The equation which can be solved by using the given system of equations; y = 3x³ - 7x² + 5 and y = 7x^4 + 2x is 3x³ - 7x² + 5 = 7x^4 + 2x. Option B is correct.
We are given;
y = 3x³ - 7x² + 5
y = 7x^4 + 2x
We will solve the given equation by substitution method:
Using the substitution method, let us substitute y = 7x^4 + 2x in the equation y = 3x³ - 7x² + 5, we get,
3x³ - 7x² + 5 = 7x^4 + 2x
So, 3x³ - 7x² + 5 = 7x^4 + 2x will be solved by using the given system of equations.
Thus, the equation which can be solved by using the given system of equations; y = 3x³ - 7x² + 5 and y = 7x^4 + 2x is 3x³ - 7x² + 5 = 7x^4 + 2x. Option B is correct.
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What is the least angle measure by which this figure can be
rotated so that it maps onto itself?
• 45°
•90°
•180°
•360°
The least angle at which given figure maps onto itself is 180°. This can be understand by using magnitude of symmetry.
What is symmetry?
In common parlance, the term "symmetry" describes a sense of lovely proportion and balance. A more precise definition of "symmetry" can be found in mathematics, where it typically refers to an object that is unaffected by certain transformations like translation, reflection, rotation, or scaling. Although these two interpretations of "symmetry" can occasionally be distinguished from one another, they are intricately linked and are therefore discussed jointly in this article. Aspects of mathematical symmetry can be seen in abstract objects like theoretical models, language, and music, as well as in the passage of time, as a spatial relationship, through geometric transformations, and in other types of functional transformations.
A figure in the plane has rotational symmetry if the figure can be mapped into itself by a rotation between 0° to 360° about the center of figure.
The given figure has one line of symmetry,
figure is divided into two parts that can overlap
angle will be = 360/2=180° .
So, the smallest angle is 180°.
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A concession stand serves hot dogs and
hamburgers at a ratio of 3 to 2. Based on this
ratio, how many hamburgers will be served if
there are a total of 60 hot dogs served? Use a
tape diagram to model your thinking.
Using ratios we know that 40 hamburgers will be served.
What are ratios?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.So, a number of hamburgers that will be served are:
The ratio of hotdogs and hamburgers = 3:2The total number of hotdogs served is 60.So, the number of hamburgers will be:
3/60 = 2/x3x = 60×23x = 120x = 120/3x = 40Therefore, using ratios we know that 40 hamburgers will be served.
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Correct question:
A concession stand serves hot dogs and hamburgers at a ratio of 3 to 2. Based on this ratio, how many hamburgers will be served if there are a total of 60 hot dogs served?
A 9-member team plans to run a 4-mile relay race. Distance markers are placed on the racecourse every 0.25 mile. a. Place an X on the number line at the approximate locations where the relay exchanges will take place. b. Will any of the relay exchanges take place at any of the 0.25-mile markers? If so, which one(s)? List the locations of all of the exchanges in decimal form.
Relay exchanges will not take place at any of the 0.25-mile markers
The calculated relay exchanges are
0.44440.88891.33331.77782.22222.66673.11113.55564How to find the relay exchangesThe number of team members which is 9 is equal to the number of relay exchanges in the 4-mile race.
This will result to the relay exchanges occurring at every 4/9, and repeated addition of 4/9 will give the other points, and the list is
4/9, 8/9, 4/3, 16/9, 20/9, 8/3, 20/9, 32/9, and 4 in fraction
In decimal form this will be listed in four decimal place
0.4444
0.8889
1.3333
1.7778
2.2222
2.6667
3.1111
3.5556
4
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Find the value of x
Transversal angles, interior exterior angles, parallel
Answer:
115°
Step-by-step explanation:
They are the same angle because we know the lines are parallel.
Answer:
115°
Step-by-step explanation:
alternate exterior, they're the same
a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. he wants the area to be 20,000 20,000 square feet. what is the least amount of fencing he can use to create the area for his sheep?
Using the concepts of area of rectangle, we got that 72 feet is the the least amount of fencing he can use to create the area for his sheep.
Lets, suppose that the length of rectangle as x feet,
and width of rectangle as y feet.
So perimeter of rectangle as 2×( length + breadth)
We are given perimeter of rectangle as 72 feet
So, length of two sides of rectangle + width of rectangle=72feet.
