Answer:
[tex]c = 5[/tex]
Step-by-step explanation:
Given
[tex]f(c) = M[/tex]
[tex]f(x) = x^2 - x + 1[/tex]
[tex]Interval: [1,8][/tex]
[tex]M = 21[/tex]
Required
Find c using Intermediate Value theorem
First, check if the value of M is within the given range:
[tex]f(x) = x^2 - x + 1[/tex]
[tex]f(1) = 1^2 - 1 + 1[/tex]
[tex]f(1) = 1[/tex]
[tex]f(x) = 8^2 - 8 + 1[/tex]
[tex]f(x) = 57[/tex]
[tex]1 \le M \le 57[/tex]
[tex]1 \le 21 \le 57[/tex]
M is within range.
Solving further:
We have:
[tex]f(c) = f(x) = M[/tex]
[tex]f(x) = 21[/tex]
Substitute 21 for f(x) in [tex]f(x) = x^2 - x + 1[/tex]
[tex]21 = x^2 - x + 1[/tex]
Express as quadratic function
[tex]x^2 - x + 1 - 21 = 0[/tex]
[tex]x^2 - x - 20 = 0[/tex]
Expand
[tex]x^2 + 4x - 5x - 20[/tex]
[tex]x(x+4)-5(x+4)=0[/tex]
[tex](x - 5)(x+4) = 0[/tex]
[tex]x - 5 = 0[/tex] or [tex]x + 4= 0[/tex]
[tex]x = 5[/tex] or [tex]x = -4[/tex]
The value of [tex]x = -4[/tex] is outside the [tex]Interval: [1,8][/tex]
So:
[tex]x = 5[/tex]
[tex]f(c) = f(x) = M[/tex]
[tex]f(c) = f(5) = 21[/tex]
By comparison:
[tex]c = 5[/tex]
Solve the inequality
-5x > 35
Answer:
x is greater than or equal to -8
Step-by-step explanation:
35/-5 is 7 and since the sign is greater than that means that -5x will be greater than 35
PLEASE ANSWER QUICKLY THX
Answer:
a. 5sqrt5 (sqrt 5 * sqrt 5 * sqrt 5 = sqrt125 = 5sqrt5)
b. 10sqrt10 (sqrt10 * sqrt10 * sqrt10 = 1000sqrt = 10sqrt10)
c. xsqrtx
Twelve less than the cube of the sum of six times a number and three.
Answer:
[tex](6 * n + 3)^{3}[/tex] - 12
Step-by-step explanation:
Twelve less than the cube of the sum of six times a number and three.
1. Change the words into numbers and math symbols.
Twelve = 12
Less than = subtract -
sum of six times a number and three = (6 * n + 3)
cube = exponent 3
2. Write the problem.
[tex](6 * n + 3)^{3}[/tex] - 12
determine whether the ordered pair (3,-5) is a solution to the system -2x+y=-11 & -2x-2y=-4
Answer:
No.
Step-by-step explanation:
-2(3)-5=-6-5=-11
-2(3)-2(-5)=-6+10=4, not -4.
A fireman has 12 ft. ladder and a 16 ft ladder. He leans the 12 ft ladder against a house at an angle of 57 degrees. He leans the 16 ft ladder against a house 30-degree angle. Which ladder will he climb to the higher height? Explain the answer please
Answer:102
Step-by-step explanation:
Simplify the expression 4(5a+b)−9a+3
Answer: 11a+4b+3
Step-by-step explanation: 4(5a+b)−9a+3
(4)(5a)+(4)(b)+−9a+3
20a+4b+−9a+3
(20a+−9a)+(4b)+(3)
11a+4b+3
Given the statement ΔQRS ≅ ΔXYZ, list all congruent parts you can conclude about the two triangles. Explain.
Answer:
Side QR is congruent to Side XY.
Side RS is congruent to Side YZ.
Side SQ is congruent to Side ZX.
Angle Q is congruent to Angle X.
Angle R is congruent to Angle Y.
Angle S is congruent to Angle Z.
Step-by-step explanation:
Side QR is congruent to Side XY because triangle QRS is congruent to triangle XYZ and each point of a triangle is in corresponding order with a point of the other triangle. For example, Q matches up with X since they both are listed first in their respective sequence.
Find ML.
3x + 11
45
10x - 12
Please help me! I will mark brain list if you help :) thank you!
Answer:
58
Step-by-step explanation:
45=((3x+11)+(10x-12))÷2
90=13x-1
13x=91
x=7
ML=10(7)-12
=58
Using midline interval, the value of ML is 58.
What is midline interval?
The distance from the "midline of the interval to either end line is called midline interval".
According to the question,
The line JK is 3x+11, the line ML is 10x - 12. In order to find the value of ML.
The formula to calculate value of ML is midline value = [tex]\frac{(x1 + x2)}{2}[/tex].
