Solutions for the system 10x^2 -y=48
2y=16x^2+48
Answers
Solutions are (x, y) = (-6, 312) and (6, 312).
_____
Divide the second equation by 2, then substitute the expression for y into the first equation. Solve the quadratic for x.
.. 10x^2 -(8x^2 +24) = 48
.. 2x^2 -72 = 0
.. 2(x -6)(x +6) = 0
.. x = -6 or 6
.. y = 8x^2 +24 = 8*36 +24 = 312 . . . for either value of x
Answer:
Solutions are (x, y) = (-6, 312) and (6, 312).
Step-by-step explanation:
Related Questions
Which statements about the opposite of −12 are true? Select each correct answer. −12 and its opposite are on located on the same side of zero on a number line. The opposite of the opposite of −12 is −12 . The opposite of −12 is −112 . −12 and its opposite are located the same distance from zero on a number line.
there's more than 1 answer
Answers
The opposite of the opposite of -12 is -12
The opposite of -12 is 12, and the opposite of 12 is -12.
-12 and its opposite are located the same distance from zero on a number line.-see attached picture
The true statements about the opposite of -12 are that the opposite of the opposite of -12 is -12 and -12 and its opposite are located the same distance from zero on a number line. The opposite of -12 is +12.
Explanation:In mathematics, the opposite of a number is also called its additive inverse, which is the number that, when added to the original number, will result in zero. −12 and its opposite, +12, are indeed located on opposite sides of zero on a number line, not on the same side. The second statement is true, the opposite of the opposite of −12 is indeed −12. The third statement is incorrect, the opposite of −12 is +12, not −112. The fourth statement is also true, −12 and its opposite are both 12 units away from zero on a number line, so they're at the same distance from zero.
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If a student scored 82 points on a test where the mean score was 78.2 and the standard deviation was 6.7. the student's z score is .
Answers
x = data value
m= mean
sd = standard deviation
z= (82-78.2) / 6.7
=0.567
=0.57
please translate 2 minus the product of a number and 9 is 20.
Answers
2 minus the product of a number and 9 is 20.
2-9n=20 <== equation
number=n minus= - (9 and n are next to each other, so that means they are being multiplied) It is equal to 20.
I hope this helps!
~kaikers
The statement '2 minus the product of a number and 9 is 20' translates to the equation 2 - 9x = 20. Solving for x, we find the solution x = -2, meaning the number in question is -2.
The student is asking to translate the phrase '2 minus the product of a number and 9 is 20' into a mathematical equation. The 'product of a number and 9' can be represented as '9x' where 'x' is the unknown number. Therefore, translating the entire phrase, we end up with the equation: 2 - 9x = 20.
To solve for 'x', we first bring '9x' to the other side of the equation by adding '9x' to both sides, resulting in 2 = 9x + 20. Subsequently, we subtract 20 from both sides, yielding -18 = 9x, and then we divide both sides by 9 to find the value of 'x'. So, x = -18 / 9, which simplifies to x = -2.
The solution for the equation is x = -2, which means the number we were looking for is -2.
how can you be able to find an area
Answers
Melissa bought a cake that cost $75. the sales-tax rate is 10 percent. what is the total amount she paid for the cake
Answers
Answer:
The total amount that Melissa paid for the cake is $82.5
Step-by-step explanation:
we know that
The total amount that Melissa paid for the cake is equal to the cost of the cake plus the sales tax
we have that
the cost is equal to $75
Find the sales tax
The sales tax is 10%, therefore find the 10% of the cost of the cake
10%=10/100=0.10
so
(0.10)*$75=$7.5
Adds the cost and the sales tax
$75+$7.5=$82.5
convert 3(3.14)/8 radians to degrees
Answers
3pi/8 * 180/pi = 67.5
A chord of a circle is a line segment connecting any point on the circle to the center of the circle.
Answers
Answer:
FALSE
Step-by-step explanation:
A chord of a circle is a line segment that connects two points on the circle.
Answer:
FALSE
Step-by-step explanation:
The area of circular garden is 530.66 feet2. What is the circumference of the garden? (Use 3.14 for .
