Answer:
The minimal number for the objective function P =20x+16y is: 780
The value of x then is: 15
and the value of y then is : 30
Step-by-step explanation:
We are given a system of inequalities as:
y is less than or equal to 2x
i.e. y ≤ 2x--------(1)
x + y is greater than or equal to 45
i.e. x+y ≥ 45 ------------(2)
and x is less than or equal to 30.
i.e. x ≤ 30 -----------(3)
On plotting these inequalities we get the boundary points as:
(15,30) , (30,60) and (30,15)
( Since, the optimal solution always exist at the boundary point )
The optimal function is given by:
Minimize P = 20x+16y
Hence, at (15,30) we get:
P= 780
at (30,60) we get:
P= 1560
at (30,15) we get:
P= 840
This means that the minimal value of the function is 780
and the value exist at (15,30)
Answer this please, thank you !
Answer:
m∠ADC=55°
Step-by-step explanation:
step 1
Find the value of x
we know that
m∠CDE+m∠EDF=180° ----> by supplementary angles (form a linear pair)
substitute the given values
[tex](2x+1)\°+(x-7)\°=180\°[/tex]
solve for x
[tex]2x+x=180+6[/tex]
[tex]3x=186[/tex]
[tex]x=62[/tex]
step 2
Find the measure of angle ∠ADC
we know that
m∠ADC=m∠EDF ----> by vertical angles
m∠EDF=(x-7)°
substitute the value of x
m∠EDF=(62-7)°=55°
therefore
m∠ADC=55°
Simplify 34x+13xy+12y
Answer:
Step-by-step explanation:
47x+12y
The animal shelter charges $119 to adopt a pet. On Saturday, 2 dogs and 7 cats were adopted. How much money did the animal shelter receive from those adoptions?
Mrs. Battle is designing a brick walkway to install in her front yard.
How many square feet of bricks will be needed for the walkway?
A 130
B 122
C 94
D 80
Answer:
B 122
Step-by-step explanation:
just thinking ur her
the total heigh of bill mary and rob is 180 cm bob is twice as tall as bill and mary is 28 cm taller than bill how tall is rob
Answer:
Rob is 76 cm tall.
Step-by-step explanation:
Let b = height of bill.
Let m = height of Mary.
Let r = height of Rob.
"the total heigh of bill mary and rob is 180 cm"
b + m + r = 180 Equation 1
"bob* is twice as tall as bill"
*I think you meant Rob is twice as tall as Bill.
r = 2b
"mary is 28 cm taller than bill"
m = b + 28
Substitue r = 2b and m = b + 28 into Equation 1.
b + b + 28 + 2b = 180
4b + 28 = 180
4b = 152
b = 38
r = 2b
r = 2(38) = 76
Rob is 76 cm tall.
Rob height is 76cm.
Given that,
Total height of Bill, Mary and Rob is 180cm.Rob is twice tall as Bill.Mary is 28cm taller than Bill.We need to find the height of Rob.According to the given data, computation of the data are as follows,
Let Bill height be X, then Rob height is 2X and Mary height is X + 28.
So, X + 2X + X + 28 = 180cm
4X = 180 - 28
X = 152 [tex]\div[/tex] 4
X = 38
Hence, Bill height = X = 38cm
Rob height = 2X = 76cm
Mary height = X + 28 = 66cm
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Which problem
Can we solve with 6x6
Answer:
C. because you would multiply each of the 6 cars by the amount of people it can hold which is 6
How many solutions does the system of equations below have?
y= 3x + 4
y+ 6 = 3x
Answer:
0.
Step-by-step explanation:
If you take these two equations to a graphing calculator, you'll find that they are parallel. I. E. they don't intercept.
A solution to a system of equations is when they intercept, so if they don't intercept, that means no solution.
Answer: No solution
Step-by-step explanation:
The car salesman earns $850 per week plus 20% commission for each car the salesman sells. The salesman sold a used car for $2000 last week, which represents the amount of money the salesman took home? Show Work!
(A) $850.00
(B) $860.00
(C) $1,250.00
(D) $2,850.00
Answer:
The answer is C. $1,250.00
Step-by-step explanation:
850+2,000×20%
First you add 850 and 2,000 and that will turn out to 2,850
2,850×20%
Then you take that 2,850 and multiply it by 20% and that would be 1,250
850+2,000×20%
2,850×20%
1,250
I hope that this helps and may I receive brainliest please
June is 16 less than 11 times the average number of tornado's in december
Answer:
The average number of tornado's in December is 22 and the average number of tornado's in June is 226
Step-by-step explanation:
The complete question is
The average number of tornado's in June is 16 less than 11 times the average number of tornado's in December. If the difference between the average number of tornado's in June and December is 204,determine the average number of tornado's in December and June.
Let
x ----> the average number of tornado's in June
y ----> the average number of tornado's in December
we know that
[tex]x=11y-16[/tex] ---> equation A
[tex]x-y=204[/tex] ----> equation B
solve the system by substitution
substitute equation A in equation B
[tex]11y-16-y=204[/tex]
solve for y
[tex]10y=204+16[/tex]
[tex]10y=220[/tex]
[tex]y=22[/tex]
Find the value of x
[tex]x=11y-16[/tex] ----> [tex]x=11(22)-16=226[/tex]
therefore
The average number of tornado's in December is 22 and the average number of tornado's in June is 226
Which equation has a graph that lies entirely above the x-axis?
Oy= -(x + 7)2 + 7
O y=(x-77²-7
y = (x – 7)2 + 7
y = (x – 7)
Answer:
y = [tex](x-7)^{2}[/tex] + 7Step-by-step explanation:
The graph that will lie above the x-axis will be having only positive values throughout its domain,
So, We have to check which graph is having y > 0 for every x.
y = -[tex](x+7)^{2}[/tex] + 7clearly y will be negative for many values of x , as coefficient of variable is negative.
y = [tex](x-7)^{2}[/tex] - 7Put x = 0, you will get y as negative .
y = [tex](x-7)^{2}[/tex] + 7Since, Square of anything will always be positive , and here constant term is also positive , so, It will always be positive .
Thus, it is having its graph always above x axis.
y = x - 7Put x = 0 , y = -7, which is negative
Answer:
Option C.
Step-by-step explanation:
The vertex form of a parabola is
[tex]y=a(x-h)^2+k[/tex]
where, a is constant, (h,k) is vertex.
If a<0, then it is a downward parabola and if a>0, then it is an upward parabola.
A downward parabola never lies entirely above the x-axis.
First equation is
[tex]y=-(x+7)^2+7[/tex]
It is a downward parabola and vertex is (-7,7).
Second equation is
[tex]y=(x-7)^2-7[/tex]
It is an upward parabola and vertex is (7,-7).
Third equation is
[tex]y=(x-7)^2+7[/tex]
It is an upward parabola and vertex is (7,7).
Fourth equation is
[tex]y=(x-7)[/tex]
It is a linear equation with y-intercept -7.
Only equation 3 is an upward parabola whose vertex lies above the x-axis.
Hence the correct option is C.
Evaluate. 2^−2⋅(12⋅3)−5^3 Enter your answer in the box.
Answer:
-116
Step-by-step explanation:
Answer:
-116
Step-by-step explanation:
2^-2=1/2^2=1/4
5^3=5*5*5=125
12*3=36
-------------------------
1/4(36)-125
9-125=-116
A bean plant grows at a constant rate for a month. After 10 days, the plant is
35 centimeters tall. After 20 days, the plant is 55 centimeters tall.
Which equation models the height of the plant, y, after x days?
