Answers
Step-by-step explanation:
I think substitution would be the easiest since you already have one of the variables solved for.
[tex]y=-x^2+4x+5\\y=x+1\\x+1=-x^2+4x+5\\x^2-3x-4=0\\(x-4)(x+1)=0\\x-4=0\\x=4\\x+1=0\\x=-1[/tex]
(You can just set the equations equal to each other since they both equal y).
Now, to get the points, plug in x = 4 and x = -1 into one of the equations (I'm going to plug them into y = x+1 because that one is much simpler)
[tex]y(4)=4+1\\y(4)=5\\y(-1)=-1+1\\y(-1)=0[/tex]
So, your final points are:
(4,5) and (-1,0)
Answer: A
Step-by-step explanation:
We can use substitution to solve this problem. Since we are given y=-x²+4x+5 and y=x+1, we can set them equal to each other.
-x²+4x+5=x+1 [subtract both sides by x]
-x²+3x+5=1 [subtract both sides by 1]
-x²+3x+4=0
Now that we have the equation above, we can factor it to find the roots.
-x²+3x+4=0 [factor out -1]
-1(x²-3x-4)=0 [factor x²-3x-4]
-1(x+1)(x-4)=0
This tells us that x=-1 and x=4.
We can narrow down our answer to A, but let's plug in those values to be sure it is correct.
-(-1)²+4(-1)+5=(-1)+1 [exponent]
-1+4(-1)+5=-1+1 [multiply]
-1-4+5=-1+1 [add and subtract from left to right]
0=0
-------------------------------------------------------------------------------------------
-(4)²+4(4)+5=(4)+1 [exponent]
-16+4(4)+5=4+1 [multiply]
-16+16+5=4+1 [add and subtract from left to right]
5=5
Therefore, we can conclude that A is the correct answer.
Related Questions
For any real number √a²
a
- |al
lal.
-a
Answers
Answer:
|a|
Step-by-step explanation:
For any positive or negative a, when you square it, the answer is positive.
The square root symbol means the principal square root. For a positive number, the principal square root is positive. To make sure the square root is always non-negative, use absolute value.
Answer: |a|
Children arrive at a house to do Halloween trick-or- treating according to a Poisson process at the unlucky rate of 13/hour. What is the probability that the time between the 15th and 16th arrivals will be more than 4 minutes ? (Hint: Think exponential.)
a) e e-2 = 0.1353
b) e-13/15 = 0.4204
c) e-1 = 0.3679
d) 1-2-1 = 0.6321
Answers
Answer:
0.4204 probability, option b.
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Children arrive at a house to do Halloween trick-or- treating according to a Poisson process at the unlucky rate of 13/hour
13 arrivals during an hour, which means that the mean time between arrivals, in minutes is of [tex]\mu = \frac{13}{60} = 0.2167[/tex]
What is the probability that the time between the 15th and 16th arrivals will be more than 4 minutes ?
This is P(X > 4). So
[tex]P(X > 4) = e^{-0.2167*4} = 0.4204[/tex]
So the correct answer is given by option b.
Is this a function? Yes or no?
Answers
Answer:
NO
Step-by-step explanation:
NO
The frequency distribution below summarizes the home sale prices in the city of Summerhill for the month of June. Determine the lower class limits.
Answers
Answer:
79.5, 110.5, 141.5, 172.5, 203.5, 234.5
Step-by-step explanation:
Given
The attached distribution
Required
The lower class limits
To do this, we simply subtract 0.5 from the lower interval
From the attached distribution, the lower intervals are:
80.0, 111.0, 142.0, 173,0 .......
So, the lower class limits are:
[tex]80.0-0.5 = 79.5[/tex]
[tex]111.0-0.5 = 110.5[/tex]
[tex]142.0-0.5 = 141.5[/tex]
[tex]173.0-0.5 = 172.5[/tex]
[tex]204.0-0.5 = 203.5[/tex]
[tex]235.0-0.5 = 234.5[/tex]
solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!
