Answers
Answer: Choice B
h(c) = 1 for at least one c between -3 and 4
====================================================
Explanation:
Draw an xy axis system. Plot the points (-3,-1) and (4,2) on this grid. These points come from the fact that h(-3) = -1 and h(4) = 2. These are the endpoints of the h(x) function.
Next, draw horizontal lines through both points. Also, draw vertical lines through the two points as well. A rectangle will form.
The region inside this rectangle is all we care about.
We're told that h(x) has endpoints mentioned earlier, and h(x) is continuous, so that means we have some curve or line through the two points. One such example is shown below. There are infinitely many possible curves to draw out as long as they stay in the rectangle.
----------------------
After you have your h(x) function curve drawn, draw a horizontal line through y = 1 on the y axis. This is the dashed line in the diagram below.
This horizontal line crosses the green h(x) curve at one point or more. In my example, it does so at one point only. However, you could easily draw h(x) so that it crosses y = 1 as many times as you want (just have it squiggle up and down multiple times).
This shows that h(c) = 1 is possible when [tex]-3 \le c \le 4[/tex]. Here c is playing the role of x since it is the input of a function. The h(c) is the output, so that's the y value.
This says that for some input between -3 and 4, it's possible to get an output of 1.
-------------------------
Here's a real world example of the intermediate value theorem.
Let's say the endpoints are A and B, and they are two towns.
The h(x) curve is a road connecting the towns.
To go from A to B, or vice versa, we need to cross over some border that is between the towns. The border in this case is the dashed horizontal line in the diagram.
side note: A special use of the intermediate value theorem is to show that a root exists on some interval (if you know the function changes between positive to negative, or vice versa).
Related Questions
Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-2, 2)A(−2,2)A, left parenthesis, minus, 2, comma, 2, right parenthesis, B(6, 2)B(6,2)B, left parenthesis, 6, comma, 2, right parenthesis, C(6, 3)C(6,3)C, left parenthesis, 6, comma, 3, right parenthesis, and D(-2, 3)D(−2,3)D, left parenthesis, minus, 2, comma, 3, right parenthesis.
What is the area of rectangle ABCDABCDA, B, C, D?
Answers
The area of rectangle ABCD with the given vertices is: 8 units².
What is the Area of a Rectangle?Area of rectangle = (length)(width).
Given the following vertices:
A(-2, 2)B(6, 2)C(6, 3)D(-2, 3)Area = (length)(width) = (AB)(BC)
AB = |-2 - 6| = 8 units
BC = |2 - 3} = 1 unit
Area of rectangle = (8)(1) = 8 units².
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Answer: 8
Step-by-step explanation:
Find the value for x that makes the given equation true. - -4(3x – 7) + 5x = -2x + 8
Answers
Answer:
Okay this might be slightly confusing but I'll try to make it simple. x = -10
Step-by-step explanation:
-4 ( 3x - 7 ) + 5x = -2x + 8 1. get rid of parenthesis first. -4 times 3x = -12x and -4 times -7 is 28
-12x + 28 + 5x = -2x + 8 2. Combine any like terms on each side of the equation. -7x + 28 = -2x + 8 3. Get rid of the smallest x value by adding to both sides -7x
+7x +7x
28 = -2x + 8 4. subtract 8 from both sides to get rid of it. (you wanna get x alone)
-8 -8
20 = -2x 5. Divide both sides by -2 to get 1x (which is x)
/-2 /-2
x = -10
A baseball player starts the season with 77 career home runs. Ten games into the
season, he has hit 2 home runs. Assume he continues at this pace. Write an
equation for the number of career home runs he has hit. How many career home
runs would you expect him to have at the end of the season (162 games)?
Answers
If there are a total of 162 games, and every then games the player hits 2 home runs, we can divide the total amount of games by 10 then multiply the quotient by 2.
162 / 10 is approximately 16.
16 × 2 = 32
32 + 77 = 109 career home runs
Using the slope intercept relation, the required equation and the number of home runs at season end would be ;
y = 0.2x + 77109Recall :
y = bx + cc = initial number of hime runs = 77b = slope y = total career home runs x = number of games playedSlope, b = 2 home runs per 10 games = 2/10 = 0.2
The expression can be represented thus:
y = 0.2x + 77Number of home runs at the end of the season :
x = 162
y = 0.2(162) + 77
y = 32.4 + 77
y = 109.4
y = 109
Hence, Total number of hime runs would be 109.
