Answer:
[tex]b=-a^2-c[/tex]
Step-by-step explanation:
4.A counterexample can be used to show that a conjecture is false. Below are three
conjectures students made after visiting a zoo. Write a counterexample that shows that each
conjecture is false.
a. There are always more elephants in a zoo than giraffes.
TS
b. The oldest leatherback sea turtle in captivity is 33 years old.
c. American bison are never over 6 feet tall.
Answer:
Step-by-step explanation:
1. In some zoos the are more elephants than giraffes, then this conjecture can be true sometimes, however, this can not always be true because some zoo could have more giraffes
2. This can be true unless that turtle ages, or another is found that is taken into captivi9ty and found to be older
3. While most American bison are usaually below 6 feet, that is no gureantee there is no occasaional taller American Bison.
I do not know if these meet your teacher's starndard, but I hope they do. Please thanks and rate!
I know you’re supposed to change the bounds and break up the integral, but for some reason, I can’t get the 44/3. Can someone explain how to solve this definite integral?
First, look for the zeroes of the integrand in the interval [0, 6] :
x² - 6x + 8 = (x - 4) (x - 2) = 0 ⇒ x = 2 and x = 4
Next, split up [0, 6] into sub-intervals starting at the zeroes we found. Then check the sign of x² - 6x + 8 for some test points in each sub-interval.
• For x in (0, 2), take x = 1. Then
x² - 6x + 8 = 1² - 6•1 + 8 = 3 > 0
so x² - 6x + 8 > 0 over this sub-interval.
• For x in (2, 4), take x = 3. Then
x² - 6x + 8 = 3² - 6•3 + 8 = -1 < 0
so x² - 6x + 8 < 0 over this sub-interval.
• For x in (4, 6), take x = 5. Then
x² - 6x + 8 = 5² - 6•5 + 8 = 3 > 0
so x² - 6x + 8 > 0 over this sub-interval.
Next, recall the definition of absolute value:
[tex]|x| = \begin{cases}x & \text{for }x \ge0 \\ -x & \text{for }x < 0\end{cases}[/tex]
Then from our previous analysis, this definition tells us that
[tex]|x^2 - 6x + 8| = \begin{cases}x^2 - 6x + 8 & \text{for }0<x<2 \text{ or } 4<x<6 \\ - (x^2-6x+8) & \text{for }2<x<4\end{cases}[/tex]
So, in the integral, we have
[tex]\displaystyle \int_0^6 |x^2-6x+8| \, dx = \left\{\int_0^2 - \int_2^4 + \int_4^6\right\} (x^2 - 6x + 8) \, dx[/tex]
Then
[tex]\displaystyle \int_0^2 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_0^2 = \frac{20}3 - 0 = \frac{20}3[/tex]
[tex]\displaystyle \int_2^4 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_2^4 = \frac{16}3 - \frac{20}3 = -\frac43[/tex]
[tex]\displaystyle \int_4^6 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_4^6 = 12 - \frac{16}3 = \frac{20}3[/tex]
and the overall integral would be
20/3 - (-4/3) + 20/3 = 44/3
A book club charges an initial joining fee of $30.00. The cost per book is $7.00. The graph shows the cost of belonging to the club as a function of books purchased. How will the graph change if the cost per book goes up by $1.50? (The new function is shown by the dotted line.)
Answer:
$82.50
Step-by-step explanation:
You add seven dollars to $1.50 and you would get the sum of 8.50 then you multiply the amount of books purchased. The Equation is 5($8.50) + $30.00= 82.50
Sorry if I get this wrong.
three less than a number is -18
Answer:
-15
Step-by-step explanation:
work in reverse
-18 is three less than something
that means that something is 3 more than -18
so
add 3 to -18
-18+3= -15
help with this please i dont understand?
a) Evaluate the given function at each value of x. We have f(x) = 2x + 3.
