Complete the square to write each equation in vertex form. Then, state whether the vertex is a minimum or a maximum and give its coordinates.
Answers
Answer:
vertex form: y = (x + 1)² - 3 the vertex is minimum coordinates of the vertex: (-1, -3)Step-by-step explanation:
[tex]y=x^2+2x-2\\\\y=x^2+2x+1-1-2\\\\\bold{y=(x+1)^2-3}[/tex]
a = 1 > 0 ← it means the parabla opens up, so, the vertex is minimum
The vertex form is y = a(x - h)² + k, where (h, k) is the vertex
So, from y = (x + 1)² - 3 the vertex is: (-1, -3)
Related Questions
The length of the rectangle is X units more than its
width. The width of the rectangle is 11 units and the
length of the wire that is used to make this rectangle
is a maximum of 57 units. Represent this situation
using an inequality.
Answers
Answer: [tex]2x+44 \le 57\\\\[/tex]
Explanation:
W = width
W = 11
L = length
L = width+x
L = 11+x
P = perimeter of the rectangle
P = 2L+2W
P = 2*(11+x)+2*11
P = 22+2x+22
P = 2x+44
The perimeter is at max 57 units because it is the length of wire used. Think of it like fencing around a piece of land. Be sure not to mix up the length of the wire with the rectangle length; those are two different things.
Anyways, because the perimeter maxes out at 57, this means either P = 57 or P < 57.
This leads to:
[tex]P \le 57\\\\2x+44 \le 57\\\\[/tex]
Kyle puts all of his craft beads into a bag. Exactly 1/3 of the beads are blue and 5/16 are red. What is the unit rate of blue beads to red beads in Kyle's bag?
Answers
The unit rate of blue beads to red beads in Kyle's bag is 1(1/15).
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
Blue beads = 1/3
Red beads = 5/16
The unit rate of blue beads to red beads.
= 1/3 ÷ 5/16
= 1/3 x 16/5
= 16/15
= (16/15) / 1
= 1(1/15) / 1
Thus,
The unit rate is 1(1/15).
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write an explicit formula for an,the nth term of the sequence 72,12,2
Answers
Answer:
[tex]a_n = 432 \cdot \left(\frac{1}{6}\right)^n[/tex] OR [tex]a_n = 72 \cdot \left(\frac{1}{6}\right)^{n-1}[/tex]
Step-by-step explanation:
The first term is 72, and each term is equal to the previous term multiplied by 1/6. This yields the expression [tex]a_n = 72 \cdot \left(\frac{1}{6}\right)^{n-1}[/tex], which is equivalent to [tex]a_n = 432 \cdot \left(\frac{1}{6}\right)^n[/tex].
Answer:
[tex]n _{th} = n _{1} {r}^{n - 1} \\ n _{th} = 72 \times 12 {}^{(n - 1)} \\ n _{th} = 72 \times ( {12}^{n} .12^(-1)) \\ n _{th} = 6 × {12}^{n} [/tex]
Which of the following is the graph of f(x)=2(x−4)2−1?
Answers
Answer:
there is no graph but it's a positive graph and a few of the points would be (3,-5) (4,-1) (5,3) (6,7)
Step-by-step explanation:
(d) At a football match, there are 29 800 people, correct to the nearest 100. (i) At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people. Calculate the lower bound for the number of minutes it takes for all the people to leave.
Answers
The lower bound for the number of minutes that it takes for all people to leave is of:
70 minutes.
How to obtain the lower bound for the number of minutes that it takes for each person to leave?At a football match, there are 29 800 people, correct to the nearest 100. The fewest number of people that can be there, hence, is of:
29,750.
(as 29749 would be rounded to 29,700).
At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people, hence the fastest rate is given as follows:
424 people per minute.
(as 425 people would be rounded to 450).
Hence the time it would take is obtained applying the proportion as follows:
29750/424 = 70 minutes.
(lower bound is fewest time, hence lowest number of people leaving at the fastest rate).
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PLEASE HELP!!!!!! Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim. Choose the correct option based on the problem information.
Use a significance level of α = 0.01 to test the claim that μ > 2.85. The sample data consist of 9 scores for which = 3.1 and s = 0.6. Identify the correct null and alternative hypotheses.
