Answer:
To find the area of a triangle, we can use the formula:
Area = (base * height) / 2
To find the area of triangle ABC, we first need to find the base and the height.
Since angle B is 75 degrees, we can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle A: 180 - 75 - 90 = 15 degrees.
Then, we can use the fact that the measure of an angle in a triangle is proportional to the length of the side opposite that angle to find the length of side AC:
AC/AB = m∠A/m∠B
AC = (m∠A/m∠B) * AB
Substituting, we get:
AC = (15/75) * 12 = 3
Now that we know the base and the height of the triangle, we can use the formula to find the area:
Area = (3 * 12) / 2 = 18
Therefore, the area of triangle ABC is 18 square cm.
choose the equation of the graphed function.
Answer:
J
Step-by-step explanation:
shifts to the right by 1
a deck of playing cards has 52 cards of which 12 are face cards what are the odds the top 3 are face cards
In a deck of playing cards has 52 cards of which 12 are face cards, The odds are 33 / 3315 or 0.01 that the top 3 are face cards.
The total number of cards was 52, and there were 12 face cards.
Probability equals the number of possible outcomes divided by the total number of possibilities.
The first attempt had a probability of 12/52,
the second attempt had a probability of 11/51,
and the third attempt had a probability of 10/50.
Therefore, the probability that each of the three cards are face cards is equal to 12 / 52 × 11 / 51 × 10 / 50 = 1320 / 132600 = 132 / 13260 = 33 / 3315
the probability that all three are face cards = 0.00995475113 ≈ 0.01
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Solve the equation and enter the value of x below.
x+ 272 = 298
Answer:
x = 26
Step-by-step explanation:
x + 272 = 298
x = 298 -272
x = 26
I hope my answer helps you.
Guide
Leo argues that the measure of an exterior angle of a triangle is
equal to the sum of the measures of the two remote interior angles of
the triangle. He uses the diagram shown in his argument.
Xº
Leo writes the steps listed.
Step 1.r+x=180, since the sum of the measures of supplementary
angles is 180°
Step 2. p+q+r=180, since the sum of the measures of the angles
of any triangle is 180°
Which equations follow from step 1 and step 2 that Leo could use to
complete his argument?
r+x=p+q+r
r+x-r=p+q+r-r
x=p+q
p+q+r=180
bp+q+r-r=180-r
p+q=180-r
x+r=p+q+r
x+r-r=p+q+r+r
x=p+q+2r
(r+x) + (p+q+r)=180+180
2r+x+p+q=360
Answer:
Step-by-step explanation: It looks like Leo is trying to prove that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle. From the equations given, it seems that Leo is using the fact that the sum of the measures of supplementary angles is 180 degrees, and the sum of the measures of the angles of any triangle is 180 degrees, to try to prove his statement. Some equations that Leo could use to complete his argument might include:
x = p + q, which follows from the equation r + x = 180 and the substitution of p + q + r = 180
p + q = 180 - r, which follows from the equation p + q + r = 180 and the substitution of r + x = 180
x = p + q + 2r, which follows from the equation x + r = p + q + r and the substitution of r + x = 180
It's not clear from the information given whether these equations are sufficient to prove Leo's statement, as we don't have any information about the values of p, q, r, or x. However, these equations might be a good starting point for Leo to continue his argument.
A soccer team earned money to travel to a tournament by earning $12 per hour to paint over graffiti in their neighborhood
for t hours. Their coach said she would double any money they earned.
How much did the soccer team earn in all?
Please write your answer as an expression
The expression for the total amount earned in t hours is 24t.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Amount earned per hour = $12
Amount earned in t hour = 12t
The amount is double.
The amount earned per hour.
= 2 x 12t
= 24t
Thus,
The total amount earned in t hours is 24t.
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For a ride on a rental scooter, All paid a $7 fee to start the scooter plus 7 cents per minute of the ride. The total bill for All's ride was $20.58. For how many
minutes did All ride the scooter?
minutes
X
Answer:
194 minutes
Step-by-step explanation:
First you subtract $7 from $20.58 because that was the start fee and get 13.58. Then divide 13.58 by 0.07, and get 194.
