Ileana have to invest for 8 years :
What is Simple interest?Simple interest is a simple and straightforward formula for figuring out how much interest will be charged on a loan. Simple interest is calculated by dividing the daily interest rate by the principle and the number of days between payments.
How do you calculate simple interest?The principal amount must be multiplied by the time, interest rate, and time period in order to calculate simple interest. Simple Interest = Principal x Interest Rate x Time is the written formula.
Given Data:Principal amount = $15,500
interest = $5,084
Time = ?
Rate = 4.1% simple interest
Solution:to find the simple interest :
I = [tex]\frac{(p*t*r)}{100}[/tex]
Then:
Time = [tex]\frac{I*100}{P*R}[/tex]
= [tex]\frac{(5084*100)}{(15500*4.1)}[/tex]
= [tex]\frac{508400}{63,550}[/tex]
= 8 years
Ileana have to invest for 8 years
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A scientist uses a submarine to study ocean life.
She begins 86 feet below sea level.
After traveling down for 3 seconds, she's 193 feet below sea level.
Find the rate of change in the submarine's elevation in feet per second. Round your answer to the nearest tenth.
Answer: 35.7 feet per second.
Step-by-step explanation: The scientist starts at -86 feet. Then she goes to -193 feet. The difference here is 193-86 = 107 feet. That means she traveled 107 ft in 3 seconds. 107/3 = 35 with a remainder of 2. 2/3 approximately equals 0.6666667. We need to round to the nearest tenth which is 0.7. So, we are left with 35.7.
Choose the numbers that are terminating decimals. Select all that apply.
A. 0.032
B. 0.999...
C. 0.525
D. 0.75
Answer: A, C, and D
Step-by-step explanation:
A terminating decimal is a decimal that has an end. In other words, [tex]\frac{1}{4} =0.25[/tex] is one, but [tex]\frac{1}{3} =0.3333...[/tex] is not.
✓ A. 0.032
✗ B. 0.999...
✓ C. 0.525
✓ D. 0.75
Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). give the interval of convergence for the resulting series
The power series is
g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....
To deduce the power series of g(x) from the power series for f(x) and identify its radius of convergence
The power series for f(x) is just the geometric series derived from 1/1-y ,setting y=2x.
Its radius of convergence is 0.5
Let,
f(x)= 1/1-2x = 1+ (2x) + (2x)2 + .........+(2x)n......+....
The power series expansion (geometric series),
valid for I2xI < 1 , IxI < 0.5
so, radius of convergence = 0.5
The power series for g(x) is found by integrating term by term the power series of f(x) (upto a constant). The radius of converngence of g(d) is the same as that of f(x) (from general theory) =0.5
Now, g(x) = ln(1-2x)
= -2 [tex]\int\limits^a_b {(1/1-2x)} \, dx = -2 \int\limits^a_b {f(x)} \, dx[/tex]
=-2 [tex]\int\limits^a_b {[1+(2x)+ (2x)2 +........+ (2x)n+.......]} \, dx[/tex]
g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....
is the power series expansion for g(x).
radius of convergence =0.5
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What is the height of a rectangular prism with a volume of 80 cubic feet and a base area of 25 square feet?
Volume=80cubic feet
Length×Width×Height =80cubic feet
Base area×Height =80cubic feet
25square feet×Height =80cubic feet
Height =80÷25
=3.2feet
The height of the rectangular prism is 3.2 feet.
To determine the height of a rectangular prism with a volume of 80 cubic feet and a base area of 25 square feet,
The volume of a rectangular prism, that is V = lwh, where l is the length, w is the width, and h is the height of the prism.
Given:
Volume (V) = 80 cubic feet
Base area (A) = 25 square feet
We know that the base area is equal to the product of the length and width:
A = lw.
Calculate the length (l) and width (w) from the given base area:
We know that A = lw, and A = 25 square feet.
If we assume the length to be greater than the width, we can express the base area as lw = 25.
We need to find two factors of 25 that have a difference as small as possible. The factors of 25 are 1, 5, and 25.
We can choose l = 5 feet and w = 5 feet.
