He product of two positive numbers is 750. The first number is 5 less than the second number. The equation x(x – 5) = 750 can be used to find x, the value of the greater number. What is the value of the greater number?
Solution
Here the second number is "x"
The first number is "x - 5"
The equation is x (x - 5) = 750
[tex]x^{2}[/tex]- 5x = 750
Subtract 750 from both sides, we get
[tex]x^{2} -5x -750 =0\\[/tex]
Solving the above quadratic equation using quadratic formula, we get
[tex]x = \frac{-b+/- \sqrt{b^{2}-4ac } }{2a}[/tex]
Here we have to plug in a =1, b = -5 and c = -750 in the above formula, we get
[tex]x = \frac{5 +/-\sqrt{3025} }{2}[/tex]
When we simplify the above expression is...
x = 30 and x = -25
x = -25 cannot be the solution since it is negative value.
x = 30 is the solution.
Here "x" represents the second number which is 30, that is the greater number.
Therefore, the answer is 30.
Answer:
30
Step-by-step explanation:
You can try the answer choices to see what works.
15·10 ≠ 750
25·20 ≠ 750
30·25 = 750 . . . . the larger number is 30
50·45 ≠ 750
Geometry help please Two Column Proofs
Tomas buys a trumpet for $108.90. He will make 10 equal payments to pay for the trumpet. What is the amount of each payment that tomas will make?
Tomas will make 10 equal payments of $10.89 each to pay off the total cost of the trumpet which is $108.90.
This question involves simple division, the process of sharing an amount equally. Here, Tomas is dividing the total cost of a trumpet, which is $108.90, into 10 equal payments.
To find the amount of each payment, you simply divide the total cost by the number of payments. So, $108.90 divided by 10 gives us $10.89. Therefore, each payment Tomas will make for his trumpet is $10.89.
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Final answer:
Tomas will make 10 equal payments of $10.89 each to pay for the trumpet that costs $108.90 in total.
Explanation:
Tomas buys a trumpet for $108.90 and plans to make 10 equal payments to pay off the full amount. To find the amount of each payment, we divide the total cost by the number of payments. So, we calculate $108.90 ÷ 10, which results in each payment being $10.89. Therefore, each payment Tomas will make is $10.89.
A father leaves his money to his four children the first received 1/3 the second received 1/6 and the third received 2/5 how much did the remaining child receive
Answer:
The remaining child got a fraction of [tex]\frac{1}{10}[/tex].
Step-by-step explanation:
Lets take the fraction of the money fourth child got is [tex]x[/tex]
Addition of all these fractions should be equal to 1.
⇒[tex]\frac{1}{3} +\frac{1}{6} +\frac{2}{5} +x=1[/tex]
⇒[tex]\frac{10+5+12+30x}{30} =1[/tex] (Taking a common denominator)
⇒[tex]\frac{27+30x}{30} =1[/tex]
⇒[tex]27+30x=30[/tex]
⇒[tex]30x=3[/tex]
⇒[tex]x=0.1[/tex]
Therefore,
The remaining child got a fraction of [tex]\frac{1}{10}[/tex].
By calculating the combined fractions of the inheritance received by the first three children, we've determined that 27/30 of the inheritance has been allocated. Subtracting this from the whole leaves us with 3/30, which simplifies to 1/10 of the inheritance for the remaining child.
The student has asked about how much the remaining child will receive from a father's inheritance if the first received 1/3, the second received 1/6, and the third received 2/5 of the inheritance. To answer this, let's first add up the portions of the inheritance that the first three children received:
First child: 1/3
Second child: 1/6
Third child: 2/5
Now, we will find a common denominator to add these fractions. The least common multiple of 3, 6, and 5 is 30. Let's convert each fraction:
First child: 1/3 = 10/30
Second child: 1/6 = 5/30
Third child: 2/5 = 12/30
Now, add these fractions:
10/30 + 5/30 + 12/30 = 27/30
Once we add up these portions, we get 27/30 which represents the total part of the inheritance that has been given out to the first three children. To find out the portion for the remaining child:
30/30 (the whole inheritance) - 27/30 (the part given away) = 3/30
Reducing the fraction 3/30 gives us 1/10. So, the remaining child would receive 1/10 of the inheritance.
The population p (in millions) of Italy from 1990 through 2008 can be approximated by the model p=56.8e^o.oo15t , where t represents the year with t=0 corresponding to 1990
-Find the populations of Italy in 2000 and 2008
-Use the model to predict the populations of Italy in 2015 and 2020
Answers:
Year 2000: 57.7 millionsYear 2008: 58.4 millionsYear 2015: 59.0 millionsYear 2020: 59.4 millionsExplanation:
The given model provides a function that allows to approximate the population of Italy from 1990 through 2008 and predict the populations for other years, assuming validity of the same model over the coming years.
You only need to convert the year into the variable t and subsitute in the model.
1. Calculate t for every year of your interest:
Year t = year - 1990
1990 1990 - 1990 = 0 (initial value)
2000 2000 - 1990 = 10
2008 2008 - 1990 = 18
2015 2015 - 1990 = 25
2020 2020 - 1990 = 30
2. Calculate the population as per the model:
[tex]p = 56.8e^{0.0015(10)}=57.7[/tex]
t = 18[tex]p = 56.8e^{0.0015(18)}=58.4[/tex]
t = 25[tex]p = 56.8e^{0.0015(25)}=59.0[/tex]
t = 30[tex]p = 56.8e^{0.0015(30)}=59.4[/tex]
A store is selling candy for $8 for 16 bags. How much will it cost if you need to have 84 bags?
What is the contrapositive of the statement “If a polygon is a square, then it has four right angles.”
Answer:
If a polygon has not got four right angles then it is not a square.
Step-by-step explanation:
Contrapositive is
if A implies B then not B implies not A.
Alexis received an 85,89, and 92 on three tests. How many points does she need to score on her next test in order to have an average of at least 90?
94
for her average to be at least 90 then letting x be the score she requires on her next test, then
[tex]\frac{85+89+92+x}{4}[/tex] = 90 ( solve for x )
multiply both sides by 4 to eliminate the fraction
85 + 89 + 92 + x = 360
266 + x = 360 ( subtract 266 from both sides )
x = 94
A company can sell 2000 magazine subscriptions at $40 each. For each $5 increase in the price, it will sell 200 fewer subscriptions. What subscription price will provide the maximum revenue for the company?
$55
$40
$45
$50
ANSWER
The subscription price of $45 provides the maximum revenue for the company
EXPLANATION
When the price is $[tex]40[/tex], the company sells [tex]2000[/tex] quantities.
The total revenue accrued
[tex]=40\times2000[/tex]
[tex]=$80,000[/tex]
When the price increases to $[tex]45[/tex] the quantity sold will decrease by 200 magazines which is [tex]2000-200=1800[/tex]
The total revenue accrued
[tex]=45\times 1800[/tex]
[tex]=81000[/tex] dollars
When the price increases to $[tex]50[/tex] the quantity sold will decrease by 200 magazines again which is [tex]1800-200=1600[/tex]
The total revenue accrued
[tex]=50\times 1600[/tex]
[tex]=80000[/tex] dollars
When the price increases to $[tex]55[/tex] the quantity sold will decrease by 200 magazines which is [tex]1600-200=1400[/tex]
The total revenue accrued
[tex]=55\times 1400[/tex]
[tex]=77000[/tex] dollars
Hence a subscription price of $45 provides the maximum revenue for the company.
Your local radio station is having their yearly music player and concert ticket giveaway. For one minute, every 5^\text{th}5 th 5, start superscript, t, h, end superscript caller will win a music player and every 7^\text{th}7 th 7, start superscript, t, h, end superscript caller will win concert tickets. You were just the first caller to win both a music player and concert tickets! What number caller were you?
Answer:
You were the 35th caller.
Step-by-step explanation:
For one minute, every 5th caller will win a music player and every 7th caller will win concert tickets.
If you were just the first caller to win both a music player and concert tickets, that means we need to find a least number which is divisible by both 5 and 7.
Actually we will find the LCM(Least common multiple) of 5 and 7.
[tex]5=1*5\\ \\ 7=1*7\\ \\ So, LCM = 1*5*7=35[/tex]
That means, you were the 35th caller.
Answer:
35
Step-by-step explanation:
A toy company has determined that the revenue generated by a particular toy is modeled by the following equation: 10x - 0.025x² The variable x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars. What is the maximum revenue the company can earn with this toy?
Answer:
Maximum revenue = 1000 thousands of dollars.
Explanation:
We have the revenue equation [tex]r(x)=10x - 0.025x^2[/tex], where x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars.
At maximum revenue the derivative of equation is zero
So, [tex]r'(x)=0\\ \\10 - 0.025*2x=0\\ \\ x=10/0.05\\ \\ x=1000/5=200[/tex]
So maximum revenue is when 200 thousands of toys are produced.
Maximum revenue, [tex]r(200)=10*200 - 0.025*200^2\\ \\ r(200)=1000[/tex]
Maximum revenue = 1000 thousands of dollars.
Least common multiple of 26,39 using prime factorization
26 is a multiple of 2 but 39 isn't
39 is a multiple of 3 but 26 isn't
Dividng by the next three prime numbers, neither 26 nor 39 is a multiple of 5, 7, or 11
Moving up to the sixth prime number (13), we see that BOTH 26 and 39 are divisible by 13. 26 = 2 * 13 and 39 = 3 * 13 and 13 is the lowest common multiple of 26 and 39.
HELP HELP HELP DUE TODAY PLEASEEE WILL GIVE ANYTHING
What is the recursive rule for the sequence?
4.4, 5.8, 7.2, 8.6, 10, …
an=an−1−1.4 , where a1=4.4
an=an+1+1.4 , where a1=4.4
an=an+1−1.4 , where a1=4.4
an=an−1+1.4 , where a1=4.4
Answer:
a_n=a_(n−1)+1.4 , where a_1=4.4
Step-by-step explanation:
Given a sequence as
4.4, 5.8, 7.2, 8.6, 10, …
We find that first term is 4.4
II term = 5.8 = 4.4+1.4
III term = 7.2 = 5.8+1.4
Iv term = 8.6 = 7.2+1.4
V term = 10.0 = 8.6+1.4
i.e. each term is got by adding 1.4 to the previous term.
In other words, this is an arithmetic sequence with I term =4.4 and d = common difference =1.4
I term = a_1 = 4.4
and a_2 = a_1+1.4 and so on.
Hence correct answer is
a_n=a_(n−1)+1.4 , where a_1=4.4
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
A cleaning company charges x dollars per hour to clean floors and y dollars per hour to clean the rest of a house.
• When the company spends 2 hours to clean floors and 3 hours to clean the rest of a house, the total charge is $80.
• When the company spends 1 hour to clean floors and 4 hours to clean the rest of a house, the total charge is $100.
Which ordered pair represents the hourly charges to clean floors and to clean the rest of the house?
A) (2, 12)
B) (4, 24)
C) (12, 2)
D) (24, 4)
The answer is b. I see you got it. You are welcome.
Find the value of k so that 48x-ky=11 and (k+2)x+16y=-19 are perpendicular lines.
Answer: k = -1 +/- √769
Step-by-step explanation:
48x - ky = 11
-48x -48x
-ky = -48x + 11
[tex]\frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}[/tex]
[tex]y =\frac{48x}{k} - \frac{11}{k}[/tex]
Slope: [tex]\frac{48}{k}[/tex]
*************************************************************************
(k + 2)x + 16y = -19
- (k + 2)x -(k + 2)x
16y = -(k + 2)x - 19
[tex]\frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}[/tex]
[tex]y = -\frac{(k + 2)x}{16} - \frac{19}{16}[/tex]
Slope: [tex]-\frac{(k + 2)}{16}[/tex]
**********************************************************************************
[tex]\frac{48}{k}[/tex] and [tex]-\frac{(k + 2)}{16}[/tex] are perpendicular so they have opposite signs and are reciprocals of each other. When multiplied by its reciprocal, their product equals -1.
[tex]-\frac{(k + 2)}{16}[/tex] * [tex]\frac{k}{48}[/tex] = -1
[tex]\frac{(k + 2)k}{16(48)}[/tex] = 1
Cross multiply, then solve for the variable.
(k + 2)(k) = 16(48)
k² + 2k - 768 = 0
Use quadratic formula to solve:
k = -1 +/- √769
HELP giving BRAINLIEST !!!!
