Answers
(2x + 2)(2x + 6) = 0
zeros : x = -1 , x = -3
Related Questions
Dr. Steve is working with a new radioactive substance in his lab. He currently has 64 grams of the substance and knows that it decays at a rate of 25% every hour.
Identify whether this situation represents exponential growth or decay. Then determine the rate of growth or decay, r, and identify the initial amount, A.
Answers
[tex]y=A(1-r)^{x}[/tex]
where
[tex]y[/tex] is the amount after a time [tex]x[/tex]
[tex]A [/tex] is the initial amount
[tex]r[/tex] is the the decay percent in decimal form
The first ting we are going to do is find [tex]r[/tex] by dividing our decay rate of 25% by 100%: [tex]r= \frac{25}{100} =0.25[/tex].
We also know from our problem that [tex]y=64[/tex]. Lets replace [tex]y[/tex] and [tex]r[/tex] in our formula:
[tex]64=A(1-0.25)^{x} [/tex]
[tex]64=A(0.75)^{x} [/tex]
We know now that our decay rate is 0.75, and since 0.75<1, we can conclude that this situation represents exponential decay.
Now, to find the initial amount, we are going to solve our equation for [tex]A[/tex]:
[tex]64=A(0.75)^{x} [/tex]
[tex]A= \frac{64}{0.75 ^{x} } [/tex]
Notice that [tex]A[/tex] will depend on the number of ours [tex]x[/tex].
Answer:
This situation models exponential decay because the substance decays with time.
The radioactive substance decays at the rate of : 25%
r=25/100 =0.25
The initial amount of substance is 64 grams. So, . A=64
Step-by-step explanation:
The point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = (x – 12). What is the standard form of the equation for this line?
Answers
.. y -1 = (1/4)(x -12)
.. 4y -4 = x -12 . . . . multiply by 4
.. x -4y = -4 +12 . . . add 12-4y
.. x -4y = 8 . . . . . . . the equation in standard form
How do I answer this equation? -3x+y=12. I'm supposed to find the function for it bt I don't know how. Can you guys help me out please
Answers
You can do this by adding 3x to both sides which would result in y = 3x + 12.
Also, math teachers typically want functions expressed in terms of f(x) instead of y. So, you can replace your y with that to get the final answer of f(x) = 3x + 12.
Answer:
[tex]y=3x+12[/tex]
Step-by-step explanation:
We have been given an equation in standard form [tex]-3x+y=12[/tex]. We are asked to write our given equation as a function.
We know that the function represents a relationship between input and output, where each input gives exactly single output.
To write our given equation as a function we need to convert our given equation into slope-intercept form of equation because in slope-intercept form, there is exactly one y output for each input of x.
[tex]y=mx+b[/tex], where,
m = Slope,
b = The y-intercept.
To convert our given equation into slope-intercept form, we need to get y on left side of our equation.
[tex]-3x+3x+y=3x+12[/tex]
[tex]y=3x+12[/tex]
Now our equation is in form of a function, where each value of x gives exactly one y value.
What is the area of a sector with a central angle of 3π5 radians and a diameter of 21.2 cm? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.
Answers
Area of a circumference=π*r²
for diameter=21.2 cm---------> r=10.6 cm
A=π*10.6²--------> A=π*112.36 -------> A=352.81 cm²
if 2π radians (full circumference) has an area of -----> 352.81 cm²
3π/5 radians-------------------------------------> X
X=[(3π/5)*(352.81)]/2π---------> X=105.84 cm²
the answer is 105.84 cm²
Write the slope-intercept equation of the line parallel to 5y = 2x + 20 that goes through (-1, 3).
Answers
The first thing I'll do is solve "5y = 2x + 20" for "y=", so that I can find my reference slope:
y = (2/5)x + 4;
So the reference slope from the reference line is m = 2/5;.
Now I need to find two new slopes, and use them with the point they've given me; namely, with the point (-1, 3). They want me to find the line through (4, –1) that is parallel to 5y = 2x + 20; that is, through the given point, they want me to find a line that has the same slope as the reference line.
Since a parallel line has an identical slope, then the parallel line through (-1, 3) will have slope m = 2/5. Now I have a point and a slope! So I'll use the point-slope form to find the line: y - 3 = (2/5)( x + 1);
Finally, y = (2/5)x + 17/5;
Isaac deposits $1,500 in a savings account that earns 5% per year. How much interest will the money have earned at the end of 4 years? $60 $300 $450 $600
Answers
Hope this helps :)
Answer:
The interest earned at the end of 4 years is B) $300.