• If x = -2, then
f(-2) = 2 (-2) + 3 = -4 + 3 = -1
• If x = -1, then
f(-1) = 2 (-1) + 3 = -2 + 3 = 1
• If x = 0, then
f(0) = 2 (0) + 3 = 0 + 3 = 3
and so on.
b) Kind of a silly question. Of course f(x) is a function, the instructions for part (a) say so!
But the real reason f(x) is indeed a function is that no single value of x returns more than one value of f(x).
3. Vocabulary Suppose △MNP ∼△RST. How can you identify corresponding parts?
4. Reasoning Suppose △ABC ∼△TUV. Determine whether each pair of measures is equal.
a. the measures of ∠A and ∠T
b. the perimeters of the two triangles
c. the ratios of the sides BC/UV and AC/TV
5. Reasoning e scale of a map is 1 in. : 100 mi. Is the actual distance between two towns 100 times the map distance between the two towns? Explain.
Similar triangles may or may not have congruent sides, but the ratio of the corresponding sides will always be congruent.
(3) Corresponding sides of △MNP and △RST
Given that △MNP ∼△RST.
This means that, the corresponding sides are:
MN and RSMP and RTNP and ST(4) The equal measures
Given that △ABC ∼△TUV
This means that, the corresponding angles are equal, but corresponding sides are not.
So, the equal measures are:
(a). the measures of ∠A and ∠T (c). the ratios of the sides BC/UV and AC/TVThe unequal measure is:
(b). the perimeters of the two triangles(c) Scale mapping
The scale mapping is given as:
[tex]Ratio = 1\ in : 100\ mi[/tex]
The above scale means that 1 inches on the scale represents 100 miles of the actual distance.
Take for instance, 5 inches would represent 500 miles.
500 is 5 times 100
Hence, the actual distance between two towns 100 times the map distance between the two towns
Read more about similar triangles at:
https://brainly.com/question/14285697
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Finding missing sides- similar triangles Algebraic practice )
Answer:
x=7.85
Step-by-step explanation:
Give the triangles we know that:
[tex] \frac{cd}{fh} = \frac{de}{hg} = \frac{ce}{gf} [/tex]
Now we can substitute like usual
[tex] \frac{78}{fh} = \frac{117}{54} = \frac{ce}{5x + 1} [/tex]
Now we simplify the fraction in the middle
the middles fraction will =13/6
Therefore:
[tex] \frac{78}{fh} = \frac{13}{6} [/tex]
so 13fh=468
Therefore: fh=36
Now we can use the Pythagorean theorem
so
[tex]gf = \sqrt{ {54}^{2} - {36}^{2} } [/tex]
so gf=18√5
so 5x+1=18√5
so 5x=-1+18√5
so x=7.85
(I'm not too sure about this one tho)
Which choice is equivalent to the product below?
V8,5
O A. 4/10
O B. 10-12
C. 13
O D. 22/10
Answer:
Option D
2√10
Step-by-step explanation:
√8 • √5 = √8 × 5 = √40 = 2√10
Thus, √8 • √5 = 2√10
-TheUnknownScientist 72
Solve for X
show your work
Answer:
alternate exterior angles are equal .
17x + 2 = 18x - 2
x = 2 + 2
x = 4
Step-by-step explanation:
For what value(s) of k is + 3 a factor of 3 + 5 2 + − 9
FAST FASTTTT
Answer:
56
Step-by-step explanation:
The price of a bicycle is $108.00 plus 7% sales tax. What is the sales tax on this bicycle in dollars and cents?
Answer:
$7.56
Step-by-step explanation:
7% = 0.07
108.00 x 7% = $7.56
An angle measures 157.2° more than the measure of its supplementary angle. What is the measure of each angle?
Two supplementary angles equal 180 degrees
Subtract the difference from 180:
180-157.2 = 22.8
Divide by 2:
22.8 /2 = 11.4
One angle is 11.4
Now add the difference to 11.4
11.4 + 157.2 = 168.6
The second angle is 168.6
Answer: 11.4 and 168.6
4e-4=e-4
help me plsssssssssssssssssssssss
Answer:
E= 0 Good luck answering the other questions :)
Step-by-step explanation:
I need help plz.....
Answer:
(c) y^2/16 -(x -7)^2/9 = 1
Step-by-step explanation:
The center, focus, and vertex are on a vertical line, so the hyperbola opens in the direction of the y-axis. The y-term will have the positive coefficient.
The vertex-center distance in the y-direction is 4, so the denominator of the y-term is 4^2 = 16. The denominator of the x-term is 5^2 -16 = 9, where 5 is the center-focus distance.
The equation is ...
y^2/16 -(x -7)^2/9 = 1
help me please i'll mark as brainliest asap
Answer:
a. A(x) = 3x² - 8x + 5
b. x = ⁸/₃
Step-by-step explanation:
a.
A(x) = shaded area
A(x) = (2x - 3)² - (x - 2)²
= 4x² - 12x + 9 - (x² - 4x + 4)
= 4x² - x² - 12x + 4x + 9 - 4
= 3x² - 8x + 5
b.
ΔABF area = ⁵/₄ cm²
A(x) = 4(⁵/₄)
= 5
Substitution:
3x² - 8x + 5 = A(x) = 5
3x² - 8x + 5 = 5
3x² - 8x = 0
x(3x - 8) = 0
3x - 8 = 0
x = ⁸/₃
x = 0
Since x > 2, x = 0 is not valid;
So, x = ⁸/₃
What is the equation for the parabola with a focus F(13/11,0)?
Answer:
B.ON THE EDGE
Step-by-step explanation:
The table shows the proof of the relationship between the slopes of two parallel lines. What is the missing reason for step 2?
A.
Pythagorean theorem
B.
application of the distance formula
C.
application of the slope formula
D.
transitive property
The missing reason for step 2 is the application of the slope formula option (C) application of the slope formula is correct.
What is a distance formula?It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
As we know,
Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.
From the graph of two parallel lines:
r ║ s
The slope is the ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Thus, the missing reason for step 2 is the application of the slope formula option (C) application of the slope formula is correct.
Learn more about the distance formula here:
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#SPJ5
5. 4
Which input value produces the same output value for
the two functions on the graph?
(
*)
3
NO
O x= -1
O x = 0
O x= 1
O x= 2
-5 -3 -2 -
4
х
91x)
Answer:
x=1......................
The average annual cost (including tuition, room, board, books, and fees) to attend a public college takes nearly a third of the annual income of a typical family with college-age children (Money, April 2012). At private colleges, the average annual cost is equal to about 60% of the typical family's income. The following random samples show the annual cost of attending private and public colleges.
Private colleges: 52.8, 43.2, 45.0, 33.3, 44.0, 30.6, 45.8, 37.8, 50.5, 42.0.
Public colleges: 20.3, 22.0, 28.2, 15.6, 24.1, 28.5, 22.8, 25.8, 18.5, 25.6, 14.4, 21.8.
Required:
a. Based on your computation of the two sample means and the two sample standard deviations, find the degrees of freedom.
b. What is the point estimate of the difference between the two population means?
c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges.
The vertice of triangle ABC are A(8,4), B(6,3) and C(5-5). Find the angle between the side AB and BC.
Answer:
Step-by-step explanation:
Use law of cosines
c² = a² + b² - 2abcosθ
cosθ = (c² - a² - b²) / -2ab
c = length of AC = √(8 - 5)² + (4 - (-5))² = √90
b = length of AB = √(8 - 6)² + (4 - 3)² = √5
a = length of BC = √(6 - 5)² + (3 - (-5))² = √65
cosθ = (√90² - √65² - √5²) / -2√65√5
cosθ = 20 / -36.05551...
cosθ = - 0.5547001
θ = 123.69°
x - y = -4
-5 + 6y = 22
The answer is (-2,2) but i just need to show the work for it so please help with that.
Answer:
(-2, 2).
Step-by-step explanation:
x - y = -4
-5x + 6y = 22 Multiply the first equation by 5:
5x - 5y = -20 Now Add the last 2 equations:
y = 2.
Substitute y = 2 in the first equation:
x - 2 = -4
x = -4 + 2
x = -2.
Answer:
x=1/2, y=9/2. (1/2, 9/2).
Step-by-step explanation:
x-y=-4
-5+6y=22
--------------
y=x-(-4)
y=x+4
-5+6(x+4)=22
-5+6x+24=22
6x+24-5=22
6x+19=22
6x=22-19
6x=3
x=3/6
x=1/2
y=1/2+4=1/2+8/2=9/2.
What is 5x + 12 < 2 ?
Answer:
x < -2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTerms/Coefficients
Step-by-step explanation:
Step 1: Define
Identify.
5x + 12 < 2
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 12 on both sides: 5x < -10[Division Property of Equality] Divide 5 on both sides: x < -2Answer:
x < - 2
Step-by-step explanation:
5x + 12 < 2 ( subtract 12 from both sides )
5x < - 10 ( divide both sides by 5 )
x < - 2
what is the equation for: 32 is the sum of a number x and 9
Answer:
x + 9 = 32
Step-by-step explanation:
answer for x is 32 - 9 = 23
3.8×102+1.7×103 giving answer in standard form
Answer: 5.15 x 10^2
Step-by-step explanation:
3.8 x 103 + 1.7 x 103 = 5 x 103 = 515 = 5.15 x 10^2
Elements that do not belong to a set belong to its
Answer:
What do you mean for this question?
Step-by-step explanation:
Give specific details
Tara placed $1200 in a savings account which compounds interest continuously at a rate of 1.4%.
How much will she have in the account after 3 years?
Round your answer to the nearest dollar.
Do NOT round until you have calculated the final answer.
Answer:
$1,251
Step-by-step explanation:
Formula: [tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Plug the values into the formula; solve:
[tex]r = \frac{r}{100}[/tex]
[tex]r = \frac{1.4}{100}[/tex]
[tex]r = 0.014[/tex]
0.014 rate per year
[tex]A = Pe^{rt}[/tex]
[tex]A = 1,200.00^{(2.71828)}^{(0.014)(3)}[/tex]
[tex]A = $1,251.47\\[/tex]
1,251.47 is 1251 rounded because the first value after the decimal point is not greater or equal to 5.
Answer:
1251
Step-by-step explanation:
find the following right triangle, find the side length x
Answer:
x=41
Step-by-step explanation:
9²+40²=x²
81+1600=x²
1681=x²
√1681=√x²
41=x
a jar has 654 jelly beans emily says the jar has 710 jelly beans, Find the percent error of emily's estimate
Answer:0.07% because 710-654 is 56 and 56 divided by 710 is 0.07
Answer:
8.56%Step-by-step explanation:
Find the difference between the actual and estimate, this is the error:
710 - 654 = 56Find the percent error, which is the error over the actual:
56/654*100% = 8.56%There are 8 triangles and 6 circles. What is the simplest ratio of total circles to total shapes
Ratio of total circles to total shapes is 4 : 7
An equation is an expression that shows the relationship between two or more variables and numbers.
There are 8 triangles and 6 circles. The ratio of total circles to total shapes is given by:
Ratio of total circles to total shapes = 8 circles : (8 + 6) shapes
Ratio of total circles to total shapes = 8 : 14 = 4 : 7
Find out more about equation at: https://brainly.com/question/2972832
Genes are sections of DNA that code for a particular trait. Genes are?
Answer:
Genes are DNA transferred to off spring by parents
Answer:
Genes are sections of DNA that code for a particular trait. Genes are nucleic acids.
Step-by-step explanation: