Answer:
a) The location of the turning point is approximately \(V(x,y) = (-0.25, -2,1)\).
b) Roots are approximately \(x_{1} \approx -1.3\) and \(x_{2} \approx 0.8\).
c) \(f(1.5) \approx 4\)
Step-by-step explanation:
a) The figure presents the graphic of a parabola, that is, a second order polynomial, with an absolute minimum (vertex). The turning point of the graphic, that is, the point in which behavior of the curve changes, is the vertex. Hence, the location of the turning point is approximately \(V(x,y) = (-0.25, -2,1)\)
b) According to the Quadratic Formula, second-order polynomials can have either two real roots or two conjugated complex roots. In this case, we have two real roots. A root corresponds with the point of the curve that passes through x-axis. In this case, roots are approximately \(x_{1} \approx -1.3\) and \(x_{2} \approx 0.8\).
c) \(f(1.5)\) is the function evaluated at \(x = 1.5\), that is, the value on y-axis associated with \(x = 1.5\). Lastly, we conclude that \(f(1.5) \approx 4\).
What should you substitute for y in the bottom equation to solve the system by the substitution method?
A. y=3x+15
B. y =-x-5
C. y=x+5
D. y=-3-15
2(3b-2)<4b+8 solve each inequality.
Answer:
b < 6
Step-by-step explanation:
\(2(3b-2)<4b+8\)
\(6b-4<4b+8\)
\(6b-4b<8+4\)
\(2b<12\)
\(b<\frac{12}{2}\)
\(b<6\)
Hope this helps
Melissa wants to put a ribbon border around a sign in her classroom shaped like the right
triangle below. If ribbon costs $0.82 cents per foot, how much will it cost her to buy the ribbon for her sign
Answer:
$19.68 for each foot
Step-by-step explanation:
Answer:
$19.68
Step-by-step explanation:
no <3
How do you do the second one?
Answer:
9
Step-by-step explanation:
First, all the sides of a rhombus are congruent (equal).
So, we just set the side values equal to each other.
This gives us:
6x-5 = 4x+13
-4x -4x
2x-5 = 13
+5 +5
2x = 18
Then, divide both sides by 2
x = 9
Hope this helps!
Ken spent $740 of his salary on an oven and 3 4 of the remaining money on a laptop. If he had 1 5 of his salary left, how much was his salary?
Let's denote Ken's salary as "S". The amount left after buying the oven is S - $740. Then, 1/4 of this amount is equal to 1/5 of his salary:
From the given information, we know that Ken spent $740 on an oven and 3/4 of the remaining money on a laptop. This means he has 1/4 of the remaining money left.
(1/4)(S - $740) = 1/5S
To solve for S, we can multiply both sides of the equation by 20:
5(S - $740) = 4S
Solving this equation will give us the value of Ken's salary.
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A plane slices a double-napped cone at a slight angle to the base of the cone without intersecting the base. Which conic section is formed? CircleEllipseHyperbolaParabola
Hyperbola will form out from the cone.
Double napped coneThe generator, vertex, and vertical axis are three crucial components of the double-napped cone. Conic sections or conics are the curves that result from the division of a double-napped cone into sections by a plane.
HyperbolaA plane intersects with both parts of a double cone to form a hyperbola, which is an open curve with two branches. The hyperbola will be symmetrical regardless of whether the plane is parallel to the axis of the cone or not.
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Use the reduced-row-echelon method and the co factor method to find the inverse of (
−2
3
3
−5
)
The inverse of the matrix (
−2 3
3 −5
) using the reduced-row-echelon method and the cofactor method is (
−5 −3
−3 −2
).
To find the inverse of a matrix using the reduced-row-echelon method, we augment the given matrix with the identity matrix of the same size and perform row operations to transform the given matrix into the reduced-row-echelon form. The resulting augmented matrix will have the inverse of the original matrix on the right-hand side.
Using the reduced-row-echelon method, we can perform row operations to convert the given matrix (
−2 3
3 −5
) into the reduced-row-echelon form, resulting in (
1 0
0 1
) on the right-hand side. The left-hand side of the augmented matrix will then be the inverse of the given matrix, which is (
−5 −3
−3 −2
).
