The system of equations used to find roots of the equation is y=12x³-5x and y=2x²+x+6.
Given the equation is 12x³-5x=2x²+x+6.
A set of equations containing one or more variables is called a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations.
Firstly, separate the given equation into two parts by equating the left-hand side and right-hand side with 0, we get
12x³-5x=0
2x²+x+6=0
Now, to make a system of equations replace 0 with y as we know that system of equations contains two variables, we get
12x³-5x=y
2x²+x+6=y
Hence, the system of equations used to find the roots of the equation 12x³-5x=2x²+x+6 is y=12x³-5x and y=2x²+x+6.
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What is the product of the...
Step-by-step explanation:
the answer is C) 8x^5y - 6x^4y^2
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There are five different points on a line. how many segments are there on the line?
There are 10 line segments on a line with five different points on it.
What are a line and a line segment?Line:
A line is formed with infinite points and it is extended infinitely along a straight path in both directions.
Line segment:
The part of the line that lies between two distinct points on the line. This is also called the shortest distance between two points on the line.
How many segments are there on the line with five different points?Consider a line with five points on it as A, B, C, D, and E.
So, the possible line segments are
AB, AC, AD, AE, BC, BD, BE, CD, CE, DE
So, there are 10 line segments are formed on line with five different points.
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Four students are trying to find the rule that translates point N(–2, –4) to N prime (2, 4). Each student’s reasoning is shown below. Raheem: The rule is (x times (negative 1), y times (negative 1)) because Negative 2 times (negative 1) = 2 and Negative 4 times (negative 1) = 4. Casey: The rule is (x + 2, y + 4) because the image is (2, 4). Andrew: The rule is (x + 4, y + 0) because the coordinates are opposites. Lo: The rule is (x + 4, y + 8) because Negative 2 + 4 = 2 and Negative 4 + 8 = 4. Which student is correct?
Answer:
Raheem
Step-by-step explanation:
If 1/2 is the fraction representing the ratio of corresponding sides of two similar
triangles, the ratio of the areas of the triangles would be:
Answer:
1/4
Step-by-step explanation:
The ratio of the areas is the square of the ratio of the lengths of sides.
(1/2)² = 1/4
Answer: 1/4
Natalie is ordering a burrito. For the main protein, she is given the option of veggie, chicken, carnitas, or carne asada. For the beans, she is given the option of no beans, black beans, or pinto beans. How many possible order combinations are there?
Answer: 12
Step-by-step explanation:
For this counting question, we need to figure out the possible choices for each selection.
For main protein, there are four options, so we can make four slots
_ _ _ _
For beans, there's three options, so we can make three slots
_ _ _
Doing some casework, we know that 4*3 = 12, which is the answer.
Determine the equation of the parabola shown in the diagram in vertex form.
By the vertex form of the parabola, the equation of the parabola shown in the diagram is equal to the quadratic equation y - 1 = (2/3) · (x - 3)².
How to determine the equation of the parabola in vertex form
Parabolae are represented mathematically by second order polynomials, which can be described either in standard form or in vertex form. In accordance to the picture, we have a parabola with a vertical axis of symmetry. The formula in vertex form is described by this expression:
y - k = C · (x - h)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constantPlease notice that vertices represent the absolute extreme of the parabola. We can determine the equation by knowing the vertex and another point. Let be (h, k) = (3, 1) and (x, y) = (0, 7), then we find that the vertex constant is:
7 - 1 = C · (0 - 3)²
6 = 9 · C
C = 2/3
By the vertex form of the parabola, the equation of the parabola shown in the diagram is equal to the quadratic equation y - 1 = (2/3) · (x - 3)².
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Alice is able to produce 3 dozen cupcakes in 90 minutes. How many cupcakes can she produce in 8 hours
Answer:
[tex]\boxed{192~cupcakes}[/tex]
Step-by-step explanation:
dozen = 12
3 × 12 = 36 cupcakes
I.
36 cupcakes ---------------- 90 minutes
x ---------------- 60 minutes
[tex]x=\dfrac{36\cdot 60}{90 } ~ cupcakes\\\\x=24~cupcakes[/tex]
II.
24 cupcakes ---------------------- 60 minutes = 1 hour
y ---------------------- 8 hours
[tex]y=\dfrac{8\cdot 24 }{1} ~cupcakes\\\\\boxed{y=192~cupcakes}[/tex]
They will produce 192 cupcakes in 8 hours.
PLEASE HELP!!!
