Answer:
Step-by-step explanation:
step 1:
determining the values for standard form for the equation of a line,
y = mx + c
Step 2:
calculation of m, where m is the gradient or slope which determines how steep the line is.
step 3:
calculation of c, where c is the height at which the line crosses the y - axis also known as y - intercept
IfmZC = 142° and m LI = 48°, find mU B.
The minor arc UB in the circle measures 46 degrees,
What is the measure of arc UB?The external angles theorem states that "the measure of an angle formed by two secant lines, two tangent lines, or a secant line and a tangent line from a point outside the circle is half the difference of the measures of the intercepted arcs.
It is expressed as;
External angle = 1/2 × ( major arc - minor arc )
From the diagram:
External angle I = 48 degrees
Major arc ZC = 142 degrees
Minor arc UB = ?
Plug these values into the above formula and find the minor arc UB:
External angle = 1/2 × ( major arc - minor arc )
48 = 1/2 × ( 142 - minor arc )
Multiply both sides by 2:
2 × 48 = 2 × 1/2 × ( 142 - minor arc )
2 × 48 = ( 142 - minor arc )
96 = ( 142 - minor arc )
96 = 142 - Minor arc
Minor arc = 142 - 96
Minor arc = 46°
Therefore, the minor arc measures 46 degrees.
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if the graph of f(x) =3^x shifted 6 units to the right, what is the equation of the new graph
Find the value of x
A. 16
B. 6
C. 4√5
8. √5
please help- (in need of answer please don't put gibberish this is serious work)
Answer:
W = V/(LH)
Step-by-step explanation:
All we are doing is isolating W. Since V=LWH, then dividing both sides by LH will put W by itself on the right-hand side, you have V/(LH) = W as your equation
Rotate the triangle 180 counterclockwise around the origin and enter the coordinates. Enter the number that belongs in the green box A (1,-1) B (4,-2) C (2,-4)
Answer:
A''(-1, 1), B''(-4, 2), C''(-2, 4)
Step-by-step explanation:
When rotated 180°, the symbol of the coordinames change
i.e., if x = 2 it becomes x = -2 and if y = -4, it becomes y = 4
so the coordinates A(1, -1), B(4, -2), C(2, -4)
change to A''(-1, 1), B''(-4, 2), C''(-2, 4)
Find the measure of UK
95°
T
99 °
U
87 R
S
?
K
What is the third term of the sequence defined by the recursive rule f(1)=0.2,
f(n)=2fn(n-1)/5+1?
Answer:
f(3) = 1.432
Step-by-step explanation:
You want to know the third term of the sequence defined by ...
f(1) = 0.2f(n) = (2/5)f(n-1) +1SequenceThe terms of the sequence can be found one at a time by evaluating the recursive relation. The attached calculator output shows the first three terms are ...
f(1) = 0.2 . . . . . . . given
f(2) = 0.4(0.2) +1 = 1.08
f(3) = 0.4(1.08) +1 = 1.432
The third term of the sequence is 1.432.
__
Additional comment
The explicit form of the function is ...
f(n) = 5/3 -11/3(2/5)^n
Terms will asymptotically approach a value of 5/3.
<95141404393>
what is the amplitude of the sinusoids graph?
y=2sin3x
Step-by-step explanation:
Y = 2 sin 3x '2' is the amplitude
( 'sin x' usually has amplitude of '1'...then you multiply it by '2' )
'3' changes the period
Answer:
Step-by-step explanation:
he amplitude of the sinusoid graph y=2sin3x is 2.
The school cafetteria recently served a new kind of snack to all the senior high school student. They want to know if more than 50% of the student like the newly served snack, thus, the cafeteria conducted a survey for asking 60 random selection of students whether they like (1), or Do not like (0), the new snack. They responses are show as follows
The cafeteria can conclude that a majority of the senior high school students like the newly served snack.
To determine if more than 50% of the students like the newly served snack, we need to analyze the responses of the 60 randomly selected students.
