8) or a line on a coordinate plane line with point A at (1,10) and point B at (7,4): What is the midpoint of the line?
A = (X1,Y1 )= (1,10)
B= (X2,Y2)= (7,4)
To find the midpoint we have to add each coordinate and divide it by 2:
midpoint x = (x1+x2)/2 = (1+7) /2 = 8/2 =4
Midpoint y= (y1+y2)/2 = (10+4)/2 = 14/2 = 7
So , the midpoint of the line is (4,7)
If C=15, what values of A and B complete Ax+By=C for the graph shown? Write the standard form.
If C = 15 , then the values of A and B will be A = 3, B = 5 and equation in standard form is 3x + 5y = 15 .
In the question ,
the equation is given
the equation is Ax + By = C
also given that C = 15 ,
so , Ax + By = 15
From the graph we see that when x = 5 , y = 0
substituting , in Ax + By = 15 , we get
A(5) + B(0) = 15
5A = 15
A = 3 .
also when x = 0 , y = 3
Substituting in Ax + By = 15 , we get
A(0) + B(3) = 15
3B = 15
B = 5
so , the equation in standard form is 3x + 5y = 15 .
Therefore , If C = 15 , then the values of A and B will be A = 3, B = 5 .
Learn more about Equation here
https://brainly.com/question/18894822
#SPJ1
I'm sorry I need to do this fast so could you explain this to me
Answer:
(a)
• C(x)=88000+5500x
,• R(x)=7500x
(b)55 times
Explanation:
Let the number of performances = x
• The cost of producing the musical = $88,000
,• The cost per performance = $5900
(a)Thus, the total cost for x performances:
[tex]\text{Cost,C(x)}=88000+5900x[/tex]The revenue per performance is $7500, therefore, the equation for revenue is:
[tex]R(x)=7500x[/tex](b)To break even, the cost must be equal to revenue.
[tex]\begin{gathered} C(x)=R(x) \\ 88000+5900x=7500x \end{gathered}[/tex]Next, solve for x.
[tex]\begin{gathered} 88000=7500x-5900x \\ 88000=1600x \\ x=\frac{88000}{1600} \\ x=55 \end{gathered}[/tex]The musical must be performed 55 times to break even.
Answer this question and show me how to check it
In order to rewrite these values in the standard form, let's calculate the product with the power of 10 from each number.
For the length, we have:
[tex]\begin{gathered} 8\cdot10^4 \\ =8\cdot10000 \\ =80000\text{ meters} \end{gathered}[/tex]For the thickness, we have:
[tex]\begin{gathered} 5\cdot10^{-6} \\ =5\cdot0.000001 \\ =0.000005\text{ meters} \end{gathered}[/tex]What is the range of the function graphed below?у654GO2-11.2.3.4.5.6-5.-5.-4.-3.-2-112136 N4..5க
From the given graph
The end points of the curve is y = + 3 and y = -3
The point + 3 is shadded while point - 3 is not shadded hence
The range of the function is
[tex]-3GP 3: Haley is making admission tickets to the middle school dance. So far she has made 112 tickets, and her planis to make 320 tickets.What percent of the admission tickets has Haley produced so far?VerbalPractionDecimal
The 100% of tickets are 320 tickets (this is Haley's goal), she made 112 tickets. To determine what percentage of 320 does 112 represent you can use cross multiplication:
320 ____ 100%
112 _____ x%
Both relations are at the same ratio so that
[tex]\begin{gathered} \frac{100}{320}=\frac{x}{112} \\ x=112(\frac{100}{320}) \\ x=35 \end{gathered}[/tex]112 tickets represent 35% of 320, which means that she made 35% of the admission tickets so far.
As shown in the diagram below, a ladder 5 feet long leans against a wall and makes an angle of 65° with the ground. Find, to the nearest tenth of a foot, the distance from the wall to the base of the ladder.
The diagram representing the scenario is a right angle triangle is shown below.
Taking 65 degrees as the reference angle,
BC = length of the ladder = hypotenuse
AB = the distance from the wall to the base of the ladder = adjacent side
To find AC, we would apply the Cosine trigonometric ratio which is expressed as
Cos# = adjacent side/hypotenuse
Thus,
Cos 65 = AB/5
AB = 5Cos65
AB = 2.1
Therefore, the distance from the wall to the base of the ladder is 2.1 feet
Bella has a bucket of Legos. She chose a Lego,recorded the color, and placed it back in the bucket.She did this 40 times. The table shows the results.ColorNumberRed4White10Blue8Green18Based on the results in the table, what is theexperimental probability that the next time Bellachooses a Lego it will be a white or blue?
Answer
Probability that the next time Bella chooses a Lego, it will be a white or blue
= (9/20)
= 0.45
Explanation
The probability of an event is calculated as the number of elements in the event divided by the total number of elements in the sample space.
Number of white or blue legos = 10 + 8 = 18
Total number of legos = 4 + 10 + 8 + 18 = 40
Probability that the next time Bella chooses a Lego, it will be a white or blue
= (18/40)
= (9/20)
= 0.45
Hope this Helps!!!
Find the absolute change and the relative change in the following case.The average sale of a house decreased from $333,000 in February 2008 to $188,000 in February 2013.wwwThe absolute change is(Simplify your answer. Type an integer or a decimal.)
Given:
The average sale of a house decreased from $333,000 in February 2008 to $188,000 in February 2013.
Required:
To find the absolute change and the relative change.
Explanation:
The absolute change is
[tex]\begin{gathered} =188,000-333,000 \\ =-145,000 \end{gathered}[/tex]The relative change is
[tex]\begin{gathered} =100\times(\frac{188,000-333,000}{333,000}) \\ \\ =100\times(-0.4354) \\ \\ =-43.54\% \\ \\ =-44\% \end{gathered}[/tex]Final Answer:
Absolute change = -145,000
Relative change = -43.54%
calculate the value of m if the lines 3x-my=15 makes an angle of 45° with the line 3x+5y=7please help me to solve this?
To find angle between two lines, we use the formula,
[tex]\tan \theta=\frac{m_1-m_2}{1+m_1m_2}[/tex]Where
θ is the angle between two lines
m1 is the slope of the first line
m2 is the slope of the second line
First Line Equation:
[tex]\begin{gathered} 3x-my=15 \\ my=3x-15 \\ y=\frac{3}{m}x-\frac{15}{m} \end{gathered}[/tex]The slope is 3/m
Second Line Equation:
[tex]\begin{gathered} 3x+5y=7 \\ 5y=-3x+7 \\ y=-\frac{3}{5}x+\frac{7}{5} \end{gathered}[/tex]The slope is -3/5
The angle between the two lines is 45°.
Let's substitute the known information into the formula and figure out the value of 'm':
[tex]undefined[/tex]line has a slope of 2 and includes the points (–1,k) and (0,10). What is the value of k?
Answer:
k=8
Step-by-step explanation:
METHOD 1:
We will create an equation for slope intercept, y=2x+ 10Then we replace x with -1, y=2(-1)+10Multiply -1 and 2, y=-2+10Combine like terms, so y=8Because y=k, k=8METHOD 2:
We can also use [tex]\frac{y_{2}- y_{3} }{x_{2}- x_{1} } =2[/tex]We replace all values we know, so that we get, [tex]\frac{10-k}{0-(-1)}=2[/tex]Then we subtract -1 for 0 so we get, [tex]\frac{10-k}{1} =2[/tex]Then remove the 1 because anything divided by 1 is the dividend, 10-k=2Subtract two from both sides so 8-k=0add ka on both sides so 8=kidentify the term of the expression 11r + 7s then give the coefficient of each terms
We have an expression:
[tex]11r+7s[/tex]It has 2 terms with two unknowns: r and s.
Their coefficients are 11 for r and 7 for s.
Answer:
11r+7s is the expression.
11r and 7s are the terms.
11 and 7 are the coefficients.
r and s are the variables or unknowns.
Formula: [tex]t = 50 + \frac{n - 40}{4} [/tex]Where T is temperature in Fahrenheit and N is a number of chirps per minute. If T=60°F, find the number of chirps per minute.
In order to find the value of N in the equation when T = 60, we just need to apply the value of T and then calculate the value of N.
So we have that:
[tex]\begin{gathered} T=50+\frac{N-40}{4} \\ 60=50+\frac{N-40}{4} \\ \frac{N-40}{4}=10 \\ N-40=40 \\ N=80 \end{gathered}[/tex]So the number of chirps per minute is 80
Solve the following problems. Include the sketch of a normal curve and in finding the area refer on the standard normal curve table.What percent if the area under the normal curve between z = 0 and z = 1.63?
Answer:
44.84%
Explanation:
To find the percent of the area under the normal curve between z = 0 and z = 1.63, we need to calculate the following probability
P(0 < z < 1.63)
So, we can sketch the normal curve as follows
Then, using the standard normal curve, we get
P(0 < z < 1.63) = P(z < 1.63) - P(z < 0)
P(0 < z < 1.63) = 0.9484 - 0.5
P(0 < z < 1.63) = 0.4484
Then, the percentage is 44.84%
Find the length of AB.A А.AB = [ ? ]m140°8 mB.Round your answer to the nearest hundredth.Enter
The length AB represents the length of the minor arc in the circle. The formula required to find the length is given as:
[tex]\begin{gathered} l=\frac{\theta}{360}\text{ x 2}\pi r \\ \text{where }\pi\text{ =3.142} \\ \end{gathered}[/tex]We substitute the values of the angle = 140 degrees and the radius= 8m, to find the length of the arc AB
[tex]\begin{gathered} \text{Length(AB) =}\frac{140}{360}\text{ x 2 x 3.142 x 8} \\ \text{Length(AB) =0.3889 x 2 x 3.142 x 8} \\ \text{Length(AB)}=\text{ 19.55m} \end{gathered}[/tex]In conclusion, the length AB = 19.55m
3A. Explain in your own words how to find the domain of a function if you know its equation.B. Find the domain of f (x) =√9-7x6x?+13x-15Be sure to show relevant work.
Solution
Step 1
A)The domain refers to all real values of x for which the function is defined. The values of x for which the function is undefined are not a part of the domain. If you are given the equation then you can find the domain of that function by solving/ factorizing the denominator of the equation to find the zero(s) of the equation in the denominator. These values gotten are the values of x that will make the function undefined and hence are not part of the domain. Every other real value of x apart from these zero(s) obtained is part of the domain.
B)
Step 1
Factorize the denominator of the equation to find the zeroes of the equation
[tex]6x^2+13x-15=0[/tex]Step 2
Find the required factors to replace 13x and is equal to -90x²
[tex]\text{These factors are 18x and -5x}[/tex]Step3
Replace 13x with these factors
[tex]6x^2+18x-5x-15=0[/tex]Step 4
Factorize the equation and find the values of x
[tex]\begin{gathered} (6x^2+18x)(-5x-15)=0 \\ 6x(x+3)\text{ -5(x+3)=0} \\ (6x-5)(x+3)=0 \\ 6x-5\text{ = 0} \\ 6x=5 \\ x=\frac{5}{6}\text{ OR} \\ x+3=0 \\ x=-3 \end{gathered}[/tex]Hence, the domain of the function is all real values of x except -3 and 5/6
A. Edmonds Community College is opening a five credit hour section of Business Pre-Calculus for thewinter quarter. An instructor and room for the quarter cost $12,700. Additionally, it costs $31.00 perstudent per quarter after the matching money from the state is considered. The college charges $83 per credit hour. Being a non-profit, they just need to break even in each class. What is the minimum numberof students they need to let the section run?Minimum Number of Students_____Round your answer UP to the nearest wholenumber.
Let's list down the given information in the question.
Instructor and a room = $12, 700
Cost per student = $31.00
Cost per credit hour = $83
If the charge per credit hour is $83 and the section to be run is for 5 credit hours then, total charge is $83 x 5 = $415. This means every student will have to pay $415 for the subject Business Precal.
On the other hand, the college spent $12700 for the instructor and the room as well as $31 per student.
Assuming that x = the number of students, then we can have the equation below:
[tex]12,700+31x\leq415x[/tex]where 31x is the cost per student per quarter and 415x is the charge per student for the subject Business Precal. The cost of the school must be less than or equal to its total charges to the school.
From that inequality, let's solve for x.
[tex]\begin{gathered} 12,700+31x\leq415x \\ \text{Subtract 31x on both sides.} \\ 12,700\leq384x \\ \text{Divide both sides by 384.} \\ 33.07\leq x \\ 34\leq x \end{gathered}[/tex]Hence, the minimum number of students they need to let the section is 34.
At 34 students, the school will be able to spend $13, 754 and its total charges to the student is $14, 110.
Whereas, at 33 students, the school will be able to spend $13, 723 but their total charges to the student is only $13, 695.
Hence, they need at least 34 students in order to run the section Business PreCal.
