Answers
Answer:
[tex]\textsf{The parabola has a vertex at $\left(\:\boxed{-3}\:,\boxed{-7}\:\right)$, has a p-value of $\boxed{-1}$ and it}[/tex]
[tex]\textsf{$\boxed{\sf op\:\!ens\;to\;the\;left}$\:.}[/tex]
Step-by-step explanation:
The given directrix of the parabola is x = -2, which is a vertical line.
The directrix is perpendicular to the axis of symmetry. Therefore, this means that the parabola has a horizontal axis of symmetry.
The focus of a parabola is a fixed point located inside the curve. The x-coordinate of the given focus is x = -4. As this is to the left of the directrix, it means that the parabola opens to the left.
The standard form of a horizontal parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
Vertex = (h, k)Focus = (h+p, k)Directrix: x = (h - p)Axis of symmetry: y = kAs the focus is (-4, -7), then:
[tex]\begin{aligned}(h+p, k)&=(-4,-7)\\\\\implies k&=-7\\\implies h+p&=-4\end{aligned}[/tex]
As the directrix is x = -2, then:
[tex]h - p=-2[/tex]
To find the value of h, sum the equations involved h and p to eliminate p:
[tex]\begin{array}{crcccr}&h &+& p& =& -4\\+&h& -& p& = &-2\\\cline{2-6}&2h&&& =& -6\\\cline{2-6}\\\implies &h&&&=&-3\end{array}[/tex]
To find the value of p, substitute the found value of h into one of the equations:
[tex]\begin{aligned}-3 - p&=-2\\p&=-3+2\\p&=-1\end{aligned}[/tex]
Therefore, the values of h, k and p are:
h = -3k = -7p = -1The parabola has a vertex at (-3, -7), has a p-value of -1 and it opens to the left.
The parabola has a vertex at (-3, y), has p-value of 1 and it equation is
(x + 3)² = 4y.
What is the equation of the parabola?To find the equation of the parabola with the given focus and directrix, we can use the standard form equation of a parabola:
(x - h)² = 4p(y - k)
where (h, k) is the vertex of the parabola and "p" is the distance from the vertex to the focus (and also from the vertex to the directrix).
Given:
Focus: (-4, -7)
Directrix: x = -2
1. Finding the vertex:
Since the directrix is a vertical line, the vertex lies on the line that is equidistant from the focus and directrix. In this case, it lies on the line x = (-4 + (-2))/2 = -3.
Therefore, the vertex of the parabola is (-3, y).
2. Finding the p-value:
The distance from the vertex to the focus (and also to the directrix) is the same. In this case, the distance is |-3 - (-4)| = 1.
Therefore, the value of "p" is 1.
3. Writing the equation of the parabola:
Using the vertex (-3, y) and the p-value of 1, we can write the equation of the parabola:
(x - h)² = 4p(y - k)
(x - (-3))² = 4(1)(y - y)
Simplifying, we get:
(x + 3)² = 4(y - y)
(x + 3)² = 4y
So, the equation of the parabola is (x + 3)² = 4y.
The vertex of the parabola is (-3, y) and the p-value is 1.
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Related Questions
Dewan’s bank account balance is -$16.75. He deposits checks totaling $23.59. What is his new balance? -$1.08
Answers
Answer:
$6.84
Step-by-step explanation:
This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.
Original balance: -$16.75Deposit: $23.59New balance: -$16.75 + $23.59 = $6.841cm on a picture of a swimming pool represents 1200cm of the actual swimming pool. The length of the pictured swimming pool is 4.5cm and the width is 3cm. What is the perimeter of the actual swimming pool? Express your answer in meters.
Answers
Answer:
180 meters
Step-by-step explanation:
To find the perimeter of the actual swimming pool, you need to first find the length and width of the actual swimming pool by multiplying the length and width of the pictured swimming pool by the scale factor of 1200 cm.
Length of actual swimming pool = 4.5 cm × 1200 cm = 5400 cmWidth of actual swimming pool = 3 cm × 1200 cm = 3600 cmPerimeter of actual swimming pool = (5400 cm + 3600 cm) × 2 = 18000 cm.Now that we know that the perimeter of the actual pool is 18000 centimeters, we need to convert that to meters! Keep in mind that:
100cm = 1mNow we can divide 18000 by 100:
18000 cm ÷ 100 = 180 m
Therefore, the perimeter of the actual swimming pool is 180 m.
The length of a rectangle is 4 ft longer than its width. If the perimeter of the rectangle is 32 ft, find its area.
Answers
To find the area of a rectangle, we need to know its length and width. Let's solve the problem step by step:
Let's assume that the width of the rectangle is represented by "w" (in feet).
According to the given information, the length of the rectangle is 4 feet longer than its width, which means the length can be represented as "w + 4" (in feet).
The perimeter of a rectangle is calculated by adding up all the sides. In this case, the perimeter is given as 32 feet.
Since a rectangle has two pairs of equal sides (length and width), we can express the perimeter equation as the following:
2(length + width) = perimeter
Substituting the values into the equation, we get:
2(w + (w + 4)) = 32
Simplifying the equation, we have:
2(2w + 4) = 32
4w + 8 = 32
4w = 24
w = 6
Now we know that the width of the rectangle is 6 feet. To find the length, we can substitute this value back into the equation for the length:
Length = w + 4 = 6 + 4 = 10 feet
The width is 6 feet, and the length is 10 feet. Now we can calculate the area of the rectangle:
Area = Length × Width = 10 × 6 = 60 square feet
Answer: The area of the rectangle is 60 square feet.
Corelise has 3 wooden bookcases that contain all of her books. The first bookcase has 3 shelves with 22 books on each shelf. The second bookcase has 4 shelves with 18 books on each shelf. The third bookcase has 5 shelves with 17 books on each shelf.
Part A
Write an expression for how many books she has.
A.
(
3
×
22
)
+
(
4
×
18
)
+
(
5
×
17
)
B.
(
3
+
22
)
×
(
4
+
18
)
×
(
5
+
17
)
C.
(
3
+
22
)
+
(
4
+
18
)
+
(
5
+
17
)
D.
(
3
×
22
)
+
(
4
+
18
)
+
(
5
×
17
)
Part B
Stephan has 230 books. Does Corelise have more than Stephan?
Yes or no
, she has
2,7,13,23
more or fewer
than Stephan.
Answers
Answer:
A
Step-by-step explanation:
3x16
+
4x18
+
5x17
The base of a triangle is 3 inches more than two times the height. If the area of the triangle is 7 in.² find the base and height.
Answers
Answer:
Let's denote the height of the triangle as "h" inches.
According to the given information, the base of the triangle is 3 inches more than two times the height. Therefore, the base can be expressed as (2h + 3) inches.
The formula to calculate the area of a triangle is:
Area = (1/2) * base * height
Substituting the given values, we have:
7 = (1/2) * (2h + 3) * h
To simplify the equation, let's remove the fraction by multiplying both sides by 2:
14 = (2h + 3) * h
Expanding the right side of the equation:
14 = 2h^2 + 3h
Rearranging the equation to bring all terms to one side:
2h^2 + 3h - 14 = 0
Now, we can solve this quadratic equation. We can either factor it or use the quadratic formula. In this case, let's use the quadratic formula:
h = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, the values are:
a = 2
b = 3
c = -14
Substituting these values into the quadratic formula:
h = (-3 ± √(3^2 - 4 * 2 * -14)) / (2 * 2)
Simplifying:
h = (-3 ± √(9 + 112)) / 4
h = (-3 ± √121) / 4
Taking the square root:
h = (-3 ± 11) / 4
This gives us two possible solutions for the height: h = 2 or h = -14/4 = -3.5.
Since a negative height doesn't make sense in this context, we discard the negative solution.
Therefore, the height of the triangle is h = 2 inches.
To find the base, we substitute this value back into the expression for the base:
base = 2h + 3
base = 2(2) + 3
base = 4 + 3
base = 7 inches
Hence, the base of the triangle is 7 inches and the height is 2 inches.
Step-by-step explanation:
-The answer for the height is 5.5 units.
-The base of the triangle is aproximately 2.5454 units.
To answer this problem, you have to set an equation with the information you're given. If you do it correctly, it should look like this:
7=1/2(3+2h)
-Now, you have to solve for h:
7=1.5+h
7-1.5=h
5.5=h
-Now that you have the height, you plug it in into the triangle area formula to solve for the base:
7=1/2(b)5.5
7=2.75b
7/2.75=b
b≈2.5454
-To make sure that the corresponding values for the base and height are correct, we plug the values in and this time we are going to solve for a(AREA):
A(triangle)=1/2(2.5454)(5.5)
A=1/2(13.9997)
A=6.99985 square units
-We round the result to the nearest whole number and we get our 7, which is the given value they gave us.
PLEASE HELPPPPPPP NEED NOW
Answers
Answer:
BC = 24 units
Step-by-step explanation:
This is an isosceles triangle which always has:
two legs that are congruent to each other (i.e., equal),and two angles that are congruent to each other.In this triangle, the legs CA and BA are congruent so CA = BA and the angles C and B are congruent to each other so angle C = angle B.
Thus, we can find x by setting CA and BA equal to each other:
(3x - 15 = x + 33) + 15
(3x = x + 48) - x
(2x = 48) / x
x = 24
Thus, x = 24
Since the length of BC is x and x = 24, BC is 24 units long.
what is (0.3)0 in binominal distribution
Answers
Answer:
When p, the probability of success, is zero in a binomial distribution, the probability of getting exactly k successes in n trials is also zero for all values of k except when k is zero (i.e., when there are no successes).
So, in the case of (0.3)^0, the result would be 1, because any number raised to the power of 0 is equal to 1. Therefore, the probability of getting zero successes in a binomial distribution when the probability of success is 0.3 is 1.
NEED NOW PLEASE HELP OUT
Answers
Answer:
x=50
Step-by-step explanation:
Make this equal to 180.
x+3x-35+x-35 = 180
5x = 180 + 70
5x=250
x=50
Find the net area of the following curve on the interval [0, 2].
(SHOW WORK)
f(x) = ex - e
Answers
The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.
To find the net area of the curve represented by the function f(x) = ex - e on the interval [0, 2], we need to calculate the definite integral of the function over that interval. The net area can be determined by taking the absolute value of the integral.
The integral of f(x) = ex - e with respect to x can be computed as follows:
∫[0, 2] (ex - e) dx
Using the power rule of integration, the antiderivative of ex is ex, and the antiderivative of e is ex. Thus, the integral becomes:
∫[0, 2] (ex - e) dx = ∫[0, 2] ex dx - ∫[0, 2] e dx
Integrating each term separately:
= [ex] evaluated from 0 to 2 - [ex] evaluated from 0 to 2
= (e2 - e0) - (e0 - e0)
= e2 - 1
The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.
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Dylan's mom told him that she would replace each one of his dimes with a quarter. If he uses all of his coins, determine if Dylan would then have enough money to buy a game priced at $20.98 if he must also pay an 8% sales tax.
Answers
First, we need to know the initial value of Dylan's dimes and the number of dimes he has. Since the value of a dime is $0.10, we'll assume that each dime is worth $0.10.
Let's say Dylan initially has "x" dimes. Therefore, the initial value of his dimes would be 0.10x.
Now, since his mom replaces each dime with a quarter, the value of each quarter is $0.25. So, the value of his quarters would be 0.25x.
The total value of his coins after the replacement would be the sum of the initial value of dimes and the value of quarters, which is 0.10x + 0.25x = 0.35x.
Now, to determine if Dylan has enough money to buy the game priced at $20.98, we need to consider the 8% sales tax. To calculate the total amount including tax, we multiply the game price by (1 + tax rate):
Total amount including tax = $20.98 * (1 + 0.08) = $22.65.
Now, we can set up an inequality to check if Dylan has enough money:
0.35x ≥ $22.65.
Dividing both sides of the inequality by 0.35, we get:
x ≥ $22.65 / 0.35.
x ≥ $64.71.
Therefore, Dylan would need to have at least $64.71 worth of dimes (before replacement) in order to have enough money to buy the game after his mom replaces each dime with a quarter.
Note: If Dylan has fewer dimes, the total value of his coins would be lower, and he would not have enough money to buy the game.
the population of a certain state can be estimated by the equation p=80.7t+18,312.3, where p represents the population of the state in thousands of people t years since 2010
Answers
The estimated population of the state in the year 2022 is 19,280,700 people.
The given equation represents the population of a certain state as a function of time, where p is the population in thousands of people and t is the number of years since 2010.
The equation is given as p = 80.7t + 18,312.3.
To estimate the population of the state, we substitute the value of t into the equation. For example, if we want to estimate the population in the year 2022 (12 years since 2010), we substitute t = 12 into the equation:
p = 80.7(12) + 18,312.3
= 968.4 + 18,312.3
= 19,280.7.
The estimated population of the state in the year 2022 is 19,280,700 people.
We can estimate the population for any given year by substituting the corresponding value of t into the equation.
It's important to note that the population is given in thousands of people, so we multiply the final result by 1,000 to obtain the population in actual numbers.
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What is the solution, if any, to the inequality |3x|\ge0? all real numbers no solution x\ge0 x\le0
Answers
Answer:
all real numbers
Step-by-step explanation:
Try a negative number, a positive number and zero for x.
All of them work.
Answer: all real numbers
Graph the function f(x)= 3+2 in x and its inverse from model 1.
Answers
The graph of the function and its inverse is added as an attachment
Sketching the graph of the function and its inverseFrom the question, we have the following parameters that can be used in our computation:
f(x) = 3 + 2ln(x)
Express as an equation
So, we have
y = 3 + 2ln(x)
Swap x and y in the above equation
x = 3 + 2ln(y)
Next, we have
2ln(y) = x - 3
Divide by 2
ln(y) = (x - 3)/2
Take the exponent of both sides
[tex]y = e^{\frac{x - 3}{2}}[/tex]
Next, we plot the graphs
The graph of the functions is added as an attachment
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Find the length of KL.
Answers
Answer:
KL = 6
Step-by-step explanation:
We see that the length of IL includes IJ, JK, and Kl and is 26.
Since IL = 26 and IJ + JK + KL = IL, we can subtract the sum of the lengths of IJ and Jk from IL to find KL:
IL = IJ + JK + KL
26 = 9 + 11 + KL
26 = 20 + KL
6 = KL
Thus, the length of KL is 6.
We can confirm this fact by plugging in 6 for KL and checking that we get 26 on both sides of the equation when simplifying:
IL = IJ + JK + KL
26 = 9 + 11 + 6
26 = 20 + 6
26 = 26
Thus, our answer is correct.
Find the limit (if the limit exists). Solve in two different ways.
Answers
The limit of the trigonometric expression is equal to 0.
How to determine the limit of a trigonometric expression
In this problem we find the case of a trigonometric expression, whose limit must be found. This can be done by means of algebra properties, trigonometric formula and known limits. First, write the entire expression below:
[tex]\lim_{\Delta x \to 0} \frac{\cos (\pi + \Delta x) + 1}{\Delta x}[/tex]
Second, use the trigonometric formula cos (π + Δx) = - cos Δx to simplify the resulting formula:
[tex]\lim_{\Delta x \to 0} \frac{1 - \cos \Delta x}{\Delta x}[/tex]
Third, use known limits to determine the result:
0
The limit of the trigonometric function [cos (π + Δx) + 1] / Δx evaluated at Δx → 0 is equal to 0.
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Find the measure of the numbered angles
Look at picture for reference
Show work when possible
Answers
The measure of the numbered angles in the rhombus is determined as angle 1 = 90⁰, angle 2 = 57⁰, angle 3 = 45⁰, and angle 4 = 45⁰.
What is the measure of the numbered angles?The measure of the numbered angles is calculated by applying the following formula as follows;
Rhombus has equal sides and equal angles.
angle 2 = angle 57⁰ (alternate angles are equal)
angle 1 = 90⁰ (diagonals of rhombus intersects each other at 90⁰)
angle 3 = angle 4 (base angles of Isosceles triangle )
angle 3 = angle 4 = ¹/₂ x 90⁰
angle 3 = angle 4 = 45⁰
Thus, the measure of the numbered angles in the rhombus is determined as angle 1 = 90⁰, angle 2 = 57⁰, angle 3 = 45⁰, and angle 4 = 45⁰.