Analyzing the responses:
Out of the 60 students surveyed, we have:
- Number of students who responded with "1" (liking the snack): 32 students.
- Number of students who responded with "0" (not liking the snack): 28 students.
To determine the percentage of students who liked the snack, we divide the number of students who liked it by the total number of students surveyed and multiply by 100: (32/60) * 100 = 53.33%.
Since the percentage of students who liked the newly served snack is 53.33%, which is greater than 50%, we can conclude that more than 50% of the students like the snack based on the given survey results.
Therefore, the cafeteria can conclude that a majority of the senior high school students like the newly served snack.
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A person leaves home and walks 5 miles west, then 6 miles southwest.
How far from home is she?
The person is approximately 7.73 miles from home.
To solve this problem, we can use the Pythagorean theorem and trigonometry. Let us assume that the person starts from the origin (0, 0) and walks 5 miles west, which takes her to the point (-5, 0) on the x-axis.
If we assume that the starting point is (0, 0) and we assign a coordinate system, then the point reached after walking 5 miles west can be represented as (-5, 0). Similarly, the point reached after walking 6 miles southwest can be represented as (-3, -6).Then, she walks 6 miles southwest, which forms a 45-degree angle with the x-axis. We can represent this vector as (6 cos 45°, -6 sin 45°) = (3√2, -3√2).
To find the total distance from home, we need to add the magnitude of these two vectors using the Pythagorean theorem:
d =[tex]\sqrt((-5)^2 + (-3\sqrt2)^2)[/tex]≈ 7.73 miles
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Express in simplest radical form show work
Answer:
-33x√2
Step-by-step explanation:
[tex]-5x\sqrt{98}+2\sqrt{2x^2}\\\\= -5x\sqrt{2*7^{2} } + 2(x\sqrt{2} )\\\\= -5x(7)(\sqrt{2} ) + 2x\sqrt{2} \\\\= -35x\sqrt{2} +2x\sqrt{2} \\\\= (-35+2)x\sqrt{2}\\ \\=-33x\sqrt{2}[/tex]
4,5,6,8,9,9,10,12,12,12,17,17,18,18
Yuri’s sister Karina is 12 years old. In the equation below, y represents Yuri’s age in years.
12 = 3 y minus 2
Which statement accurately relates their ages?
Yuri is 3 years younger than twice Karina’s age.
Yuri is 2 years younger than triple Karina’s age
Karina is 3 years younger than twice Yuri’s age.
Karina is 2 years younger than triple Yuri’s age.
Yuri is 2 years younger than triple Karina’s age
Answer:
yo
Step-by-step explanation:
i think its d
one number is seven less than a second number. Six times the first is 10 more than 2 times the second. Find the numbers.
I need help with a question
The function for which f(x) is equal to f⁻¹(x) is: C. [tex]f(x) = \frac{x+1}{x-1}[/tex]
What is an inverse function?In this exercise, you are required to determine the inverse of the function f(x) with an equivalent inverse function f⁻¹(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;
[tex]f(x) = y = \frac{x+6}{x-6} \\\\x=\frac{y+6}{y-6}[/tex]
x(y - 6) = y + 6
y = xy - 6x - 6
f⁻¹(x) = (-6x - 6)/(x - 1) ⇒ Not equal.
Option B.
[tex]f(x) = y = \frac{x+2}{x-2} \\\\x=\frac{y+2}{y-2}[/tex]
x(y - 2) = y + 2
y = xy - 2x - 2
f⁻¹(x) = (-2x - 2)/(x - 1) ⇒ Not equal.
Option C.
[tex]f(x) = y = \frac{x+1}{x-1} \\\\x=\frac{y+1}{y-1}[/tex]
x(y - 1) = y + 1
y - xy = x + 1
f⁻¹(x) = (x + 1)/(x - 1) ⇒ equal.
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Seafloor rocks from a secret area above the Arctic Circle will recently analyzed by the globe. The company had a contract with spacegov.bids to test the rocks for nickel. Zieglow found that setting samples from the first location were composed of an average of 8.43% nickel. Six samples from the second location yielded an average of 7.81% nickel. What was the overall average nickel content of the rock samples
Answer:
The overall average nickel content of the rock samples is approximately 7.97%.
Step-by-step explanation:
To find the overall average nickel content of the rock samples, we need to take into account the number of samples from each location. Since we know the average nickel content of each set of samples, we can use a weighted average formula:
overall average nickel content = (total nickel content from first location + total nickel content from second location) / (total weight of samples from both locations)
To calculate the total nickel content from each location, we need to multiply the average nickel content by the number of samples:
total nickel content from first location = 8.43% x 1 sample = 8.43%
total nickel content from second location = 7.81% x 6 samples = 46.86%
To calculate the total weight of the samples from both locations, we need to add up the number of samples:
total weight of samples from both locations = 1 + 6 = 7
Now we can substitute these values into the formula and calculate the overall average nickel content:
overall average nickel content = (8.43% + 46.86%) / 7 ≈ 7.97%
Therefore, the overall average nickel content of the rock samples is approximately 7.97%.
Which of the following functions is graphed below ?
Answer:
A) [tex]\displaystyle y=\left \{ {{x^3-4,\,x\leq 1} \atop {x^2-3,\,x > 1}} \right.[/tex]
Step-by-step explanation:
The first "piece" of the piecewise function, [tex]y=x^3-4[/tex], contains [tex]x=1[/tex] because of the closed dot there.
The second "piece" of the piecewise function, [tex]y=x^2-3[/tex], doesn't contain [tex]x=1[/tex] because of the open dot there.
What occurs between the two pieces is called a jump discontinuity.
Therefore, A is the correct answer.
Here is a unit circle with point P at (1, 0) Find the coordinates of P after the circle rotates the given amount counter clockwise around its center
1. 1/3 of a full rotation: ?
2 1/2 of a full rotation: ?
3. 2/3 of a full rotation: ?
1. 1/3 of a full rotation: The coordinates of point P after rotating 1/3 of a full rotation counterclockwise are approximately (0.5, 0.866).
2. 1/2 of a full rotation: The coordinates of point P after rotating 1/2 of a full rotation counterclockwise are (-1, 0).
3. 2/3 of a full rotation: The coordinates of point P after rotating 2/3 of a full rotation counterclockwise are approximately (-0.5, -0.866).
1/3 of a full rotation:
To find the coordinates of point P after rotating 1/3 of a full rotation counter clockwise, we need to determine the angle of rotation.
A full rotation around the unit circle is 360 degrees or 2π radians.
Since 1/3 of a full rotation is (1/3) [tex]\times[/tex] 360 degrees or (1/3) [tex]\times[/tex] 2π radians, we have:
Angle of rotation = (1/3) [tex]\times[/tex] 2π radians
Now, let's use the properties of the unit circle to find the new coordinates.
At the initial position, point P is located at (1, 0).
Rotating counterclockwise by an angle of (1/3) [tex]\times[/tex] 2π radians, we move along the circumference of the unit circle.
The new coordinates of point P after the rotation will be (cos(angle), sin(angle)).
Substituting the angle of rotation into the cosine and sine functions, we get:
New coordinates of P = (cos((1/3) [tex]\times[/tex] 2π), sin((1/3) [tex]\times[/tex] 2π))
Calculating the values:
cos((1/3) [tex]\times[/tex] 2π) ≈ 0.5
sin((1/3) [tex]\times[/tex] 2π) ≈ 0.866
Therefore, the coordinates of point P after rotating 1/3 of a full rotation counterclockwise are approximately (0.5, 0.866).
1/2 of a full rotation:
Following a similar process, when rotating 1/2 of a full rotation counterclockwise, we have an angle of (1/2) [tex]\times[/tex] 2π radians.
