An inequality greater than (-3) but less than or equal to 3 is as follows:
- 3 < x ≤ 3
What is an inequality?An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.
An inequality have the following signs:
<>≤≥Therefore, an inequality greater than (-3) but less than or equal to 3 can be represented as follows:
Note the value we are comparing is x.
Hence,
- 3 < x ≤ 3
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algebra 2: help please
a scuba diver enters the water 1m away from her boat. She dives down and then resurfaces 12m away from her boat. Her diving path id in the shape of a quadratic function, where x is the distance away from the boat and y is the distance away from the surface of the water, and negative values of y are below the water. She reaches a maximum depth of 30.25m below the surface of the water.
Her diving partner wants to estimate the diver’s depths at different points away from the boat. What is the diver’s depth when she is 4m away from the boat?
Answer:
24 m depth
Step-by-step explanation:
The quadratic function modeling depth will have zeros at x=1 and x=12, the distances in meters from the boat where the diver is at the surface.
Quadratic functionThe factored form of a quadratic function can be written as ...
y = a(x -p)(x -q)
where p and q are zeros of the function. The value 'a' is a vertical scale factor.
Here, we are given y=0 at the surface, at points where x=1 and x=12. This means the function can be written as ...
y = a(x -1)(x -12)
Scale factorTo find the value of 'a', we can use the maximum depth value. That depth will be halfway between the function zeros, at x = (1+12)/2 = 6.5
-30.25 = a(6.5 -1)(6.5 -12)
30.25 = 5.5²·a = 30.25a ⇒ a=1
Model of depthThen the function modeling the diver's depth in meters is ...
y = (x -1)(x -12)
And the depth at x=4 will be ...
y = (4 -1)(4 -12) = 3(-8) = -24 . . . . meters
The diver's depth is 24 meters when she is 4 m away from the boat.
Find the measure of the indicated angle to the nearest degree.
Answer:
24.315°
Step-by-step explanation:
First use the pythagorean theorem to get the missing side since this is a right triangle.
a^2 + b^2 = c^2 →
b^2 = c^2 – a^2 →
b = (c^2 – a^2)^½
b = (17^2 – 7^2)^½
b = (289 – 49)^½
b = √240.
Then use the law of cosines to find the angle in between.
b^2 = a^2 + c^2 - 2ac * cos(B) →
b^2 - a^2 - c^2 = -2ac * cos(B) →
a^2 + c^2 – b^2 / 2ac = cos(B) →
cos^-1(a^2 + c ^2 – b^2 / 2ac) = C →
B = cos^-1(a^2 + c ^2 – b^2 / 2ac)
B = cos^-1(49 + 289 – √240 / 238)
B ≈ 75.685°.
A = 180 – B
A = 180 – 75.685
A = 24.315°
Graduate management aptitude test (gmat) scores are widely used by graduate schools of business as an entrance requirement. suppose that in one particular year, the mean score for the gmat was 473, with a standard deviation of 104. what values are three standard deviations within the mean?
The values that exist two standard deviations above and below the mean are 681 and 265.
How to determine the values?The given parameters exist:
Mean = 473
Standard deviation =104
The values above and below the mean exist calculated utilizing:
[tex]$x=\bar{x} \pm n \sigma$[/tex]
In this case n = 2.
So, we have, [tex]$x=\bar{x} \pm 2 \sigma$[/tex]
The value above is:
x = 473 + 2 [tex]*[/tex] 104 = 681
The value below is:
x = 473 - 2 [tex]*[/tex] 104 = 265
Therefore, the values that exist two standard deviations above and below the mean are 681 and 265.
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how many lengths of strings measuring 0.8meters long can be cut from a piece of string measuring 0.5kilometers
0.0016
reduce expression if possible by canceling the common factors
The graph f(x) = (x + 2) ^ 2 - 7 is translated 3 units up, resulting in the graph g(x) . Which equation represents the new function, g(x) ?
