The prices in dollars at which Nathan can make a profit of at least $471, 000 are $55 and $9
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the profit (P) in thousands for security camera with price of x, hence for a profit of at least $471, 000:
-(x - 32)² + 1000 ≥ 471
-(x² - 64x + 1024) + 1000 ≥ 471
-x² + 64x - 1024 + 1000 - 471 ≥ 0
-x² + 64x - 495 ≥ 0
x = 55 or x = 9
The prices in dollars at which Nathan can make a profit of at least $471, 000 are $55 and $9
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Check all of the functions that are odd. f(x)=x3-x2 f(x)=x5-3x3 2x f(x) = 4x 9 f (x) = startfraction 1 over x endfraction
The odd functions are f(x)=x⁵-3x³+2x and f(x)=1÷x.
Given functions are f(x)=x³-x², f(x)=x⁵-3x³+2x, f(x)=4x+9 and f(x)=1÷x.
A function is said to be odd function if and only if: f(-x) = -f(x)
For every value of x in its domain.
1. f(x)=x³-x²
Substituting -x in this, we get
f(-x)=(-x)³-(-x)²
f(-x)=-x³-x²
From above we see that
f(-x)≠-f(x)
So, this function is not odd.
2. f(x)=x⁵-3x³+2x
Substituting -x in this, we get
f(-x)=(-x)⁵-3(-x)³+2(-x)
f(-x)=-x⁵+3x³-2x
f(-x)=-(x⁵-3x³+2x)
From above we see that
f(-x)=-f(x)
So, this function is odd
3. f(x)=4x+9
Substituting -x in this, we get
f(-x)=4(-x)+9
f(-x)=-4x+9
From above we see that
f(-x)≠-f(x)
So, this function is not odd.
4. f(x)=1÷x
Substituting -x in this, we get
f(-x)=1÷(-x)
f(-x)=-(1÷x)
From above we see that
f(-x)=-f(x)
So, this function is odd.
Hence, the function f(x)=f(x)=x³-x² is not odd, f(x)=x⁵-3x³+2x is odd, f(x)=4x+9 is not odd and f(x)=1÷x is odd.
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Answer:
B.) f(x)=x5-3x3+2x is odd
D.) f (x) = 1/ x is odd
Step-by-step explanation:
just did it on edg
Draw the solution set for each of the following inequalities
Answer:
Step-by-step explanation:
Which of the following is NOT a factor of b3 +6b²?
63
062
Ob
(b + 6)
Answer:
b³
Step-by-step explanation:
The lowest common multiple of the expression is b². This because, taking out a factor of b, b ( b² + 6b ), taking out a factor of b², b² ( b + 6 ),
taking out a factor of ( b + 6 ), ( b + 6 ) b². As a result b² is only the option which is not a factor.
It is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring. True or False
It is a true statement that it is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring.
What is a cubic equation?A cubic equation is one in which the highest power of the variable present is 3. A quartic equation is one in which the highest power is 4. When we have a cubic or a quartic equation, the usual approach is to reduce the equation to a quadratic equation and solve by factorization.
Thus, it is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring.
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Adele is 5 years older than Timothy. In 3 years, Timothy will be 2/3 of Adele’s age. What is Adele’s age.
Answer:
12
Step-by-step explanation:
Let a = Adele's current age
Let t = Timothy's current age
Adele is 5 years older than Timothy:
a = t + 5 {equation 1}
In 3 years Timothy will be 2/3 of Adele's age:
(2/3)(a + 3) = t + 3 {equation 2}
Since we are looking for Adele's age, let's rearrange equation 1 to:
t = a - 5
Substitute that into equation 2 and solve for a.
(2/3)(a+3) = a - 5 + 3
(2/3)(a + 3) = a - 2
Multiply through by 3 to clear the fraction
2(a+3) = 3a - 6
2a + 6 = 3a - 6
Add 6 to both sides, subtract 2a from both sides
12 = a
Adele is 12 years old
This means Timothy is 7 years old.
Check equation 2 to verify:
(2/3)(a + 3) = t + 3
(2/3)(12+3) = 7 + 3
(2/3)(15) = 10
10 = 10
Answer is correct
Brad bought an MP3 player on sale at a 20%
discount from its regular price of $120. If there
is a 5% sales tax that is calculated on the sale
price, how much did Brad pay?