New coordinates of P = (cos((1/2) [tex]\times[/tex] 2π), sin((1/2) [tex]\times[/tex] 2π))
Calculating the values:
cos((1/2) [tex]\times[/tex] 2π) = cos(π) = -1
sin((1/2) [tex]\times[/tex] 2π) = sin(π) = 0
Therefore, the coordinates of point P after rotating 1/2 of a full rotation counterclockwise are (-1, 0).
2/3 of a full rotation:
For a rotation of 2/3 of a full rotation counterclockwise, the angle is (2/3) [tex]\times[/tex] 2π radians.
New coordinates of P = (cos((2/3) [tex]\times[/tex] 2π), sin((2/3) [tex]\times[/tex] 2π))
Calculating the values:
cos((2/3) [tex]\times[/tex] 2π) ≈ -0.5
sin((2/3) [tex]\times[/tex] 2π) ≈ -0.866
Therefore, the coordinates of point P after rotating 2/3 of a full rotation counterclockwise are approximately (-0.5, -0.866).
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Find the equations of the asymptotes of the hyperbola defined by the equation shown below. If necessary, round to the nearest tenth. 100pts
The equations of the asymptotes of the hyperbola are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.
To find the equations of the asymptotes of the hyperbola defined by the equation:
[tex]-25x^2 + 81y^2 + 100x + 1134y + 1844 = 0[/tex]
We can rewrite the equation in the standard form by isolating the x and y terms:
[tex]-25x^2 + 100x + 81y^2 + 1134y + 1844 = 0[/tex]
Rearranging the terms:
[tex]-25x^2 + 100x + 81y^2 + 1134y = -1844[/tex]
Next, let's complete the square for both the x and y terms:
[tex]-25(x^2 - 4x) + 81(y^2 + 14y) = -1844\\-25(x^2 - 4x + 4 - 4) + 81(y^2 + 14y + 49 - 49) = -1844\\-25((x - 2)^2 - 4) + 81((y + 7)^2 - 49) = -1844[/tex]
Expanding and simplify
[tex]-25(x - 2)^2 + 100 - 81(y + 7)^2 + 3969 = -1844\\-25(x - 2)^2 - 81(y + 7)^2 = -1844 - 100 - 3969\\-25(x - 2)^2 - 81(y + 7)^2 = -4913[/tex]
Dividing both sides by -4913:
[tex](x - 2)^2/(-4913/25) - (y + 7)^2/(-4913/81) = 1[/tex]
Comparing this equation to the standard form of a hyperbola:
[tex](x - h)^2/a^2 - (y - k)^2/b^2 = 1[/tex]
We can determine that the center of the hyperbola is (h, k) = (2, -7). The value of [tex]a^2[/tex] is (-4913/25), and the value of [tex]b^2[/tex] is (-4913/81).
The equations of the asymptotes can be found using the formula:
y - k = ±(b/a)(x - h)
Substituting the values we found:
y + 7 = ±(√(-4913/81) / √(-4913/25))(x - 2)
Simplifying:
y + 7 = ±(√(4913) / √(81)) × √(25/4913) × (x - 2)
y + 7 = ±(√(4913) / 9) × √(25/4913) × (x - 2)
Rationalizing the denominators and simplifying:
y + 7 = ±(5/9) ×(x - 2)
Finally, rearranging the equation to isolate y:
y = ±(5/9)x - 10/9 - 7
Simplifying further:
y = ±(5/9)x - 79/9
In light of this, the equations for the hyperbola's asymptotes are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.
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Answer:
[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]
Step-by-step explanation:
First, rewrite the given equation in the standard form of a hyperbola by completing the square.
