Answer: x^2+2x-63
Step-by-step explanation:
Quadratic Equation = x^2-(Sum of Solution)x+(Product of Solution)
=x^2-(7-9)+(7*(-9))
=x^2+2x-63
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solve for x.
[tex]\frac{2}{3}x=\frac{4}{9}[/tex]
[tex]x=\frac{8}{27} \\\\x=\frac{2}{3} \\\\x=2\\\\x=3[/tex]
Step-by-step explanation:
[tex] \frac{2x}{3} = \frac{4}{9} \\ 2x \times 9 = 4 \times 3 \\ 18x = 12 \\ x = \frac{12}{18} \\ x = \frac{2}{3} [/tex]
x=2/3
I hope it helped you
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Is y = 2x^3+5 a linear function
Answer:
No
Step-by-step explanation:
No, y = 2x^3 + 5 is not a linear function. A linear function is a function that can be written in the form y = mx + b, where m and b are constants and x is the independent variable.
In the function y = 2x^3 + 5, we have a cubic term (x^3), which means that the function is not linear. The graph of a cubic function will have a curved shape, unlike a linear function, which will always be a straight line.
Write a polynomial, P(x), in factored form given the following requirements.
Degree: 4
Leading coefficient 1
Zeros at x=5, x=−2 and x=−3
y-intercept at (0,60)
The polynomial, P(x), in factored form is P(x) = (x - 5)(x + 2)^2(x + 3)
Writing the polynomial, P(x), in factored formFrom the question, we have the following requirements that can be used in our computation:
Degree: 4Leading coefficient 1Zeros at x=5, x=−2 and x=−3y-intercept at (0,60)The polynomial, P(x), in factored form is represented as
P(x) = (x - zeros)
So, we have
P(x) = (x - 5)(x + 2)^2(x + 3)
(x + 2) has an exponent of 2 because it makes the polynomial have a degree of 4
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What's the next form?
Answer:
I think it's 3
Step-by-step explanation:
it's skipping 2 after every three
The directional derivative of f= x^2 y z^3 along x = e^-t , y = 1 + 2 sint , z = t -cost at t =0
The directional derivative of f = x²yz³ along vector i + 2j + 2k at x = [tex]e^{-t}[/tex] , y = 1 + 2 sin t , z = t -cost at t =0 is 2/3.
Given that the functions are,
x = [tex]e^{-t}[/tex]
y = 1 + 2 sin t
z = t - cos t
At t = 0 the point will be,
x = e⁰ = 1
y = 1 + 2 sin 0 = 1
z = 0 - cos 0 = -1
So the point is (1, 1, -1).
The vector is,
a = i + 2j + 2k
unit vector of a = (i + 2j + 2k)/√(1² + 2² + 2²) = (i + 2j + 2k)/3
Given the function is, f = x²yz³
Grad. f = 2xyz³.i + x²z³.j + 3x²yz².k
directional derivative is given by
= (Grad. f)*(unit vector of a) at (1, 1, -1)
= (2xyz³.i + x²z³.j + 3x²yz².k)*(i + 2j + 2k)/3 at (1, 1, -1)
= (2xyz³ + 2x²z³ + 6x²yz²)/3 at (1, 1, -1)
= (-2 - 2 +6)/3
= 2/3
Hence required directional derivative is 2/3.
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The question is incomplete. The complete question will be -
"The directional derivative of f= x^2 y z^3 along vector i + 2j + 2k at x = e^-t , y = 1 + 2 sin t , z = t -cost at t =0"
what's 253 divided by 4 and pls show work!
Answer:
253 divided by 4 is 63.25.
Here's the work:
```
4) 253.00
24
---
13
12
---
13
12
---
1
```
Therefore, the answer is 63.25.
how to get the greatest common factor of 152,171 and 57
To find the greatest common factor (GCF) of three numbers, you can use the prime factorization method:
1. Find the prime factorization of each number:
- 152 = 2^3 * 19
- 171 = 3 * 3 * 19
- 57 = 3 * 19
2. Identify the common prime factors: 19 is the only common prime factor.
3. Multiply the common prime factors together: 19.
Therefore, the greatest common factor of 152, 171 and 57 is 19.
How do I solve this question? I need to know what the base is, what the width is, and what the height is. Thanks if you can help!!! And I will need this ASAP if you can, thanks again!!!
Answer:
I assume you are referring to a rectangular prism with dimensions of 7 feet by 13 feet by 5 feet and you are trying to identify which dimension represents the length, width, and height.
In a rectangular prism, the length is typically considered the longest dimension, while the width and height are interchangeable depending on the orientation of the prism.
So, in this case, it is likely that the 13 feet dimension represents the length, while the 7 feet and 5 feet dimensions represent the width and height (in either order). However, it is important to note that without more context, it is impossible to know for sure which dimension is which.
