \ g(x)=8ln(x)\ \ \ \ g(f(-2))=?\\\\f(-2)=e^{6*(-2)}\\\\f(-2)=e^{-12}\\\\Hence,\\\\g(f(-2))=8ln(e^{-12})\\\\g(f(-2))=8*(-12)\\\\g(f(-2))=-96[/tex]
Answer:
-96
Step-by-step explanation:
Given:
[tex]\begin{cases}f(x)=e^{6x}\\ g(x)=8 \ln (x) \end{cases}[/tex]
To find g[f(-2)], substitute x = -2 into the function f(x):
[tex]\implies f(-2)=e^{6 \times -2}=e^{-12}[/tex]
Then substitute the function f(-2) in place of the x in function g(x):
[tex]\implies g[f(-2)]=8 \ln \left(e^{-12}\right)[/tex]
[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]
[tex]\begin{aligned}\implies g[f(-2)]&=-12\cdot 8 \ln \left(e\right)\\&=-96 \ln \left(e\right)\end{aligned}[/tex]
Apply the log law: ln(e) = 1
[tex]\begin{aligned}\implies g[f(-2)]&=-96 \ln \left(e\right)\\&=-96(1)\\&=-96\end{aligned}[/tex]
---------------------------------------------------------------------
As one calculation:
[tex]\begin{aligned}g[f(-2)]&=8 \ln \left(e^{6 \times -2}\right)\\& = 8 \ln \left(e^{-12}\right)\\& = -12 \cdot 8 \ln \left(e\right)\\& = -96(1)\\& = -96\end{aligned}[/tex]
If using the method of completing the square to solve the quadratic equation x 2 + x + 9 = 0, which number would have to be added to "complete the square"?
Answer:
Below
Step-by-step explanation:
To complete the square, the coefficient of x^2 must be 1 ( it is already)
then take 1/2 of the x coefficient .... 1/2.... square it and add it to both sides of the equation
x^2 + x + 1/4 + 9 = 1/4
then you can reduce this to
( x+ 1/2)^2 + 9 = 1/4 for further 'solving'
A manager of a self-service car wash charges a flat fee in addition to a fee per minute, x, for use of the services. The expression 5+0.75x models the scenario.
Which statement is true?
Responses
The coefficient 5 represents a cost of $5 per minute for use of the services, while the term 0.75x represents the flat fee of $0.75.
The coefficient 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes.
The constant 5 represents a cost of $5 per minute for use of the services, while the term 0.75x represents the flat fee of $0.75.
The constant 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes.
The constant 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes. Therefore, option D is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 5+0.75x.
In the given expression, 5 is constant term and 0.75x is another term.
In the term 0.75x, 0.75 is the coefficient of x
In the expression 5+0.75x, 5 is fixed price and 0.75 is price for second or minute or hour or year and x can be number seconds or minutes or hours or years.
Therefore, option D is the correct answer.
To learn more about an expression visit;
https://brainly.com/question/28170201.
#SPJ1
the statement [tex]2(\frac{1}{2} x-5)[/tex], then x=20 is justified by what property?
The statement 2(1 / 2 x - 5), when x = 20 is justified by the property of substitution.
How to find the property that justify the statement?Substitution property in mathematics is a property that helps in substituting the value of a variable into an algebraic expression to solve a given problem.
Therefore, by substituting the value of x in the algebraic expression, the expression will be solved.
Hence,
2(1 / 2 x - 5) , when x = 20
Therefore,
2(1 / 2 (20) - 5)
2(10 - 5)
2(5) = 10
Hence, the property is substitution property.
learn more on expression here: https://brainly.com/question/5217895
#SPJ1
the confidence interval approach is the correct method by which to determine sample size. true false
The confidence interval approach is the correct method by which to determine sample size. True
Confidence Interval:
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.
In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.
Your desired confidence level is usually one minus the alpha (α) value you used in your statistical test:
Confidence level = 1 − α
Learn more about The confidence interval approach here
https://brainly.com/question/10540936
#SPJ4
PLease help meh im begging you
Determine the measurement of ∠A, the angle marked in red.
The measure of ∠A is __________Degrees?