Given equation:
[tex]-25x^2+81y^2+100x+1134y+1844=0[/tex]
Arrange the equation so all the terms with variables are on the left side and the constant is on the right side:
[tex]-25x^2+100x+81y^2+1134y=-1844[/tex]
Factor out the coefficient of the x² term and the coefficient of the y² term:
[tex]-25(x^2-4x)+81(y^2+14y)=-1844[/tex]
Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:
[tex]-25(x^2-4x+4)+81(y^2+14y+49)=-1844-25(4)+81(49)[/tex]
Factor the two perfect trinomials on the left side and simplify the right side:
[tex]-25(x-2)^2+81(y+7)^2=2025[/tex]
Divide both sides by the number of the right side so the right side equals 1:
[tex]\dfrac{-25(x-2)^2}{2025}+\dfrac{81(y+7)^2}{2025}=\dfrac{2025}{2025}[/tex]
[tex]\dfrac{-(x-2)^2}{81}+\dfrac{(y+7)^2}{25}=1[/tex]
[tex]\dfrac{(y+7)^2}{25}-\dfrac{(x-2)^2}{81}=1[/tex]
As the y²-term is positive, the hyperbola is vertical (opening up and down).
The standard equation of a vertical hyperbola is:
[tex]\boxed{\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1}[/tex]
Therefore, comparing this with the rewritten equation:
h = 2k = -7a² = 25 ⇒ a = 5b² = 81 ⇒ b = 9The formula for the equations of the asymptotes of a vertical hyperbola is:
[tex]\boxed{y=\pm \dfrac{a}{b}(x-h)+k}[/tex]
Substitute the values of h, k, a and b into the formula:
[tex]y=\pm \dfrac{5}{9}(x-2)-7[/tex]
Therefore, the equations for the asymptotes are:
[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]
D
Drag the expressions to the correct locations on the image. Not all expressions will be used.
Consider this quotient.
(2³ - 8z + 6) ÷ (2² - 2x + 1)
Use long division to rewrite the quotient in an equivalent form as q(z) +
2³ - 8z + 6
2² - 2x + 1
where g(z) is the quotient, r(2) is the remainder, and b(z) is the divisor.
-5z + 4
Reset
H
Next
-11x + 12
x + 2
The solution to the polynomial division in quotient and remainder form is: (x + 2) + (-5x + 4)/(x² - 2x + 1)
How to carry out Long Division of Polynomials?The polynomials we want to divide are:
x³ - 8x + 6 by x² - 2x + 1 and as such we can write it as:
x + 2
x² - 2x + 1|x³ - 8x + 6
- x³ - 2x² + x
2x² - 9x + 6
- 2x² - 4x + 2
-5x + 4
Thus, the solution expressed in quotient and remainder form is:
(x + 2) + (-5x + 4)/(x² - 2x + 1)
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how can you write the expression with a rationalized denominator?
3 sqrt 2 / 3 sqrt 6
see photo attached for answers
The expression (3√2) / (3√6) with a rationalized denominator is 3√9 / 6. Option C is the correct answer.
To rationalize the denominator in the expression (3√2) / (3√6), we can multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of √6 is -√6, so we multiply the expression by (-√6) / (-√6):
(3√2 / 3√6) * (-√6 / -√6)
This simplifies to:
-3√12 / (-3√36)
Further simplifying, we have:
-3√12 / (-3 * 6)
-3√12 / -18
Finally, we can cancel out the common factor of 3:
- 3√9 / - 6.
Simplifying further, we get:
3√9 / 6.
Option C is the correct answer.
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1.Lim as x approaches 0
(sin3x)/(2x-Sinx)
2. Lim as x approaches infinity
x^-1 lnx
3. Lim x approaches infinity
x/ e^x
Using L’Hospals rule for all
Lim as x approaches 0: (sin3x)/(2x-Sinx)
Taking the derivative of the numerator and denominator separately:
Numerator: d/dx(sin3x) = 3cos3x
Denominator: d/dx(2x - sinx) = 2 - cosx
Now, evaluate the limit using L'Hôpital's Rule:
Lim as x approaches 0: (3cos3x)/(2 - cosx)
Plugging in x = 0:
Lim as x approaches 0: (3cos(0))/(2 - cos(0))
= 3/2
Therefore, the limit as x approaches 0 of (sin3x)/(2x-Sinx) is 3/2.
