Answer:
3
Step-by-step explanation:
Given a polynomial with zeros x = a, x = b, x = c
Then the factors are (x - a), (x - b) and (x - c)
and the polynomial is the product of the factors
f(x) = k(x - a)(x - b)(x - c) ← k is a multiplier
here the zeros are x = - 3, x = 0, x = 4, thus the factors are
(x - (- 3)), (x - 0) and (x - 4), that is
(x + 3), x and (x - 4)
let k = 1, then
f(x) = x(x + 3)(x - 4) → 3
Answer:
F(x) = x(x + 3)(x – 4)
Step-by-step explanation:
The polynomial function has zeros at -3, 0, and 4 is F(x) = x(x + 3)(x – 4)
x(x + 3)(x – 4), set each part = 0 to find the solutions
x(x + 3)(x – 4) = 0
x = 0
x + 3 = 0; x = -3
x - 4 = 0; x = 4
find the sum or difference. make sure your answer is simplified. work must be shown.
3/4x+1/20x
[tex]\bf \cfrac{3}{4x}+\cfrac{1}{20x}\impliedby \textit{so let's use an LCD of 20x} \\\\\\ \cfrac{(5)3~~+~~(1)1}{20x}\implies \cfrac{15+1}{20x}\implies \cfrac{16}{20x}\implies \cfrac{4}{5x}[/tex]
Suppose a diver dove from a diving platform 4 feet above the water and stopped at –8 feet to pick up some scallops. Which expression models this situation and tells how far below the diving platform she is?
A. –4 + |–8|
B. |4| + |8|
C. 4 – |–8|
D. 4 + |–8|
Answer: Option D.
Step-by-step explanation:
By definition, the absolute value of a number is its distance from 0 on a number line. We know that the distances cannot be negative. Then:
[tex]|-a|=a[/tex]
We can assume that the water is at level 0.
We know that the diver dove from a diving platform, which is 4 feet above the water, and then she stopped at -8 feet to pick up some scallops.
This indicates that she stopped at 8 feet below the water.
Therefore, in order to find how far below the diving platform the diver is, we must add 4 feet and the absolute value of -8 feet.
Then, the expression that models this situation is:
[tex]4+|-8|[/tex]
Notice that it matches with the expression shown in Option D.
The weather forecast for the day shows a 45% chance of
rain, a 45% chance of lightning, and a 25% chance of lightning
and rain. Which statement is correct?
A. The chance of rain and the chance of lightning are
independent because .2025 = .25
B. The chance of rain and the chance of lightning are
independent events because .45 = .45
C. The chance of rain and the change of lightning are
dependent events because .2025 2.25
D. The chance of rain and the chance of lightning are
dependent events because .45 = .45
Answer:
C
Step-by-step explanation:
If two events are independent, the probability of both happening are:
P(A and B) = P(A) × P(B)
In this case, if rain and lightening were independent:
P(rain and lightening) = P(rain) × P(lightening)
P(rain and lightening) = 0.45 × 0.45
P(rain and lightening) = 0.2025
However, we're told that P(rain and lightening) is 0.25, not 0.2025.
Since 0.2025 ≠ 0.25, the events are not independent, so they are dependent.
What is the I-value of the solution of the system of equatIons
x + 3y = 13 and 3x - y = –11?
The I-value of the solution of the given system of equations is -2.
Explanation:The I-value of the solution of the given system of equations can be found by solving the equations simultaneously.
We can solve the system of equations using the method of substitution or the method of elimination. In this case, let's use the method of substitution.
First, solve one equation for x in terms of y or vice versa. Let's solve the second equation for x:
3x - y = -11 => 3x = y - 11 => x = (y - 11)/3
Now substitute this value of x into the first equation:
x + 3y = 13 => (y - 11)/3 + 3y = 13 => (y - 11 + 9y)/3 = 13 => 10y - 11 = 39 => 10y = 50 => y = 5
Finally, substitute the value of y back into one of the original equations to find the value of x. Let's substitute y = 5 into the second equation:
3x - 5 = -11 => 3x = -6 => x = -2
Therefore, the solution to the system of equations is x = -2 and y = 5. The I-value of the solution is x, so the I-value is -2.
