Based on the calculations, the length (L) of this rectangle is equal to 5 feet.
What is a rectangle?A rectangle can be defined as a type of quadrilateral in which its opposite sides are equal and all the angles formed are right angle.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.Given the following data:
Area of rectangle, A = 35 square feet.
Width of rectangle, W = (L + 2) feet.
Substituting the given parameters into the formula, we have;
35 = L(L + 2)
35 = L² + 2L
L² + 2L - 35 = 0
Solving the quadratic equation by using the factorization method, we have:
L² + 7L - 5L - 35 = 0
L(L + 7) - 5(L + 7) = 0
(L + 7)(L - 5) = 0
Therefore, the length (L) of this rectangle is equal to 5 feet since the dimension can not be negative.
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If a nonlinear system of equations contains one linear function that touches the quadratic function at its minimum, then the system has which of the following?
A. No solution
B. Infinitely many solutions
C. One solution
D. Two solutions
Answer:
C. One solution
Step-by-step explanation:
You want to know the number of solutions of a system of equation such that the graph of the linear function touches the graph of the quadratic function at its minimum.
SolutionsThe number of real solutions of the system of equations is equal to the number of points of intersection of their graphs. The problem statement tells you the graphs intersect at one point, so there is one solution.
__
Additional comment
The linear function can only touch the minimum of a quadratic if its graph is a horizontal line.
<95141404393>
Write the following using algebraic notation, using the letter x for any
unknown numbers:
think of a number, double it, then add fifteen.
[tex] = x \times 2 + 15 \\ = 2x + 15[/tex]
DOUBLING IT MEANS MULTIPLYING IT BY 2
THEN ADD 15 AS SHOWN ABOVE.
HOPE THIS HELPS
For f(x) = 3x²-x+5, 2f(-3) - f(2)
Answer:
55
Step-by-step explanation:
First solve for f(-3):
[tex]f(-3) = 3(-3)^2-(-3)+5[/tex]
[tex]f(-3)=3(9)+3+5[/tex]
[tex]f(-3)=27+3+5[/tex]
[tex]f(-3) = 35[/tex]
Second solve for f(2):
[tex]f(2) = 3(2)^2-(2)+5[/tex]
[tex]f(2) = 3(4)-(2)+5[/tex]
[tex]f(2) = 12-2+5[/tex]
[tex]f(2) = 15[/tex]
Now plug in f(-3) and f(2) to the expression:
[tex]2(f(-3))-(f(2)) =[/tex]
[tex]2(35)-(15)=[/tex]
[tex]70-15=55[/tex]
-8>-3t-10 can someone help
Answer:
t > -2/3
Step-by-step explanation:
−8>−3t−10
Step 1: Flip the equation.
−3t−10<−8
Step 2: Add 10 to both sides.
−3t−10+10<−8+10
−3t<2
Step 3: Divide both sides by -3.
−3t/−3 < 2/−3
t > −2/3
For the function f(x)=4x+4,
find (a) f(x+h),
(b) f(x+h)−f(x), and
(c) f(x+h)−f(x) h.
(a) f(x+h)=?
Step-by-step explanation:
a)
[tex]f(x+h) = 4(x+h)+4[/tex]
[tex]f(x+h)=4x+4h+4[/tex]
b)
[tex]f(x+h)-f(x)=4x+4h+4-(4x+4)[/tex]
[tex]f(x+h)-f(x)=4x+4h+4-4x-4[/tex]
[tex]f(x+h)-f(x)=4h[/tex]
c)
[tex]f(x+h)-f(x)h=4x+4h+4-h(4x+4)[/tex]
[tex]f(x+h)-f(x)h=4x+4h+4-4hx+4h[/tex]
[tex]f(x+h)-f(x)h=-4hx+8h+4x+4[/tex]
Write the fractions in order from least to greatest: 2/9, 1/6, 1/5, 3/10
Answer:
1/5,1/6,2/9,3/10
Step-by-step explanation:
hope it helps helps and have a nice day! :)
3. John and Savanah are saving money to go on a trip to Mexico. They need at least $2,545 in order to go. John tutors English and Savanah works as a babysitter to raise money. John charges $15 per hour and Savanah charges $20 per hour. The number of hours that Savanah has scheduled is no more than five times the number of hours John has scheduled. Savanah will babysit at least 40 hours.. Write a set of constraints to model the problem, with x representing the number of hours John tutors and y representing the number of hours Savanah babysits. Answer:
The group of restrictions used to simulate the issue includes
y<5x andy [tex]\geq[/tex] 40hours How to construct a set of restrictions to represent the issue:The issue includes the following information.
They need a minimum of $2,545 divided by the hours John instructs and the hours Savanah watches children.There is a maximum of a five-fold difference between the number of hours Savanah has booked and that John has.At least 40 hours will be spent watching the children by Savanah.The following are the restrictions for modeling the issue: There is a maximum of a five-fold difference between the number of hours Savanah has booked and that John has.
Savanah will provide childcare for at least 40 hours, with no more than meaning it is not larger than that which suggests it is less than, Hence, y<5x
Meaning "at least 40 hours" is "at least 40 hours." 40 hours or more may be expressed as
y ≥ 40 hours
The two necessary restrictions are represented as y< 5x and y=> 40 hours in an inequality model.
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15) A sample of 4 different calculators IS randomly selected from a group
containing 46 that are defective and 26 that have no defects. What is the
probability that all four of the
calculators selected are defective? Round to four
decimal places.
A) 0.1021
B) 0.1586
C) 0.1666
D) 10.9154
Answer:
C) 0.1666
Step-by-step explanation:
The probability of selecting a calculator that is defective can be defined as: [tex]\frac{46}{46+26}[/tex]
The 46 in the numerator is the number of calculators that are defective in the group. The 46 + 26 represents the total amount of calculators since 46 are defective and 26 are not defective and assuming a calculator can only be defective or not defective then these are the total number of calculators in the group.
This gives you a probability of approximately: [tex]\frac{46}{72}[/tex] or approximately 0.638889
We can multiply independent events to find the combined probability of these events occurring. So we have to assume you put the calculator back into group after selecting one.
If this is the case we simply multiply 46/72 * 46/72 * 46/72 * 46/72 or (46/72)^4 to get an approximate probability of: 0.1666
Taylor wants to use a scale factor of 12 to make a smaller drawing of the door image shown. Part of her work is shown. Finish her work to find the height and width of her scale drawing
the height and width of her scale drawing is respectively:
height = 1*1/2inch
width = 3/4 inch
what is dimension?Dimension are the measure of the size or distance of an object or region or space in one direction.
so, all we needs to do is multiply is dimension of the original door image by the scale factor , to get the height and width of the scale drawing.
height: 3 inch x 1/2 =3x1/2=3/2=1x1/2 inch
width: 1x 1/2 inch x 1/2 =3/2 x 1/2= 3x1/2x2=3/4 inch
hence , the height and width of the scale drawing is respectively= 1x 1/2 inch ,3/4 inch
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1 3/4 x 4 2/6 nnnnnnnnnnn
The result of the multiplication operation yields 7 7/12
Multiplication of numbersFrom the question, we are to multiply the given fractions. The given fractions are
1 3/4 and 4 2/6
First, we will convert the fractions to improper fractions
Converting 1 3/4 to an improper fraction
1 3/4 = 7/4
Converting 4 2/6 to an improper fraction
4 2/6 = 26/6
Thus,
The multiplication operation becomes
7/4 × 26/6
= 7/4 × 13/3
= 91/12
= 7 7/12
Hence, the product of the given numbers is 7 1/12
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Write a situation in which positive and negative numbers are used to describe values that have opposite meaning. What does 0 represent in this situation you created? (10 points)
A situation in which positive and negative numbers are used to describe values that have opposite meaning is that John is on top of a mountain that is 2000 above sea level and his friend is diving and is below 2000 feet.
The thing that 0 represents is the addition in the sea level.
How to illustrate the information?Based on the information illustrated, the situation will be that John is on top of a mountain that is 2000 above sea level and his friend is diving and is below 2000 feet.
Therefore, the addition will be:
= 2000 + (-2000)
= 2000 - 2000
= 0
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Find the direction angle of v for the following vector.v=−6i−2jWhat is the direction angle of v?
Given:
v is the given vector.
[tex]v=-6i-2j[/tex]To find:
Find the direction angle of v.
Formula to find the direction:
[tex]\tan \theta=\frac{y}{x}[/tex]From the given vector x and y are:
[tex]x=-6\text{ \& y=-2}[/tex][tex]\begin{gathered} \tan \theta=\frac{-2}{-6} \\ \theta=\tan ^{-1}(\frac{1}{3}) \\ \theta=18.4\degree \end{gathered}[/tex]An actor bought a pearl, diamond, and ruby necklace for his famous wife for $54,000. In 2011 this necklace was auctioned for $11,379,600. The auction price was what percent of the original purchase price?
This necklace sold at auction for $11,379,600 in 2011. The percentage of the initial purchase price was represented by the auction price is 2.1%.
Given that,
For $54,000, an actor purchased a pearl, diamond, and ruby necklace for his well-known wife. This necklace sold at auction for $11,379,600 in 2011.
We have to find what percentage of the initial purchase price was represented by the auction price.
Let us take the percentage as x%.
Necklace sold at auction=the percentage multiplied by the actual price
We get,
$11,379,600 =x%($54,000)
x%=$11,379,600/$54,000
x%=2.1%
Therefore, the percentage of the initial purchase price was represented by the auction price is 2.1%.
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Members of the marching band line up in 6 rows of 8.
Answer: 6x8
Ur answers should be 48 and again we did repeated addition so
6+6+6+6+6+6+6+6 or we can do 12+12+12+12 or 24+24 which we should know use 48
Step-by-step explanation:
how to find the measure of L
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
he deatails of the solution are as follows:
rom tjhe triangle, we can see that Traingle KLM is an isosceles triangle, such that Angle J = 52.3 degrees suchn that:
[tex]Angle\text{ J = Angle K = 52. 3}^0(\text{ base angles are equal\rparen}[/tex]Now, we have that:
[tex]\begin{gathered} Angle\text{ J +Angle K + Angle L = 180}^0 \\ 52.\text{ 3}^0+52.\text{ 3}^0+\text{ Angle L = 180}^0 \\ 104\text{. 6 }^0+\text{ Angle L = 180}^0 \\ Angl\text{e L = 180}^0-104\text{. 6}^0 \\ Angle\text{ L = 75.4}^0 \end{gathered}[/tex]ONCLSUSION:
The measure of Angle L =
[tex]75.\text{ 4}^0[/tex]2. A different pool had an area that is of the form
▢ × 102 + ▢ × 101 + 6
and that can be written in the form x3 ,
where x is a whole number.
A) Decide what your number could be.
B) What is the perfect square number that is closest to the number you chose? What would the side length of a square pool with that area be?
C) Estimate the side length of a square pool with the area you chose in part a).
The area of the pool given by the expression, ∆ × 102 + ∆ × 101 + 6, gives;
A) The whole number x = 33
B) The perfect square number closest to 33 is 36
The side length of a square pool with an area of 36 square units is 6 units
C) The side length of a square pool with the area chosen in part A is 33•√33
What is a mathematical expression?An expression is a mathematical statement which consists of 2 or more numbers and, or variables joined together by mathematical operators.
A) The given equations for the pool is presented as follows;
Area of the pool = ∆ × 102 + ∆ × 101 + 6
Area of the pool = x³
x = A whole number
Expressing the word problem mathematically gives;
∆ × 102 + ∆ × 101 + 6 = x³
203•∆ + 6 = x³
Which gives;
[tex] \displaystyle{ \triangle = \frac{ {x}^{3} - 6}{203} }[/tex]
Using a graphing calculator, when x = 33, we get;
[tex] \displaystyle{ \triangle = \frac{ {33}^{3} - 6}{203} = 177 }[/tex]
The value of the number is x = 33 and ∆ = 177
B) The perfect square that is closest to x = 33 is 36
The side length of a square pool with an area of 36 is √(36) = 6
C).The area of the pool chosen is 33³ = 35937
The side length of a square pool with an area of 35937 is √(35937) = 33•√(33)
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In an experiment, college students were given either four quarters or a $1 bill and they could either keep the money or
spend it on gum. The results are summarized in the table. Complete parts (a) through (c) below.
Using the probability concept, we have that:
a) The probability is of 0.244.
b) The probability is of 0.756.
c) A student given a $1 bill is more likely to have kept the money.
What is a probability?A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.
For item a, we have that out of 11 + 34 = 45 students who were given a $1 bill, 11 spent the money, hence the probability is given as follows:
p = 11/45 = 0.244.
For item b, we have that out of 11 + 34 = 45 students who were given a $1 bill, 34 kept the money, hence the probability is given as follows:
p = 34/45 = 0.756.
For item c, we have that a student given a $1 bill is more likely to have kept the money, as 0.756(kept) > 0.244(spent), which are the two probabilities we found in the previous items.
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help pls!! In the figure below, N is between M and O, and O is between N and P. If NO=2, NP = 8, and MP=15, find MO.
The distance between MO is 9.
How to find MO ?From the question MP is straight line and O & N is points between M & P.
No is 2NP is 8MP is 15so the total length of line is 15
Need to find MO , To find MO = MP - (NP - NO)
= 15 - (8 -2)
= 15 - 6 = 9
The MO is 9.
To find points in graph :
To find a line that's parallel to a line and goes through a particular point, use the point's coordinates for (x1, y1) in point slope form: y - y1 = m (x - x1).The slope intercept formula y = mx + b is used when you know the slope of the line to be examined.Use the slope and one of the points to solve for the y-intercept.One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.To learn more about finding distance refer :
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List the angles of the triangle in order from largest to smallest.Question options:A) ∠A, ∠C, ∠BB) ∠C, ∠B, ∠AC) ∠B, ∠C, ∠AD) ∠A, ∠B, ∠C
Angles opposite to shorter sides are shorter. Then, the shortest angle is opposed to the shortest side.
Since the shortest side has a length 2.8 and is opposed to the angle A, then the shortes angle is A.
The next shortest side is that opposite to B, which has a length of 3.4.
And finally, the largest side has a length of 4.7 and it's opposite to the angle C.
Therefore, the list of angles from largest to smallest, is:
[tex]\angle C,\angle B,\angle A[/tex]Given mn, find the value of x.
t
(7x-1)⁰
(5X-23)°
[tex](5x - 23) + (7x - 1) = 180 \\ 5x + 7x - 23 - 1 = 180 \\ 12x - 24 = 180 \\ 12x = 180 + 24 \\ 12x = 204 \\ \frac{12x}{12} = \frac{204}{12} \\ x = 17[/tex]
x=17°
I used the reasons CORRESPONDING ANGLES AND ANGLES ON A STRAIGHT LINE.Find the center, transverse axis, vertices, foci, and asymptotes. Graph the equation.y² -x² =25
What are the asymptotes?
The asymptote with positive slope is, and the asymptote with negative slope is.
The values are as follows:
center: y²/25-x²/25 = 1
transverse axis : b = 5
Vertices: (0,5) and (0,-5)
Foci: (0,5√2) and (0,-5√2)
Asymptotes: y = x and y = -x
An asymptote is a line being approached by a curve but never touching the curve. i.e., an asymptote is a line to which the graph of a function converges. We usually do not need to draw asymptotes while graphing functions.
Types of Asymptotes:
1) Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k.
2) Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k.
3) Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b.
y² -x² =25 up down hyperbola with (h,k) = (0,0) a = 5 and b = 5
(y-k)²/a²-(x-h)²/b² = 1 is the standard equation of up-down hyperbola.