Answers
Answer:
[0.25, 2]
Step-by-step explanation:
We have
4t² ≤ 9t-2
subtract 9t-2 from both sides to make this a quadratic
4t²-9t+2 ≤ 0
To solve this, we can solve for 4t²-9t+2=0 and do some guess and check to find which values result in the function being less than 0.
4t²-9t+2=0
We can see that -8 and -1 add up to -9, the coefficient of t, and 4 (the coefficient of t²) and 2 multiply to 8, which is also equal to -8 * -1. Therefore, we can write this as
4t²-8t-t+2=0
4t(t-2)-1(t-2)=0
(4t-1)(t-2)=0
Our zeros are thus t=2 and t = 1/4. Using these zeros, we can set up three zones: t < 1/4, 1/4<t<2, and t>2. We can take one random value from each of these zones and see if it fits the criteria of
4t²-9t+2 ≤ 0
For t<1/4, we can plug in 0. 4(0)²-9(0) + 2 = 2 >0 , so this is not correct
For 1/4<t<2, we can plug 1 in. 4(1)²-9(1) +2 = -3 <0, so this is correct
For t > 2, we can plug 5 in. 4(5)²-9(5) + 2 = 57 > 0, so this is not correct.
Therefore, for 4t^2 ≤ 9t-2 , which can also be written as 4t²-9t+2 ≤ 0, when t is between 1/4 and 2, the inequality is correct. Furthermore, as the sides are equal when t= 1/4 and t=2, this can be written as [0.25, 2]
In your office desk drawer you have 10 different flavors of fruit leather. How many distinct flavor groupings can you make with your fruit leather stash?
Answers
You have 10 different flavors. Just multiply the ten with another ten.
what is the slope of a line parallel to the line whose equation is 2x+5y=10
Answers
Answer:
1. The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is
2.
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
The line y = -2x + 5 is parallel to the line y = -2x + 3
The line y = x + 7 is perpendicular to the line
y = -2x + 3
3. The equation of the line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = x - 2
Step-by-step explanation:
Let us revise some rules
The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The slopes of the parallel lines are equal
The product of the slopes of the perpendicular lines is -11. The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is
2.
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
The line y = -2x + 5 is parallel to the line y = -2x + 3
The line y = x + 7 is perpendicular to the line
y = -2x + 3
3. The equation of the line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = x - 2
Step-by-step explanation:
Let us revise some rules
The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The slopes of the parallel lines are equal
The product of the slopes of the perpendicular lines is -11. The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is
2.
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
The line y = -2x + 5 is parallel to the line y = -2x + 3
The line y = x + 7 is perpendicular to the line
y = -2x + 3
3. The equation of the line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = x - 2
Step-by-step explanation:
Let us revise some rules
The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The slopes of the parallel lines are equal
The product of the slopes of the perpendicular lines is -11. The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is
2.
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
The line y = -2x + 5 is parallel to the line y = -2x + 3
The line y = x + 7 is perpendicular to the line
y = -2x + 3
3. The equation of the line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = x - 2
Step-by-step explanation:
Let us revise some rules
The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The slopes of the parallel lines are equal
The product of the slopes of the perpendicular lines is -1
Question 2
A force F=5i+3j-2k is applied to move a block of cement from A(0,1,1) to B(4.-1,3).
Determine the work done by the force.
Answers
The work is simply the dot product of the force and displacement (which I assume are given in Newtons and meters, respectively):
W = F • d
W = (5i + 3j - 2k) N • ((4i - j + 3k) m - (j + k) m)
W = (5i + 3j - 2k) • (4i - 2j + 2k) Nm
W = (20 - 6 - 4) Nm
W = 10 J
From the table below, determine whether the data shows an exponential function. Explain why or why not.
x
3
2
1
–1
y
8
2
0.5
0.125
a. No; the domain values are at regular intervals and the range values have a common factor 0.25. b. No; the domain values are not at regular intervals although the range values have a common factor. c. Yes; the domain values are at regular intervals and the range values have a common factor 4. d. Yes; the domain values are at regular intervals and the range values have a common factor 0.25.
Answers
9514 1404 393
Answer:
b. No; the domain values are not at regular intervals although the range values have a common factor.
Step-by-step explanation:
The differences between x-values are ...
-1, -1, -1, -2 . . . . not a constant difference
The ratios of y-values are ...
2/8 = 0.5/2 = 0.125/0.5 = 0.25 . . . . a constant difference
The fact that the domain values do not have a common difference renders the common factor of the range values irrelevant. The relation is not exponential.
5/6 ÷ 1/3 - 2/3 (2/5)
Answers
Answer:
[tex] \frac{67}{30} \: \text{or} \:2 \frac{7}{30} [/tex]
Step-by-step explanation:
5/6 ÷ 1/3 - 2/3 (2/5)
= 5/6 ÷ 1/3 - 2/3 × 2/5= 5/2 - 2/3 × 2/5= 5/2 - 4/15= 67/30 or 2 7/30Hope it helps you! ＼(^ᴥ^)／
Linda found that the cost to get a swimming pool installed in her backyard is a linear function of the pool's area. A swimming pool with an area of 1,000 square feet can be installed for $50,000, whereas the installation of an 800 square foot swimming pool costs $35,000. Select the correct graph that models the given relationship.
Answers
Answer:
$35,000
Step-by-step explanation:
if $50,000 is to install an area of 1,000 square feet swimming pool and $35,000 can be used to install an 800 square foot swimming pool I think the best graph model is 800 square feet for $35,000 for a cost cut of $15,000 is a good bargain
A computer monitor is listed as being 22 inches. This distance is the diagonal distance across the screen. If the screen measures 12 inches in height, what is the actual width of the screen to the nearest inch?
22 inches
18.43 inches
25.05 inches
32.5 inches
Answers
Answer
The width of the screen is 18.43.
Explanation
Use the Pythagorean Theorem (a^2+b^2=c^2) to find the height.
In a right triangle, a and b are legs. In this instance, a and b would be the height and width of the computer monitor. Let's say the height is a and the width is b (you're trying to find b). The hypotenuse of a right triangle is c. For the computer monitor, c is the diagonal.
So put in everything you know to find b; 12^2+b^2=22^2.
12^2 is 144 and 22^2 is 484. Now you have 144+b^2=484. When you simplify, you get b^2=340. When you simplify again, you find that b is about 18.43.
CAN SOMEONE HELP ME ON ANALYZING DOT PLOTS!!!
Answers
Answer:
yes
Step-by-step explanation:
but I can't see them here
Find the distance between the points (-5, -4) and (3, 1).
On a coordinate plane, points are at (3, 1), (negative 5, negative 4).
Answers
Step-by-step explanation:
it will help u
2(-x-4)+3=-7x+5+5x
Pls help!!!!!!!!
Answers
1 Simplify
−
7
x
+
5
+
5
x
−7x+5+5x to
−
2
x
+
5
−2x+5.
2
(
−
x
−
4
)
+
3
=
−
2
x
+
5
2(−x−4)+3=−2x+5
2 Expand.
−
2
x
−
8
+
3
=
−
2
x
+
5
−2x−8+3=−2x+5
3 Simplify
−
2
x
−
8
+
3
−2x−8+3 to
−
2
x
−
5
−2x−5.
−
2
x
−
5
=
−
2
x
+
5
−2x−5=−2x+5
4 Cancel
−
2
x
−2x on both sides.
−
5
=
5
−5=5
5 Since
−
5
=
5
−5=5 is false, there is no solution.
No Solution
what is the correct equation ?
Answers
Answer:
B
Step-by-step explanation:
B is the correct equation
In 2013, the Public Religion Research Institute conducted a survey of 1,033 adults, 18 years of age or older, in the continental United States. One of the questions on their survey was as follows:
Answers
Answer:
Probability[Number of people from church] = 0.26 (Approx.)
Step-by-step explanation:
Given:
Total number of adult in survey = 1,033
Missing information:
Number of people from church = 269
Find:
Probability[Number of people from church]
Computation:
Probability of an event = Number of favourable outcomes / Number of total outcomes
Probability[Number of people from church] = Number of people from church / Total number of adult in survey
Probability[Number of people from church] = 269 / 1,033
Probability[Number of people from church] = 0.2604
Probability[Number of people from church] = 0.26 (Approx.)
Find the value of x pls help
Answers
9514 1404 393
Answer:
x = 36°
Step-by-step explanation:
The exterior angle is equal to the sum of the remote interior angles. A linear pair is supplementary. So, you can find x either of two ways:
2x = x + (180 -4x) ⇒ 5x = 180 ⇒ x = 36
Or ..
4x = x + (180 -2x) ⇒ 5x = 180 ⇒ x = 36
The value of x is 36°.
The total mass of 8 identical dictionaries is 9.92 kilograms. What is the mass, in kilograms, of one dictionary? Enter your answer in the space provided
Answers
WILL GIVE BRAINLIEST!!!
Write as a polynomial: 14b + 1 - 6(2 - 11b)
Answers
Answer:
80b-11
Step-by-step explanation:
14b + 1 - 6(2 - 11b)
Distribute
14b+1-12+66b
Combine like terms
80b-11
Answer:
80b - 11
Step-by-step explanation:
what is the problem ?
just multiply it out and combine terms.
14b + 1 - 6(2 - 11b) = 14b + 1 - 12 + 66b = 80b - 11
Which expression has a value of 15 when it equals
2
49-57
3--5
61-28
28
19
Answers
Answer:
it is 61-28 but I not sure u can scan for any application to make sure u get it ur answer thx for
Suppose f(x,y,z) = x2 + y2 + z2 and W is the solid cylinder with height 7 and base radius 2 that is centered about the z-axis with its base at z = −2. Enter θ as theta.
A) As an iterated integral, ∭WfdV = ∫BA∫DC∫FE dzdrdθ with limits of integration.
B) Evaluate the integral.
Answers
In cylindrical coordinates, W is the set of points
W = {(r, θ, z) : 0 ≤ r ≤ 2 and 0 ≤ θ ≤ 2π and -2 ≤ z ≤ 5}
(A) Then the integral of f(x, y, z) over W is
[tex]\displaystyle\iiint_W(x^2+y^2+z^2)\,\mathrm dV = \int_0^{2\pi}\int_0^2\int_{-2}^5r(r^2+z^2)\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
(B)
[tex]\displaystyle \int_0^{2\pi}\int_0^2\int_{-2}^5r(r^2+z^2)\,\mathrm dz\,\mathrm dr\,\mathrm d\theta = 2\pi \int_0^2\int_{-2}^5(r^3+rz^2)\,\mathrm dz\,\mathrm dr \\\\\\= 2\pi \int_0^2\left(zr^3+\frac13rz^3\right)\bigg|_{z=-2}^{z=5}\,\mathrm dr \\\\\\= 2\pi \int_0^2\left(\frac{133}3r+7r^3\right)\,\mathrm dr \\\\\\= 2\pi \left(\frac{133}6r^2+\frac74r^4\right)\bigg|_{r=0}^{r=2} \\\\\\= 2\pi \left(\frac{110}3\right) = \boxed{\frac{220\pi}3}[/tex]
the graph function f(x) is illustrated in figure below (-2,1) ,(-1,2) ,(1,2) ,(2,3) .Use the transformation techniques to graph the following functions
a) y=f(x)-2
b) y=f(-x)
Answers
Answer:
a) y = f(x) - 2 (x, y) ⇒ (x, y - 2)b) y = f(-x) (x, y) ⇒ (-x, y)a) y=f(x)-2
(-2, 1) → (-2, 1 - 2) = (-2, -1)(-1, 2) → (-1, 2 - 2) = (-1, 0)(1, 2) → (1, 2 - 2) = (1, 0)(2, 3) → (2, 3 - 2) = (2, 1)b) y=f(-x)
(-2, 1) → (-(-2), 1) = (2, 1)(-1, 2) → (-(-1), 2) = (1, 2)(1, 2) → (-1, 2)(2, 3) → (-2, 3)Need the answers from a - e
Answers
Answer:
10
Step-by-step explanation:
Sorry. I needed to answer this question to get access.
which is the correct answer ?
Answers
Answer:
11/12 cups
Step-by-step explanation:
2/3+1/4 = ( 2x4 + 3x1 )/( 3x4 ) = ( 8+3 )/12 = 11/12
Solve the system, or show that it has no solution. (If there is no solution, enter NO SOLUTION. If there are an infinite number of solutions, enter the general solution in terms of x, where x is any real number.)
20x − 80y = 100
−14x + 56y = −70
(x, y) =
Answers
Answer:
The system has an infinite set of solutions [tex](x,y) = (x, \frac{x-5}{4})[/tex]
Step-by-step explanation:
From the first equation:
[tex]20x - 80y = 100[/tex]
[tex]20x = 100 + 80y[/tex]
[tex]x = \frac{100 + 80y}{20}[/tex]
[tex]x = 5 + 4y[/tex]
Replacing on the second equation:
[tex]-14x + 56y = -70[/tex]
[tex]-14(5 + 4y) + 56y = -70[/tex]
[tex]-70 - 56y + 56y = -70[/tex]
[tex]0 = 0[/tex]
This means that the system has an infinite number of solutions, considering:
[tex]x = 5 + 4y[/tex]
[tex]4y = x - 5[/tex]
[tex]y = \frac{x - 5}{4}[/tex]
The system has an infinite set of solutions [tex](x,y) = (x, \frac{x-5}{4})[/tex]
1) What is the opposite of adding 5?
2) What is the opposite of subtracting 20?
3) What is the opposite of multiplying by 1/2?
4) What is the opposite of dividing by 10?
Answers
Answer:
1) subtracting 5
2) adding 20
3) dividing by 2 (multiplying by 1/2)
4) multiplying by 1/10 (dividing by 10)
Step-by-step explanation:
There are four main operations in math: adding, subtracting, multiplying, and dividing. Each of the operations has an opposite. Adding and subtracting are opposites and multiplying and dividing are opposites. This means that subtracting can undo adding and vice versa; additionally, dividing can undo multiplying or vice versa. So, to find the opposite of something switch the operation to the opposite and keep the number. However, it is important to note that with multiplying and dividing you can also find the opposite by keeping the operation while changing the number to the reciprocal.
Which choice correctly shows the line y = -x?
А
B
NOW
-
1 2 3 4
NH
-4 -3 -2 -1 1 2 3 4
UN
С
2
1 2 3 4
-4-3-2/4 1 2 3 4
-4 -3 -2 -3
NA
2
At
2
Answers
Answer:
The answer is A
Step-by-step explanation:
Hope this helps
A decorative wall in a garden is to be built using bricks that are 5 1/2 inches thick and mortar joints are 1/4 inch thick. What is the height of the wall?
Answers
Step-by-step explanation:
how many layers of bricks are used ?
also, I assume, the thickness of bricks means actually their height when laid.
but still, I cannot answer that, as nothing indicates if there is only one layer of bricks or 2 or 3 or 4 or ...
when 5 is added to 2 times a number , the results is 45. find the number
Answers
Answer:i think its 20
Step-by-step explanation: 20 x 2 is 40 plus 5 is 45
Answer:
✓ x - the number 5 + 2x = 45 2x = 45 - 5 2x = 40 x = 20 5 + 2(20) = 45 5 + 40 = 45 45 = 45 Hope this helps. :-) the answer is 20
Step-by-step explanation: Algebra.com
