Use the Intermediate Value Theorem to show that the polynomial function has a zero in the given interval.
Answers
Given:
[tex]f(x)=10x^4-4x^2+5x-1;\lbrack-2,0\rbrack[/tex]Using the intermediate value theorem,
[tex]\begin{gathered} f(x)=10x^4-4x^2+5x-1 \\ f(-2)=10(-2)^4-4(-2)^2+5(-2)-1 \\ f(-2)=160-16-10-1=133 \\ \text{and} \\ f(0)=10(0)^4-4(0)^2+5(0)-1=-1 \end{gathered}[/tex]So, we have find value c between [-2,0].
[tex]\begin{gathered} f(x)=0 \\ 10x^4-4x^2+5x-1=0 \\ \Rightarrow x=-1\text{ it satisfies the equation} \\ \text{Also, -1}\in\lbrack-2,0\rbrack \end{gathered}[/tex]It shows that, the above polynomial function has zero in the given interval.
Also, the value of f(-2) = 133
Related Questions
Mrs. Thornton asked her students to draw a figure with a perimeter of 4x + 4. Shown below are 4 drawings madeby her students. (They are not drawn to scale.) Which one is NOT correct?А2x+11B2x2C.X + 4XDX+ 1X+ 1сdba
Answers
The perimeter is 4x+4
the formula of the perimeter of a rectangle is
[tex]P=2l+2w[/tex]for the first drawing
[tex]P=2(2x+1)+2(1)=4x+2+2=4x+4[/tex]It is correct
for the second drawing
[tex]P=2(2x)+2(2)=4x+4[/tex]It is correct
for the third drawing
[tex]P=2(x+4)+2x=2x+8+2x=4x+8[/tex]It is not correct
for the fourth drawing
[tex]P=2(x+1)+2(x+1)=2x+2+2x+2=4x+4[/tex]it is correct
As we can see the incorrect draw is C.
What’s 51,053 minus 12,947?
Answers
Answer:
The answer you're looking for would be 38,106.
Step-by-step explanation:
May I have Brainliest please? I am so close to getting my next ranking! I just need 3 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
- 12,947
—————
38106
Use gaussian elimination to solveThe buries pay their babysitter $5 per hour before 11 p.m. and $7.50 after 11p.m. One evening they went out for 5 hours and paid the sitter $35.00. What time did they come home?
Answers
Let m represents the number of hours the buries spent before 11p.m
Let n represent the number of hours the buries spent after 11p.m
m + n = 5 -----------equation (1)
5m + 7.5n = 35 -------equation (2)
Using Gaussian elimination method to solve the simultaneous equations, we have
[tex]\begin{bmatrix}{1} & {1} & {5} \\ {5} & {7.5} & {35} \\ {} & {} & \end{bmatrix}-\begin{bmatrix}{\square} & {\square} & {\square} \\ {\square} & {\square} & {\square} \\ {\square} & {\square} & {\square}\end{bmatrix}[/tex]The value of m = 1, while n = 4
This implies the buries spent 4 hours after 11 p.m
That means they come home by 3 a.m
Graph the solution set of each system of inequalities.19. 4x-y52x + 2y <6
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The graph is given by:
10,720MasteryLook at the image below.4Course suRatios, rateArithmetic10Course cheTest yourthe skillsWhat is the area of the triangle?
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The given triangle is not the regular drawing of a triangle. We need to identify the height and base.
From the diagram, the height = 10
base = 4
Substitute the values:
[tex]\begin{gathered} \text{Area of the triangle = }\frac{1}{2}\times\text{ 10}\times4 \\ \text{Area of the triangle = 20 units}^2 \end{gathered}[/tex]The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90%pure fruit juice. The company is attempting to produce a fruit drink that contains 75% pure fruit juice. How many pints of each ofthe two existing types of drink must be used to make 170 pints of a mixture that is 75% pure fruit juice?First fruit drink:pintsХ5?Second fruit drink: pints
Answers
Let
x ----> number of pints of the First fruit drink
y ----> number of pints of the Second fruit drink
we have that
x+y=170 -------> x=170-y ----> equation A
65%=0.65
90%=0.90
75%=0.75
so
0.65x+0.90y=0.75(170) -----> equation B
Solve the system of equations
substitute equation A in equation B
0.65(170-y)+0.90y=0.75(170)
solve for y
110.5-0.65y+0.90y=
Hello, I need help simplifying question 16 i please, thanks
Answers
Given -
i. 5cot²θ + 5
To Find -
Simplification =?