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If SV is a perpendicular bisector of RT, which statement is true?
Answers
Answer:
The correct answer is A
Step-by-step explanation:
PLEASE ANSWER FAST.
The question is in the picture.
(question 24)
Answers
Answer:
As the values of x increase both function decrease in value.
Step-by-step explanation:
Find two consecutive integers whose sum is eleven less than three times the smaller integer.
Answers
Answer:
If you call the smaller integer "x" and the greater integer "y", then:
x+y=3x-11 The sum of the two is 11 less than 3 times the smaller
y=x+1 Because they are consecutive, the greater must be 1 more than the smaller
Then you can solve for x:
x+(x+1)=3x-11 Substitute x+1 for y
2x+1=3x-11 Combine like terms
2x+12=3x Add 11 to both sides
12=x Subtract 2x from both sides
The smaller integer is 12, thus the greater integer is 1 more or 13.
Check:
12+13=3(12)-11
25=36-11
25=25 Yes, so the integers are 12 and 13
Step-by-step explanation:
thats pretty much it
hii i need help with a geometry problem. the picture is attached. i'll mark you brainliest!!
Answers
Answer:
i would wanna say the first one
Step-by-step explanation:
∆GAS ≅ ∆IOL by rule ASA , SAA
We say that ∆GAS ≅ ∆IOL because m∠G = m∠I , m∠A = m∠L and AS = LO ( which means that these triangles are congruent under the ASA or SAA congruence postulate . )
Therefore ,
∆GAS ≅ ∆ILO by rule ASA , SAAClue 1: The GCF of the mystery pair is 7. Clue 2: The LCM of the mystery pair is 70. Clue 3: Both of the numbers in the mystery pair have two digits. Clue 4: One of the numbers in the mystery pair is odd and the other is even. What is the mystery pair?
Answers
Answer:
14 and 35 I believe.
Since the GCF of 14 and 35 is 7, the LCM is 70 (14×5 and 35×2), they both have 2 digits, and one is even (14) and the other is odd (35).
I hope this helped!
The mystery pair would be required for numbers 14 and 35.
What is HCF?The highest common factor is defined as the set of numbers with the highest common multiple. The highest positive integer with more than one factor in the set is HCF.
What is Prime Factorization?Prime Factorization is defined as any number that may be expressed as a product of prime numbers that has been said to be prime factorized. Any integer with exactly two factors 1 and the number itself. is said to be a prime number.
We need to write 70 as the product of its prime factors, which is 70.
⇒ 2 × 5 × 7
14 × 5 and 35 × 2
Given that the GCF of the mystery pair is 7
And the LCM of the mystery pair is 70.
Here the GCF of 14 and 35 would be 7
As per the given condition,
The required numbers in the pair have two digits,
Therefore, the even number is 14, and the odd is 35.
Hence, the mystery pair would be required for numbers 14 and 35.
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Kacey rode her bicycle 227 miles in 7 hours. How many miles did kacey travel per hour?
Answers
Answer:
39
Step-by-step explanation:
Answer:
32.4825
hope this helped :)
Find the measure of the missing value in the
pair of similar polygons. (Shapes not drawn to
scale.)
17.5 ft
25 ft
25 ft
w
18 ft
Answers
Answer:
12.6
Step-by-step explanation:
The two left sides have lengths, so this allows you to establish the ratio of the lengths of the sides of the triangles,
left triangle : right triangle
ratio = 25 : 17.5
The bottom sides are also in the same ratio.
ratio = 18 : w
Write a proportion by setting the ratios equal and solve for w.
25/17.5 = 18/w
Cross multiply.
25w = 17.5 * 18
25w = 315
w = 12.6
Answer: 12.6
-5 -2q = 9
please help me
Answers
Answer:
q = -7
Step-by-step explanation:
-5 - 2q = 9
Add 5 to both sides of the equation.