With semi-axis is a and semi-conjugate axis is b.
and centre (h,k).
Center = (y-0)²/5²-(y-0)²/5² = 1
= y²/25-x²/25 = 1
The axes are a = 5 and b = 5
transverse axis is b = 5
The foci are given by (h, k+c) and (h, k-c), where c = √a²+b²
c = √5²+5² = 5√2
therefore, the foci are (0,5√2) and (0,-5√2).
The vertices are (h, k+a) and (h, k-a)
(h,k) = (0,0) and a = 5 and b = 5
vertices are (0,5) and (0,-5)
Asymptotes are y = x and y = -x.
Therefore, the summary is as follows:
center: y²/25-x²/25 = 1
transverse axis : b = 5
Vertices: (0,5) and (0,-5)
Foci: (0,5√2) and (0,-5√2)
Asymptotes: y = x and y = -x
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Please Help me solve this
The value of f'(x) at x = 1 is 1 for first order derivative of x^x^3.
A derivative in calculus is the rate of change of a quantity y with respect to another quantity x. It is also termed the differential coefficient of y with respect to x. Differentiation is the process of finding the derivative of a function.
Given that, x^x^3 and we have to find the first order derivative with respect to x and then find the value at x = 1.
Let's proceed to solve this question accordingly.
let f(x) = x^x^3
The first order derivative = f'(x) = d/dx(x^x^3)
First apply the generalized power rule, then we have
= x^x^3.d/dx(ln(x)x^3)
Applying the power rule, we get
= x^x^3 (d/dx(x^3).ln(x)+x^3.d/dx(ln(x)))
= x^x^3 (3x^2 ln(x) +x^3.1/x)
= x^x^3 (3x^2ln(x) +x^2)
On simplifying, we will get
= x^x^3+2(3ln(x)+1)
f'(x) = d/dx(x^x^3) = x^x^3+2(3ln(x)+1)
Now, at x = 1, we get
f'(x) = d/dx(x^x^3) = x^x^3+2(3ln(x)+1) = 1
Therefore, f'(x) = d/dx(x^x^3) = x^x^3+2(3ln(x)+1) = 1 is the required answer.
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5. Geometry Audrey draws a triangle that has
these sides: s, s, and is. When the length of s
is doubled, the new perimeter is twice the old
perimeter less 14. What are lengths of
the triangle?
The length of each side is less than sum of the lengths of the other two sides and greater than the difference between these lengths.
2s is not less than 1/2s+ 2/3s
What is a triangle?A triangle is polygon with the three edges and three vertices. It is one of the basic shapes in the geometry. A triangle with the vertices A, B, and C is denoted Δ ABC.
In the Euclidean geometry, any three points, when the non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. two-dimensional Euclidean space). In the other words, there is the only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only Euclidean plane, there is only one plane and all triangles are contained in it; however, in the higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in the Euclidean geometry, and in the particular, the Euclidean plane, except where otherwise noted.
new triangle perimeter is = 2s + 1/2s + 2/3s
This new triangle, however, cannot be created physically because
The length of each side is less than sum of the lengths of the other two sides and greater than the difference between these lengths.
2s is not less than 1/2s+ 2/3s
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write 7843 to nearest thousand with explanations
Solve I =prt for p when I =5,480,r =.04, and t=7. Round your answers to two decimal pla
We are asked to find the simple interest associated with a principal of 5480 , an annual rate of 0.04 (4%) and at the end of 7 years:
We use the simple interest formula:
I = P r t
in our case: I = (5480) (0.04) (7) = 1534.4
So the interest is: 1534.40
We answer using two decimal places because this is refering to cents of a dollar.
