Hi there!
[tex]\large\boxed{(-\infty, 9)}[/tex]
We can find the range using completing the square:
y = -x² - 2x + 8
Factor out a -1:
y = -(x² + 2x) + 8
Use the first two terms. Take the second term's coefficient, divide by 2, and square:
y = -(x² + 2x + 1) + 8
Remember to add by 1 because we cannot randomly add an additional number into the equation:
y = -(x² + 2x + 1) + 8 + 1
Simplify:
y = -(x + 1)² + 9
Since the graph opens downward (negative coefficient), the range is (-∞, 9)
A walking path across a park is represented by the equation y = -4x + 10. A new path will be built perpendicular to this path. The paths will intersect at the point (4, -6). Identify the equation that represents the new path.
Answer: [tex]y=\frac{1}{4}x-7[/tex]
Step-by-step explanation:
The perpendicular slope of the line(m) = [tex]-\frac{1}{m}[/tex]:
m = -4 ⇒ [tex]-\frac{1}{m} =-\frac{1}{(-4)} =\frac{1}{4}[/tex]The function formula is y = mx + b, where the y-intercept(b) is found by substituting in the values of a point on the line ⇒ (4, -6):
[tex]y=\frac{1}{4}x+b\\-6=\frac{1}{4}(4)+b\\-6=1+b\\b=-6-1=-7[/tex]
So the perpendicular equation is [tex]y=\frac{1}{4}x-7[/tex].
if f(x)=x+8 and g(x)=-4x-3 find (f+g)(x)
Answer:
for this case we have the following functions:
f (x) = x + 8
g (x) = -4x - 3
Subtracting the functions we have:
(f - g) (x) = f (x) - g (x)
(f - g) (x) = (x + 8) - (-4x - 3)
Rewriting:
(f - g) (x) = x + 8 + 4x + 3
(f - g) (x) = 5x + 11
Answer:
D. (f - g) (x) = 5x + 11
A, B and C are collinear points. B is between A and C. AB=3x+4 BC=4x-1 AC=8x-9 Find AC
Answer:
[tex]AC = 87[/tex]
Step-by-step explanation:
Given
[tex]AB = 3x + 4[/tex]
[tex]BC = 4x -1[/tex]
[tex]AC = 8x - 9[/tex]
Required
The value x
Since A, B and C are collinear, then;
[tex]AC = AB + BC[/tex]
This gives:
[tex]8x - 9 =3x+4+4x-1[/tex]
Collect like terms
[tex]8x - 3x - 4x = 9 + 4-1[/tex]
[tex]x = 12[/tex]
We have:
[tex]AC = 8x - 9[/tex]
[tex]AC = 8*12 - 9[/tex]
[tex]AC = 87[/tex]
The slope of diagonal OA is ? and its equation is ?
Answer:
Slope = [tex]\frac{4}{3}[/tex]
Equation of the line → [tex]y=\frac{4}{3}x[/tex]
Step-by-step explanation:
Let the equation of diagonal OA is,
y = mx + b
Here, m = Slope of the line OA
b = y-intercept
Slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of the line passing through O(0, 0) and A(3, 4) will be,
m = [tex]\frac{4-0}{3-0}[/tex]
m = [tex]\frac{4}{3}[/tex]
Since, line OA is passing through the origin, y-intercept will be 0.
Therefore, equation of OA will be,
[tex]y=\frac{4}{3}x[/tex]
Find the mean or average of these savings accounts $215, $156,$318, $75, and $25
Answer:
157.8
Step-by-step explanation:
Add them all up to get 789 and divide them by 5 as there are five numbers to get the answer:)
The vector w = ai + bj is perpendicular to the line ax + by = c and parallel to the line bx - ay = c. It is also true that the acute angle between intersecting lines that do not cross at right angles is the same as the angle determined by vectors that are either normal to the lines or parallel to the lines. Use this information to find the acute angle between the lines below.
5x + 9y = 2, 7x + 2y = 1
The angle is _______ radians.