The cofactor method is another approach to finding the inverse of a matrix. It involves finding the cofactor matrix of the given matrix, which is obtained by taking the determinants of the minor matrices and applying alternating signs. The cofactor matrix is then transposed and divided by the determinant of the original matrix to obtain the inverse.
In this case, the determinant of the given matrix is (-2*(-5) - 3*3) = 1. The cofactor matrix of (
−2 3
3 −5
) is (
−5 −3
−3 −2
). Transposing and dividing it by the determinant yields the same result as obtained using the reduced-row-echelon method.
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Penelope invested $89,000 in an account paying an interest rate of 6}% compounded continuously. Samir invested $89,000 in an account paying an interest rate of 6⅜% compounded monthly. To the nearest hundredth of a year, how much longer would it take for Samir's money to double than for Penelupe's money to double?
To solve the problem, we need to find out how much longer it would take for Samir's money to double compared to Penelope's money, given that Penelope invested $89,000 in an account with a continuous interest rate of 6%, while Samir invested $89,000 in an account with a monthly compounded interest rate of 6⅜%.
For Penelope's investment, we can use the formula for continuous compounding, which is A = Pe^(rt), where A is the amount of money after t years, P is the initial investment, r is the interest rate as a decimal, and e is the natural logarithm base. We know that Penelope invested $89,000 and we want to find t such that A = 2P = $178,000. Thus, we have:
$178,000 = $89,000e^(0.06t)
Dividing both sides by $89,000 and taking the natural logarithm of both sides, we get:
ln(2) = 0.06t
Solving for t, we get:
t = ln(2)/0.06 ≈ 11.55 years
For Samir's investment, we can use the formula for monthly compounded interest, which is A = P(1 + r/12)^(12t), where A, P, r are the same as before, and t is the time in years divided by 12. Similarly, we know that Samir invested $89,000 and we want to find t such that A = 2P = $178,000. Thus, we have:
$178,000 = $89,000(1 + 0.0638/12)^(12t)
Dividing both sides by $89,000 and taking the logarithm (base 1 + r/12) of both sides, we get:
log(2)/log(1 + 0.0638/12) = 12t
Solving for t, we get:
t ≈ 11.80/12 = 0.98 years
To find the difference in time it takes for Samir's money to double compared to Penelope's, we subtract the time it takes for Penelope's money to double from the time it takes for Samir's money to double:
0.98 - 11.55 ≈ -10.57
However, this answer doesn't make sense in the context of the problem, since it's negative. After reviewing our solution, we realized that we made a mistake in the calculation of t for Penelope's investment. We need to find the time it takes for Penelope's investment to double with annual compounding, not continuous compounding. The formula for this is t = (ln(2))/(ln(1 + r)), where r is the annual interest rate as a decimal.
Plugging in the numbers, we get:
t = (ln(2))/(ln(1 + 0.06)) ≈ 11.55 years
This is the same as the time we got for Samir's investment, so the difference in time it takes for their money to double is:
0.98 - 11.55 ≈ -10.57
Again, this answer doesn't make sense in the context of the problem, since it's negative. Therefore, we need to revise our solution and approach the problem differently.
What are the coordinates of the image of vertex D after a reflection across the x-axis?
(5, 3)
(–5, –3)
(–3, 5)
(3, –5)
Answer:
(-3,5) ia the answer
Step-by-step explanation:
It is because when you reflect it across the x axis the first coordinate will be negative and the second number is positive since its in the second square of the graph, so it is more of a resonable guess.
Answer:
A 5 3
Step-by-step explanation:
The graph shows two lines, A and B.
A graph is shown with x- and y-axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 2, 6 with the ordered pair 6, 2. Another straight line labeled B joins the ordered pair 0, 3 with the ordered pair 4.5, 6.
Part A: How many solutions does the pair of equations for lines A and B have? Explain your answer.
Part B: What is the solution to the equations of lines A and B? Explain your answer.
Answer:
(3, 5)Step-by-step explanation:
See attached
Part AThere is one solution as lines intersectPart BSolution is the intersection point, which is (3, 5)Answer:
Part A: There is one solution because the intersect point is the answer and there is only one intersect point.
Part B: The solution is (3,5) because (3,5) is the intersect point for the equation and the answer is going to be the intersect point.
Step-by-step explanation:
What is the m∠AHE
m
∠
A
H
E
to the nearest whole number?
Answer:
Below
Step-by-step explanation:
As I posted ....looks to be 147°
If the monetary multiplier is 6, then the reserve ratio must be:_______
a) 0.06.
b) 0.167.
c) 1.67.
d) 0.6.
The formula relating the monetary multiplier and the reserve ratio shows that as the monetary multiplier increases, the reserve ratio decreases. If the monetary multiplier is 6, the reserve ratio must be 0.167.
To determine the reserve ratio given the monetary multiplier, we can use the formula:
Monetary Multiplier = 1 / Reserve Ratio
Given that the monetary multiplier is 6, we can substitute this value into the formula:
6 = 1 / Reserve Ratio
To isolate the reserve ratio, we can take the reciprocal of both sides of the equation:
1 / 6 = 1 / (1 / Reserve Ratio)
1 / 6 = Reserve Ratio
Therefore, the reserve ratio must be 1/6 or approximately 0.167.
Among the given options, b) 0.167 represents the correct answer.
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The roof rafter of a house has been raised to a height of 13 yards at the ridge. Half of the length of the run measures 9 yards. Find
the length of the rafter. Round to the nearest 100th.
Answer:
15.81 = ?
Step-by-step explanation:
Since this is a right triangle we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
9^2 + 13^2 = ?^2
81 +169 = ?^2
250 = ?^2
Taking the square root of each side
sqrt(250) =?
15.8113883= ?
To the nearest 100th
15.81 = ?
Answer:
Using Pythagorean theorem:- \(a^{2} +b^{2} =c^{2}\)
a= 13
b= 9
c= ? ( length)
\(13^{2} +9^{2} =?^{2}\)
\(13^{2} =169\)
\(9^{2} =81\)
\(169+81=?^{2}\)
\(250=?^{2}\)
\(\sqrt{250}=15.811\)
\(?=15.81\)
OAmalOHopeO
Which of the following numbers is NOT a solution of the inequality: 6x + 11 > 7x - 2?
Answer:
x<13
Step-by-step explanation:
x < 13 is the solution of the inequality; 6x + 11 > 7x - 2
What is an inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality'.
Given that, an inequality 6x + 11 > 7x - 2
On solving for x, we get,
6x + 11 > 7x - 2
6x + 11 +2 > 7x
13 > x
x < 13
Hence, x < 13 is the solution of the inequality; 6x + 11 > 7x - 2
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Can someone answer this?!
a) 1999
b) 2013
Step-by-step explanation:\( \large \bf{p = \frac{184.64 + 0.7524 {t}^{2} }{1 + 0.0028 {t}^{2} } }\)
a) p = 200\( \bf \longrightarrow{200= \frac{184.64 + 0.7524 {t}^{2} }{1 + 0.0028 {t}^{2} } }\)
\(\bf \longrightarrow{200 + 0.56 {t}^{2} = 184.64 + 0.7524 {t}^{2} }\)
\(\bf \longrightarrow{0.7524 {t}^{2} - 0.56 {t}^{2} = 200 - 186.64}\)
\(\bf \longrightarrow{0.1924 {t}^{2} = 15.36}\)
\(\bf \longrightarrow{ {t}^{2} = 79.83}\)
\(\bf \longrightarrow{t = 8.93}\)
\(\bf \longrightarrow{t = 9 \: years}\)
\(\bf \longrightarrow{ \boxed{ \sf{T \: = 1990 + 9 = 1999}}}\)
(b) p = 266\(\bf \longrightarrow{266= \frac{184.64 + 0.7524 {t}^{2} }{1 + 0.0028 {t}^{2} } }\)
\(\bf \longrightarrow{266 + 0.7448 {t}^{2} = 184.64 + 0.7524 {t}^{2} }\)
\(\bf \longrightarrow{0.7524 {t}^{2} - 0.7448 {t}^{2} = 266 - 184.64}\)
\(\bf \longrightarrow{0.0076 {t}^{2} = 81.36}\)
\(\bf \longrightarrow{ {t}^{2} = 529}\)
\(\bf \longrightarrow{t = 23 \: years}\)
\(\bf \longrightarrow{ \boxed{ \sf{T \: = 1990 + 23 = 2013}}}\)
KInda need to hurry first answer gets brainlist
Answer: d
Step-by-step explanation:
Answer:
I think the answer to your question is 3x-5y^2 i am not sure.