-2q = 14
Divide both sides by -2.
q = -7
Lerna's Hydra is a mythological character that appears in some stories such as the 12 Tasks of Hercules. The Hydra was a one-headed monster but when it is cut off, 2 more heads grow in its place. If a hero tried to conquer it by cutting off all of its heads every day, how many heads would the Hydra have on the third day? And at the end of 10 days of trying to kill it? *
Answers
Answer:
Step-by-step explanation:
Initially the monster is one-headed, when it is cut off, 2 more heads grow in its place, when the two heads are cut off, 4 will grow in its place. This will go on an on and the amount of heads that grows each day will form a geometric sequance as shown;
1, 2, 4...
The nth term of an arithmetic sequence is expresses as;
[tex]T_n = ar^{n-1}[/tex] where;
a is the first term
r is the common ratio
n is the number of terms
To get the number of heads that the Hydra have on the third day, we will have to find the fourth term of the sequence since the first cutting was done the next day (second day).
from the sequence above;
a = 1
r = 2/1 = 4/2 = 2
T4 = 1(2)^{4-1}
T4 = 2^3
T4 = 8
Hence the hydra will have 8 heads on the third day.
To know the number of heads at the end of 10 days, we will find the 11th term of the progression
T11 = 1(2)^{11-1}
T4 = 2^10
T4 = 1024
He will have 1024 heads after 10 days of trying to kill the monster.
The number of heads that would the Hydra have on the third day is 8
And, at the end of 10 days of trying to kill it is 1024.
The calculation is as follows:a = 1
r = 2 by 1 = 2
T4
= 8
So the hydra will have 8 heads on the third day.
Now
To know the number of heads at the end of 10 days, we will determine the 11th term of the progression
= 1024
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A 24-roll package of toilet paper is $14.88. If the price per roll stays the same, what would be the price of a ten-roll package?
Answers
Answer:
Step-by-step explanation:
1. Factor the expression completely 20x^4+80x^3-5x^2-20x
Answers
Answer:
5x(x+4)(2x+1)(2x−1)
Step-by-step explanation:
If you could travel back in time one year, what advice would you give yourself?
10 sentence required for the brainlleist if 2 people answer
1
Answers
Answer:
To keep my head up and focus on the good instead of the bad. To understand that life gets hard. I would remind myself that I'm worth it and I am a strong person. I would tell myself that whatever bad happens, something good will come out of it. To remind myself that all the bad I've been through is only making me a stronger person. And I would remind myself that everything happens for a reason, whether I see it now or I see it later on down the road. I would remind myself that it's never too late to change for the better. I would tell my self "you made it this far, your strong". And I would tell myself that I can do whatever I put my mind to. And that nothing is impossible.
Hope this helps :)
Step-by-step explanation:
If someone could travel back in time one year, the advice I would give myself would be to embrace change and adaptability. The world is constantly evolving, and it is important to stay open-minded and flexible in order to thrive.
I would encourage myself to be proactive in seeking opportunities for growth and learning, even if they seem daunting or unfamiliar at first. Additionally, I would remind myself to prioritize self-care and mental well-being. It is easy to get caught up in the hustle and bustle of daily life, but taking time for oneself is crucial.
Whether it be spending time in nature, practicing mindfulness, or pursuing hobbies and interests, nurturing my own happiness should be a priority. Lastly, I would advise myself not to dwell on past mistakes or missed opportunities.
Every setback is an opportunity for growth, and it is important to learn from these experiences rather than letting them define me. By adopting a positive mindset and focusing on the present moment, I can ensure that I make the most of every opportunity that comes my way.
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how to find the sequence
X. Y
0. 0
1. 1.5
2. 4
3. 7.5
4. 12
Answers
Answer:
they add one half to each number
Pleasssssse help meeeeee
Answers
Answer: [tex]x \geq 3[/tex]
The graph has a closed circle pointing to the right
A really fast armadillo can cross a road that is 20.00 meters wide in 10.00 seconds. What is the speed of the armadillo?
A. 2.0 m/s
B. 10 seconds
c. 10 meters
D. 200 m/s
Answers
Answer:
A
Step-by-step explanation:
Speed= Distance/time
20m/10s=2 m/s
Help me please
Find the slope
Answers
Answer:
this is a negative slope.