=>2x+y=72 feet----------(eq1)
Now, we know that area of rectangle is given by =(length × breadth),or
=>(x × y)=20000
Putting values of y from eq1,we get
=>x × (72-2x)=20000
=>72x-2x²=20000
We need to find the least amount of fencing, so we find the local minima by using the differentiation
=>d(72x)/dx-d(2x²)/dx=d(20000)/dx
=>72-4x=0
=>x=18feet
Therefore, y=72-2×18=72-36=36feet
Hence, length of rectangle is 18 feet, and width is 36 feet
Therefore, length of fencing is =2x+y=2×18+36=72 feet.
Hence, if a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. he wants the area to be 20,000 square feet, then the least amount of fencing he can use to create the area for his sheep is 72 feet.
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(Complete question) is:
a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. Perimeter of rectangle is given as 72 feet. He wants the area to be 20,000 square feet. what is the least amount of fencing he can use to create the area for his sheep?
A polynomial function P(x) with rational coefficients has the given roots. Find two additional roots of P(x)=0. 17+7 and 2i
The two additional roots are:-0.17-7i and -2i
Given,
A polynomial function P(x) with rational coefficients has the given roots.
P(x) = 0.17+7i and 2i
we are asked to determine the two additional roots of the given P(x).
we know that a+bi is a root of P(x)=0, then a-bi is also a root of P(x)=0
we have:
0.17+7i and 2i are two roots pf P(x)
so, -0.17-7i and -2i are two additional roots of P(x).
Hence we get the required roots.
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kent spent 5/6 hour washing dishes on Monday as shown on the number line . kent washed dishes for the same amount of time on Tuesday and Wednesday. much time did kent spend washing dishes during those 3 days
Answer:150 minutes easy?
Step-by-step explanation:
Cooper's Cafe has regular coffee and decaffeinated coffee. This morning, the cafe served 96
coffees in all, 72 of which were regular. What percentage of the coffees were regular?
Answer:
75%
Step-by-step explanation:
To solve this equation, we need to turn the fraction 72/96 into a percentage.
72 ÷ 96 = 0.75
0.75 as a percentage is 75%
Therefore, 75% of the coffees were regular.
f a certain cannon is fired from a height of 9.3 meters above the ground, at a certain angle, the height of the cannonball above the ground, h, in meters, at time, t, in seconds, is found by the function h(t) = - 4.9t^2 + 30.5t + 9.3. Find the time it takes for the cannonball to strike the ground.
The amount of time it takes for the cannonball to strike the ground is equal to 6.516 seconds.
How to determine the amount of time?Based on the information provided, we can logically deduce that the height (h) in meters, of this cannonball during above the ground is related to time by the following function:
h(t) = - 4.9t² + 30.5t + 9.3.
Generally speaking, the height of this cannonball would be equal to zero (0) when it strikes the ground. Therefore, we would equate the height function to zero (0):
0 = - 4.9t² + 30.5t + 9.3.
4.9t² - 30.5t - 9.3 = 0
Next, we would solve the quadratic equation by using the quadratic formula:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-(-30.5)\; \pm \;\sqrt{(-30.5)^2 - 4(4.9)(-9.3)}}{2(4.9)}\\\\x = \frac{30.5\; \pm \;\sqrt{930.25\; + \;182.28}}{9.8}\\\\x = \frac{30.5\; \pm \;\sqrt{1112.53}}{9.8}[/tex]
Time, x = (30.5 ± 33.3546)/9.8
Time, x = (30.5 + 33.3546)/9.8
Time, x = 63.8546/9.8
Time, x = 6.516 seconds.
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how do you graph x=6
Answer: it’s a vertical line going through the point (6,0)
Step-by-step explanation: this is because when you only have an x value the line is going to be vertical line through the x value on that axis
For this exponential
function,
what is the output value (y),
when the input value (x) is O?
y = 12.5x
*it’s not 1*
After solving the exponential function y = 12.5ˣ, the value of y = 1.
What is an exponential function?The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0.
The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
So, the exponential function:
y = 12.5ˣ
We know that x is 0.
The exponential function rule states that when the power is 0, the answer is always 1.
y = 12.5ˣ
y = 12.5⁰
y = 1
Therefore, after solving the exponential function y = 12.5ˣ, the value of y = 1.