Step-by-step explanation:
I hope this helps, have a nice day
use parametric equations and simpson's rule with n = 8 to estimate the circumference of the ellipse 16x^2 4y^2 = 64. (round your answer to one decimal place.)
Thus, parametric equation for the circumference of the ellipse : C ≈ 15.3.
To estimate the circumference of the ellipse given by the equation 16x^2 + 4y^2 = 64, we first need to find the parametric equations. Let's divide both sides of the equation by 64 to get:
x^2 / 4^2 + y^2 / 2^2 = 1
Now, we can use the parametric equations for an ellipse:
x = 4 * cos(t)
y = 2 * sin(t)
Now, we can find the arc length function ds/dt. To do this, we'll differentiate both equations with respect to t and then use the Pythagorean theorem:
dx/dt = -4 * sin(t)
dy/dt = 2 * cos(t)
(ds/dt)^2 = (dx/dt)^2 + (dy/dt)^2 = (-4 * sin(t))^2 + (2 * cos(t))^2
Now, find ds/dt:
ds/dt = √(16 * sin^2(t) + 4 * cos^2(t))
Now we can use Simpson's rule with n = 8 to estimate the circumference:
C ≈ (1/4)[(ds/dt)|t = 0 + 4(ds/dt)|t=(1/8)π + 2(ds/dt)|t=(1/4)π + 4(ds/dt)|t=(3/8)π + (ds/dt)|t=π/2] * (2π/8)
After plugging in the values for ds/dt and evaluating the expression, we find:
C ≈ 15.3 (rounded to one decimal place)
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what is x:6-3(3x-5)= -24
To solve x:
1- Use distributive property to remove the parenthesis:
\(\begin{gathered} a(b\pm c)=ab\pm ac \\ \\ 6-9x+15=-24 \\ 21-9x=-24 \end{gathered}\)2- Subtract 21 in both sides of the equation:
\(\begin{gathered} 21-21-9x=-24-21 \\ -9x=-45 \end{gathered}\)3- Divide both sides of the equation into -9:
\(\begin{gathered} \frac{-9}{-9}x=\frac{-45}{-9} \\ \\ x=5 \end{gathered}\)Then, x is 5What is the positive solution of x^2– 36 = 5x?
Answer:
9 and -4
Step-by-step explanation:
Sketch the line 4x+3y=11
sketch of the line 4x + 3y = 11, slope (-4/3), y-intercept of the line y = 11/3
Step 1: Convert the equation to slope-intercept form (y = mx + b) by solving for y:
3y = -4x + 11
y = (-4/3)x + 11/3
Step 2: Identify the slope and y-intercept:
From the equation in slope-intercept form, we can see that the slope (m) is -4/3 and the y-intercept (b) is 11/3.
Step 3: Plot the y-intercept:
On the y-axis, mark a point at y = 11/3 (approximately 3.67). This is the y-intercept of the line.
Step 4: Use the slope to find additional points:
Using the slope of -4/3, we can find other points on the line. The slope represents the change in y for every 1 unit change in x. So, starting from the y-intercept, we can move down 4 units and to the right 3 units to find the next point, and continue this pattern to find more points.
Step 5: Connect the points:
Once you have a few points on the line, you can connect them with a straight line. Make sure the line extends beyond the plotted points to show that it continues indefinitely.
The resulting line should have a negative slope (-4/3) and be slanting downward from left to right.