Step-by-step explanation:
x^2 +4x +4 -7 is
y=x^2+4x-3
Answer: g(x)=(x+2)²-4.
Step-by-step explanation:
g(x)=f(x)+3
g(x)=(x+2)²-7+3
g(x)=(x+2)²-4.
4ln x -8=12 its giving me other equations
The solution of the given logarithmic equation is x = 28.1
How to solve the logarithmic equation?
Here we have the logarithmic equation:
4*ln(x - 8) = 12
And we want to solve this for x.
Remember the relations:
[tex]ln(e^x) = x\\e^{ln(x)} = x[/tex]
First, we divide both sides by 4:
[tex]ln(x - 8) = 12/4 = 3[/tex]
Then, if we apply the exponential equation to both sides of our equation, we get:
[tex]e^{ln(x - 8)} = e^{3}\\\\x - 8 = e^3\\\\x = e^3 + 8 = 28.1[/tex]
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Which equation represents a population of 370 animals that decreases at an annual rate of 11% ?
The equation represents a population of 370 animals that decreases at an annual rate of 11% is [tex]p=370(0.89)^{t}[/tex].
What is an exponential function?It is defined as the function that rapidly decreases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1.
Given that,
A population of 370 animals that decreases at an annual rate of 11%
a = 370, r = 11%
p = [tex]a(1-r)^{t}[/tex]
= [tex]370(1-0.11)^{t}[/tex]
p = [tex]370(0.89)^{t}[/tex]
Hence, The equation represents a population of 370 animals that decreases at an annual rate of 11% is [tex]p=370(0.89)^{t}[/tex].
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90 times 2.5 divided by 3 +200,000?
Answer:
200,075
Step-by-step explanation:
90 times 2.5 = 225
225 divided by 3 = 75
75 + 200,000 = 200,075
Answer: 200075
Step-by-step explanation:
90 * 2.5 = 225
225 / 3 = 75
75 + 200,000 = 200,075
Urve revolves around the x-axis. if you cannot evaluate the integral exactly, use your calculator to approximate it. (round your answer to four decimal places. ) y = 16 − x2 from x = −1 to x = 1
The value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.
Given the equation y=16-[tex]x^{2}[/tex] and the limit of the integral be x=-1,x=1.
We are required to find the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1.
Equation is relationship between two or more variables that are expressed in equal to form.Equation of two variables look like ax+by=c.It may be linear equation, quadratic equation, or many more depending on the power of variable.
Integration is basically opposite of differentiation.
y=16-[tex]x^{2}[/tex]
Find the integration of 16-[tex]x^{2}[/tex].
=16x-[tex]x^{3}/3[/tex]
Now find the value of integration from x=-1 to x=1.
=16(1)-[tex](1)^{3}/3[/tex]-16(-1)-[tex](-1)^{3}/3[/tex]
=16(1)-1/3+16-1/3
=32-2/3
=(96-2)/3
=94/3
Hence the value of integration of y=16-[tex]x^{2}[/tex] from x=-1 to x=1 is 94/3.
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You are on a jungle expedition and come to a raging river. You need to build a bridge across the river. You spot a tall tree directly across from you on the opposite bank (point ). You place a pole in the ground to mark the position directly across from the tree. From the spot you are standing, you walk directly downstream 16 feet and place another pole (point ). You keep walking down stream and mark a third spot with a pole that is 7 feet from your last pole (point ). Turning perpendicular from the last pole, you walk away from the river 9 feet to another position and place a fourth pole (point ).
a. Determine if the two triangles are similar. Explain which similarity theorem you used and why.
b. Use proportions to calculate the distance across the river.
A large tree is close to point and we could chop it down at an angle to reach point and safely cross the river.
c. How tall does the tree need to be to span the river from point to ?
Daniela recorded the low temperatures during the school day last week and this week. Her results are shown in the table below.