Step-by-step explanation:
Isaac deposits $1500 in a savings account.
Principle (P) = $1500
Rate of interest (r) = 5% = [tex]\frac{5}{100} = 0.05[/tex]
Time (t) = 4 years
We know that the simple interest formula (i) = P.r.t
Now plug in the given values in the above formula, we get
= 1500 times 0.05 times 4
= 75 times 4
Simple interest = $300
So, the interest earned at the end of 4 years is $300.
Answer is B) $300
Which system of equations can you
use to find the roots of the equation
2x3 + 4x2 – x + 5 = –3x2 + 4x + 9?
y = 2x3 + x2 + 3x +5
y =9
y = 2x3 + x2
y = 3x + 14
y = 2x3 + 4x2 – x + 5
y = –3x2 + 4x + 9
Answers
Roots are both: x=-4, x= -1/2 , x= 1
Proof:
Solve for x over the real numbers:
2 x^3 + 4 x^2 - x + 5 = -3 x^2 + 4 x + 9
Subtract -3 x^2 + 4 x + 9 from both sides:
2 x^3 + 7 x^2 - 5 x - 4 = 0
The left hand side factors into a product with three terms:
(x - 1) (x + 4) (2 x + 1) = 0
Split into three equations:
x - 1 = 0 or x + 4 = 0 or 2 x + 1 = 0
Add 1 to both sides:
x = 1 or x + 4 = 0 or 2 x + 1 = 0
Subtract 4 from both sides:
x = 1 or x = -4 or 2 x + 1 = 0
Subtract 1 from both sides:
x = 1 or x = -4 or 2 x = -1
Divide both sides by 2:
Answer: x = 1 or x = -4 or x = -1/2
Answer:
c the last one
Step-by-step explanation:
Graph y = sin(x) on the graphing calculator. Use the graph to determine the height of the barnacle with respect to water level as the boat has traveled the given distance. When the boat has traveled 7 meters, the height of the barnacle is approximately:
Answers
Answer:
The height of the barnacle is approximately is, 0.657 meters.
Step-by-step explanation:
Given the graph below of y =sin(x) ......[1]
Let y be the height of the barnacle and x be the distance the boat has traveled
Given: The boat has traveled 7 meters
i.e, x = 7 meters
to find the height y :
Substitute the value of x =7 meters in [1] we have;
y = sin(7) ≈0.657.
Therefore, the height of the barnacle is approximately is, 0.657 meters.
you can see also in the graph as shown below:
Answer:
1st is C 2nd is B
Step-by-step explanation:
Isabela had a taxable income of $82350 and filed her federal income tax return with the single filing status. Using the table below find the amount she has to pay in taxes.
Answers
Answer:
B. $16,778.00.
Step-by-step explanation:
The product of 0.1400 × 6.02 × 1023 will have how many significant figures?
Answers
0.1400 has 4 sig figs, 6.02 has 3, and 1023 has 4. when calculating significant figures for a multiplication or division equation, the product or quotient will have the same amount of significant figures as the number with the least amount of significant figures (in this case: 6.02).
Answer:
3
Step-by-step explanation:
We are given that an expression
[tex]0.1400\times 6.02\times 10^{23}[/tex]
We have to find the number of significant figures in the product .
In 0.1400 , there are 4 significant figures
In [tex]6.02\times 10^{23}[/tex], there are three significant figures
[tex]0.1400\times 6.02\times 10^{23}[/tex]
[tex]0.8428\times 10^{23}[/tex]
In multiplication, we have to precise the final answer to least significant figures.
Therefore, the final answer=[tex]0.843\times 10^{23}[/tex]
Hence, three significant figures in the product.
What are the equations of the horizontal asymptotes of y = (4e^x+7)/(e^x-1) in the xy plane?