Find a quadratic equation which has solutions x=9+9square root of 13and x=9-9square roof of 13. Write the quadratic form in the simplest standard form x^2+bx+c
We can write the quadratic in standard form as:
y = x² -18x - 1053
How to find the quadratic equation?For a quadratic equation whose solutions are:
x = x₁
x = x₂
We can write it as:
y = (x - x₁)*(x - x₂)
Here the solutions are:
x = 9 + 9√13
x = 9 - 9√13
Then we can write the quadratic as:
y = (x - 9 - 9√13)*(x - 9 + 9√13)
Expanding that:
y = x² -18x - 81*13
y = x² -18x - 1053
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The weight of oranges growing in an orchard is normally distributed with a mean weight of 6.5 oz. and a standard deviation of 1 oz. Using the empirical rule, determine what interval would represent weights of the middle 99.7% of all oranges from this orchard.
i Got u Bro! Answer:(3.5, 9.5)
:D
write a quadratic function that passes through points (5,0) (9,0) (7,-20)
The quadratic function that passes through points is P(x) = 5(x - 5)(x - 9)
Writing the quadratic function that passes through pointsFrom the question, we have the following requirements that can be used in our computation:
Zeros at (5,0) (9,0) Point (7,-20)The quadratic function, P(x), in factored form is represented as
P(x) = a * product of (x - zeros)
So, we have
P(x) = a(x - 5)(x - 9)
Using the point (7, -20), we have
a(7 - 5)(7 - 9) = -20
So, we have
a = 5
Recall that
P(x) = a(x - 5)(x - 9)
So, we have
P(x) = 5(x - 5)(x - 9)
Hence, the function is P(x) = 5(x - 5)(x - 9)
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A mini-flashlight
is in the shape of a
rectangular prism. It is in. wide, 14in.
tall, and in. long. What is its volume?
Answer:
63 cubic inches
Step-by-step explanation:
To find the volume of the rectangular prism mini-flashlight, we need to multiply its length, width, and height.
Given that the width is 3 inches, the height is 14 inches, and the length is 1.5 inches, we have:
Volume = length x width x height
Volume = 1.5 in x 3 in x 14 in
Volume = 63 cubic inches
Therefore, the volume of the mini-flashlight is 63 cubic inches.
Write an equation then find the value of y when x =16. Show all work.
The equation can be y = 3x + 7, evaluating it in x = 16 we will get:
y = 55
How to write and evaluate an equation?We can write a linear equation, which is the simplest type of equations.
For example, let's define:
y = 3x + 7
Now the evaluation.
We want to find the value of y when x = 16. To do so, we need to evaluate the equation in x = 16, that means replacing the variable x by the number, then we will get.
y = 3*16 + 7
y = 55
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suppose that a population parameter is .7 and many samples were taken. if the size of each sample is 30 what is the standard error
The standard error is 0.0912.
The standard error (SE) is a measure of the precision of the sample mean estimate compared to the true population mean. To calculate the SE, we use the formula SE = standard deviation / square root of sample size.
In this scenario, the population parameter is 0.7, and the sample size is 30. If we assume that the sample mean is an unbiased estimator of the population mean, then the SE can be calculated using the above formula. However, we do not know the standard deviation of the population, so we use the sample standard deviation as an estimate.
Assuming the sample is large enough to assume normality, the formula becomes SE = [tex]\sqrt{(0.7*0.3)/30}[/tex] = 0.0912. Therefore, the standard error for a sample size of 30 is 0.0912. This means that if we were to take multiple samples of size 30 from the same population, the standard deviation of the means of those samples would be around 0.0912 away from the population parameter of 0.7 on average.
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1,1,2,-1,1,-2,-1 find the next number in the sequence
Answer:
The next number in the sequence is -2.
Here's how to find it:
- Start with the first two numbers: 1 and 1.
- Add them together to get 2.
- The third number in the sequence is 2.
- Add the second and third numbers together to get 1.
- The fourth number in the sequence is 1.
- Subtract the third and fourth numbers to get -3.
- The fifth number in the sequence is -3.
- Add the fourth and fifth numbers to get -2.
- The sixth number in the sequence is -2.
- Subtract the fifth and sixth numbers to get -1.
- The seventh number in the sequence is -1.
- Add the sixth and seventh numbers to get -3.
- The eighth number in the sequence is -3.
- Subtract the seventh and eighth numbers to get 2.
- The ninth number in the sequence is 2.
- Add the eighth and ninth numbers to get -1.
- The tenth number in the sequence is -1.
- Subtract the ninth and tenth numbers to get -3.
- The eleventh number in the sequence is -3.
- Add the tenth and eleventh numbers to get -4.
- Therefore, the next number in the sequence is -4.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the distance between these points.
