Answer:
(2, 5 )
Step-by-step explanation:
Given a quadratic in standard form : y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = 3x² - 12x + 17 ← is in standard form
with a = 3 and b = - 12, thus
[tex]x_{vertex}[/tex] = - [tex]\frac{-12}{6}[/tex] = 2
Substitute x = 2 into the function for corresponding value of y
y = 3(2)² - 12(2) + 17 = 12 - 24 + 17 = 5
vertex = (2, 5 )
Triangle ABC has verrocktes A (2,-1) B ( -3,0) and C ( -1,4) . Find the vertices of the image of triangle and after a translation of 2 units up
Answer:
A(2,1) , B(-3,2) , C(-1,6)
Step-by-step explanation:
A translation of 2 units up means the y values will be shifted up 2 units
A (2,-1) -> A(2,1)
B (-3,0) -> B(-3,2)
C (-1,4) -> C(-1,6)
The vertices of the image of triangle ABC after a translation of 2 units up are A' (2, 1), B' (-3, 2), and C' (-1, 6), found by adding 2 to the y-coordinate of each original vertex.
The student has asked how to find the vertices of the image of triangle ABC after a translation of 2 units up. To do this, we simply add 2 to the y-coordinate of each vertex of the triangle. Here are the steps for the translation:
For vertex A (2, -1), the new position after translation is A' (2, -1 + 2) or A' (2, 1).
For vertex B (-3, 0), the new position after translation is B' (-3, 0 + 2) or B' (-3, 2).
For vertex C (-1, 4), the new position after translation is C' (-1, 4 + 2) or C' (-1, 6).
Therefore, the vertices of the image of triangle ABC after the translation are A' (2, 1), B' (-3, 2), and C' (-1, 6).
4. The coordinates of the vertices of rectangle
ABCD are A(3,-2), B(3, 2), C(-3, 2), and
D(-3, -2).
a. Rectangle ABCD is rotated 90° about the
origin. What are the coordinates of the
vertices of rectangle A'B'C'D'?
b. What are the measures of the angles of
A'B'C'D'?
Answer: a) A'=(2, 3), B'=(-2,3), C'=(-2,-3) D'=(2,-3)
b) the measure of each angle is 90 degrees.
Step-by-step explanation:
a) To find the coordinates you need to know that (x,y) is changed to (-y,x). This means that they are flipped and changed from either negative to positive or positive to negative.
b) Each angle is 90 degrees because that shape is a rectangle with all equal right angles.
The coordinates of the vertices of rectangle A'B'C'D' after rotating rectangle ABCD 90° about the origin are A'(-2,-3), B'(-2,3), C'(-2,-3), and D'(2,-3). All angles in rectangle A'B'C'D' measure 90°.
Explanation:When a point is rotated 90° about the origin, the new coordinates can be found using the formula (y, -x). Therefore, applying this to each vertex of the rectangle, A'(3,-2) becomes A'(-2,-3), B'(3, 2) becomes B'(-2,3), C'(-3, 2) becomes C'(-2,-3) and D'(-3, -2) becomes D'(2,-3).
Since A'B'C'D' is a rectangle, all its angles are right angles. This means all the angles measure 90°.
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Does anyone know this?
Answer: yes
Step-by-step explanation:
Answer:
10 degrees
Step-by-step explanation:
Divide 360 by however many sides or angles are within the polygon.
360/x
360/36
10
A weather forecast states that there is a 20% probability of rain in the next three days. Describe a simulation you could perform using random numbers to find the experimental probability that it will not rain on any of the next 3 days.
To simulate the 20% probability of rain over three days, generate a random number between 1 and 100 for each day. Count the trials where all three numbers are between 21 to 100 as 'non-rainy' days. The experimental probability of no rain in three days is the ratio of 'non-rainy' trials to total trials.
Explanation:Probability is a branch of mathematics that studies randomness and the chance of an event occurring. In this case, we can perform a simulation to experimentally determine the probability that it will not rain on the next 3 days even though there is a forecast of a 20% chance of rain.
One way to perform the said simulation is by using random numbers from 1 to 100. Why? Because probability can be expressed as a percentage, and the range from 1 to 100 encompasses all percentage possibilities (0% to 100%). So, for each day, we can generate a random number in this range. If the generated number falls in the range 1-20 (which represents the 20% predicted chance of rain), we consider that day as a 'rainy day'. If it falls in the range 21-100, we consider it a 'non-rainy day'.
We repeat this process for three days. The experimental probability of it not raining on all three days will be the ratio of favorable outcomes (all three numbers landing in the 'non-rainy day' range) to the total number of trials.
