We know that
• The gardener used at most 56 feet of fencing.
,• The length of the fence is four feet longer than the width.
Remember that the perimeter of a rectangle is defined by
[tex]P=2(w+l)[/tex]Now, let's use the given information to express as inequality.
[tex]2(w+l)\leq56[/tex]However, we have to use another expression that relates the width and length.
[tex]l=w+4[/tex]Since the length is 4 units longer than the width. We replace this last expression in the inequality.
[tex]\begin{gathered} 2(w+w+4)\leq56 \\ 2(2w+4)\leq56 \\ 2w+4\leq\frac{56}{2} \\ 2w+4\leq28 \\ 2w\leq28-4 \\ 2w\leq24 \\ w\leq\frac{24}{2} \\ w\leq12 \end{gathered}[/tex]The largest width possible is 12 feet.
Now, we look for the length.
[tex]\begin{gathered} 2(12+l)\leq56 \\ 24+2l\leq56 \\ 2l\leq56-24 \\ 2l\leq32 \\ l\leq\frac{32}{2} \\ l\leq16 \end{gathered}[/tex]Therefore, the largest measure possible for the length is 16 feet.what is the flying distance between the greenhouse and the stadium
The flying distance between the greenhouse and the stadium = 5 units
Explanations:The coordinates of the greenhouse: (-6, 0)
The coordinates of the stadium: (-2, 3)
The distance between two points of coordinates (x₁, y₁) and (x₂, y₂) is given as:
[tex]D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]For the flying distance between the greenhouse and the stadium:
x₁ = -6, y₁ = 0, x₂ = -2, y₂ = 3
Substitute these values into the distance equation given above:
[tex]\begin{gathered} D\text{ = }\sqrt[]{(-2-(-6))^2+(3-0)^2} \\ D\text{ = }\sqrt[]{(-2+6)^2+3^2} \\ D\text{ = }\sqrt[]{4^2+3^2} \\ D\text{ = }\sqrt[]{16+9} \\ D\text{ = }\sqrt[]{25} \\ D\text{ = 5} \end{gathered}[/tex]The flying distance between the greenhouse and the stadium = 5 units
Find the exact length of the floor clearance, using metres.
the length of the floor clearance is 2.8 m
Explanationas we have 2 similar triangles ( ABC and AED) we can set a proportion
Step 1
a)let
[tex]ratio=\frac{vertical\text{ side}}{horizontal\text{ side}}[/tex]so
for triangle ABC ( divide the given measure by 100 to obtain meters)
[tex]ratio_1=\frac{0.30\text{ m}}{0.40\text{ m}}=\frac{3}{4}[/tex]and
for triangle AED
let
[tex]ratio_2=\frac{2.1}{floor\text{ clearance}}[/tex]Step 2
as the ratio is the same, set the proportion
[tex]\begin{gathered} ratio_1=ratio_2 \\ \frac{3}{4}=\frac{2.1}{floor\text{ clerance}} \\ solve\text{ for floor clearance} \\ floor\text{ }cleareance=\frac{2.1*4}{3} \\ floor\text{ }cleareance=2.8\text{ m} \end{gathered}[/tex]therefore, the length of the floor clearance is 2.8 m
I hope this helps you
18 18 After bisecting the original angle, there are two angles that each measure 18°. Which statement is true? A) The original angle of 2° was bisected into two congruent angles. B) The original angle of 9° was bisected into two congruent angles. Eliminate The original angle of 36° was bisected into two congruent angles. D) The original angle of 72° was bisected into two congruent angles.
After bisecting the original angle, there are two angles that each measure 18°. Which statement is true? A) The original angle of 2° was bisected into two congruent angles. B) The original angle of 9° was bisected into two congruent angles. Eliminate The original angle of 36° was bisected into two congruent angles. D) The original angle of 72° was bisected into two congruent angles.
we know that
when bisecting an angle, the angle is divided into two equal parts
so
The original measure of the angle is
18(2)=36 degrees
therefore
The statement that is true is
The original angle of 36° was bisected into two congruent angleshow do I solve this linear equations by substitution x=5 x + y = 4
Substitute 5 for x in the equation x+y=4 to obtain the value of y.
[tex]\begin{gathered} 5+y=4 \\ y=4-5 \\ =-1 \end{gathered}[/tex]So solution of the equations is (5,-1).
The figure below is a net for a right rectangular prism. Its surface area is 432 m2 andthe area of some of the faces are filled in below. Find the area of the missing faces,and the missing dimension.
The surface area is the sum of all the areas in the given prims, then we have:
[tex]SA=72+72+48+48+2A[/tex]Plugging the value for the surface area and silving for A we have:
[tex]\begin{gathered} 432=72+72+48+48+2A \\ 432=240+2A \\ 2A=432-240 \\ 2A=192 \\ A=\frac{192}{2} \\ A=96 \end{gathered}[/tex]Now that we know the missing area we can know the missing dimension:
[tex]\begin{gathered} 96=8x \\ x=\frac{96}{8} \\ x=12 \end{gathered}[/tex]Therefore the missing length is 12.
Find the measure of ZGHJ and LGIJ.68°H 31GK115angle GH) =degreesangle GIJ =degrees
Step 1: Find arc angle GJ
The sum of the arc angles of a circle is 360°.