A. H0: μ = 2.85. H1: μ > 2.85.
B. H0: μ ≥ 2.85. H1: μ < 2.85.
C. H0: μ > 2.85. H1: μ ≤ 2.85.
D. H0: μ ≠ 2.85. H1: μ = 2.85.
Answers
Answer:
C. H0: μ > 2.85. H1: μ ≤ 2.85.
Step-by-step explanation:
hope it helps
what is (-5q-8) - (q+3)
Answers
The answer would be −6q−11
Answer:
-6q-11
Step-by-step explanation:
At a certain time of day a person 6 ft casts a 4ft shadow. How long is the shadow cast by a 21ft tree at the same time?
Answers
Answer:
Designate the unknown shadow length by s. Shadows cast at the same time and place are proportional to the height of the object casing the shadow. Therefore:
4/6 = s/21, or s = [4(21)]/6 = 14 feet.
What is the value of the expression 5x(3+6)-8
Answers
Answer:
45x - 8
Step-by-step explanation:
Answer:
Nodijsikmjkf
Step-by-step explanation:
45x-8
K Rick's dad used a ladder to hang up their Christmas lights on the roof. When he leaned the ladder against the house, it created a triangle. If the height of the wall measures 12 feet, the ladder measures 15 feet, and Rick's dad put the base of the ladder 9 feet from the wall, what is the area of the triangle that is created? A 36 feet2 B) 54 feet 67.5 feet? D 90 feet
Answers
Answer:
A) 36 pies
Step-by-step explanation:
The tables show the prices for ordering team jerseys from two different companies. You can use the information to write ratios showing the relationship between the cost and the corresponding number of jerseys. 1/5=5 25/5=5 50/10=5 75/15=5. 5/1=5 20/5=4 40/10=4 69/15=4. These ratios are all equivalent. These ratios are not all equivalent. This relationship is proportional. This relationship is not proportional. Explain how you can tell whether a group of ratios represents a proportional relationship.
Answers
Even though this relationship is proportional, not all of these ratios are equal.
What is the solution to the 3 to 5 ratio?Verify that the ratios provided are equal. The ratios of 3:5 and 15:25 are both equal. Because the first ratio 3: 5 can be derived by multiplying the ratio 15: 25 by 5 on both the numerator and denominator. The initial ratio of 3: 5 can be multiplied by 5 to get the ratio 15: 25, and vice versa.
What is an illustration of a 4:1 ratio?This indicates that you would require an 8 fl oz can (a quarter of a quart) of Part B if you were ordering a quart of Part A. You will have 1.25 after combining Parts A and B.
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SOMEONE HELP ME PLEASE
What is the least common multiple of 4, 9, and 12?
Answers
Answer:
36 I think
Step-by-step explanation:
jxjejjirirjxjd
Answer:
36
Step-by-step explanation:
4 x 9 = 36
9 x 4 = 36
12 x 3 = 36
Write the given expression as the sine of an angle
sin(105°) cos(35°) + sin(35°) cos(105°)
Will give brainiest.
Answers
Answer:
sin140°
Step-by-step explanation:
Using the addition formula for sine
sin(A + B) = sinAcosB + cosAsinB
Given
sin105°cos35° + sin35°cos105°
= sin105°cos35° + cos105°sin35° ← right side of expansion above
= sin(105 + 35)°
= sin140°
sydney is selling is comic book selection on the internet the scatter plot
Answers
What is the question please?
In Duck Creek, a bicycle license plate consists of one letter followed by one digit; for example, $Q7$ or $J1$. How many different license plates are possible
Answers
On solving the provided question, we can say that by permutation 26 possible letters x 10 possible digits = 260 possible plates
what is permutation?The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of
26 possible letters x 10 possible digits =
26 x 10 =
260 possible plates
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GIVING BRAINLIST
GIVING BRAINLIST
PLS HELP
Answers
Answer:It could be 10, 2, 3
Step-by-step explanation:
basically as long as the lengthxwidthxheight=60, then it should be fine
Answer:
Their are multiple ways you could do this but you can use 10 as the length, 3 as the width, and 2 as the height
Step-by-step explanation:
The formula for the volume of a rectangular prism is v=l*w*h so plugging in our values would give us 10*3*2 which is equal to 60.
Help me with this ASAP!!
Answers
Gordon thought there would be 54
guests attending the event, but there
were actually 61. What was his percent
error?