If we perform a large number of these three-day simulations, we'll have a good estimate of the experimental probability. The Law of Large Numbers ensures that as more trials are conducted, the experimental probability will approach the theoretical probability.
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3x+5=2x+8 it’s urgent!need step by step
Answer:
x =3
Step-by-step explanation:
step 1:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3*x-5-(2*x-8)=0
step 2:solve x+3=0
subtract 3 from both sides
step 3: x=-3
answer:x= -3
Answer:x=3
Step-by-step explanation:
Move variable to the left side and change its sign
3x-2+5=8
Move constant to the right side and change its sign
3x-2x=8-5
Combine like terms
X=3
ABCD is a parallelogram. Segment AC = 4x + 10. Find the value of x and y.
Answer:
The values of x and y in the diagonals of the parallelogram are x=0 and y=5
Step-by-step explanation:
Given that ABCD is a parallelogram
And segment AC=4x+10
From the figure we have the diagonals AC=3x+y and BD=2x+y
By the property of parallelogram the diagonals are congruent
∴ we can equate the diagonals AC=BD
That is 3x+y=2x+y
3x+y-(2x+y)=2x+y-(2x+y)
3x+y-2x-y=2x+y-2x-y
x+0=0 ( by adding the like terms )
∴ x=0
Given that segment AC=4x+10
Substitute x=0 we have AC=4(0)+10
=0+10
=10
∴ AC=10
Now (3x+y)+(2x+y)=10
5x+2y=10
Substitute x=0, 5(0)+2y=10
2y=10
[tex]y=\frac{10}{2}[/tex]
∴ y=5
∴ the values of x and y are x=0 and y=5
Mateo has drawn a line to represent the parallel cross-section of the triangular prism. Is he correct? Explain.
Answer:
No
Step-by-step explanation:
A triangular prism has a uniform cross-section.A parallel cut of the solid will produce a cross section which is parallel to the triangular base.
A right prism contains uniform cross-sections, meaning the area of each cross-section is the same.
In this case, the position of the line indicating a cut will not produce polygons congruent to the base.
A grocer has two kinds of candies, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
Answer: 55 lbs of $0.40 and 45 lbs of $1.40
Step-by-step explanation:
Let's say that we have two buckets, one that weighs x pounds and the candies in it are $0.40 per pound and another that weighs 100-x pounds (because we know the two added together must be 100 pounds) and the candies in it are $1.40 per pound.
There is a third bucket that is made when you combine the two, it weighs 100 pounds and the candies in it are $0.85. Multiply the cents per pound by the pounds of the candy for each bucket and you get this equation:
0.4 * x + 1.4 (100-x) = 0.85 * 100
Solve!
0.4x + 140 - 1.4x = 85
-x + 140 = 85
-x = -55
x = 55
From this we get that 100 - x = 45.
So, the answer is 55 lbs of $0.40 and 45 lbs of $1.40
ANSWER: 55 lbs of $0.40 and 45 lbs of $1.40
Step-by-step explanation:
Let's say that we have two buckets, one that weighs x pounds and the candies in it are $0.40 per pound and another that weighs 100-x pounds (because we know the two added together must be 100 pounds) and the candies in it are $1.40 per pound.
There is a third bucket that is made when you combine the two, it weighs 100 pounds and the candies in it are $0.85. Multiply the cents per pound by the pounds of the candy for each bucket and you get this equation:
0.4 * x + 1.4 (100-x) = 0.85 * 100
Solve!
0.4x + 140 - 1.4x = 85
-x + 140 = 85 .
-x = -55
x = 55
From this we get that 100 - x = 45.
So, the answer is 55 lbs of $0.40 and 45 lbs of $1.40
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Mr. Anderson had $40.95 that he wanted to divide evenly among his seven children. How much should each child receive? Don't forget to include the $ sign.
Answer:
5.85
Step-by-step explanation:
$40.95 / 7 =5.85
Determine which type of transformation is illustrated in the figure.
