Word Problem #1:
You are in a submarine at a depth of some unknown value x. The submarine rises 15 feet. After this point, you are able to record the depth to be 18 feet below sea level.
x = original depth
15 = height you rise up
-18 = final depth
x+15 = final depth
x+15 = -18 is the equation we solve to find the value of x
=========================================================
Word Problem #2:
You are in debt to your friend. Debt is represented by negative numbers. For example, writing -2 means you are 2 dollars in debt. If you start off being x dollars in debt, but pay off $15, then you will have a balance of x+15 dollars. If this new final balance is -18, then we can say x+15 = -18
So in short: you go from x dollars in debt to 18 dollars in debt after paying off $15 to your friend.
The mass of a marine organism, in pounds, p years after it is born is given by the polynomial function R(p)=−4p2+300p. Find the mass when p=20 years .
Answer:
R(p) = -4p^2 + 300p when p=20.
R(p) = -4(20)^2 + 300(20)
R(p) = -1600 + 6000
R(p) = 4400
The mass when p=20 years is 4400.
multiply the polynomial (2x^2+5x+5)(4x-3)
So I simplify the expression and it is..
8x^3 + 14x^2 + 5x − 15
____
I hope this helps, as always. I wish you the best of luck and have a nice day, friend..
What values are excluded from the domain and range of the function f(x)= x+3/2x+5?
Answer:
B. Domain: -5/2
Range: 1/2
Step-by-step explanation:
If you plug -5/2 for x, it becomes no solution due to the zero in the denominator.
If you plug 1/2 for y and let your calculator do its thing, it becomes no solution.
Because these values cannot be solved for in the equation, they are excluded from the domain and range.
Edit: I got it correct on the Unit Review on edge.
The domain and range values that are excluded from the function given as f ( x ) = ( x + 3 ) / ( 2x + 5 ) are x = -5/2 and y = 0
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
The function f(x) = (x + 3)/(2x + 5) has certain values that are excluded from its domain and range.
The function f(x) is defined for all real numbers except for the values of x that make the denominator (2x + 5) equal to zero.
Therefore, the values of x that are excluded from the domain of f(x) are those that satisfy the equation 2x + 5 = 0.
2x + 5 = 0
2x = -5
x = -5/2
The range of f(x) is all real numbers except for zero (0), because it is never equal to zero.
Hence , the values excluded from the domain of f(x) are x = -5/2 and the values excluded from the range of f(x) are y = 0
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which is the completly factored form of 3x2-12x-15?
Answer:
(3x-15)(x+1)
Step-by-step explanation:
Given an expression in the form ax²+bx+c, where a,b and c are constants, we can factor it by first finding the two numbers that when multiplied equal to ac and when added equal to b
The expression 3x²-12x-15 can be factored as follows:
The two numbers that can be added to give 3×(-15) and when added result to -12 are -15 and 3.
Thus, 3x²+3x-15x-15
3x(x+1)-15(x+1)
The simplified form becomes: (3x-15)(x+1)
Answer:
A
Step-by-step explanation:
3(x + 1)(x – 5)
Which of the following circles have their centers in the third quadrant? Check all that apply.
Answer:
B and D
Step-by-step explanation:
The center of the first one is (-3,6)
The center of the second one is (-9,-12)
The center of the third one is (-14,14)
The center of the fourth one is (-16,-3)
The first one has center in the 2nd
The second one has center in 3rd
The third one has center in the 2nd
The fourth one has center is the 3rd
Answer:
The correct answer options are B. [tex](x + 9)^2 + (y + 12)^2 = 36[/tex] and D. [tex](x + 16)^2 + ( y + 3)^2 = 17[/tex].
Step-by-step explanation:
We know that the formula of a circle is [tex](x - h)^2 + (y - k)^2 = r^2[/tex] where [tex]k[/tex] is the value of the ordinate, [tex]h[/tex] is the value of the abscissa and [tex] r [/tex] is the radius of the circle.