Answer:
$100.8
Step-by-step explanation:
Discount=20% of 120 =24
Before tax: BP=120-24=96
After Tax BP=105% of 96=$100.8
Which proportion is not true?
A. 2/3 = 4/6
B. 5/8 = 25/40
C. 9/10 = 81/90
D. 4/7 = 24/28
Answer:
D. 4/7 = 24/28
Step-by-step explanation:
In any proportion, the value of the numerator and denominator does not change if is multiplied by the same value.
We know that 4*6 = 24, so the numerator holds true. However, 7*6 is 42. In the same vein, 7*4 is 28, so the denominator would hold true. However, 4*4 is 16. Thus, the proportion has not been multiplied by the same value.
In order to get 24/28 from 4/7, you would have to multiply by 6/4, which is not the same value.
Dr. Silas studies a culture of bacteria under a microscope. The function b_1(t)=1200(1.8)^t represents the number of bacteria t hours after Dr. Silas begins her study.
The number of bacteria in a second study is modeled by the function b_2(t)=1000(1.8^t.
What does the value of 1000 represent in this situation?
What does the difference of 1200 and 1000 mean between the two studies?
The _ means the 1&2 is under the b
The value of 1000 represent the initial population of bacteria in the study and the difference of 1200 and 1000 mean difference between the initial populations in the studies.
What are exponential Function ?Exponential functions are are written as y(x) = abˣ
Here
a is the initial population
b is the rate of growth or decrease
x is the time taken
The Given exponential function is
[tex]\rm b_1(t) = 1200( 1.8 )^t\\\\b_2(t) = 1000 (1.8)^t[/tex]
From the standard equation of Exponential function
(a) a = 1200 and 1000 is the initial population of the bacteria
(b)The difference of 1200 and 1000 means the difference between the initial populations in the studies
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The height "h" of a ball thrown straight up with a velocity of 88 ft/s is given by h = -16t^2 + 88t where "t" is the time it is in the air. For how many seconds the ball is in the air before it hits the ground?
Answer:
t=5.5
Step-by-step explanation:
The ball hits the ground when h = 0.
[tex]-16t^2 + 88t = 0 \\ \\ 2t^2 - 11t =0 \\ \\ t(2t-11)=0 \\ \\ t=0, 5.5[/tex]
However, as the answer must be positive, t=5.5
Please help!
P(A) = 1/3
P(B) = 2/9
P(A U B) = 4/9
Find P(A ∩ B).
A. 1
B. 1/3
C. 1/9
D. 20/18
Answer:
[tex]\sf C. \quad \dfrac{1}{9}[/tex]
Step-by-step explanation:
Addition Law for Probability
[tex]\sf P(A \cup B)=P(A)+P(B)-P(A \cap B)[/tex]
Given:
[tex]\sf P(A)=\dfrac{1}{3}=\dfrac{3}{9}[/tex]
[tex]\sf P(B)=\dfrac{2}{9}[/tex]
[tex]\sf P(A \cup B)=\dfrac{4}{9}[/tex]
Substitute the given values into the formula and solve for P(A ∩ B):
[tex]\implies \sf P(A \cup B) = P(A)+P(B)-P(A \cap B)[/tex]
[tex]\implies \sf \dfrac{4}{9} = \sf \dfrac{3}{9}+\dfrac{2}{9}-P(A \cap B)[/tex]
[tex]\implies \sf P(A \cap B) = \sf \dfrac{3}{9}+\dfrac{2}{9}-\dfrac{4}{9}[/tex]
[tex]\implies \sf P(A \cap B) = \sf \dfrac{3+2-4}{9}[/tex]
[tex]\implies \sf P(A \cap B) = \sf \dfrac{1}{9}[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=P(A)+P(B)-P(A\cup B)[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{1}{3}+\dfrac{2}{9}-\dfrac{4}{9}[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{3+2-4}{9}[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{1}{9}[/tex]
Evaluate the expression [tex]\sqrt[5]{3125{e}^{\frac{11 \pi }{2} i}}[/tex], leaving your answer in polar form.
[tex]\sqrt[5]{3125e^{\frac{11\pi}{2}i}}\\=\\\sqrt[5]{3125}\sqrt[5]{e^{\frac{11\pi}{2}}i}\\\\=5e^{\frac{11\pi}{10}i}\\\\\boxed{5\left(\cos \left(\frac{11\pi}{10} \right)+i \sin \left(\frac{11\pi}{10} \right) \right)}[/tex]
Use clustering estimation to find the approximate total in the following question.
What is the estimated total of 674, 692, 724, and 739?
ill make you brainliest
The estimated total of 674, 692, 724, and 739 is: 2800.
Clustering estimation techniqueTo find the sum using clustering estimation technique first step is to round each number to the nearest 10s.
674 into 670
692 into 690
724 into 720
739 into 740
Second step is to add
Addition=670+690+720+740
Addition=2820
2820 to the nearest 100s is 2800.
Therefore the estimated total of 674, 692, 724, and 739 is: 2800.
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Divide 10000 among Irfan and asim in the ratio 2:3
Step-by-step explanation:
ratio of ifran and Asim= I:A
2:3
rule of equation= TOTAL ratio=total amount
=(addition of the two ratios which are 2 and 3=5) and 1000
=5=1000
ratio of ifran(2)=? cross multiplication
=2×1000÷5
=400
=5=1000
ratio of Asim(3)=? cross multiplication
=3×1000÷5
=600
Answer:
Step-by-step explanation:
Irfan and Asim's ratio is 2:3, which means Irfan gets 2 parts while Asim gets 3. There are 5 parts in total, and this equals 10000. Let parts be p. [tex]5p=10000\\\\p=2000[/tex]
This means Irfan gets 2p = 4000 and Asim gets 3p = 6000.
Hope you have a nice day and you really should mark this as the brainliest :)
Assume that each of the n trials is independent and that p is the probability of success on a given trial. Use the binomial probability formula to find P(x).
n=15, x=2, p=5
P(x)=
Using the binomial distribution, it is found that P(X = 2) = 0.0032.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
n = 15, x = 2, p = 0.5.
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{15,2}.(0.5)^{2}.(0.5)^{13} = 0.0032[/tex]
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I want to fence in a square vegetable patch. The fencing for the east and west sides cost $7 per foot, and the fencing for the north and south sides cost $4 per foot. Find the total cost (I'm dollars) of the fencing as a function of the length (in feet) of a side x.
The total cost of the fencing is a function of the length of a side x (feet) is 10x + 14y.
How to find the perimeter?The perimeter is made by adding the south, north, east, and west side.
Given that
The cost of fencing for the east and west sides is $7 per foot, and the cost of fencing for the north and south sides is only $5 per foot.
We have to find total cost of the fencing is a function of the length of a side x (feet).
The east and west fencing cost is $7/ft but the south and north fencing cost is $5/ft.
x = north and south fencing
y = the east and west sides, then you can get this equation.
Total cost= (south +north) × 5 + (east+ west) × 7
Total cost =(x + x) × 5 + (y+ y) × 7
Total cost = 5(2x) + 7(2y)
Total cost = 10x + 14y
Hence, the total cost of the fencing is a function of the length of a side x (feet) is 10x + 14y.
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A discount store had monthly sales of $86,600 and spent 14% of it on promotions. how much was spent on promotion?
The amount spent on promotion by the store on monthly sales of $86,600, when they are spending 14 percent on promotion is $12,124.
The percent signifies the hundredth part of the whole.
When informed that the promotion is 14 percent of the monthly sales of $86,600.
Therefore, to calculate the total amount spent on promotion, we calculate 14 percent of 86600.
Therefore, the total amount on promotion = 14% of $86,600 = $ (14/100 * 86,000) = $ (14*866) = $12,124.
Therefore, the amount spent on promotion by the store on monthly sales of $86,600, when they are spending 14 percent on promotion is $12,124.
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A construction company is building a drainage ditch that is shaped like a "V". The ditch will be 10 feet wide at ground level and 5 feet deep at its lowest point. The depth of the ditch increases at a rate of 1 vertical foot for every 1 horizontal foot out from the lowest point at the center of the ditch .If x is the horizontal distance from the left edge of the ditch, in feet, determine which absolve value function models the ditch's vertical depth below ground level, in feet.
