Answer:
The value of x = -0.46
Step-by-step explanation:
∵ [tex]4e^{5x}-e^{-x}=-3e^{2x}[/tex] ÷ [tex]e^{-x}[/tex]
∴ [tex]\frac{4e^{5x}}{e^{-x}}-\frac{e^{-x}}{e^{-x}}=\frac{-3e^{2x}}{e^{-x}}[/tex]
* Subtract the power of the same bases
∴ [tex]4e^{6x}-1=-3e^{3x}[/tex]
* Let [tex]e^{3x}=y[/tex]
∴ [tex]e^{6x}=y^{2}[/tex]
∴ 4y² - 1 = -3y
∴ 4y² + 3y - 1 = 0 ⇒ factorize
∴ (4y - 1)(y + 1) = 0
∴ y + 1 = 0 ⇒ y = -1
∴ 4y - 1 = 0 ⇒ 4y = 1 ⇒ y = 1/4
∵ [tex]y=e^{3x}[/tex]
∴ y = -1 refused ([tex]e^{ax}[/tex] never gives -ve value)
∴ [tex]e^{3x}=1/4[/tex] ⇒ insert ln in both sides
∵ [tex]lne^{ax}=axln(e)=ax[/tex] ⇒ ln(e) = 1
∴ 3xln(e) = ln(1/4)
∴ 3x = ln(1/4)
∴ x = [ln(1/4)] ÷ 3 = -0.46
PLZZZZZZ NEED HELP!!!!!!!!
ANSWER
5.5
EXPLANATION
We can use the cosine rule to find the missing side length.
The cosine rule is given as;
[tex] {a}^{2} = {b}^{2} + {c}^{2} - 2bc \cos( A) [/tex]
Let the missing side be "a".
Then,
[tex] {a}^{2} = {9}^{2} + {6}^{2} - 2 \times 9 \times 6 \cos(37 \degree) [/tex]
[tex] {a}^{2} = 81+ 36- 86.253[/tex]
[tex] {a}^{2} = 30.74736[/tex]
[tex]a = \sqrt{30.747} [/tex]
[tex]a \approx5.5[/tex]
Therefore the missing side length is approximately 5.5 units to the nearest tenth.
Solve for x in the given interval.
sec x= -2√3/3, for π/2 ≤x≤π
Answer:
b. [tex]x=\frac{5\pi}{6}[/tex]
Step-by-step explanation:
The given function is
[tex]\sec x=-\frac{2\sqrt{3} }{3},\:\:for\:\:\frac{\pi}{2}\le x \le \pi[/tex]
Recall that the reciprocal of the cosine ratio is the secant ratio.
This implies that;
[tex]\frac{1}{\cos x}=-\frac{2\sqrt{3} }{3}[/tex]
[tex]\Rightarrow \cos x=-\frac{3}{2\sqrt{3} }[/tex]
[tex]\Rightarrow \cos x=-\frac{\sqrt{3}}{2}[/tex]
We take the inverse cosine of both sides to obtain;
[tex]x=\cos^{-1}(-\frac{\sqrt{3}}{2})[/tex]
[tex]x=\frac{5\pi}{6}[/tex]
1) Write an expression to represent the pattern.
19, 27, 35, 43...
A: y = 11x + 8
B: y = 8x + 11
C: y = 19x
D: 8x = 11
2) Write an expression to represent the sequence.
71, 62, 53, 44...
A: y = 9x + 80
B: y = 9x + 71
C: y = -9x + 80
D: y = -9x + 71
Answer:
1. B 2. C
Step-by-step explanation:
1. B is the answer because if you add 8 times 1 to 11 you get 19 and if you add 8 times 2 to 11 you get 27 so that is the expression to represent the pattern.
2. C is the answer because if you add -9 times 1 to 80 you get 71 and if you add -9 times 2 to 80 you get 62 so that is the expression to represent the pattern.
?2300 is invested in 4 years at 5% per year simple interest work out the total interest
Answer:
460
Step-by-step explanation:
I=P x r x t
P is the principal amount, $2300.00.
r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.
t is the time involved, 4....year(s) time periods.
So, t is 4....year time periods.
To find the simple interest, we multiply 2300 × 0.05 × 4 to get that:
The interest is: $460.00
Quest Manufacturing is building a product that costs $200 to start to build and $6.40 per unit sold. The company plans to sell each unit for $10.50. The company wrote an inequality to determine the minimum number of units (u) that it needs to sell to break even or make a profit on the product. 10.50u ≥ 200 6.40u What is the minimum amount of units that the company needs to sell to break even or make a profit on the product?
Answer:
49 units
Step-by-step explanation:
10.50u ≥ 200 + 6.40u solve for u....
4.10u ≥ 200 (subtract 6.40u to both sides)
u ≥ 200/4.10 (divide both sides by 4.10)
u ≥ 48.78
Any number of units greater than 48.78, but they can't sell parts of a unit, so 49 is the minimum number of units that need to be sold to make a profit
What is the value of the y-coordinate of the y-intercept of the function shown below? F(x)=-3x^2+5x-4
Answer:
The y-coordinate of the y-intercept is [tex]-4[/tex]
Step-by-step explanation:
we know that
The y-intercept is the value of y when the value of x is equal to zero
so
In this problem we have
[tex]F(x)=-3x^2+5x-4[/tex]
Find the y-intercept
For [tex]x=0[/tex]
[tex]F(0)=-3(0)^2+5(0)-4=-4[/tex]
The y-intercept is the point [tex](0,-4)[/tex]
therefore
The y-coordinate of the y-intercept is [tex]-4[/tex]
Answer:
The value would be -4.
Step-by-step explanation:
Write ln x^2+3 Iny a single logarithm (Picture provided)
Answer: option a.
Step-by-step explanation:
To solve the given exercise nad write the expression as a single logarithm, you must keep on mind the following properties:
[tex]ln(a)+ln(b)=ln(ab)\\m*ln(a)=ln(a)^m[/tex]
Therefore, by applying the properties shown above, you can rewrite the expression given, as following:
[tex]lnx^{2}+3lny=lnx^2+lny^3=ln(x^2y^3)[/tex]
Then, the answer is the option a.
A cylinder with a radius of 1 cm and a height of 21 cm has the same volume as a cone with a height of 7 cm. What is the radius of the cone? A) 3 cm B) 5 cm C) 7 cm D) 9 cm
Answer:
A) 3 cmStep-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
We have r = 1cm and H = 21cm. Substitute:
[tex]V=\pi(1^2)(21)=21\pi\ cm^3[/tex]
The formula of a cone:
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have V = 21π cm³ and H = 7cm. Substitute:
[tex]\dfrac{1}{3}\pi(r^2)(7)=21\pi[/tex] divide both sides by π
[tex]\dfrac{1}{3}(7)(r^2)=21[/tex] divide both sides by 7
[tex]\dfrac{1}{3}r^2=3[/tex] multiply both sides by 3
[tex]r^2=9\to r=\sqrt9\\\\r=3\ cm[/tex]
Answer:
A 3cm
Step-by-step explanation:
Nisha did the work below to solve an equation.
Step 1 7b+3.2b-5=18.92
Step 2 10.2b-5=18.92
Step 3 5.2b= 18.92
Step 4 b=3.64.
In which step did Nisha make her first error?
Step 1
Step 2
Step 3
Step 4
Answer: step 3
I just took the test and got a 100%
Answer:
Step 3
Step-by-step explanation:
Here, the given expression,
[tex]7b + 3.2b - 5 = 18.92[/tex]
Since, when we solve the given expression the steps of solution are as follows,
Step 1 : 7b + 3.2b - 5 = 18.92
Step 2 : 10.2b - 5 = 18.92 ( Combining like terms in left side )
Step 3 : 10.2b = 23.92 ( Adding 5 on both sides )
Step 4 : b = 4.6 ( Dividing both sides by 10.2 )
Hence, by the above explanation it is clear that she made her mistake in step 3 ( she did not add 5 on right side )
A picture measuring 4" high by 6" wide is to be enlarged so that the width is now 9”. How tall will the picture be?
The original width was 6 inches, the new width is 9 inches.
Divide the new width by the original width to find the scale factor:
9/6 = 1.5
Now multiply the original height by the scale factor to find the new height:
4 x 1.5 = 6 inches.
At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle (blue) with a radius of 11 m. The inner edge of the sidewalk is a circle (orange) with a radius of 9 m. Find the approximate AREA of the larger circle (blue). use 3.14 for pi
Answer:
380.13 m
Step-by-step explanation:
You first need to write down the Area formula for a circle which is A=pi x radius^2 .
So 11^2 x 3.1415...
121 x 3.1415... = 380.13 m
The length of a rectangular field is 7 m less than 4 times the width. The perimeter is 136m ?. Find the width and the length of the rectangle
➷ The perimeter is the total of all the lengths / widths
The lengths can be represented by 4x - 7
The width can be represented by x
2 times the length + 2 times the width would equal the perimeter
2(x) + 2(4x - 7) = 136
Simplify:
2x + 8x - 14 = 136
10x - 14 = 136
Add 14 to both sides:
10x = 150
Divide both sides by 10:
x = 15
The width is equal to 15m
The length is 4(15) - 7 = 53m
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Ms. Thomas buys 3 pounds of sliced ham to make sandwiches. It takes 1 3 lb of ham for each sandwich. How many ham sandwiches can Ms. Thomas make with the ham she's purchased? A) 3 sandwiches B) 6 sandwiches C) 9 sandwiches D) 12 sandwiches
Answer:
Option C [tex]9\ sandwiches[/tex]
Step-by-step explanation:
we know that
using proportion
[tex]\frac{1}{(1/3)}\frac{sandwich}{pounds}=\frac{x}{3}\frac{sandwiches}{pounds}\\ \\x=3*3\\ \\x=9\ sandwiches[/tex]
Answer:
9
Step-by-step explanation:
I got the answer from USATestprep
Use the laws of logarithms and the values given below to evaluate the logarithmic expression.
log7=0.8451 log5=0.6990
log3=0.4771 log2=0.3010
log12
Answer:
B
Step-by-step explanation:
We can use the logarithm property shown below to evaluate this:
[tex]Log(x*y*z)=logx+logy+logz[/tex]
Now we can write Log 12 as Log (2*2*3).
Using the rule, we can write:
Log (2*2*3) = Log 2 + Log 2 + Log 3
We are given values of Log 2 and Log 3, plugging these we get:
Log (2*2*3) = Log 2 + Log 2 + Log 3
Log (2*2*3) = 0.3010 + 0.3010 + 0.4771 = 1.0791
Answer choice B is right.
We can factor out 12 using 2 and 3.
log(12) = log(2^2 * 3)
Rewrite it using the product rule [ log(xy) = log(x) + log(y) ]
log(2^2 * 3) = 2 log(2) + log(3)
Simplify using the given values.
2(0.3010) + 0.4771
0.602 + 0.4771
1.0791
Therefore, the answer is b. ≈ 1.0791
Best of Luck!
Please help 50 points
Answer:
Step-by-step explanation:
Left Frame
Consecutive angles (angles that are one after another) add up to 180 degrees. (The are supplementary).
9x + 6x = 180o Combine like terms
15x = 180o Divide by 15
15x/15 =180/15
x = 12
===============
You could do this the way it is done in the more formal proof.
9x + 6x + 9x + 6x = 360 Combine like terms: each quadrilateral = 180o
30x = 360 Perform Division Property of equality
x = 360/30 Do the division
x = 12
Right frame
The left side of line 3 is the substitution property.
<A = 9x
<B = 6x
<C = 9x
<D = 6x
The left side of line 4 is 30x. This comes from 9+6 + 9 + 6
The right side of line 5 is the division property of equality
Answer:
the pdf wnt lad gimme dem pons doe
Step-by-step explanation:
Find the height of a square pyramid that has a volume of 25 3/5 meters and a base with 4 meter sides
ANSWER
The height of the square pyramid is 4.8m
EXPLANATION
The volume of a square pyramid is calculated using the formula:
[tex]Volume = \frac{1}{3}(base \: area) \times height[/tex]
It was given that;
The volume of the square pyramid is
[tex]25 \frac{3}{5} {m}^{3} [/tex]
The side length of the square base is
[tex]4m[/tex]
We substitute the given values and then solve for the height.
[tex]25 \frac{3}{5} = \frac{1}{3}( {4}^{2} ) \times height[/tex]
We solve for the height to obtain;
[tex]height = \frac{25 \frac{3}{5} }{ \frac{16}{3} } [/tex]
We simplify to get;
[tex]height = 4.8m[/tex]
Hence, the height of the square pyramid is 4.8 meters.
Answer:
The height of the square pyramid is 4.8 meters.
Step-by-step explanation:
I just know
She buys 3 roses she want the 1/4 of the flowers in the arrangement to be roses . How many more flowers must she buy ?
Answer:
1 1/4
Step-by-step explanation:
rigjt answer
PLEASE HELP QUICK AND EXPLAIN. I'M OFFERING 20PTS (More than it's worth) AND BRAINLIEST ANSWSER
Answer:
Step-by-step explanation:
(a) when there is a negative in front of the leading coefficient (- x^2), that is a reflection over the x axis. a regular parabola opens up. In this case, the negative in front of the first term makes it open downward.
-f(x) is a reflection so -2x^2 would open downward.
(b) the vertex of the parabola is -b/2a
in this problem a x^2 + bx + c = y
-2x^2 + 4x + 3 = y
a = -2, b = 4, c = 3
formula for vertex -b/2a = -4/2(-2) = -4/-4 = 1 This is the x-value of the vertex. Plug back into original equation to find the y value.
(1, ?) -2(1)^2 + 4(1) + 3 = 5
vertex is (1,5) and is above the x axis
A circle has a circumference of 7{,}8507,8507, comma, 850 units. What is the radius of the circle?
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=7850 \end{cases}\implies 7850=2\pi r\implies \cfrac{7850}{2\pi }=r\implies 1249.37\approx r[/tex]
Answer:
1249.37 units
Step-by-step explanation:
Jimmy is planning to paint the gate of his house. The gate has a glass panel. Painting the gate costs $2.50 per square foot. How much will he have to spend to paint the gate? PLEASE HELP!!
Answer:
[tex]\$103.75[/tex]
Step-by-step explanation:
step 1
Find the area of the gate
The area of the gate is equal to the area of a trapezoid minus the area of the rectangular glass panel
[tex]A=\frac{1}{2}(10+7)(5)-(0.71)(1.43)= 41.5\ ft^{2}[/tex]
step 2
Find the cost
Multiply the total area by $2.50
so
[tex]41.5*2.50=\$103.75[/tex]
I think I got everything but the c part. Can someone help me
you got everything right
Use the laws of logarithms and the values given below to evaluate the logarithmic expression (picture provided)
Answer: option b.
Step-by-step explanation:
To solve the given exercise, you must keep on mind the following law of logaritms:
[tex]m*log(a)=log(a)^m[/tex]
Descompose 8 into its prime factors:
[tex]8=2*2*2=2^3[/tex]
Therefore, you can rewrite the expression given, as following:
[tex]log8=log2^3=3log2[/tex]
You know that [tex]log2=0.3010[/tex]
Then, when you substitute, you obtain:
[tex]3*0.3010[/tex]≈0.9030
Factor out 8 using 2.
log(8) = log(2^3)
Use the product rule [ log(xy) = log(x) + log(y) ] to simplify.
log(2^3) = 3 log(2)
Simplify using the given value for 2.
3(0.3010)
0.9030
Therefore, log(8) ≈ 0.9030 (Option B)
Best of Luck!
Water boils at 100 degree, C. This is 400 percent more than my room's temperature. What is my room's temperature?
Your room temperature is 25°C.
Step-by-step explanation:
hope this helps!
what is the solution to the equation below?
x - |-20| = |-34|
a· -54
b· -14
c· 14
d· 54
[tex]x - |-20| = |-34|\\x-20=34\\x=54[/tex]
I need help on #20 please
Answer:
P = 10x³ + 4x² + 8x + 6
Step-by-step explanation:
The perimeter of a rectangle is twice the sum of length and width.
P = 2(L+W) = 2((x³ +2x² -6x +12) +(4x³ +10x -9))
= 2(5x³ +2x² +4x +3) . . . . collect terms inside parentheses
P = 10x³ +4x² +8x +6
A parallelogram has sides of 18 and 26 ft, and an angle of 39° . Find the shorter diagonal
Answer:
16.51
Step-by-step explanation:
In a parallelogram, the opposite angles are always equal in measure. So two of the angles in the parallelogram measure 39 degrees each.
The sum of angles of the parallelogram must be 360 degrees. Let the other two angles be x degree each. We can set up the following equation for the angles:
39 + 39 + x + x = 360
78 + 2x = 360
2x = 282
x = 141
This means, the other two angles measure 141 degree each. The shorter diagonal will be opposite to the shorter angle.
Hence, the diagonal opposite to the angle 39 degree will be the shorter one. A diagonal divides the parallelogram in two triangles. So we will have two sides and an included angle and we have to find the third side of the triangle which can be found using the law of cosines. Let the third side be c as shown in image below, using the law of cosines, we can write:
[tex]c^{2} = a^{2}+ b^{2} -2ab cos(\gamma)\\\\c^{2}=18^{2}+26^{2}-2(18)(26)cos(39)\\\\ c^{2}=272.59\\\\ c=16.51[/tex]
Thus the shorter diagonal will be 16.51 feet in measure.
To find the shorter diagonal of a parallelogram with given side lengths and angle, use the formula √(a^2 + b^2 - 2abcosθ).
Explanation:To find the shorter diagonal of a parallelogram, we need to use the formula:
Shorter diagonal = √(a^2 + b^2 - 2abcosθ)
Where a and b are the sides of the parallelogram and θ is the angle between them.
Using the given information, we have a = 18 ft, b = 26 ft, and θ = 39°.
Substituting these values into the formula, we get:
Shorter diagonal = √(18^2 + 26^2 - 2(18)(26)cos(39°))
Calculating this expression gives us:
Shorter diagonal ≈ 9.15 ft
Please HELP....Solve and graph the inequality. 45x + 5 < −3
Step-by-step explanation:
4/5x+5<-3
4/5x<-8
4x<-40
x<-10
If Seven cookies are shared equally by four people how many cookies will each person get
Final answer:
Each person will get 1 cookie and there will be 3 cookies leftover.
Explanation:
In this scenario, we have 7 cookies that are being shared equally among 4 people. To find out how many cookies each person will get, we divide the total number of cookies by the number of people.
So, 7 cookies divided by 4 people = 1.75 cookies per person.
Since we can't divide a cookie into fractions, each person will get 1 cookie and there will be 3 cookies leftover.
PLEASE HELP!! TIMED QUESTION!!!!
Solve the system of equations below.
4x -y=16
2x + 3y = -2
A. (5,4)
B. (5,-4)
C. (4,-5)
D. (-5,4)
[tex]\begin{cases}4x - y = 16 \\2x + 3y = - 2 \end{cases} \\ \Leftrightarrow \begin{cases}4x - y = 16 \\4x + 6y = - 4 \end{cases} \\ \Leftrightarrow \begin{cases}x = \frac{y + 16}{4} \\7y = - 20 \end{cases} \\ \Leftrightarrow \begin{cases}x = \frac{23}{7} \\y = - \frac{20}{7} \end{cases}[/tex]
Maybe you wrote the system wrong somewhere because there is no right answer
Solve using proper methods. Show work. (25 POINTS)
Initially a tank contains 10,000 liters of liquid at the time t = 0 minutes a tap is opened, a liquid then follows out of the tank. The volume of the liquid V liters, which remains in the tank after t minutes is given by V = 10,000(0.933)^t
a) Find the value of V after 5 minutes.
b) Find how long, to the nearest second, it takes for half of the initial amount of liquid to follow out of the tank.
c) The tank is regarded as effectively empty when 95% of the liquid has flowed out. Show that it takes almost three quarters of an hour for this to happen.
d) (i) Find the value of 10,000 - V when t = 0.001 minutes
(ii) Hence or otherwise, estimate the initial flow rate of the liquid. Give your answer in liters per minute, correct to two significant figures.
Answer:
a) 7069.82 Liters
b) 600 seconds
c) Shown below
d) (i) 0.6935 liters (ii) Since 0.6935 liters in 0.001 minute, so 693.5 liters per minute is as estimate (in liters per minute)
Step-by-step explanation:
a)
We simply put 5 into t of the equation and get the value of V. So:
[tex]V=10,000(0.933)^t\\V=10,000(0.933)^5\\V=7069.82[/tex]
So after 5 minutes the amount remaining is 7069.82 Liters
b)
half of the initial amount is half of 10,000 which is 5000. So we substitute 5000 into V and solve for t using logarithms.
Note: [tex]ln(a^b)=blna[/tex]
Thus, we have:
[tex]V=10,000(0.933)^t\\5000=10,000(0.933)^t\\0.5=(0.933)^t\\ln(0.5)=ln((0.933)^t)\\ln(0.5)=tln(0.933)\\t=\frac{ln(0.5)}{ln(0.933)}\\t=9.99[/tex]
Thus, t = 9.9949 minutes.
To get answer in seconds, we multiply by 60. Thus 9.9949*60= 600 seconds
c)
95% empty means 5% remaining. 5% of 10,000 = 0.05 * 10,000 = 500. We plug in 500 into V and solve for t as the previous step. Shown below:
[tex]V=10,000(0.933)^t\\500=10,000(0.933)^t\\0.05=0.933^t\\ln(0.05)=ln(0.933^t)\\ln(0.05)=tln(0.933)\\t=\frac{ln(0.05)}{ln(0.933)}\\t=43.1972[/tex]
So it takes around 43.1972 minutes to empty 95%. Since three-quarters of an hour is [tex](\frac{3}{4})(60)=45[/tex] minutes, we have shown that the time it takes (43.1972 minutes) is very close to three-quarters of an hour.
d)
We plug in 0.001 into t and find V. Then we subtract that value from 10,000. This is just finding how much water has been removed in 0.001 minutes. Let's do this:
[tex]V=10,000(0.933)^t\\V=10,000(0.933)^{0.001}\\V=9999.3065\\Now\\10,000 - 9999.3065 = 0.6935[/tex]
So, 0.6935 liters