B. [tex](x + 9)^2 + (y + 12)^2 = 36[/tex]
[tex][x - (-9)]^2 + [y - (-12)]^2 = 6^2[/tex]
Center (-9, -12)
D. [tex](x + 16)^2 + ( y + 3)^2 = 17[/tex]
[tex][x - (-16)]^2 + [y - (-3)]^2 =\sqrt{17}[/tex]
Center (-16, -3)
Cot^2 x-csc^2 x=-1 for all values of x. True or false
Answer:
TRUE
Step-by-step explanation:
The well known trigonometry identity states that cot^2(x) + 1 = csc^2(x), rearrangin the equation we have that cot^2(x) - csc^2(x) = -1, which is exactly the expression in the statement. Therefore, the expression is TRUE.
one hundred fifty-six thousandths in decimals Can u please answer this ASAP I will give you 20 points
Here it is: 0.156
That is the decimal representation of 156/1000
.156.
If they are “thousandths” then you know there is 3 decimal places.
Hope this helps!
what is the number of roots for polynomial function of f(x) = (x^2 + 6)^2
Answer:
x=±√6i
Step-by-step explanation:
[tex](x^{2} +6)^{2} =0[/tex]
[tex]x^{2}+6=0[/tex]
[tex]x^{2} =-6[/tex]
x=±√6i
Sam and Erica are playing a board game. They spin a pointer to determine whether to move forward or back. They call a number cube to determine how many spaces to play. What is the probability of moving forward an even number of spaces?
Answer:
Answer is 1/4.
Step-by-step explanation:
The sample space of an event is the list of all possible outcomes.
Let F represent moving forward and B represent moving backward.
This makes the sample space for the game
F1, F2, F3, F4, F5, F6
B1, B2, B3, B4, B5, B6
There are 6 ways to move forward; only 3 of these are even numbers.
This is 3 ways out of 12 possible moves.This makes the probability
3/12.
3/12=1/4
Thus the probability of moving forward an even number of spaces
is 1/4....
Answer:the answer is 1/4
Step-by-step explanation:
the number of pieces of popcorn in a large movie theater popcorn bucket is normally distributed, with a mean of 1610 and a standard deviation of 10. Approximately what percentage of buckets contain between 1600 and 1620 pieces of popcorn?
A. approximately 68%
B. approximately 75%
C. approximately 95%
D. approximately 99.7%
Answer:
A. Approximately 68%
Step-by-step explanation:
Number of pieces of popcorn in a bucket is normally distributed.
Mean = μ = 1610
Standard deviation = б = 10
We know that in normal distribution, approximately 34% of bags will fall with in one standard deviation on one side. On both sides within the range of 1 standard deviation, 34 + 34 = 68 % of bags will fall.
A table of normal distribution about mean is attached for better understanding.
Our range is:
1600 to 1620
1610 - 10 to 1610 + 10
μ ± б
mean ± 1 standard deviation
Our range is within 1 standard deviation. Hence, Approximately 68% of buckets contain between 1600 and 1620 pieces of popcorn.
Answer:
A 68
Step-by-step explanation:
plz Simplify using i. √-15√-4
The expression √-15√-4 is simplified to -2√15 using the imaginary unit i, where i represents the square root of -1. We do this by simplifying each square root with i and then multiplying the results together, remembering that i^2 equals -1.
Explanation:To simplify the expression using i, where i is the imaginary unit we define as the square root of -1, we have √-15√-4. We can start by simplifying each square root separately using i:
√-15 = √(15 × -1) = √15 × √i = √15i
√-4 = √(4 × -1) = √4 × √i = 2i
Now, you simply multiply the two results together:
√15i × 2i = (√15 × 2) × (i × i) = 2√15 × i²
Since i² equals -1, our expression simplifies to:
2√15 × -1 = -2√15
Therefore, the simplified form of the expression √-15√-4 using i is -2√15.