A. f(x) = |x + 5| − 5
B. f(x) = -|x − 5| − 5
C. f(x) = -|x − 5| + 5
D. f(x) = |x − 5| − 5
The absolve value function that models the ditch's vertical depth below ground level, is B. f(x) = -|x − 5| − 5
How to illustrate the function?From the information given, it was stated that the ditch will be 5 feet deep at its lowest point. Also, x is the horizontal distance from the left edge of the ditch.
Now, the absolve value function that models the ditch's vertical depth below ground level will start with a (-) sign since it's below ground level. The appropriate function will be f(x) = = -|x − 5| − 5
In conclusion, the correct option is B.
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Which best describes the relationship between the lines?
2x – y = −1
4x – 2y = 6
same line
perpendicular
neither
parallel
same line preparations
Answer:
Parallel
Step-by-step explanation:
So the best way to compare two lines is to convert it into slope-intercept form which is given in the form of: y=mx+b where m is the slope, and b is the y-intercept, in this form it's really easy to see if they're the same line, parallel, or perpendicular.
Original Equation:
2x - y = -1
Subtract 2x from both sides
-y = -2x - 1
Divide both sides by -1
y = 2x + 1
Original Equation:
4x - 2y = 6
Subtract 4x from both sides
-2y = -4x + 6
Divide both sides by -2
y = 2x - 3
As you can see both equations have a slope of 2, but different y-intercepts, so they're not the same line, but they'll also never intersect, because they increase by the same amount, thus they are parallel
Perform the indicated operation and write the answer in the form a + bi.
(3 +81) (4-3i)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: 36 + 23 i[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: (3 + 8i)(4 - 3i)[/tex]
[tex]\qquad \tt \rightarrow \: (3 \sdot 4)+ (3 \sdot - 3i) + (8i \sdot4) + (8i \sdot - 3i)[/tex]
[tex]\qquad \tt \rightarrow \: 12 - 9i + 32i - (24 {i}^{2} )[/tex]
[tex]\qquad \tt \rightarrow \: 12 + 23i -( 24 \sdot - 1)[/tex]
[tex]\qquad \tt \rightarrow \: 12 + 23i + 24[/tex]
[tex]\qquad \tt \rightarrow \: 36 + 23i[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
[tex]\Large\maltese\underline{\textsf{A. What is Asked \space}}[/tex]
Perform the indicated operation and write the answer with the form a+bi.
2 numbers given, one of which is complex
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!\space\space}}[/tex]
Multiply these two numbers, just like you always multiply binomials.
[tex]\bf{(3+8i)(4-3i)}[/tex] | multiply
[tex]\bf{3\times4+3\times(-3i)+8i\times4+8i\times(-3i)}[/tex] | simplify
[tex]\bf{12-9i+32i-24i^2}[/tex] | this can be simplified A LOT
[tex]\bf{12+23i-24i^2}[/tex] | as strange as it may seem, this can be simplified even more, because isn't i^2 the same as -1?
[tex]\bf{12+23i-24\times(-1)}=12+23i+24}[/tex] | add 12 and 24
[tex]\bf{36+23i}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=36+23i}[/tex]. The answer is written in the form a+bi, as requested.
[tex]\boxed{\bf{aesthetic\not101}}[/tex]
Can someone help me
The value of (g . f) (0) is -2 and the value of (g . f) (1) is 1.
What is a Function?A function is a law that relates a dependent and an independent variable.
The value of the two functions is given
The value of (g . f) (0)
= g(f(0))
From the table of f(x) at x = 0
= g(1)
From the table of g(x) at x =1
=-2
The value of (g . f) (1)
= g(f(1))
From the table of f(x) at x = 1
= g(0)
From the table of g(x) at x =0
=1
Therefore, the value of (g . f) (0) is -2 and the value of (g . f) (1) is 1.
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Find the value of [tex]\frac{1^2+1*2+2^2}{1^3*2^3} + \frac{2^2+2*3+3^2}{2^3*3^3} +...+\frac{9^2+9*10*10^2}{9^3*10^3}
Observe that the [tex]n[/tex]-th term in the sum is
[tex]\dfrac{n^2 + n(n+1) + (n+1)^2}{n^3(n+1)^3} = \dfrac{3n^2 + 3n + 1}{n^3 (n+1)^3} \\\\ ~~~~~~~~ = \dfrac{(n+1)^3 - n^3}{n^3(n+1)^3} \\\\ ~~~~~~~~ = \dfrac1{n^3} - \dfrac1{(n+1)^3}[/tex]
Then the sum telescopes, and we have
[tex]\displaystyle \sum_{n=1}^{9} \frac{n^2 + n(n+1) + (n+1)^2}{n^3 (n+1)^3} = \sum_{n=1}^{9} \left(\frac1{n^3} - \frac1{(n+1)^3}\right) \\\\ ~~~~~~~~ = \left(\frac1{1^3} - \frac1{2^3}\right) + \left(\frac1{2^3} - \frac1{3^3}\right) + \cdots + \left(\frac1{8^3} - \frac1{9^3}\right) + \left(\frac1{9^3} - \frac1{10^3}\right) \\\\ ~~~~~~~~ = \frac1{1^3} - \frac1{10^3} \\\\ ~~~~~~~~ = 1 - \frac1{1000} = \boxed{\frac{999}{1000}}[/tex]
The sum of the series is 999/1000 .
What is a Series ?A series is a sequence of expression in a certain pattern.
The series of n terms is given
[tex]\rm \frac{1^2+1*2+2^2}{1^3*2^3} + \frac{2^2+2*3+3^2}{2^3*3^3} +...+\frac{9^2+9*10*10^2}{9^3*10^3}[/tex]
nth term of the series is given by
[tex]\rm T_n = \rm \dfrac{n^2 + n(n+1)+ (n+1)^2}{n^3*(n+1)^3}[/tex]
On simplification it can be written as
[tex]\rm T_n = \rm \dfrac{3n^2 + 3n+1}{n^3*(n+1)^3}\\\\T_n = \rm \dfrac{3n(n +1)+1}{n^3*(n+1)^3}\\\\\\T_n = \rm \dfrac{ (n +1)^3 - n^3}{n^3*(n+1)^3}\\\\T_n = \rm \dfrac{ 1}{n^3} - \dfrac{1}{(n+1)^3}[/tex]
The sum of terms from 1 to 9 is given by
∑ ( [tex]\rm \frac{ 1}{n^3} - \frac{1}{(n+1)^3}[/tex])
= [tex]\rm \dfrac{1}{1^3} - \dfrac{1}{2^3} + \dfrac{1}{2^3} - \dfrac{1}{3^3}+ .......... + \dfrac{1}{9^3} - \dfrac{1}{10^3}[/tex]
= (1/1³) - (1/10³)
= 999/1000
Therefore the sum of the series given is 999/1000
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Ozzie Foster deposits $2,000 at the end of each year (ordinary annuity) into an Individual Retirement Account at Bishop Bank. The account pays 7% compounded annually. a) How much will be in the account in 25 years? b) If Ozzie had deposited the $2,000 at the beginning of each year (annuity due), how much would be in the account in 25 years?
The ordinary annuity and annuity due as required in the task content are; $126,498.08 and $135, 431.43 respectively.
What is the annuity due?a) The amount which would be in the account in 25 years can be evaluated by means of the annuity factor obtained from the table under column 7% and row 25 years and hence, the value in 25 years would be; $2,000 × 63.24904
= $126,498.08.
b) For the annuity due case; the future value is;
= (1+0.07) × $2000((1+0.07)^(25) - 1)/0.07
= (1.07) × $2000(5.43-1)/0.07
= $135, 431.43.
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find the size of the angles marked with letters in each diagram
enter your answer in scientific notation
Answer:
[tex]1.7x10^{4}[/tex]
Step-by-step explanation:
To divide the scientific notation, divide 5.1 to 3 then subtract the exponents of your ten - following the quotient rule.
5.1/3 = 1.7, then 9-5 = 4
final answer is [tex]1.7x10^{4}[/tex]
HELP ME PLEASE I WILL GIVE POINTS THANK YOU SO MUCH
The angle of X is 108°
Given,
XW ≅ YZ
∠Z = 72°
then ∠X = ?
Properties of trapezoid are:
The base sides are the only pair of sides that are parallel. Other than the base, the remaining sides are all non-parallel and equal in length. The length of the diagonals is constant. the same for the base angles.We know that from the figure that ∠Z = ∠V & ∠W = ∠U
∵ Isosceles trapezoid rule
And sum of all the angles in a trapezoid = 360°
Now, 2 × 72 = 144
∴ 360 ₋ 144 = 216°
Now sum of other two angles = 216°
one angle = 216/2
= 108°
Therefore the angle of ∠X is 108°
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A line is parallel to y = 5x + 3 and
intersects the point (3, 9).
What is the equation of this
parallel line?
y = 5x + [?]
Answer:
y = 5x - 6
Step-by-step explanation:
1. In a linear equation, it is represented by y = mx + b
2. A line parallel to another has the same slope (m) but a different y-intercept (b)
3. So we know that it is y = 5x as the first half. However, we need to find the new y-intercept.
4. Let's plug in the point we know into the equation, and see what amount we are missing (the y-intercept)
5. y = 5(3)
6. y = 15, however, we know that y = 9. That's a difference of -6.
This shows us that the y-intercept is -6 making the full equation:
y = 5x - 6
We can check by putting the point back into the equation:
y = 5(3) - 6
y = 15 - 6
y = 9
This correlates with the original point, we have solved the equation.
Solve the equation on the
interval [0, 2π).
4(sin x)² - 2 = 0
The solutions to the equation on the given interval are;
x = π/4, 3π/4, 5π/4, 7π/4.
What is the solution to the equation on the interval?Given that;
4(sin x)² - 2 = 0Interval = [ 0, 2π )4(sin x)² - 2 = 0
Add 2 to both sides and divide both sides 4
4(sin x)² - 2 + 2 = 0 + 2
4(sin x)² = 2
(4(sin x)²)/4 = 2/4
(sin x)² = 1/2
Square both sides
√((sin x)²) = ±√(1/2)
sin x = ±√(1/2)
sin x = ±(√2)/2
Next, we solve for x
Not that 180° = π
x = sin⁻¹ ( (√2)/2 ) = 45° = 180°/4 = π/4
x = π/4
Since the sine function is positive in the first and second quadrant, we subtract the reference angle from π to find the solution in the second quadrant.
x = π - π/4
x = 3π/4
Now, we find the period of sin x
2π / |b|
We know that, the distance between a number and zero is 1
2π / 1
2π
Hence, period of sin x function is 2π, values will repeat every 2π radians in both direction.
Since sine function is negative in third and fourth quadrant,
x = 2π + π/4 + π
x = 5π/4
Now, add 2π to every negative angle to get a positive angle
x = 2π + ( - π/4 )
x = 2π×4/4 - π/4
x = ((2π × 8) - π ))/4
x = (8π - π)/4
x = 7π/4
Therefore, the solutions to the equation on the given interval are;
x = π/4, 3π/4, 5π/4, 7π/4.
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Rodrick is visiting the local museum exhibit and has a maximum of $30 dollars to spend. The entry ticket cost $7. He can spend g dollars. Write an inequality that can find g and the amount of money Rodrick can spend at the gift shop.
Entry ticket = $7
Gift shop money = $g
Maximum to spend = $30
Inequality => 7+g ≤ 30
Hope it helps!
keiko david and tony have a total of 106$ in their wallets. david has $6 less than keiko tony has 2 times what david has. how much do they have in their wallets? Please help
Keiko have $31 in her wallet.
David have $25 in his wallet.
Tony have $50 in his wallet.
Step-by-step explanation:Keiko
Let x = the amount in Keiko’s wallet.
David
David has $6 less than Keiko .
x - 6
Tony
Tony has has two times what David has.
2(x - 6)
The total sum of their money = 106
Keiko
x + x - 6 + 2(x - 6) = 106
2x - 6 + 2x - 12 = 106
4x - 18 = 106
4x = 106 + 18
4x /4 = 124/4
x = 31
Therefore Keiko have $31 in her wallet.
David
x - 6
31 - 6 = 25
Therefore David have $25 in his wallet.
Tony
2(x - 6)
2(31 - 6)
2(25) = 50
Therefore Tony have $50 in his wallet.
To check your work out
31 + 25 + 50 = 106
Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0
How to determine the equations?The given parameters are:
Length = y
Width = y - 5
Area = 750
The area of a rectangle is:
Area = Length * Width
So, we have:
y * (y - 5) = 750
Expand
y^2 - 5y = 750
Rewrite as:
y^2 - 5y - 750 = 0
Factorize
(y + 25)(y – 30) = 0
Hence, the equations that can be used are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0
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Complete question
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room?