Lim as x approaches infinity: x^-1 lnx
Taking the derivative of the numerator and denominator separately:
Numerator: d/dx(x^-1 lnx) = (1/x)lnx
Denominator: d/dx(1) = 0
Since the denominator is 0, we cannot apply L'Hôpital's Rule. However, we can still evaluate the limit:
Lim as x approaches infinity: x^-1 lnx
As x approaches infinity, the natural logarithm (lnx) grows without bound, so the overall limit is 0.
Therefore, the limit as x approaches infinity of x^-1 lnx is 0.
Lim x approaches infinity: x/ e^x
Taking the derivative of the numerator and denominator separately:
Numerator: d/dx(x) = 1
Denominator: d/dx(e^x) = e^x
Now, evaluate the limit using L'Hôpital's Rule:
Lim as x approaches infinity: 1/ e^x
As x approaches infinity, the exponential function e^x grows without bound, so the overall limit is 0.
Therefore, the limit as x approaches infinity of x/ e^x is 0.
1. The annual sale volumes of three products X, Y, Z whose sale prices per unit are GHS 3.50, GHS 2.75, GHS 1.50 respectively, in two different markets I and II are shown below: Product Market X Y Z I 6000 9000 1300 II 12000 6000 17000 Find the total revenue in each market with the help of matrices.
Answer:
Step-by-step explanation:
To find the total revenue in each market, we can calculate the product of the sale volumes and sale prices per unit using matrices.
Let's represent the sale volumes as a matrix V and the sale prices per unit as a matrix P:
V = [6000 9000 1300]
[12000 6000 17000]
P = [3.50]
[2.75]
[1.50]
To calculate the total revenue in each market, we need to perform matrix multiplication between V and P, considering the appropriate dimensions. The resulting matrix will give us the total revenue for each product in each market.
Total revenue = V * P
Calculating the matrix multiplication:
[6000 9000 1300] [3.50] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]
[12000 6000 17000] [2.75] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]
Performing the calculation:
[60003.50 + 90002.75 + 13001.50] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]
[120003.50 + 60002.75 + 170001.50] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]
Simplifying the calculation:
[21000 + 24750 + 1950] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]
[42000 + 16500 + 25500] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]
[47650] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]
[84000] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]
Therefore, the total revenue in Market I is GHS 47,650 and the total revenue in Market II is GHS 84,000.
When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object
with mass 4 kg, the acceleration of the object is 9 m/s². When the same force acts upon another object, its acceleration is 6 m/s². What is the mass of this
object?
Step-by-step explanation:
a = k/m or ma = k
using 4 and 9 4* 9 = k = 36
then the equation becomes:
ma = 36
using a = 6
6 * m = 36 shows m = 6 kg
10. A triangular prism is shown.
a. Find the area of the base.
b. Find the volume of the prism.
d
5 cm
10 cm
3 cm
8 cm
5 cm
Answer:
Step-by-step explanation:
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 11 yards long, and the height of the equilateral triangle is 9.5 yards. The pyramid's slant height is 17 yards. What is its surface area?
The surface area of the triangular pyramid is approximately 331.93 square yards.
To find the surface area of the triangular pyramid, we need to calculate the areas of its individual components and then sum them up.
The triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 11 yards long, and the height of the equilateral triangle is 9.5 yards. The formula to calculate the area of an equilateral triangle is:
Area = (√3/4) * [tex]side^2[/tex]
Plugging in the values, we get:
Area of the base equilateral triangle = (√3/4) * 11^2 ≈ 52.43 square yards
The triangular pyramid also has three triangular faces. Each face is an isosceles triangle, with two sides measuring 11 yards (same as the sides of the base equilateral triangle) and a slant height of 17 yards. We can use the formula for the area of an isosceles triangle:
Area = (1/2) * base * height
Since the base of the isosceles triangle is 11 yards and the height is 17 yards, the area of each triangular face is:
Area of each triangular face = (1/2) * 11 * 17 = 93.5 square yards
Now, we can calculate the total surface area of the triangular pyramid by summing up the areas of the base and the three triangular faces:
Surface area = Area of the base equilateral triangle + 3 * Area of each triangular face
Surface area = 52.43 + 3 * 93.5
Surface area ≈ 331.93 square yards
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The data below shows the money Paritosh spends on a weekend. What will be the central angles of each of these categories?with the numbers 40 100 50 50
The central angles for the categories with the numbers 40, 100, 50, and 50 are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.