Angle CAE is congruent to angle___
Angle CBF is congruent to angle___
Answer:
Angle CAE is congruent to angle CBE
Angle CBF is congruent to angle CAF
===================================================
Explanation:
Angle CAE is an inscribed angle that subtends the minor arc CE
Minor arc CE is the distance around the circle from C to E following the shorter path. All minor arcs are smaller than 180 degrees.
What other inscribed angle also subtends minor arc CE? That would be inscribed angle CBE
Notice that CAE and CBE both have "C" and "E" as the first and last items. The only change is the middle letter. This is a quick nonvisual way to determine inscribed angles.
Recall that if two inscribed angles subtend the same arc, then they are congruent. Therefore, angle CAE is congruent to angle CBE
-------------------
For similar reasoning, angles CBF and CAF are congruent inscribed angles that subtend minor arc CF.
For more information, check out the inscribed angle theorem. Also I recommend using GeoGebra as a handy tool.
Through how many degrees does the hour hand of a clock travel between 3:00pm and 3:15pm?
Answer:
90 degrees
Step-by-step explanation:
the clock is a circle so the entire # of degrees is 360.
there are 12 sections on the clock so 360 /12 =30
so each section is 30 degrees.
if you go from 3:00 to 3:15, that is 3 sections.
so 3 times 30 is 90
Based on a poll, 867 of 1050 randomly selected adult said that they always wear seat belts. Construct and interpret a 97% confidence interval for the proportion of adults who always wear seat belts.
The 97% confidence interval for the proportion of adults is 0.801<P<0.851.
Given that 867 adults are randomly selected from 1050 who always wear seat belts.
A confidence interval refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.
Let's assume n=1050 and x=867
Find the sample proportion by dividing the given proportion with sample size as,
[tex]\begin{aligned}\hat{p}&=\frac{x}{n}\\\hat{p}&=\frac{867}{1050}\\ \hat{p}&=0.826 \end[/tex]
Find the α by subtracting the given confidence interval that is 97% from 1 as
α=1-(97÷100)
α=1-0.97
α=0.03
To find the critical value that is [tex]Z_{\frac{\alpha}{2}}[/tex] by dividing alpha with 2,
[tex]\begin{aligned}Z_{\frac{\alpha}{2}}&=Z_{\frac{0.03}{2}}\\ Z_{\frac{\alpha}{2}}&=Z_{0.015}\end[/tex]
From this table which is shown in the figure it says that the critical value is
[tex]Z_{crit}=\pm 2.17[/tex]
Use this formula to find the confidence interval [tex]P=\hat{p}\pm Z_{Crit}\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Substitute the values in the formula,
[tex]\begin{aligned}P&=0.826\pm 2.17\times \sqrt{\frac{0.826(1-0.826)}{1050}}\\ P&=0.826\pm 2.17\times \sqrt{\frac{0.826\times 0.174}{1050}}\\ P&=0.826\pm 2.17\times 0.0116995\\ P&=0.826\pm 0.025\end{aligned}[/tex]
Hence, a 97% confidence interval for the proportion of adults who always wear seat belts is 0.801<P<0.851.
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A
B
Value: 10
AB=
12√2
BC=
45°
Find the missing side lengths. (Enter your answer
without units.)
C
Answer:
12
Step-by-step explanation:
This is a special triangle with angle measure 45-45-90
The side lengths for this special right triangle is as follows:
The side length that sees angle measure 90 is represented by a[tex]\sqrt{2}[/tex]
The side lengths that see angle measures 45 is represented by a
We can see from the image hypotenuse (the side that sees angle 90)
is given as 12[tex]\sqrt{2}[/tex] that means a = 12
So the missing side lengths (both see angle measure 45) = 12
Find the midpoint of a A(3, -1) and B(x, y) is P(4, - 5). Find the coordinates of B. pls answer it is urgent i will mark him or her brainlest
Answer:
is this tye required answer
Triangles F G H and F J H share common side F H. Sides F G and G H are congruent. Sides F J and J H are congruent.
Which explains whether ΔFGH is congruent to ΔFJH?
They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.
They are congruent because opposite sides of a parallelogram are congruent.
They are not congruent because only one pair of corresponding sides is congruent.
They are not congruent because only two pairs of corresponding sides are congruent.
ΔFGH is congruent to ΔFJH They are not congruent because only one pair of corresponding sides is congruent.
The correct option is (C)
What is Congruency?Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.
Given:
ΔFGH and ΔFJH share common side FH. Sides FG and GH are congruent.
As, per the information, it can be seen that the triangles are not congruent as one pair of corresponding side is not congruent.
