[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex]\large\bm{ -4}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Before performing any calculation it's good to recall a few properties of integrals:
[tex]\small\longrightarrow \sf{\int_{a}^b(nf(x) + m)dx = n \int^b _{a}f(x)dx + \int_{a}^bmdx}[/tex]
[tex]\small\sf{\longrightarrow If \: a \angle c \angle b \Longrightarrow \int^{b} _a f(x)dx= \int^c _a f(x)dx+ \int^{b} _c f(x)dx }[/tex]
So we apply the first property in the first expression given by the question:
[tex]\small \sf{\longrightarrow\int ^3_{-2} [2f(x) +2]dx= 2 \int ^3 _{-2} f(x) dx+ \int f^3 _{2} 2dx=18}[/tex]
And we solve the second integral:
[tex]\small\sf{\longrightarrow2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot(3 - ( - 2)) }[/tex]
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} 2dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot5 = 2 \int^3_{-2} f(x)dx10 = }[/tex]
Then we take the last equation and we subtract 10 from both sides:
[tex]\sf{{\longrightarrow 2 \int ^3_{-2} f(x)dx} + 10 - 10 = 18 - 10}[/tex]
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 8}[/tex]
And we divide both sides by 2:
[tex]\small\longrightarrow \sf{\dfrac{2 { \int}^{3} _{2} }{2} = \dfrac{8}{2} }[/tex]
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx=4}[/tex]
Then we apply the second property to this integral:
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 4}[/tex]
Then we use the other equality in the question and we get:
[tex]\small\sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx = 8 + 2 \int ^3_{-2} f(x)dx = 4}[/tex]
[tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =4}[/tex]
We substract 8 from both sides:
[tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx -8=4}[/tex]
• [tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =-4}[/tex]
pls help a gurlll out
Answer:
x = 15°
Step-by-step explanation:
165 and x are on a straight line which means they are supplementary.
Set up the equation and solve for x:
165 + x = 180
x = 180 - 165
x = 15
If my goal was to be above 85% I my final number was 80 what was my percentage for the month?
Using it's concept, your percentage for the month was of 94.12%.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
P = a/b x 100%
In this problem, your goal was of 85, with a grade of 80, hence the percentage is:
P = 80/85 x 100% = 94.12%.
Hence, your percentage for the month was of 94.12%.
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In a study of 825 randomly selected medical malpractice lawsuits, it was found that 500 of them were dropped or dismissed. Use a 0.01 significance level to test the claim that most medical
malpractice lawsuits are dropped or dismissed.
I found the z score but does anyone know how to find the p-value?
Using the z-distribution, since the p-value of the test is less than 0.01, there is enough evidence to conclude that the claim is correct.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the proportion is above 0.5, hence:
[tex]H_0: p \leq 0.5[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the proportion is above 0.5, hence:
[tex]H_1: p > 0.5[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the parameters are:
[tex]n = 825, \overline{p} = \frac{500}{825} = 0.606, p = 0.5[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.606 - 0.5}{\sqrt{0.5(0.5)}{825}}}[/tex]
z = 6.1.
What is the p-value?We have a right-tailed test, as we are testing if the proportion is greater than a value. Using a z-distribution calculator, with z = 6.1, the p-value is of 0.
Since the p-value is less than 0.01, there is enough evidence to conclude that the claim is correct.
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Christie has $200 in her bank account. Every month, she deposits $20 into her account.
The equation of the line that models the amount of money, y, in her account x months from now is y = x .
Answer:
y = 20x + 200
Step-by-step explanation:
The 200 is the constant. It is only added once, but the monthly deposits are added at 20 every month.
After 1 month:
y = 20x + 200
y = 20(1) + 200
y = 20 + 200
y =220 money deposited.
After 2 months:
y = 20x + 200
y = 20(2) + 200
y = 40 + 200
y =240 money deposited.
After 3 months:
y = 20x + 200
y = 20(3) + 200
y = 60 + 200
y = 260 money deposited
And so on, and so on, and so on...
Please help, need for hw and cant find the fourth degreee
The quartic equation behind the graph is y = - 2 · x⁴ + 4 · x³ + 6 · x² - 8 · x - 8.
How to derive the expression for a quartic function
Quartic functions are fourth grade polynomials and according to the fundamental theorem of algebra, such kind of expressions have at least two real roots and at most four real roots. The graph of the picture shows a polynomial with two roots of multiplicity 2: x₁ = - 1, x₂ = 2.
y = a · (x + 1)² · (x - 2)² (1)
Where a is the leading coefficient.
If we know that (x, y) = (0, 4), then the leading coefficient of the polynomial is:
4 = a · (0 + 1) · (0 - 2)
4 = - 2 · a
a = - 2
Then, the quartic equation is equal to:
y = - 2 · (x + 1)² · (x - 2)²
y = - 2 · (x² + 2 · x + 1) · (x² - 4 · x + 4)
y = - 2 · [(x² + 2 · x + 1) · x² + (x² + 2 · x + 1) · (- 4 · x) + (x² + 2 · x + 1) · 4]
y = - 2 · (x⁴ + 2 · x³ + x² - 4 · x³ - 8 · x² - 4 · x + 4 · x² + 8 · x + 4)
y = - 2 · (x⁴ - 2 · x³ - 3 · x² + 4 · x + 4)
y = - 2 · x⁴ + 4 · x³ + 6 · x² - 8 · x - 8
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an employee at a factory is paid $9.25 per hour plus a $8.00 bonus for every 20 transformers assemble.
Answer:
Step-by-step explanation
Answer:
$13.47 per hour
Step-by-step explanation:
Total earnings = 9.25 (h) + 8 (t/20)
Where h is the number of hours and t is the number of transformers.
Since he worked for 36 hours and assembled 380 transformers:
Total earnings = 9.25 (36) + 8 (380/20)
Total earnings = 333+152 = $485
Finally, to find how much he earned per hours, we simply have to divide the result by the number of hours worked (36):
485/36 = $13.47 per hour.
jelissa determined she needs to have 800000 for retirement in 30 years. her account earns 6% interest
a. how much would she need to deposit in the account each month
b. how much total money will she put into the account.
c. how much total interest will she earn
The required answers are calculated by using the simple interest formula:
a. She needs to deposit $793.65 in the account each month
b. The total money she put into an account for a year is $285,714.29
c. The total interest she earns is $514,285.71
What is the formula for simple interest?The formula for the simple interest is
A = P(1 + RT)
Where,
A - amount after T years
P - principal amount
R - the rate of interest
T - time (years)
Calculation:It is given that,
A = 8,00,000
T = 30 years
R = 6% = 0.06
So,
a. Finding the amount needs to deposit in the account each month:
We have A = P(1 + RT)
⇒ P = A/(1 + RT)
On substituting,
P = 8,00,000/(1 + 0.06×30)
= 8,00,000/2.8
= $285,714.29(per year)
Thus, the amount needs to deposit in the account for each month
= P/T×12
= 285,714.29/30×12
= $793.65
b. Finding the total money that she put into account:
That is nothing but,
P = A/(1 + RT)
On substituting,
P = 8,00,000/(1 + 0.06×30)
= 8,00,000/2.8
= $285,714.29(per year)
c. FInding the total interest:
We have I = A - P
⇒ I = 8,00,000 - 285,714.29
∴ I = $514,285.71
Therefore, a. $793.65, b. $285,714.29, and c. $514,285.71
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EVALUATE THE FOLLOWING:
A) 85!/82!
B) nC0
C) nPn
Answer:
Step-by-step explanation:
85!/82! = 85*84*83 = 592620
n choose 0 is always equals 1
n P n also always equals 1
Carlos went to PetSmart to get his hamster an exercise ball. There was a small one with a 5 inch diameter and a 13 inch ball. How much more space (volume) is in the larger than the smaller? Round to the nearest tenth.
Answer:
150.8 in³
Step-by-step explanation:
The volume of the 5 inch ball is
[tex]\frac{4}{3}\pi (5/2)^{3}[/tex]
The volume of the 13 inch ball is
[tex]\frac{4}{3}\pi (13/2)^{3}[/tex]
Subtracting these volumes, we get about 150.8 in³.
The amount of space (volume) that is in the larger spherical ball than the smaller will be 1,084.8 in.³
What is the Volume of a Spherical Solid?To find the volume of a sphere, which is the amount of space the solid contains, the formula used is given as: 4/3 πr³,
where r is the radius of the sphere, which is half the measure of the diameter.
Diameter of the smaller spherical ball = 5 inches
Radius = 5/2 = 2.5 inches
Volume of the smaller spherical ball = 4/3 πr³ = 4/3 × π × 2.5³
Volume ≈ 65.5 in.³
Diameter of the larger spherical ball = 13 inches
Radius = 13/2 = 6.5 inches
Volume of the larger spherical ball = 4/3 πr³ = 4/3 × π × 6.5³
Volume of the larger spherical ball ≈ 1,150.3 in.³
The amount of space (volume) that is in the larger spherical ball than the smaller.
= 1,150.3 - 65.5
The amount of space (volume) that is in the larger spherical ball than the smaller will be 1,084.8 in.³
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Which is the best approximation of the solutions to the system of equations graphed below?
According to the direct inspection, we conclude that the best approximation of the two solutions to the system of quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)
What is the solution of a nonlinear system formed by two quadratic equations?
Herein we have two parabolae, that is, polynomials of the form a · x² + b · x + c, that pass through each other twice according to the image attached to this question. We need to estimate the location of the points by visual inspection on the Cartesian plane.
According to the direct inspection, we conclude that the best approximation of the two solutions, that is, the point where the two parabolae intercepts each other, to the system of two quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)
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17, 18, 22, 31, 47, ? Continue the pattern
Answer:
17 +1^2=18
18+2^2=22
22+3^2=31
31+4^2=47
47+5^2=72
72+6^2=108
Step-by-step explanation:
Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as
y
=
−
10.51
x
+
15.05
and the
r
=
−
0.45
.
The proportion of the variation in y that can be explained by the variation in the values of x is 0.2025
How to determine the proportion of the variation in y that can be explained by the variation in the values of x?The complete question requires that we calculate the proportion of the variation in y that can be explained by the variation in the values of x
The given parameters in the question are:
The regression equation is reported as
y = − 10.51x + 15.05
r = − 0.45
Take the square of both sides in the equation r = − 0.45
r^2 = − 0.45^2
Evaluate the squares
r^2 = 0.2025
This represents the proportion of the variation in y that can be explained by the variation in the values of x
Hence, the proportion of the variation in y that can be explained by the variation in the values of x is 0.2025
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A
a = 10
C = 15
B
b
Find the length of b using
the Pythagorean Theorem.
Hint: a² + b² = c²
Round your answer to the nearest tenth.
Applying the Pythagorean theorem, the length of b, to the nearest tenth, is: 11.2.
What is the Pythagorean Theorem?The Pythagorean theorem is the theorem that is applied when finding any length of a right triangle. Where a and b are the smaller sides of the right triangle, and c is the longest side (hypotenuse) of the right triangle, the Pythagorean theorem states that: a² + b² = c².
We are given the following regarding a right triangle:
a = 10 (one of the smallest side)
c = 15 (the longest side/hypotenuse)
Plug in the values into a² + b² = c²:
10² + b² = 15²
100 + b² = 225
Subtract 100 from both sides
100 + b² - 100 = 225 - 100
b² = 125
Square both sides
√b² = √125
b ≈ 11.2
The length of b, to the nearest tenth, is: 11.2.
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PLEASE HELP ME! I WILL AWARD BRAINLIEST TO WHOEVER ANSWERS THE QUESTION BEST!
Given the height of the person, angle of elevation and distance from the building, the height of the building is 60 feet.
What is the height of the building?
Given the data in the question;
Angle of elevation θ = 35°Distance between the person and the building | Adjacent = 80ftHeight of the person h = 4ft.Height of the building from the eye level | opposite = xSince the scenario depicts a right angle triangle, we use trigonometric ratio.
tanθ = Opposite / Adjacent
We height of the building from the eye level x
Substitute given into the equation,
tan( 35 ) = x / 80ft
x = tan( 35 ) × 80ft
x = 0.7002075 × 80ft
x = 56ft
Now, to get the height of the building, we add the height of the person and the height of the building from the eye level of the person.
Height of building = x + 4ft
Height of building = 56ft + 4ft
Height of building = 60ft
Therefore, given the height of the person, angle of elevation and distance from the building, the height of the building is 60 feet.