A. y+35 = 2(x+10)
B. y - 35 = 2(x - 10)
C. y - 10 = 2(x - 35)
D. y - 35 = 1/2 (x - 10)
Answer:
B. y - 35 = 2(x - 10)
Step-by-step explanation:
The height of the plant, y, after x days could be modeled by the equation
y-y0=k(x-xo) (1),where y0 was the initial height at 'x0'th. day, and k is the constant of proportionality.From equation (1), k could be evaluated as follows:k=(y-y0)/(x-x0) From the problem statement, we may determine k by plugging in the given values, e.g. y0= 35, x0=10, y=55, x=20.Thus,k=(55-35)/(20-10)=2Therefore, the model equation becomesy-35=2(x-10)Answer:
the answer is B
Step-by-step explanation:
solve the equation y=11.3x + 13.8 estimates the amount that businesses will spend, in billion of dollars on a certain business technology where x is the number of years after 2000 for what years will the spending be more than $59 billion where spending will be more than $59 billion more than blank years after 2000
Answer:
Spending will be more than $59 billion more than 4 years after 2000.
Step-by-step explanation:
Given:
[tex]y=11.3x + 13.8[/tex]
x is the number of years.
Business spending is $59 billion.
Hence we can say that y = $59.
Now Substituting the value of y in above equation we will find the value of x in number of years.
[tex]11.3x+13.8=59\\11.3x=59-13.8\\ 11.3x= 45.2\\\\x=\frac{45.2}{11.3} = 4 years.[/tex]
Hence we can say that,
After 4 years after 2000 the spending will be more than $59 billion.
or
Spending will be more than $59 billion more than 4 years after 2000.
The equation demonstrates that the spending will exceed $59 billion more than 4 years after 2000.
Explanation:To solve the problem, we first need to set the equation y = 11.3x + 13.8 to greater than 59, as we are trying to find out when the spending will be more than $59 billion. The equation will therefore be, 11.3x + 13.8 > 59.
Then, we subtract 13.8 from both sides of the equation to isolate the term with x, resulting in 11.3x > 45.2.
Finally, we divide each side by 11.3 to solve for x, which will give us x > 4. Consequently, the spending will be more than $59 billion more than 4 years after 2000.
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£150in the ratio of 4:1
Answer:
£120:£30
Step-by-step explanation:
A ratio of 4:1 is also a ratio of 4x:x, as long as x is not equal to 0.
4x + x = 150
5x = 150
x = 30
4x = 4(30) = 120
4:1 = 120:30
Answer: £120:£30
Julio tenía 2/3 de una tablilla de chocolate en el recreo comió 1/5 que fracción de la tablilla le queda?
Answer:
7/15 de la tablilla de chocolate le va a quedar.
Step-by-step explanation:
2/3 se converte en 10/15
y 1/5 se converte en 3/15
Entonces le va a quedar 10/15-3/15 = 7/15 de la tablilla de chocolate.
Answer:
2/3 - 1/5 = 7/15
Step-by-step explanation:
tienes que obtener denominadores iguales para restar las fracciones para obtener una respuesta. El denominador que tiene 3 y 5 igual es 15. así que tienes que multiplicar 3 por 5 y 5 por 3 y todo lo que hagas abajo deberías hacerlo al number de arriba.
Danielle has $6.65 worth of change in nickels and dimes. If she has 5 times as many nickels as dimes, how many of each type of coin does she have?
Answer:
95 nickels 19 dimes
Step-by-step explanation:
d=dimes
5d=nickels
0.05(5d) + 0.10(d) = 6.65
0.25d + 0.10d = 6.65
0.35d=6.65
Divide by 0.35
d= 19 (19 coins)
19 dimes =$1.9
6.65-1.9= $4.75
Nickels=$4.75
4.75/0.05 = 95 coins
19*5=95
114 coins in total
19*0.10 = 1.9
95*0.05=4.74
4.75+1.9= 6.65
Answer:
There are 19 dimes and 95 nickels
Step-by-step explanation:
Represent the numbers of nickels and dimes by n and d. Then n = 5d.
The value of the nickels is $0.05n and that of the dimes is $0.10d. Together these two amounts come to $6.65:
$0.05n + $0.10d = $6.65.
But n = 5d.
Substituting 5d for n, we get:
$0.05(5d) + $0.10d = $6.65
Combining the two terms on the left, we get:
0.25d + 0.10d = 6.65, or
0.35d = 6.65.
Solving for d, we get d = 6.65/0.35, or d = 19. Since n = 5d, n = 5(19) = 95.
There are 19 dimes and 95 nickels.
The ratio of boys to girls on the bus is 3:2. If there are 18 boys on the
bus, how many girls are on the bus?
Answer:
12 girls 18 boys Total 30 students
Step-by-step explanation
x=number of girls
18/3 = x/2
3x=18*2
3x=36
x=12
Other proof
x= number of groups
3x +2x = 30
5x=30
x=6
3*(6) + 2*(6) = 30
18+12=30
When y is 4, p is 0.5, and m is 2, x is 2. If x varies directly with the product of p and m and inversely with y, which equation models the situation?
When y is 4, p is 0.5, and m is 2, x is 2. If x varies directly with the product of p and m and inversely with y, which equation models the situation?
xpmy=8
xy/pm=8
xpm/y=0.5
x/pmy=0.5
Answer:The equation models the situation is [tex]\frac{x y}{p m}=8[/tex]
Solution:Given that
x is 2, y is 4, p is 0.5, and m is 2
x varies directly with the product of p and m
x varies inversely with y
[tex]\text {Product of } p \text { and } m=p \times m=p m[/tex]
x varies directly with the product of p and m
[tex]=>x \propto p m[/tex] ---- eqn 1
As x varies inversely with y,
[tex]=>x \propto \frac{1}{y}[/tex] ----- eqn 2
From (1) and 2, we can say that
[tex]x \propto \frac{p m}{y}[/tex]
[tex]\Rightarrow x=k \frac{p m}{y}[/tex]
where k is constant of proportionality
[tex]\Rightarrow \frac{x y}{p m}=k[/tex] ---- eqn 3
On substituting given values of x = 2, y = 4, p = 0.5 and m= 2 in eqn (3) we get
[tex]\frac{x y}{p m}=\frac{2 \times 4}{0.5 \times 2}=k[/tex]
[tex]\begin{array}{l}{\frac{x y}{p m}=\frac{8}{1}=k} \\\\ {=>\frac{x y}{p m}=8}\end{array}[/tex]
Hence correct option is second that is [tex]\frac{x y}{p m}=8[/tex]
Answer:
B
Step-by-step explanation:
Factoring a Linear Binomial:
Please include steps:
18+ 6v
Answer:
6(3 + v)
Step-by-step explanation:
Given
18 + 6v ← factor out 6 from each term
= 6(3 + v) ← in factored form
PLEASE HELP ME FAST!
The balance in two separate bank accounts grow each month at different rates. The growth rates for both accounts are represented by the functions f(x)=3^x and g(x)=5x+25. In what month is the f(x) balance greater than the g(x) balance? Show your work!
P.S Whoever gives me a good answer and shows their work I will make as Brainliest!
Answer:
From fourth month onwards, the growth rate of [tex]f(x)[/tex] is greater than that of [tex]g(x)[/tex].
Step-by-step explanation:
Given:
The growth rates of both bank accounts are given as:
[tex]f(x)=3^x\\g(x)=5x+25[/tex]
Now, as per question, we need to find the value of 'x' when the value of [tex]f(x)>g(x)[/tex]. Or,
[tex]3^x>5x+25[/tex]
Now, we can do this by checking the values of 'x' by hit and trial method.
Let [tex]x=1[/tex]. The inequality becomes:
[tex]3^1>5(1)+25\\3>30(False)[/tex]
Let [tex]x=2[/tex]. The inequality becomes:
[tex]3^2>5(2)+25\\9>35(False)[/tex]
Let [tex]x=3[/tex]. The inequality becomes:
[tex]3^3>5(3)+25\\27>40(False)[/tex]
Let [tex]x=4[/tex]. The inequality becomes:
[tex]3^4>5(4)+25\\81>45(True)[/tex]
Therefore, the value of 'x' for which [tex]f(x)>g(x)[/tex] is 4.
So, from the fourth month onwards, the balance in [tex]f(x)[/tex] becomes greater than [tex]g(x)[/tex].
The graphical solution is shown below to support the same.
From the graph, we can conclude that after the 'x' value equals 3.4, the graph of [tex]f(x)[/tex] lies above of [tex]g(x)[/tex]. Hence, [tex]f(x)>g(x)[/tex] for [tex]x>3.4[/tex]
declan ran 500 meters in 5 minutes . calculate the unit rate
Answer:
100 meters in 1 minute
Step-by-step explanation:
500/5=100
To find the unit rate of a question, divide.
500 / 5 = 100
100 meters per minute.
______
Best Regards,
Wolfyy :)
Kyle has a notebook for each of his 13 classes.He puts 5 stickers on each notebook.There are 10 stickers on each sheet.How many sheets of stickers will Kyle need?
13 * 5 = 65
So, he needs 65 stickers
65/10 = 6.5
He will need 7 sheets, but will only use 6 and a half sheets.
Kyle will need to buy 7 sheets of stickers to have enough for all 13 of his notebooks, given that each notebook requires 5 stickers and each sheet contains 10 stickers.
Explanation:Kyle needs a total of 65 stickers for his 13 notebooks, since he puts 5 stickers on each notebook. There are 10 stickers per sheet, so to find out how many sheets Kyle needs, we divide the total number of stickers by the number of stickers per sheet: 65 stickers ÷ 10 stickers/sheet = 6.5 sheets. Since Kyle cannot buy half of a sticker sheet, he will need to buy 7 sheets of stickers to have enough for all his notebooks.
I NEED HELP PLS THIS IS DUE IN 3 HOURS
Factor the following trinomials. (Hint: Solve the equations first.)
x^2−2x−2
and
Factor the following trinomials. (Hint: Solve the equations first.)
x2−6x+4
(these are 2 different problems pls HELP!)
Answer:
Part 1) [tex]x^{2} -2x-2=(x-1-\sqrt{3})(x-1+\sqrt{3})[/tex]
Part 2) [tex]x^{2} -6x+4=(x-3-\sqrt{5})(x-3+\sqrt{5})[/tex]
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
Part 1)
in this problem we have
[tex]x^{2} -2x-2=0[/tex]
so
[tex]a=1\\b=-2\\c=-2[/tex]
substitute in the formula
[tex]x=\frac{-(-2)(+/-)\sqrt{-2^{2}-4(1)(-2)}} {2(1)}\\\\x=\frac{2(+/-)\sqrt{12}} {2}\\\\x=\frac{2(+/-)2\sqrt{3}} {2}\\\\x_1=\frac{2(+)2\sqrt{3}} {2}=1+\sqrt{3}\\\\x_2=\frac{2(-)2\sqrt{3}} {2}=1-\sqrt{3}[/tex]
therefore
[tex]x^{2} -2x-2=(x-(1+\sqrt{3}))(x-(1-\sqrt{3}))[/tex]
[tex]x^{2} -2x-2=(x-1-\sqrt{3})(x-1+\sqrt{3})[/tex]
Part 2)
in this problem we have
[tex]x^{2} -6x+4=0[/tex]
so
[tex]a=1\\b=-6\\c=4[/tex]
substitute in the formula
[tex]x=\frac{-(-6)(+/-)\sqrt{-6^{2}-4(1)(4)}} {2(1)}[/tex]
[tex]x=\frac{6(+/-)\sqrt{20}} {2}[/tex]
[tex]x=\frac{6(+/-)2\sqrt{5}} {2}[/tex]
[tex]x_1=\frac{6(+)2\sqrt{5}}{2}=3+\sqrt{5}[/tex]
[tex]x_2=\frac{6(-)2\sqrt{5}}{2}=3-\sqrt{5}[/tex]
therefore
[tex]x^{2} -6x+4=(x-(3+\sqrt{5}))(x-(3-\sqrt{5}))[/tex]
[tex]x^{2} -6x+4=(x-3-\sqrt{5})(x-3+\sqrt{5})[/tex]
what is 1/6 ÷ -2/9 please
Answer:0.0009
Step-by-step explanation:
Answer:
1/6+−2/9=−1/18
Step-by-step explanation:
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
(16×33)+(−29×22)=?