Answer:
x= 222 degress
Step-by-step explanation:
x − 3y = −12 2x − y = 1 (1 point) a line includes points 0 comma 1 and negative 3 comma negative 4. A line includes points 0 comma negative 4 and negative 6 comma negative 2 a line includes points 0 comma 4 and 1 comma 3. A line includes points negative 2 comma 2 and negative 4 comma 0 a line includes points 0 comma negative 1 and 1 comma negative 3. A line includes points 6 comma negative 10 and 3 comma negative 11 a line includes points 0 comma 4 and 3 comma 5. A line includes points 1 comma 1 and 2 comma 3
By graphing the system of equations, we can see that the solution is (3, 5).
How to solve the system of equations?
I assume we want to solve the following system of equations graphically:
x - 3y = -12
2x - y = 1
To do so we only need to graph both the lines on the same coordinate axis and find the point where the lines do intersect. The graph can be seen below.
There we can see that the intersection is at (3, 5), so that is the solution of the system of equations.
Learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
If a fair die is rolled 4 times, what is the probability, rounded to the nearest thousandth, of getting at least 3 twos?
7.08 is the probability, rounded to the nearest thousandth.
What does the math term "probability" mean?
The simple definition of probability is the likelihood that something will occur.
We can discuss the probabilities of various outcomes to determine how likely they are whenever we are uncertain about the result of an event. Statistics describes the examination of events subject to probability.
Probability of getting a six on rolling a dice = 1/3
Here ,
n = 4 , p = 1/3
So, For P(X <= 1) = P(X = 0) + P(x = 1)
4C0 * (1/6)^0 * (1 - 1/3)^(4-0) + 4C1 * (1/3)^1 * (1-1/3)^(4-1)
= 1 * 1 * (5/3)^4 + 4 * (1/3) *
= 5.75 + 1.33
= 7.08
= 7.08 (nearest thousandth)
Learn more about Probability
brainly.com/question/11234923
#SPJ1
complete this working to write 9³ as a power of 3
9³=9x9x9
so 9³= 3x3x3x ____
so 9³=3^y where y=____
Answer: y=6
Step-by-step explanation:
If using the method of completing the square to solve the quadratic equation x 2 + 2 x + 16 = 0
Answer:
Step-by-step explanation:
[tex]x^{2} +2x+16=0\\x^{2} +2x+1-1+16=0\\(x^{2} +2x+1)-1+16=0\\(x+1)^{2} +15=0\\(x+1)^{2}=-15[/tex]
The solution does not exist because all numbers squared are greater than zero.
True or false. When y is positive, the value of y^2 is always greater than the value of y. Why?
however if you have 0.5^2 which is 0.25 is that not smaller than 0.5
Answer: False
Step-by-step explanation:
If [tex]y=0.5[/tex], then [tex]y^2=0.25[/tex], whereas [tex]y=0.5[/tex].
Therefore, this is a counterexample. Hence, the statement is false.
browns are expected to win with probability of 60% against their opponent, while steelers are also expected to win with probability of 40% against their opponent. the outcome of each game can be either a win or a loss (i.e., no ties). if you bet $10 on one of these two teams to win and another one to lose, no matter which one wins or loses, i.e., your bet is that only one team (browns or steelers) wins, what net payout will you be promised in a fair betting game in case your bet works out?
Net payout will you be promised in a fair betting game in case your bet works out is $0 .
Given :
browns are expected to win with probability of 60% against their opponent, while steelers are also expected to win with probability of 40% against their opponent. the outcome of each game can be either a win or a loss (i.e., no ties). if you bet $10 on one of these two teams to win and another one to lose, no matter which one wins or loses, i.e., your bet is that only one team (browns or steelers) wins .
P ( browns ) = 60 / 100 = 0.60
P ( steelers ) = 40 / 100 = 0.40
Net payout = Number of wins * 10 - Number of loses * 10
= 1 * 10 - 1 * 10
= 10 - 10
= $0.
