To prove that there exists a unique real number solution to the equation x³ + x² - 1 = 0 between x = 2/3 and x = 1, we can use the Intermediate Value Theorem and the property of the derivative.
Explanation:To prove that there exists a unique real number solution to the equation x³ + x² - 1 = 0 between x = 2/3 and x = 1, we can use the Intermediate Value Theorem.
First, we substitute x = 2/3 into the equation and get a negative value (-1/27). Then, we substitute x = 1 into the equation and get a positive value (1).
Since the function is continuous between x = 2/3 and x = 1, and it changes sign, there must exist a solution somewhere between them.
To show that the solution is unique, we can use the fact that the derivative of the function, 3x² + 2x, is always positive for all real numbers.
This implies that the function is strictly increasing, so it can only intersect the x-axis at one point.
the quotient of two numbers subtracted from 20
Choose all of the following relationships that represent functions. please help!!
The answers are B and C
C;
In a dilation, the ratio of the length of a side on the image to the length of its corresponding side on the pre-image is called the __________ __________.
A. center of dilation
B. scale factor
C. mapping rule
D. expansion or contraction
Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?
Answer:
[tex]y=-3x+14[/tex], slope intercept form
[tex]3x+y =14[/tex], standard form
Step-by-step explanation:
[tex]y + 1 = -3(x - 5)[/tex]
We need to write the given equation in slope intercept form or standard form
slope intercept form is [tex]y=mx+b[/tex]
To get slope intercept form , we need to get y alone
[tex]y + 1 = -3(x - 5)[/tex] ( multiply -3 inside the parenthesis )
[tex]y+1=-3x+15[/tex] , subtract 1 on both sides
[tex]y=-3x+14[/tex]
Standard form is [tex]Ax + By = C[/tex]
To get standard form we keep x term and y term on the left hand side
[tex]y=-3x+14[/tex]
Add 3x on both sides
[tex]3x+y =14[/tex]
PLEASE ANSWER WORTH 99 POINTS
Each serving of a cereal is 80 calories. Which expression can be used to find the number of calories in 3 servings?
80 x 3
80 divided by 3
3 divided by 80
80 - 3
Help me solve this plzz!!Simplify:
How many solutions are there to the following system of equations? Use any method you like, but be sure to show all work.
4x – 14y = 6
–2x + 7y = –3
Please please help! I'm really bad at this! Please show your work so I can understand
Suppose △ ITH ≅ △ APG
Which congruency Statement is true?
A) IH ≅ AG
B) TH ≅ AG
C) IT ≅ AG
D) TH ≅ AP
Answer: A) IH ≅ AG
Step-by-step explanation:
A property of congruent triangles is known as CPCTC which says that the congruent parts of the corresponding triangle are congruent.
We are given that Δ ITH ≅ Δ APG , then the every part of Δ ITH must be congruent to the corresponding part of Δ APG.
i.e. Corresponding sides of Δ ITH and Δ APG are congruent.
Since Side IH in Δ ITH is corresponding to side AG in Δ APG [First and last letter]
Then, IH ≅ AG
I NEED HELP SOOOO MUCH IM SOOO LOST I WILL GIVE A BRAINLIEST TO THE PERSON WHO INCLUDES ALL WORK, CORRECT ANSWER,AND EVERYTHING MAKES SENSE.
(Variables on both sides of an equation)
Solve: 5(a-1)-15=3(a+2)+4
For a car rental, the rental agency charges $21.00$21.00 per day, plus $0.23$0.23 for each additional mile above 125125. find a function for the cost of a rental where x is the number of miles driven.
State the vertex as an ordered pair.
y = -|3x +5|+7
4.5+1.5k=18−3k
solve for k
Answer: I think its 3
Step-by-step explanation:
4.5+4.5=9 and 3*3=9 so 18-9=9 so K=3
The value of k is 3.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 99 is an equation.
We have,
4.5 + 1.5k = 18 - 3k
Combine like terms on one side.
1.5k + 3k = 18 - 4.5
4.5k = 13.5
Divide both sides with 4.5
k = 3
Thus,
The value of k is 3.
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Plz some one help!!!!!!!
Suppose an amount increase by 100%, then decreases by 100%. Find the final amount.Would the situation change if the original increase was 150%? Explain your reasoning.
I will give you 10 points if you help me
In a study, the sample is chosen by writing everyones name on a playing card, shuffling the deck, then choosing the top 20 cards what is the sampling method
Simple random sampling is much better than others because it saves time and it is the most reliable method of obtaining information where every single member of the population is chosen randomly. or by chance. Each has an equal chance to be selected.
SamplingIt is a process applied in statistical analysis in which a predetermined number of observations is taken from a large population.
Given
The sample is chosen by writing everyone's name on a playing card, shuffling the deck, then choosing the top 20 cards.
To find
The sampling method for this condition.
How to choose the sampling method?So, simple random sampling is much better than others because it saves time and it is the most reliable method of obtaining information where every single member of the population is chosen randomly. or by chance. Each has an equal chance to be selected.
More about the sampling link is given below.
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Find the area of the triangle with vertices: q(3,-4,-5), r(4,-1,-4), s(3,-5,-6).
Answer:
(√6)/2 square units
Step-by-step explanation:
The area of a triangle is half the magnitude of the cross product of the vectors representing adjacent sides.
QR = (4-3, -1-(-4), -4-(-5)) = (1, 3, 1)
QS = (3 -3, -5-(-4), -6-(-5)) = (0, -1, -1)
The cross product is the determinant ...