Step-by-Step Explanation -
We know that
[tex]cot\theta\text{ = }\frac{\cos\theta}{\sin\theta}[/tex]So, simply putting it in the given equation:
[tex]\begin{gathered} =\text{ }5\frac{\cos^2\theta}{\sin^2\theta}\text{ + 5 } \\ \\ =\text{ 5}\frac{\lparen\cos^2\theta+\sin^2\theta\rparen}{\sin^2\theta} \\ \\ We\text{ know taht }\sin^2\theta\text{ + }\cos^2\text{ = 1} \\ \\ So,\text{ } \\ \\ =\text{ }\frac{5}{\sin^2\theta} \end{gathered}[/tex]Final Answer -
= 5/sin²θ
how does you solve Vertices: (0,7), (0,-7) Co vertices: (2,0), (-2,0)
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As according to given conditions let us draw these 4 points on the graph:
So the center is (0,0)
So the equation is:
[tex]\frac{(x-0)^2}{4}+\frac{(y-0)^2}{49}=1[/tex]CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
The value of sin Ф will be [tex]2\sqrt{6} /5[/tex] .
What are trigonometric function?A right-angled triangle's angle can be related to side length ratios using trigonometric functions, which are real functions in mathematics. They are extensively employed in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more. The term "Circular" is another name for trigonometric functions. A triangle's angle functions can be used to define functions. It implies that these trig functions can be used to determine the relationship between a triangle's angles and sides. There are several trigonometric identities and formulas that show the relationship between the functions and aid in determining the triangle's angles. Here is an in-depth explanation of all these trigonometric functions and their formulas.
sin²Ф + cos²Ф = 1
sinФ = [tex]\sqrt{1 - 1/25}[/tex]
= [tex]2\sqrt{6} /5[/tex]
To know more about trigonometric function, visit:
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Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Find a) A ∩ B ∩ C. b) A ∪ B ∪ C. c) (A ∪ B) ∩ C. d) (A ∩ B) ∪ C.
Answers
b) AuBuC = {0,1,2,3,4,5,6,7,8,9,10}
c) (AuB)nC ; (AuB) = {0,1,2,3,4,5,6,8,10}
:. (AuB)nC = {4,5,6,8,10}
d) (AnB)uC ; (AnB) = {0,2,4,6}
:. (AnB)uC = {0,2,4,5,6,7,8,9,10}
What is the slope of a line that goes through (2,6) and (4,12)?
Answers
Answer:
Slope = 3
Explanation:
To determine the slope of the line that goes through the given points: (2,6) and (4,12), we use the slope formula.
[tex]\text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}[/tex]Substituting the points, we have:
[tex]\begin{gathered} \text{Slope}=\frac{12-6}{4-2} \\ =\frac{6}{2} \\ =3 \end{gathered}[/tex]The slope of the line is 3.
Find the distance between each pair of points using the distance formula - round to the nearest 10th
Answers
Explanation: Below we have the distance formula
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step 1: Now let's identify the values of the variable as follows
Step 2: Now we can substitute the values on the distance formula as follows
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(-4_{}-(-2))^2+(4_{}-0_{})^2} \\ d=\sqrt[]{(-4_{}+2)^2+(4_{}_{})^2} \\ d=\sqrt[]{(-2)^2+16^{}} \\ d=\sqrt[]{4^{}+16} \\ d=\sqrt[]{20} \\ d=4.472135955 \\ d\cong4.5 \end{gathered}[/tex]Final answer: So the distance between the pair of points rounded to the nearest tenth is 4.5
what is the x intercept?