V = lwh.
80 = 5 * 5 * h
Divide both sides of the equation by 25:
80/25 = h.
h = 16/5 = 3.2 feet.
Therefore, the height of the rectangular prism is 3.2 feet.
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Jessica fills a cube shaped tank that has an edge of 70 cm with water from a tap. Water flows into the tank at a rate of 7L per minute. How long will it take to fill the tank fully?
The volume of the tank is (70 cm)³ = 343,000 cm³.
Now,
1 mL = 1 cm³
1 L = 1000 mL
so we convert the given rate to
[tex]\dfrac{7\,\rm L}{1\,\rm min} \cdot \dfrac{1000\,\rm mL}{1\,\rm L} \cdot \dfrac{1\,\mathrm{cm}^3}{1\,\rm mL} = \dfrac{7000\,\mathrm{cm}^3}{1\,\rm min}[/tex]
Then the time it will take to fill up the tank is
[tex]343,000\,\mathrm{cm}^3 \cdot \dfrac{1\,\rm min}{7000\,\mathrm{cm}^3} = \boxed{49\,\rm min}[/tex]
A professional basketball team won 48 games and lost 32. what fraction of the games did the team win?
Answer:
48/80 = 6/10
Step-by-step explanation:
48 wins
+ 32 lost
= 80 total games
Then the fraction of the games win is:
48/80
= 6/10
Answer:3/5 of the games
Step-by-step explanation: The total number of games played by the team is 48+32 = 80 games. out of hose 80, they won 48 so they won 48/80 games. We can simplify this by dividing both sides by 8 to get 6/10. Which is 60%. Finally we can simplify again by dividing the fraction by 2/2 to get 3/5.
Charlie began hiking from her campsite back to her car. Her campsite was located 9 miles from her car. She had walked for 1 hour and was 2 miles from her campsite when she realized she had forgotten her water bottle. She hurried back to her campsite in 0.5 hours, collected her water bottle, and rested for 0.5 hours. Then she began hiking back to her car at a quicker pace. She hiked for 3 more hours before she reached her car. Which graph represents Charlie's distance from her car at different times?
The Distance - Time graph that represents that represents Charlie's trip is attached accordingly.
What is a Distance - Time Graph?A distance-time graph can be used to illustrate the distance traveled by an item moving in a straight line.
The gradient of the line in a distance-time graph equals the speed of the item. The quicker the item moves, the higher the gradient (and the steeper the line).
What is the use of a Distance - Time Graph?Some of the uses of the distance-time graph are;
The position of the object at a time can be detected using the distance - time graphThe D-T Graph can provide the speed at which a person or an object is traveling.Learn more about Distance - Time Graph:
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Determine the convergence or divergence of the sequence with the given nth term. if the sequence converges, find its limit. (if the quantity diverges, enter diverges. ) an = 21/n
The given sequence [tex]2^{\frac{1}{n} }[/tex] converges with limit 1.
According to the given question.
We have a sequence,
[tex]a_{n} = 2^{\frac{1}{n} }[/tex]
Since, we know that
The sequence of real numbers [tex]S_{n}[/tex], where n goes from 1 to infinity has a limit L, the the sequence is convergent to L. If the sequence doesn't have limit then it is divergent.
The nth root function is strictly increasing for positive real values.
Therefore,
[tex]1^{\frac{1}{n} } \leq 2^{\frac{1}{n} } \leq n^{\frac{1}{n} }[/tex] [tex]\forall \ n\geq 2[/tex]
Also,
[tex]\lim_{n \to \infty} n^{\frac{1}{n} } = 1[/tex]
[tex]\implies \lim_{n \to \infty} 1^{\frac{1}{n} } =1[/tex] ( by squeeze theorem)
Thereofore,
[tex]\lim_{n \to \infty}2^{\frac{1}{n} } =1[/tex]
So, the given sequecence has a limit i.e. 1. Which means [tex]2^{\frac{1}{n} }[/tex] is a convergent sequence.
Hence, the given sequence [tex]2^{\frac{1}{n} }[/tex] converges with limit 1.