Low Temperatures during the School Day This Week and Last Week
Low Temperatures
This Week (Degrees Fahrenheit)
42
38
45
46
39
Low Temperatures
Last Week (Degrees Fahrenheit)
56
58
52
62
62
Daniela used the steps below to find a relationship between the difference in the mean temperatures and the mean absolute deviations of the data sets.
This Week Last Week
Step 1
Find the mean.
StartFraction 42 + 38 + 45 + 46 + 39 over 5 EndFraction = 42
Find the mean.
StartFraction 56 + 58 + 52 + 62 + 62 over 5 EndFraction = 58
Step 2
Find the mean absolute deviation.
StartFraction StartAbsoluteValue 42 minus 42 EndAbsoluteValue + StartAbsoluteValue 38 minus 42 EndAbsoluteValue + StartFraction StartAbsoluteValue 45 minus 42 EndAbsoluteValue + StartFraction StartAbsoluteValue 46 minus 42 EndAbsoluteValue + StartFraction StartAbsoluteValue 39 minus 42 EndAbsoluteValue over 5 EndFraction = 2.8
Find the mean absolute deviation.
StartFraction StartAbsoluteValue 56 minus 58 EndAbsoluteValue + StartAbsoluteValue 58 minus 58 EndAbsoluteValue + StartFraction StartAbsoluteValue 52 minus 58 EndAbsoluteValue + StartFraction StartAbsoluteValue 62 minus 58 EndAbsoluteValue + StartFraction StartAbsoluteValue 62 minus 58 EndAbsoluteValue over 5 EndFraction = 3.2
Step 3 Find the ratio of the differences of the means compared to the mean absolute deviation.
StartFraction 42 over 2.8 EndFraction = 15 Find the ratio of the differences of the means compared to the mean absolute deviation.
StartFraction 58 over 3.2 EndFraction = 18.125
Step 4 The difference in the means is about StartFraction 15 + 18 over 2 EndFraction = 16.5 times the mean absolute deviations.
In which step did Daniela make the first error?
Based on the information given about the temperature, Daniela made her error on step 3 because it says: "Find the ratio of the differences of the means compared to the mean absolute deviation.
How to illustrate the error?From the information given, it van be seen that Daniela recorded the low temperatures during the school day last week and this week and her results are shown in the table.
Here, she didn't find the difference between the today and last week means. She just put the mean as a whole.
Therefore, Daniela made her error on step 3 because it says: "Find the ratio of the differences of the means compared to the mean absolute deviation. This was the error.
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400 people were surveyed for this grab how many more people prefer vanilla than do strawberry
Using proportions, it is found that 68 more people prefer vanilla than do strawberry.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Researching this problem on the internet, it is found that, out of 400 people:
35% preferred vanilla.18% preferred strawberry.Hence the amounts are:
V = 0.35 x 400 = 140.S = 0.18 x 400 = 72.The difference is:
140 - 72 = 68.
68 more people prefer vanilla than do strawberry.
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Michael is constructing a circle circumscribed about a triangle. he has partially completed the construction. what should be his next step in the construction?
Answer:
Connect the arcs to make a perpendicular bisector
If h(x) = 5 x and k (x) = startfraction 1 over x endfraction, which expression is equivalent to (k circle h) (x)?
The equivalent expression to [tex](k o h)(x)[/tex]is [tex]\frac{1}{5 + x}[/tex]
Therefore [tex](k o h)(x) = \frac{1}{5 + x}[/tex]
Given that the functions h is defined by h(x)=5+x
and k is defined by k (x) = [tex]\frac{1}{x}[/tex]
To find the composition of k and h that is: (k o h) (x)
Therefore
k (h(x)) = k (5+x)
k (h(x)) = [tex]\frac{1}{5+ x}[/tex]
The equivalent expression to is [tex]\frac{1}{5+ x}[/tex]
What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.Expressions are syntactic devices. It must be properly constituted, which means that the permissible operators must have the right amount of inputs in the right places, legal characters for these inputs, a clearly defined order of operations, etc.The syntax requirements must be followed for a string of symbols to be considered a valid mathematical expression.To learn more about Expression with the given link
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PLS HELP ITS MATH PLS
Answer:
Step-by-step explanation:
y=-1/2x+6
Erin has developed a new lotion that will help children with sensitive skin. she invests $15,225 in equipment to manufacture and package her lotion. each bottle costs $3.25 to manufacture and sells for $12. how many bottles of lotion must she make and sell before her business breaks even? a. 998 bottles b. 1740 bottles c. 174 bottles d. 1269 bottles
Her business will break even when she contains sold 1740 bottles of her lotion.
How many bottles of lotion must she make and sell before her business breaks even?Given: She invests $15,225 in equipment to manufacture and package her lotion each bottle costs $3.25 to manufacture and sells for $12.
"Break even" occurs when Revenue = Costs.
($12/bottle)x = $15225 + ($3.25)x
Simplifying the above equation, we get
$8.75x = $15225
Diving both sides of the equation by 8.75, we get
$8.75x/8.75 = $15225/8.75
x = 1740 bottles
Therefore, the value of x = 1740 bottles.
Her business will break even when she contains sold 1740 bottles of her lotion.
Therefore, the correct answer is option b. 1740 bottles.
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Students in Ms. Valendra’s science class planted 13 in different places around the school yard. After one month, they measured the heights of the conifers. They rounded each measurement to the nearest 1/4
Considering the dot plot, it is found that the tallest conifer is 3.25 inches taller than the shortest conifer.
What does a dot plot shows?It shows, with dots, the number of times that each of the measures appears in a data-set.
Researching this problem on the internet, and finding the dot plot, we have that:
The shortest conifer measures 6 and 1/4 = 6.25 inches.The tallest conifer measures 9.5 inches.The difference is:
9.5 - 6.25 = 3.25 inches.
Hence the tallest conifer is 3.25 inches taller than the shortest conifer.
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Solve the system of equations by substitution.
3 /8 x +1/3y =17/24
x + 7y = 8
By substitution, the value of x and y are 1 and 1 respectively.
How to solve system of equation?3 / 8 x + 1 /3 y = 17 / 24
x + 7y = 8
x = 8 - 7y
Let's substitute the value of x in equation(ii)
3 / 8(8 - 7y) + 1 / 3 y = 17 / 24
3 - 21 / 8 y + 1 / 3 y = 17 / 24
1 / 3 y - 21 / 8 y = 17 / 24 - 3
8y - 63y/24 = 17 - 72/ 24
-55y / 24 = -55 / 24
cross multiply
-1320y = -1320
divide both sides by -1320
y = -1320 / -1320
y = 1
Hence,
x + 7(1) = 8
x = 8 - 7
x = 1
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Bob's favorite restaurant were salmon filet and filet mignon. The restaurant served 70 specials in all, 80% of which were salmon filets. How many salmon filets did the restaurant serve?
By working with percentages, we will see that they served 56 salmon filets.
How many salmon filets did the restaurant serve?
Here we know that the restaurant served 70 specials in total, such that 80% of these were salmon filets.
So we just need to calculate what is the 80% of 70.
This is just given by:
70*(80%/100%) = 70*0.8 = 56
This means that they served 56 salmons filet.
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The chart below shows conversion between gallons and fluid ounces.
Conversion Chart
Gallons
Fluid Ounces
2
256
3
384
4
512
6
?
What is the missing value in the table?
======================================================
Explanation:
To go from gallons to fluid ounces (abbreviation fl oz), we multiply by 128
For example, 2 gallons becomes 2*128 = 256 fl oz as shown in the table.
Another example: 3 gallons = 3*128 = 384 fl oz.
Therefore, 6 gallons would be 6*128 = 768 fl oz.
To go in reverse, from fl oz to gallons, we divide by 128.
Geometry: fill in the blanks, ASAP!!!
5. Alternate interior angles: ∠1 ≅ ∠5; ∠5 ≅ ∠7 and ∠4 ≅ ∠6
6. Alternate exterior angles: ∠3 ≅ ∠9 and ∠2 ≅ ∠8
7. Corresponding angles: ∠2 ≅ ∠6; ∠3 ≅ ∠7; ∠5 ≅ ∠9; ∠4 ≅ ∠8 and ∠1 ≅ ∠3
8. Vertical angles: ∠2 ≅ ∠4; ∠3 ≅ ∠5; ∠7 ≅ ∠9; and ∠6 ≅ ∠8 .
9. ∠1 and ∠7.
What are the Special Pairs of Angles Formed by a Transversal and Parallel Lines?If two lines that are cut across by a transversal are parallel, the following special angles are formed:
Corresponding angles which are congruent: they share the same corner and lie along a transversal.Alternate interior angles which are congruent: they lie opposite each other along the transversal inside each parallel lines.Alternate exterior angles which are congruent: they lie opposite each other along the transversal outside each parallel lines.Vertical Angles which are congruent: they are directly opposite each other and share the same vertex but they are non-adjacent.Given the image given, we can identify the following special angles:
5. Alternate interior angles: ∠1 ≅ ∠5; ∠5 ≅ ∠7 and ∠4 ≅ ∠6
6. Alternate exterior angles: ∠3 ≅ ∠9 and ∠2 ≅ ∠8
7. Corresponding angles: ∠2 ≅ ∠6; ∠3 ≅ ∠7; ∠5 ≅ ∠9; ∠4 ≅ ∠8 and ∠1 ≅ ∠3
8. Vertical angles: ∠2 ≅ ∠4; ∠3 ≅ ∠5; ∠7 ≅ ∠9; and ∠6 ≅ ∠8 .
9. ∠1 ≅ ∠3 and ∠3 ≅ ∠7. So the two angles would be ∠1 ≅ ∠7.
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Leo is 23 years old and works for a company that matches his 401(k) contribution up to 4.6%. the interest rate for his 401(k) is 5.32%. if he puts away 8% of his $65,000 salary every year, how much would he have saved in 10 years? round your answer to the nearest cent. a. $7110,127.51 b. $104,564.67 c. $65,582.40 d. $62,269.66
The amount saved in 10 years is = $1,04,461.13
The correct option is B.
Future:An annuity is a series of payments that are distributed evenly over time.
One way to express the future value of an annuity of payment P for n years is,
Total salary is $65000
The interest rate is 5.32%
Trent save 8% of his salary every year.
Company puts 4.6% of salary every year.
[tex]\text { Future Value }=\mathrm{P} \times \frac{\left(1+\frac{i}{n}\right)^{n t}}{\frac{i}{n}}[/tex]
Given:
Total salary is $65000
The interest rate is 5.32%
Trent save 8% of his salary every year.
Company puts 4.6%of salary every year.
The 8% of salary is calculated as:
[tex]\text { Amount } &=\frac{8}{100} \times 65000\\[/tex]
[tex]&=\$ 5200[/tex]
The following information is available on the company's put:
[tex]\text { Amount } &=\frac{4.6}{100} \times 65000\\[/tex]
[tex]&=\$ 2990[/tex]
Total amount as follows:
[tex]\begin{aligned}\text { Amount } &=5200+2990 \\&=\$ 8190\end{aligned}[/tex]
The future value can be obtained as follows
[tex]\begin{aligned}\mathrm{FV} &=8190 \times \frac{(1+0.053)^{10}-1}{0.053} \\&=8190 \times 12.75 \\&=1,04,461.13\ \\\end{aligned}[/tex]
Hence, the amount saved in 10 years is = $1,04,461.13
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If $1= rs 115.4 ( buying rate ) and $1=rs116.20(selling rate). find the profit while selling and buying $6000.
The profit is Rs.4800.
What is profit?When, in a transaction, the selling price is greater than the cost price, it means we earn a profit. It is calculated with the help of the formula: Profit = Selling price - Cost price.