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Answer: C
Step-by-step explanation: edge
IJ=
Measure of IJ
Help me thanks
Answer: 11
Step-by-step explanation:
By the secant-secant theorem,
[tex]5(5+7)=(JK)(15)\\\\60=(JK)(15)\\\\JK=4\\\\\implies IJ=15-4=11[/tex]
How many solutions exist for the system of equations graphed below?
Answer: one
Step-by-step explanation:
When a system of equations is graphed the solutions are the point of intersections. Here, we only have one point of intersection since these are both linear equations. That means there is only one solution.
PLEASE show me a fifth-degree polynomial with three terms in standard form
Answer:
a. 6x^5- 3x^3+ 21
b. (6x^5+ 4x^4+21) - (4x^5+ 3x^4+11)= 2x^5+ x^4+10
Step-by-step explanation:
The degree of the polynomial is the highest power of the terms of the polynomial .e.g
x³+ 2ax+ b² is a polynomial of 3rd degree because the highest power of the terms given is 3.
As we need a polynomial of 5th degree the highest power will be
5.6x^5+ 4x^4+ 3x^3+ 5x^2+ x+21
But this polynomial has 5 terms. We need a 5th degree polynomial with three terms so it can be any one of the following
6x^5- 3x^3+ 21
6x^5+ 4x^4+21
6x^5+ 5x^2+21
6x^5 + x+21
All of the above polynomials are in the standard form because the powers of the terms are given in decreasing order. The first term has the highest power and so on.
Part B:
Suppose we have 2 polynomials
6x^5+ 4x^4+21 and 4x^5+ 3x^4+11
When the closure property of subtraction is applied
(6x^5+ 4x^4+21) - (4x^5+ 3x^4+11)
= 6x^5+ 4x^4+21 - 4x^5- 3x^4-11 → coefficients are changed b/e of subtraction
= 2x^5+ x^4+10
the coefficients are changed because of subtraction.
In Polynomials the sign is changed due to subtraction and same degree terms ( like terms) are subtracted to get the answer.
Part of the graph of the function f(x) = (x + 4) (x - 6) is shown below. A 2 Which statements about the function are truc? Select two options.
The true options include the following:
The vertex of the function is at (1,–25).The graph is negative on the entire interval –4 < x < 6.What is a Graph?This is defined as a pictorial representation of data or variables in an organized manner.
Function f(x) = (x + 4)(x – 6)
Graph intersects the x-axis at points (-4,0) and (6,0).
x-coordinate of vertex = -4+6/2 = 1
y-coordinate of vertex = (1+4) (1-6) = 5(-5) = -25
The vertex is at the point (1,-25).
The graph is positive for all x< -4 or x>6.
The graph is negative for –4 < x < 6.
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Answer:
The Three options are
1. m∠5 + m∠6 = 180° ...........Linear Pair
2. ∠ 2+ ∠ 3 = ∠ 6.................Exterior angle Property of Triangle
3. m∠2 + m∠3 + m∠5 = 180° .....Triangle Sum Property
Step-by-step explanation:
Consider Δ ABC with Exterior angles as
∠ 1 , ∠ 4 ,and ∠ 6
Exterior angle Property of Triangle:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
For Exterior ∠ 1 we have
∠ 1 = ∠ 5 + ∠ 3 .................Exterior angle Property of Triangle
Similarly,
For Exterior ∠ 4 we have
∠ 4 = ∠ 5 + ∠ 2.................Exterior angle Property of Triangle
Similarly,
For Exterior ∠ 6 we have
∠ 6 = ∠ 2 + ∠ 3.................Exterior angle Property of Triangle
Triangle Sum Property:
Ina triangle sum of the measures of angles is equal to 180°
∴ m∠2 + m∠3 + m∠5 = 180° .....Triangle Sum Property
Linear Pair:
The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
∴ m∠5 + m∠6 = 180° ...........Linear Pair
Answer:
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Step-by-step explanation:
got it correct on my test
Triangles A B C and N M Q are shown. Sides B C and N M are congruent. Angles A B C and Q N M are congruent. Angles B C A and N M Q are both right angles.
Nessa proved that these triangles are congruent using ASA. Roberto proved that they are congruent using AAS. Which statement and reason would be included in Roberto’s proof that was not included in Nessa’s proof?
Given: AngleB ≅ AngleN; BC ≅ NM; AngleC is right; AngleM is right
Prove: TriangleABC ≅ TriangleQNM
AngleA ≅ AngleQ because of the third angle theorem.