A. composition
B. dilation
C. reflection
D. translation
which expressions are equivalen to 2^5/6^5
[tex]\text{Hey there!}[/tex]
[tex]\bf{Which\ expressions\ are\ equivalent\ to\ \dfrac{2^5}{6^5}?}[/tex]
[tex]\bf{First:\ 2^5=2\times2\times2\times2\times2=4\times4\times2=16\times2\rightarrow32}[/tex]
[tex]\rightarrow\bf{2^5=32}[/tex]
[tex]\bf{Second: \ 6^5 = 6\times6\times6\times6\times6=36\times36\times2 = 1296\times6\rightarrow7,776}[/tex]
[tex]\rightarrow\bf{6^5=7,776}[/tex]
[tex]\bf{You\ can\ convert\ your\ new\ equation \ to (\text{ If this is helpful to you}):}\\\bf{\dfrac{32}{7,776}}[/tex]
[tex]\mathsf{\dfrac{32\div32}{7776\div32}}\\\\\mathsf{32\div32 = 1\leftarrow Your\ numerator}\\\\\mathsf{7,776\div32=243\leftarrow Your\ denominator}\\\\=\dfrac{1}{243}\\\\\boxed{\mathsf{Answer\#1: \dfrac{32}{7,776}}}\checkmark\\\\\boxed{\mathsf{Answer\#2:\dfrac{1}{243}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Find m<1
A. 57
B. 123
C. 132
D. 93
Step-by-step explanation:
[tex] \angle 1 [/tex] is the exterior angle of the given [tex] \triangle. [/tex]
Therefore, by remote exterior angle theorem.
[tex] \therefore \: m \angle \: 1 = 60 \degree + 63\degree \\ \\ \huge \red{ \boxed{\therefore \: m \angle \: 1 = 123 \degree }}[/tex]
Kevin is 4 times as old as Daniel and is also 6 years older than Daniel.
How old is Daniel?
Answer:
2 years
Step-by-step explanation:
K = 4D. K = D + 6
4D = D + 6
-D. -D
3D = 6
3. 3
D = 2
Answer:
d=2
Step-by-step explanation:
We can use the given information to write down two equations that describe the ages of Kevin and Daniel.
Let Kevin's current age be k and Daniel's current age be d.
k=4d
k=d+6
Now we have two independent equations, and we can solve for our two unknowns.
Since we are looking for d, and both of our equations have k alone on one side, this is a convenient time to use elimination.
Subtracting the second equation from the first equation, we get:
0=4d-(d+6)
which combines the information about d from both of our original equations.
Solving for d, we get: 3d = 6.
d=2
If $1800 is invested at 2% interest compounded annually find the total amount in 3 years.
Answer:
$1910.1744
Step-by-step explanation:
To start we have to calculate how much the total will give us in one year, for this we divide the number by 100 and multiply it by 102, so we will get that 2% in one year
(1800 / 100) * (100 + 2) =
18 * 102
1836
Now we will repeat the procedure but instead of using the 1800 we will use the 1836 which will be what we will have when the first year ends.
(1836 / 100) * (100 + 2) =
18.36 * 102
1872.72
Finally we do the same with the new number
(1872.72 / 100) * (100 + 2) =
18.7272 * 102
1910.1744
So in conclusion putting $1800 at the end of the 3 years we will get $1910.1744
$1910.1744 - $1800 = $110.1744
that is the exact amount of the profit that we will obtain.
Step 2 - Identify which formula we use to prove certain properties of polygons.
Below are the properties of triangles/quadrilaterals you’ve been working with closely. Look at the properties given, then match it with the formula you would use to prove it. ( Hint: think about the type of answers we expect from each of the formulas listed - use your answers from Step 1 to help!)
**You could use each choice more than once!
_____ 1.) Both pairs of opposite sides are congruent.
_____ 2.) Both pairs of opposite sides are parallel.
_____ 3.) Diagonals are congruent.
_____ 4.) Diagonals bisect each other.
_____ 5.) Diagonals are perpendicular.
_____ 6.) Sides of polygon create a right angle.
_____ 7.) A triangle is isosceles/equilateral.
a.) Midpoint Formula
b.) Slope Formula
c.) Distance Formula
Properties of polygons.
Step-by-step explanation:
(1) Both pair of opposite sides are congruent. Distance Formula
(2) Both pairs of opposite sides are parallel. Slope Formula
(3) Diagonals are congruent . Distance Formula
(4) Diagonals bisect to each other. Midpoint Formula
(5) Diagonals are perpendicular. Slope Formula
(6) Sides of polygon create a right angle. Slope Formula
(7) A triangle is isosceles /equilateral. Distance Formula
Alonso stands 8 yards west of Gregory. He then walks 10 yards north and discovers an arrowhead. How far is the arrowhead from Gregory’s position?
