Answers
Since we have to solve it graphically, we need to plot the function:
Here, we can see that the point where the graph touches the y axis is when x = 2
The solution to the equation is x = 2
Related Questions
Find the probability of getting a 1, 5, or 6 when you roll a standard six-sided die.Select the correct answer below:1/61/31/22/35/6
Answers
Step 1
Write out the expression for the probability of an event occurring
[tex]Pr(\text{event occurring) = }\frac{number\text{ of required outcomes}}{\text{Total number of outcomes}}[/tex]Where,
Total of required outcomes= 6
Step 2
Find the probability of getting a 1
[tex]Pr(1)=\text{ }\frac{1}{6}[/tex]Step 3
Find the probability of getting a 5
[tex]Pr(5)\text{ =}\frac{1}{6}[/tex]Step 4
Find the probability of getting a 6
[tex]Pr(6)=\frac{1}{6}[/tex]Step 4
Find the probability of getting a 1,5 or 6
[tex]Pr(1,5\text{ or 6)=Pr}(1)+Pr(5)+Pr(6)_{}[/tex][tex]\begin{gathered} Pr(1,5\text{ or 6) = }\frac{1}{6}+\frac{1}{6}+\frac{1}{6} \\ Pr(1,5\text{ or 6) = }\frac{1}{2} \end{gathered}[/tex]Hence, the probability of getting a 1, 5 or 6 when you roll a standard six-sided die = 1/2
Scooby needs to ship some DVDs. He has 16 comedy movies, 12 scary movies and 8 action movies. He can pack only one type of DVD in each box and he must pack the same number of DVDs in each box. What is the greatest number of DVDs Scooby can pack in each box?A.2B.4C.6D.8
Answers
He has 16 comedy movies, 12 scary movies and 8 action movies.
He can pack only one type of DVD in each box and he must pack the same number of DVDs in each box
So, we need to find the greatest common factor between 16 , 12 and 8
16 = 2 * 2 * 2 * 2
12 = 2 * 2 * * 3
8 = 2 * 2 * 2
---------------------------------
2 * 2 = 4
So,
The greatest number of DVDs Scooby can pack in each box = 2 * 2 = 4
The answer is option B. 4
----------------------------------------------------------
More explanations :
So, he will pack 16 comedy movies at 4 packs, each pack has 4 DVDs
And he will pack 12 scary movies at 3 packs, each pack has 4 DVDs
And he will pack 8 action movies at 2 packs, each pack has 4 DVDs
So, the total number of packs = 4 + 3 + 2 = 9 packs
Find a best-fit linear model for the following data:xy−3196−2139−1820251−322−893−146y = −57xy = 57xy = 57x + 25y = −57x + 25
Answers
Explanation
We are given a set of x and y values in the table
To compute the best-fit model for the data, we will use the graphing calculator
From the graph above, we have the function to be
[tex]y=-57x+25[/tex]Thus, the answer is y= -57x +25
b Exit Ticket COS 28 = C 12 tan 28 = b с 12 28 b Download image X
Answers
Answer
b = 22.6 units
c = 25.6 units
Explanation
In a right angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
For this question,
Hypotenuse = c
Opposite = 12
Adjacent = b
Trignometric ratios can then be used to find b and c.
CAH and TOA
Cos 28° = (Adj/Hyp)
Cos 28° = (b/c)
Tan 28° = (Opp/Adj)
Tan 28° = (12/b)
Cross multiply
b = 12/(Tan 28°)
b = 12/0.5317
b = 22.57
We can then solve for c
Cos 28° = (b/c)
Cos 28° = (22.57/c)
Cross multiply
c = (22.57/Cos 28°)
c = (22.57/0.8829)
c = 25.56 units
Hope this Helps!!!
At Fry's supermarket, each 12-1b bag of apples costs $4. Write an equation to represent the relationship between the number of pounds of apples, p, and cost, c I
Answers
if a 12 lb bag costs $4, then a 1 lb bag costs $4/12, which is equal to $1/3 dollars, so if we let p be the number of pounds that we are going to buy and c the amount that we must pay
[tex]c=\frac{1}{3}p[/tex]that is the relation between c and p
An angle measures 83∘. Find a. its supplement and b. its complement.
Answers
Let
A = Angle (83°)
S = Supplement of A
C = Complement of A.
1) Finding the Supplement of A.
Supplementary angles are the angles whose sum is equal to 180°.
Then,
A + S = 180
Substituting A, we can find S.
83 + S = 180
S = 180 - 83
S = 97°
2) Finding the Complement of A.
Complementary angles are the angles whose sum is equal to 90°.
Then,
A + C = 90
83 + C = 90
C = 90 - 83
C = 7 °C.
Answer:
Supplement = 97 °C
Complement = 7 °C
Find Sec A and Cot B exactly if a=8 and b=7
Answers
The given triangle is right angle triangle with side a = 8 and b 7
Apply pythagoras theorem for the side c;
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
Hypotenuse² = Perpendicular² + Base²
Here, perpendicular, a =8 and Base b = 7
[tex]\begin{gathered} c^{2}=a^{2}+b^{2} \\ c^{2}=8^{2}+7^{2} \\ c^2=113 \\ c=\sqrt[]{113} \end{gathered}[/tex]The trignometric ratio for sec of an angle define as the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.
[tex]\begin{gathered} \sec A=\frac{Hypotenuse}{Adjacent\text{ side of angle A}} \\ \sec A=\frac{c}{b} \\ \sec A=\frac{\sqrt[]{113}}{7} \end{gathered}[/tex]The trignometric ratio for cosine of angle define as the ratio of the adjacent side to the the opposite side of the angle,
[tex]\begin{gathered} CotB=\frac{\text{Adjacent side to angle B}}{\text{Opposite side to angle B}} \\ CotB=\frac{a}{b} \\ CotB=\frac{8}{7} \end{gathered}[/tex]Answer; a)
[tex]\text{SecA}=\frac{\sqrt[]{113}}{7},\cot B=\frac{8}{7}[/tex]
(-3x² + 6x - 12) + (5x + 9) is equivalent to expression
Answers
I am confused. Please help. Give answer options and simple explanation. Thanks!
Answers
Given the functions
[tex]\begin{gathered} f(x)=2x^2+4x-5 \\ g(x)=6x^3-2x^2+3 \end{gathered}[/tex][tex]\begin{gathered} (f-g)(x)=f(x)-g(x) \\ =2x^2+4x-5-(6x^3-2x^2+3) \\ =2x^2+4x-5-6x^3+2x^2-3 \\ =-6x^3+2x^2+2x^2+4x-5-3 \\ =-6x^3+4x^2+4x-8 \end{gathered}[/tex]The final answer is OPTION C
need answer with steps[tex](7 + 9i) + ( - 5i)[/tex]
Answers
Gy, this is the solution:
(7 + 9i) + ( - 5i)
Solving the parenthesis:
7 + 9i - 5i
7 + 4i
Elizabeth is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The total cost of the gym membership over t months is given by the equation C = 25t + 100. What is the y-intercept of the equation and what is its interpretation in the context of the problem?
Answers
The y-intercept of the equation is 100
For this problema the y-intercep is equal to the one-time fee
john ran at a pace of 3.5 miles per hr for a distance of 10.5 miles. how many minutes did it take them to run 10.5miles? use the distance formula: d= rt to where d is total distance, r is rate and t is time
Answers
d=rt
divide both-side of the equation by r
t =d/r
distance = 10.5 miles
we will go ahead and find the rate r
r = 3.5/60
r=0.05833
substituting into t= d/r
t = 10.5 / 0.05833
t=180 minutes
A train is traveling at a constant speed of 105 mph how many feet does a travel in three seconds remember that 1 mile is 5280 feet
Answers
We are given that a train is traveling at the following constant speed:
[tex]v=\frac{105\text{ miles}}{hour}[/tex]We are asked to determine the distance after 3 seconds. To do that, let's remember that speed is the ratio between distance and time, that is:
[tex]v=\frac{d}{t}[/tex]Where:
[tex]\begin{gathered} d=\text{ distance} \\ t=\text{ time} \end{gathered}[/tex]Since we want to determine the distance we will multiply both sides of the equation by "t":
[tex]vt=d[/tex]Now, we substitute the values:
[tex]\frac{105\text{ miles}}{hour}\times(3s)=d[/tex]Since the velocity is given per unit of hour, we need to convert the 3 seconds into hours. We do that using the following conversion factor:
[tex]1\text{hour}=3600s[/tex]Now we multiply the time by the conversion factor:
[tex]3s\times\frac{1h}{3600s}=\frac{1}{1200}h[/tex]Now we substitute in the formula for the distance:
[tex]\frac{105\text{ miles}}{hour}\times(\frac{1}{1200}hour)=d[/tex]Solving the operations:
[tex]\frac{7}{80}miles=d[/tex]Now, we convert the miles into feet using the given conversion factor:
[tex]1\text{mile}=5280\text{feet}[/tex]Now, we multiply by the conversion factor:
[tex]d=\frac{7}{80}\text{miles}\times\frac{5280feet}{1mile}[/tex]Solving the operations:
[tex]d=462feet[/tex]Therefore, the distance is 462 feet.
2 by 6 rectangle is inscribed in circle 5 by 6 rectangle is inscribed in circle 2 by 15 rectangle is inscribed in circle 1 by 12 rectangle is inscribed in circle what is the circumference?
Answers
21:51
it seems that your questions has multiple questions in it. Unfortunately, the tutoring app is meant to answer only one problem per session. So, I encourage you to start another session with your the remainder of the questionsk, so one of my colleague can help you out.
can you see what I'm writing?
did the teacher go wrong in making the square in the circle?! that’s what the question is asking pls help
Answers
Given two arcs, we follow the steps:
1) Label the intersection point of each pair of arcs as U and V:
2) Next, we need to construct the perpendicular bisector of the segment UV and label the intersection points to the circumference as P and Q:
3) Finally, we draw four line segments connecting the successive points on the circumference of the circle:
Looking at the steps given in the problem, the answer is:
The teacher makes a mistake in Step 2
Write a equivalent unit rate to running 5/4 a mile in 9 minutes
Answers
To determine the unit rate to running 5/4 a mile in 9 minutes you have to determine the distance in miles run in one minute.
You can use corss multiplication to do the calculation:
9min____5/4miles
1min_____xmiles
[tex]\begin{gathered} \frac{\frac{5}{4}}{9}=\frac{x}{1} \\ x=\frac{5}{36} \end{gathered}[/tex]The unite rate is 5/36miles/minute, expressed as a decimal value is 0.14miles/min
In triangle ABC, angle A is a right angle. What are possible measurements for B & C?
Answers
Given the triangle ABC.
Angle A is a right angle which equals 90 degree.
And sum of angles in a triangle equals 180 degree.
[tex]\begin{gathered} A+B+C=180^0 \\ 90^0+B+C=180^0 \\ B+C=180^0-90^0 \\ B+C=90^0 \end{gathered}[/tex]So, the possible measurement of B and C must be the ones who's sum is 90 degree.
[tex]\begin{gathered} 40\text{ \& 50 }\rightarrow40+50=90 \\ 30\text{ \& 60}\rightarrow30+60=90 \\ 45\text{ \& 45}\rightarrow45+45=90 \\ 80\text{ \& 30}\rightarrow80+30=110 \\ 60\text{ \& 40}\rightarrow60+40=100 \end{gathered}[/tex]Therefore, the ones whose sum equals 90 degree are the answers;
[tex]\begin{gathered} 40\text{ \& 50} \\ 30\text{ \& 60} \\ 45\text{ \& 45} \end{gathered}[/tex]Find bc if your answer is not an integer, leave it in simplest radical form
Answers
Hello!
We know that this is a right triangle and the angle C is 45º.
Knowing it, we have:
Considering the information above, we must use the sine of 45º to calculate the value of side BC, look:
[tex]\sin(45\degree)=\frac{\mathrm{opposite}}{\mathrm{hypotenuse}}[/tex]As we know, the sine of 45º is:
[tex]\sin(45)=\frac{\sqrt{2}}{2}[/tex]Let's replace all the values in the formula:
[tex]\begin{gathered} \sin(45\operatorname{\degree})=\frac{\mathrm{oppos\imaginaryI te}}{\mathrm{hypotenuse}} \\ \\ \dfrac{\sqrt{2}}{2}=\frac{10}{\mathrm{BC}} \\ \\ \mathrm{BC}\sqrt{2}=10\cdot2 \\ \mathrm{BC}\sqrt{2}=20 \\ BC=\frac{20}{\sqrt{2}} \\ \\ BC=\frac{20\cdot\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}}=\frac{20\sqrt{2}}{\sqrt{4}}=\frac{20\sqrt{2}}{2}=\boxed{10\sqrt{2}\text{ ft}} \end{gathered}[/tex]Answer:Alternative B.
A bag contains 31 coins, some dimes and some quarters. The total amount of money in the bag is $4.45. How many dimes and how many quarters are in the bag?_____dimes_____quarters
Answers
A bag contains 31 coins, some dimes and some quarters. The total amount of money in the bag is $4.45. How many dimes and how many quarters are in the bag?
_____dimes
_____quarters
we know that
1 quarter=$0.25
1 dime=$0.10
Let
x -----> the number of quarters
y ----> the number of dimes
we have that
x+y=31 ------> equation A
0.25x+0.10y=4.45 -----> equation B
Solve the system of equations
Isolate the variable x in equation A
x=31-y ------> equation C
Substitute equation C in equation B
so
0.25(31-y)+0.10y=4.45
solve for y
7.75-0.25y+0.10y=4.45
0.25y-0.10y=7.75-4.45
0.15y=3.30
y=22 dimes
Find the value of x
x=31-22
x=9 quarters
therefore
the answer is
22 dimes9 quartersLast year, Jenny opened an investment account with $7400. At the end of the year, the amount in the account had decreased by6.5%. How much is this decrease in dollars? How much money was in her account at the end of last year?
Answers
if the decreasing amount is 6.5% the r in our decay function will be:
[tex]1-0.065=0.935[/tex]and in one yeat t=1 so the equation will be:
[tex]\begin{gathered} y=7400(0.936)^1 \\ y=6925.4 \end{gathered}[/tex]Solve the equation.5/6=1/3+d
Answers
We have the following equation
[tex]\begin{gathered} \frac{5}{6}=\frac{1}{3}+d \\ \end{gathered}[/tex]We substract 1/3 each side:
[tex]\begin{gathered} -\frac{1}{3}+\frac{5}{6}=-\frac{1}{3}+\frac{1}{3}+d \\ -\frac{1}{3}+\frac{5}{6}=0+d \\ -\frac{1}{3}+\frac{5}{6}=d \\ \end{gathered}[/tex]We multiply each side of the fraction 1/3 by 2:
[tex]-\frac{1}{3}=-\frac{1\cdot2}{3\cdot2}=-\frac{2}{6}[/tex]Then
[tex]\begin{gathered} -\frac{1}{3}+\frac{5}{6}=d \\ -\frac{2}{6}+\frac{5}{6}=d \\ \frac{3}{6}=\frac{1}{2}=d \end{gathered}[/tex]Answer: d = 1/2Can you please throughly explain this question. I don't get it.
Answers
In graphing y > 2x - 7, a dashed line is used.
Answer: True
Explanation
Whenever we graph > or < , the boundary line is not inclusive of the range of solutions. Hence, we use a dashed line on the boundary.
On the other hand, whenever we have the inequality <= or >= , the
answer: true
explanation: my teacher just did it
Prove #8Given: PR congruent to TR angle P is congruent to angle T
Answers
Reason: Given
[tex]\angle P\cong\angle T[/tex]Reason: Given
[tex]m\angle PRQ\cong m\angle SRT[/tex]Reason: Definition of Vertical angles
If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent by ASA (Angle-Side-Angle).
if m<10=77, m<7=47 and m<16=139, find the measure of the missing angle m<15=?
Answers
Step 1: Quoting the theorem of a straight line
The theorem of a straight line says Total angles on a straight line is equal to 180°.
Step 2:
m<16 and m<15 are angles on a straight line from the diagram given,
[tex]\begin{gathered} \text{where} \\ m<16=139^0 \\ m<15=\text{?} \\ \text{therefore,} \\ m<16+m<15=180^0 \\ 139^0+m<15=180^0 \\ \text{Collecting like terms} \\ m<15=180^0-139^0 \\ m<15=41^0 \end{gathered}[/tex]Hence the value of m<15= 41°.
With the enthusiasm for statistics at an all-time high, students were found sprinting from their vehicle to the classroom just to be the first person to grab a seat. The times of the students were recorded (in seconds) and given in the stemplot below.What is the 9th fastest time a student took to go from his/her vehicle to a seat in the classroom? Make sure to use labels and avoid the use of abbreviations
Answers
The 9th fastest time is 28 seconds
Explanation:We have been given a stem plot diagram of the time it took the students to grab a seat.
We need to find the 9th fastest time
To do this, we first need to list out the time in seconds:
13, 14, 15, 19, 19
21, 27, 27, 28
32
45, 49, 49
Since the right side is empty, there is no list of 50 plus
62, 62
combining the list (all in seconds):
13, 14, 15, 19, 19, 21, 27, 27, 28, 32, 45, 49, 49, 62, 62
The lower the number, the faster the time. Since the list is ordered in ascending order, we will count to the 9th place
The ninth place on the list = 28
The 9th fastest time a student took to go from his/her vehicle to a seat in the classroom is 28 seconds
I need help with math
Answers
a)
3000x - 2000 = 10 000
Add 2000 to both-side of the equation
3000x - 2000 + 2000 = 10 000 + 2000
3000x = 12000
Divide both-side of the equation by 3000
3000x/3000 = 12000/3000
x = 4
b) -2x/3
[tex]\frac{-2x}{3}-\frac{x}{7}=\text{ 17}[/tex]Multiply through the equation by 21
[tex]21(\frac{-2x}{3})-21(\frac{x}{7})=\text{ 17(21)}[/tex][tex]7(-2x)\text{ - 3x =357}[/tex]-14x - 3x = 357
-17x = 357
Divide both-side of the equation by -17
x = -21
c)
[tex]\frac{5}{2}x-\frac{1}{3}=\text{ 13}[/tex]Add 1/3 to both-side of the equation
[tex]\frac{5x}{2}=13\text{ +}\frac{1}{3}[/tex][tex]\frac{5x}{2}=\text{ }\frac{39+1}{3}[/tex][tex]\frac{5x}{2}=\frac{40}{3}[/tex]cross-multiply
15x = 80
Divide both-side of the equation by 15
x= 5.33
d)
[tex]\frac{3}{10}+\frac{2x}{5}=\frac{1}{2}[/tex]multiply through the equation by 10
[tex]10(\frac{3}{10})+10(\frac{2x}{5})=10(\frac{1}{2})[/tex]3 + 2(2x) = 5
3 + 4x = 5
subtract 3 from both-si
Use the graph to find the indicated values:line with y intercept at (0,3) and x intercept at (2,0)f(0)=AnswerIf f(x)=0 then x=?Answerf^{-1}(0)=AnswerIf f^{-1}(x)=0 then x=?Answer
Answers
From the graph:
[tex]f(0)=3[/tex]If:
[tex]\begin{gathered} f(x)=0 \\ then \\ x=2 \end{gathered}[/tex]For the last ones, we can use this fact:
The domain of the inverse of a function is the same as the range of the original function. Therefore:
[tex]f^{-1}(0)=2[/tex]If:
[tex]\begin{gathered} f^{-1}(x)=0 \\ then \\ x=3 \end{gathered}[/tex]3(2x - 5) – 4x > 7x + 10.Please help
Answers
EXPLANATION.
To solve the inequality we must follow some steps:
1.1.the number 3 must multiply the values that are inside the parentheses
Can you please help me out with a question
Answers
To find the point S we first need to find the equation of the circle which is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h,k) is the center and r is the radius.
In this case we don't have the radius but we know that the radius is the distance between the center and any point on the circle, then the radius is equal to the distance:
[tex]\begin{gathered} r=d(A,R)=\sqrt[]{(5-3)^2+(4-(-1))^2} \\ =\sqrt[]{4+25} \\ =\sqrt[]{29} \end{gathered}[/tex]hence the equation of the circle is:
[tex](x-3)^2+(y+1)^2=29[/tex]Now that we have this equation we need to determine which of the options given fullfil the equation. From the options given we conclude that the only point that fullfils the equation is the point D, this come from the fact that:
[tex]\begin{gathered} (1-3)^2+(-6+1)^2=29 \\ 4+25=29 \\ 29=29 \end{gathered}[/tex]Therefore this point is in the circle. Therefore we conclude that the coordinates of point D are (1,-6) and the answer is D.
This can be seen in the graph below:
Nathan and Tony hiked in the woods yesterday and came home with poison ivy. Tony has 5 times as many spots as Nathan. How many spots does Nathan have, x? Which table represents this situation?
Answers
Here, we want to get the correct equation and select the correct table
From the question, we have it that Tony has 5 times what Nathan had
Hence, given that Nathan has x, Tony has 5 times this and we have it as;
[tex]5\times x\text{ = 5x}[/tex]What this mean is that the right column of the table will be 5 times what is on the left column
Hence, the correct table here is the table with the heading 5x