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Select the correct answer.
Graph the following system of inequalities.
y ≥x-2
y ≤-4x - 2
y
-6-5
6
0 1 2 3 4
X
9
5
2
F
6
12 RE
NUE
F
4 5 6
Answer:
I don't understand the formatting after the first two equations.
Step-by-step explanation:
See attached graph.
Samantha and mia each left julia’s house at the same time. mia walked north at 7 kilometers per hour. samantha ran west at 11 kilometers per hour. how far apart were they after one hour? round the answer to the nearest tenth. a right triangle. a point at the angle with measure 90 degrees is labeled julia's house. a line drawn north is labeled 7 kilometers and a line drawn west is labeled 11 kilometers.
Samantha and Mia are 13 km apart from each other.
What is Pythagorean ?A right triangle's squared sides add up to the hypotenuse's squared length, according to the Pythagorean Theorem.
Mia is 7 kilometers north of Julia's home as she walked at a speed of 7 kilometers per hour.
Samantha walked at an average speed of 11 km/h, and she is now 11 kilometers west of Julia's home.
A right-angled triangle is formed by Julia's house, Mia and Samantha's locations after one hour, and the figure's points.
Hypotenuse of the triangle, which measures distance between the females
the Pythagorean theorem,
H² = P² + B²
H² = 7² + 11²
H² = 49 + 121
H = √170
H = 13.038
H = 13km
Between them, there is a 13 kilometer distance.
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The Pyramid of Giza is shown. It has a base length of 230 meters and a height of 150 meters.
The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m.
The area of the base is
m2.
The volume is
m3.
the area and volume of the Pyramid of Gaza are 139, 840 m²
and 52950 m³ respectively.
How to determine the parametersThe formula for volume and area of a square pyramid are given thus;
Volume, V= [tex]a^2\frac{h}{3}[/tex]
Area , [tex]A=a^2+2a \sqrt{\frac{a^2}{4}+ h^2 }[/tex]
Where
a is the base lengthh is the heightSubstitute the values;
Area = [tex]230^2 + 2(230) \sqrt{\frac{230^2}{4}+ 150^2 }[/tex]
Area = [tex]52900 + 460 + \sqrt{13225 + 22500}[/tex]
Area = [tex]52900 + 460(189)[/tex]
Area = 52900 + 86, 940
Area = 139, 840 m²
Volume , v = [tex]230^2 + \frac{150}{3}[/tex]
Volume = 52900 + 50
Volume = 52950 m³
Thus, the area and volume of the Pyramid of Gaza are 139, 840 m²
and 52950 m³ respectively.
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answer is in the attachment below
goodluck!!
Any help is appreciated!
Answer:
∠a=40°, ∠b=50°, ∠c=115°.
Step-by-step explanation:
∵The opposite vertex angles are equal,
∴∠a=40°.
∴∠b=90°-∠a=90°-40°=50°.
∠c=180°-65°=115°.
Find the area of the shaded region. Round the answer to the nearest
tenth decimal place.
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Area of shaded region = 2571.66 in²[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Radius of smaller circle = 25 in
Radius of larger circle = 25 + 13 = 38 in
Area of ring : Area of larger circle - Area of smaller circle
[tex]\qquad❖ \: \sf \:\pi {(38)}^{2} - \pi {(25)}^{2} [/tex]
[tex]\qquad❖ \: \sf \:\pi( {38}^{2} - 25 {}^{2} )[/tex]
[tex]\qquad❖ \: \sf \:3.14(1444 - 625)[/tex]
[tex]\qquad❖ \: \sf \:3.14(819)[/tex]
[tex]\qquad❖ \: \sf \:2571.66 \: \: in {}^{2} [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Area = 2571.66 in²Find the 4 terms in the sequence given [tex]an=n^2+4[/tex]
Answer:
a₁ = 5
a₂ = 8
a₃ = 13
a₄ = 20
Step-by-step explanation:
Given sequence formula
aₙ = n² + 4
Requirement of the question
Find the 4 terms in the sequence
Substitute 4 values into the sequence formula
a₁ = (1)² + 4 = 1 + 4 = [tex]\Large\boxed{5}[/tex]
a₂ = (2)² + 4 = 4 + 4 = [tex]\Large\boxed{8}[/tex]
a₃ = (3)² + 4 = 9 + 4 = [tex]\Large\boxed{13}[/tex]
a₄ = (4)² + 4 = 16 + 4 = [tex]\Large\boxed{20}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Kaley solved 10 x 5 x 2 using the equations below.
10 x 5 x 2 = (10 × 5) × 2
= 50 x 2
= 100
Use the equations below to solve 10 x 5 x 2 in a different way.
10 x 5 x 2
= 10 x (
= 10 x
=
= 100
=
x 2)
Answer + Step-by-step explanation:
10 × 5 × 2
= 10 × (5 × 2) (associative property)
= 10 × (10)
= 10 × 10
= 100
for f(x) = x+1 and g(x)= 2x+3, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d.(gof)(2)
Answer:
a) 2x + 4
b) 2x + 5
c) 8
d) 9
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=x+1\\g(x)=2x+3 \end{cases}[/tex]
Function composition is an operation that takes two or more functions and combines them into a single function.
(f o g)(x) means find g(x) first and then substitute the result into f(x).
(g o f)(x) means find f(x) first and then substitute the result into g(x).
Part (a)
[tex]\begin{aligned}(f \circ g)(x) & = f[g(x)]\\& = g(x)+1\\ & = (2x+3)+1\\& = 2x+4\end{aligned}[/tex]
Part (b)
[tex]\begin{aligned}(g \circ f)(x) & = g[f(x)]\\& = 2[f(x)]+3\\& = 2(x+1)+3\\ & = 2x+2+3\\& = 2x+5\end{aligned}[/tex]
Part (c)
[tex]\begin{aligned}(f \circ g)(2) & = f[g(2)]\\& = g(2)+1\\ & = (2(2)+3)+1\\ & = (4+3)+1\\& = 8\end{aligned}[/tex]
Part (d)
[tex]\begin{aligned}(g \circ f)(2) & = g[f(2)]\\& = 2[f(2)]+3\\& = 2(2+1)+3\\ & = 2(3)+3\\ & = 6+3\\& = 9\end{aligned}[/tex]
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(fog)(x)
f(g(x))f(2x+3)2x+3+12x+4(gof)(x)
g(f(x))g(x+1)2x+2+32x+5(fog)(2))
2(2)+48(gof)(2)
2(2)+59If a system reliability of 0. 998 is required, what reliability of two components in series is required?
The reliability of two components in series is 0.996.
To find the reliability of the engine, we need all the two components to work. Each components has a reliability of 0.998, so to find the reliability of the engine we need to find the probability of all two components working.
Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.
We can find this probability multiplying all the ten reliabilities:
P = 0.998^2 = 0.996004
Rounding to three decimal places, we have P = 0.996
The reliability of the engine is 0.996.
Hence,
The reliability of two components in series is 0.996.
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find the perimeter of the figure below, composed of a rectangle and two semicircles
.
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
Let's consider the shape given to us:
⇒ a rectangle with two semicircles cutout on the edges
⇒ perimeter/circumference of the two semicircles can count as one
circle
Let's solve:
Circumference = circumference of two semicircle[tex]\hookrightarrow \text{Total circumference} =\frac{1}{2} *\pi *\text{ diameter} +\frac{1}{2} *\pi * \text{diameter}\\= \pi *\text{diameter}=10\pi =10 * 3.14 = 31.4[/tex]
Total Perimeter = 31.4 + 14 + 14 = 31.4 + 28 = 59.4Answer: 59.4 square units
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
[tex]f(x)=-2(x-3)^2+2[/tex]
Step-by-step explanation:
To find the x-intercept, substitute 0 for y and solve for x. To find the y-intercept, substitute 0 for x and solve for y.
x-intercept(s): (2,0),(4,0)
y-intercept(s): (0,−16)
Answer:
D f(x) = -2(x - 3)² + 2
Step-by-step explanation:
The y-intercept occurs at x = 0.
A
f(x) = 2x(x + 14) - 64
f(0) = -64 Not -16
B
f(x) = (x + 4)² + 2x
f(0) = 16 Not -16
C
f(x) = (x - 16)² + 4
f(0) = 260 Not -16
D
f(x) = -2(x - 3)² + 2
f(0) = -18 + 2 = -16 <-------------------- this is it
A gardener uses 1/3 of a liter of water to water 2/7 of a garden.
Answer:
[tex]\boxed{\sf 1\dfrac{1}{6}\ liters \ of \ water}[/tex]
Explanation:
Let the total water required water the entire ground be g
Equation:
[tex]\sf \dfrac{2}{7}\:g = \dfrac{1}{3} \ liters \ of \ water[/tex]
rearranging
[tex]\sf g = \dfrac{7(1)}{3(2)}[/tex]
simplify
[tex]\sf g = \dfrac{7}{6} \ liters \ of \ water[/tex]
rewrite in mixed fraction
[tex]\bf g = 1\dfrac{1}{6}\ liters \ of \ water[/tex]
The water required to water the entire ground is 1 1/6 liters.
A student is trying to solve the system of two equations given below: equation p: y z = 6 equation q: 8y 7z = 1 which of these is a possible step used in eliminating the y-term? (y z = 6) ⋅ −8 (y z = 6) ⋅ 7 (8y 7z = 1) ⋅ 7 (8y 7z = 1) ⋅ 8
Correct option for solving the system of two equation is ([tex]y\times z =6[/tex])[tex]\times -8[/tex] .
What is simultaneous linear equation?
A system of simultaneous linear equations is any set of two or more linear equations that share the same unknown variables. Finding values for the unknown variables that simultaneously satisfy all of the equations is required to solve such a system.
Simultaneous linear equations are two linear equations in two variables put together.
The ordered pair (x, y) that satisfies both linear equations is the system of simultaneous linear equations' solution.
Given,
Equation p: [tex]y+z=6[/tex]
Equation q: [tex]8y+7z=1[/tex]
To solve the above simultaneous linear equation multiply the equation p with (-8)
[tex](y+z=6)\times -8[/tex] ...................................................... Equation (1)
Now add Equation (1) with Equation (q)
[tex]-8y-8z=-48[/tex]
+ [tex]8y+7z=1[/tex]
⇒ [tex]-z=-47[/tex]
⇒ [tex]z=47[/tex]
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PLS HELP ASAP! THX
Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6
Find (h-g)(2.1)
The value of the polynomial difference when the value of x is 2.1 is -3.51
Difference of polynomialsPolynomials are functions that has a leading degree of 3 and above. Given the following polynomial expression below;
g(x)= 2x^2+3x-9 and;
h(x)=x^2+2x-6
Take the difference
(h-g)(x) = h(x) - g(x)
Substitute
(h-g)(x) = x^2+2x-6 - (2x^2+3x-9)
(h-g)(x) = x^2+2x-6-2x^2-3x+9
(h-g)(x) = -x^2-x+3
Substitute the value of x to have;
(h-g)(2.1) = -(2.1)^2 - 2.1 + 3
(h-g)(2.1) = -4.41 + 0.9
(h-g)(2.1) = -3.51
Hence the value of the polynomial difference when the value of x is 2.1 is -3.51
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A figure has vertices at A(—3, 2), B(—l, —l), and C(—4, —2). After a transformation,the image of the figure has vertices at A'(3, 2), B'(l, —l), and C'(4, —2). Draw the preimage and image. Then identify the transformation
Answer:
rotate 180° about origin
The preimage and image of the figure are given below. The transformation rule that is applied is (x, y) → (-x, y).
Given a triangle with vertices A(—3, 2), B(—l, —l), and C(—4, —2), which is preimage. Further, an image is created of this triangle that has vertices at A'(3, 2), B'(l, —l), and C'(4, —2). As shown in the given figure.
Now, as per the image and preimage in the given graph. The image is the reflection of the preimage about the y-axis. This can be verified as when the image and preimage are reflected about the y-axis the vertices change as:
(x, y) → (-x, y)
A(-3, 2) → A'(3,2)
B(-1, -1) → B'(1, -1)
C(-4, -2) → C'(4,-2)
Hence, the transformation rule is (x, y) → (-x, y).
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pls help will mark this brainlest
The ordered pairs (0,13) and (10, 0) are joined to best draw the line of best fit for the given scatter plot. So, option 4 is correct.
How to draw the line of best fit for a scatter plot?For the given scatter plot, to draw a line of best fit, the slope is to be calculated. The slope of the required line is calculated by
m = [n(∑xy) - (∑x)(∑y)]/[n(∑x²) - (∑x)²]
Where,
∑xy = sum of the product of x and y values
∑x = sum of x values
∑y = sum of y values
∑x² = sum of square values of x
n = total number of scatter points
And the y-intercept is calculated by
b = [∑y - m(∑x)]/n
Where m is the slope obtained above
Calculation:The given scatter plot has the coordinate points:
(0,14), (1, 11), (2, 9), (3, 10),(4, 7), (5, 7), (6, 5), (7, 5), (8, 3), (9, 1), (10, 0)
Such that n = 11
Then the required components are calculated as follows:
∑x = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
∑y = 14 + 11 + 9 + 10 + 7 + 7 + 5 + 5 + 3 + 1 + 0 = 72
∑xy = (0 × 14) + (1 × 11) + (2 × 9) + (3 × 10) + (4 × 7) + (5 × 7) + (6 × 5) + (7 × 5) + (8 × 3) + (9 × 1) + (10 × 0) = 220
∑x² = 0² + 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8² + 9² + 10² = 385
Then the slope is calculated as follows:
slope m = [n(∑xy) - (∑x)(∑y)]/[n(∑x²) - (∑x)²]
On substituting,
m = [11(220) - (55)(72)]/[11(385) - (55)²]
⇒ m = -14/11 = -1.2727273 ≅ -1.3
∴ m = -1.3
Then calculating the y-intercept:
we have b = [∑y - m(∑x)]/n
On substituting,
b = [72 - -1.3(55)]/11
∴ b = 13
Then the slope-intercept form of the required line is
y = -1.3x + 13
When x = 0,
y = -1.3(0) + 13 = 13
When y = 0,
0 = -1.3x + 13
⇒ 1.3x = 13
⇒ x = 13/1.3 = 10
Therefore, the coordinates (0, 13) and (10, 0) give the best draw for the line of best fit.
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Need this soon please -
Select the correct answer.
What is the inverse of function
f(x)=√x + 7
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Option A is correct[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Find inverse of given function :
[tex]\qquad❖ \: \sf \:y = \sqrt{x} + 7[/tex]
[tex]\qquad❖ \: \sf \: \sqrt{x} = y - 7[/tex]
[tex]\qquad❖ \: \sf \:x = (y - 7) {}^{2} [/tex]
Next, replace x with f-¹(x) and y with x ~
[tex]\qquad❖ \: \sf \:f {}^{ - 1} (x) = (x - 7) {}^{2} [/tex]
we got our inverse function.
Condition : x should be greater or equal to 7
because we will get same value of y for different x if we also include values less than 7.
[tex] \qquad \large \sf {Conclusion} : [/tex]
Correct option is A[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:[tex]\longrightarrow\bold{f(x)= \sqrt{7}}[/tex]
To solve for the inverse of a function we begin by re-writing the function as an equation in terms of y.