[tex]\text{det}\left|\begin{array}{ccc}i&j&k\\1&3&1\\0&-1&-1\end{array}\right|=-2i+j-k[/tex]
The magnitude of this is ...
|QR × QS| = √((-2)² +1² +(-1)²) = √6
The area of the triangle is half this value:
Area = (1/2)√6 . . . . square units
What is the percent increase from 42 acres to 72acres
Light travels 9.45 \cdot 10^{15}9.45⋅10 15 9, point, 45, dot, 10, start superscript, 15, end superscript meters in a year. there are about 3.15 \cdot 10^73.15⋅10 7 3, point, 15, dot, 10, start superscript, 7, end superscript seconds in a year. how far does light travel per second?
We are given that the distance light travel is:
9.45 x 10^15 meters / year
And that there is:
3.15 x 10^7 seconds / year
So the distance light travels per second is:
distance = (9.45 x 10^15 meters / year) * (1 year / 3.15 x 10^7 seconds)
distance = 3 x 10^8 meters / second
The distance of the light travel per second is 3 x 10^8 meters/second
We are given that the distance light travel is
9.45 x 10^15 meters / year
And that there is
3.15 x 10^7 seconds / year
So the distance light travels per second is:
What is the distance light travels per second?It is defined as the distance that light travels in free space in one second.
Therefore we get,
distance = (9.45 x 10^15 meters / year) * (1 year / 3.15 x 10^7 seconds)
distance = 3 x 10^8 meters / second.
Therefore the distance of the light is 3 x 10^8 meters/second.
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P=(20+0.5x)+ 0.15(20+0.5x)
Compare the square root of 7 and 2.1
Please Help me!!!!!! Simplify the expression AND show your work:
sqrt(4x^2/3y)
For the given expression, the simplified form is [tex]\frac{2x\sqrt{3y} }{3y}[/tex]
From the question, we are to simplify the expression sqrt(4x^2/3y).
The expression is [tex]\sqrt{\frac{4x^{2} }{3y} }[/tex]
We can write that,
[tex]\sqrt{\frac{4x^{2} }{3y} } = \frac{\sqrt{4x^{2}}}{\sqrt{3y}}[/tex]
Then,
[tex]\frac{\sqrt{4x^{2}}}{\sqrt{3y}} = \frac{2x}{\sqrt{3y} }[/tex]
To simplify further, we can rationalize the denominator
We get
[tex]\frac{2x}{\sqrt{3y} } = \frac{2x}{\sqrt{3y} } \times \frac{\sqrt{3y} }{\sqrt{3y} }[/tex]
Then,
[tex]\frac{2x}{\sqrt{3y} } \times \frac{\sqrt{3y} }{\sqrt{3y} } = \frac{2x\sqrt{3y} }{3y}[/tex]
Hence, for the given expression, the simplified form is [tex]\frac{2x\sqrt{3y} }{3y}[/tex]
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A number cube is rolled 25 times. A number less than four comes up 20 times. What is the experimental probability that a number less than four is rolled?
a number less than four came up 20 out of 25 rolls
so the probability was 20/25 which reduces to 4/5
joni borrowed money from her aunt and agreed to pay her 5% simple annual interest. At the end of 3 years, she owes $30 in interest. how much did jodi originally borrow? A. 150
B. 200
C.220
D. 300
Answer:
B
Step-by-step explanation:
Rita earns $17.00 per hour. If she gets a 6% raise, what will be her new hourly wage?
multiply 17 by 6%
17 * 0.06 = 1.02 increase
17 +1.02 = 18.02 new hourly wage
Based upon statistical studies, it takes about one-third less time for fans to exit a game as it does for them to enter and find their seats. If the ingress for the stadium is 3,000 fans per hour, what is the egress?
Answer:
4500 fans per hour
Step-by-step explanation:
Use k as the constant of proportionality to write the equation expressing the relationship: y varies inversely as x.
If y = 25 and k = 50, what is x?
1/2
2
1,250
Answer: 2
Step-by-step explanation: i got it right :)
What is the solution to -5m = -40? m = -8 m = 200 m = -200 m = 8
Loretta and her family are going on vacation. Their destination is 610 miles from their home. Loretta is going to share some of the driving with her dad. Her average speed while driving is 55 mph and her dad's average speed while driving is 65 mph. The plan is for Loretta to drive for this first 4 hours of the trip and her dad to drive for the remainder of the trip
Final answer:
To determine how long Loretta's father drives, we deduct the distance Loretta drives (220 miles) from the total trip distance, then divide the remainder (390 miles) by her father's average speed (65 mph), resulting in 6 hours of driving time for her father. The total trip time is 10 hours.
Explanation:
The question is about calculating travel times and distances using average speed. Loretta and her family are traveling 610 miles with Loretta driving the first 4 hours of the trip at 55 mph and her dad driving the remainder at 65 mph. To calculate the distance Loretta drives, we multiply her driving time by her average speed (4 hours * 55 mph = 220 miles). Then, we subtract that distance from the total trip distance to find out how far her dad drives (610 miles - 220 miles = 390 miles). To calculate how long her dad drives, we divide his driving distance by his average speed (390 miles / 65 mph).
Now let's solve the dad's driving time:
390 miles / 65 mph = 6 hours. So, Loretta's dad would drive for 6 hours. The total driving time for the trip is the sum of both Loretta's time and her dad's time: 4 hours + 6 hours = 10 hours.
A city council has to use its resources to improve either the water supply or the drainage system. At which level is this decision made?
A city council has to use its resources to improve either the water supply or the drainage system. At which level is this decision made?
The asnswer is: Government
You plan to take $450 u.s. on a trip to south africa. how many rands is this if one u.s. dollar equals 3.70 rands?
The areas of: FGHM is 12, MHIJ is 36, EFNL is 24, LNJK is 48. EGIK is a rectangle cut into the rectangles with given areas. What is the area of the shaded quadrilateral EMIN?