Final answer:
To determine the I-value for the given equations, we apply algebraic methods to solve for x and y; however, it's not possible to find an I-value without further context as I typically represents current in electrical engineering.
Explanation:
To find the I-value of the solution to the system of equations x + 3y = 13 and 3x - y = -11, we can use the method of substitution or elimination. However, the question seems to be a mix of content as it initially presents equations that are typical of algebra but then refers to finding a value for I1 which is more in line with physics or engineering contexts, particularly with circuit analysis where I represents current. Since we are given two standard linear equations, we will solve them as algebraic expressions to find the values of x and y.
Solution:
First, we solve one of the equations for one variable and then substitute it into the other. Let's solve the first equation for x:
x = 13 - 3y
Next, we substitute this expression for x in the second equation:
3(13 - 3y) - y = -11
Simplify and solve for y:
39 - 9y - y = -11
-10y = -11 - 39
-10y = -50
y = 5
Now, substitute y into the expression we found for x:
x = 13 - 3(5)
x = 13 - 15
x = -2
The solution to the system of equations is x = -2 and y = 5. If the variable I is meant to represent the current in a circuit, this solution does not directly provide the I-value without additional context of the circuit's parameters.
What is the length of the diagonal of a poster board with dimensions 22 inches by 28 inches? Round to the nearest tenth.
Answer:
The length of the diagonal of a poster board is [tex]35.6\ in[/tex]
Step-by-step explanation:
Let
x----> the length of the diagonal of a poster board
we know that
Applying the Pythagoras Theorem
[tex]x^{2}=22^{2}+28^{2} \\ \\x^{2}=1,268\\ \\x=35.6\ in[/tex]
Answer:
The length of the diagonal of a poster board is 35.6 inches.
Step-by-step explanation:
To find : What is the length of the diagonal of a poster board with dimensions 22 inches by 28 inches?
Solution :
The dimensions of a poster board is
Length = 22 inches
Breadth = 28 inches
The diagonal is given by,
[tex]D=\sqrt{L^2+B^2}[/tex]
[tex]D=\sqrt{22^2+28^2}[/tex]
[tex]D=\sqrt{484+784}[/tex]
[tex]D=\sqrt{1268}[/tex]
[tex]D=35.60[/tex]
Therefore, the length of the diagonal of a poster board is 35.6 inches.
A biologist is researching a newly-discovered species of bacteria. He puts 200 bacteria into what he has determined to be a favorable growth medium. Nine hours later, he measures 380 bacteria. Assuming exponential growth, find the growth equation and use it to determine the number of bacteria after eight hours.
Note: Once you find the equation, round a and b to the nearest hundredth to determine the solution.
358
351
344
360
Answer:
354.
Step-by-step explanation:
Exponential growth:
380 = 200e^(k*9) where k is a constant to be found.
e^9k = 380/200 = 19/10
ln e^9k = ln 1.9
9k = ln 1.9
k = ln 1.9 / 9
k = 0.071
After 8 hours:
Number of bacteria =
200*e^(8*0.071)
= 354.
What is (-6x) to the third power
Answer:
-216 x^3
Step-by-step explanation:
(-6x)^3
This is really (-6x)* (-6x) * (-6x)
-216 x^3
Find an equation of variation where y varies directly as x and y = 0.8 when x = 0.4
Answer:
y = 2x
Step-by-step explanation:
Given that y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 0.8 when x = 0.4
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{0.8}{0.4}[/tex] = 2
y = 2x ← equation of variation
To find an equation of direct variation given that y = 0.8 when x = 0.4, we use the form y = kx to determine the constant k, which is 2. Thus, the equation of variation is y = 2x.