Step-by-step explanation:
put these fractions to least to greatest 8/9 6/9 5/9 7/9 please help
Answers
help!!!! due now ( right answer's only)
Answers
Answer:
Minimum, Vertex(1,-7) and sorry what do you mean by aos? i dont get that please type in the comments I'll answer that too. Hope you understand the rest
Step-by-step explanation:
The vertex of a parabola means the stationary point/turning point which is denoted by the following:
[tex]x=\frac{-b}{2a} \\[/tex]
and for y we just simply put the value of x that we get into the equation so lets get started
The equation [tex]y=x^2-2x-6[/tex] is a quadratic equation
and if we compare it by the standard form [tex]y=ax^2+bx+c[/tex] we get the following values
a=1 , b=-2 , c=-6
and now for the vertex
[tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-(-2)}{2(1)} \\x=\frac{2}{2} \\x=1[/tex]
and now for y
[tex]y=x^2-2x-6\\y=(1)^2-2(1)-6\\y=1-2-6\\y=-7[/tex]
so the vertex is (1,-7)
and the graph is minimum not maximum because the value of a is greater than 0 if the value of a>0 then the graph is minimum and if the value of a<0 meaning a is negative the graph is maximum and here in the equation a=1 which means a>0 then our graph is minimum.
Answer:
hey we were talking in the comment section with someone else 16 min ago and that chat maxed out so he made another one and wants you to come back. Just letting you know.
Step-by-step explanation:
Suppose a person starts the day by drinking 3 cups of coffee containing 130 mg of caffeine EACH.
Let C = mg of caffeine remaining in the body and let t = hours since the 390 mg of caffeine was consumed. Write a function C(t) that expresses the amount of caffeine remaining in the body as a function of time.
Answers
Answer:
C = t * 3
Step-by-step explanation:
ILL MARK BRAINLIST IF YOU GET IT RIGHT .which expression is equivalent to s - t?
Answers
Answer:
s(6)×t(6)
hope this helps
Are there supposed to be answer choices?
i know it’s a lot to ask for but what are the answers for all of these you get 100 points and you get marked brainliest
Answers
Find the product
(7+2u) (7-2u)
Options:
a) 49+4u
b) 49-4u(square root sign)
c) 4u(square root sign) - 49
Answers
Answer:
b
Step-by-step explanation:
if you mean squared and not square root, then it would be b because if you factor it back out, you will get the original expression back because of the subtraction of perfect squares.
Answer:
b) [tex]\boxed{\bold{(7+2u)(7-2u)=49-4u^2}}[/tex]Step-by-step explanation:
[tex](7+2u) (7-2u)=(7)(7)+(7)(-2u)+(2u)(7)+(2u)(-2u)=\\\\=49-14u+14u-4u^2=\ \underline{49-4u^2}[/tex]
What is 3/5 as a percent?
Answers
Answer:
3/5 as a percent is 60% hope that helps
1. What is 10% of 75?
Answers
Answer:
7.5
Step-by-step explanation:
i hope this helps!!
Nine years ago, Tarah opened a savings account with her bank. She started with a balance of $359 and has not made any withdrawals or deposits since then. If her interest rate is 8% each year, how much interest has accrued using simple interest?
Total Interest = $
What is Tarah's new total balance?
New Balance Total = $
Answers
Answer:
Total interest = $28.72
New balance = $ 387.72
Explanation: Tarah has $359 in the bank. To find the amount of interest, multiply 359 by .08.
She gets $28.72 interest annually.
In one year, she will make $387.72. (Add the total interest to her original balance)
Plz mark brainliest:)
Express the following number as a decimal:
2 x 10^-6
Answers
Answer:
0.000002
Step-by-step explanation:
2* 10^-6
is the same as
2 * 0.000001
which is
0.000002
Answer:
The answer is: 0.000002
Step-by-step explanation:
Have a great day!
quadrilateral ADCD Is the image of quadrilateral ABCD UNDER TRANSLATION
Answers
Answer:
Step-by-step explanation:
espera y termino y te ayudo vale que me falta poco vale
Answer:
ABCD-AEFG
Step-by-step explanation: