The original fraction has a denominator that is 3 less than the numerator. If we define the numerator as x, then the denominator is x-3, and the fraction can be written as x/(x-3).
If 1 is added both to the numerator and denominator, the resulting fraction is equal to 10/7.
Then, we can write:
[tex]\begin{gathered} \frac{x+1}{(x-3)+1}=\frac{10}{7} \\ \frac{x+1}{x-2}=\frac{10}{7} \\ 7(x+1)=10(x-2) \\ 7x+7=10x-20 \\ 7x-10x=-20-7 \\ -3x=-27 \\ x=\frac{-27}{-3} \\ x=9 \end{gathered}[/tex]With the value of x, we can replace it in the fraction and know the value of it:
[tex]\frac{x}{x-3}=\frac{9}{9-3}=\frac{9}{6}=\frac{3}{2}[/tex]Answer: The fraction is 9/6, that can be simplified to 3/2 or 1.5.
I need help, I did 1-2b, but i do not mind someone answering it either way so I can double check, but I am mainly stuck with 2c and if someone can tell me the answer and as to why, it would mean a lot and you can get brainlest if it is the right answer :)(Not a multiple choice question)
Absolute Minimum: an absolute minimum point is a point where the function obtains its least possible value.
The given function :
[tex]f(x)=x^4-4x^3-x^2+12x-2[/tex]In the graph of the f(x) , the least value of x of the given curve is : (-0.939)
and the f(x) at x = (-0.939) is -10.065
The absolute minimum value is (x,y) = (-0.939, -10.065)
To round off in the nearest hundredth : (x, y) = (-0.94, -10.07)
Answer : (x, y) = (-0.94, -10.07)
Let A = {0, 2, 4, 6}, B = {1, 2, 3, 4, 5}, and C = {1, 3, 5, 7}. Find AU (BNC).{
Solution:
Given that;
[tex]\begin{gathered} A=\left\{0,2,4,6\right\} \\ B=\left\{1,2,3,4,5\right\} \\ C=\left\{1,3,5,7\right\} \end{gathered}[/tex]For B∩C, i.e . common elements between bot sets
[tex]B\cap C=\lbrace1,3,5\rbrace[/tex]Then, A∪(B∪C), i.e. all the elements in A and B∩C
[tex]A∪\left(B∪C\right)=\lbrace0,1,2,3,4,5,6\rbrace[/tex]Hence, A∪(B∪C) is
[tex]\begin{equation*} \lbrace0,1,2,3,4,5,6\rbrace \end{equation*}[/tex]Find the interest odf the loan using banker's ruleP - $350,- = 4.8%, t = 150 days
i = P r T
interest: i
Principal = $350
Interest rate : 4.8% (in decimal form, 4.8/100 = 0.048)
time = t = days/365 = 150/360
Replacing:
i= 350 (0.048) (150/360) = 7
Suppose a basketball player has made 359 out of 449 free throws. If the player makes the next 3 free throws, I will pay you $39. Otherwise you pay me $43.
Step 2 of 2 : If you played this game 623 times how much would you expect to win or lose?
Answer: expect to lose 679.07 dollars
==========================================================
Explanation:
Assuming each free throw is independent of any other, the probability of making the next free throw is 359/449
The probability of making 3 in a row is (359/449)^3 = 0.511145 approximately which represents the probability of earning the $39
That must mean 1-0.511145 = 0.488855 is the approximate probability of losing $43
Let's make a table of outcomes and their associated probabilities.
X = amount of money the player earns (the person shooting the free throws)
[tex]\begin{array}{|c|c|} \cline{1-2}\text{X} & \text{P(X)}\\\cline{1-2}39 & 0.511145\\\cline{1-2}-43 & 0.488855\\\cline{1-2}\end{array}[/tex]
Then from here we'll multiply each X and P(X) value for each separate row.
Example: 39*0.511145 = 19.934655
Let's form a third column of these products
[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{X} & \text{P(X)} & \text{X}*\text{P(X)}\\\cline{1-3}39 & 0.511145 & 19.934655\\\cline{1-3}-43 & 0.488855 & -21.020765\\\cline{1-3}\end{array}[/tex]
Add up everything in the X*P(X) column and you should get roughly -1.08611 which rounds to -1.09
The player expects, on average, to lose about $1.09 each time they play this game. Playing 623 times means they should expect to lose 623*1.09 = 679.07 dollars
Of course, given the nature of this random process, it's not a guarantee they will lose this amount. This is just the average of many attempts.
Given the measure -845°, which answer choice correctly gives an angle measure coterminal with the given angle and on the interval,0 < 0 < 360
Given the measure -845° we can find its coterminal measure on the interval, [0,360) below
Explanation
For angles measured in degrees
[tex]\begin{gathered} β=α±360*k,where\text{ }k\text{ }is\text{ }a\text{ }positive\text{ }integer \\ -845°=\frac{-169}{36}π≈-4.694π \\ Coterminal\text{ }angle\text{ }in\text{ \lbrack}0,360°)range:\text{ 235\degree, located in the third quadrant.} \end{gathered}[/tex]Answer: Option A
propriate symbols and/or words in your submissionSolve for the indicated measure.5. R = 19°, ZB = 56°, find mZT.6. R = 19, ZB'S 56°, find mZS.7. R = 19°, ZB = 56°, find mZC.8. True or false?AABC = AZXY9. Are the two triangles congruent?Yes or no?10. Use the image below to complete the proof.Identify the parts that are congruent by the given reason in the proof.STATEMENTS REASONSAB = DC GivenAB || DC Given2.Alternate Interior Angles TheoremReflexive Property of CongruenceSAS Congruence Theorem3.4.
ok
The sum of the internal angles in a triangle equals 180°
R + B = T = 180
Substitution
19 + 56 + T = 180
T = 180 - 19 - 56
T = 105°
Result:
T = 105°
What is 58 divided into 7275
Answer:125.431034
Step-by-step explanation:
Use the Distibutive Property: Expand -3(x + 3)
The distributive property of multiplication states the following:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]So, for the given expression, we have:
[tex]-3(x+3)=(-3)\cdot x+(-3)\cdot3=-3x-9[/tex]The distance to the nearest exit door is less than 200 feet.
ANSWER
d < 200
EXPLANATION
If d is the distance to the nearest exit door, and this distance is less than 200 feet, then the inequality to represent this situation is d < 200.
v+1.6>-5.5
nnnnnnnnnnnn
Answer:
v > -7.1
Step-by-step explanation:
Write a multiplication expression to represent each situation. Then find each product and explain its meaning. Ethan burns 650 calories when he runs for 1 hour. Suppose he runs 5 hours in one week.
We know that
• Ethan burns 650 calories per hour.
If he runs 5 hours we just have to multiply this time with the given rate.
[tex]650\cdot5=3,250[/tex]Therefore, Ethan burns 3,250 calories in 5 hours.Suppose that $2000 is invested at a rate of 2.8%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 5 years.Do not round any intermediate computations, and round your answer to the nearest cent.
Solution:
Given the amount invested, P; the rate, r, at which it was invested and the time, t, it was invested.
Thus,
[tex]\begin{gathered} p=2000, \\ \\ r=2.8\text{ \%}=0.028 \\ \\ t=5 \end{gathered}[/tex]Then, we would solve for the total amount, A, using the formula;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ Where; \\ n=4 \end{gathered}[/tex]Thus;
[tex]\begin{gathered} A=2000(1+\frac{0.028}{4})^{(4)(5)} \\ \\ A=2000(1.007)^{20} \\ \\ A=2299.43 \end{gathered}[/tex]ANSWER: $2,299.43
Write an equation for a rational function with:
Vertical asymptotes at x = -5 and x =
-6
x intercepts at x = -3 and x = -4
y intercept at 4
Equation for a rational function is 10(x2 + 7x + 12) / (x2 + 11x + 30) = 0.
What is Rational Function?
Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers; they can be found in any field K.
So this will be a rational function with the vertical asymptotes given by the denominators:
(x + 5) and (x + 6).
The x-intercepts will be provided by the numerator,
which will be:
a(x + 3)(x + 4)
The letter an is a constant.
Given that (0,4) is the y intercept, we have:
4 = a(0+3)(0+4) / (0+5)(0+6)
4= 12a / 30
12a = 120
now,
a = 120/12,
a = 10,
and a = 1.
Now,
a(x+3)(x+4) / (x+5)(x+6) = 0
10 (x^2 + 7x + 12) / (x^2 + 11x + 30) = 0
Hence, We have the following equation for a rational function:
10 (x2 + 7x + 12) / (x2 + 11x + 30) = 0.
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on a map where each unit represents one kilometer two marinas are located at p(4,2) and q(8,12). if a boat travels in a straight line from one marina to the other how far does the boat travel. Answer choices: 14 kilometers 2^296 kilometer 2^5 kilometers
Solution
Step 1:
Write the two given points:
p(4,2) and q(8,12)
Step 2
Find the distance between the two points:
[tex]\begin{gathered} Distance\text{ = }\sqrt{(8-4)^2+(12-2)^2} \\ \\ =\text{ }\sqrt{4^2+10^2} \\ \\ =\text{ }\sqrt{16+100} \\ \\ =\text{ }\sqrt{116} \\ \\ =\text{ 2}\sqrt{29} \end{gathered}[/tex]Answer
[tex][/tex]Michael earns (2x3 + 3x) every month. His wife earns (3x2 + 6) every month. x represents the number of days they work in a month. What is the total earnings in a month?2x3 - 3x2 + 3x - 62x3 + 3x2 + 3x + 66x5 + 21x3 + 18x(2x3 + 3x) / (3x2 + 6)
From the question, we can derive the following:
Micheal earns 2x³ + 3x
His wife earns 3x² + 6
If x represents the number of days they work, in a month, we are asked to find the total earnings in a month.
So we will have:
(2x³ + 3x) + (3x² + 6)
Adding up the two earnings:
2x³ + 3x² + 3x + 6
So, (2x³ + 3x² + 3x + 6) is the total earnings in a month.
So the correct answer is the second option wich is (2x³ + 3x² + 3x + 6).
New York City is a popular field trip destination. This year the senior class at High School A and
the senior class at High School B both planned trips there. The senior class at High School A
rented and filled 2 vans and 6 buses with 244 students. High School B rented and filled 4 vans
and 7 buses with 298 students. Every van had the same number of students in it as did the buses.
Find the number of students in each van and in each bus.
There are eight students in each van and 38 students are in each bus.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
Let the number of students fit into a van would be v
And the number of students fit into a bus would be b
School A:
2v + 6b = 244 ...(i)
2v = 244 - 6b
v = 122 - 3b
School B:
4v + 7b = 298 ...(ii)
Substitute the value of v = 122 - 3b in the equation (ii),
4(122 - 3b) + 7b = 298
Solve for b to get b = 38.
Substitute the value of b = 38 in equation (i),
2v + 6(38) = 244
2v + 228 = 244
2v = 16
v = 8
Therefore, eight students are in each van and 38 students are in each bus.
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80% of _ = 20?4-4-4-
Let
x -----> the missing number
we know that
80%=80/100=0.80
so
0.80x=20
solve the linear equation for x
Divide by 0.80 both sides
x=20/0.80
x=25
the answer is 25
A plane intersects both bases of a cylinder, passing through the center of each baseof the cylinder. What geometric figure will be formed from this intersection?
When a plane intersects both bases of a cylinder, passing through the center of each base of the cylinder, the cross section formed is a rectangle.
Tasty Subs acquired a food-service truck on October 1, 2024, for $23,100. The company estimates a residual value of $1,500 and a six-year service life. Required:Calculate depreciation expense using the straight-line method for 2024 and 2025, assuming a December 31 year-end.
The company estimates a residual value of $1,500 and a six-year service life.
It is given that,
Cost of truck delivery = $ 23100
Salvage value = $ 1500
Useful life = 6 years
Depreciation expenses by using the straight-line method are calculated as,
[tex]Depreciation\text{ expenses p.a = }\frac{cost\text{ - salvage value }}{useful\text{ life}}[/tex]Substituting the value in the formula,
[tex]\begin{gathered} Depreciation\text{ expenses p.a = }\frac{23100\text{ - 1500}}{6} \\ Depreciation\text{ expenses p.a = }\frac{21600}{6} \\ Depreciation\text{ expenses p.a = 3600} \end{gathered}[/tex]Thu
Leila triples her recipe that calls for 2/5 of a cup of flour. Leila has 1 cup of flour. Does she have enough to triple her recipe?
no
yes
Answer:
No
Step-by-step explanation:
3 × [tex]\frac{2}{5}[/tex] = [tex]\frac{6}{5}[/tex] = 1 [tex]\frac{1}{5}[/tex] cups required to triple her recipe
she only has 1 cup
so does not have enough to triple her recipe
Answer:
No
Step-by-step explanation:
If she triples it that means you need to triple the 2/5 so she would neew 6/5 of flour which is 1/5 more than what she has.
10 of 25Jackie and Ruth both studied very hard for their history test. Ruth studied 2 hours less than twice as many hours as Jackie.Together,"heir study time was 10 hours. How many hours did Ruth study for her history test?
Answer: 6 hours
Explanation:
We have that "Ruth studied 2 hours less than twice as many hours as Jackie". I will call the hours that Ruth studied "R" and the hours that Jackie studied "J". The first equation is as follows:
[tex]R=2J-2[/tex]The hours that Ruth studied as 2 less than twice as many as Jackie. This will be referred to as equation 1.
Now, we are told that "Together, their study time was 10 hours" so we have the following equation:
[tex]R+J=10[/tex]This will be our equation 2.
The next step is to substitute equation 1 into equation 2:
[tex]2J-2+J=10[/tex]And we solve for J.
Combining like terms:
[tex]3J-2=10[/tex]We add +2 on both sides of the equation to cancel the -2 on the left side:
[tex]\begin{gathered} 3J-2+2=10+2 \\ 3J=12 \end{gathered}[/tex]And we divide both sides by 3:
[tex]\begin{gathered} \frac{3J}{3}=\frac{12}{3} \\ \\ J=4 \end{gathered}[/tex]Jackie studied for 4 hours.
Since we are asked for Ruth, we substitute J=4 into the equation 1:
[tex]\begin{gathered} R=2J-2 \\ R=2(4)-2 \\ R=8-2 \\ R=6 \end{gathered}[/tex]Ruth studied for 6 hours.
Find the lateral surface area and volume of the object in picture below
So first of all we have to find the lateral surface of the truncated pyramid. This surface is composed of 4 equal trapezoids. The are of a trapezoid is given by half the sum of its bases multiplied by its height. The large base of these faces are 6' long, the short base are 5' long and their height are 2.1' long. Then the area of each trapezoid is:
[tex]\frac{(6^{\prime}+5^{\prime})}{2}\cdot2.1^{\prime}=11.55in^2[/tex]Then the total lateral surface is:
[tex]11.55in^2\cdot4=46.2in^2[/tex]Then we need to find the volume of the truncated pyramid. This is given by the following formula:
[tex]\frac{1}{3}h(a^2+ab+b^2)[/tex]Where a and b are the bottom and top side of its two square faces and h is the height of the pyramid i.e. the vertical distance between bases. The lengths of the bases is 5' and 6' whereas the height of the pyramid is 2' then its volume is given by:
[tex]\frac{1}{3}\cdot2^{\prime}\cdot(5^{\prime2}+6^{\prime}\cdot5^{\prime}+6^{\prime2})=60.7in^3[/tex]In summary, the lateral surface is 46.2in² and the volume is 60.7in³.
The change in the value of a stock is represented by the rational number -5.90 describe in words what this means
The change in the value of a stock which is represented by the rational number -5.90 means that the stock decreased by 5.90 units.
Whenever we use negative value to describe change, it means that the value of that particular entity that been decreased by that number.
On the contrary, If we are using positive value to describe change, it means that the value of that particular entity that been increased by that number.
For example:- The change in total money possessed by Daniel is $ 50 means there is an increase of $ 50 in the money with Daniel.
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Hello, I need help completing this math problem. I will include a picture. Thank you so much!
From the given picture, we can see that the figure is a right triangle, so we can apply Pythagorean theorem, that is,
[tex]5^2+8^2=x^2[/tex]where x denotes the missing length. Then, our equation give us
[tex]\begin{gathered} x^2=25+64 \\ x^2=89 \end{gathered}[/tex]By taking square root to both side, we have
[tex]\begin{gathered} x=\sqrt[]{89} \\ x=9.4339 \end{gathered}[/tex]Therefore, by rounding this result to the nearest tenth, the answer is 9.4 ft
David had $350. After shopping, he was left with $235. If c represents the amount he spent, write an equation to represent this situation. Then use the equation to find the amount of money David spent.(Not sure if I'm expressing this correctly.)c = amount spent350 - c = 235c= 115
Given:
David had $350. After shopping, he was left with $235.
Required:
If c represents the amount he spent, write an equation to represent this situation. Then use the equation to find the amount of money David spent.
Explanation:
We know c is the amount spent
So,
Available amount = Total amount - spent amount
235 = 350 - c
c= 350 - 235
c = 115
Answer:
Hence, David spent $115.
which number is 5 more than 8009998
A number which is 5 more than 8009998 is 8010003
In this question we need to find a number which is 5 more than 8009998.
Let x be a number which is 5 more than 8009998.
We get the required number by adding 5 to 8009998.
so, we write it down as:
x = 8009998 + 5
x = 8010003
Therefore, a number which is 5 more than 8009998 is 8010003
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Line k contains the points (-9,4) and (9,-8) in the xy-coordinate plane. What are the two other points that lie on line k?
Answer
D. (-3, 0) and (3, -4)
Explanation
Let the coordinate of the points be A(-9, 4) and B(9, -8).
We shall look for the gradient m of line using
m = (y₂ - y₁)/(x₂ - x₁)
Substitute for x₁ = -9, y₁ = 4, x₂ = 9 and y₂ = -8
m = (-8 - 4)/(9 - -9) = -12/18 = -2/3
From option A - D given, only C and D would have the same gradient of -2/3 as line AB
To know the correct option, we shall look for the equation of the line AB, that is,
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
(y - 4)/(x - -9) = (-8 - 4)/(9 - -9)
(y -4)/(x + 9) = -12/18
(y - 4)/(x + 9) = -2/3 -----------*
Between option C and D, only D satisfies the equation *
That is, using (-3, 0), we have (0 - 4)/(-3 + 9) = -4/6 = -2/3
Also, using (3, -4), we have (-4 - 4)/(3 + 9) = -8/12 = -2/3
Give the first four terms of the geometric sequence for which A1 = -7 and r = -4.07 7 7 74, 16, 64, 256 -7,28, -112, 448 -7, -11, -15, -1928. -112, 448. - 1792
Given:
[tex]\begin{gathered} firstterm(a_1\text{) = -7} \\ \text{common ratio (r) = -4} \end{gathered}[/tex]Required: First four terms
The nth term of a geometric sequence :
[tex]a_{n\text{ }}=a_1\text{ }\times r^{n-1}[/tex]Hence, we can obtain the next four terms by substituting
[tex]\begin{gathered} \text{when n = 1, a}_1\text{ = -7} \\ n=2,a_2\text{ =-7 }\times(-4)^{2\text{ - 1}} \\ a_2\text{ = -7 }\times\text{ -4} \\ =\text{ 28} \\ \\ \text{when n =3, a}_3\text{ = -7 }\times(-4)^{3\text{ -1 }} \\ a_3\text{ = -7 }\times\text{ 16} \\ =\text{ -112} \\ \\ \text{when n = 4, a}_4\text{ = }-7\text{ }\times(-4)^{4-1} \\ a_4\text{ = -7 }\times\text{ -64} \\ =\text{ 448} \end{gathered}[/tex]2.05x0.004 I know the answer is 0.0082 but when I multiply it myself I get 0.08200?
2 . 0 5 0
0 . 0 0 4
---------------------------------
8 2 0 0
+ 0 0 0 0
0 0 0 0
0 0 0 0
------------------------------
0 . 0 0 8 2 0 0 =
-----------------------------
which of the following liner equations passes through points (-1,5) and (1,5)?
Hence, the correct option is Option D. None of the choices are correct.