To find an equation of direct variation where y varies directly as x, we use the form y = kx, where k is the constant of variation.
Given that y = 0.8 when x = 0.4, we can substitute these values into the equation to find k.
Solving for k, we get k = y / x = 0.8 / 0.4 = 2. Therefore, our equation of variation is y = 2x.
The ratio of boys to girls at a local sports club is 3-1.if there are 45 girls how many boys are there
Answer:
I'm pretty sure the answer is 43
because you have to minus 2 from the girls each time to get the boy answer. Hope this helps :)
Step-by-step explanation:
HELP NEEDED ASAP!! What is the length of AC
Answer:
(144) is the homogeneous mixture
Answer:
Ac = 144
Step-by-step explanation:
From the figure we can see two similar triangles,Ratio of sides of similar triangles are equal.
To find the value of x
From the figure we can write,
7/84 = x/(156 - x)
1/12 = x/(156 - x)
156 - x = 12x
13x = 156
x = 156/13 = 12
To find the value of AC
AC = 156 - x
= 156 - 12
= 144
Therefore AC = 144
Merlin Industries bought a laptop for $2,100. It is expected to depreciate at a rate of 14% per year. What will the value of the laptop be in 5 years? Round to the nearest dollar.
Question 4 options:
$912
$988
$1,806
$4,043
988
A year later will depreciate $294
The following year $253
On the third year $217
The fourth year. $187
And the 5th year. $161
Answer:
$988Step-by-step explanation:
[tex]100\%-14\%=86\%=0.86\\\\0.86\cdot\$2,100-\text{after the first year}\\0.86\cdot(0.86\cdot\$2,100)=0.86^2\cdot\$2,100-\text{after the second year}\\0.86\cdot(0.86^2\cdot\$2,100)=0.86^3\cdot\$2,100-\text{after the third year}\\\vdots\\0.86^5\cdot\$2,100\approx\$988-\text{after the fifth year}[/tex]
Plzzzzzzzz help me this is really hard
Answer:
4dg=40cg
Because dg to cg rate is 1:10
Answer:
4000 cgs
Step-by-step explanation:
This one requires 2 sets of brackets. You are best to work in grams.
1 dg = 10 grams
1 cg = 0.01 grams.
I wouldn't fret about this if I were you. This is the first time I've actually used these units. Most likely if you really need them, you can just look them up.
4 dg * [10 grams / 1 dg] * [ 1 cg / 0.01 grams]
40 grams * 1 cg / 0.01 grams
= 4000 cgs.
Notice the first set of brackets get's rid of the dgs
the second set of brackets gets rid of the grams.
which of these triangle pairs can be mapped to each other using a reflection and a translation
Answer:
B
Step-by-step explanation:
If you have the a,b,c,d
Solve (-18^3+17x+6)/(3x+2)
Answer:
[tex]\frac{17x-5826}{3x+2}[/tex]
Step-by-step explanation:
The polynomial - 18x³ + 17x + 6 is divided by 3x + 2. Then the polynomial will be - 6x² + 4x + 3.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
- 6x² + 4x + 3
3x + 2 ) - 18x³ + 17x + 6
- 18x³ - 12x²
+ 12x² + 17 x + 6
+ 12x² + 8x
+ 9x + 6
+ 9x + 6
0
More about the division link is given below.
https://brainly.com/question/369266
#SPJ2
The sale price of apples at a local grocery store is $1.35 for the first pound and $1.10 for each additional pound. Which function rule shows how the cost of apples, y, depends on the number of pounds, x?
1.)y = 1.10(x – 1) + 1.35
2.)y = 1.10x + 1.35
3.) y = 1.35x + 1.10
4.)y = (1.10 + 1.35)x
Answer:
1.) y = 1.10(x – 1) + 1.35
Step-by-step explanation:
When x pounds of apples are purchased, the number of "additional" pounds is (x-1). The cost of those additional pounds is then added to the cost of the first pound to get ...
y = 1.10(x -1) +1.35
_____
Comment on the function rule
Personally, I think it is easier to write the rule as y = 1.10x +0.25, considering the first pound to have a $0.25 premium added to its otherwise $1.10 cost. This saves an operation when evaluating the formula for some value of x.
The point (-3,4) is reflected across the x-axis. What is the coordinates of its new location?
Semd a pic of a graph bc I dont have paper
The point (-3,4) when reflected across the x-axis results in new coordinates (-3, -4), changing the sign of the y-coordinate.
The question asks for the new coordinates of a point after being reflected across the x-axis. Reflecting a point across the x-axis changes the sign of the y-coordinate but leaves the x-coordinate unchanged. Therefore, if we have a point (-3, 4) and we reflect it across the x-axis, the x-coordinate remains -3, and the y-coordinate, which is 4, will become -4, resulting in the new coordinates (-3, -4).
the line that passes through the points (-5,-6) and (-3,2) and the line with equation y=x-4 intersect at what point?
Answer:(-6,-10)
Step-by-step explanation:
Let’s say that A is (-5,-6) and B is (-3,2). The slope of AB is (-6-2)/(-5+3)=(-8)/(-2)=4
The equation of AB is:
y-2=4(x+3)
y=4x+14
The lines intersect in:
4x+14=x-4
3x=-18
x=-6
(-6,-10)
What is the volume of the following triangular prism? 252 yd 3 126 yd 3 42 yd 3 84 yd 3
(I just did this quiz lol)
Answer:
42 yards
Step-by-step explanation
we know that
The volume of the triangular prism is equal to
where
B is the area of the triangular base
H is the height of the prism
Convert 9 Ft to yd
Remember that
1 ft=1/3 yd
9 ft=9*(1/3)=3 yd
Find the area of the base B
we have
substitute the values in the formula
v=BH
v=(6)(7)=42 yd
Answer:
42
Step-by-step explanation:
What is the mean absolute deviation of the data set?
{8, 11, 12, 17}
Enter your answer in the box. Round to the nearest tenth, if necessary.
Answer: The Mean Absolute Deviation (MAD) is 2.5.
Step-by-step explanation:
The mean absolute deviation of the data set {8, 11, 12, 17} is calculated by first finding the average of the numbers, then calculating the absolute deviations from this mean, and finally averaging those deviations to get a MAD of 2.5.
To calculate the mean absolute deviation (MAD) of the data set {8, 11, 12, 17}, we first find the mean of the data set and then find the average of the absolute deviations from this mean. The mean (average) of the data set is calculated by adding all the numbers together and dividing by the number of numbers, which in this case gives us (8 + 11 + 12 + 17) / 4 = 48 / 4 = 12.
We then calculate the absolute deviations from this mean for each number: |8 - 12| = 4, |11 - 12| = 1, |12 - 12| = 0, and |17 - 12| = 5. Finally, we calculate the average of these absolute deviations: (4 + 1 + 0 + 5) / 4 = 10 / 4 = 2.5. Therefore, the mean absolute deviation of the data set {8, 11, 12, 17} is 2.5.
What is the range of the function f(x) = 3x - 12 for the domain (-2, 2)?
A. (3,12)
B. 4-6, -18)
c. (6, 18)
D. (12,3)
When x=-2
f(x) =3(-2) -12 =-6-12=-18
When x=2
f(x) = 3(2)-12=6-12=-6
So For the domain (-2,2)
Range of the function f(x) is (-18,-6)
So (-18 ,-6). is your answer.
Hope it helps....
Regards,
Leukonov/Olegion.
The range of the function f(x) = 3x - 12 for the domain (-2, 2) is (-18, -6). This is determined by finding the function's output at x = -2 and x = 2, which are the endpoints of the specified domain.
The question asks for the range of the function f(x) = 3x - 12 given the domain (-2, 2). To determine the range, we calculate the output values of the function using the endpoints of the domain.