(Type an exact answer, using pi as needed)
Answer:
fgvilgiuhuikj
Step-by-step explanation:??????????????
The dimensions of a closed rectangular box are measured as 60 centimeters, 50 centimeters, and 70 centimeters, with an error in each measurement of at most 0.2 centimeters. Use differentials to estimate the maximum error in calculating the surface area of the box.
Answer:
The maximum error in calculating the surface area of the box is 72 square centimeters.
Step-by-step explanation:
From Geometry, the surface area of the closed rectangular box ([tex]A_{s}[/tex]), in square centimeters, is represented by the following formula:
[tex]A_{s} = w\cdot l + (w + l)\cdot h[/tex] (1)
Where:
[tex]w[/tex] - Width, in centimeters.
[tex]l[/tex] - Length, in centimeters.
[tex]h[/tex] - Height, in centimeters.
And the maximum error in calculating the surface area ([tex]\Delta A_{s}[/tex]), in square centimeters, is determined by the concept of total differentials, used in Multivariate Calculus:
[tex]\Delta A_{s} = \left(l+h\right)\cdot \Delta w + \left(w+h\right)\cdot \Delta l + (w+l)\cdot \Delta h[/tex] (2)
Where:
[tex]\Delta w[/tex] - Measurement error in width, in centimeters.
[tex]\Delta l[/tex] - Measurement error in length, in centimeters.
[tex]\Delta h[/tex] - Measurement error in height, in centimeters.
If we know that [tex]\Delta w = \Delta h = \Delta l = 0.2\,cm[/tex], [tex]w = 60\,cm[/tex], [tex]l = 50\,cm[/tex] and [tex]h = 70\,cm[/tex], then the maximum error in calculating the surface area is:
[tex]\Delta A_{s} = (120\,cm + 130\,cm + 110\,cm)\cdot (0.2\,cm)[/tex]
[tex]\Delta A_{s} = 72\,cm^{2}[/tex]
The maximum error in calculating the surface area of the box is 72 square centimeters.
Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 110 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah. (a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.)
Answer:
z (min) = 2079
L = 26 D = 39.6 S = 16.5
Step-by-step explanation:
L numbers of hours assigned to Lisa
D numbers of hours assigned to David
S numbers of hours assigned to Sara
Objective Function to minimize:
z = 30*L + 25*D + 18*S
Constraints:
Total time available
L + D + S ≤ 110
Lisa experience
L ≥ 0.4 * ( L + D ) then L ≥ 0.4*L + 0.4*D
0.6*L - 0.4*D ≥ 0
To provide designing experience to Sara
S ≥ 0.15*110 then S ≥ 16.5
Time for Sara
S ≤ 0.25 * ( L + D ) S ≤ 0.25*L + 0.25*D or -0.25*L - 0.25*D + S ≤0
Availability of Lisa
L ≤ 50
The Model is:
z = 30*L + 25*D + 18*S to minimize
Subject to:
L + D + S ≤ 110
0.6*L - 0.4*D ≥ 0
S ≥ 16.5
-0.25*L - 0.25*D + S ≤0
L ≤ 50
L ≥ 0 ; D ≥ 0 , S ≥ 0
After 6 iterations optimal ( minimum ) solution is:
z (min) = 2079
L = 26 D = 39.6 S = 16.5
The formula that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize the total cost is z = 30L + 25D + 18S and the minimum z is 2079.
Given :
The company estimates that 110 hours will be required to complete the project.Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers.To provide a label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time.The number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers.Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah.The formula that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize the total cost is given by:
z = 30L + 25D + 18S
The constraints are given by:
1) L + D + S [tex]\leq[/tex] 110
2) L [tex]\geq[/tex] 0.4(L + D)
L [tex]\geq[/tex] 0.4L + 0.4D
0.6L - 0.4D [tex]\geq[/tex] 0
3) S [tex]\geq[/tex] 0.15(110)
S [tex]\geq[/tex] 16.5
Now, to minimize 'z' then use:
[tex]\rm -0.25L-0.25D+S\leq 0[/tex]
L [tex]\leq[/tex] 50
L [tex]\geq[/tex] 0, D [tex]\geq[/tex] 0, S [tex]\geq[/tex] 0
Now, the minimum z is given by:
z = 2079
L = 26, D = 39.6, S = 16.5
For more information, refer to the link given below:
https://brainly.com/question/23017717
Which are the roots of the quadratic function f(q) = 92 – 125?
Answer:
There are no solution/no roots for f(q) = 92 - 125
Question 23 (5 points)
A triangle has two interior angles with the measurement of 68° and 54º. What's the
measurement of the third interior angle?
55°
620
58°
65°
Answer:
58°
Step-by-step explanation:
Given that,
The measure of two interior angles are 68° and 54º.
We need to find the measurement of the third interior angle.
We know that, the sum of angles of a triangle is equal to 180°. Let the angle is x. So,
x+68+54 = 180
x+122 = 180
x = 180-122
x = 58°
So, the measure of the third interior angle is equal to 58°.
a+in=√1+i÷1-i,prove that a^2+b^2=1
Answer with Step-by-step explanation:
We are given that
[tex]a+ib=\sqrt{\frac{1+i}{1-i}}[/tex]
We have to prove that
[tex]a^2+b^2=1[/tex]
[tex]a+ib=\sqrt{\frac{(1+i)(1+i)}{(1-i)(1+i)}}[/tex]
Using rationalization property
[tex]a+ib=\sqrt{\frac{(1+i)^2}{(1^2-i^2)}}[/tex]
Using the property
[tex](a+b)(a-b)=a^2-b^2[/tex]
[tex]a+ib=\sqrt{\frac{(1+i)^2}{(1-(-1))}}[/tex]
Using
[tex]i^2=-1[/tex]
[tex]a+ib=\frac{1+i}{\sqrt{2}}[/tex]
[tex]a+ib=\frac{1}{\sqrt{2}}+i\frac{1}{\sqrt{2}}[/tex]
By comparing we get
[tex]a=\frac{1}{\sqrt{2}}, b=\frac{1}{\sqrt{2}}[/tex]
[tex]a^2+b^2=(\frac{1}{\sqrt{2}})^2+(\frac{1}{\sqrt{2}})^2[/tex]
[tex]a^2+b^2=\frac{1}{2}+\frac{1}{2}[/tex]
[tex]a^2+b^2=\frac{1+1}{2}[/tex]
[tex]a^2+b^2=\frac{2}{2}[/tex]
[tex]a^2+b^2=1[/tex]
Hence, proved.
Several factors influence the size of the F-ratio. For each of the following, indicate whether it would influence the numerator or the denominator of the F-ratio, and indicate whether the size of the F-ratio would increase or decrease. a. Increase the differences between the sample means. b. Increase the sample variances.
Answer:
(a) Increase the differences between the sample means this will increase the Numerator.
(b) Increase the sample variances will increase the denominator.
Step-by-step explanation:
F Ratio = Variance between treatments/ Variance within treatments.
Here,
(a) Increase the differences between the sample means:
- Will increase the Numerator and
- Size of the F-ratio would increase
(b) Increase the sample variances:
- Will increase the denominator and
- Size of the F Ratio would decrease.
Find the area of the geometric figure.
3 yd
3 yd
Traperoid
7 yd
Step-by-step explanation:
The question isn't clear, so I'll just give you a formula to find the area of trapezoid,
(a+b)*h/2, where a = base side, b = top side, h = height.
So, let's say two sides are 3 yd and 7 yd, and height is 3 yd, so the area becomes,
(3+7)*3/2
= 10*3/2
= 30/2
= 15 yd²
Answered by GAUTHMATH
سا (a) From the definition of derivatives determine dy÷dx if y = -2÷x
Step-by-step explanation:
Given: [tex]y = -\dfrac{2}{x}[/tex]
Derivative of a power function [tex]x^n[/tex]:
[tex]\dfrac{d}{dx}(x^n) = nx^{n-1}[/tex]
Therefore,
[tex]\dfrac{dy}{dx}=-2(-1)x^{-2} = \dfrac{2}{x^2}[/tex]
equivalent fraction of 9/11
Answer:
1822
Step-by-step explanation:
The fraction 1822 is equal to 911 when reduced to lowest terms.