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choose the statement that is false.group of answer choicesa 95% confidence interval is wider than a 90% confidence intervalwhen sampling for means and thinking about the central limit theorem, the n should always be >30.when estimating the standard deviation in calculating confidence intervals, make sure you use the t tables.reducing the variation of a process will increase the width of a given confidence interval relative to that process.
Reducing the variation of a process will increase the width of a given confidence interval relative to that process.
Option C is correct .
What is a confidence interval?
In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as a confidence interval. By employing the dimensions of values used in the computation of the intervals, it is simple to establish the link between components of two confidence intervals. The width is a fundamental component in these range estimates, which are affected by sample size, etc.
Hence, reducing the variation of a process will increase the width of a given confidence interval relative to that process is false.
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The graph of a line passes through the points (0, -2) and (6, 0). What is the equation of the line?
will give brainlist
Answer:
y=0.3x-2
Step-by-step explanation:
first find the gradient
m=y2-y1/x2-x1
m=0-(-2)/6-0
m=0.3
then use this equation
y-y1=m(x-x1)
y-(-2)=0.3(x-0)
y+2=0.3x-0
y=0.3x-2
Can some smart person help me out here!!!
Answer:
the answer is C I'm studying this right now
From the figure shown, if b = 3
units, determine:
Moment of inertia about the x-axis, in
units4
Moment of inertia about the y-axis, in
units4
Polar moment of inertia passing through point
O, in units4
To calculate the moment of inertia about the x-axis, the moment of inertia about the y-axis, and the polar moment of inertia passing through point O, we need to determine the geometric properties of the given figure, such as the shape and dimensions.
To calculate the moment of inertia about the x-axis, we need to determine the area of the figure and the distance of each element from the x-axis. The moment of inertia about the x-axis, denoted as Ix, is given by the sum of the individual moments of inertia of each element about the x-axis.
Similarly, to calculate the moment of inertia about the y-axis (Iy), we need to determine the area of the figure and the distance of each element from the y-axis. The moment of inertia about the y-axis is given by the sum of the individual moments of inertia of each element about the y-axis.
The polar moment of inertia passing through point O (J) represents the resistance of the entire figure to torsional or rotational deformation. It is the sum of the moments of inertia about the x-axis and y-axis, denoted as Ix and Iy, respectively.
The specific calculation method will depend on the shape and dimensions of the figure. For example, if the figure is a rectangle, the formulas for calculating the moments of inertia and the polar moment of inertia can be found in engineering mechanics or solid mechanics textbooks.
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Which expression(s) have the same value as 100?
Expression A: 202-3(102)
Expression B: 8(42) + 24
Expression C: 152-53
Complete the equation so that it has infinitely many solutions.
Enter the correct answer in the box in the equation.
Answer:
(2x-286)
Step-by-step explanation:
Answer:
(2x-286
Step-by-step explanation:
step by step
Mark me brainliest
Suppose Sine (x) = four-fifths and cos(x) < 0. What is the value of cos(2x)?
Answer:
B. -7/25
Step-by-step explanation:
E2020
The values of cos2x, when sinx = 4/5 is, -7/25. So option B is correct
What is trigonometry?Trigonometry is a branch of mathematics, which deals with the study of right angle triangles. Trigonometry is concerne
d with specified functions of angles and their applications to calculations.
There are 6 commonly used functions in trigonometry with their name and abbreviations-
sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec)
Given that,
sinx = 4/5
cos2x = ?
cos2x = 1 - 2 sin²x
cos2x = 1 - 2× (4/5)²
cos2x = 1- 32/25
cos2x = -7/25
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“growth or decay right” it cut out the picture
Help! i’ve been stuck on these problems for a bit now
Answer:
Growth
Growth
Decay
Decay
what does this equal??
Answer:
I think 3
Step-by-step explanation:
Solve the following equation for the variable given
Sole Y=mx+b for b
The solution for b is y-mx in the equation y=mx+b.
The given equation is y=mx+b
y equal r=to m times of x plus b
We need to solve for b in the equation
To solve we have to isolate b from the equation
Subtract mx from both sides
y-mx=b
Hence, the solution for b is y-mx in the equation y=mx+b.
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