Answer:
he following system of equations can be used to find the roots of the equation
x3 + 72 = 5x2 + 18x.
y = x3 + 72
y = 5x2 + 18x
Graph this system of equations on the graphing calculator.
How many intersection points can you see in the default viewing window?
✔ 1
Adjust the window so you can find all of the points of intersection for the system of equations.
What are the roots of the original polynomial equation? Check all that apply.
–6
0
✔ 6
✔ –4
✔ 3
8
Step-by-step explanation:
no
Susie and Amelia solved the same equation using two separate methods. Their work is shown in the table below:
Answer:
(C)
Step-by-step explanation:
Explanation of Susie's method:
The given equation is:
[tex]2x-3=4x-2[/tex]
[tex]2x-2x-3=4x-2x-2[/tex]
[tex]-3=2x-2[/tex]
[tex]-3+2=2x[/tex] ( she made a mistake when she subtracted 2)
[tex]-1=2x[/tex]
[tex]x=-\frac{1}{2}[/tex]
Susie made a mistake in step 4 when she subtracted 2,
Thus, option C is correct.
Which value of k would cause the system of linear equations 35x+14y=119 and 5x+2y=k to have an infinite number of solutions?
The value of k in the equation is k = 17 and the equation 5x + 2y = 17 and
5x + 14y = 119 has infinite number of solutions
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Now , the value of A is
35x + 114y = 119 be equation (1)
Let the second equation be represented as B
Now , the value of B is
5x + 2y = k
For the system of equations to have infinite number of solutions ,
equation (1) = equation (2)
So , 5x + 2y = 35x + 114y
And , 7 ( 5x + 2y ) = 35x + 114y
So , the value of k = 119/7
On simplifying the equation , we get
k = 17
Therefore , the value of k is 17
Hence , the value of k from the equation is k = 17
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anna owes home antiques Whose value is 160000 today assuming normal growth. however anna believes the value will grow at 16% per year for the next three years she wants to take this rapis growth ibto consideration when valuing the buisness for potential sale find the future value of the buisness in three years then use that future value to find the present value at a rate 8% compounded annually
Find the center and radius of a circle defined by the equation x^2+yy^2+4x-8y+13=0
PLEASEEEEE HELPPPP ASAP NEED TO GET RIGHT!!!! WILL GIVE THANKS
Line GJ is tangent to point A at point G.
What is m∠AGJ?
A rocket is launched into the air. The projectile motion of the rocket can be modeled using h(t) = 112t –16t2, where t is the time since launch in seconds and h(t) is the height of the rocket at time t. When will the rocket be 196 feet in the air?
A.) after 2.0 seconds
B.) after 3.5 seconds
C.) after 4.5 seconds
D.) after 7.0 seconds
*The answer is B, after 3.5 seconds. If anyone wants to properly explain how this is the correct answer, I will give you brainliest.*
.
h ( t ) = 112 t - 16 t²
When the rocket is 196 feet in the air:
196 = 112 t - 16 t²
16 t² - 112 t + 196 = 0
divide everything by 4 ( just makes numbers smaller and easier to work with)
4 t² - 28 t + 49 = 0
Now factor the equation:
( 2 t - 7 )² = 0
2 t - 7 = 0
2 t = 7
t = 7 : 2
t =
3.5 s
The rocket will be 196 feet in the air after 3.5 seconds.
Tuna provides 30 calories per ounce . On a graph representing the relationship between the number of ounces of tuna a person consumes and the number of calories the tuna provides which quantity should be graphed on the x-axis
Answer:
Ounces of tuna will go on the x axis and calories on the y axis. This is because the relationship between the number of ounces a person eats and the calories he consumes then is a positive correlation (a line with a positive slope which goes from lower left to upper right) with x being the independent variable. As x increases, y increases. In other words you can ONLY change the amount of calories you consume WHEN you change the amount of ounces you eat. You can't change the number of calories independent of the number of ounces. The independent variable goes along the x axis, cuz the x variable always represents the independent variable.
Step-by-step explanation:
Is it possible for one point to be in two different planes?
Yes, it is possible for one point to be in two different planes. Imagine this: take the point in the corner of a room. That point is part of 3 planes (both walls and the floor).
To add, in mathematics, a plane is a flat, two-dimensional surface.
Answer:
Yes, it is possible for one point to be in two different Planes.
This can be explained in following way.
The Intersection of two plane is a line.And on a line infinite number of point lies.
So,"yes" one point or Infinite number of points can be common between two different planes.
A realty developer sell residential lots fir 4,000 per square meter plus a processing free of 25,000. one of the lots the realty developer is seling cost 625,000.
Solve for x: 3/4x+5/8=4x
a pizza delivery shop averages 21 minutes per delivery with a standard deviation of 3 minutes. what is the probability that a pizza takes less than 15 minutes to be delivered?
We have the mean, μ = 21 and the standard deviation, σ = 3
We want P(X<15)
Standardizing gives:
P(X<15) = P(Z<(15-21)/3)
P(X<15) = P(Z< -2) ⇒ When the value of the z-score is negative, we will
read the value of z<2 on the z-table then subtract the answer from 1
P(X<15) = 1 - P(Z<2)
P(X<15) = 1 - 0.9772
P(X<15) = 0.0228
the probability that pizza takes less than 15 minutes to be delivered is 0.0228
= 2.28%
Round answer as needed
The odds that you will pick a heart from a standard deck of 52 cards is 13:39. TRUE or FALSE
the odds of picking a heart is 13:39.
the statement is TRUE.
To determine whether the statement is true or false, we need to calculate the odds of picking a heart from a standard deck of 52 cards and compare it to the given odds of 13:39.
Step 1: Calculate the number of hearts in a standard deck.
A standard deck of 52 cards contains 13 hearts.
Step 2: Calculate the total number of cards in the deck.
A standard deck of 52 cards contains 52 cards.
Step 3: Calculate the odds of picking a heart.
The odds of picking a heart can be expressed as the ratio of the number of favorable outcomes (hearts) to the number of unfavorable outcomes (non-hearts).
Number of hearts: 13
Number of non-hearts: 52 - 13 = 39
So, the odds of picking a heart is 13:39.
Now, let's compare the calculated odds (13:39) with the given odds (13:39).
Since the calculated odds match the given odds, the statement is TRUE.
Eduardo bought a refrigerator with a sticker price of $2400. If he paid $35 a week for two years, what was the approximate markup rate on the refrigerator?
A. 65.9%
B. 51.7%
C. 34.1%
D. 75.8%
Answer:
The correct answer is option B
Step-by-step explanation:
Payment done per week [tex]= 35 dollar\\[/tex]
Total number of weeks in a year [tex]= 52 weeks\\[/tex]
Total number of weeks in two year [tex]= 104 weeks\\[/tex]
Total amount paid in two weeks
[tex]= 35 * 104\\=3,640\\[/tex]
The make up rate is basically the amount paid over and above $2400
[tex]=(\frac{3640 - 2400}{2400} ) * 100\\= 51. 7 perecent[/tex]
What is the answer to this?
What is the length of chord AB ?
A. 5.8 ft
B. 5.5 ft
C. 6.1 ft
D. 6.25 ft
Simplify 7x + (x – 4)(x + 5) – 5x.
Answer:
x^2 + 3x – 20
Step-by-step explanation:
I just did the assignment
(06.02)The graph shows the number of weeks a movie has been in theaters and the number of tickets sold each week
Which statement best describes the relationship between the number of weeks a movie has been in theaters and the number of tickets sold?
As the number of weeks increases, the number of tickets sold decreases.
As the number of weeks increases, the number of tickets sold increases.
As the number of weeks decreases, the number of tickets sold decreases.
No relationship can be determined.
As the number of weeks increases, the number of tickets sold decreases so option (A) will be correct.
What is a graph?The link between lines and points is described by a graph, which is a diagrammatic representation of a network. A graph is made up of some points and the distance between two.
In another word, graph is geometrical relation of the analytical variable.
For example to draw the equation y = 6x +8 this will draw a straight line in the coordinate geometry.
In the given question it is clearly visible that as the weeks in theater are increasing the points are going down on the y-axis which is tickets sold.
As the number of weeks increases, the number of tickets sold decreases hence option (A) will be correct.
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A cone-shaped hat is shown:
A cone is shown with slant height 18 cm and radius 5.7 cm. The unknown height is labeled with a question mark, and the line joining the tip of the cone to the base is perpendicular to the base.
What is the approximate height of the hat?
3.51 centimeters, because height = Square root of the difference of 18 and 5.7
17.07 centimeters, because height = Square root of the difference of the squares of 18 and 5.7
18.88 centimeters, because height = Square root of the sum of the squares of 18 and 5.7
4.87 centimeters, because height = Square root of the sum of 18 and 5.7
Answer:
B. 17.07 centimeters, because height = Square root of the difference of the squares of 18 and 5.7.
Step-by-step explanation:
The formula of height (h) of a cone is: [tex]h=\sqrt{l^2-r^2}[/tex], where,
[tex]l[/tex] = Slant height of cone,
[tex]r[/tex] = Radius of cone.
Upon substituting slant height = 18 cm and radius = 5.7 cm, we will get,
[tex]h=\sqrt{(18)^2-(5.7)^2}[/tex]
[tex]h=\sqrt{324-32.49}[/tex]
[tex]h=\sqrt{291.51}[/tex]
[tex]h=17.0736639301586348\approx 17.07[/tex]
Therefore, the height of cone is 17.07 cm and option B is the correct choice.
3. Suppose e and f are real numbers where e>0 and f<0.
(a) Is -e+f positive or negative. Explain how you know.
(b) Is e-f positive or negative? Explain how you know.
(c) Is f-e positive or negative. Explain how you know.
Which expression represents the area of the shaded triangle?
Answer:
B. [tex]\frac{1}{2}\times (5.7)\times (1.9)[/tex]
Step-by-step explanation:
We have been given an image of a triangle. We are asked to choose the correct option that represents the area of the shaded region.
We know that the area of a triangle is half the product of its height and base.
Upon looking at our given diagram we can that shaded region is in form of triangle and the height of both triangles is 5.7 meters. We can also see that the base of shaded triangle is 1.9 meters.
[tex]\text{Area of triangle}=\frac{1}{2}\times (\text{Height *Base})[/tex]
[tex]\text{Area of shaded region}=\frac{1}{2}\times (5.7)\times (1.9)[/tex]
Therefore, option B is the correct choice.
Answer:
b.
Step-by-step explanation:
Bao Yu is completing the square to solve the polynomial equation.
x2 – x – 3 = 0
What should be her first step?
adding –x to both sides of the equation
adding –3 to both sides of the equation
isolating the first term, x2
isolating the constant, –3
Solution:
The square of the given equation can be completed as below:
Here we will make the terms on left hand side such that it gets the form of [tex]a^2\pm2ab+b^2=(a\pm b)^2[/tex]
[tex]x^2-x-3=0\\\\\text{Isolate the constant}\\\\x^2-x=3\\\\x^2-2\times\frac{1}{2}\times x +\frac{1}{2}^2=3+ \frac{1}{2}^2\\\\(x-\frac{1}{2})^2=\frac{13}{4}\\[/tex]
Hence the correct option is isolating the constant , -3.
The polynomial equation x^2 – x – 3 = 0 is a quadratic equation, and the first step in completing the square is (d) isolating the constant, –3
What are polynomials?Polynomials are expressions that are represented with variables and coefficients
Below are the steps taken to determine Bao Yu's first step
The equation is given as:
x^2 – x – 3 = 0
Isolate the constant -3 in the equation.
So, we have:
x^2 – x = 3
Hence, the first step in completing the square is (d) isolating the constant, –3
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You have $50 in your savings account.Each week you deposit $5 in your account. Write an expression that models the situation.
The product of three and a number is thirty-three. What is the number? N = 11 N = 30 N = 36
Answer:
Step-by-step explanation:
N=11
Why is sin(20) = sin(160) = -sin(200) = -sin(340)?
Answer:
see.
Step-by-step explanation:
The value of sin is the same at the same distance from the cuadrant limit of the point. For the case of 20°, we have that the sin is the same in the following case:
As 20 is positive we use the limit cuadrant at 90°. The distance of 20 to 90 is 70. So, sin(20)=sin(90+70)=sin(160).
Also we have that sin(x) is a odd function, so sin(-x)=-sin(x), so
sin(-20°)= -sin(20°)
-sin(-20°)=sin(20°)
-sin(340°)=sin(20°).
and,
sin(-160°)=-sin(160°)
-sin(-160°)=sin(160°)
-sin(200°)=sin(160°)=sin(20°).
Given 2 events a and b, and that p(a)=0.30, p(b)=0.45, p(a u b)=0.60. find the probability p(a∩b).
If you were to add all odd numbers between 1 and 11 (both inclusive), the result would be
Final answer:
By adding all the odd numbers from 1 to 11 inclusive (1, 3, 5, 7, 9, 11), the sum is 36.
Explanation:
If you were to add all odd numbers between 1 and 11 (both inclusive), the odd numbers are: 1, 3, 5, 7, 9, and 11. To find the result of adding these numbers together, you simply add each one sequentially:
1 + 3 = 4
4 + 5 = 9
9 + 7 = 16
16 + 9 = 25
25 + 11 = 36
So, the result of adding all the odd numbers from 1 to 11 inclusive is 36.
Solve log 6 60 - log 6 30
A.) 2
B.) log 6 2
C.) 5
D.) log 6 30
Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F + G) (2) =
Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F - G) (6) =
Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F G) (2) =
Answer with Step-by-step explanation:
F = {(0, 1), (2, 4), (4, 6), (6, 8)}
G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F+G)(2)=F(2)+G(2)
= 4+5
= 9
F = {(0, 1), (2, 4), (4, 6), (6, 8)}
G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F - G) (6) =F(6)-G(6)
=8-9
=-1
F = {(0, 1), (2, 4), (4, 6), (6, 8)}
G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F.G) (2) =F(2).G(2)
= 4×5
= 20
Write the interval (3,20] as an inequality and using set notation