A salesperson at a jewelry store earns 9% commission
each week. Last week, Heidi sold $680 worth of jewelry.
How much did she make in commission? How much did
the jewelry store make from her sales?
Heidi earned [enter your response] in commission
Answer:
1/ Heidi earned $61.20 in commission
2/ The jewelry store makes $618.80 from hers sales
Step-by-step explanation:
9% = 0.09
First, take 680 times 0.09 = $61.20
Heidi earned $61.20 in commission
For the second question
Take 680 - 61.20 = $618.8
The jewelry store makes $618.80 from its sales
Natalie is the creator of Better Brain, a new mindfulness app for teens. The app currently has 1,262 downloads, and Natalie has set a goal of doubling the downloads every month.
Write an exponential equation in the form y=a(b)x that can model Natalie's goal for the number of downloads, y, in x months.
The exponential equation of the given statement will be equal to, 1262 ×[tex](2)^x[/tex].
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
Total number of downloads initially = 1,262
Let the number of months be x.
Then, the equation will be,
y = 1262[tex](2)^x[/tex]
Here, y is the total number of songs.
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pls ans this question
Answer:
11 cm
Step-by-step explanation:
2x+x+6+x+4=30
4x+10=30
-10. -10
4x=20
/4. /4
x=5
now we find each length to find the longest
2(5)
10 cm
5+6
11 cm
5+4
9 cm
11 is the biggest one
Hopes this helps have a wonderful day
please answer ASAPPPP
formula: y = mx + b
current points we know:
m = 1/2
x = 10
y = 0
so we solve for the b value.
0 = 1/2 (10) + b
0 = 5 + b
(inverse operation we subtracted 5 on both sides)
-5 = b
so the equation for a line with slope 1/2 passing through the point (10,0) is
y = (1/2)x + (-5) or y = (1/2)x - 5
(not sure if this is correct...)
what can we conclude about the endogeneity of an explanatory variable if the ols and 2sls estimates are significantly different? assume that the instrument used was exogenous.
Note that assuming that the instrument used was exogenous, one can conclude about the endogeneity of an explanatory variable if the OLS and 2SLS estimates are significantly different: "The explanatory variable is endogenous and therefore 2SLS should be considered." (Option C)
What is 2SLS?Two-stage least squares (2SLS) regression analysis is a statistical approach used in structural equation analysis. The OLS approach has been extended using this methodology. It is employed when the error terms of the dependent variable are associated with the independent variables.
The ordinary least squares (OLS) approach is a linear regression methodology used to estimate a model's unknown parameters. The strategy is based on reducing the sum of squared residuals between the expected and actual values.
2SLS is utilized as an alternate strategy when we encounter endogeneity Problems in OLS. Endogeneity arises when the explanatory variable correlates with the error word. Then we utilize 2SLS, which employs an instrumental variable. The outcome will be different because if there is endogeneity in the model, OLS will produce biased results.
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Full Question:
What can we conclude about the endogeneity of an explanatory variable if the OLS and 2SLS estimates are significantly different? Assume that the instrument used was exogenous. Select one:
a. The explanatory variable is not endogenous and therefore using 2SLS is ill-advised.
b. The explanatory variable is not endogenous and therefore OLS should not be used.
c. The explanatory variable is endogenous and therefore using 2SLS should be considered.
d. The explanatory variable is endogenous and therefore OLS should be used.
You are in charge of getting food for the class from the corner store. You can buy
chips for $2 or a hoagie for $5. There are 19 students in the class, so you need to buy
at least 19 items, and you have $77 total.
Write a system of equations to represent this situation. Use x to represent the number
of chips and y to represent the number of hoagies.
Separate each inequality with a comma,
The system of inequalities to represent the situation is 2x + 5y ≤ 77, x + y ≥ 19
How to represent a situation with inequality?You are in charge of getting food for the class from the corner store. You can buy chips for $2 or a hoagie for $5.
There are 19 students in the class, so you need to buy at least 19 items, and you have $77 total.