Barney has a swimming pool in his backyard. Calculate the volume of the swimming pool. Round your answer to the nearest whole number. a0 cubic feet
Answer:
1593 us gallons
Step-by-step explanation:
Answer:
159
Step-by-step explanation:
a number multiplied by 1/3 is 1/18
Answer:
1/6
Step-by-step explanation:
[tex]\frac{1}{3}x=\frac{1}{18}\\3(\frac{1}{3}x=\frac{1}{18} )\\[/tex]
[tex]x=3/18\\x=1/6[/tex]
Write each fraction in simplest form 6/9 4/10 15/20 29/24 16/56 45/72 18/60 32/72
Answer:
6/9=2/3
4/10=2/5
15/20=3/4
29/24 stays the same because 29 is a prime number
16/56=2/7
45/72=5/8
18/60=3/10
32/72=4/9
Step-by-step explanation:
If both the numerator and denominator are even, then you can divide them by 2 until one or both of them become odd. If the number on both the top and bottom add up to a multiple of three, then you can divide the numbers by three. And it goes on to every prime number.
Order 5.505,5.55, 0.555, 5.005 from greatest to least.
Answer: 5.55, 5.505, 5.005, 0.555
Step-by-step explanation:
The ordered sequence from greatest to least for the numbers 5.505, 5.55, 0.555, 5.005 is: 5.55, 5.505, 5.005, 0.555. This is done by comparing the values by comparing the digits at each decimal place, from left to right.
Explanation:To order the numbers 5.505, 5.55, 0.555, 5.005 from greatest to least, we would look at the digits in their decimal places from left to right. Starting from the first place, 5.55 is the largest as it is the only number with a '5' in the hundredth place. Next, both 5.505 and 5.005 have '5' in the units place. However, 5.505 has a '5' in the thousandth place, while 5.005 has '0'. Therefore, 5.505 is larger. Finally, 0.555 is the smallest as it is less than 1. So, the numbers, ordered from greatest to least are: 5.55, 5.505, 5.005, 0.555.
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Simplify the expression.
(a^3/2)^3
The simplified expression is [tex]\(\frac{a^9}{8}\)[/tex].
To simplify the expression [tex]\((a^3/2)^3\)[/tex], follow these steps:
1. Apply the power of a power rule, which states that [tex]\((x^m)^n = x^{m \times n}\)[/tex]. In this case, [tex]\(x = a^3/2\)[/tex], [tex]\(m = 1\)[/tex], and [tex]\(n = 3\)[/tex].
2. Distribute the exponent over the numerator and the denominator:
[tex]\((a^3/2)^3 = (a^3)^3 / (2)^3\)[/tex].
3. Apply the power of a power rule to [tex]\((a^3)^3\)[/tex]:
[tex]\((a^3)^3 = a^{3 \times 3} = a^9\)[/tex].
4. Apply the power of a power rule to [tex]\(2^3\)[/tex]:
[tex]\(2^3 = 8\)[/tex].
5. Combine the results to get the simplified expression:
[tex]\(\frac{a^9}{8}\)[/tex].
Therefore, the expression [tex]\((a^3/2)^3\)[/tex] simplifies to [tex]\(\frac{a^9}{8}\)[/tex].
NEED URGENT HELP!!!!!!!!)
A bag has 7 blue marbles, 3 red, 2 green, and 8 white. You pick a marble, record its color, and return it. If you repeat this process 150 times, how many times can you expect to pick a blue or red marble? Write your answer as a percent!
Answer:
50%
Step-by-step explanation:
The total number of marbles is 7 + 3 + 2 + 8 = 20
Blue or red means that the total on any one draw is 7 + 3 = 10
You would expect to draw blue or red 1/2 the time.
Out of 150 throws, you would get 1/2 * 150 which is 75 but that is not what you are asked.
% = (1/2 ) * 100 = 50% of the time
Which is the graph of y – 3 =-2/3 (x + 6)?
Answer:
First graphStep-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
We have the equation:
[tex]y-3=-\dfrac{2}{3}(x+6)\\\\y-3=-\dfrac{2}{3}(x-(-6))[/tex]
the coordinates of the point is (-6, 3).
Only on the first graph the line passes through the point (-6, 3).
Answer:
A
Step-by-step explanation:
What is the length of AC? Round to the nearest tenth.
Answer:
AC ≈ 10.5 cm (1 dec. place )
Step-by-step explanation:
Given
tan55° = [tex]\frac{15}{b}[/tex]
Multiply both sides by b
b × tan55° = 15 ( divide both sides by tan55° )
AC = b = [tex]\frac{15}{tan55}[/tex] ≈ 10.5 cm
Which of the following terms correctly describe the object below? Check all that apply
Answer:
Step-by-step explanation:
Solid
Prism
Cube
Answer:
The correct options are A,C and E.
Step-by-step explanation:
We need to find the correct terms for the given figure.
From the given figure it is clear that the figure is a cube. We know that cube is a 3D figures and it is also known as square prism or solid.
Therefore, the correct options are A,C and E.
Square and polygon are 2d figures. So, these terms are not correct for given figure.
The sides of a pyramid are triangular which meet at the top.
Therefore, the correct options are B, D and F.
Which of the following shows a number in a fraction form? A. 3/7 B.3 C.1/2 D.3.7
A. and C. are fractions. this is because they are only proportions of a whole unless they are a mixed number. but in this case, these numbers do not go over 1 (a whole).
Answer: Option A and Option C
[tex]\frac{3}{7}[/tex] and [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The numbers in the form of fraction have the following form:
[tex]\frac{b}{c}[/tex]
Where b is known as numerator and c is known as denominator.
To know which of the numbers shown has a fraction form, identify all those with the form [tex]\frac{b}{c}[/tex]
Then you can see that the answer is option A and option C
[tex]\frac{3}{7}[/tex] and [tex]\frac{1}{2}[/tex]
Solve for x: y = x + 4
That's too easy...
[tex]y=x+4\\x=y-4[/tex]
A map has a scale of 3.5 inches = 20 kilometers. If the distance between two cities on the map is 4.9 inches, what is the actual distance between the two cities?
Answer:
28 i think.
Step-by-step explanation:
Answer:
The actual distance between the two cities is 28 kilometers
Step-by-step explanation:
A map has a scale of 3.5 inches = 20 kilometers
Distance between two cities on the map = 4.9 inches
We can use the unitary method in this question to get the actual distance between two cities
∵ 3.5 inches on the map = 20 kilometers
∴ 1 inch distance on the map = [tex]\frac{20}{3.5}[/tex] kilometers
∴ 4.9 inches on the map = [tex]\frac{20}{3.5}\times 4.9[/tex]
= 28 kilometers
Therefore, the actual distance between the two cities is 28 kilometers.
which graph or graphs appear to show a sinusoid ?
Answer:
D
Step-by-step explanation:
Sinusoid graphs look like regular waves.
It is obvious that only I and III look like waves.
II is known as a stepwise function.
Option: D is the correct answer.
D. I and III only
Step-by-step explanation:The graph of a sinusoidal function is a smooth periodic graph.The graph is continuous all over the x-axis and also it repeats itself after every fixed interval.From the graph that is provided to us we observe that the graph I is a sinusoidal graph since it is similar to a graph of sine graph.
Also, the graph II is not a continuous graph and hence it can't be a graph of sinusoidal graph.
Also, graph III is similar to a graph of sine function and hence it represent a graph of a sinusoidal graph.
what is 6 times the quantity x plus 4?
Answer: 6x + 4
6x represents 6 times the quantity x.
+ 4 represents plus 4.
Put 6x and + 4 together to get 6x + 4.
Which number can each term of the equation be multiplied by to eliminate the fractions before solving? 6 – x + = x + 5 2 3 6 12
Answer:its 12
Step-by-step explanation:
The number can each term of the equation be multiplied by to eliminate the fractions before solving is 12, the correct option is D.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that;
Equation 6 – x + = x + 5
Now,
the least common multiple of 2 and 3, which are the denominators of the fractions in the equation. Multiplying each term by 12 will clear the fractions and result in an equivalent equation without fractions. For example: 12(6 - x + ) = 12(x + 5) 2 3 Simplifying, we get: 72 - 12x + 4 = 12x + 60. This is an equation without fractions that can be solved for x.
Therefore, by the given equation the answer will be 12.
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I WILL GIVE BRAINLIEST What is the value of x?
Answer:
A 30
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
100 = 70+x
Subtract 70 from each side
100-70 = 70-70 +x
30 =x
Choose the quadratic equation that has a leading coefficient of 1 and solutions 3 and -2.
Options:
A.) x^2+x+6=0
B.) x^2-x-5=0
C.) x^2+x+5=0
D.) x^2-x-6=0
Answer:
Option D [tex]x^{2} -x-6=0[/tex]
Step-by-step explanation:
Verify each quadratic equation
case A) we have
[tex]x^{2} +x+6=0[/tex]
This quadratic equation has a leading coefficient of 1
Substitute the value of x=3 and x=-2 in the equation
For x=3
[tex](3)^{2} +(3)+6=0[/tex]
[tex]18=0[/tex] ----> is not true
therefore
x=3 is not a solution of the quadratic equation
case B) we have
[tex]x^{2} -x-5=0[/tex]
This quadratic equation has a leading coefficient of 1
Substitute the value of x=3 and x=-2 in the equation
For x=3
[tex](3)^{2} -(3)-5=0[/tex]
[tex]1=0[/tex] ----> is not true
therefore
x=3 is not a solution of the quadratic equation
case C) we have
[tex]x^{2} +x+5=0[/tex]
This quadratic equation has a leading coefficient of 1
Substitute the value of x=3 and x=-2 in the equation
For x=3
[tex](3)^{2} +(3)+5=0[/tex]
[tex]17=0[/tex] ----> is not true
therefore
x=3 is not a solution of the quadratic equation
case D) we have
[tex]x^{2} -x-6=0[/tex]
This quadratic equation has a leading coefficient of 1
Substitute the value of x=3 and x=-2 in the equation
For x=3
[tex](3)^{2} -(3)-6=0[/tex]
[tex]0=0[/tex] ----> is true
therefore
x=3 is a solution of the quadratic equation
For x=-2
[tex](-2)^{2} -(-2)-6=0[/tex]
[tex]4+2-6=0[/tex]
[tex]0=0[/tex] ----> is true
therefore
x=-2 is a solution of the quadratic equation
A car travels 85 kilometers per hour. What is the equivalent speed in meters per hour?
The equivalent speed in meters per hour is 85000 m/hr.
What is speed?Speed exists as a scalar quantity that describes how fast an object is moving, regardless of its direction.
Speed exists as the time rate at which an object exists moving along a path, while velocity exists as the rate and direction of an object's movement. Put another way, speed exists as a scalar value, while velocity is a vector.
Here given that,
A car travels 85 kilometers per hour.
Using, the general conversion method.
1 km = 1000 m
= ( 85 km/hr ) (1000 m/1km)
The unit km cancels = 85000 m/hr
Hence, 85000 m/hr is the equivalent speed in meters per hour.
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85,000 meters per hour.
If a car travels 85 kilometers per hour, to find the equivalent speed in meters per hour, we need to convert kilometers into meters. Since 1 kilometer is equal to 1,000 meters, we multiply the speed in kilometers by 1,000 to get the speed in meters.
So, the car's speed in meters per hour would be:
85 km/h × 1,000 m/km = 85,000 meters per hour.
This conversion is straightforward and is based on the relationship that 1 km = 1,000 m.
What is the solution to this equation?
x² + 101 = 1
A. 10i, -10i
B. 10,-10
c. -10
D. 10i
Answer:
A. 10i and -10i
Step-by-step explanation:
We are given our equation as
[tex]x^2+101=1\\[/tex]
Let us subtract 101 from both hand sides
[tex]x^2+101-101=1-101\\[/tex]
[tex]x^2=-100[/tex]
Now taking square roots on both hand sides
[tex]\sqrt{x^{2}}} = \sqrt{-100}[/tex]
[tex]x=\sqrt{100} * \sqrt{-1}[/tex]
[tex]x=10 * (+i) \\x=10*(-i)\\[/tex]
[tex]x=+10i \\x=-10i\\[/tex]