Answer:
48 seeds germinated
Step-by-step explanation:
you have 60 seeds, and 80% of them germinated
80% = 0.80
\(60* 0.80 = 48\)
48 seeds
Answer: 48 seeds germinated
Step-by-step explanation:
60/100= 0.6
0.6x80=48
The area of a rectangle is calculated using the equation Area = length x width
What is the area of rectangle ABCD?
A. 6 Square Units
B. 441 Square Units
C. 21 Square Units
D. 49 Square Units
Answer:
441 (I think)
Step-by-step explanation:
I saw the answer in a quora post
If f(x) = sin x + 2x + 1 and g is the inverse function of f, what is the value of g'(1) ?.
Answer:
1/3
Step-by-step explanation:
\(g(f(x))=x \\ \\ g'(f(x))f'(x)=1 \\ \\ g'(f(x))=\frac{1}{f'(x)} \\ \\ g'(f(x))=\frac{1}{\cos x+2} \\ \\ g'(f(0))=\frac{1}{\cos(0)+2} \\ \\ g'(1)=\frac{1}{3}\)
Pls Help I need this in soon and am stuck, am giving out 25 points
Answer:
12
Step-by-step explanation:
Find the measure. Assume that segments that appear to be tangent are tangent. m RQ
To find the measure of angle RQ, we need more information about the problem or the given diagram. Please provide additional details or describe the diagram so that I can assist you further in determining the measure of angle RQ.
Determining the measure of an angle typically requires information about the relationship between different line segments or angles in a given figure. This could involve angles formed by intersecting lines, parallel lines, perpendicular lines, or triangles. Without any specific context or diagram, it is not possible to determine the measure of angle RQ. So please provide additional information or describe the diagram so that I can help you find the measure you're looking for.
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Simplify the expression
12 + 3p - 6 + p - r + r - 6
Answer:
4P
Step-by-step explanation:
PLS MAKE ME AS BRAINLIST
Find the first four nonzero terms in a power series expansion about x=0 for a general solution to the given differential equation.
w''-8x^2w'+w=0
Type an expression in terms of a0 and a1 that includes all terms up to order 3.
To find the power series expansion about x=0 for the general solution to the given differential equation, let's assume a power series solution of the form:
w(x) = ∑(n=0 to ∞) a_n x^n
where a_n represents the coefficients of the power series.
Differentiating w(x) with respect to x, we have:
w'(x) = ∑(n=0 to ∞) a_n*n*x^(n-1) = ∑(n=1 to ∞) a_n*n*x^(n-1)
Differentiating w'(x) with respect to x, we have:
w''(x) = ∑(n=1 to ∞) a_n*n*(n-1)*x^(n-2) = ∑(n=0 to ∞) a_(n+2)*(n+2)*(n+1)*x^n
Now, substituting these expressions into the differential equation, we get:
∑(n=0 to ∞) a_(n+2)*(n+2)*(n+1)*x^n - 8x^2 * ∑(n=1 to ∞) a_n*n*x^(n-1) + ∑(n=0 to ∞) a_n*x^n = 0
To simplify this equation, we need to separate the terms and adjust the indices:
a_2*2*1 + a_3*3*2*x + ∑(n=2 to ∞) a_(n+2)*(n+2)*(n+1)*x^n - 8∑(n=1 to ∞) a_n*n*x^n + ∑(n=0 to ∞) a_n*x^n = 0
Grouping the terms with the same power of x, we have:
[2a_2 - 8a_1] + [6a_3 - 8a_2]x + ∑(n=2 to ∞) [a_(n+2)*(n+2)*(n+1) - 8a_n*n]x^n + ∑(n=0 to ∞) a_n*x^n = 0
Equating the coefficients of each power of x to zero, we can find the expressions for a_2, a_3, and the terms up to order 3:
2a_2 - 8a_1 = 0 => a_2 = 4a_1
6a_3 - 8a_2 = 0 => a_3 = (8/6)*a_2 = (8/6)*4a_1 = (16/3)a_1
The terms up to order 3 are:
a_0 + a_1*x + 4a_1*x^2 + (16/3)a_1*x^3
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a block of ice in the shape of a right circular cone with a radius of 30cm and a height of 10 cm starts melting in a uniform way, preserving its shape and proportions. The height decreasing at a rate of 2 cm/hr. How fast is the volume decreasing when the height is 1 cm
The rate of change of volume dV/dt when the height is 1 cm is approximately equal to -2,820 π/3 cm³/h.
Let V be the volume of the block of ice, h be the height of the block of ice, and r be the radius of the block of ice. It is given that r = 30 cm, h = 10 cm, and dh/dt = -2 cm/h. We need to find the rate of change of volume dV/dt when the height is 1 cm.
To find the rate of change of volume dV/dt, we can use the chain rule of differentiation.
dV/dt = dV/dh × dh/dt
We know that the volume of a right circular cone is given by:
V = 1/3 πr²h
When the radius is constant, we get:
dV/dh = 1/3 πr²dh/dh = 1/3 πr²
Also, we know that dh/dt = -2 cm/h.
Substituting the values of r, h, and dh/dt in the formula for dV/dt, we get:
dV/dt = (1/3 × π × (30)²) × (-2)= -2,820 π/3
The rate of change of volume is approximately equal to -2,820 π/3 cm³/h. The negative sign shows that it is decreasing.
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Plz help very important question
9514 1404 393
Answer:
g(2a) = 8a
Step-by-step explanation:
Put the argument where the variable is and simplify.
g(a) = 4a
g(2a) = 4(2a) = 8a
g(2a) = 8a
Suppose you deposit $24500 into an savings account earning 2% annual interest compounded continuously. To pay for all your music downloads, each year you withdraw $1000 in a continuous way.
Let A(t) represent the amount of money in your savings account t years after your initial deposit.
(A) Write the DE model for the time rate of change of money in the account. Also state the initial condition.
dA/dt=
A(0)=
(B) Solve the IVP to find the amount of money in the account as a function of time.
A(t)=
(C) When will your money run out?
t= years
(A) dA/dt = 0.02A - 1000
A(0) = $24,500
(B) A = (1000 ± Ke^t) / 0.02
(C) t = ln(1000 / K) years
(A) To write the differential equation (DE) model for the time rate of change of money in the account, we consider that the money in the account is continuously compounded with an annual interest rate of 2%. The rate of change of money in the account, dA/dt, is given by the difference between the continuous deposit and the continuous withdrawal.
dA/dt = 0.02A - 1000
Here, 0.02A represents the continuous interest earned on the account balance, and 1000 represents the continuous withdrawal.
The initial condition is A(0) = $24,500, as given in the problem.
(B) To solve the initial value problem (IVP) and find the amount of money in the account as a function of time, we can separate variables and integrate the differential equation:
1/(0.02A - 1000) dA = dt
Integrating both sides:
∫(1/(0.02A - 1000)) dA = ∫dt
Applying integration, we get:
ln(|0.02A - 1000|) = t + C
where C is the constant of integration.
Taking the exponential of both sides:
|0.02A - 1000| = e^(t + C)
Since the constant of integration C can be positive or negative, we can rewrite the equation as:
0.02A - 1000 = ±e^t * e^C
Simplifying further:
0.02A - 1000 = ±Ke^t
Here, K represents the constant resulting from combining the constants e^C.
Solving for A, we have:
0.02A = 1000 ± Ke^t
A = (1000 ± Ke^t) / 0.02
(C) To determine when the money will run out, we set A(t) = 0 and solve for t:
(1000 ± Ke^t) / 0.02 = 0
1000 ± Ke^t = 0
±Ke^t = -1000
Since e^t is always positive, the equation implies that K must be negative to satisfy the equation. Thus, we can rewrite it as:
-Ke^t = -1000
Dividing both sides by -K, we get:
e^t = 1000 / K
Taking the natural logarithm of both sides:
t = ln(1000 / K)
Therefore, the money will run out at t = ln(1000 / K) years.
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write a for loop that prints the integers 0 through 39, each value on a separate line.
In programming, a loop is a control structure that allows us to execute a block of code repeatedly. A for loop is a type of loop that is commonly used when we need to repeat a set of instructions for a specific number of times.
In this case, we want to print the integers 0 through 39, each value on a separate line.
Here's an example of a for loop in Python that accomplishes this:
for i in range(40):
print(i)
In this loop, the variable `i` takes on the values 0 through 39, one at a time, on each iteration of the loop. The range(40) function generates a sequence of integers from 0 to 39, which is used to control the loop.
The print() function outputs the value of `i` to the console on each iteration, followed by a newline character which creates a new line for each value.
To break this down further, the 'for' keyword initiates the loop and the `in` keyword specifies the range of values for the loop. The `range()` function generates a sequence of integers starting at 0 and ending at 39.
The `print()` function outputs each value to the console followed by a newline character which creates a new line for each value. This loop will execute a total of 40 times, printing each value on a separate line.
In summary, the for loop is a powerful and flexible tool in programming that allows us to automate repetitive tasks. In this example, we used a for loop to print the integers 0 through 39, each on a separate line, in a concise and efficient manner.
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find the distance between the points (4,22) and (20,10)
Answer: (16,-12)
Step-by-step explanation: just cuz... just listen linda
Answer:
(16,-12)
Step-by-step explanation:
I used a graph to get this answer
Which numbers are between 4 over 6 and 7 over 5
Answer:
21/30, 22/30, 23/30..........39/30, 40/30, 41/30
Step-by-step explanation:
Numbers between 4/6 and 7/5 are:
Making the same demoninator, which is 30 (LCM)
Therefore, now the new numbers are 20/30 and 42/30.
Now,
the numbers between are 20/30 and 42/30:
21/30, 22/30, 23/30..........39/30, 40/30, 41/30
Hope it helps!
Mark as brainliest!
Thanks!!!
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0
Which division expression is shown in the model?
1
col
3
÷2
314
÷2 2÷
Divide Fractions: Fractional Quotients Quiz - Level F
13
2
3
-
+ +
3
The division expression shown in the model attached to this question is 1/2 ÷ 3
How to determine which division expression is shown in the model?The model missing in the question is added as an attachment
In the model, we have
Shaded sections = 3
Partitons = 1/2
This means that
Division expression = Partitons ÷ Shaded sections
Substituting the above expressions, we have
Division expression = 1/2 ÷ 3
This means that the division expression is 1/2 ÷ 3
When the expression is solved, we have
Division expression = 1/6
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Complete question
Which division expression is shown in the model?
See attachment
If a box with a square cross section is to be sent by a delivery service, there are restrictions on its size such that its volume is given by V = x²(135 - 5x), where x is the length of each side of the cross section (in inches). (a) Is V a function of x? Yes, V is a function of x. No, V is not a function of x. (b) If V = V(x), find V(11) and V(23). (If V is not a function of x, enter DNE.) V(11) = in ³ V(23) = in 3 (c) What restrictions must be placed on x (the domain) so that the problem makes physical sense? (Enter your answer using interval notation. If V is not a function of x, enter DNE.)
a) Yes, V is a function of x.
b) V(11) = 9680 in³ ; V(23) = 5290 in³
c) domain is [0, 27].
Given
V = x²(135 - 5x), where x is the length of each side of the cross section (in inches).
(a) Yes, V is a function of x.
To prove it, check whether each value of x gives a unique value of V.
If every value of x corresponds to a unique value of V, then it is a function of x.
(b) If V = V(x), V(11) and V(23) are :
To find V(11), substitute x = 11 in V(x) equation.
V(11) = 11²(135 - 5 * 11)
= 11²(80)
= 9680 in³
To find V(23), substitute x = 23 in V(x) equation.
V(23) = 23²(135 - 5 * 23)
= 23²(10)
= 5290 in³
(c) Since it is not possible to have a negative length of a side of a box, x cannot be negative.
Therefore, the domain must be x ≥ 0.
Also, the volume of a box cannot be negative, so we set V(x) ≥ 0.
Therefore,
x²(135 - 5x) ≥ 0
x(135 - 5x) ≥ 0
x(5x - 135) ≤ 0
x ≤ 0 or x ≤ 27
Therefore, the domain is [0, 27].
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reflects about a line such that N is the reflection of B and O is the reflection of C. Point N is shown on the coordinate plane, but point O is not. The coordinates of point O are ( , ).
The coordinates of point O of the given Reflection is; 5, 5
What is coordinates of point ?
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
According to my investigation, the coordinate points are shown on the picture below.
The junction of these two lines should tell us the location of point O because N is the reflection of B and O is the reflection of C.
If we were to draw a line to the right of N and a vertical line below C, this intersection would reveal the location of point O.
By doing so, point O is located at (5,5).
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For science class, a student recorded the high and low temperatures, in Fahrenheit, over a ten-day period in September. The data is shown in the table.
Low Temperature, x 26 28 30 32 34 35 37 38 41 45
High Temperature, y 49 50 57 54 60 58 64 66 63 72
What is the correlation for a linear model of this data? Round to the nearest hundredth.
The correlation coefficient for the data-set in the table is given as follows:
r = 0.95
What is a correlation coefficient?A correlation coefficient is a statistical measure that indicates the strength and direction of a linear function between two variables.
The coefficients can range from -1 to +1, with -1 indicates a perfect negative correlation, 0 indicates no correlation, and +1 indicates a perfect positive correlation.
The points for this problem are given as follows:
(26, 49), (28, 50), (30, 57), (32, 54), (34, 60), (35, 58), (37, 64), (38, 66), (41, 63), (45, 72).
Inserting these points into a calculator, the correlation coefficient is given as follows:
r = 0.95. (rounded to the nearest hundredth).
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Solve the right triangle. Round decimal answers to the nearest tenth.
Answer:
Step-by-step explanation:
take angle A as reference angle
using cos rule
cos A = adjacent/hypotenuse
cos A =10/15
cos A =0.66
\(A=cos^{-1} (0.6666)\)
A=48.194
A=48.2
angle A + angle B + angle C =180 degree (being sum of interior angles of a triangle)
48.2 + angle B + 90 =180
138.2 + angle B =180
angle B =180-138.7
angle B =41.8
for BC
using pythagoras theorem
a^2 + b^2 = c^2
AC^2 + BC^2 = AB^2
10^2 + BC^2 = 15^2
100 + BC^2 = 225
BC^2 = 225-100
BC^2 = 125
\(BC=\sqrt{125}\)
BC=5\(\sqrt{5}\)
BC=11.2
Pls i need this !!!!
Answer:
$40
Step-by-step explanation:
The interest on $4,000 at 3% for 4 months would be $40 if we round.
Please help!! Identify each line or segment that intersects ⊙ T.
The identified lines or segments that intersect circle T are: B. chords: PQ, RS, and WX; secants: none; tangents: v and u; diameter: WX; radii: WT and TX.
What is a Chord?A chord is defined as a line segment in a circle that has its two endpoints on the circumference of the circle. The longest chord in a circle is a diameter.
For example, the chords in the circle T, are: PQ, RS, and WX.
What is a Secant?A secant is a line segment that has one end on the circumference of a circle, and extends out of a circle. There are no secants in circle T.
What is a Tangent?Tangents are line segments that have touches the circumference of a circle but do not cross the circle.
For example, the tangents in circle T are, v and u.
What is a Diameter?A diameter can be described as a line that divides a circle into two halves. The diameter in the circle given is: WX.
What is a Radius?Radii are lines that has one endpoint at the center of a circle and the other endpoint on the circumference of a circle.
The radii in circle T are: WT and TX.
In summary, the identified lines or segments that intersect circle T are: B. chords: PQ, RS, and WX; secants: none; tangents: v and u; diameter: WX; radii: WT and TX.
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Olivia's family took a road trip to the Grand Canyon. Olivia fell asleep after they had travelled 243 miles. If the total length of the trip was 900 miles, what percentage of the total trip had they travelled when Olivia fell asleep?
The percentage of the total distance is 73%.
Calculating percentage:In mathematics, the percentage of a number is a ratio expressed as a fraction of 100. The that we use to represent the percentage is the sign “%”. The calculate the percentage of a number we use the following formula.
Percentage% = [ value of number ]/ [Total value ] × 100
Here we have
Olivia fell asleep after they had traveled 243 miles.
The total length of the trip was 900 miles.
The distance that traveled when Olivia fell asleep
= 900 miles - 243 miles
= 657 miles
The percentage of the total trip they traveled when Olivia fell asleep
= (657/900) × 100 = 73%
Therefore,
The percentage of the total distance is 73%.
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Does the point ( 4 , 47) lie on the line y = 10 x – 3 ?
Show your working .
Answer
Step-by-step explanation:
To find out if a point (x, y) is on the graph of a line, we plug in the values and see if we get a true statement, such as 10 = 10. If we get something different, like 6 = 4, we know that the point is not on the line because it does not satisfy the equation. In the given choices, when we plug in (1, 10) we get 10 = 7 + 2, which is false, making this is the desired answer.
(4, 47) gives 47 = 10(4) - 3 = 37
47=37 is a false statement
Jerry’s monthly salary was $3,050 last year. This year his monthly salary is $3,350. What percent increase in salary did Jerry receive?
Answer:
Increase of 9.3%
Step-by-step explanation:
Hence, the percent increase in salary did Jerry receive is \(4.68\)%.
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Here given that,
Jerry’s monthly salary was $\(3,050\) last year. This year his monthly salary is $\(3,350\).
His monthly salary in last year is $ \(3050\).
In this year his salary is $\(3350\).
So, the increase in salary is
\(3350-3050=300\)
And the overal salary is $ \(3050+3350=6400\)
So, the percent increase in salary did Jerry receive is
\(\frac{300}{6400}\) × \(100=4.68\)
Hence, the percent increase in salary did Jerry receive is \(4.68\)%.
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what is the equation of a line that passes through the point (5,-3) and is parallel to 6x+3y=-12
The equation of a line passing through the point (5,-3) and parallel to 6x+3y=-12 is y =-2x+7.
What does equation of parallel lines mean?Parallel lines are those that never intersect. As a result, two parallel lines must have the same slope but different intercepts (if they had the same intercepts, they would be identical lines).
The equation of the line is 6x+3y=-12.
6x+3y=-12
3y =-12-6x
y = -2x-4
The slope of this line is -2.
Because parallel lines have the same slope, the new line will also have a slope of -2.
You now have a point (5,-3) and a slope; thus, use the Point-Slope form to solve the equation of a line.
y-y₁= m(x-x₁)
y+3 = -2(x -5)
y+3 = -2x+10
y =-2x+7
The equation of a line passing through the point (5,-3) and parallel to 6x+3y=-12 is y =-2x+7.
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explain how x\(x^{2} +6^{x} +5\) equals \((x+5)(x+1)\)
Answer:
To show how x² + 6x + 5 is equivalent to (x + 5)(x + 1), we can use the FOIL method, which stands for First, Outer, Inner, and Last.
First, we multiply the first term of each factor: x and x, which gives x².
Next, we multiply the outer terms of each factor: x and 1, which gives x.
Then, we multiply the inner terms of each factor: 5 and x, which gives 5x.
Finally, we multiply the last term of each factor: 5 and 1, which gives 5.
Adding up these terms, we get:
x² + x + 5x + 5
Simplifying by combining like terms, we get:
x² + 6x + 5
This is the same as the original expression. Therefore, we have shown that:
x² + 6x + 5 = (x + 5)(x + 1)
Step-by-step explanation:
phoebe wants to buy a tv. store 1 sells the tv for 300. store 2 has a tv that cost 250,but marks up the price by 25% .from which store should phone buy the tv
Answer:
Store 1
Step-by-step explanation:
store 2. tv is 250
250+25%
250+62.50=312.50
an archway has vertical sides 10 feet high. the top of an archway can be modleled by the quadratic fuction f(x)=-0.5x^2+10 where x is the horizontal distance, in feet, along the archway. how far apart are the walls of the anrchway?
The walls of the archway are approximately 8.94 feet apart.
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The given quadratic function f(x) = -0.5x² + 10 models the height of the archway at a distance of x feet from the center of the arch.
Since the archway has vertical sides, the maximum height of the archway occurs at its center, which is the vertex of the parabolic function.
The x-coordinate of the vertex of a quadratic function f(x) = ax² + bx + c is given by -b/2a.
In this case, the quadratic function is f(x) = -0.5x² + 10, so its vertex is at x = -b/2a = -0 / (2 * (-0.5)) = 0.
Therefore, the maximum height of the archway occurs at x = 0.
Substituting x = 0 into the quadratic function f(x) = -0.5x²+ 10, we get:
f(0) = -0.5(0)² + 10 = 10
Therefore, the height of the archway at its center is 10 feet.
Since the archway has vertical sides, its height will be 10 feet at a distance of 0 feet from the center on both sides.
We need to find the horizontal distance between the two points where the height of the archway is also 10 feet.
Substituting f(x) = 10 into the quadratic function f(x) = -0.5x² + 10, we get:
10 = -0.5x² + 10
Simplifying this equation, we get:
x² = 20
Taking the square root of both sides, we get:
x = ±√(20) ≈ ±4.47
Therefore, the two points where the height of the archway is 10 feet are at x = -4.47 and x = 4.47. The distance between these two points is:
distance = 2 * 4.47 = 8.94 feet (rounded to two decimal places)
Therefore, the walls of the archway are approximately 8.94 feet apart.
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PR and os are diameters of circle T. What is the
measure of SR?
50°
* 80°
• 100°
120
Answer:
100degrees
Step-by-step explanation:
Find the diagram attached
From the diagram
<PQT =<TRS = 40
Since the triangle STR is isosceles, here,
<TSR =<TRS = 40
Also the sum of angle in a triangle is 189, hence:
Arc SR+<TSR +<TRS = 18₩
ArcSR +40+40=180
ArcSR +80=180
ArcSR = 180-80
ArcSR = 100degrees
Hence the measure of SR is 100degrees
The measure of arc SR is 100°. The correct option is the third option - 100°
Calculating the measure of an Arc
From the question, we are to determine the measure of arc SR.
The measure of arc SR = <STR
Now, we will determine the measure of <STR
In the diagram, T is the center of the circle.
∴ TP and TQ are radii.
Then, we can conclude that ΔPQT is an isosceles triangle.
Recall: Base angles of an isosceles triangle are equal.
∴ <PQT = <TPQ = 40°
Now, consider ΔPQT
<QTP + <TPQ + <PQT = 180° (Sum of angles in a triangle)
<QTP + 40° + 40° = 180°
<QTP + 80° = 180°
<QTP = 180° - 80°
<QTP = 100°
Also, in the diagram, <QTP and <STR are vertically opposite angles
NOTE: Vertically opposite angles are equal
That is, <QTP = <STR
∴ <STR = 100°
Hence, the measure of arc SR is 100°. The correct option is the third option 100°
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Here is the complete and correct question:
Line PR and Line QS are diameters of circle T. What is the measure of Arc SR?
50°
80°
100°
120°
Please find the attached image
4x + 6 = 8x – 10 graphing
Answer:
Step-by-step explanation: First things first, you have to have the variables on one side. To do that, subtract 4x from each side.
4x + 6 = 8x - 10
-4x -4x
Now you have your equation that is ready to graph.
6 = 4x - 10
Use a graphing calculator and put in the equation. You can also go to desmos.com
When you are done you will see your graph as well as the answer.
In geometry a
is a location. It has no size. It is
represented by a dot.
Points play a crucial role in defining distances, angles, and relationships between different geometric objects, providing a foundation for the study of geometry.
In geometry, a point is a fundamental concept that represents a precise location in space. It is a basic building block from which geometric figures and shapes are constructed. A point has no size, shape, or dimensions. It is often denoted by a dot or a small letter, such as point A (A). Points are used to describe the positions of other geometric elements, such as lines, curves, and polygons. They serve as reference markers and can be connected to form line segments and rays.
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Determine the reduced exact values for the root of f(x) = x^2+10x-5
The reduced exact values for the root of f(x) = x² + 10·x - 5, obtained using the quadratic formula are; x = (-5 + √(30)) and x = (-5 - √(30))
What is the quadratic formula?The quadratic formula is a formula that is used to find the roots of a quadratic equation, by plugging in the coefficients of a quadratic equation into the formula.
The roots of the quadratic function, f(x) = x² + 10·x - 5, can be obtained using the quadratic formula as follows;
The quadratic formula, which can be used to find the roots of the quadratic function, f(x) = a·x² + b·x + c is; x = (-b ± √(b² - 4·a·c))/(2·a)
The function f(x) = x² + 10·x - 5, indicates;
a = 1, b = 10, and c = -5, therefore;
x = (-10 ± √(10² - 4 × 1 × (-5)))/(2 × 1) = (-10 ± √(120))/2
(-10 ± √(120))/2 = (-5 × 2 ± 2 × √(30))/2
(-5 × 2 ± 2 × √(30))/2 = (-5 ± √(30))/2
The roots of the quadratic function are;
x = (-5 + √(30))/2, and x = (-5 - √(30))/2
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