To calculate the central angles for each category based on the given numbers 40, 100, 50, and 50, we need to find the proportion of each value to the total sum of all the values. Let's proceed with the following steps:
Step 1: Calculate the total sum of the given numbers: 40 + 100 + 50 + 50 = 240.
Step 2: Find the proportion of each value by dividing it by the total sum and multiplying it by 360 (since a full circle has 360 degrees).
Central angle for the first category: (40/240) * 360 = 60 degrees.
Central angle for the second category: (100/240) * 360 = 150 degrees.
Central angle for the third category: (50/240) * 360 = 75 degrees.
Central angle for the fourth category: (50/240) * 360 = 75 degrees.
The central angles for each category based on the given numbers are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.
These central angles represent the relative proportions of each category's spending in relation to the total spending. They can be used to create a pie chart or visualize the distribution of expenses in a circular graph.
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y=1x^2 + 2x - 3 in vertex and intercept form
The vertex and the x-intercepts of the quadratic equation are:
The vertex is (-1, -4)
The x-intercepts are -3 and 1.
To express the quadratic equation [tex]y = x^2 + 2x - 3[/tex]in vertex and intercept form, we need to complete the square to find the vertex and rewrite the equation in terms of the x-intercepts.
First, let's complete the square to find the vertex. We can do this by taking half the coefficient of x, squaring it, and adding/subtracting it to both sides of the equation:
[tex]y = x^2 + 2x - 3\\y = (x^2 + 2x + 1) - 1 - 3\\y = (x + 1)^2 - 4[/tex]
Now we have the equation in the form [tex]y = a(x - h)^2 + k[/tex], where the vertex is at the point (-h, k). The vertex is (-1, -4).
Next, let's find the x-intercepts by setting y = 0:
[tex]0 = x^2 + 2x - 3\\0 = (x + 3)(x - 1)[/tex]
The x-intercepts are -3 and 1.
In vertex and intercept form, the equation is:
[tex]y = (x + 1)^2 - 4[/tex]
The vertex is (-1, -4)
The x-intercepts are -3 and 1.
This form allows us to easily identify the vertex and the x-intercepts of the quadratic equation.
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Carson is buying items at a store. His total comes to $41.09. He uses a gift
card and cash to pay the total. After using the gift card, he pays the
remaining $27.74 with cash. Which percentage best describes the part of
the total that Carson paid for with the gift card?
A. 28%
B. 30%
C. 33%
D. 36%
Francine currently has $55,000 in her 401k account at work, and plans to contribute $8,000 each year for the next 10 years. How much will she have in the account in 10 years, if the account averages a 4% annual return?
Answer:
Step-by-step explanation:
To calculate the future value of Francine's 401k account in 10 years, considering an annual contribution of $8,000 and an average annual return of 4%, we can use the formula for the future value of a series of regular payments, also known as an annuity.
The formula for the future value of an annuity is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value
P is the payment amount
r is the interest rate per period
n is the number of periods
In this case:
P = $8,000 (annual contribution)
r = 4% or 0.04 (annual interest rate)
n = 10 (number of years)
Calculating the future value:
FV = $8,000 * [(1 + 0.04)^10 - 1] / 0.04
FV = $8,000 * (1.04^10 - 1) / 0.04
FV ≈ $8,000 * (1.480244 - 1) / 0.04
FV ≈ $8,000 * 0.480244 / 0.04
FV ≈ $8,000 * 12.0061
FV ≈ $96,048.80
Therefore, Francine will have approximately $96,048.80 in her 401k account in 10 years if the account averages a 4% annual return and she contributes $8,000 each year.