Answers
Answer:
x intercept is -2
Step-by-step explanation:
If f(1) = 3, then what ordered pair is in f? (_,_)
Answers
Given:
if f(1) = 3
We are to find the ordered pair that is in f.
f(1) = 3 is a fuction.
f(1) = 3
Then,
f(x) = 3
f(x) = y
So,
f(1) = 3
Therefore,
x = 1, y = 3
So the ordered pair of f is (1, 3)
Leah just accepted a job at a new company where she will make an annual salary of $65000. Leah was told that for each year she stays with the company, she will be given a salary raise of $2500. How much would Leah make as a salary after 6 years working for the company? What would be her salary after t years? Salary after 6 years: Salary after t years:
Answers
Explanation
Step 1
let s represents the salaray
let t represents the number of years she works.
she will make an annual salary of $65000. Leah was told that for each year she stays with the company, she will be given a salary raise of $2500
hence.
[tex]S=65000+2500t[/tex]and, we have the function for the salary:
for example, after 1 year
it means, t=1
replace
[tex]\begin{gathered} S=65000+2500t \\ S=65000+2500\cdot1 \\ S=65000+2500 \\ S=67500 \end{gathered}[/tex]so After 6 years
it is, when t= 6
[tex]\begin{gathered} S=65000+2500t \\ S=65000+2500\cdot6 \\ S=65000+15000 \\ S=80000 \end{gathered}[/tex]I hope this helps you
Pizza Orders Pizza Corner sells medium andlarge specialty pizzas. A medium Meat Lovers pizza costs$10.95, and a large Meat Lovers pizza costs $14.95. OneSaturday a total of 50 Meat Lovers pizzas were sold, andthe receipts from the Meat Lovers pizzas were $663.50.How many medium and how many large Meat Loverspizzas were sold?
Answers
Let x = number of medium Meat Lovers pizza sold
Let y = number of large Meat Lovers pizza sold
The cost of a medium Meat Lovers pizza is $10.95
Hence, the cost of x medium Meat Lovers pizza is $10.95x
The cost of a large Meat Lovers pizza is $14.95
Hence, the cost of y large Meat Lovers pizza is $14.95y
Since the total cost of Meat Lovers pizza sold is $663.50
This
Answer:
Let x = number of medium Meat Lovers pizzas sold
Let y = number of large Meat Lovers pizzas sold.
The cost of a medium Meat Lovers pizza is $10.95
Hence, the cost of x medium Meat Lovers pizza is $10.95x
The cost of a large Meat Lovers pizza is $14.95
Hence, the cost of y large Meat Lovers pizza is $14.95y
Since the total cost of Meat Lover's pizza sold is $663.50
This
Step-by-step explanation:
Please help me with this problem:The data shows the number of grams of fat found in 9 different health bars.11, 11.5, 10.5, 17, 14.5, 14.5, 18, 17, 19What is the IQR (interquartile range) for the data? 6.25714.517.5
Answers
The interquartile range = 6.25
Explanation:The given dataset is:
11, 11.5, 10.5, 17, 14.5, 14.5, 18, 17, 19
Rearrange the data in ascending order
10.5, 11, 11.5, 14.5, 14.5, 17, 17, 18, 19
The number of terms in the data, N = 9
The lower quartile is calculated as:
[tex]\begin{gathered} Q_1=(\frac{N+1}{4})^{th}term \\ \\ Q_1=\frac{9+1}{4}^{th}term \\ \\ Q_1=2.5th\text{ term} \\ \\ Q_1=\frac{11+11.5}{2} \\ \\ Q_1=\frac{22.5}{2} \\ \\ Q_1=11.25 \end{gathered}[/tex]The upper quartile is calculated as:
[tex]\begin{gathered} Q_3=(\frac{3(N+1)}{4})^{th\text{ }}term \\ \\ Q_3=\frac{3(9+1)}{4}th\text{ terms} \\ \\ Q_3=7.5th\text{ term} \\ \\ Q_3=\frac{17+18}{2} \\ \\ Q_3=17.5 \end{gathered}[/tex]The interquartile range = Upper quartile - Lower quartile
The interquartile range = 17.5 - 11.25
The interquartile range = 6.25
An onion soup recipe calls for 3 2/3 cups of chopped onions Katrina has already chopped 1 1/3 cups of onions she wants to know how many more cups she needs to chop what X be the number of cups of onions Katrina still needs to chop write an equation to describe the situation
Answers
To determine the number of cups she still needs to chop we need to subtract the amount she already chopped to the amount she needs, then we have the equation:
[tex]x=3\frac{2}{3}-1\frac{1}{3}[/tex]This can be written as:
[tex]x+1\frac{1}{3}=3\frac{2}{3}[/tex]Now, we solve it:
[tex]\begin{gathered} x=3\frac{2}{3}-1\frac{1}{3} \\ x=\frac{11}{3}-\frac{4}{3} \\ x=\frac{7}{3} \end{gathered}[/tex]Therefore she needs to chop 7/3 more cups of onions.