Hence, the system of inequality to represent this situation is as follows:
let
x = number of chips
y = number of hoagies
Therefore, the inequalities is as follows:
2x + 5y ≤ 77
x + y ≥ 19
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use the squeeze theorem to find the following limit when b − |x − a| ≤ f(x) ≤ b + |x − a|.
By using the squeeze theorem, we conclude that, [tex]$$\lim _{x \rightarrow a} f(x)=b .$$[/tex]
Limit of a function, Squeeze Law:
The squeeze theorem states that if f(x) ≤ g(x) ≤ h(x) for all numbers, and at some point x=k we have f(k)=h(k), then g(k) must also be equal to them. We can use the theorem to find tricky limits like sin(x)/x at x=0, by "squeezing" sin(x)/x between two nicer functions and using them to find the limit at x=0
We say that a function f(x) approaches a limit L approaches a, or, [tex]$\lim _{x \rightarrow a} f(x)=L$[/tex]
if, for every number [tex]$\epsilon > 0$[/tex], however small, such that [tex]$|f(x)-L| < \epsilon$[/tex],
there always exists a number δ>0 such that
[tex]|x-a| < \delta \text {. }[/tex]
The Squeeze Law:
Suppose that g(x) ≤ f(x) ≤h(x) in some neighborhood of a and also that
[tex]$$\lim _{x \rightarrow a} g(x)=L=\lim _{x \rightarrow a} h(x)$,[/tex]
then,
[tex]$$\lim _{x \rightarrow a} f(x)=L .$$[/tex]
We have to find the limit of f(x) as x approaches to x.
Let [tex]$b-|x-a|=g(x)$[/tex] and [tex]$b+|x-a|=h(x)$[/tex].
Then we have the inequality, g(x) ≤ f(x) ≤h(x)
Let us see what happens to g(x) and h(x) as [tex]$$x \rightarrow a$.[/tex]
[tex]$$\begin{aligned}g(x) & =b-|x-a| \\\\lim _{x \rightarrow a} g(x) & =\lim _{x \rightarrow a} b-|x-a| . \\& =b\end{aligned}$$[/tex]
Similarly,
[tex]$$\begin{aligned}h(x) & =b+|x-a| \\\lim _{x \rightarrow a} h(x) & =\lim _{x \rightarrow a} b+|x-a| . \\& =b\end{aligned}$$[/tex]
We have the conditions required by the Squeeze law,
[tex]$$\lim _{x \rightarrow a} g(x)=b=\lim _{x \rightarrow a} h(x)$$[/tex]
so we conclude that, [tex]$$\lim _{x \rightarrow a} f(x)=b .$$[/tex]
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If the m<2 = 58° and the m<13 = 111°, find the measures of angles 1, 5, 8, 14, 18.
Note: x || m and z || y
The value of angle 1 is 122°.
The value of angle 5 is 58°
The angle of angle 8 is 58°
The angle of angle 14 is 122°
The angle 18 is 58°
How to calculate the angles?It should be noted that this information deals with angles. It should be noted that the value of angle on a straight line is 180°.
In this situation, the value of angle 1 will be:
= 180° - 58°
= 122°
Also it should be noted that vertically opposite angles are equal. Therefore, angle 5 will be 58°.
In this situation, it should also be noted that alternate angles are the same. Hence, Thai gives the value of the angles for angles 8, 14 and 18.
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At a real estate agency, an agent sold a house for $306,000. The commission rate is 7.5% for the real estate agency and the commission rate for the agent is 20% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
There are [enter your response] workers in all
I NEED THE ANSWER RN PLS‼️‼️
Answer:
a 22950
b 4590
Step-by-step explanation:
7.5% of 306,000 is 22950
20% of 22950 is 4590
Find the measure of angle 1
A. 133 degree
B. 47 degree
C. 63 degree
D. 70 degree
Please help quickly!!!
(Picture provided)
Answer:
C, 47°
Step-by-step explanation:
All triangles equal 180°
To find the measure of angle 1, subtract the other angles from 180°
180 - 70 - 63 = 47
Can someone explain this?