The following table shows the breakdown of opinions for both faculty and students in a recent survey about the new restructuring of the campus to include an Honors College . Find the probability that a randomly selected person is either a student opposed to the change or a faculty member who has an opinion either for or againstExpress your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
Answer:
[tex]0.416667[/tex]Explanation:
Here, we want to calculate the probability that a randomly selected person is either a student opposed to the change or a faculty member who has an opinion either for or against
We need to get these values
The count of students who are opposed is 59
The count of faculty members who have an opinion either for or against is 16 + 10 = 26
This gives a total of 85
Now, we need to divide this by the total number of students which is 204
Mathematically, we have that as:
[tex]\frac{85}{204}\text{ = 0.416667}[/tex]
E) 2 x+$7=$12I need help
To solve the following equation we are going to use inverse operations to solve equations, that means addition and subtraction are inverse operations, multiplication and division too.
Then,
[tex]\begin{gathered} \frac{1}{2}x+7=12 \\ \frac{1}{2}x=12-7 \\ x=5\cdot2 \\ x=10 \end{gathered}[/tex]8. If the measure of angle 5 = 53 and the measure of angle 7 = 125, what is 1 point the measure of angle 2? * # 1 1 3 2 4 5 6 7 O 53 degrees 55 degrees 72 degrees O 127 degrees The correct measurement is not given
Finding Angles between Lines.
The Pythagorean theorem Find each missing length to the nearest length
To find any missing length in a right triangle, we use the Pythagorean Theorem:
[tex]a^2=b^2+c^2[/tex]Where a is the length of the hypotenuse, the longest side.
In the given right triangle:
• a=8.9
,• b=4
,• c=8
We check if this satisfies the Pythagorean Theorem:
[tex]\begin{gathered} a^2=4^2+8^2 \\ a^2=16+64 \\ a^2=80 \\ a=\sqrt[]{80} \\ a=8.9\text{ units} \end{gathered}[/tex]Thus, we see that the Pythagorean Theorem holds.
The equation for line G can be written as Y=7/2x wine H includes the point -2 and -3 and is parallel to line G what is the equation of line H
The equation of H passing through (-2,-3) and parallel to G is 7x - 2y + 8 = 0
Given :
Equation of G is Y = 7/2x
2Y = 7x
7x - 2Y = 0
Slope of G = -a/b = -7/-2 = 7/2
Since H is parallel to G , slope of H = slope of G
slope of H = 7/2
Equation of line H passing through (-2,-3) and slope m = 7/2 is
y - y1 = m(x - x1)
y - (-3) = 7/2(x - (-2))
y + 3 = 7/2(x + 2)
2(y + 3) = 7(x + 2)
2y + 6 = 7x + 14
7x - 2y + 8 = 0
Slope of equation ax + by + c = 0 is -a/b.
Equation of line passing through points (x1,y1) and slope m is y-y1=m(x-x1).
If two lines are parallel , there slopes will be equal.
To learn more about straight lines , click the link below
https://brainly.com/question/13763238
#SPJ1
If an inscribed angle intercepts the diameter of a circle, what degree measure is the intercepted arc?
The measure is 90°.
Since it intercepts half of the circle.
help meeeeeeeeeeeeeeee pleasee
Answer:
[tex]\sqrt{18}[/tex] inches
Step-by-step explanation:
A = 18 sqr inches
s = [tex]\sqrt{18}[/tex]
A = s^2
A = [tex]\sqrt{18}[/tex] inches x [tex]\sqrt{18}[/tex] inches
A = 18 sqr inches
c/4=16 can you help me solve
[tex]\frac{C}{4} =16[/tex]
Multiply both sides by 4:
[tex](\frac{C}{4} )\times(4)=(16)\times(4)[/tex]
[tex]\fbox{C=64}[/tex]
Hope this helps!
Deshawn says that he can evaluate the numerical expression 7 + (3 × 8) − 5 without parentheses and get the same answer. Is Deshawn correct? Explain how you know.
When Deshawn says that he can evaluate the numerical expression without the parentheses and get same value, he is correct.
How to calculate the value?In the information, the expression given is illustrated as:
7 + (3 × 8) − 5
= 7 + 24 - 5
= 31 - 5
= 26
Without the parentheses, the value will be:
= 7 + 3 × 8 - 5
= 7 + 24 - 5
= 31 - 5
= 26
Therefore, since we have some value, he is right.