Aline has a slope of -3/4 and a y-intercept of 5. Write an equation insiope-intercept for that could represent this situation."
Answers
Here, we want to write an equation in the slope-intercept form
Mathematically, we have this as;
[tex]y\text{ = mx + b}[/tex]b is the slope and m is the y-intercept
Thus, substituting the values we have in the question;
m = -3/4 and b = 5
Thus, we have the equation as;
[tex]y\text{ = -}\frac{3}{4}x\text{ + 5}[/tex]Mitsu borrowed $1,250. She made 36 payments of $45.15 each. Howmuch did she pay in interest?a. $375.40b. $162.54c. $1,625.40d. $37.54
Answers
Amount borrowed = $1,250
Amount paid per payment = $45.15
Number of times payment was made = 36
This implies
The total amount paid is
[tex]36\times\text{\$}45.15=\text{\$}1625.40[/tex]Hence, the total amount paid = $1,625.40
Interest is calculated using
Interest = Total amount paid - Amount borrowed
Hence, the interest is
[tex]\begin{gathered} I=\text{\$}1625.40-\text{\$}1250 \\ I=\text{\$}375.40 \end{gathered}[/tex]Therefore, the interest she paid is $375.40
a chemist has 30% and 60% Solutions of acid available how many liters of each solution should be mixed to obtain 120 liters of 34% acid solution
Answers
Answer:
104 litres of 30% solution and 16 litres of 60% solution.
Explanation:
Let us call x the litres of 30% solution and y the litres of 60% solution.
Now, we know that the end result is 120 litres of a solution; therefore, we have
[tex]x+y=120[/tex]Morover, we are also
A square coffee table has an area of 1936 square inches. What is the length of one side of the table?
Answers
The area of square is 1936 sq.inches.
Explanation :To find the side of the coffee table.
Use the area of square .
[tex]A=side^2[/tex]Substitute the value of area to find the side.
[tex]\begin{gathered} 1936=side^2 \\ \text{side}=\sqrt[]{1936} \\ \text{side}=44in \end{gathered}[/tex]Answer :Hence the length of one side of the table is 44 in.
To find the equation of a regression line, ŷ = ax + b, you need these formulas:Sya=rstb=ỹ alA data set has an r-value of 0.553. If the standard deviation of the x-coordinates is 3.996, and the standard deviation of the y-coordinates is 6.203,what is the slope of the line to three decimal places?A. 0.858B. 1.165C. 2.807D. 0.356
Answers
Solution
- The solution steps are given below:
[tex]\begin{gathered} r=0.553 \\ S_x=3.996 \\ S_y=6.203 \\ \\ \text{ We have been given that:} \\ a=r\frac{S_y}{S_x} \\ \\ \text{ Since }a\text{ is the slope, we have that:} \\ a=0.553\times\frac{6.203}{3.996} \\ \\ a=0.8584231...\approx0.858 \end{gathered}[/tex]Final Answer
The slope is 0.858
Answer:
.0858
Step-by-step explanation:
There are 110 calories per 177.4 grams of Cereal X. Find how many calories are in 246.5 grams of this cereal There are ? calories in 246.5 grams of this cereal ( round to the nearest whole number as needed )
Answers
We can solve this question by means of the rule of three, which can be stated as
[tex]\begin{gathered} 110\text{ calories ----------- 177.4 grams} \\ \text{ x ---------------- 246.5 grams} \end{gathered}[/tex]then by using cross-multiplication to calculate x, we have
[tex]x\cdot177.4\text{ grams=(110 calories)}\cdot(246.5\text{ grams)}[/tex]so, by dividing both sides by 117.4 grams, x is given as
[tex]\begin{gathered} x=\frac{\text{(110 calories)}\cdot(246.5\text{ grams)}}{177.4\text{ grams}} \\ x=152.54667\text{ calories} \end{gathered}[/tex]Therefore, by rounding this result to the nearest whole nuymber, there are 153 calories in 246.5 grams of cereal
write 77.56 as a scientific notation
Answers
The scientific notation/standard form of 77.56 can be represented below
[tex]7.756\times10^1[/tex]The logic behind it is we shift the dot backward until it get to the last number. The number of step we took represent the exponential of 10.
Please help me resolve this, I’m not able Part (a)
Answers
To determine the volume of a cylinder you can use the following formula:
[tex]V=\pi r^2h,[/tex]where h is the height, and r is the radius of the cylinder.
Substituting:
[tex]\begin{gathered} r=6ft, \\ h=9ft \end{gathered}[/tex]in the formula, you get:
[tex]V=\pi(6ft)^2(9ft).[/tex]Finally, you get:
[tex]V=324\pi ft^3.[/tex]Answer: [tex]324\pi ft^3.[/tex]19. A wooden box has 20 cm on each edge. Find its volume.A. 875 cu. cmB. 8 000 cu. cmC. 8 875 cu. cm
Answers
Given:
Length of the edge of wooden box = 20 cm
Required:
The volume of wooden box.
Explanation:
The volume of cubical box is given as,
[tex]\begin{gathered} Volume\text{ = Edge}^3 \\ Volume\text{ = 20 cm }\times\text{ 20 cm }\times\text{ 20 cm} \\ Volume\text{ = 8000 cm}^3 \end{gathered}[/tex]Answer:
Thus the volume of the wooden box is 8000 cu. cm. The correct answer is option B.
what is the solution for y=2x+2 and y = 3x. I need a system of equation.
Answers
The given system of equations are,
[tex]\begin{gathered} y=2x+2 \\ y=3x \end{gathered}[/tex]Equating both equation implies,
[tex]\begin{gathered} 2x+2=3x \\ x=2 \end{gathered}[/tex]Put 2 for x in the equation y=2x+2 implies,
[tex]\begin{gathered} y=(2\times2)+2 \\ y=6 \end{gathered}[/tex]The solutions are x=2 , y=6.
use the diagrams to answer the following questions Number 9
Answers
GIVEN:
We are given the circle with radius 5 units as shown in diagram number 9.
Required;
To determine the
(a) Diameter
(b) Circumference
(c) Area
Step-by-step solution;
The diameter of any given circle is twice the length of the radius.
This means for the circle given, we have;
[tex]\begin{gathered} Radius=5 \\ \\ Diameter=2\times R \\ \\ Diameter=2\times5 \\ \\ Diameter=10 \end{gathered}[/tex]The circumference of a circle is given by the formula;
[tex]C=2\pi r[/tex]Taking the value of pi as,
[tex]\pi=3.14[/tex]We now have the circumference as;
[tex]\begin{gathered} C=2\times3.14\times5 \\ \\ C=31.4\text{ }units \end{gathered}[/tex]The area of a circle is given by the formula;
[tex]A=\pi r^2[/tex]Therefore, we now have;
[tex]\begin{gathered} A=3.14\times5^2 \\ \\ A=3.14\times25 \\ \\ A=78.5\text{ }units^2 \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} Diameter=10\text{ }units \\ \\ Circumference=31.4\text{ }units \\ \\ Area=78.5\text{ }units^2 \end{gathered}[/tex]-3x^2 – 24x – 13 = -13
Answers
oh,