[tex]\bold{Becomes,}[/tex]
Next step we switch sides for x and y variables and then solve for the y variable as shown below,
[tex]\longrightarrow\sf{y= \sqrt{x}+7}[/tex]
[tex]\bold{Then,}[/tex]
[tex]\longrightarrow\sf{x= \sqrt{y}+7}[/tex]
[tex]\small\bold{Solve \: for \: y \: and \: subtract \: 7 \: from \: the \: both \: }[/tex] [tex]\bold{sides,}[/tex]
[tex]\longrightarrow\sf{x-7= \sqrt{y}}[/tex]
[tex]\small\bold{Square \: both \: sides }[/tex]
[tex]\sf{(x-7)^2=(\sqrt{y})^2}[/tex]
[tex]\sf{(x-7)^2=y}[/tex]
We now re-write in function notation. Take note however that this is the inverse:
[tex]\bold{Where \: y}[/tex] [tex]\sf{=(x-7)^2 }[/tex]
[tex]\longrightarrow\sf{y= (x-7)^2 }[/tex]
[tex]\huge\mathbb{ \underline{ANSWER:}}[/tex]
[tex]\large\boxed{\sf A. \: \: f^{-1}(x)= (x − 7)^2 , \: for \: \underline > 7 }[/tex]
help please !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!111
Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.
Given solution of a question done by two people.
Jenna's method
5(30+4)
(5)(30)+(5)(4)
150+20=170
Mia's method
5(30+4)
5(34)=170
We are required to find why they have achieved at the same answer.
Jenna and Mia have achieved at the same answer because they both have adopted the right method.Jenna's method is the equation in its simplest form. Addition of that is easily understood. While Mia's method is just valid as Jenna's some people may have trouble remembering the steps of multiplication within parantheses as well as being able to look at large multiplication problem and automatically knowing the answer or being able to get the answer as fast as simple addition.
Hence Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.
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Dean's father, Franco, is 5 times his age. Dean is 8 years older than his sister, Helen. The sum of their ages is 62 years. How old is each person
Answer:
dean = 10
franco = 50
helen = 2
steps
you want to get the age of one of the people first
'is' means equal
'older than' means plus
'sum' means total by adding
d
f = 5d
d = 8 + h
d + f + h = 62
make sure there is 1 letter to solve for
d = 8 + h -> h = d - 8
f = 5d
d = d
d + f + h = 62
d + (5d) + (d-8)
7d - 8 = 62
7d = 70
d = 10
f = 50
h = 2
Find the general equation of the plane through the point (3, 2, 5) that is parallel to the plane whose general equation is 2x 3y − z = 0.
The plane we want and the plane we're given are parallel, so they share the same normal vector. The normal to [tex]2x+3y-z=0[/tex] is the vector (2, 3, -1), since [tex](2,3,-1)\cdot(x,y,z)=0[/tex].
Then the plane we want has equation
[tex](2,3,-1) \cdot (x-3, y-2, z-5) = 0 \\\\ \implies 2(x-3) + 3(y-2) - (z-5) = 0 \\\\ \implies \boxed{2x + 3y - z = 7}[/tex]
Small numbers that are added to avoid unfair scoring of low-probability outcomes are called ___.
Small numbers that are added to avoid unfair scoring of low-probability outcomes are called pseudocodes
How to complete the blank?From the statement, we have the following highlights:
The numbers are small numbers Adding the numbers is used to avoid unfair scoring of low-probability outcomesThe term for the statements in the above highlight is pseudocodes
This is because pseudocodes are false codes or small numbers
Hence, the small numbers that are added to avoid unfair scoring of low-probability outcomes are called pseudocodes
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A spirit shop outside the hockey stadium sells merchandise representing the three school districts that built the arena. the entrances to the arena, the spirit shop, and the parking lot form the vertices of a triangle. the planning committee has decided to erect a memorial statue and would like it to be equidistant from the entrances to the arena, the spirit shop, and the parking lot. at what point should the statue be located? explain your answer.
Point E is where the statue should be placed.
What is called a triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.Triangles are three-sided shapes. The various kinds of triangles go by various names. The angles' size and the sides' length determine the type of triangle (corners). Equilateral, isosceles, and scalene triangles are the three varieties of triangles based on the length of the sides.The triangle is most frequently seen in our daily lives on traffic signs. The signs are triangular in shape and equilateral, which means that all three of their sides are the same length and have the same angle.At what point should the statue be:
The intersection of the doors to the arena, the spirit store, and the parking lot forms a triangle, with Point E in its center. The radius of the circumscribed circle will therefore equal the distance from the statue to each vertex, placing it at the same distance from all three landmarks.
Point E is where the statue should be placed.
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