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What does ! mean in a math problem?
Divide each number in sequence from that number to 1.
Add each number in sequence from that number to 1.
Multiply each number in sequence from that number to 1.
Subtract each number in sequence from that number to 1.
It is an exciting problem.
! is shorthand for the factorial function. If [tex]n[/tex] is a non-negative integer, then
[tex]n! = n\times(n-1)\times(n-2)\times\cdots3\times2\times1[/tex]
with [tex]0! = 1[/tex].
So how to compute [tex]n![/tex] ?
Multiply each number in sequence from that number to 1.
How to find exponential function?
[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:[tex]\bold{y=Ce^{kt}}[/tex][tex]\bold{(5,5)}[/tex][tex]\bold{(0, \dfrac{6}{7} )}[/tex][tex]\small\leadsto\bold{Substitute:}[/tex]
[tex]\longrightarrow\sf{ \dfrac{6}{7}= Ce^{k*0}}[/tex]
[tex]\longrightarrow\sf{\dfrac{6}{7}= C*e^0}[/tex]
[tex]\longrightarrow\sf{e^0=1}[/tex]
[tex]\therefore\sf{C= \dfrac{6}{7} }[/tex]
[tex]\therefore\sf{5=Ce^{k*5}}[/tex]
[tex]\\[/tex]
[tex] \bold{Solve \: to \: find \: k:}[/tex]
[tex]\longrightarrow\sf{5 = \dfrac{6}{7} *e^{k5}}[/tex]
[tex]\longrightarrow\sf{ \dfrac{7*5}{6} *e^{5k}}[/tex]
[tex]\longrightarrow\sf{In=( \dfrac{35}{6} ) = 5k}[/tex]
[tex]\longrightarrow\sf{1.76=5k}[/tex]
[tex]\longrightarrow\sf{k=\dfrac{1.76}{5} = 0.352}[/tex]
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
[tex]\large\sf{\boxed{\sf \dfrac{6}{7}= e^{0.352*t}}}[/tex]
Find the dy/dx using implicit differentiation
x³-3x²y+2xy² = 12
The dy/dx of equation [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex] is [tex](6xy-3x^{2} -2y^{2} )/(4xy-3x^{2})[/tex].
Given an equation [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex].
We are required to find dy/dx of the equation.
Equation is like a relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c.
Differentiation is basically finding the change in variables.
It may be linear equation, quadratic equation,cubic equation or many more depending on the power of the variable present in the equation.
Equation:[tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex]
Differentiating with respect to x.
3[tex]x^{2}[/tex]-3([tex]x^{2}[/tex]*dy/dx+y*2x)+2(x*2y*dy/dx+[tex]y^{2}[/tex])=0
3[tex]x^{2} -3x^{2} dy/dx-6xy+4xy dy/dx+2y^{2}[/tex]=0
Taking dy/dx at one side and take the other part to other end.
[tex]-3x^{2} dy/dx+4xy dy/dx[/tex]=[tex]6xy-3x^{2} -2y^{2}[/tex]
dy/dx=[tex](6xy-3x^{2} -2y^{2})/(4xy-3x^{2} )[/tex]
Hence the dy/dx of equation [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex] is [tex](6xy-3x^{2} -2y^{2} )/(4xy-3x^{2})[/tex].
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Write the equation y=-3x+3 in function notation using f(x) to denote the function.
Answer:
f(x) = -3x + 3
Step-by-step explanation:
cual es el valor x-2=1
How many pairs of two digit natural numbers have a difference equal to 50
The number exists 99, then 99 - 49 = 50
Therefore, the pair of two-digit numbers exist between 99 and 49.
What is the difference?In math, the word difference exists as the outcome of subtracting one number from another.
Let the first pair of two-digit numbers be xy and the second pair of numbers be yx.
we want a two-digit number, a two-digit number begins from 10 and ends with a two-digit number that exists 99.
Let the difference of 50 exists possible when we take the biggest two-digit number
Therefore, the number exists 99
99 - 49 = 50
Therefore, the pair of two-digit number exists 99 and 49.