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Correct question:
For this exponential function, what is the output value (y), when the input value (x) is O?
y = 12.5ˣ
5.8, 6.328, 5.8042, 5.84 order these numbers from least to greatest
Answer:
Step-by-step explanation:
5.8, 5.8042, 5.84, 6.328
Miranda buys 5.1 pounds of avocados at the local store. How much does
one pound of the fruit cost if she is billed $16.83 for the purchase?
The cost of one pound is $3.3 or the rate of per pound fruits is $3.3.
What is meaning of one pound?
Pound is an unit to measure mass of an object. The plural form of pound is pounds.
What is the unitary method?
The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given that Miranda buys 5.1 pounds of avocados at the local store. The cost of the fruits is $16.83.
Apply unitary method to calculate the cost of 1 pound:
The cost 5.1 pounds fruit is $16.83.
The cost 1 pound fruit is $16.83/5.1 = $3.3.
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what is the answer to 365 x 240?
Answer:87,600
Step-by-step explanation:
pls help sjajgdjsiaysgdhwiudhh
Answer:
scalene acute
Step-by-step explanation:
scalene = 2 sides are the same and one is different
acute = all three angles are smaller than 90
A local farmer had a mouse problem in his barn. He estimated there were about 800
mice to start with. He adopted some cats and noticed that the number of mice was
decreasing by 8%/wk. The graph models the number of mice x weeks after the
farmer adopted the cats.
Identify and interpret the key features of the exponential function modeled in terms
of this situation!
Answer: try a c and e
Step-by-step explanation:
I need help please!!!!
Answer: -10/6
Step-by-step explanation:
Using the Slope Formula which is, [tex]\frac{y_{2} -y_1}{x_2-x_1}[/tex] you can substitute the numbers. This leads to [tex]\frac{-1 -9}{-1-(-7)}[/tex] which will get you, [tex]\frac{-10}{6}[/tex].
In 2010, there were 3,669 people living in Bridgeview, IL. Chicago, IL has 681 times as
many people. How many more people live in Chicago?
Answer:
There are roughly 2,488,600 more people living in Chicago.
You operate a theme park and want to use the temperature outside and the day of the week to predict how many people will be in attendance each day. While testing this model, you also want to see if the relationship between temperature and theme park visitors will be curvilinear. You decide not to test for interactions. How many betas will be in your model aside from the y-intercept?.
Three betas will be in our model aside from the y-intercept.
In the given question, we have to find how many betas will be in your model aside from the y-intercept.
You operate a theme park and want to use the temperature outside and the day of the week to predict how many people will be in attendance each day.
While testing this model, you also want to see if the relationship between temperature and theme park visitors will be curvilinear.
You decide not to test for interactions.
From the given question,
We have y intercept that means our model well be
[tex]y=\beta_{0}+x_{1}\beta _{2}+x_{2}\beta _{2}+x_{1}x_{2}\beta _{12}[/tex]
where [tex]\beta _{1}[/tex] is for temperature and [tex]\beta _{2}[/tex] is day of the week.
3 betas are there aside intercept of y.
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|x-3| = |9-2x| solve the following question
Answer:
x = 4 or x = 6
Step-by-step explanation:
to solve the inequality
solve both
x - 3 = 9 - 2x OR x - 3 = - (9 - 2x)
x - 3 = 9 - 2x ( add 2x to both sides )
3x - 3 = 9 ( add 3 to both sides )
3x = 12 ( divide both sides by 3 )
x = 4
OR
x - 3 = - (9 - 2x)
x - 3 = - 9 + 2x ( subtract 2x from both sides )
- x - 3 = - 9 ( add 3 to both sides )
- x = - 6 ( multiply both sides by - 1 )
x = 6
f(x) = x^2. What is g(x)?
Answer:
[tex]\textsf{B.} \quad g(x)=-x^2-2[/tex]
Step-by-step explanation:
Transformations
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]
[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.[/tex]
[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.[/tex]
From inspection of the given graph, we can see that g(x) is function f(x) reflected in the x-axis and translated 2 units down.
Given function f(x):
[tex]f(x)=x^2[/tex]
Reflected in the x-axis:
[tex]-f(x) \implies g(x)= -x^2[/tex]
Translated 2 units down:
[tex]-f(x)-2 \implies g(x)=-x^2-2[/tex]
Therefore:
[tex]g(x)=-x^2-2[/tex]
Note:
If the leading coefficient of a quadratic function is positive, the parabola opens upwards.
If the leading coefficient of a quadratic function is negative, the parabola opens downwards.
Therefore, as g(x) opens downwards, the term in x² will be negative.
The perimeter of an isosceles triangle is 48 inches. Each leg is 6 inches less than two times the base.
Find the length of each side of the triangle.
The length of two same sides of isosceles triangle is 18 inches and the third side of the triangle is 12 inches.
According to the question,
We have the following information:
The perimeter of an isosceles triangle is 48 inches. Each leg is 6 inches less than two times the base.
We know that in an isosceles triangle two sides are equal.
Let's take the base of the triangle to be x inches.
Other sides = (2x-6) inches
So, we have the following expression:
2x-6+2x-6+x = 48
5x-12 = 48
5x = 48+12
5x = 60
x = 60/5
x = 12 inches
Now, the other two sides of triangle:
2*12-6
24-6
18 inches
Hence, the length of two same sides of isosceles triangle is 18 inches and the third side of the triangle is 12 inches.
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Find negative absolute value of negative three fifths.
−3.5
negative three fifths
three fifths
3.5
-4 is the absolute value of -3.5 and three fifths.
What is Expression?An expression is combination of variables, numbers and operators.
negative absolute value of negative three fifths.
−3.5-3/5
Three fifths means three by five
-3.5-3/5
(-5(3.5)-3)/5
Minus seventeen point five minus three divided by five
-17.5-3/5
Minus twenty point five divided by five
-20.5/5
Minus four point one
-4.1
-4
Hence -4 is the absolute value of -3.5 and three fifths.
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Why is the product of two rational numbers always rational?
Select from the drop-down menus to correctly complete the proof.
Let ab and cd represent two rational numbers. This means a, b, c, and d are
Choose...
, and
Choose...
. The product of the numbers is acbd, where bd is not 0. Because integers are closed under
Choose...
, acbd is the ratio of two integers, making it a rational number. Integers or rational numbers.
The product of two rational numbers is always rational because (ac/bd) is the ratio of two integers, making it a rational number.
We need to prove that the product of two rational numbers is always rational. A rational number is a number that can be stated as the quotient or fraction of two integers : a numerator and a non-zero denominator.
Let us consider two rational numbers, a/b and c/d. The variables "a", "b", "c", and "d" all represent integers. The denominators "b" and "d" are non-zero. Let the product of these two rational numbers be represented by "P".
P = (a/b)×(c/d)
P = (a×c)/(b×d)
The numerator is again an integer. The denominator is also a non-zero integer. Hence, the product is a rational number.
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There are 20 people in a room. 4 of them are people you know. When 2 people are selected at random at the same time, what is the probability that at least one of them is someone you know?
(this is a basic question but its 4am, my brain isnt working properly)
Answer:
4/20=1/5 or 20% or 0.2
Step-by-step explanation:
if u write 4/20 simplify it which becomes 1/5
u can write in percentage or in decimal depending on what the question wants
unit 3 function notation and evaluating function homework gina wilson (all things algebra), 2013
Answer:
b
Step-by-step explanation:
it is the answer
a hammer get 300miles on 20 gallons of gas. How many miles can it cover on 50 gallons of gas
Answer:
750 miles
Step-by-step explanation:
20 gallons -------------- 300 miles
1 gallon ---------------- 300/20 = 15 miles
50 gallons -------------- 15x50 = 750 miles
Solve (x – 3)2 = 49. Select the values of x.
Answer:
27.5
Step-by-step explanation:
2x-6=49
2x=55
x=27.5
Find the value of ? in the figure below
Answer:
Step-by-step explanation:
24
a boat travels 12 miles up the river in the same amount of time it takes to travel 32 miles down the same river. if the current is 5 miles per hour, what is the speed of the boat in still water?
Answer:
11 mi/h
Step-by-step explanation:
You want the speed of the boat when it travels 12 miles upstream against a current of 5 mph in the same time it travels 32 miles downstream with the current.
TimeThe relation between time, speed, and distance is ...
time = distance/speed
If b represents the speed of the boat, the times upstream and downstream are the same, so we have ...
(12 mi)/(b -5) = (32 mi)/(b+5)
Multiplying by the product of the denominators gives ...
12(b+5) = 32(b-5) . . . . . . also divided by "mi"
12b +60 = 32b -160 . . . . multiply by (b+5)(b-5)
220 = 20b . . . . . . . . . . . . add 160 -12b
11 = b . . . . . . . . . . . . . . . . . divide by 20
The speed of the boat in still water is 11 miles per hour.
__
Additional comment
Each trip took 2 hours.