Answer:
Distance [tex]=\sqrt{164}\ \approx12.80\ yards[/tex]
Step-by-step explanation
Pythagorean theorem :
In a right triangle
[tex](Hypotenuse)^2=(Perpendicular)^2+(base)^2[/tex]
From the diagram
[tex]perpendicular = 10\ yards\\\\Base = 8\ yards \\\\Hypotenuse = distance\ (d)\\\\(d)^2=(10)^2+(8)^2\\(d)^2=100+64\\(d)^2=164\\d=\sqrt{164}\ \approx12.80\ yards[/tex]
Kareem has 216 role playing games cards . his goal is to collect all 15 set of cards. There are 72 cards in a set . How many more cards does kareem need to reach his goal
Answer:
864 cards
Step-by-step explanation:
72 cards per set times 15 sets = 1080 cards - 216 cards he already has =864 cards
20 points
Please help
Answer:
I = 0.5[tex]t^{4}[/tex] + 6.5t³ + 16t² + 10t
Step-by-step explanation:
Given
V = [tex]\frac{I}{R}[/tex] ( multiply both sides by R )
I = VR
= (0.5t³ + 6t² + 10t)(t + 1) ← distribute
= 0.5[tex]t^{4}[/tex] + 6t³ + 10t² + 0.5t³ + 6t² + 10t ← collect like terms
= 0.5[tex]t^{4}[/tex] + 6.5t³ + 16t² + 10t
what is 8.7
7 reapeating forever
as a fraction
also answer fast and the explanation Is not needed
THANKS
Answer:
55
Step-by-step explanation:
Jesse finished the first race in two minutes and seven seconds. Tim finished 12 seconds faster than Jesse. Juan finish eight seconds faster then Tim. How long did it take Juan to finish.
To find out how long it took Juan to finish, we add the time differences to Jesse's time. Tim finished 12 seconds faster than Jesse and Juan finished 8 seconds faster than Tim.
Explanation:To find out how long it took Juan to finish, we need to add the time differences to Jesse's time. First, we know that Tim finished 12 seconds faster than Jesse, so we can add 12 seconds to Jesse's time which becomes 2 minutes and 19 seconds. Next, we know that Juan finished 8 seconds faster than Tim, so we can add 8 seconds to Tim's time which becomes 2 minutes and 27 seconds. Therefore, it took Juan 2 minutes and 27 seconds to finish the race.
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I need an answer as soon as possible please! Thank youu
Find the total surface area of a square based prism (cuboid) of height 4cm, given that the side length of its base is 6cm.
please show working out
Total surface area of the square pyramid is 1476 cm².
Step-by-step explanation:
Step 1:Total surface area of a pyramid = 12pl + B. Here p is perimeter of the base which is a square = 4 × side, l is the slant height and B is the area of the base = side²
Step 2:Find perimeter of the base
⇒ p = 4 × side = 4 × 6 = 24 cm
Step 3:Find the slant height of the prism. l² = height² + (side/2)² (Based on Pythagoras Theorem)
⇒ l² = 4² + (6/2)² = 16 + 9 = 25
⇒ l = √25 = 5 cm
Step 4:Find the area of the base of the pyramid.
⇒ B = side² = 6² = 36 cm²
Step 5:Calculate total surface area of the pyramid.
⇒ TSA = 12 × 24 × 5 + 36 = 1440 + 36 = 1476 cm²
Melissa's family is on vacation. They spend $125 per day on food
and entertainment. They have budgeted only up to $750 for food
and entertainment. How many days of vacation can they afford?
How do you show your work if the answer is *6*???
Answer:6
Step-by-step explanation:
Dividing 750 by 125 you get 6
The cost c, in dollars, of a taxi ride is related to the
distance d, in miles, of the ride. The cost for taxi A is
given by the equation c = 3.5d + 2, and the cost for
taxi B is given by c= 3d + 5. For what distance is
the cost of each taxi ride the same? How much would
this trip cost?
Answer:
(3 , 2.5)
the trip would cost $12.5
12.5 = 3.5 (3)+2
12.5 = 3 (2.5)+5
Step-by-step explanation:
The distance at which the cost of each taxi is the same is 6 miles.
The trip would cost $23.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 - 9 is an equation.
We have,
Taxi A:
c = 3.5d + 2
Taxi B:
c = 3d + 5
Where c is the cost of the taxi after d distance.
Now,
The cost of the taxi is the same.
3.5d + 2 = 3d + 5
3.5d - 3d = 5 - 2
0.5d = 3
d = 3/0.5
d = 30/5
d = 6
The cost of the taxi at d = 6.
c = 3.5d + 2 = 3.5 x 6 + 2 = 21 + 2 = 23
c = 3d + 5 = 3 x 6 + 5 = 18 + 5 = 23
Thus,
The cost of both taxis is the same after 5 miles.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
i have no clue
Step-by-step explanation:
ask someone else
A bag contains blue marbles and red marbles, 58 in total. The number of blue marbles is 4 more than 5 times the number of red marbles. How many blue marbles are there?