Answers
A cake recipe suggests a cooking temperature of 325 °F if the batter is less than one inch thick and 350 °F if the batter is more than one inch thick. If the cake batter has a volume of 110 in3 and your cake pan is 9 inches by 11 inches, what does the oven need to be set at if the oven temperature settings are in degrees Celsius? (round to nearest whole number) A) 140 °C B) 163 °C C) 177 °C D) 190 °C
Answers
Answer C
the shape of cake pan is usually cuboid
volume of cuboid = length * breadth * height
110 = 9 *11 * height
height = 10/9 = 1.11 inches
so, the batter is more than 1 inch thick,
the temperature required is 350 degree F or 177 degree C
what is the sum of the rational expressions below? 2x-1/7x + x/x-2
a. 9x^2-5x+2/7x^2-2
b. 9x^2-5x+2/7x^2-14x
c. 3x-1/8x-2
d. 2x^2-5x+2/7x^2-14x
Answers
x-4 (2x+3x/2x-1) ( the 2x's cancel)
x-4 (3x/-1)
x-4 (-3x) (expand)
-3x^2 + 12x=0
-3x^2= -12x (bring 12x to other side making it negative)
-3x^2/3x= -12x/-3x (divide both sides by -3x)
x=4
Hope that helps
You know the first term of the numerator wil be 2x^2 +7x^2 = 9x^2, and the last term of the denominator will be 7x(-2) = -14x.
This is sufficient work to identify selection B as the correct choice.
True or False 68oz < 4lb 6oz
Answers
Answer:true!!!
Step-by-step explanation:
A tree on a hillside casts a shadow c = 235 ft down the hill. if the angle of inclination of the hillside is b = 16° to the horizontal and the angle of elevation of the sun is a = 46°, find the height of the tree. (round your answer to the nearest foot.)
Answers
Final answer:
By using the tangent function with the effective angle formed by the difference between the sun's elevation and the hill's incline, and the length of the shadow, we calculate the height of the tree to be approximately 136 feet.
Explanation:
To find the height of a tree on a hillside, we utilize the given angles and the length of the shadow it casts. The shadow is cast down the hill (c = 235 ft) with the hill inclining at an angle of 16° to the horizontal (b) and the sun's angle of elevation at 46° (a). To solve this, we can use trigonometry, specifically the concept of similar triangles and the tangent function, which relates the angle to the ratio of the opposite side over the adjacent side in a right triangle.
First, we find the effective angle Θ the sun's rays make with the hillside, which is the difference between the sun's elevation angle and the hill's inclination angle: Θ = 46° - 16° = 30°. Then, using the tangent function which involves the height of the tree (h) and the length of the shadow (c), we set up the equation tan(Θ) = h / c. Substituting the values gives tan(30°) = h / 235 ft.
Next, we solve for h: h = 235 ft x tan(30°). Calculating this, we find h is approximately 135.7 ft. Therefore, rounding to the nearest foot, the height of the tree is 136 feet.
The set of points (2, 3), (9, 3), (9, –2), and (2, –2) identifies the vertices of a quadrilateral. Which is the most specific description to tell which figure the points form?
A parallelogram
B square
C rectangle
D trapezoid
Answers
Answer:
C rectangle
Step-by-step explanation:
All the coordinates of the setpoint are (x,y) so, you need to draw the axis and you'll found a rectangle (attached)
It is not a square because its side and height are not equal.
It is not a parallelogram because there are no diagonals.
It is not a trapezoid because it has parallels sides.
It's a rectangle because it has two pairs or parallels, one longer than the other.
Olive wants to invite friends over for some ice cream. She has a total of 8 pints of ice cream in her freezer. If she splits each pint into 1/2 pint servings, how many servings of ice cream will olive have?
Answers
Olive has a total of 8 pints of ice cream
If she splits each pint into 1/2 pint servings----------> 8/(1/2)-----> 8*2=16
the answer is 16 servings of ice cream
Solve 12 = x/4 algebraically. Then, check your answer.
Answers
this is found by simplifying both sides of the equation , then isolating the variable
Write a number sentence that compares 3/5 and 5/6
Answers
Solve the equation x^16 – 2x^15 – x^14 + 4x^13 – x^12 – 2x^11 + x^10 = 0 in the real number system.
a) x = 0 with multiplicity 10, x = –1 with multiplicity 4, x = 1 with multiplicity 2
b) x = 0 with multiplicity 10, x = –1 with multiplicity 3, x = 1 with multiplicity 3
c) x = 0 with multiplicity 10, x = –1 with multiplicity 2, x = 1 with multiplicity 4
d) x = –1 with multiplicity 2, x = 1 with multiplicity 4
Answers
x^10
x^10(x^6 - 2x^5 - x^4 + 4x^3 - x^2 - 2x + 1) = 0
So far we know that D won't work.
x - 1 is a factor because putting 1 in for the xs in the expression inside the brackets gives 0 Now you need to do a division. I'm going to assume you can do that.
Using division, I get
x^5 - x^4 - 2x^3 + 2x^2 + x - 1 Now divide x - 1 into this mess again. You get
x^4 - 2x^2 + 1 which factors into
(x^2 - 1)(x^2 - 1) which factors into
(x - 1)(x + 1)(x - 1)(x + 1) = 0
The first two divisions add (x -1)(x - 1)
========================
So we have (x - 1) with a multiplicity of 4 and (x + 1) with a multiplicity of 2
or x = 1 with a multiplicity of 4 and x = -1 with a multiplicity of 2 and x = 0
with a multiplicity of 10
That's the answer.
===========================
C <<<< ===== Answer.
Answer:
C:x = 0 with multiplicity 10, x = –1 with multiplicity 2, x = 1 with multiplicity 4
Match each area to its corresponding radius or diameter of the circle.(All areas are approximate.) Tiles area: 221.5584 square units area: 78.5 square units area: 452.16 square units area: 36.2984 square units area: 314 square units area: 886.2336 square units Pairs radius: 12 units arrowBoth diameter: 16.8 units arrowBoth radius: 3.4 units arrowBoth diameter: 10 units arrowBoth
Answers
Area circle=pi*r²--------------> r=√(A/pi)
case 1) 221.5584 square units area -------------> r=√(221.5584/pi)=8.398 units
Diameter=2r-----> 2*8.4=16.8 units
case 2) 78.5 square units area-------------> r=√(78.5/pi)=5 units
Diameter=2r-----> 2*5=10 units
case 3) 452.16 square units area -------------> r=√(452.16/pi)=12 units
Diameter=2r-----> 2*12=24 units
case 4) 36.2984 square units area -------------> r=√(36.2984/pi)=3.4 units
Diameter=2r-----> 2*3.4=6.8 units
case 5) 314 square units area -------------> r=√(314/pi)=10 units
Diameter=2r-----> 2*10=20 units
case 6) 886.2336 square units -------------> r=√(886.2336/pi)=16.8 units
Diameter=2r-----> 2*16.8=33.6 units
A right triangle has legs that are 15 feet and 25 feet long. What is the length of the hypotenuse? Enter your answer as a decimal in the box. Round your answer to the nearest hundredth.
Answers
Hope this helps!
Sara wrote 524 words in her journal. Then she crossed out 56 words and added 95 new words. How many words are written in her journal now?
Answers
The system of equations is graphed on the coordinate plane. y=−12x−1y=14x−4 A graph with a blue line passing through coordinates (0, -4) and (4, -3) and a red line passing through coordinates (0, -1) and (4, -3). Enter the coordinates of the solution to the system of equations in the boxes. ( , )
Answers
case 1)
system of equations is
y=−12x−1
y=14x−4
using a graph tool
see the attached figure
the solution of the system is the point (0.115,-2.385)
case 2)
system of equations is
blue line passing through coordinates A (0, -4) and B (4, -3)
red line passing through coordinates C(0, -1) and D (4, -3)
using a graph tool
see the attached figure
the solution of the system is the point (4,-3)
There are 100 books in the library. There are non-fiction and fiction books. Write the fraction of the books that are fiction.
Answers
Let
x--------------------- > non-fiction books.------------------ > x=60
y--------------------- > fiction books.
we know that
x+y=100
y=100-x=100-60=40
the fiction books. are y=40
if 100%----------------------- > 100 books
X---------------------------- > 40
X=40*100/100=40%
40%-------------- > 40/100=20/50=2/5
the answer is
the fraction of the books that are fiction is (2/5)
3.1 Q15
An athlete whose event is the shot put releases a shot. When the shot whose path is shown by the graph to the right is released at an angle of 70°, it's height, f(x), in feet, can be modeled by:
[tex]f(x)=-0.06x^2 + 2.7x + 5.9[/tex]
where x is the shot's horizontal distance, in feet, from its point of release.
What is the maximum height of the shot and how far from it's point of release does this occur?
Answers
Find x-coordinate of the vertex (horizontal distance)
The function above is in standard form of ax² + bx + c = 0
In standard form of ax² + bx + c = 0, we could find the x-coordinate of the vertex by the formula of
[tex]x= -\cfrac{b}{2a} [/tex]
Extract the information of a and b from the function f(x) = -0.06x² + 2.7x + 5.9
a = -0.06
b = 2.7
Input the value of a and b to the formula of x-coordinate of the vertex
x = [tex]-\dfrac{b}{2a} [/tex]
x = [tex]- \dfrac{2.7}{2 \times (-0.06) \\} [/tex]
x = [tex]- \dfrac{2.7}{-0.12} [/tex]
x = [tex] \dfrac{2.7}{0.12} [/tex]
x = 22.5
The x-coordinate represents the horizontal distance. So the maximum height occurs when the distance is 22.5 feet far from its point of release.
Find y-coordinate of the vertex (the maximum height)
To find the maximum height, input the value of x-coordinate of the vertex to the function.
f(x) = -0.06x² + 2.7x + 5.9
f(22.5) = -0.06(22.5)² + 2.7(22.5) + 5.9
f(22.5) = -0.06(506.25) + 60.75 + 5.9
f(22.5) = -30.375 + 60.75 + 5.9
f(22.5) = 36.275
The maximum height is 36.275 feet
The maximum height reached by the shot is 36.375 feet. This occurs at a horizontal distance of 22.5 feet from its point of release.
Explanation:This is a question about the maximum height of a shot put. The equation presented here is a quadratic function, and it has the form of a parabola. The maximum value of a parabola that opens downwards (as in this case, where the coefficient of x2 is negative) is given at its vertex.
To find the 'x' coordinate of the vertex, use the formula -b/2a, where 'a' is the coefficient of x2 and 'b' is the coefficient of 'x'. In this case, 'a' is -0.06, and 'b' is 2.7. -b/2a = -(2.7)/(2*-0.06) equals 22.5 feet. This is the horizontal distance from the point of release where the shot reaches the maximum height. To find the maximum height, substitute the value of 'x' into the equation, f(22.5) = -0.06*(22.5)2 + 2.7*22.5 + 5.9. This gives the maximum height as 36.375 feet.Learn more about Maximum Height of Shot here:
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Sylvia is going to pick out a souvenir hat while she is on vacation. She knows the price of the hat will increase by 5% when she pays sales tax. She writes the expression h + 0.05h to find the total amount she will pay for the hat if it costs h dollars. Jin correctly writes another expression, 1.05h, that will also find the the total amount Sylvia will pay for the hat if it costs h dollars. Use the drop-down menus to explain what each part of Sylvia's and Jin's expressions mean.
Answers
Answer:
Step-by-step explanation:
Answer and step-by-step explanation:
Sylvia's expression is h+0.05h.
The variable h represents the cost of the hat.
0.05 represents the 5% sales tax; 5% = 5/100 = 0.05.
0.05h represents the amount of tax paid on the hat. To find a percent of a number, we multiply the decimal form of the percent by the original amount.
The total cost is given by h+0.05h.
Jin's expression is 1.05h.
The variable h represents the cost of the hat.
1.05 represents 100% of the cost of the hat plus the additional 5% tax; 100+5 = 105%; 105% = 105/100 = 1.05.
Together the total cost is given by 1.05h.
A hurricane has a large eye of about 80 miles. How many kilometers wide is the eye?
Answers
It is given that a hurricane has a large eye of about 80 miles.
We have to determine about how many kilometers wide is the eye.
Since 1 mile = 1.6 kilometers (approximately)
To convert the unit 'mile' into 'kilometer' ,
we have to multiply the given number by '1.6'.
So, 80 miles = [tex] 80 \times 1.6 = 128 [/tex] kilometers.
So, the hurricane eye is about 128 kilometers wide.
Final answer:
To convert 80 miles to kilometers, multiply by the conversion factor of 1.60934, resulting in an eye of the hurricane that is approximately 128.75 kilometers wide.
Explanation:
To convert the size of a hurricane's eye from miles to kilometers, we use the conversion factor that 1 mile is approximately equal to 1.60934 kilometers. If a hurricane has an eye that is about 80 miles wide, we need to multiply this distance by the conversion factor to obtain the width in kilometers.
Step-by-step Conversion:
Identify the width of the hurricane's eye in miles: 80 miles.
Use the conversion factor: 1 mile = 1.60934 kilometers.
Multiply the width in miles by the conversion factor to get the width in kilometers: 80 miles * 1.60934 km/mile = 128.7472 kilometers.
Therefore, the eye of the hurricane is approximately 128.75 kilometers wide.
64 is 4 times the difference between Sarah's age a and 44 assume Sarah is older than 44 write an equation to determine Sarah's age a
Answers
.. 64 = 4(s -44)
___
Sarah is 60.
Answer:
Sarah's age is 60.
Step-by-step explanation:
We have that Sarah's age is a.
The problem states that 64 is 4 times the difference between Sarah's age a and 44.
So
[tex]a - 44 = \frac{64}{4}[/tex]
[tex]a - 44 = 16[/tex]
[tex]a = 44 + 16[/tex]
[tex]a = 60[/tex].
Sarah's age is 60.
From the sample space sequals={1, 2, 3, 4,..., 15} a single number is to be selected at random. given event a, that the selected number is even, and event b, that the selected number is a multiple of 4, find p(upper a vertial line upper ba∣b).