Learn more about numbers on:
brainly.com/question/25710806
#SPJ1
where can we put parentheses in (21+21)÷7 to make it equivalent to 6
Answer:
we don't need to put parenthesis to the expression:
(21+21) ÷ 7
Explanation:
The expression (21+21)÷7 is already equivalent to 6 because to solve the equation, we first need to make the sum and then the division:
(21+21) ÷ 7
42 ÷ 7
6
Therefore, we don't need to put parenthesis to the expression:
(21+21) ÷ 7
Based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why HIJ KLM? Check all that apply. A. HL B. HA C. AAS D. LL E. ASA F. LA
The congruency postulates or theorem that could be given as reasons why ΔHIJ ≅ ΔKLM are;
B. HA
C. AAS
What makes two triangles congruent?Two triangles are congruent is they satisfy one of the congruency theorems which includes;
AAS; Angle-angle-Side congruency postulateASA; Angle-Side-Angle congruency postulateSAS; Side-Angle-Side congruency postulateSSS; Side-Side-Side congruency postulateHL; Hypotenuse length congruency theoremHA; Hypotenuse angle congruency theoremThe information in the diagram of the question are;
Angle ∠IHJ in triangle ΔHIJ is congruent to a angle ∠LKM in ΔKLM
Angle ∠IJH in triangle ΔHIJ is congruent to angle ∠LMK in triangle ΔKLM
Segment [tex]\overline{IJ}[/tex] in triangle ΔHIJ is congruent to [tex]\overline{LM}[/tex] in triangle ΔKLM
The information in the question can be described as follows;
Two adjacent angles and a non included angle in triangle ΔIJH are congruent to two angles and the non included side in ΔKLM
Therefore;
Triangle ΔHIJ is congruent to triangle ΔKLM by Angle-Angle-Side, AAS congruency postulateAngle ∠IHJ in triangle ΔHIJ = 90° and angle ∠LKM in triangle ΔKLM = 90°
Therefore, triangle ΔHIJ and triangle ΔKLM are right triangles
The hypotenuse side in triangle ΔHIJ is congruent to the hypotenuse side of ΔKLM
From the diagram, angle ∠IJK is congruent to angle ∠LMK, therefore;
Triangle ΔHIJ is congruent to ΔKLM by Hypotenuse-Angle, HA congruency postulateHypotenuse Angle, HA, congruency theorem states that two triangles are congruent if the hypotenuse side and the acute angle of one right triangle are congruent the hypotenuse side and one acute angle of the other right triangle
The correct options are; B. HA, and C. AAS
Learn more about the rules of congruency between triangles here:
https://brainly.com/question/1675117
#SPJ1
Gabriel McKernan, a radio announcer, is married, earns $368.23 weekly, and claims 2 allowances. According to the tablebelow, what amount will be withheld for FIT?
The about withheld for the FIT tax, considering the given table, is of:
B. 8.
How to obtain the amount withheld by the FIT tax?The table gives the fixed amount withheld by the FIT tax, considering the weekly pay and the number of allowances claimed.
For Gabriel McKernan, the amount of tax paid is obtained as follows:
Fourth interval of payment, as a weekly salary of $368.23 is between 360 and 370. Married, as this table is only for married people.Two allowances.Hence the amount of taxes paid by Gabriel McKernan is found looking at the fifth column of the last row of the table, and is of 8.
Thus the correct option regarding how much he pays for the FIT tax is given by option B.
More can be learned about taxes at https://brainly.com/question/2170674
#SPJ1
Jewels homework Culver's multiplication with powers of 10 the first questions of her homework is 32.4 * 10
Match each data set with the value that best describes its center.6 2 4 9Data set A: 2, 3, 1, 4, 2,0,0Data set B: 6.4, 5, 6, 5, 7, 8, 7Data set C: 1, 4, 0, 2, 4, 4, 6, 7Data set D: 7, 8, 10, 11, 8, 9, 10, 9, 11
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
data set
center = ?
Step 02:
We must analyze the data sets to find the solution.
Data set A: 2, 3, 1, 4, 2, 0 , 0 ===> 4
Data set B: 6 , 4, 5, 6, 5, 7, 8, 7 ===> 6
Data set C: 1, 4, 0, 2, 4, 4, 6, 7 ===> 2
Data set D: 7, 8, 10, 11, 8, 9, 10, 9, 11 ===> 9
That is the full solution.