Write an equation for a parabola with x-intercepts (-3,0) and (4,0) which passes through the point (2,-40)
The parabolic equation that passes through the points is y = 29/7x^2 + -27/7x - 342/7
What are parabolic equations?Parabolic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the equation of the parabola?The given parameters are
x-intercepts (-3,0) and (4,0)
Point = (2,-40)
From the definition above, we have the form to be
y = ax^2 + bx + c
Substitute (-3,0) and (4,0) in the above equation
So, we have
0 = a(-3)^2 + b(-3) + c
0 = a(4)^2 + b(4) + c
This gives
9a -3b + c = 0
16a + 4b + c = 0
Substitute (2,-40) in the above equation y = ax^2 + bx + c
a(2)^2 + b(2) + c = -40
So, we have
4a + 2b + c = -40
The equations become
9a -3b + c = 0
16a + 4b + c = 0
4a + 2b + c = -40
Using a graphing tool, we have
a = 29/7, b = -27/7 and c = -342/7
So, we have
y = ax^2 + bx + c
This gives
y = 29/7x^2 + -27/7x - 342/7
Hence, the equation is y = 29/7x^2 + -27/7x - 342/7
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There are 28 students in a class.
16 of the students are girls.
What proportion are boys?
Write your answer in two ways.
Answer:
3:7
Step-by-step explanation:
Given:
There are 28 students in a class16 of the students are girls.To Find:
What proportion of the students are boys.Formula used:
No. of boys = Total students - No. of girlsUsing the formula, we have
No. of boys = 28 - 16 = 12
Proportion of boys = 12/28 = 3/7
So, proportion of boys = 3:7.
Katie wants to save at least $280 to go on the math team field trip. He currently has $112 saved.
If he has 8 weeks left to save, which inequality and graph represent the amount of money per week he needs to save to meet the goal?
He must save 21 dollars per week to meet the goal.
How to find the amount to be saved?Given,
Katie wants to save at least $280
He currently has $112 saved.
If he has 8 weeks left to save.
Solution:
The amount to be saved is $280 - $112 = $168
If he has 8 weeks left to save,
Per week he must save = $168/8
= $21
He must save 21 dollars per week to meet the goal.
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Find the x-intercept of the function g(x)=8x²-10x-3
To find the x-intercepts of the function g(x), we must set it equal to 0 and solve for x.
We have the following:
[tex]\begin{gathered} g(x)=8x^2-10x-3 \\ if\text{ g(x)=0} \\ \Rightarrow8x^2-10x-3=0 \end{gathered}[/tex]we can use the quadratic formula to get the roots of the polynomial:
[tex]\begin{gathered} a=8 \\ b=-10 \\ c=-3 \\ x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \Rightarrow x_{1,2}=\frac{-(-10)\pm\sqrt[]{(-10)^2-4(8)(-3)}}{2(8)}=\frac{10\pm\sqrt[]{196}}{16} \\ \Rightarrow x_{1.2}=\frac{10\pm14}{16} \\ \Rightarrow x_1=\frac{10+14}{16}=\frac{24}{16}=\frac{3}{4} \\ \Rightarrow x_2=\frac{10-14}{16}=\frac{-4}{16}=-\frac{1}{4} \end{gathered}[/tex]therefore, the x-intercepts of the function g(x) are the points (3/4,0) and (-1/4,0)
(11, 3) and (4, 3) on a coordinate plane?
The midpoint of the given points (11, 3) and (4, 3) on the coordinate plane is ( 15/2, 3 ).
How calculate the midpoint between two point?A midpoint is simply a point that divides a line segment into two equal halves.
The midpoint formula is expressed as;
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
Given the data in the question;
Point 1( 11, 3 )
x₁ = 11y₁ = 3Point 2( 4, 3 )
x₂ = 4y₂ = 3Midpoint = ?
To find the midpoint, plug the given points into the midpoint formula above and simplify.
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
M = ( ( 11 + 4 )/2, ( 3 + 3 )/2 )
M = ( ( 15 )/2, ( 6 )/2 )
Midpoint M = ( 15/2, 3 )
Therefore, the midpoint of the given coordinates is ( 15/2, 3 ).
Learn more about the midpoint formula here: brainly.com/question/14687140
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