40 points
Answers
heyy! i’ll give brainliest help asap pls
Answers
Answer:
I think the best answer is Marble
hope this helps
have a good day :)
Step-by-step explanation:
Answer: I would go with B:
Step-by-step explanation: if not then its gott to be A
4. Determine the type of triangle with the given set of side lengths. Show your work. A. a = 8, b = 15, c = 17 B. a = 6, b= 15, c = 18 C. a = 7, b = 10, c = 12
Answers
So A is a triangle, and B is a triangle, and C is a right triangle (or a right-angled triangle)
Define Pythagoras Theorem.The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.
What is right angle triangle?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
A. a = 8, b = 15, c = 17
We can use the Pythagorean theorem to determine the type of triangle:
c² = a² + b²
17² = 8² + 15²
289 = 64 + 225
289 ≠ 289
Therefore, this is not a right triangle.
B. a = 6, b= 15, c = 18
We can use the Pythagorean theorem to determine the type of triangle:
c² = a² + b²
18² = 6² + 15²
324 = 36 + 225
324 ≠ 324
Therefore, this is not a right triangle.
C. a = 7, b = 10, c = 12
We can use the Pythagorean theorem to determine the type of triangle:
c² = a² + b²
12² = 7² + 10²
144 = 49 + 100
144 = 144
Therefore, this is a right triangle.
So A is a triangle, and B is a triangle, and C is a right triangle (or a right-angled triangle)
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6) What is the Converse of the following
statement: If you do your homework,
then you can go to the movies,
A) If you do your homework, then you can go to the movies.
B) If you don't do your homework, then you can't go to the movies.
C) If you went to the movies, then you did your homework.
D) If you didn't go to the movies, then you didn't do your homework.
uh
Answers
Answer:
B) If you don't do you homework, then you can't go to the movies
11
Which improper fraction is equivalent to 5 ?
40
Answers
Answer:
211/40, B
Step-by-step explanation:
Make it an improper fraction:
5 x 40 = 200, 200 + 11 = 211
211/40, B
Points D, B, and E are collinear. Find the value of a so that points A, B, and C
are collinear.
Answers
Answer:
Since A, O and B are collinear,
i.e.,
∠
A
O
B
=
180
∘
or,
∠
A
O
D
+
∠
D
O
C
+
∠
B
O
C
=
180
∘
(
x
−
10
)
∘
+
(
4
x
−
25
)
∘
+
(
x
+
5
)
∘
=
180
∘
Or,
x
+
4
x
+
x
−
10
∘
−
25
∘
+
5
∘
=
180
∘
Or,
6
x
−
30
∘
=
180
∘
Or,
6
x
=
180
∘
+
30
∘
=
210
∘
Or,
x
=
210
∘
6
=
35
∘
∠
B
O
C
=
x
+
5
∘
=
35
∘
+
5
∘
=
40
∘
Adrian drives 14 miles east on Broadmoor and 10 mies south on 5th street each day to get to work. Find the number miles Adrian would drive if he took the diagonal path along Skyline Drive instead? NO LINKS!!!
Answers
Answer:
just add all the numbers
Step-by-step explanation:
please follow me,
follow you back...
Answer:
The answers is 17.2 miles
Step-by-step explanation:
Please help!!!! How do you write 0.0174 in scientific notation?
Answers
Answer:
1.74*10^-2
Step-by-step explanation:
use as decimal with ones place times 10 to the powe of minus something
Karen used a fork that had a mass of about 28 ?
A)grams
B)kilograms
Answers
Answer:
is A
Step-by-step explanation:
I hope and this helps you
can anyone solve this?
Answers
Answer:
the yo u thichi cutis lo u you
Answer:
its the same thing look at the coordinates
Step-by-step explanation:
What is the radius of a circle with a diameter of 24 m?
Answers
12 m
Step-by-step explanation:
24/2 = 12
I hope this helps you, have a good day!
Answer:
answer: 12
Step-by-step explanation:
The radius is just half of the diameter since the diameter is 24 we just have to divide that by 2 to get the answer so 24 ÷ 2 = 12 so 12 is the radius Hope that helps!
heelllppp please!!!!!!!
Answers
Answer:
7.9
Step-by-step explanation:
area of circle equals π× 5 = 15.7
area of half of the circle equals 15.7÷2
=7.85
now round it of and it's 7.9
Please help !!!!!!!!!!!
Answers
Answer:
84
Step-by-step explanation:
6×6 is 36, and there are two of these squares so the area of the squares together is 72. 3×4 is 12 and 72+12 is 84. Hope this helps :)
No problem