Answer:
49 blue marbles
Step-by-step explanation:
From the question we are given;
Total number of marbles = 58 Blue marbles are 4 more than 5 times the red marblesWe need to determine the number of blue marbles;
Assuming the number of red marbles is x
Then, blue marbles will be 5x + 4
Therefore;
x + 5x + 4 = 58
6x + 4 = 58
6x = 54
x = 9
5x + 4 = 5(9) + 4 = 49
Therefore, the red marbles are 9 while the blue marbles are 49
Hence there are 49 blue marbles
–2(5n + 7) + 8n = 2(1 – 3n)
Answer:
n = 4
Step-by-step explanation:
Solve using the distributive property. This means you can multiply the number outside the brackets with each number inside the brackets. Then isolate "n" by moving all other numbers to the right side, leaving "n" alone on the left.
–2(5n + 7) + 8n = 2(1 – 3n) Distribute
(5n)(-2) + (7)(-2) + 8n = (1)(2) – (3n)(2) Multiply with each number in brackets
–10n + (–14) + 8n = 2 – 6n Remove brackets around –14
–10n – 14 + 8n = 2 – 6n Adding a negative is subtracting it's positive
–14 –2n = 2 – 6n
–14 + 14 –2n = 2 + 14 – 6n Add 14 to both sides
–2n = 16 – 6n
–2n + 6n = 16 – 6n + 6n Add 6n to both sides
4n = 16
4n/4 = 16/4 Divide both sides by 4
n = 4 Solved for "n"
Check answer by substituting "4" whenever there is "n" in the original equation. Then solve each side.
–2(5n + 7) + 8n = 2(1 – 3n)
–2(5(4) + 7) + 8(4) = 2(1 – 3(4)) Solve inside brackets
–2(20 + 7) + 32 = 2(1 – 12) Distribute
(20)(–2) + (7)(–2) + 32 = (1)(2) – (12) (2) Multiply where necessary
–40 + (–14) + 32 = 2 – 24 Simplify
–22 = –22 Same answer
LS = RS Left side equals right side
The answer we found is correct.
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e
x
√
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2
x
+
4
d
x
∫
e
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d
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i dont know why i did thus
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I really need Help with this equation Please!!!!
Answer:
Option D: - 6; [tex]$ \textbf{-5}\frac{\textbf{5}}{\textbf{2}} $[/tex]; [tex]$ \textbf{-4}\frac{\textbf{1}}{\textbf{5}} $[/tex].
Step-by-step explanation:
The sequence is defined by:
[tex]$ A(n) = -6 + (n - 1)\bigg( \frac{1}{5} \bigg ) $[/tex]
To find the first term of the sequence simply substitute n = 1.
First term of the sequence:
[tex]$ A(1) = -6 + (1 - 1)\bigg( \frac{1}{5} \bigg ) $[/tex]
[tex]$ = - 6 $[/tex]
Fourth term of the sequence:
[tex]$ A(2) = -6 + (4 - 1) \bigg ( \frac{1}{5} \bigg) $[/tex]
[tex]$ = - 6 + 3\bigg( \frac{1}{5} \bigg) $[/tex]
[tex]$ = \frac{- 30 + 3}{5} $[/tex]
[tex]$ = \frac{-27}{5} $[/tex]
[tex]$ = \frac{-25 - 2}{5} $[/tex]
[tex]$ = - 5 - \frac{2}{5} $[/tex]
[tex]$ = -5\frac{2}{5} $[/tex] is the required answer.
Tenth term of the sequence:
[tex]$ A(10) = - 6 + (10 - 1) \bigg( \frac{1}{5} \bigg) $[/tex]
[tex]$ = - 6 + 9\bigg( \frac{1}{5} \bigg) $[/tex]
[tex]$ = \frac{-30 + 9}{5} $[/tex]
[tex]$ = \frac{-21}{5} $[/tex]
[tex]$ = \frac{-20 - 1}{5} $[/tex]
[tex]$ = - 4 - \frac{1}{5} $[/tex]
[tex]$ = -4\frac{1}{5} $[/tex] is the required answer.
i need help PLEASE!!!!
Answer:
Only B and C are correct
Step-by-step explanation:
Answer:
B edit: C is also correct and E isnt my bad
Step-by-step explanation:
The difference of d and 6 times 2
for the equation 2(d-6)