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5. A person observes that from point A, the angle of elevation to the top of a cliff at D is 30°. Another person at point B, notes that the angle of elevation to the top of the
cliff is 45°. If the height of the cliff is 80.0 m, find the distance between A and B. Show the steps of your solution.
Answers
Answer:
In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg. So AC = 80√3.
In a 45°-45°-90° triangle, both legs are congruent. So BC = 80.
AB = AC - BC = (80√3 - 80) meters
= 80(√3 - 1) meters
= about 58.56 meters
The distance between points A and B is approximately 138.6 meters.
To find the distance between points A and B, we can use the concept of trigonometry and the given information.
Let's denote the distance between points A and B as x.
From point A, the angle of elevation to the top of the cliff at point D is 30°. This means that in the right triangle formed by points A, D, and the top of the cliff, the opposite side is the height of the cliff (80.0 m) and the adjacent side is x. We can use the tangent function to calculate the length of the adjacent side:
tan(30°) = opposite/adjacent
tan(30°) = 80.0/x
Simplifying the equation, we have:
x = 80.0 / tan(30°)
Using a calculator, we can find the value of tan(30°) ≈ 0.5774.
Substituting the value, we get:
x = 80.0 / 0.5774
Calculating the value, we find:
x ≈ 138.6 meters
In light of this, the separation between positions A and B is roughly 138.6 metres.
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advanced functions
solve 4(8-2x)=256
Answers
Answer:x=-28
Step-by-step explanation:
Distribute the 4 on the left side of the equation:
32 - 8x = 256
Move the constant term to the right side of the equation:
-8x = 256 - 32
-8x = 224
Divide both sides of the equation by -8 to isolate x:
x = 224 / -8
x = -28
Similar Triangles
Determine whether the triangles are similar. If so, write a similarity statement. If not, what would be sufficient to
prove the triangles similar? Explain your reasoning.
I need help on number 1 and 2
Answers
The equivalent ratio of the corresponding sides and the triangle proportionality theorem indicates that the similar triangles are;
1. ΔAJK ~ ΔSWY according to the SAS similarity postulate
2. ΔLMN ~ ΔLPQ according to the AA similarity postulate
3. ΔPQN ~ ΔLMN
LM = 12, QP = 8
4. ΔLMK~ΔLNJ
NL = 21, ML = 14
What are similar triangles?
Similar triangles are triangles that have the same shape but may have different sizes.
1. The ratio of corresponding sides between the two triangles circumscribing the congruent included angle are;
24/16 = 3/2
18/12 = 3/2
The ratio of each of the two sides in the triangle ΔAJK to the corresponding sides in the triangle ΔSWY are equivalent and the included angle, therefore, the triangles ΔAJK and ΔSWY are similar according to the SAS similarity rule.
2. The ratio of the corresponding sides in each of the triangles are;
MN/LN = 8/10 = 4/5
PQ/LQ = 12/(10 + 5) = 12/15 = 4/5
The triangle proportionality theorem indicates that the side MN and PQ are parallel, therefore, the angles ∠LMN ≅ ∠LPQ and ∠LNM ≅ ∠LQP, which indicates that the triangles ΔLMN and ΔLPQ are similar according to the Angle-Angle AA similarity rule
3. The alternate interior angles theorem indicates;
Angles ∠PQN ≅ ∠LMN and ∠MLN ≅ ∠NPQ, therefore;
ΔPQN ~ ΔLMN by the AA similarity postulate
LM/QP = (x + 3)/(x - 1) = 18/12
12·x + 36 = 18·x - 18
18·x - 12·x = 36 + 18 = 54
6·x = 54
x = 54/6 = 9
LM = 9 + 3 = 12
QP = x - 1
QP = 9 - 1 = 8
4. The similar triangles are; ΔLMK and ΔLNJ
ΔLMK ~ ΔLNJ by AA similarity postulate
ML/NL = (6·x + 2)/(6·x + 2 + (x + 5)) = (6·x + 2)/((7·x + 7)
ML/NL = LK/LJ = (24 - 8)/24
(24 - 8)/24 = (6·x + 2)/((7·x + 7)
16/24 = (6·x + 2)/(7·x + 7)
16 × (7·x + 7) = 24 × (6·x + 2)
112·x + 112 = 144·x + 48
144·x - 112·x = 32·x = 112 - 48 = 64
x = 64/32 = 2
ML = 6 × 2 + 2 = 14
NL = 7 × 2 + 7 = 21
MN = 2 + 5 = 7
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Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 1.9. In 1983, about 1600 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2003?
Answers
First, let's calculate the number of years between 1983 and 2003:
2003 - 1983 = 20 years
Using the exponential growth formula:
N = N0 * (growth factor)^t
Where:
N0 is the initial value (number of deaths in 1983)
(growth factor) is the common ratio or growth multiplier
t is the time in years
Given:
N0 = 1600 (number of deaths in 1983)
growth factor = 1.9 (common ratio)
t = 20 (years)
Using the formula, we can calculate:
N = 1600 * (1.9)^20
Calculating this expression:
N ≈ 1600 * 6.1917364224
N ≈ 9907.58
Therefore, if the trend had continued unchecked, approximately 9908 people would have died from AIDS in the U.S. in 2003.
50 PTS!!!!!!!!!!! I NEED HELP!!!!!
Answer this question based on the table above. Choose the right answer.
Is the statement true that between 1966 and 1976 the average number of miles flown per passenger increased by one-third. (Yes or no)
Answers
Answer:
No
Step-by-step explanation:
To determine if the average number of miles flown per passenger increased by one-third between 1966 and 1976, we need to compare the increase in miles flown during that period.
According to the given table:
In 1966, the average number of miles flown per passenger was 711 miles.In 1976, the average number of miles flown per passenger was 831 miles.To find the increase in miles flown, subtract the 1966 value from the 1976 value:
[tex]\begin{aligned}\sf Increase\; in\; miles\; flown &= \sf 831 \;miles - 711\; miles\\&= \sf 120\; miles\end{aligned}[/tex]
Therefore, the average number of miles flown per passenger between 1966 and 1976 increased by 120 miles.
To check if the increase is one-third of the initial value, we need to calculate one-third of the 1966 value:
[tex]\begin{aligned}\sf One\;third \;of \;711 \;miles &= \sf \dfrac{1}{3} \times 711\; miles\\\\ &= \sf \dfrac{711}{3} \; miles\\\\&=\sf 237\;miles\end{aligned}[/tex]
Since the increase in miles flown (120 miles) is not equal to one-third of the initial 1966 value (237 miles), the statement that the average number of miles flown per passenger increased by one-third between 1966 and 1976 is not true.
Solve each equation for the angle in standard position, for 0° ≤ 0 < 360° (nearest tenth, if necessary).
a) tan 0 = 1 / √3
b) 2cos 0= √3
Answers
Answer:
Step-by-step explanation:
a) To solve the equation tan θ = 1/√3, we can find the angle whose tangent is 1/√3 by taking the inverse tangent (arctan) of 1/√3.
θ = arctan(1/√3)
θ ≈ 30.0°
Therefore, the angle in standard position that satisfies tan θ = 1/√3 is approximately 30.0°.
b) To solve the equation 2cos θ = √3, we can isolate the cosine term by dividing both sides of the equation by 2.
cos θ = √3 / 2
Now, we can find the angle whose cosine is √3/2 by taking the inverse cosine (arccos) of √3/2.
θ = arccos(√3/2)
θ ≈ 30.0°
Therefore, the angle in standard position that satisfies 2cos θ = √3 is approximately 30.0°.
PLEASE HELP
Suppose that the functions fand g are defined for all real numbers x as follows.
f(x) = 5x
g(x)=4x-4
Write the expressions for (g.f)(x) and (g-f)(x) and evaluate (g+f)(2).
(g•f)(x) =
(g-f)(x) =
(g+r) (2)=
Answers
= 20x^2 - 16
(g - f)(x) = (4x - 4) - (5x)
= (-1x) - 4
= -x -4
(g + f)(2) = (4(2) - 4) + (5(2))
= 4 + 10
= 14
PLEASE HELP! EXPLAIN THOROUGHLY EACH QUESTION SHOULD BE ANSWERED IN A 2 SENTENCE EXPLINATION AND I WILL MARK IT BRAINLIEST!
7.
This figure shows a quadrilateral made of triangle ABF
and triangle DEC
.
a. What does it mean for triangles to be congruent?
b. Jane is told that angle A
is congruent to angle D
and angle B
is congruent to angle E
She concludes that the triangles are congruent because of AAA. Explain why she thinks this, and whether or not you think she is right.
c. George is told the same thing as Jane, but he concludes that the triangles are congruent because of ASA. Explain why he thinks this, and whether or not you think he is right.
d. Are there any other ways the two triangles could be congruent with the information Jane and George have been given? Explain why you think this.
Answers
The required answers of the given questions are answered below.
a), b), c), d)
What is quadrilateral?A quadrilateral is geometric structure enclosed in 4 sides.
A) Because,
1) the angle A = Angle D
2) its has a common side
3) the angle D = Angle B
∵ ΔEAB ≅ EDC
Thus, Both the triangle is congruent by ASA.
B.)
Jane conclusion is also write for AAA
because by angle E is congruent to angle B, implies angle F is congruent to angle C.
So that is why Jane conclude AAA.
C.) George conclusion is also perfect
George thinks the following conditions-
1) the angle A = Angle D
2) its has a common side
3) the angle D = Angle B
∵ ΔEAB ≅ EDC
Thus, Both the triangle is congruent.
Hence, Both the triangles are congruent by SSS.
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Answers
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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Find the sum of the first 33 terms of the following series, to the nearest
integer.
2, 11, 20,...
Answers
Step-by-step explanation:
Common difference , d, is 9
Sn = n/2 ( a1 + a33) a33 = a1 + 32d = 2 + 32(9) = 290
S33 = 33/2 ( 2+290) = 4818
please answer ASAP I will brainlist
Answers
Answer:
(a) To find the average cost in 2011, substitute 11 for x in the function.
g(11) = -1,736.7 + 1,661.6 ln 11 = $2,247.64
The average cost in 2011 was $2,247.64.
(b) Using the graphing calculator, graph the function in the viewing window
[6, 15] by [1,000, 3,000].
The correct graph is B.
(c) A. The average cost increases at a slower rate as time goes on.
A tour group has $83 to buy train tickets. Each ticket costs $18. How many train tickets can
the group buy?
Answers
You read online that a 15 ft by 20 ft brick patio would cost about $2,275 to have professionally installed. Estimate the cost of having a 25 by 26 ft brick patio installed.
Answers
Answer:
$4929
Step-by-step explanation:
I assume the cost is proportional to the area.
15 ft × 20 ft = 300 ft²
25 ft × 26 ft = 650 ft²
650/300 = x/$2275
300x = 650 × $2275
x = $4929
Answer: $4929
Complete the following number sequence. 2, 4, 7, __, 16, __, 29, __
Answers
The completed sequence would then be: 2, 4, 7, 9, 16, 19, 29.
To complete the given number sequence, let's analyze the pattern and identify the missing terms.
Looking at the given sequence 2, 4, 7, __, 16, __, 29, __, we can observe the following pattern:
The difference between consecutive terms in the sequence is increasing by 1. In other words, the sequence is formed by adding 2 to the previous term, then adding 3, then adding 4, and so on.
Using this pattern, we can determine the missing terms as follows:
To obtain the third term, we add 2 to the second term:
7 + 2 = 9
To find the fifth term, we add 3 to the fourth term:
16 + 3 = 19
To determine the seventh term, we add 4 to the sixth term:
__ + 4 = 23
Therefore, the missing terms in the sequence are 9, 19, and 23.
By identifying the pattern of increasing differences, we can extend the sequence and fill in the missing terms accordingly.
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