Answers
E={1,2,3,4,5....14,15}.... sample space
A={2,4,6,...14} ..... even numbers
B={4,8,12} ............multiples of 4
To find: P(A|B)
We deduce from above that
P(A)=7/15
P(B)=3/15
P(A ∩ B)=3/15 since B is a subset of A.
The conditional probability P(A|B) is the probability of A happening given B has already happened.
So if a number has been selected, and it is known that B has happened, (i.e. multiple of 4), we know that there is a 100% probability A has happened (even).
Mathematically, P(A|B) is defined as P(A ∩ B)/P(B).
So
P(A|B)
=P(A ∩ B)/P(B)
=(3/15)/(3/15)
=1 (as reasoned above).
Answer: P(A|B)=1
The probability of randomly selecting an even number given that the number is a multiple of 4, or p(A|B), is 1.
Explanation:The question is asking for the conditional probability p(A|B), meaning the probability of event A (number is even) given that event B (number is a multiple of 4) has already occurred. In this sample space, there are 8 even numbers {2, 4, 6, 8, 10, 12, 14, 16} and 4 multiples of 4 {4, 8, 12, 16}. Therefore, the probability of picking an even number out of the ones that are multiples of 4 is as follows:
First, determine the probability of event A within event B by dividing the number of favorable outcomes (even numbers and multiples of 4) by the total outcomes of event B. In this case, all multiples of 4 are even numbers, so there are 4 favorable outcomes.
Calculating p(A|B): Number of instances where A and B occur together / Number of instances where B occurs = 4 / 4 = 1
Therefore, the probability of randomly selecting an even number given that the number is a multiple of 4, p(A|B), is 1.
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Solve the following word problem. A man travels from Town X to Town Y at an average rate of 50 mph and returns at an average rate of 40 mph. He takes a 1/2 hour longer than he would take if he made the round trip at an average of 45 mph. What is the distance from Town X to Town Y?
______ miles
Answers
Distance from Town X to Town Y = 100 miles
Distance = Speed x Time
Speed while going = 50 mph , Speed while returning = 40 mph
Let the time taken while going = t hours
So, the time taken while returning = t + 0.5 hours
Distance while going = Distance while coming backSo, 50 t = 40 ( t + 0.5)
50 t = 40x + 20
50 t - 40 t = 10x = 20
10 t = 20
t = 20 / 10 = 2
Hence, distance = 50 t = 40 ( t + 0.5 )
= 50 x 2 ; or 40 x 2.5 = 100
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The distance from Town X to Town Y is 180 miles. This is determined by setting up and solving an equation based on the given speeds and time difference.
Explanation:The subject of this question is Mathematics, specifically it is a problem in a genre called distance, speed, time problems. Let's denote the distance from Town X to Town Y as 'd' miles. The man covers this distance twice - once going and once coming back. The time he takes to travel from X to Y is d/50 and to travel back from Y to X is d/40.
So, the actual total time he spends travelling is (d/50 + d/40) hours. If he made the round trip at an average speed of 45 mph, he would take (2d/45) hours (distance = speed x time). Given that the actual journey took a 1/2 hour longer than this, we can create the following equation:
(d/50 + d/40) = 2d/45 + 1/2.
Solving this equation for 'd', we get d = 180 miles. So, the answer is that the distance from Town X to Town Y is 180 miles.
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what is the square root of 64 multiplied by 72 divided by the sum of 43 plus 0
Answers
.. (√64)*72/(43 +0) = 8*72/43
.. = 576/43
.. = 13 17/43
.. ≈ 13.395
Use the graph to find the local minimum and the local maximum for the given function.
Answers
On the interval [-3, 0] the minimum is -16.
On the interval [0, 3] the maximum is 3.75.
On the interval [0, 3] the minimum is -3.
In the interval [-3, 0] the local minimum is -16 and In the interval [0, 3], the local maximum is 4 and local minimum is -3.
What is Local Maxima and Local Minima?
The local maxima and minima are the input values for which the function gives the maximum and minimum output values respectively. The y - coordinate of local maxima is called local maximum and that of local minima is called as local minimum.
Given is a graph of a function.
In the graph the local maximum is the y - coordinate that has maximum value at any specific input. Similarly, local maximum is the y - coordinate that has minimum value at any specific input.
PART A
In the interval [-3, 0], the local minimum is -16
PART B
In the interval [0, 3], the local maximum is 4 and local minimum is -3.
Therefore, in the interval [-3, 0] the local minimum is -16 and In the interval [0, 3], the local maximum is 4 and local minimum is -3.
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