Answer:
ln(60)
Step-by-step explanation:
We have the equation [tex]5e^x=300[/tex]. We can divide both sides of the equation by 5, getting [tex]e^x=60[/tex]. Finally, we can take the natural log of both sides, getting that x is equal to [tex]\ln(60)[/tex].
Which of the following statements is true?
A.
the segment bisects segment
B.
the segment DE bisects segment
C.
the segment is perpendicular to segment
D.
segment is congruent to segment
The correct statement about the line segment is,
⇒ the segment DE bisects segment AC.
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
Triangle ABC is shown in figure.
Now, We can see that;
⇒ AE = EC
Hence, the segment DE bisects segment AC.
Thus, The correct statement about the line segment is,
⇒ the segment DE bisects segment AC.
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Select the correct solution set.
x + 17 ≤ -3
A.{x | x ≤ 14}
B.{x | x ≤ -20}
C.{x | x ≥ -20}
if one tenth of a number is added to 2. the result is half of that number. what is the number?
Answer:
5
Step-by-step explanation:
According to the given question, the calculation of number is shown below:-
Let the number be x.
[tex]\frac{1}{10}[/tex] of x will be added to the number of 2, so that the result is half of x.
[tex]2 + \frac{1}{10} x = \frac{1}{2} x[/tex]
Now we will solve the above equation
[tex]2=\frac{1}{2} x-\frac{1}{10} x\\\\2=\frac{2x}{5}\\\\10=2x\\\\\frac{10}{2} =x\\\\[/tex]
x = 5
Therefore the correct answer is 5
Hence, the number based on the given information provided in the question is 5
Which inequality is shown in this graph?
(0, 2) (-1,-2)
a) y>=-4x+2
b) y>=4x+2
c) y<=-4x+2
d) y<=4x+2
Answer:
B y ≥ 4x + 2
Step-by-step explanation:
1. find slope of the line: (y² - y¹) / (x² - x¹)
(0, 2) and (-1, -2)
(-2 - 2) / (-1 - 0) = -4 / -1 = 4
y = 4x + 2*
*+2 because that is the y-intercept as shown by point (0, 2)
2. the line is solid, therefore the inequality is ≤ or ≥. dashed line would mean < or >
3. the shaded region is on the right side of the line, so the values are greater than. therefore, you use ≥
4. final equation: y ≥ 4x + 2
Edna transferred a balance of $1400 to a new credit card at the beginning of
the year. The card offered an introductory APR of 2.9% for the first 3 months
and a standard APR of 22.1% thereafter. If the card compounds interest
monthly, which of these expressions represents Edna's balance at the end of
the year? (Assume that Edna will make no payments or new purchases during
the year, and ignore any possible late payment fees.)
Answer:
(1400)(1+0.029/12)3(1+0.221/12)9
Step-by-step explanation:
A p e x
Answer:
Step-by-step explanation:
Just so you know how it looks on the page
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an = (n − 2)! n!
Answer: Diverging
Step-by-step explanation:
Find explanations in the attached file
The perimeter of an equilateral triangle with a side length of 12 units is:
Answer:
Hey there!
An equilateral triangle has all sides equal to each other, so the perimeter would be 3x, where x is the length of one side.
Thus, the perimeter for this equilateral triangle would be 3(12)=36
Hope this helps :)
Answer:
[tex]\boxed{Perimeter = 36 \ units}[/tex]
Step-by-step explanation:
Perimeter = sum of all sides
Perimeter = 12 +12 + 12
Perimeter = 36 units
PLEASE PLEASE PLEASE HELP
Answer:
1) 18
2) P
Step-by-step explanation:
1) Multiply the top number by itself and then reverse the digits!
9*9 = 81 reversed is 18
2) Seems to be the number of line ends a letter has when you write it down. P only has one end, at the bottom.
Answer:
P
Step-by-step explanation:
2.
The number of strokes of the letter that come to an end.
The bottom of the A has two sticks that come to an end.
A = 2
The B has no sticks coming to an end.
B = 0
The C and an upper and a lower stroke coming to an end.
C = 2
D has none.
D = 0
E has 3 sticks coming to an end.
E = 3
etc.
M has 3.
N has 2.
O has 0.
P has 1 stick coming to an end.
Q has none.
R has 2.
S has 2.
T has 3.
U has 2.
V has 2.
W has 3.
X has 4.
Y has 3
Z has 2.
Of all letters after L, only P has exactly 1 stroke coming to an end.
Answer: P
if 5x - 17 = -x +7, then x =
Answer:
x=4
Step-by-step explanation:
5x - 17 = -x +7
Add x to each side
5x+x - 17 = -x+x +7
6x -17 = 7
Add 17 to each side
6x-17+17 = 7+17
6x =24
Divide each side by 6
6x/6 = 24/6
x = 4
Answer:
4
Step-by-step explanation:
5x - 17 = -x + 7
Add x on both sides.
5x - 17 + x = -x + 7 + x
6x - 17 = 7
Add 17 on both sides.
6x - 17 + 17 = 7 + 17
6x = 24
Divide both sides by 6.
(6x)/6 = 24/6
x = 4
Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29
Answer:
[tex]\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }[/tex]
Step-by-step explanation:
Hello,
I assume that we are working in [tex]\mathbb{C}[/tex], otherwise there is only one zero which is 1. Please consider the following.
First of all, we can notice that 1 is a trivial solution as
[tex]p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0[/tex]
It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.
[tex]p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b[/tex]
Let's identify like terms as below.
a-1 = -5 <=> a = -5 + 1 = -4
b-a = 33
-b = -29 <=> b = 29
So
[tex]\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }[/tex]
Now, we need to find the zeroes of the second factor, meaning finding x so that:
[tex]x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ <=> x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ <=>(x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\<=>x-2=\pm 5i \ \text{ add 2 } \\ \\ <=> x = 2+5i \ \text{ or } \ x = 2-5i[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Triangle ABC, with vertices A (3,0), B (2,4), and C (4,2)undergoes a transformation to form triangle ABC with vertices A(3.0), B (2, -4) and C(4, -2). this type of transformation that triangle ABC undegoes is a ___________. If triangle ABC undergoes a transformation to form triangle A"B"C" with vertices A(-3.0) B(-2, -4) and C(-4, -2), then the typeof transformation that triangle A'B'C' undergoes is a ____________.
Answer:
1st blank: X axis reflection
2nd blank: Y axis reflection
Step-by-step explanation:
If you drew the first triangle and then the second triangle on a piece of paper, you would notice that it would reflect across the corresponding axis.
So the solution is to just draw it out.
Answer:
reflection across the x axis and the second is a reflection across the y axis.
What is the solution to the system of equations? y = –3x + 6 y = 9
Next number in this series is? 2 2 1/2 1 1/2 2
First, let's figure out the pattern that this series follows. We can see that the first number is increased by 1/2 to get to 2 1/2. Then, the second number is decreased by 1 to get to 1 1/2. Finally, the pattern repeats.
So, let's apply this pattern to find the next number in this series.
2, 2 1/2, 1 1/2, 2, 1
The next number in this series is 1.
Hope this helps!! :)
For the functions f(x)=x4−x3−7x2+9x−2 and g(x)=x−1, find (f/g)(x) and (f/g)(2).
Answer:
[tex](f/g)(x)=\frac{x^4-x^3-7x^2+9x-2}{x-1} =x^3-7x+2\,\,\,for\,\,x\neq 1[/tex]
[tex](f/g)(2)=-4[/tex]
Step-by-step explanation:
[tex](f/g)(x)=\frac{x^4-x^3-7x^2+9x-2}{x-1} =x^3-7x+2\,\,\,for\,\,x\neq 1[/tex] and undefined for x = 1.
Notice that (x-1) is in fact a factor of f(x), so the quotient of the two functions introduces a "hole" for the new function at x = 1.
f(2) can be found by simply evaluating the expression for x = 2:
[tex](f/g)(2)=2^3-7(2)+2=-4[/tex]
An appliance company determines that in order to sell x dishwashers, the price per dishwasher must be p = 420 - 0.3x. It also determines that the total cost of producing x dishwashers is given by C(x) = 5000 + 0.3x2. How many dishwashers must the company produce and sell in order to maximize profit? g
The company must produce and sell 350 dishwashers in order to maximize profit.
How to determine the number of dishwashersTo determine the number of dishwashers the company must produce and sell in order to maximize profit, we need to find the value of x that corresponds to the maximum point of the profit function.
The profit (P) is given by the equation:
P(x) = Revenue - Cost
The revenue is calculated by multiplying the price per dishwasher (p) by the number of dishwashers sold (x):
Revenue = p * x
The cost is given by the function C(x):
Cost = C(x)
Therefore, the profit function can be expressed as:
P(x) = p * x - C(x)
Substituting the given expressions for p and C(x):
P(x) = (420 - 0.3x) * x - (5000 + 0.3x²)
Expanding and simplifying the equation:
P(x) = 420x - 0.3x² - 5000 - 0.3x²
Combining like terms:
P(x) = -0.6x² + 420x - 5000
To find the value of x that maximizes profit, we need to find the vertex of the quadratic function. The x-coordinate of the vertex can be determined using the formula:
x = -b / (2a)
In our case, a = -0.6 and b = 420:
x = -420 / (2 * -0.6)
x = -420 / (-1.2)
x = 350
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350 dishwashers must the company produce and sell in order to maximize profit.
Maxima means a point at which the function attains the maximum value.
Given the following information:
Price per dishwasher, p = 420 - 0.3x
Total cost of producing x dishwashers, C(x) = 5000 + 0.3x2
Profit= Total Selling price- Total Cost Price
Total Selling price of x dishwasher, S.P= xp
S.P=x(420 - 0.3x)
S.P=420x - 0.3x²
Profit= 420x - 0.3x² - ( 5000 + 0.3x²)
Profit= 420x - 0.3x² - 5000 - 0.3x²
Profit= -0.6x²+420x-5000
So, profit, f(x)=-0.6x²+420x-5000
To determine the value of x so that maximum profit is possible:
1. Calculate the first derivative of profit function and calculate the value of x by equating it to zero.
2. Select that value of x for which the profit function attains the maximum value, to check the maxima calculate 2nd derivative, if it gives a negative value for the value of x. Then, x is the point of maxima for the given function.
[tex]f(x)=-0.6x^2+420x-5000\\f\prime(x)=-1.2x+420\\f\prime(x)=0\\-1.2x+420=0[/tex]
Calculating the value of x by transposing,
x=420/1.2
x=350
To check maxima, calculating second derivative.
[tex]f\prime(x)=-1.2x+420=0\\f\prime\prime(x)=-1.2[/tex]
2nd derivative is negative, it means that x=350 is the point of maxima.
Thus, a company must produce and sell 350 dishwashers in order to maximize profit.
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A tower is 40 ft tall and 20 ft wide. A model of the tower is 5 in. tall. Identify the width of the model in inches.
Answer:
The width of the model will be 2.5 inches
Step-by-step explanation:
The tower was scaled down by a factor to a smaller size in the model. We are to, first of all, determine this factor and then use it to scale down the width of the model.
Step One: Determine the scale factor from the tower height.
The scale factor is obtained from the formula:
Scale factor = model size / observed size
This will be
Height of model tower/ height of the real tower.
The height of the model tower is 5 inches which is the same as 0.416667 ft
Scale factor = 0.416667 ft/ 40ft = 0.0104
Step two: Multiply the width of the real-life tower by the scale factor to get the model width.
Width of model =20ft X 0.0104 = 0.208ft
Step three: Convert your answer back to inches.
We will now have to convert 0.208 ft back to inches by multiplying by 12
This will be 0.208 X 12 =2.5 inches.
The width of the model will be 2.5 inches
It took Malik 1 hour and 30 minutes to complete his English essay. He finished the essay at 5:30 pm. What time did he start working on the essay?
Answer:
4:00 pm
Step-by-step explanation:
To find the time it takes Malik to finish his English essay, let's start by subtracting one hour.
5:30 minus 1 hour is 4:30.
Now, subtract 30 minutes.
4:30 minus 30 minutes is 4:00.
Malik started working on his English essay at 4:00 pm.
Hope that helps.
WILL MARK BRAINLIST------ What is the least number of degrees that you could rotate Figure (b) around its center so that it appears to be unchanged?
Answer:
20*
Step-by-step explanation:
Your welcome plz mark me the brainlist
Find the value of annuity if the periodic deposit is $1500 at 8% compounded semiannually for 22 years
Answer:
The value of annuity is [tex]P_v = \$ 32058[/tex]
Step-by-step explanation:
From the question we are told that
The periodic payment is [tex]P = \$ 1500[/tex]
The interest rate is [tex]r = 8\% = 0.08[/tex]
Frequency at which it occurs in a year is n = 2 (semi-annually )
The number of years is [tex]t = 22 \ years[/tex]
The value of the annuity is mathematically represented as
[tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex](reference EDUCBA website)
substituting values
[tex]P_v = 1500 * [1 - (1 + \frac{0.08}{2} )^{-22 * 2} ] * [\frac{(1 + \frac{0.08}{2} )}{ \frac{0.08}{2} } ][/tex]
[tex]P_v = 1500 * [1 - (1.04 )^{-44} ] * [\frac{(1.04 )}{0.04} ][/tex]
[tex]P_v = 1500 * [1 - 0.178 ] * [\frac{(1.04 )}{0.04} ][/tex]
[tex]P_v = \$ 32058[/tex]
Please help with 4d.
Answer:
(Hemingway, The Old Man and the Sea)(Orwell, 1984)Step-by-step explanation:
A short web search will turn up the authors of the given titles:
The Old Man and the Sea - Hemingway
Huckleberry Finn - Twain
Moby D.ick - Melville
1984 - Orwell
Crime and Punishment - Dostoevsky
Where L is the length, in feet, of the pendulum, and π is approximately 22/7. How long must the pendulum be if one complete cycle takes 8 seconds?
Answer:
The simple pendulum should be 15.9 m long.
Step-by-step explanation:
Approximately (for small amplitudes), the period of a simple pendulum is
T = 2*pi * sqrt (L/g), L=length
using pi = 22/7, and g=9.8 m/s^2
8 = 2* 22/7 * sqrt(L/9.8)
solve for L
L = (8*7/(2*22))^2 * 9.8
= 15.874 m
That's quite a long pendulum!
A polynomial function is shown below:
f(x) = x3 - 4x2 - x + 4
Which graph best represents the function? (5 points)
Answer:
Simply plug in the polynomial into a graphing calc.
Step-by-step explanation:
Which of the following are solutions to the equation below?
Check all that apply.
x2 - 6x + 9 = 11
Answer:
x = 3 ± sqrt(11)
Step-by-step explanation:
x^2 - 6x + 9 = 11
Recognizing that this is a perfect square trinomial
(x-3) ^2 =11
Taking the square root of each side
sqrt((x-3) ^2) = ± sqrt(11)
x-3 =± sqrt(11)
Add 3 to each side
x = 3 ± sqrt(11)
Answer:
[tex]\large\boxed{\sf \ \ x = 3+\sqrt{11} \ \ or \ \ x = 3-\sqrt{11} \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=\sqrt{11} \ or \ x-3=-\sqrt{11}\\<=> x = 3+\sqrt{11} \ or \ x = 3-\sqrt{11}[/tex]
Do not hesitate if you have any question
Hope this helps
"Smokers are much more likely to speed, run red lights, and get involved in car accidents than nonsmokers."(a) Can you think of reasons why this statement might be misleading?(b) Can you suggest a causal link between smoking and car accidents?
Answer: Smokers pay less attention to driving while trying to light a cigarette.
Step-by-step explanation:
( A ) reasons for, why the given statement was misleading.
Following are the reasons for accidents
(i) Drunk Driving.
(ii) Driving during the night.
(iii) Smoking.
(iv) Unsafe lane changes.
(v) Driving the wrong way.
(vi) Bad weather e.g fog.
From the list above, it is shown that, smoking is also one of the major cause of car accidents on the roads.
( B.) Smokers tends to pay less attention to driving why trying to light a cigarette.
a sample of bacteria is growing at an hourly rate of 14% according to the exponential growth function.the sa
Answer:
pleasse elaborate more
Step-by-step explanation:
What's the common denominator of this equation?
3 - b = 6-7
Answer:
b = 4
Step-by-step explanation:
3 - b = 6 - 7
3 - b = -1
-b = -1 -3
-b = -4
b = 4
HELP PRECALC I DO NOT UNDERSTAND AT ALLLLL!!!!!!!!!!!!!!!!!!!!!!
Answer:
φ ≈ 1.19029 radians (≈ 68.2°)
Step-by-step explanation:
There are simple formulas for A and φ in this conversion, but it can be instructive to see how they are derived.
We want to compare ...
y(t) = Asin(ωt +φ)
to
y(t) = Psin(ωt) +Qcos(ωt)
Using trig identities to expand the first equation, we have ...
y(t) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)
Matching coefficients with the second equation, we have ...
P = Acos(φ)
Q = Asin(φ)
The ratio of these eliminates A and gives a relation for φ:
Q/P = sin(φ)/cos(φ)
Q/P = tan(φ)
φ = arctan(Q/P) . . . . taking quadrant into account
__
We can also use our equations for P and Q to find A:
P² +Q² = (Acos(φ))² +(Asin(φ))² = A²(cos(φ)² +sin(φ)²) = A²
A = √(P² +Q²)
_____
Here, we want φ.
φ = arctan(Q/P) = arctan(5/2)
φ ≈ 1.19029 . . . radians
Let A = 2, B = 3, C = 9, and D = 15.
Find the value of each expression listed below. -2 -14 10 2 -6 -10 14 6
-A + C - (D ÷ B)----------------------> (answer)
B × (-C) - (-D) + A----------------------> (answer)
(C + D) ÷ B + A----------------------> (answer)
D ÷ B + A - C----------------------> (answer)
Step-by-step explanation:
Put A = 2, B = 3, C = 9 and D = 15 to the given expressions.
Use PEMDAS.
-A + C - (D : B)
-2 + 9 - (15 : 3) = -2 + 9 - 5 = 7 - 5 = 2
B × (-C) - (-D) + A
3 × (-9) - (-15) + 2 = -27 + 15 + 2 = -12 + 2 = -10
(C + D) : B + A
(9 + 15) : 3 + 2 = 24 : 3 + 2 = 8 + 2 = 10
D : B + A - C
15 : 3 + 2 - 9 = 5 + 2 - 9 = 7 - 9 = -2
Evaluate the determinant for the following matrix 1, 4, 4, 5, 2, 2, 1, 5, 5
Answer:
0
Step-by-step explanation:
The determinant of this matrix is zero (0).
The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model. The silver model requires 1 minute in a grinder and 3 minutes in a bonder. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder. Because of maintenance procedures, the grinder can be operated no more than 30 hours per week and the bonder no more than 50 hours per week. The company makes $5 on each silver pen and $7 on each gold pen. How many of each type of pen should be produced and sold each week to maximize profits?
Answer:
Optimal production = 600 gold pens
Revenue = 600*7 = $4200 gold pens
Step-by-step explanation:
The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model.
A. The silver model requires 1 minute in a grinder and 3 minutes in a bonder.
B. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder.
Because of maintenance procedures,
C. the grinder can be operated no more than 30 hours per week and
D. the bonder no more than 50 hours per week.
The company makes
E. $5 on each silver pen and
F. $7 on each gold pen.
How many of each type of pen should be produced and sold each week to maximize profits?
Solution:
We will solve the problem graphically, with number of silver pens, x, on the x axis, and number of gold pens, y, on the y axis, i.e.
1. From A and C, the maximum number of silver pens
x <= 30*60 / 1 = 1800 and
x <= 50*60 /3 = 1000 ....................(1) bonder governs
2. from A & D, the maximum number of gold pens
y <= 30*60 / 3 = 600 .....................(2) grinder governs
y <= 50*60 / 4 = 750
3. From D,
x + 3y <= 30*60 = 1800 ...................(limit of grinder) ..... (3)
3x + 4y <= 50*60 = 3000 .................(limit of bonder) .......(4)
Need to maximize profit,
Z(x,y) = 5x+7y, represented by parallel lines y = -5x/7 + k such that all constraints of (3) and (4) are satisfied.
The maximum is obtained when Z passes through (360,480), i.e. at intersection of constraints (3) and (4). Using slope intercept form,
(y-480) = -(5/7)(x-360)
or y=-(5/7)x + (737+1/7) [the purple line] which violates the red line, so not a solution.
Next try the point (0,600)
(y-600) = -(5/7)(x-0), or
y = 600 - (5/7)x [the black line]
As we can see all point on the black (in the first quadrant) satisfy the constraints, so it is a feasible solution, and is the optimal solution, with a revenue of
Revenue = 600*7 = 4200 gold pens