18
22
is equivalent to 9
11
because 9 x 2 = 18 and 11 x 2 = 22
27
33
is equivalent to 9
11
because 9 x 3 = 27 and 11 x 3 = 33
36
44
is equivalent to 9
11
because 9 x 4 = 36 and 11 x 4 = 44
Answer:
18/22
Step-by-step explanation:
You can choose any number and if you multiply the top number (numerator) and the bottom number (denominator) by that same number, the fractions are equivalent.
If you choose the number 2, then multiply 9 x 2 = 18, and 11 x 2 = 22
Or multiply by 7. Then you would get an equivalent fraction of 63/77
You play basketball at your school's
indoor stadium. You have two payment
options. Option A is to buy a membership
card for $20 and pay $2 each time you
go to the gym, t. Option B is to pay $4
each time you go. Write a a linear
equation to show how many trips to the
gym would the cost be the same?
Answer:
20 + 2x = 4x
Step-by-step explanation:
So you are setting the two expressions equal to each other.
buying a membership card and paying each time looks like this: 20 + 2x where x is the number of times you go to the gym. 20 dollars base then 2 each time you go.
4 each time you go is just 4x
so just set the two equal to each other.
20 + 2x = 4x
If you solve it you will get x = something, which would be the number of times to make the two equal.
Solve the equation 2sin^2(x) = 1 for x ∈ [-π,π], expressing all solutions as exact values. please help its urgent !!
Answer:
2sin.2(x) sd s
Step-by-step explanation:
in a class of 50 student,35 are boys.what is the ratio of girls to boys in the class?
Answer:
15:35
Step-by-step explanation:
50-35=Girls
50-35=15
Your money grows at a rate of 8% a year if you originally invest $2,000 what is the function that represents your money after t years
Answer:
2000*(1.08)^t where t is years after deposit
Step-by-step explanation:
Write the ratio 4 3/5 to 1 1/5 as a fraction in lowest terms
Answer:
23/6
Step-by-step explanation:
Given fractions
4 3/5 to 1 1/5
Write 4 3/5 as improper fraction= 23/5
Write 1 1/5 as improper fraction= 6/5
Then find the ratio
23/5 : 6/5
Ratio is finding division of two terms
(23/5) / (6/5)
= 23/5 × 5/6
5 at the denominator cancel out 5 at numerator then we have
= 23/6
Hence, fraction in lowest terms here is
23/6
Using the proper terminology, how would you explain and visually demonstrate that this is not always the case?
ONLY ANSWER IF YOU KNOW THE ANSWER
Answer:
Answer is 6.
Step-by-step explanation:
The product is
[tex]15\times \frac{2}{5}[/tex]
Now, it does not means that the product of two quantities is always more than the individual quantities.
here, 2/5 is a part of whole.
So,
The product is
[tex]15\times \frac{2}{5}\\\\=3\times 2\\\\= 6[/tex]
The answer is 6 which is less than 15.
Here, it is the 2/5 part of whole 15.
A square coffee shop has sides that are 10 meters long. What is the coffee shop's area?
square meters
100
SOLUTION:
10•10= 100
what the mining of althoe
[tex]y \geqslant 3[/tex]
The question isn't well stated ; If the question intends to ask the meaning of the inequality :
Answer:
Kindly check explanation
Step-by-step explanation:
Given the inequality : y ≥ 3
This inequality statement or expression means that :
y is true for all values beginning from 3 and beyond
That is values from 3 makes the expression a true statement.
Therefore values of y for which the inequality holds or is true are :
(3,....)
What is the prime factorization of 30?
O A. 2.2.3.5
O B. 5.6
O C. 3.10
O D. 2.3.5
D. 2.3.5 is the correct answer
In the diagram, WZ=StartRoot 26 EndRoot.