A (5, 8), B(-3, 4)
AB =
The distance between the points (5, 8) and (-3, 4) is equal to 4√5 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-3 - 5)² + (4 - 8)²]
Distance = √[(-8)² + (-4)²]
Distance = √[64 + 16]
Distance = √80
Distance = 4√5 units.
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Graph the function f(x)=3x2–6x+2.
Plot the vertex. Then plot another point on the parabola
The graph of the function f(x) with vertex (1, 2) and another point (0, 2) is shown below.
Consider a function f(x) = 3x² - 6x + 2
We know that the graph of quadratic function is a parabola.
We graph the function f(x)
The graph of function f(x) is shown below.
From the graph of f(x), we can observe that the vertex of parabola is (1, 2)
For x = 0 the value of the function f(x) would be,
f(x) = 3x² - 6x + 2
f(0) = 3(0)² - 6(0) + 2
f(0) = 0 - 0 + 2
f(0) = 2
This means that the y-intercept of f(x) is (0, 2)
Therefore, the reuired graph of the function f(x) is shown below.
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Chris and Monique have equal-sized cookie cakes
cut into 8 equal slices. Chris gave away
3 slices Monique gave away 4 slices. Select
numbers and symbols from the box to write a
comparison for the fractions of cake Chris and
Monique each gave away.
Monique gave away a greater fraction of cake than Chris.
How to explain the fractionWe can represent the fraction of cake Chris gave away as 3/8, and the fraction of cake Monique gave away as 4/8 (which can be simplified to 1/2)
3/8 ______ 1/2
In order to compare the fractions, we can convert them to have a common denominator. The smallest common multiple of 8 and 2 is 8, so we can write:
3/8 = 3/8
1/2 = 4/8
Now we can fill in the symbol to complete the comparison:
3/8 < 1/2
Therefore, Monique gave away a greater fraction of cake than Chris.
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I need help 20 pointttsss!!
Answer: 132 cubic cm
Step-by-step explanation: 6 x 5 x 3= 90 + 42
Write a few sentences that contain practical information about memory, thinking, and learning and describe how it helps a student become a better learner
Memory, thinking, and learning are interconnected cognitive processes that are essential for academic success.
We have,
Memory, thinking, and learning are interconnected cognitive processes that are essential for academic success.
Research has shown that memory can be improved through techniques such as repetition, active recall, and mnemonic devices.
Critical thinking skills, such as analysis and evaluation, are important for understanding and retaining information.
Effective learning strategies include breaking down complex material into smaller, manageable parts and using visual aids to enhance understanding and retention.
Thus,
Developing these cognitive skills can help a student become a more efficient learner, retain information more effectively, and perform better academically.
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-12 divided by 3 5/9
your answer is 3.375
A poll showed that 53.2% of Americans say they believe that statistics teachers know the true meaning of life. What is the probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life. Round to 3 decimal places.
The probability that a statistics teachers do not know the true meaning of life is 46.8%
What is the probability of someone who does not believeFrom the question, we have the following parameters that can be used in our computation:
53.2% of Americans say they believe that statistics teachers know the true meaning of life.
This means that
P(Believe) = 53.2%
For the required probability, we have
P(Not believe) = 1 - P(Believe)
So, we have
P(Not believe) = 1 - 53.2%
Evaluate
P(Not believe) = 46.8%
Hence, the probability that a statistics teachers do not know the true meaning of life is 46.8%
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A mountain climber is at an elevation of 10,000 feet. If she descends 2,000 feet a day, which equation would be used to show how many days it will take to reach sea level (0 feet)?
-10,000 ÷ (-2,000)
-10,000 ÷ 2,000
10,000 ÷ 2,000
10,000 ÷ (-2,000)
Answer: The correct equation to use is, C. 10,000 ÷ 2,000
Which simplifies to: 5
Therefore, it will take 5 days for the mountain climber to descend from an elevation of 10,000 feet to sea level, assuming they descends at a constant rate of 2,000 feet per day.
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why are inverse realashinships between operations used to solve twop step inqualites
Inverse relationships between operations are used to solve two-step inequalities because they allow us to isolate the variable on one side of the inequality.
A two-step inequality involves two operations that need to be undone in reverse order to solve for the variable. Inverse relationships between operations are used to "undo" these operations, leading to an isolated variable.
For example, consider the inequality 2x + 5 > 11. The first operation being performed on x is multiplication by 2, and the second operation is adding 5. To solve for x, we need to undo these operations in reverse order.
The inverse relationship of multiplication by 2 is division by 2, and the inverse relationship of adding 5 is subtracting 5. Therefore, we can solve the inequality as follows:
2x + 5 > 11
2x > 6 (subtract 5 from both sides)
x > 3 (divide both sides by 2)
Here, we first subtracted 5 from both sides to undo the addition of 5, and then divided both sides by 2 to undo the multiplication by 2.
Inverse relationships between operations are used in two-step inequalities because they help to simplify the equation by undoing the operations one by one, leading to an isolated variable.
By using inverse relationships between operations, we can efficiently and systematically solve two-step inequalities and isolate the variable to find the solution set.
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A restaurant hired 18 servers for one banquet. They pay a full time server $21.00 per hour and a part time server $15.50 per hour. If the labor cost of the restaurant was $312.00 per hour, how many full time and part time servers were there for the banquet?
Let's assume that x servers were full-time and y servers were part-time. Then we can write two equations based on the given information:
x + y = 18 (since there were 18 servers in total)
21x + 15.5y = 312 (since the labor cost was $312 per hour)
To solve for x and y, we can use elimination or substitution. Here's one way to use elimination:
Multiply the first equation by 15.5 to get 15.5x + 15.5y = 279.
Subtract the first equation from the second equation to get 5.5x = 33.
Divide both sides by 5.5 to get x = 6.
Now we know that there were 6 full-time servers. We can substitute this value into either of the two equations to solve for y:
6 + y = 18
y = 12
Therefore, there were 6 full-time servers and 12 part-time servers at the banquet.
calculate the area of a circle whose circumference is 44cm
Answer:
153.94 square centimeters.
Step-by-step explanation:
To calculate the area of a circle when the circumference is given, you can use the formula:
Circumference = 2 * pi * r, where pi is approximately equal to 3.14 and r is the radius of the circle.
We can rearrange this formula to solve for the radius:
r = Circumference / (2 * pi)
Substituting the given value of circumference:
r = 44 cm / (2 * 3.14) = 7.006 cm (rounded to three decimal places)
Now that we have the radius, we can calculate the area of the circle using the formula:
Area = pi * r^2
Substituting the value of r:
Area = 3.14 * 7.006^2 = 153.94 cm^2 (rounded to two decimal places)
Therefore, the area of the circle is approximately 153.94 square centimeters.
1
Select the correct answer.
What does it mean when the correlation coefficient has a positive value?
O A.
OB.
O C.
O D.
When x increases, y decreases, and when x decreases, y increases.
When x increases, y increases, and when x decreases, y decreases.
When x increases, y decreases, and when x is constant, y equals zero.
When x increases, y increases, and when x is constant, y decreases.
Answer:
The correct answer is B.
When x increases, y increases, and when x decreases, y decreases.
7cm=_____ m
Customary metric units
Answer:
7 cm is equal to 0.07 m.
To convert centimeters to meters, you need to divide the number of centimeters by 100, since there are 100 centimeters in a meter.
So, 7 cm / 100 = 0.07 m.
what is the missing step in this proof GIVEN: ABC with AD/DB= CB/BB PROVE: DE||AC
The missing step in this proof is option A. ∠ABC ≅ ∠DBE
How did we arrive at this assertion?In order to bring about the SAS similarity criterion, the angle between the proportional sides should be congruent in the two triangles. Thus, the said angle is the same angle (angle B) in both triangles, which is reason for citing the reflexive property. It showcases ∠B ≅ ∠B.
Therefore, the answer choice showcasing angle B is option A. ∠ABC ≅ ∠DBE
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The complete question goes thus:
what is the missing step in this proof GIVEN: ABC with AD/DB= CB/BB PROVE: DE||AC
1. AD:DB = CE:EB Given
2. AD:DB+1 = CE:EB+1 Addition Property of Equality
3. (AD+DB)/DB = (CE+EB)/EB Using common denominators
4. AB = AD+ DB and CB = CE +EB segment addition
5. AB:DB = CB:EB Substitution property of equality
6. [Fill in missing statement from choices below] Reflexive property of congruence
7. ΔABC ~ ΔDBE SAS similarity criterion
8. ∠BAC ≅ ∠BDE Corresponding angles of similar triangles are congruent.
9. DE||AC If the corresponding angles formed by two lines cut by a transversal are congruent, then the lines are parallel.
What is the missing step in this proof?
A. ∠ABC ≅ ∠DBE
B. ∠BCA ≅ ∠BDE
C. ∠ACB ≅ ∠DEB
D. ∠BDE ≅ ∠ADE
E. ∠CAB ≅ ∠DAC
put numbers to order them from least to greatest.
-2.43
-2 2/3
2.045
2 5/9
Answer:
-2.67, -2.43, 2.045, 2.56
Step-by-step explanation:
First, we can convert -2 2/3 to a decimal by dividing 2 by 3 and subtracting the result from -2, which gives us:
-2 2/3 = -2.67
Next, we can convert 2 5/9 to a decimal by dividing 5 by 9 and adding the result to 2, which gives us:
2 5/9 = 2.56
So, the ordered list is:
-2.67, -2.43, 2.045, 2.56