Given that,
S.P =$6000
C.P = $6000
If, 1$ = Rs.115.4 (in cost price)
1$ = Rs.116.20 (in selling price)
Then,
C.P = Rs. 115.40×6000
S.P = Rs. 116.20×6000
Then,
Profit = S.P-C.P
= 116.20×6000 -115.40×6000
= (116.20-115.40)×6000
= 0.80×6000
= Rs.4800
Hence, The profit is Rs.4800.
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does someone mind helping me with this question? Thank you!
Answer:
4/9
Step-by-step explanation:
.44444.. = 4/9
0.nnnnnnnn.... = n/9
0.mnmnmnmnmn.... = mn/99
and so on
solve the following system {y=x^2-3 and {y=3x-3 graphically and algebraicallyPLEASE HELP ME IM BEGGING
Answer:
There are two solutions:
x = 0, y = -3 Point (0, -3)
x = 3, y = -6 Point (3, 6)
The solutions are at the intersections of the two individual graphs corresponding to each of the two equations (see attached figure)
Step-by-step explanation:
Use a graphing calculator or tool to plot each equation. The point of intersection of the two is the solution to the system of equations. See attached image
Algebraically
The first equation must be equal to the second equation for a unique value of y and x
[tex]y = x^2 - 3 = 3x -3\\x^2 - 3 = 3x - 3[/tex]
Subtract 3x - 3 from both sides giving
[tex]x^2 - 3 - (3x -3) = 0\\x^2 -3 -3x + 3 = 0\\x^2 - 3x = 0\\[/tex]
Factoring out x we get
[tex]x(x-3) = 0[/tex]
This means that x = 0 and also
x -3 = 0, or x = 3
Substituting for x = 0 in y = 3x-3 gives
y = 3.0 - 3 = -3
So x= 0, y = -3 is one solution (0,-3)
Substituting for x = 3 in the same equation gives
y = 3(3) - 3 = 6
So x = 3, y = 6 is another solution (3, 6)
Re-write the quadratic function below in Standard Form y=-5(x+1)²+7
Answer:
y = - 5x² - 10x + 2
Step-by-step explanation:
y = - 5(x + 1)² + 7 ← expand (x + 1)² using FOIL
= - 5(x² + 2x + 1) + 7 ← distribute parenthesis by - 5
= - 5x² - 10x - 5 + 7 ← collect like terms
= -5x² - 10x + 2 ← in standard form
Answer: y = -5x² - 10x + 2
Step-by-step explanation:
Given quadratic function
y = -5 (x + 1)² + 7
Given requirement
Quadratic Standard Form: y = ax² + bx + c
Simplify the exponents
y = -5 (x + 1) (x + 1) + 7
y = -5 (x² + x + x + 1) + 7
y = -5 (x² + 2x + 1) + 7
Expand the parenthesis by distributive property
y = (-5) · x² + (-5) · 2x + (-5) · 1 + 7
y = -5x² + (-10x) + (-5) + 7
y = -5x² - 10x - 5 + 7
Combine like terms
[tex]\Large\boxed{y=-5x^2-10x+2}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each quadratic function with its respective graph. Graph Functions Graph of quadratic functions on a coordinate plane. Upward parabola vertex is at (2, 1) in quadrant 1. Left slope at (1, 2), (0, 5) enters quadrant 3. Right slope is at (3, 2), (4, 5) in quadrant 1. arrow Both Graph shows downward parabola plotted on a coordinate plane. The parabola has vertex at (minus 1, 4). The parabola has left slope at (minus 3, 0) and right slope at (1, 0). arrowBoth Graph shows upward parabola plotted on a coordinate plane. The parabola has vertex at (3, minus 4). The parabola has left slope at (1, 0) and right slope at (5, 0). arrowBoth
The correctly matched quadratic functions are given as follows:
Part A) The function of the First graph is f(x) = (x-3) (x + 1) Part B) The function of the Second graph is f(x) = -2 (x - 1) ( x + 3) Part C) The function of the Third graph is f(x) = 0.5(x - 6) (x + 2) What is a Quadratic Function?Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term.
Quadratic equations are another name for it. The quadratic equation has the following general form: ax2 + bx + c = 0.
How do we correctly match the graphs?Recall that:
f(x) - a (x -c) (x - d)
where
a is the leading coefficientc and d are the roots or zeros of the function.Part A) First graph
We are given to know
The solutions or zeros of the first graph are
x=-1 and x=3
The parabola open up, so the leading coefficient a is positive, the function therefore, is equal to
f(x) = (x-3) (x + 1); Find the value of the coefficient a.The vertex is equal to the point (1, -4)
Substitute and solve for a
-4 = a(1-3)(1+1)
-4 = a(-2)(2)
a = 1
Hence, the function is equal to f(x) = (x-3) (x + 1)
Part B) Second Graph
We are also given to know that
The solutions or zeros of the first graph are
x=-3 and x=1
The parabola open down, so the leading coefficient a is negative
The function is equal to f(x) = a (x-1)(x+3)
Find the value of the coefficient a
The vertex is equal to the point (-1,8)
to solve for a, we must substitute:
8 = a(-1-1) (-1+3)
8 = a(-2)(2)
a = -2
Hence, the function is equal to: f(x) = -2 (x - 1) ( x + 3)
Part C)
We are given to know that the solutions or zeros of the first graph are
x=-2 and x=6
The parabola open up, so the leading coefficient a is positive
The function is equal to f(x) = a(x-6) (x+2).
Find the value of the coefficient a
The vertex is equal to the point (2,-8)
We substitute and solve for a:
-8 = a(2-6) (2+2)
-8 = a(-4)(4)
a = 0.5
Hence, the function is equal to f(x) = 0.5(x - 6) (x + 2)
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A cylinder and a cone have the same volume. The cylinder has radius x
and height y. The cone has radius 1/2x. Find the height of the cone in terms of y.
The height of the cone in terms of y is h = 12x⁴y
How to find the volume of a cone and cylinder?The cylinder and the cone have the same volume.
Volume of a cylinder = πr²h
where
r = radiush = heightTherefore,
Volume of a cylinder = πx²y
volume of a cone = 1 / 3 πr²h
where
r = radius of the coneh = height of the coneTherefore,
πx²y = 1 / 3 × π × (1 / 2x)² × h
πx²y = πh / 12x²
πx²y × 12x² / π = h
h = 12x⁴y
Therefore, the height of the cone in terms of y is h = 12x⁴y
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Which of the following shows the simplified function of csc x sin(pi/2 -x)?
Answer:
cot x
Step-by-step explanation:
using the identities
csc x = [tex]\frac{1}{sinx}[/tex]
sin([tex]\frac{\pi }{2}[/tex] - x) = cos x
then
csc x × sin ([tex]\frac{\pi }{2}[/tex] - x)
= [tex]\frac{1}{sinx}[/tex] × cosx
= [tex]\frac{cosx}{sinx}[/tex]
= cot x
Let x = a bi and y = c di and z = f gi. which statements are true? check all of the boxes that apply. x y = y x (x × y) × z = x × (y × z) x – y = y – x (x y) z = x (y z) (x – y) – z = x – (y – z)
The first one , the second one ,the fourth one are true.
What is a commutative property in math?
This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer.
1) x + y = y + x = a + c (b + d ) i true
2) ( xy )z = x (yz) = (a + bi)(c + di)( f + gi) true
3) x - y = a + bi - ( c - di ) = a - c + ( b- d )i
y - x = c + di - ( a+bi) = c-a +(d-b)i false
4) (x + y ) + z = x + ( y + z ) = a + c +f + (b +d + g)i true
5) (x - y ) - z = a + bi - ( c + di) - ( f + gi)
= a - c . f + ( b- d - g) i
x - ( y - z ) = a + bi - ( c + di - f - gi )
= a - c + f + ( b - d + g ) i
{ put the hypothesis into the equation and get the proof }
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