On a coordinate plane, parallelogram W X Y Z is shown. Point W is at (negative 2, 4), point X is at (2, 4), point Y is at (1, negative 1), and point Z is at (negative 3, negative 1).
What is the perimeter of parallelogram WXYZ?
units
units
units
units
Answer:
[tex]P = 8 + 2\sqrt{26}[/tex]
Step-by-step explanation:
Given
[tex]W = (-2, 4)[/tex]
[tex]X = (2, 4)[/tex]
[tex]Y = (1, -1)[/tex]
[tex]Z = (-3,-1)[/tex]
Required
The perimeter
First, calculate the distance between each point using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 -y_2)^2[/tex]
So, we have:
[tex]WX = \sqrt{(-2- 2)^2 + (4-4)^2 } =4[/tex]
[tex]XY = \sqrt{(2- 1)^2 + (4--1)^2 } =\sqrt{26}[/tex]
[tex]YZ = \sqrt{(1- -3)^2 + (-1--1)^2 } =4[/tex]
[tex]ZW = \sqrt{(-3--2)^2 + (-1-4)^2 } =\sqrt{26}[/tex]
So, the perimeter (P) is:
[tex]P = 4 + \sqrt{26} + 4 + \sqrt{26}[/tex]
[tex]P = 8 + 2\sqrt{26}[/tex]
The perimeter of parallelogram WXYZ is 8 + 2√26 units
Perimeter of parallelogramIn order to determine the required perimeter of the parallelogram, we will use the distance formula as shown:
D= √(x2-x1)²+(y2-y1)²
Given the coordinate of the parallelogram shown as:
W(-2, 4)
X (2, 4)
Y(1, -1)
Z(-3, -1).
Since it is a parallelogram, the opposite sides are equal that is:
WX = YZ and XY = WZ
WX = YZ = √(x2-x1)²+(y2-y1)²
WX = YZ = √(2+2)²+(4-4)²
WX = YZ =√(4)²
WX = YZ = 4 units
Similarly
XY = WZ = √(2-1)²+(4+1)²
XY = WZ = √(1)²+(5)²
XY = WZ = √26
Perimeter = 2(4)+ 2(√26)
Perimeter = 8 + 2√26
Hence the perimeter of parallelogram WXYZ is 8 + 2√26 units
Learn more on perimeter of parallelogram here: https://brainly.com/question/11185474
The population of a city this year is 200,000. The population is expected to increase by 2.5% per year over the next 10 years. Which exponential equation models this situation?
Answer:
[tex]A = 200,000(1+.025) ^{t}[/tex]
[tex]A = 200,000(1+.025) ^{10}[/tex]
Step-by-step explanation:
The half life of carbon 14 is 5,730 year suppose a fossil found with 20 percent as much of its carbon 14 as compared to a living sample how old is the fossil
3,235 years
32,346 years
1331 years
13,307 years
13,305 years
Step-by-step explanation:
[tex]A = A_02^{-\frac{t}{5730}}[/tex]
Since only 20% of the original C-14 is left, then [tex]A=0.2A_0[/tex]. We can then write
[tex]0.2A_0=A_02^{-\frac{t}{5730}}[/tex]
Taking the log of both sides,
[tex]\log 0.2 = \left(-\dfrac{t}{5730}\right)\log 2[/tex]
Solving for t,
[tex]t = \dfrac{-(5730\:\text{years})\log 0.2}{\log 2}[/tex]
[tex]\:\:\:\:\:\:\:= 13,305\:\text{years}[/tex]
What is the surface area of the rectangular prism pictured below?
3 meters
9 meters
4 meters
Answer:
108 meters with the formula lxhxw
factor the GCF out of the polynomial
Answer:
1. Find the GCF of all the terms in the polynomial.
2. Express each term as a product of the GCF and another factor.
3. Use the distributive property to factor out the GCF.
Write an equation for the function that includes the following points (2,32) and (3,64)
Answer:
32 = a*2 +b
64 = a*3 + b
Then 32 = a
32 = 32*2 +b
b = - 32
So
Y = 32a - 32
Is the equation