One question before I give my answer , Where did it say she stopped?
Answer:
ohhhh cool i go to the same school
Step-by-step explanation:
What is greater one inch or one centimeter
One inch is greater than centimeter
Yuri has 36 crayons he gives 12 to carl yuri wants to know how many crayons are left
Romona is asked to draw a tree using a scale of 1 inch 3 meters she drwas a 4 inch tree how tall is the tree
1 inch : 3 meters
x 4 x 4
4 inch : 12 meters
Answer: 12 meters
60 POINTS FOR THE THISS!!!
Does the following table show a proportional relationship between the variables x and y?
There is a certain pattern:
As x is increased by 1/4 every time, y is increased by 3 every time. You can make a proper ratio and set up proportions with these numbers.
Francesca spent 45 minutes on the internet yesterday if this is 5/6 of the time she spent on the computer,how long did she spend on the computer but not on the internet?
Answer:
37.5
Step-by-step explanation:
x= time not spent on the internet while on the computer
5/6 = 45/x
45*6/5 = x
This is the equation you should use
Please help me
10 points
Answer:
see below
Step-by-step explanation:
The following definitions apply:
if p, then q . . . . conditional statement
if q, then p . . . . converse
if ~p then ~q . . . inverse
if ~q then ~p . . . contrapositive
You have ...
p = "it is October 31"
q = "it is Halloween"
(a) The converse is ...
If it is Halloween, then it is October 31.
(b) The inverse is ...
If it is not October 31, then it is not Halloween.
(c) The contrapositive is ...
if it is not Halloween, then it is not October 31.
Find the first three terms of the sequence described by the following recursive formula:
an = 3an – 1 + 2 where a4 = 20
a1=
a2=
a3=
Answer:
a1= -2/9
a2= 4/3
a3= 6
Step-by-step explanation:
[tex]a_n = 3a_{n - 1} + 2[/tex]
a_4= 20
lets plug in 4 for n
[tex]a_4 = 3a_{4 - 1} + 2[/tex]
[tex]20= 3a_3+ 2[/tex]
Subtract 2 from both sides and then divide by 3
18 = 3a_3
[tex]6=a_3[/tex]
lets plug in 3 for n and use a3=6 to find a2
[tex]a_3 = 3a_{3 - 1} + 2[/tex]
[tex]6= 3a_2+ 2[/tex]
Subtract 2 from both sides and then divide by 3
4 = 3a_2
[tex]\frac{4}{3}=a_2[/tex]
lets plug in 2 for n and find out a1
[tex]a_2 = 3a_{2 - 1} + 2[/tex]
[tex]\frac{4}{3}= 3a_1+ 2[/tex]
Subtract 2 from both sides and then divide by 3
[tex]\frac{-2}{3}= 3a_1[/tex]
[tex]\frac{-2}{9}=a_1[/tex]
At a pet store ,davina counted 12parrots out of 20 birds ,which is an equivalent ratio of parrots to birds at the pet store
Every 3 Parrots there will be 5 Birds
3/5
Answer:
Every 3 Parrots there will be 5 Birds
3/5
Step-by-step explanation:
item 6 for what value of a is 8x−8+3ax=5ax−2a an identity?
Let's rewrite the expression as
[tex] 8x+3ax-5ax = 8-2a \iff 8x - 2ax = 8-2a \iff 2x(4-a) = 2(4-a) [/tex]
So, if [tex] a \neq 4 [/tex], you may divide both sides by [tex] 4-a [/tex], the equation becomes [tex] 2x=2 [/tex], and the only solution is [tex] x=1 [/tex], which means that this is not an identity (an indentity is tautologically true, no matter the value of x).
If instead [tex] a = 4 [/tex], you are multiplying both sides by zero, so the equation becomes
[tex] 2x \cdot 0 = 2 \cdot 0 \iff 0=0 [/tex]
So, it doesn't matter which value for x you choose, because you will always end up with [tex] 0=0 [/tex], which is obviously always true.
Please Help It Is Past Due!
Prove the Pythagorean Theorem using similar triangles. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse. Be sure to create and name the appropriate geometric figures.
Explanation:
First we consider ΔABC and ΔBCD,
∠C=∠C (common)
∠B=∠D=[tex]90\textdegree[/tex]
So, ΔABC ≈ ΔBCD (By AA similarity rule )
So by taking corresponding sides in ratios we get
[tex]\frac{AB}{BD}=\frac{AC}{BC}=\frac{BC}{CD}[/tex]
Now
[tex]AC.CD=BC.BC\\BC^{2} =AC.CD[/tex] -------- Eqn (1)
Similarly,
We consider ΔABD and ΔABC
∠A=∠A (Commom)
∠B=∠D=[tex]90\textdegree[/tex]
So,
ΔABD ≈ ΔABC (By AA similarity rule )
So by taking corresponding sides in ratios we get
[tex]\frac{BC}{BD}=\frac{AC}{AB}=\frac{AB}{AD}[/tex]
Now,
[tex]AB.AB=AC.AD\\AB^{2} =AC.AD[/tex] --------Eqn (2)
By Adding both the equation we get
[tex]AB^2+BC^2=AC.CD+AC.AD\\AB^2+BC^2=AC(CD+AD)\\AB^2+BC^2=AC.AC\\AB^2+BC^2=AC^2[/tex]
Hence, we proved the pythagorean theorem by using similarity of triangle.
HELP WILL GIVE BRAINLIEST! 45 POINTS IF YOU GIVE CORRECT ANSWER!!!!
Among the following arithmetic operations, which could the symbol □ represent given that the equation is (2□1)4+(6□3)2=10
1. Addition
2. Subtraction
3. Division
It would be subtraction because 2-1 would result into 1 multiplied by 4 would make 4 your answer. And then 6-3 would equal to 3, multiply 3 by 2, you would get 6. Then finally when you add both 4 and 6, you would get the final answer of 10.
What is the LCM of 2x, 3y, and 4z?
12xyz
24xyz
8xyz
4xyz
LCM(2, 3, 4) = 12
LCM(x, y, z) = xyz
therefore
LCM(2x, 3y, 4z) = 12xyz
the LCM is 4xyz.
The Least Common Multiple (LCM) of expressions 2x, 3y, and 4z is calculated by finding the smallest power of each individual variable and prime number base that can be divided evenly by each of the expressions. In this case, we have different variables and numerical coefficients. We must take the highest power of each distinct variable and multiply it by the highest coefficient from the numbers given to find the LCM.
Since 2, 3, and 4 are the coefficients, the highest among them is 4. We will use this and multiply by each of the variables x, y, and z. So, the LCM is 4xyz.
please help asap 30 pts
x - length of side of a square
A perimeter of a square: P = 4x
We know:
20 ≤ P ≤ 32
20 ≤ 4x ≤ 32 |divide by 4
5 ≤ x ≤ 8
Answer: b. 5 ≤ x ≤ 8
Answer:
ans in b
Step-by-step explanation:
Joyce is helping her aunt create craft kits. Her aunt has 138 pipe cleaners, what is the total numher of craft kits they can make?
Answer:
138 pipe cleaners can make 23 kit
Step-by-step explanation:
6 pipe cleaners = 1 kit
1 pipe cleaner = 1/6 kit
138 pipe cleaners = 1/6 x 138
138 pipe cleaners = 23
A line goes through the points (-6, -8) and (12, 7).
a) What is the slope of the line? Show your work
b) Write the equation of the line in point-slope form. Show your work
c) Write the equation of the line in slope-intercept form. Show your work.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have (-6, -8), (12, 7).
Substitute:
[tex]m=\dfrac{7-(-8)}{12-(-6)}=\dfrac{7+8}{12+6}=\dfrac{15}{18}=\dfrac{5}{6}[/tex]
The slope-point form:
[tex]y-y_1=m(x-x_1)[/tex]
We have m = 5/6 and (12, 7).
Substitute:
[tex]y-7=\dfrac{5}{6}(x-12)[/tex]
The slope-intercept form:
[tex]y=mx+b[/tex]
[tex]y-7=\dfrac{5}{6}(x-12)\\\\y-7=\dfrac{5}{6}x-\dfrac{5}{6}\cdot12}\\\\y-7=\dfrac{5}{6}x-\dfrac{5}{1}\cdot2\\\\y-7=\dfrac{5}{6}x-10\qquad|+7\\\\y=\dfrac{5}{6}x-3[/tex]