It looks like you are supposed to match those 20 given equations to their respective graph that the assignment gave you. Do you need help plotting them? If so, I can edit my answer and add a picture of the equations graphed.
Examine the linear graph below. Which equation represents this graph?
Answer:B) -2x + 3y = 12 represents the graph.The y-intercept is 4, and the line intercepts the x-axis at -6. Therefore, the slope of the line is 4/6=2/3. The format for a linear equation is y=(slope)x+y intercept. So the equation would be y=2/3x+4. We can see that option B simplifies that. Adding 2x from both sides of the equation and we get 3y=2x+12.
Siddhu bought an mp3 player that typically costs $120 when it was on sale for 20% off. He had to pay 7% sales tax on the sale price. How much did Siddhu pay for the mp3 player in all?
Answer:
$102.72
Step-by-step explanation:
If the mp3 player typically costs $120 and was on sale for 20% off, then the sale price would be 120 * (1 - 0.2) = $96.
If Siddhu had to pay 7% sales tax on the sale price, then the total tax he paid would be 96 * 0.07 = $6.72.
Therefore, Siddhu paid a total of 96 + 6.72 = $102.72 for the mp3 player when it was on sale with the sales tax included.
help!...Answer the questions about the following polynomial.
the blank with a drop down flap answer choices are, quartic, cubic, quadratic, linear, quintic
The expression represent a trinomial polynomial with three terms. The constant term is 1 , the leading term is 5, and the leading coefficient is 1 / 7.
What is a polynomial?A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using operations such as addition, subtraction, multiplication and division.
Trinomials are the algebraic expressions with three unlike terms. Trinomial has three terms.
A constant term is a term in an algebraic expression that does not contain any variables and therefore is constant.
The leading term is the term with the highest power of x.
The leading coefficient of a polynomial is the coefficient found with the variable that has the largest exponent.
Therefore, the expression is a trinomial polynomial. This means it has 3 terms.
The constant term of the polynomial is 1 ,
The leading term is 5, and the leading coefficient is 1 / 7.
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Help! My math teacher sucks so I hope you guys can help me with this question.
A cylinder has a volume of 5m cubed and a radius of 0.7m. What is the height of the cylinder to the nearest hundredth of a meter?
Answer:
1.80
Step-by-step explanation:
Answer:
Volume of a cylinder (v) = πr²h
Step-by-step explanation:
Given V = 5m³
r = 0.7m and π = 3.14
h= ?
using V = πr²h
5 = 3.14 x 0.7² x h
5 = 3.14 x 0.49 xh
5= 1.5386h
divide both side by 1.5386
5/1.5386 = h
h= 3.24970
h= 3.25m ( nearest hundredth)
Solve this equation . 6x = 72 for x
Answer:
x = 12
Step-by-step explanation:
6x = 72 ( isolate x by dividing both sides by 6 )
x = 72 ÷ 6 = 12
Answer:
Step-by-step explanation:
6x = 72
Here, 6 is in multiplication with the variable x.
We will move 6 to the right side. With this the 6 which was in multiplication with x will now go in division with 72, by rule.
x = 72/6
x = 12
therefore, x = 12
I need help with this question
please help
Answer:£84.45
Step-by-step explanation:
10 single packs costs £97.5
9.75x10
3 packs of 3 plus a single costs £84.45
24.90x3+9.75
2 packs of 5 costs £86.5
43.25x2
Answer:
pack of 3 rolls
Step-by-step explanation:
Two 5 packs is 86.50
Ten 1 packs are 97.50
Three 3 packs is 74.70 + 8.3 (1/3 of 3 pack) = £83
Find sin(17π/12) exactly.
I think it has to do something with splitting 17π/12 into π/3 + π/4 + 5π/6 and then using the sin/cos angle sum identities. Though when I tried this, it got complicated really quickly, so I'm not sure if this is the method I should be using.
Please refer to the photo taken.
Answer:
-(√2 +√6)/4
Step-by-step explanation:
You want the exact value of sin(17π/12).