For the lower endpoint of the domain, x = -2: f(-2) = 3(-2) - 12 = -6 - 12 = -18.
For the upper endpoint of the domain, x = 2: f(2) = 3(2) - 12 = 6 - 12 = -6.
Since the function is a straight line (which is continuous and has a constant rate of change), the range over the interval (-2, 2) is all values between f(-2) and f(2), though not including the endpoints since the domain is open. Thus, the range is (-18, -6).
The correct answer is B. (-18, -6).
estimate the answer by rounding first number to nearest tenth and second number to nearest hundred. 0.65 × 1754. have to type an integer or decimal
Answer:
1260
Step-by-step explanation:
Round 0.65 to 0.7 and round 1754 to 1800. To get 1260, I recommend an easy way to do this. I would take 18 and multiply it by 7, giving us 126. Because it was supposed to be 0.7, not 7, we multiply by 10 because 7/10 is 0.7. This gives us 126 times 10 which equals 1260.
By rounding 0.65 to the nearest tenth and 1754 to the nearest hundred, we get 0.7 and 1800 respectively. Multiplying these gives an estimated product of 1260.
Explanation:To estimate the answer by rounding the first number to the nearest tenth and the second number to the nearest hundred, we start by determining the rounded numbers. The number 0.65 rounded to the nearest tenth is 0.7, and the number 1754 rounded to the nearest hundred is 1800. Multiplying these two rounded numbers together gives us 0.7 × 1800 = 1260.
Therefore, by rounding before multiplying, we can estimate that 0.65 × 1754 is approximately 1260. This estimation technique helps simplify calculations and is very useful when an exact answer is not required, especially when dealing with large numbers or calculations that would otherwise be complex.
Two different plants grow each year at different rates, which are represented by the functions f(x) = 4x and g(x) = 5x + 2. What is
the first year the f(x) height is greater than the g(x) height?
A) year 0
B) year 1
C) Year 2
D) year 3
I believe you answer would be D
Answer:
None of them.
Step-by-step explanation:
you want to find the least value of x for which f(x)>g(x). Then replacing both expressions we have
[tex]4x>5x+2\rightarrow -2>5x-4x=x[/tex] . This means that for f to be greater than g, x should be less than -2. Since we are considering x>0, given that it represents years (which are always positive), the question does not have a correct answer.
Before soccer practice, Laura warms up by jogging around the soccer field that is 80 yards by 120 yards . How many yards does she jog if she goes around the field two times.
19200! hope this helps! good luck
Answer:
800 yards
Step-by-step explanation:
80 x 4 + 12 x 4 = 800
Hope this helps!
Help I need it
A laptop computer has a selling price of $800. This includes a 20% mark up. The computer is also being offered at a discount of 20%. A customer thinks that the seller is going to break even given this information. Is the customer correct Explain your reasoning?
A. what was the price of the laptop before the markup?
b. what is the discounted price of the laptop?
Answer: customer is incorrect
Step-by-step explanation:
I am working this from b first
b $800 x .20 (20%) = $160 discount
$800 - $160 = $640 customers price
the price of the computer after the 20% discount would be $640
a customer thinks seller is going to break even this is not true
$640 (customer cost after discount) x .20 (20% discount) =$ 128
$640 + $128 = $768
Cost of the laptop before the 20% markup is $667.67
$666.67 x .20 = $133.33
$666.67 + $133.33 = $800
$768 ≠ $667.67
what is the equation of a circle centered at the origin with a radius of 15?
Answer:
x² + y² = 225
Step-by-step explanation:
The equation of a circle centred at the origin is
x² + y² = r² ← r is the radius, so
x² + y² = 15², that is
x² + y² = 225
Can someone help me with this? ASAP.
You need to multiply the amount it is dropping per day by the number of days, so you would have 0.3d
You would then need to subtract that amount from the current level of 25 feet.
Now you have 25 - 0.3d.
This total needs to be greater than or equal to 13 feet.