Complete the multiplication and the equation becomes
318+−418=?
The two fractions now have like denominators so you can add the numerators.
Then:
3+−418=−118
This fraction cannot be reduced.
Therefore:
16+−29=−118
is jonia high risk? explain why
Answer:
Step-by-step explanation:
The Waist to Hip Ratio (WHR) is a ratio commonly expressed as a decimal that has been shown to be a good predictor of possible cardiovascular problems in both men and women. If Jonia has a WHR greater than 1, she is at “high risk” for cardiovascular problems.
Which similarity postulate or theorem can be used to verify that the two triangles shown below are similar?
Answer:
SAS Theorem
Step-by-step explanation:
It would be the SAS theorem because you know 2 sides that have an angle in common on both triangles.
Find the least common multiple of x2 - 4x – 5 and x2 – 3x – 10.
1 (x + 1)(x - 2)(x - 5)
2 (x - 1)(x - 5)(x - 2)
3 (x + 1)(x - 5)(x + 2)
4 (x - 5)(x+ 2)(x - 1)
LCM is 3 (x + 1)(x - 5)(x + 2)
Step-by-step explanation:
Given polynomials are:
x2 - 4x – 5 and x2 – 3x – 10.
Factorizing x^2-4x-5
[tex]x^2-4x-5\\= x^2-5x+x-5\\=x(x-5)+1(x-5)\\=(x+1)(x-5)[/tex]
Factorizing x^2 – 3x – 10
[tex]x^2 -3x -10\\=x^2-5x+2x-10\\=x(x-5)+2(x-5)\\=(x+2)(x-5)[/tex]
Looking at the fators of both polynomials we can see:
The LCM will be the combination of all factors of polynomials. The factor that occurs in both factorization will be written only once
Hence,
LCM is 3 (x + 1)(x - 5)(x + 2)
Keywords: Polynomials, LCM
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There are 16 ounces in one pound.
How many ounces are in 4 pounds?
A. 4
B. 12
c. 20
D. 48
E 64
Answer:
E
Step-by-step explanation:
You just multiply 16 by 4.
There are 16 ounces in one pound.
So, 64 ounces in 4 pounds.
The correct option is E.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
There are 16 ounces in one pound.
In 4 pounds,
= 16 x 4 ounces.
= 64 ounces.
Therefore, 64 ounces in 4 pounds.
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A basketball arena can hold approximately 7,000 people. Fans bought 5,134 tickets before the game. About how many more seats are left to fill before the game.
There are about 1866 seats left to fill before the game.
Step-by-step explanation:
Number of people hold be basketball arena = 7000
Tickets bought by fans = 5134
Seats left to fill = Total capacity of arena - tickets bought by fans
Seats left to fill = [tex]7000-5134[/tex]
Seats left to fill = 1866
There are about 1866 seats left to fill before the game.
Keywords: subtraction
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Complete the square to determine the minimum or maximum value of the function defined by the expression.
x2 − 10x + 15
A) maximum value at −10
B) minimum value at −10
C) maximum value at −15
D) minimum value at −15
Answer:
Option B) minimum value at −10
Step-by-step explanation:
we have
[tex]f(x)=x^{2} -10x+15[/tex]
This function represent a vertical parabola open upward (because the leading coefficient is positive)
The vertex represent a minimum
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)-15=x^{2} -10x[/tex]
Divide the coefficient of term x by 2
10/2=5
squared the term and add to the right side of equation
[tex]f(x)-15=(x^{2} -10x+5^2)[/tex]
Remember to balance the equation by adding the same constants to the other side
[tex]f(x)-15+5^2=(x^{2} -10x+5^2)[/tex]
[tex]f(x)+10=(x^{2} -10x+25)[/tex]
rewrite as perfect squares
[tex]f(x)+10=(x-5)^{2}[/tex]
[tex]f(x)=(x-5)^{2}-10[/tex] ----> function in vertex form
The vertex of the quadratic function is the point (5,-10)
therefore
The minimum value of the function is -10