Let x₁ = 3x + 11 and x₂ = 10x - 12
45 = [tex]\frac{(3x + 11) + (10x - 12 )}{2}[/tex]
90 = 3x + 11 + 10x -12
= 13x -1
13x = 91
x = 7
Substitute x = 7, in equation x₂ we get 10(7) - 12 = 70 - 12 = 58.
Hence, using midline interval the value of ML is 58.
Learn more about midline interval here
https://brainly.com/question/12992302
#SPJ2
When ringing up a customer, a cashier needs 7 seconds to process payment as well as 1.5 seconds to scan each item being purchased. If it takes 28 second s to ring up a customer ,how many items are being purchased?
Answer:
14 items
Step-by-step explanation:
What we know:
- it takes 7 seconds to process the payment
- for every item, it takes 1.5 seconds to scan
- in total, it took 28 seconds to ring up the customer
With these pieces of information, we can construct the following equation:
[tex]28=1.5x+7[/tex] when [tex]x[/tex] is equal to the number of items there is
Subtract both sides by 7
[tex]28-7=1.5x+7-7\\21=1.5x[/tex]
Divide both sides by 1.5
[tex]\frac{21}{1.5} =\frac{1.5x}{1.5} \\14=x[/tex]
Therefore, 14 items were being purchased.
I hope this helps!
Four-fifths of a spinach casserole is leftover after Sam has lunch. Jackie and Alicia each take 1/2 of the left over casserole. Jackie eats only 7/8 of her portion. What fraction of a whole casserole did Jackie eat? Express your answer as a simplified fraction.
Answer:
1/4
Step-by-step explanation:
Casserole received by Jackie and Alicie = 1/2 x 3/4 = 3/8 of the whole
Portion eaten by Jackie = 2/3 x 3/8 = 1/4 of the whole
question is the picture pls help if you can!!
Answer:
median = 2
mode = 0
Range = 10
Step-by-step explanation:
mark branliest
and if you need help just ask
In ΔXYZ, z = 81 cm, ∠Y=139° and ∠Z=6°. Find the length of y, to the nearest 10th of a centimeter.
Answer:
508.4
Step-by-step explanation:
This is on delta math
Answer:
508.4
Step-by-step explanation:
delta math
show how 4x 3/4 can be solved using multiplication and division
[tex]\frac{4}{1}[/tex] × [tex]\frac{3}{4}[/tex] = [tex]\frac{12}{4}[/tex]
[tex]\frac{12}{4}=3[/tex]
Division:[tex]4[/tex] ÷ [tex]\frac{4}{3}[/tex] OR [tex]\frac{4}{\frac{4}{3} }[/tex] = 3
what is x if 3x X= 24
Answer:
x is 8........ correct answer
ANSWER ALL THE QUESTIONS I HAVE PLEASE AND I'LL LEGIT GIVE U ALL MY POINTS IF I CAN AND GIVE YOU BRAINLIST. I NEED THAT STUFF DUE FRIDAY. PLEASE HELP PLEASEEEEEEEEE. CLICK ON MY PFP AND GO TO QUESTIONS ALL THE QUSTIONS I HAVE WILL BE ON THERE. PLEASE AND TY. AND TO YOU USERS WHO DELETE MY STUFF YALL ACT AS IF I CANT JUST POST IT AGAIN
Answer:
danggggg *_*
Step-by-step explanation:
Organize the information given in a two-way table.
Only Likes Sudoku
Only Likes Two-Way Tables
Likes Both
Total
Female
A
B
Male
D
Total
C
100 people were asked if they like playing the puzzle game sudoku, solving two-way tables, or both. 4% of the people only liked sudoku. 50% of the people who only liked sudoku were female. 90% of the people liked both. 60% of the people who liked both were female. 40 men were involved in the study.
Which of the following represents the data in the table?
choices
A. a = 2, b = 36, c= 4, d = 6
B. a = 4, b = 54, c = 4 , d = 6
C. a = 4, b = 36, c = 4, d = 2
D. a = 2, b = 54, c = 4, d = 2
Help! - Conjectures With Angles
Tommy has made a conjecture about the sum of two Obtuse angles.
' The sum of two obtuse angles cannot be an obtuse angle'
Do you agree with Tommy?
explain your reasoning
I agree with Tommy because the sum of the smallest obtuse angles (91+91⁰) is 182⁰ which is a reflex angle, not obtuse. The other obtuse angles will be bigger and so will not be obtuse either.
work out the surface area of this sphere give your answer to 1 decimal place it is 2.6cm
if you can help again I will be soo appreciated thank you
Answer:
SA : 84.9cm³
Step-by-step explanation:
Formula : 4×pi×r² as well as 4pi r²
4 x pi x 2.6²=84.94866535
1dp : 84.9
find the slope of the line that passes through the points (1,-4) and (3,-1)
Answer:
The slope is 3/2 or 1.5
Step-by-step explanation:
The slope is Rise/Run.
The difference in y-values, –1 -(-4) =3 is the rise.
the difference in x-values, 3 –1 = 2 is the run.
fine
3. a) The area of a rectangle is 15 cm. If its length is 5
breadth Hint angin breadth - Area of rectangle
Answer:
Breadth = 3 cm
Step-by-step explanation:
Given:
Area of rectangle = 15 cm²
Breadth = a
Length = 5 cm
Find:
Breadth
Computation:
Area of rectangle = l x b
15 = 5 x a
Breadth = 3 cm
5x÷5 show the steps pls 5xdivided by 5
Answer:
x
Step-by-step explanation:
In this equation (5x/5), x will end up being by itself because 5/5 = 1. The 5's cancel out and it leaves x by itself.
5x/ 5 =0
x=5/5
X=1
Hence the answer is X=1...
3)
Ten students from a class participated in a math quiz. The scores obtained by
them were recorded as follows.
11, 6, 7, 13, 1, 13, 16, 7, 13, 16
Mean :
Median :
Mode :
Range :
Answer:
Mean: 10.3
Median: 12
Mode: 13
Range: 15
Step-by-step explanation:
First, let's define what all these terms mean.
Mean is the average of all the numbers in a set of data. Median is the number in the middle of a range whenever the numbers are put in ascending order. If there are two numbers in the middle instead of one, then take the average of those two numbers. Mode is the number that occurs the most in the set of data. Range is the difference between the largest and the smallest number in a set of data.
To make things a little easier overall, let's just go ahead and put all our numbers in ascending order, which will be as follows: 1, 6, 7, 7, 11, 13, 13, 13, 16, 16.
To find the mean, just add up all the numbers and divide by how many there are. So we'll add 1 + 6 + 7 + 7... and so on to get a total of 103. Next, we'll divide that number by 10 since there are 10 students. This gives us a mean of 10.3.
Next, we'll find the median. To find this, just figure out which number(s) is in the center of your data. Since we have an even number of terms (10), we'll have two numbers in the middle, being 11 and 13. To find our median from here, just add 11 and 13 and then divide by 2. 11 + 13 = 24 and then 24 / 2 = 12. This means that our median is 12.
Next, we'll find the mode. The mode is the number that is seen the most in a set of numbers. In our set, we see that there are three 13s. Since 13 is the most frequently used number in our set, this makes it the mode.
Finally, we'll find the range. The range is just the largest number in the set minus the smallest number in the set. In our set, 16 is our largest number and 1 is our smallest. Just do 16 - 1 = 15 and we'll see that 15 is the range of the set. Hope this helps!
write an equation of the line that passes through (2, -4) and (0, -4)
During a school fundraiser contest, Georgia sold 49 coupon books and Molly sold 79 coupon books. The total number of coupon books sold during the contest was 354 books. What's the ratio of the number of coupon books that Georgia and Molly sold to the total books sold? Question 19 options: A) 128∕177 B) 79∕354 C) 49∕354 D) 64∕177
I would say it’s A
____________________________________________________
What the expression is?
Answer:
29
Step-by-step explanation:
Answer:
The answer is 29
Need help! (5 3/4 1 5/6) - 6 7/12
Answer:
Step-by-step explanation:
7/12 / 3/10 = 35/
18
= 1 17/
18
≅ 1.9444444
please provide me insight and answer to the attached photo
I need help with this ASAP
Answer:
12.56637061 ?????
Step-by-step explanation:
what is (9+8/7+6+89+65698-7875+77-88)*999999 you will give you 100 and brainlist if it is also incorrect
The answer is 57917084940
Step-by-step explanation:
1) Simplify 9 + 8/7 + 6 + 89 + 65698 - 7875 + 77 - 88 to 405420/7.
[tex] \frac{405420}{7} \times 999999[/tex]
2) Use this rule: a/b × c = ac/b.
[tex] \frac{405420 \times 999999}{7} [/tex]
3) Simplify 405420 × 999999 to 405419594580.
[tex] \frac{405419594580}{7} [/tex]
4) Simplify.
[tex]57917084940[/tex]
Therefor, the answer is 57917084940.
Amanda has three different colored pens in her book bag: blue, green and purple. The probability of randomly choosing a blue pen from Amanda’s book bag is 40%. The probability of randomly choosing a green pen from Amanda’s book bag is 10%.
Suppose Amanda has 20 pens total in her book bag. How many blue pens would Amanda expect to see in her bag?
Answer:
If there are 20 pens in total, and the probability of choosing a blue pen is 40%, then there are 0.4 times 20, or 8 blue pens in Amanda's bag.
Let me know if this helps!
The number of blue pens would Amanda expect to see in her bag is 8.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called the chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
In our daily time, there are several instances in the everyday world where we may need to draw conclusions about how everything will turn out.
Total number of pens = 20
Probability of choosing blue pen = 40%
Since,
Probability = Desire item / sample space
So,
Probability of choosing blue pen = Number of blue pens / total number of pen
0.40 = Number of blue pens / 20
Number of blue pens = 0.40 × 20 = 8
Hence "the number of blue pens would Amanda expect to see in her bag is 8".
For more information about the probability,
brainly.com/question/11234923
#SPJ2