Answers
[tex] \lim_{x \to \infty} f(x) [/tex] = n
where n is a finite number.
in your case you have to caculate separately the two limits:
a) [tex]\lim_{x \to +\infty} \frac{4 e^{x} + 7 }{ e^{x} - 1 } [/tex] = [tex] \frac{\infty}{\infty} [/tex]
To solve this, you need to regroup eˣ both on the numerator and on the denominator:
[tex]\lim_{x \to +\infty} \frac{4 e^{x} + 7 }{ e^{x} - 1 }[/tex] = [tex]\lim_{x \to +\infty} \frac{4 e^{x} (1 + \frac{7}{ e^{x} } ) }{ e^{x} ( 1 - \frac{1}{ e^{x} } ) }[/tex]
At this point the two eˣ cancel out and the parenthesis tend to 1, therefore
[tex]\lim_{x \to +\infty} \frac{4 e^{x} + 7 }{ e^{x} - 1 }[/tex] = 4
Your first horizontal asymptote is y = 4.
b) Let's calcuate now:
[tex]\lim_{x \to -\infty} \frac{4 e^{x} + 7 }{ e^{x} - 1 }[/tex] = [tex] \lim_{x \to -\infty} \frac{0 + 7}{0 - 1} [/tex] = -7
Therefore your second horizontal asymptote is y = -7
Your answer is, hence, y = 4 and y = -7 are horizontal asymptotes of the given function.
Final answer:
The horizontal asymptotes of the function y = (4e^x+7)/(e^x-1) are y = 4 and y = -7, occurring as x approaches positive and negative infinity respectively.
Explanation:
The equations of the horizontal asymptotes of the given function y = (4e^x+7)/(e^x-1) can be found by analyzing the behavior of the function as x approaches positive or negative infinity. In this function, as x approaches infinity, e^x grows much faster than any constant, so the constants can be considered negligible. Thus, the behavior of the numerator and denominator is dominated by the terms involving e^x. As x tends towards infinity, the function approaches the ratio of the coefficients of e^x, which is 4/1, meaning the horizontal asymptote is y = 4. As x tends towards negative infinity, e^x approaches zero, and the function approaches 7/(-1), so there is also an asymptote at y = -7.
It is given that there is a vertical asymptote at x = -1, where the denominator becomes zero and hence "blows up".
The radius of a circle is 1 foot. What is the length of a 45 degree arc
Answers
The length of a 45 degree arc on a circle with a radius of 1 foot is π/4 feet.
Explanation:The length of a 45 degree arc can be calculated using the formula for the circumference of a circle. The formula for the circumference is given by C = 2πr, where r is the radius of the circle. In this case, the radius is given as 1 foot. So, we can plug in the values to calculate the circumference as C = 2π(1) = 2π feet.
To find the length of a 45 degree arc, we need to find the fraction of the circumference that corresponds to a 45 degree angle. Since a full circle is 360 degrees, a 45 degree angle is 45/360 = 1/8 of the circumference. Therefore, the length of a 45 degree arc is 1/8 of the circumference, which is (1/8)(2π) feet.
Simplifying this expression, we get the length of a 45 degree arc as (1/8)(2π) = π/4 feet.
Two buildings are 200 feet apart. The height of the taller building is 50 ft. The angle of depression from the top of the taller building to the top of the shorter building is 8°. What equation below will correctly determine the height (h) of the shorter building?
Answers
200 times tan 8 = x
28.10816694 = x
28 feet
x is the "missing" part of the shorter building
so now you take 50 feet and subtract it by 28 feet and you will have the height of the shorter building
50 - 28 = 22
the shorter building is 22 ft
Two squares are drawn. The larger Square has area of 400 in.². The area of the two squares have a ratio of 1 to 4. What is the side length S of the smaller square?
Answers
For this, we use the following relationship:
A1 / A2 = 4/1
Substituting:
400 / A2 = 4/1
From here, we clear A2:
A2 = (1/4) * (400)
A2 = 100 in ^ 2
We now look for the side of the small square, we use the following relationship:
A = S ^ 2
We cleared S:
S = root (A)
S = root (100)
S = 10 in
Answer:
the side length S of the smaller square is:
S = 10 in
Answer: S=10 in
Step-by-step explanation:
The first thing we must do in this case is to find the area of the smallest square.
For this, we use the following relationship:
A1 / A2 = 4/1
Substituting:
400 / A2 = 4/1
From here, we clear A2:
A2 = (1/4) * (400)
A2 = 100 in ^ 2
We now look for the side of the small square, we use the following relationship:
A = S ^ 2
We cleared S:
S = root (A)
S = root (100)
S = 10 in
I copied the guy above me 4 points
What is the slant height of a square pyramid that has a surface area of 279 square meters and a side length of 9 meters?
Answers
Answer:
l = 11 meters
Step-by-step explanation:
Surface area = s² + 2s*l
Where "l" is the slant height
Given: Surface area = 279 ; side length s = 9
Now plug in these values in the above formula, we get
279 = 9^2 + 2*9*l
279 = 81 + 18*l
18l = 279 - 81
18l = 198
Dividing both sides by 18, we get
l = 198/18
l = 11 meters
Therefore, slant height of the square pyramid = 11 meters
Hope this will helpful.
Thank you.
Solve please This is Composite Figures :)
Answers
.. A = 2*(20 yd)^2 +(π/4)*(20 yd)^2
.. = (2 +π/4)*(400 yd^2)
.. = (800 +100π) yd^2
.. ≈ 1114.16 yd^2
The perimeter is that of a 20 yd circle and 80 yd more.
.. P = π*20 yd + 80 yd
.. ≈ 142.83 yd
Nita brings $6 to her grandma's house. these dolls represent 20% of Anita's doll collection shown in the diagram. what is the total number of dolls in Anita's doll collection
Answers
You can get this by multiplying the number in 20% by 5, which would get you to 100% and 30.
Help!! does x = 2??
An equation is shown below:
4(2x - 5) + 15 = 11
Write the steps you will use to solve the equation and explain each step.
Answers
8x=11+20-15
8x=16
x=2
Here are the steps to solve for x:
4(2x - 5) + 15 = 11
8x - 20 + 15 = 11
8x = 16
x / 8 = 16 / 8
x = 2
Therefore, your answer is correct :) Good job!
What is the equation of the axis of symmetry for the parabola y equals start fraction one over three end fraction left parenthesis x plus one right parenthesis squared minus three?
Answers
Explanation:
Our equation is
[tex]y=\frac{1}{3}(x+1)^2-3[/tex].
This is in vertex form, which is
y = a(x-h)² + k, where (h, k) is the vertex.
In our equation, h corresponds with -1 and k corresponds with -3, making the vertex (-1, -3).
The axis of symmetry is the x-coordinate of the vertex; this makes the axis of symmetry for this equation x = -1.
What is the mean absolute deviation for the data set?
{20, 24, 12, 44, 68}
16.81
17.04
17.52
17.92
Answers
Answer:
17.92
Step-by-step explanation:
I took the test and had the same question, plus the screenshot above
The Mean Absolute Deviation is 17.92.
What is Mean Absolute Deviation?The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data set. A measure of variance in a data set is the mean absolute deviation.
Take the absolute value of each digit in the data set, then deduct the mean. Next, add up the absolute values. The mean absolute deviation is then calculated by dividing the aforementioned sum by the total number of values in the data set.
Given:
Data set: {20, 24, 12, 44, 68}
Mean of the data = (20+ 24+ 12+ 44+ 68)/ 5 = 168/5
= 33.6
Mean Absolute Deviation
= {| 20- 33.6| + |24- 33.6| + |12-33.6| + | 44-33.6| + |68-33.36|} / 5
= (13.6+ 9.6 + 21.6+ 10.4 + 34.4 )/ 5
= 89.6/ 5
= 17.92
Hence, the Mean Absolute Deviation is 17.92.
Learn more about Mean Absolute Deviation here:
https://brainly.com/question/10528201
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what other information do you meed to prove ΔABE≌ΔEDA by SSS .5pts
Answers
You need to show AB ≅ ED. Knowing AEC is isosceles with base EC (2nd selection) is equivalent to knowing ∠E ≅ ∠C (1st selection). All that tells you is AC ≅ AE, which is not what you need. Likewise, the 4th selection tells you AE ≅ CE, which doesn't help, either (for the same reason).
Please help me please
Answers
the answer is 81
WILL GIVE BRAINIEST!! I need your help!
Answers
as in Q#24:
(f o g)(x)= f(g(x)) but [tex] f(x)=(x+2)^{2}[/tex] so in case of f(g(x)) means that we have to eliminate each x in the function f(x) and substitute it with the value of g(x) as the following:
[tex] f(g(x))=(g(x)+2)^{2}[/tex] but [tex]g(x)=\sqrt{x}-2[/tex] so we have to substitute with the value of g(x) in the last equation
[tex] f(g(x))= (\sqrt{x}-2+2)^{2}=(\sqrt{x})^{2}=x[/tex]
by the same way (g o f)(x), it means that g is a function of f where f is a function of x.
so [tex] (g o f)(x)=g(f(x))=\sqrt{f(x)} -2 =\sqrt{(x+2)^2} -2 =x+2-2 =x [/tex]
If you followed the same procedure, u would figure out how to solve the rest urself.