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Evaluate the following expression at x = 3 and y = -4. 7x - 3y + 2.
provide your answer below:
Answer:
35
Step-by-step explanation:
first, you look at 7x, from the previous equation, you know that x=3, so you take 7x3=21 then you evaluate -3y. as you did with x on the last one you will look at the equation for y and see that it's -4. A negative times a negative is a positive, so -4x(-3)= 12. Then you add them all together, since 12 is a positive, the equation would now look like 21+12+2. After adding all three numbers together, you get 12.
The graph shows a system of inequalities.
Graph of two inequalities. One is a solid line increasing from left to right passing through negative 3 comma 0 and 0 comma 3, and it has shading below the line. The second is a solid upward opening parabola with a vertex at 1 comma negative 4 and x-intercepts at negative 1 comma 0 and 3 comma 0. This parabola is shaded inside the curve.
Which system is represented in the graph?
A. y > x2 –2x – 3
y > x + 3
B. y < x2 – 2x – 3
y < x + 3
C. y ≥ x2 – 2x – 3
y ≤ x + 3
D. y > x2 – 2x – 3
y < x + 3
The graphed system of inequalities is:
y ≥ x^2 - 2x - 3y ≤ x + 3So the correct option is the third one.
Which system is represented by the graph?On the graph we can see that the two lines are solid, so we need to use the symbols ≤ and ≥. (If instead, we had dashed lines, then we would need to use the symbols > and <).
We also can see that the region above the parabola is shaded (the shaded region represents the region of solutions for each inequality), and the region below the line is shaded, then the system of inequalities is of the form:
y ≥ parabola.y ≤ line.Only with that, we conclude that the correct option is the third option:
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sketch the graphs of equations:
a) y=x
b) y= -x
c) y=x+5
sketch the graphs:
a) y=3x+2
b) y=3x-2
The graphs of the equations are:
In fig. 1:
a) y = x (red line)
b) y = -x (blue line)
c) y = x + 5 (green line)
In Fig. 2:
a. y = 3x + 2 (red line)
b. y = 3x - 2 (blue line)
What is the Graph of a Linear Equation?A linear equation can be expressed in slope-intercept form as, y = mx + b, where m is the slope of the line and b is the y-intercept where the line cuts across the vertical axis (y-axis).
Given the equations:
a) y = x, the slope is 1, while the y-intercept is 0. This means the line of the graph passes through the point of origin (0, 0). (It is the red line on the graph plotted).
b) y= -x, the slope is -1 (declining slope), while the y-intercept is 0. This means the line of the graph passes through the point of origin (0, 0). (It is the blue line on the graph plotted).
c) y = x + 5, the slope is 1 (rising slope), while the y-intercept is 5. This means the line of the graph passes the y-axis at 5. (It is the green line on the graph plotted).
In Figure 2, we have the second graph with the following equations:
a. y = 3x + 2, the slope is 3 (rising slope), while the y-intercept is 2. This means the line of the graph passes the y-axis at 2. (It is the red line on the graph plotted).
b. y = 3x - 2, the slope is 3 (rising slope), while the y-intercept is -2. This means the line of the graph passes the y-axis at -2. (It is the blue line on the graph plotted).
In summary, the graphs of the equations are:
In fig. 1:
a) y = x (red line)
b) y = -x (blue line)
c) y = x + 5 (green line)
In Fig. 2:
a. y = 3x + 2 (red line)
b. y = 3x - 2 (blue line)
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graph f(x)=(1/4)^x step 4: Plot the points (1, 1/4) and (-1, 4)
The graph of the function, f(x) = (1/4)ˣ, can be seen in the attached graph, following the given steps.
In the question, we are given the function, f(x) = (1/4)ˣ.
Step 1, has asked us to find the initial value of the graph, f(0).
This can be calculated by substituting x = 0, in the given function, which gives us:
f(0) = (1/4)⁰ = 1.
Step 2, has asked us to plot the initial value of the function at (0, 1). This is plotted using the graphing tools.
Step 3, has asked us to evaluate f(1) and f(-1). By substituting x = 1, and x = -1, we get:
f(-1) = (1/4)⁻¹ = 4,
f(1) = (1/4)¹ = 1/4.
Step 4, has asked us to plot the points (1, 1/4), and (-1, 4). This is plotted using the graphing tools.
Step 5, has made us identify the asymptote y = 0.
Step 6, gives us the final curve for the function, f(x) = (1/4)ˣ.
The provided question is incomplete. The complete question is:
"Graph: f(x) = (1/4)ˣ
Step 1: Calculate the initial value of the function. f(0) =
Step 2: Plot the initial value of the function at (0, 1).
Step 3: Evaluate the function at two more points. f(1) = 1/4, f(-1) = 4
Step 4: Plot the points (1, 1/4) and (-1, 4)
Step 5: Identify the horizontal asymptote of the function. The asymptote is the line y = 0
Step 6: The smooth curve that includes these points and approaches to the asymptote shows the graph of the function"
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what is 11- 2 to the 3rd power
Answer:
See below
Step-by-step explanation:
Question is unclear
could be (11-2)^3 = 9^3 = 729
could be 11 - 2^3 = 11 - 8 = 3 Pick the one you want !
3. What is f(2) if f(x) = 2x³ - 19x² +28x + 47?
O 45
O 40
O 43
O 37
Answer: C: 43
Step-by-step explanation:
As we are calling the function with 2 for x, we can substitute 2 for every x we see in the function and solve.
[tex]f(2)=2(2)^3-19(2)^2+28(2)+47\\=2(8)-19(4)+28(2)+47\\=16-76+56+47\\=43[/tex]
Hence, f(2) is 43.
What are the coordinates of the vertex of the parabola with the equation y = x2 + 2x – 3?
A
(-1, -4)
B
(1, -4)
C
(3, -4)
D
(-3, 12)
Answer:
A. (-1, -4)
Step-by-step explanation:
The vertex can be found by converting the equation from standard form to vertex form.
VertexConsidering the x-terms, we have ...
y = (x^2 +2x) -3
where the coefficient of x is 2. Adding (and subtracting) the square of half that, we get ...
y = (x^2 +2x +(2/2)^2) -3 -(2/2)^2
y = (x +1)^2 -4
Compare this to the vertex form equation ...
y = a(x -h)^2 +k
which has vertex (h, k).
We see that h=-1 and k=-4. The vertex is (h, k) = (-1, -4).
On the attached graph, the vertex is the turning point, the minimum.
8 ft
10 ft
20 ft
A trapezoid has a height of 10 feet,
and base measurements of 20 feet and
8 feet. What is the area?
[?] square feet
Hint: The formula for the area of a trapezoid is: (b₁b2). h
Enter
ग
15
The area of the trapezoid is 140 square feet
What are areas?The area of a shape is the amount of space on that shape
How to determine the area of the trapezoid?The dimensions of the trapezoid are given as:
Height = 10 feet
Parallel bases = 8 feet and 20 feet
The area of a trapezoid is calculated using
Area = 0.5 * (Sum of parallel bases) * Height
Substitute the known values in the above equation
Area = 0.5 * (8 + 20) * 10
Evaluate the equation
Area = 140
Hence, the area of the trapezoid is 140 square feet
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A COUPLE PLAN TO HAVE SIX CHILDREN. HOW MANY POSSIBLE OUTCOMES ARE IN
THE SAMPLE SPACE?
Since there are 6 elements in the given set, hence the possible outcome in the sample space is 6
What is probability?Probability is the likelihood or chance that an event will occur. Mathematically, the formula for calculating probability is expressed as:
Probability = expected outcome/Total outcome
Sample space is the total number of element in a given set of probability. The subsets if this sets are called event
Let the six children the couple plan to have ne 1, 2, 3, 4, 5,6 such that the sample space will be:
S = {1, 2, 3, 4, 5, 6}
Since there are 6 elements in the given set, hence the possible outcome in the sample space is 6
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How to make 3 dimensional object be 4 dimensional object
In order to make a 3-dimensional object into a 4-dimensional object, it's important to draw the 4-dimensional shape in a way that gives the illusion of the 3-dimensional object.
How to illustrate the information?It should be noted that shapes play an important part in geometry.
Here, to make a 3-dimensional object into a 4-dimensional object, it's important to draw the 4-dimensional shape in a way that gives the illusion of the 3-dimensional object.
Also, it should be noted that a 4D tesseract can be used to project the image.
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