Sine of sumThe sine can be written as ...
sin(17π/12) = sin(π +5/12π)
= -sin(5/12π) = -sin(2/12π +3/12π)
= -sin(π/6 +π/4)
= -(sin(π/6)cos(π/4) +cos(π/6)sin(π/4))
= -((1/2)(√2/2) +(√3/2)(√2/2))
= -(√2 +√6)/4
The sine of 17π/12 is -(√2+√6)/4.
at a baby shower 17 guests are in attendance and 5 of them are randomly selected to receive a door prize. if all 5 prizes are identical, in how many ways can the prizes be awarded?
If 5 guests are randomly selected from 17 guest and all 5 prizes are identical, there are 89107200 ways in which the prizes can be awarded.
It is given to us that -
17 guests are in attendance at a baby shower
5 of them are randomly selected for a prize
All the 5 prizes are identical
We have to find out the number of ways in which the prizes can be awarded.
In this case, we have to use the combination formula to find the required answer.
We know that the combinations of n number of objects taken r at a time can be represented by the formula as -
[tex]C(n,r) = r!\frac{n!}{(n-r)!}[/tex] ------ (1)
where,
n = total objects in the given set
r = total chosen objects from the given set
According to the given information, we have -
n = 17
r = 5
Substituting these values in equation (1), we have
[tex]C(n,r) = r!\frac{n!}{(n-r)!}\\= > C(n,r) = 5!*\frac{17!}{(17-5)!}\\= > C(n,r) = 5!*\frac{17!}{12!}\\= > C(n,r) = 89107200[/tex]
Therefore, if 5 guests are randomly selected from 17 guest and all 5 prizes are identical, there are 89107200 ways in which the prizes can be awarded.
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Find the slope of the line that passes through (9, 10) and (6, 17).
1) Simplify your answer and write it as a
proper fraction, improper fraction, or integer.
Answer:
-7/3
Step-by-step explanation:
The formula for finding the slope of a line using two points is:
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
For this case, 9 is x1, 10 is y1
6 is x2 and 17 is y2
Insert these values in the formula and solve:
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
17 - 10 7
---------- = --- = -7/3
6 - 9 - 3
I NEED THIS ASAP
Factor −6x2 + 18x.
Answer:
-6x (x-3)
Step-by-step explanation:
Branliest Pls!
Pleaseeeeeeeeee helppppppp
Comparing both given functions, we can state that: B. Function 1 has the greater rate of change; the slope is 2.
What is the Rate of Change/Slope of a Function?Another name for the rate of change of a function is the slope. It is calculated using the formula:
Slope / rate of change = change in y / change in x.
If the equation of a linear function is given in slope-intercept form as y = mx + b, the rate of change or the slope is represented by "m".
Given the first function as an equation, y = 2x - 6, the slope of this function is represented as 2. This means, the rate of change is m = 2.
To find the rate of change of function 2, use two points from the table, (1, -4) and (2, -5):
Rate of change / slope (m) = (-5 - (-4)) / (2 - 1) = -1/1
m = -1.
The slope value of 2 is greater than the slope value of -1, therefore, we can conclude that: B. Function 1 has the greater rate of change; the slope is 2.
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O No; there are y-values that have more than one x-value.
• No; the graph fails the vertical line test.
• Yes; the graph passes the vertical line test.
Yes; there are no y-values that have more than one x-value.
The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.
How do functions work?According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.
Please refer to the image instead of the graph, which is related to it.
The graphic displays a graph.
A parabola is seen on the graph.
The vertical line test determines if a graph can be a function, as is common knowledge.
The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.
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Bob pick 15 apple in 8 minute. Mary pick 16 apple in 16 minute. Suie pick 10 apple in 19 minute. Who picked apple fater?
By comparing the speeds of all the people, Bob picked apple the fastest.
What is speed?Speed is generally the change in distance per unit time. In this case instead of distance we can use the number of apples.
What is the formula of speed?For this question, speed of picking apples = no of apples / time (in minutes). For Bob, speed = 15/8 = 1.88 apples/minute
For Mary, speed = 16/16 = 1 apples/minute
For Suie, speed = 10/19 = 0.526 apples/minute
This shows that Bob picked apples the fastest.
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