What is the wavelength of an earthquake wave if it has a speed of 7 km/s and a frequency of 3 Hz?
Answers
wavelength = speed / frequency (5000m/s /10Hz)
Answer: Our wavelength will be 2333.3 m.
Step-by-step explanation:
Since we have given that
Wave speed = 7 km/ s
Frequency = 3 Hz
We need to find the wavelength of an earthquake wave:
As we know that :
[tex]Frequency=\dfrac{Wave\ speed}{wavelength}[/tex]
First we convert km/sec to m/sec.
So, 7 km/sec= 7000 m/sec
so, our wavelength becomes
[tex]\dfrac{Wave\ speed}{frequency}\\\\\\=\dfrac{7000\ m/sec}{3\ Hz}\\\\\\=2333.33\ m[/tex]
So, our wavelength will be 2333.3 m.
15.21–3.9–4.7+6.79 Calculate in the fastest way possible!
Answers
Your answer is 13.4
Hope this helps :))
Answer:
13.4
Step-by-step explanation:
=15.21-3.9-4.7+6.79
=15.21+6.79-3.9-4.7
=22-3.9-4.7
=18.1-4.7
=13.4
What is the length of z ?
Answers
Answer:
The length of z is [tex]3\sqrt{3}[/tex] unit
Step-by-step explanation:
First Label the diagram as shown in the attachment:
In right [tex]\triangle ABC[/tex];
first find the value of y:
Use Pythagoras theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides.
In [tex]\triangle ABC[/tex]
length of AB =6 unit , length of BC =y unit and the length of AC = 3+9 =12 unit
Now, using Pythagoras theorem to get the value of y;
[tex]AB^2+BC^2=AC^2[/tex]
[tex]6^2+y^2=12^2[/tex] or
[tex]36+y^2=144[/tex] or
[tex]y^2=144-36[/tex]=108 or
[tex]y=\sqrt{108}[/tex]
on simplify we get, [tex]y=6\sqrt{3}[/tex] unit
Therefore, the length of BC is [tex]6\sqrt{3}[/tex] unit.
now, in [tex]\triangle BDC[/tex]
using Pythagoras theorem to find the value of z;
[tex]BD^2+CD^2=BC^2[/tex]
Putting the values of BD = z units , BC = [tex]6\sqrt{3}[/tex] unit and DC = 9 units we have,
[tex]z^2+9^2=(6\sqrt{3})^2[/tex] or
[tex]z^2+81=108[/tex] or
Simplify:
[tex]z^2=27[/tex] or
[tex]z=\sqrt{27} = 3 \sqrt{3}[/tex]
Therefore, the value of length z is [tex]3\sqrt{3}[/tex] unit
The attendance of your club increased by 30% from last year. There are 195 people in the club now. How many people were in the club last year?
Answers
1.3n = 195
n=195÷1.3
n=150
Answer
increased by 30% from last year. There are 195 people in the club now.
How many people were in the club last year
Step-by-step explanation:
1.3n = 195
n=195÷1.3
n=150 people where in the club last year.
In an orchard, there are 15 apple trees,27 orange trees,,and a cherry tree.what is the ratio of orange trees?
Answers
What is the measure of angle C?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answers
1. You can calculate the angle C as following:
Tan⁻1α=opposite/adjacent
α=C
opposite=3
adjacent=4
2. When you susbtitute the values, you obtain:
Tan^-1(C)=(3/4)
3. Then, you have that the measure of the angle C is:
C=36.87°
Therefore, as you can see, the answer is: 36.87°
Answer:
36.87
Step-by-step explanation:
Just took the k12 test!!
.
(07.01)
Four polynomials are shown below:
A. 3 − 7x5 + x2
B. 5x3 + 5 − 3x
C. 3x + 2x3 − x2 + 6 + 2x
D. 3x3 − 5 + 2x5 + x + 2x2
Which of the above polynomials is a 5th degree trinomial?
Answers
Therefore, your answer is A because there is an x to the 5th power, and three different components (3, -7x^5, and x^2)
Answer: The answer you are looking for is option A which would be 3 - 7x^5 +x^2
Step-by-step explanation: It is a 5th degree trinomial because, there are three terms in this equation being 3, 7x^5, and x^2; this makes it a trinomial becuase there are three terms. What makes this a 5th degree is the fact that the highest exponet is 5.