AB ≅ QN because they are both opposite a right angle.
BC ≅ NM because it is given.
AngleC ≅ AngleM because right angles are congruent.
What would be included to prove both triangles are congruent by the AAS theorem is: B. AB ≅ QN because they are both opposite a right angle.
What is the AAS Congruence Theorem?The AAS congruence theorem states that two triangle are congruent if both have two pairs of corresponding congruent angles and a pair of non-included corresponding congruent sides.
In the image given, since AB and QN both lie opposite a right triangle, then they are congruent to each other.
Therefore, to prove both triangles are congruent by AAS theorem, what would be included is: B. AB ≅ QN because they are both opposite a right angle.
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Answer:
AngleA ≅ AngleQ because of the third angle theorem
Step-by-step explanation:
right on edge
Raul is building a house. On day 1, he uses 3 bags of cement. On each of the following 3 days, he uses 3 times the number of bags used the previous day. How many bags of cement does he use in the last 3 days?
Answer:
117 bags
Step-by-step explanation:
Day 1: 3 bags
Day 2: 3 × 3 = 9 bags
Day 3: 9 × 3 = 27 bags
Day 4: 27 × 3 = 81 bags
Total: 9 + 27 + 81 = 117 bags
Answer:
81 bags of cement in the last 3 days.
Step-by-step explanation:
On the first day he used 3 bags.
The second day he used twice that amount so that would be 3²=9
The third day he used twice the amount he used the second day. So that would be 9²=81.
He used 81 bags of cement in the last 3 days.
Hope this helps!
If not, I am sorry.
Jackson conducted a survey at his school about its students' favorite
sport. He chose a name at random from a list of all the students in the
school, and chose every 10th student after that for the sample.. Was this
a random sample, and if so, which sampling method did Jackson use?
OA) Yes, simple random sample.
O B) Yes, systematic random sample.
OC) Yes, stratified random sample.
OD) No, it was not a random sample.
Answer:
OB
Step-by-step explanation:
it's not a beacuasenhes not doing everyone
and we have no info on whether anyone serveylayed a sport so the only possible option is 2
You have 4/6 cup of cornmeal in your cupboard. A recipe for 2/5 muffins calls for
cup of cornmeal. How much cornmeal would you have left if you made the
muffins?
Help!
What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values.
The graph of the model is (c) and the equation of the model is (d) y = 1.030 * 3.709^x
How to determine the regression equation?From the table of values, we can see that:
As the time increases, the distance increases
However, the increment in the distance is not a linear increment.
This means that:
The graph cannot be (a) and (d); these graphs show scattered pointsThe graph cannot be (c); it shows that distance decreases, as time increasesThe graph (b) represents an exponential model.
When the points on the table are entered in a graphing calculator, we have the regression equation to be
y = 1.030 * 3.709^x
Hence, the graph of the model is (c) and the equation of the model is (d) y = 1.030 * 3.709^x
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HELP HELP HELP
Just 5 quick algebra 1 questions for 50 points!
1. x = a
2. y = b
3. It has an undefined slope.
4. You can either use, rise/run or change in y / change in x.
5. Rewrite the given equation in slope-intercept form, then determine the y-intercept, b, of the line.
What is the Equation of a Line?Equation of a line with m as slope and b as y-intercept is given as: y = mx + b.
1. Vertical lines have undefined slope. This implies that, for a given point, (a, b), the equation that models the line would be expressed as x = a, where a is the x-intercept.
Vertical line equation is: x = a.
2. Horizontal lines have 0 as a slope value, therefore, given (a, b), the equation that models the line is: y = b.
3. Equation for a vertical line cannot be written in slope-intercept form because the slope for a vertical line is undefined.
4. Using the following, rise/run or change in y / change in x, the slope (m), can be calculated given the coordinates of two points on a line.
5. To find an equation in point-slope form, e.g. y - 3 = 6(x - 4), rewrite the equation in slope-intercept form:
y - 3 = 6x - 24
y = 6x - 24 + 3
y = 6x - 21
The y-intercept, b, is: -21.
Therefore, the coordinate of the y-intercept would be: (0, -21).
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I need answer quickly
Answer:
b = 4.5
Step-by-step explanation:
a = 4
c = 6
c² = a² + b²
6² = 4² + b²
36 = 16 + b²
b² = 36 - 16
b² = 20
[tex]b = \sqrt{20} [/tex]
b = 4.5
Everyday Math
425. Cooking Natalia's pasta recipe calls for 2 pounds of pasta for 1 quart of sauce. How many pounds of pasta should Natalia cook if she has 2.5 quarts of sauce?
Answer:
5
Step-by-step explanation:
........................
Answer:
If Natalia's pasta recipe calls for two pounds of pasta for one quart of sauce.
Then she needs to cook 5 pounds of pasta if she has 2.5 quarts of sauce.
Step-by-step explanation:
Given that Natalia's pasta recipe calls for two pounds of pasta for one quart of sauce.We need to find pounds of pasta to be cooked if she has 2.5 quarts of sauce.Use the unitary method to find the pounds of pasta to be cooked.Step 1 of 2
Given that Natalia's pasta recipe calls for two pounds of pasta for one quart of sauce.
If one quart of sauce calls for two pounds of pasta,
Then to find how much pasta is needed for 2.5 quarts of sauce we need to form a proportion.
Let the pounds of pasta needed be x .
[tex]$$\begin{aligned}\frac{\text { pasta }(\text { inPounds })}{\text { Sauce }(\text { inQuarts })} &=\frac{\text { pasta }(\text { inPounds })}{\text { Sauce(inQuarts })} \\\frac{2}{1} &=\frac{x}{2.5}\end{aligned}$$[/tex]
Multiplying both sides by 2.5 we get,
[tex]$$\begin{aligned}\frac{2}{1} \times 2.5 &=\frac{x}{2.5} \times 2.5 \\x &=2 \times 2.5 \\x &=5\end{aligned}$$[/tex]
Step 2 of 2
To check if the answer is reasonable, we substitute it back in the formed proportion
[tex]$\frac{2}{1}=\frac{x}{2.5}$$[/tex]
We found x=5 hence,
[tex]$$\begin{aligned}\frac{2}{1} &=\frac{5}{2.5} \\2 &=2\end{aligned}$$[/tex]
Here, LHS =RHS
Hence, our answer is correct.
Please help ASAP
Please help ASAP
Please help ASAP
Answer:
Step-by-step explanation:
Answer:
9% only a guess.May not be correct..
the question is on the image
Answer:
nth term: 0.5n² + 2.5n + 3
Explanation:
pattern 1 = 6 bowls
pattern 2 = 10 bowls
pattern 3 = 15 bowls
pattern 4 = 21 bowls
First difference:
10 - 6 = 415 - 10 = 521 - 15 = 6Second difference:
5 - 4 = 16 - 5 = 1This is not an arithmetic nor a geometric sequence.
Solve:
2a = 2nd difference
2a = 1
a = 1/2 or 0.5
===================
3a + b = 1st difference
3a + b = 4
b = 4 - 3(1/2)
b = 2.5
====================
a + b + c = first term
1/2 + 2.5 + c = 6
c = 3
Quadratic nth term:
0.5n² + 2.5n + 3
Select the correct answer.
Serena's financial goal is to reduce debt. Which statement could make Serena's financial goal specific and timely?
Serena should focus on a certain credit card and give herself a deadline.
Serena should focus on a certain amount and track her spending.
Serena should track the amount of debt reduced over a period of six months.
Serena should track her purchases at gas stations for one year.
O A.
O B.
O C.
O D.
Serena should focus on a certain amount and track her spending. Option B
What Serena should doFrom the information given, Serena wants to reduce debt and to do this she needs to pay attention on how she borrows and the possible way to pay her debts.
Some possible ways to reduce debts include;
Develop a budgetTrack your expensesDo not take more debtPay bills in timeCheck bills carefullyThus, Serena should focus on a certain amount and track her spending. Option B
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144 = -12(x+5)
I need help with solving this problem it’s very difficult too solve
[<Answer>] (3):
Hello! I'm Avery. And I would love to help you :)
---------------------------------------------------------------------------------------------------------
[<The Explanation>}:
Step one: Distribute
[tex]144 = -12(x + 5)[/tex]
[tex]144 = -12x - 60[/tex]
Step two: Add 60 to both sides
[tex]144 = -12x - 60\\144 + 60 = -12 - 60 + 60[/tex]
Step three: Simplify
Adding..Adding..(Done!): [tex]204 = -12x[/tex]
Step four: Divide both sides by the same factor
[tex]204 = -12x\\\frac{204}{-12} = \frac{-12x}{-12}[/tex]
Last and not least..Step five:
Divide then, Cancel the terms, Move the Variable to the left...
And.. x = -17 is the answer :D
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[<Ending>] <3
Hope this helps and if it's wrong, you can't sue me! >:D
Bye! Hope this works for you :)
Have a nice day! - Avery <3