Learn more about the probability here:
https://brainly.com/question/11234923
#SPJ4
Select the correct answer. Solve the following inequality. 21 ≤ -3(x − 4) < 30 A. -3 ≤ x < 6 B. -10 < x ≤ -3 C. 28 ≤ x < 37 D. -6 < x ≤ -3
Answer:
D. -6 < x ≤ -3
Step-by-step explanation:
21 ≤ -3(x − 4) < 30
21/3 ≤ -3(x − 4)/3 < 30/3
7 ≤ -(x − 4) < 10
7 ≤ -x - (-4) < 10
7 ≤ -x + 4 < 10
7 - 4 ≤ -x + 4 - 4 < 10 - 4
3 ≤ -x < 6
(3 ≤ -x < 6)/(-1)
-3 >= x > -6 ==> when dividing by a negative number, switch the inequality
sign
-6 < x ≤ -3 ==> D
1.2x-5=6.8x-15
[tex]1.2x-5=6.8x-15\\[/tex]
Describe the 3-D figure that would be formed if the figure is rotated about the y-axis. (You can say what it looks like.)
By completing a complete revolution on the soda can-like profile about the y-axis to generates a cylinder-like solid that is the result of the combination of three cones and a cylinder.
What kind of solid is generated by rotating a profile about the y-axis?
In this problem we find a representation of a soda can-like profile, whose complete revolution generates a cylinder-like solid. This solid is the result of the combination of three truncated cones (lower trucated cone, middle cone, upper cone) and a cylinder (right cylinder). There are two axes for the rotation, a horizontal axis (x-axis) and a vertical axis (y-axis).
The first axis, that is, the horizontal axis, is along the base of the can-like profile and the second axis, that is, the vertical axis, is along a side of the can-like profile. The solid of revolution is generated by rotating around the y-axis.
In consequence, the solid generated by a revolution creates a soda can-like profiles as the result of combining three truncated cones and a cylinder.
To learn more on solid of revolution: https://brainly.com/question/23260581
#SPJ1
17. Select the correct inequality and graph for the statement.
The highest temperature possible today is 95 °F.
The correct inequality for the statement - highest temperature possible today is 95 °F
x ≤ 95 °F
How to identify the correct statementThe statement saying the highest temperature possible today is 95 °F is represented by
knowing that the temperature will never be greater than 95 °F, hence the temperature values is from 95 °F and downwards
assuming x represents the measles of the temperatures then
x is less than or equal to 95 °F means x can be any value but never greater than 95 °F
Learn more about inequality at:
https://brainly.com/question/25944814
#SPJ1
Isabella will earn $30 per hour at her new job. During training, she will earn $20
per hour. What percent of Isabella's regular hourly rate will she earn during
training?
By solving a little system of equations we will see that the percentage is 66.67%
What percent of the regular hourly rate will she earn during training?
We know that the regular hourly rate is $30 per hour, and that is the 100% in our case.
So we can write the relation:
$30 = 100%.
We know that when she is on training, she will earn $20, and this is a percentage X that we don't know yet, now we can write the relation:
$20 = X
So we have two equations:
$20 = X
$30 = 100%.
If we take the quotient between these two we will get:
$20/$30 = X/100%
If we multiply both sides by 100% (so we solve the equation for X) we will get:
($20/$30)*100% = X
66.67% = X
So she will get a 66.67% of the regular hourly rate.
Learn more about percentages:
https://brainly.com/question/843074
#SPJ1
Elena's distance and times for a training run are given by the equation y=8.5x, where x represents distance in miles and y represents time in minutes
Elena is covering a distance of 8 miles in one minute.
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.
Given is that Elena's distance and times for a training run are given by the equation → y = 8.5x
Now, if we consider the equation, it can be seen that the number {8.5} gives the unit rate or slope of the graph of the straight line. So, she is running at a speed of 8.5 miles per minute.
Therefore, Elena is running at a speed of 8.5 miles per minute.
To solve more questions on equations, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ1
What is 213 divided? Also how do you break 23 into tens and ones?
Answer:
What is 213 divided? 2 I think
Also how do you break 23 into tens and ones? It would be 2 tens and then it would be 3 ones
If a fair die is rolled 5 times, what is the probability, to the nearest thousandth, of
getting exactly o ones?
Answer:
0.402
Step-by-step explanation:
The probability of not rolling a one on any given roll is [tex]5/6[/tex].
Since the die is rolled 5 times, the probability is [tex](5/6)^5 \approx 0.402[/tex].
The number of fish in a pond decreased by this year compared to last year.
Last year, there were fish in the pond.
How many fish are in the pond this year?
Answer:
number from last year - number of decrease
Step-by-step explanation:
The numbers are missing from the problem, but this is what you need to do.
Start with the number of fish in the pond last year.
Subtract the number of decrease.