25 -0.3d ≥ 13
use the functions f(x)= 3x-4 and g(x)= x^2-2 to answer the following questions
a) complete the table
x l f(x)
______
-3 l
______
-1 l
______
0 l
______
2 l
______
5 l
______
x l g(x)
______
-3 l
______
-1 l
______
0 l
______
2 l
______
5 l
______
b) for what value of the domain (-3, -1, 0, 2, 5) does f(x)= g(x)
answer:
Step-by-step explanation:
a.[tex]f(x)=3x-4\\\\\text{Put the values of x from table to the equation of}\ f(x):\\\\f(-3)=(3)(-3)-4=-9-4=-13\\f(-1)=(3)(-1)-4=-3-4=-7\\f(0)=(3)(0)-4=0-4=-4\\f(2)=(3)(2)-4=6-4=2\\f(5)=(3)(5)-4=15-4=11\\\\\begin{array}{c|c}x&f(x)\\-3&-13\\-1&-7\\0&-4\\\bold{2}&\bold{2}\\5&11\end{array}[/tex]
[tex]g(x)=x^2-2\\\\g(-3)=(-3)^2-2=9-2=7\\g(-1)=(-1)^2-2=1-2=-1\\g(0)=0^2-2=0-2=-2\\g(2)=2^2-2=4-2=2\\g(5)=5^2-2=25-2=23\\\\\begin{array}{c|c}x&g(x)\\-3&7\\-1&-1\\0&-2\\\bold{2}&\bold{2}\\5&23\end{array}[/tex]
b.f(x) = g(x) for x = 2 (look at the tables)
Which graph represents the compound inequality? h2-5 and h<2
2 is correct, because:
1) we have a close interval
2)we must have node on x=-5
Las bases de un prisma recto son dos triangulos rectangulos cuyos catetos miden 1.5 cm y 1.8 cm, respectivamente, el prisma tiene una altura de 4.5cm. calcula su area total y volumen
Answer:
Part 1) The surface area is [tex]SA=35.1\ cm^{2}[/tex]
Part 2) The volume is equal to [tex]V=12.15\ cm^{3}[/tex]
Step-by-step explanation:
The question in English is
The bases of a right prism are two rectangle triangles whose legs measure 1.5 cm and 1.8 cm, respectively, the prism has a height of 4.5 cm. calculates its total surface area and volume
Part 1) Find the surface area
The surface area is equal to
[tex]SA=2B+Ph[/tex]
where
B is the area of the base
P is the perimeter of the base
h is the height of the prism
Find the area of the base B
[tex]B=(1.5)(1.8)=2.7\ cm^{2}[/tex]
Find the perimeter of the base P
[tex]P=2*(1.5+1.8)=6.6\ cm[/tex]
we have
[tex]h=4.5\ cm[/tex]
substitute the values
[tex]SA=2(2.7)+(6.6)(4.5)=35.1\ cm^{2}[/tex]
Part 2) Find the volume
The volume is equal to
[tex]V=Bh[/tex]
where
B is the area of the base
h is the height of the prism
we have
[tex]B=2.7\ cm^{2}[/tex]
[tex]h=4.5\ cm[/tex]
substitute
[tex]V=(2.7)(4.5)=12.15\ cm^{3}[/tex]
In the given figure find the value of x and y if AB parallel to CD
Answer:
x = 42
y = 38
Step-by-step explanation:
for y:
there is a corresponding angle at 58° so y + 20 must equal to 58. ∴y = 38°
for x :
first locate the straight angle at CD. The angle opposite 58° must also be 58° as it is vertically opposite. We have two values here.. 58° and 22°. Use your knowledge of straight angles and add 22 + 58, which equals to 80. Now subtract from 180 which = to 100°. We know that the angle sum of a Δ is 180° so add 38 and 100, which will give you 138°. Subtract from 180 to give you a total of 42°
Sorry if this was very lengthy haha
hope it helps:)