Therefore,
[tex]\begin{gathered}step2: Find the angle GKJ, the angle subtended by the arc GJ
The angle GKJ is the angle subtended by the arc GJ at the center of the circle
Therefore,
[tex]<\text{GKJ }=\text{ m < GJ }=146^o[/tex]Step 3: Find m < GHJ
From Circle theorem, we know that the angle at the center of a circle is twice the angle at the circumference
Therefore,
[tex]\begin{gathered} <\text{GKJ }=2\timesHence, m 73°Step 4: Find m < GIJFrom Circle theorem, the angles in the same segment are equalTherefore,[tex]<\text{GIJ }=Hence, m < GIJ = 73°What is f(2) for the function f(x) = 2x^2 + 6x – 5?
f(x) = 2x² + 6x – 5
To find f(2) you have to replace x = 2 into the function, as follows:
f(2) = 2(2)² + 6(2) – 5
f(2) = 2(4) + 12 – 5 Solving the square and the multiplication
f(2) = 8 + 12 – 5 Solving the multiplication
f(2) = 15
Calculate the area of the circle shown below.10 in Approximate Value_________Exact Value________(round your approximate answers to thehundredths)Circumference of the circle:_________ in?_________ in?
The radius of the circle is r=10 in.
The circumference of the circle is,
[tex]\begin{gathered} C=2\pi r \\ =2\pi\times10 \\ =20\pi \\ =62.83in \end{gathered}[/tex]Thus, the exact value of circumference is 20pi inches and the approximate value is 62.83 in.
The expression 5a + 3c can be used to find the cost of a adults and c children to attend the school play. What is the cost of 4 adults and 9 children to attend the school play?
The expression 5a + 3c can be used to find the cost of a adults and c children to attend the school play, so we have a expression as a function of the number of adults a and the number of children c. Therefore:
[tex]C(a,c)=5a+3c[/tex]What is the cost of 4 adults and 9 children to attend the school play?
[tex]\begin{gathered} a=4 \\ c=9 \\ C(4,9)=5(4)+3(9) \\ C(4,9)=20+27 \\ C(4,9)=47 \end{gathered}[/tex]$47
Simplify the square root:square root of negative 72 end rootAnswer choices Include:2 i square root of 186 i square root of 218 i square root of 22 i square root of 6
We need to simplify the next square root:
[tex]\sqrt[]{-72}[/tex]First, we need to rewrite the expression as:
[tex]\sqrt{-72}=\sqrt[]{-1}\ast\sqrt[]{72}[/tex]Where √-1 = i
Therefore:
[tex]\sqrt{-1}\ast\sqrt{72}=\sqrt[]{72}\text{ i}[/tex]Finally, we can simplify inside of the square root:
[tex]\sqrt[]{72}i=\sqrt{6\ast6\ast2}i=\sqrt{6^2\ast2}i=6i\sqrt[]{2}^[/tex]Therefore, the correct answer is "6 i square root of 2".
help me havig a hard time .
What is the conversion factor?
It is a number used to change one unit to another when it is multiplied.
Jenna wants to know how many pounds correspond to 50 tons, she does know that 1 ton = 2,000lb. Then she has the following equivalence:
50 tons ⇄ ??
1 ton ⇄ 2,000 lb
We know that if we divide both sides of the equivalence we will have the same result:
[tex]\frac{50\text{tons}}{1\text{ton}}=\frac{?\text{?}}{2000lb}[/tex]Multiplying both sides by 2000lb we have that
[tex]undefined[/tex]Skip designs tracks for amusement park rides. For a new design, the track will be elliptical. If the ellipse is placed on a large coordinate grid with its center at (0, 0), the equation x^2/2500 + y^2/8100 = 1 models the path of the track. The units are given in yards. How long is the major axis of the track? Explain how you found the distance.show the steps
Step 1
Given:
center (0,0)
the equation given should have been:
[tex]\frac{x^2}{2500}+\frac{y^2}{8100}=1[/tex]We need to identify the larger denominator. If it is under x, the ellipse is horizontal. If it is under y, the ellipse is vertical. 8100 is the larger denominator and is under y, therefore, the ellipse is vertical
Step 2
The general equation of an ellipse is given as;
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]h and k are the center values which are both 0.
a = length of the semi-major axis
b = length of the semi-minor axis
The given equation is;
[tex]\frac{x^2}{2500}+\frac{y^2}{8100}=1[/tex]which is equivalent to;
[tex]\frac{x^2}{50^2}+\frac{y^2}{90^2}=1[/tex][tex]\begin{gathered} a^2=90^2 \\ \sqrt[]{a^2}=\sqrt[]{90^2} \\ a=90\text{ yard},\text{ the semi-major ax}is \end{gathered}[/tex]The length of the major axis will thus be; 90x2=180 yards
Answer; 180 yards
which shows the line of best fit for the data
Solution:
Given:
Graphs showing lines through different points.
To get the line of best fit for the data.
The line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.
It is the line that touches most points or passes through most of the points.
From the four graphs given, the line that touches or passes through most points is;
Therefore, the graph above is the line of best fit.
The second graph is the correct answer.
Z + 24 = -33one step equation
We solve as follows:
[tex]z=-57[/tex]We operate like terms after substracting 24 from each side of the function.
Please help me with the last part of the question thanks
There is a direct proportion between two values when one is a multiple of the other.
In this case, we have:
[tex]1\text{ hour = 60 minutes}[/tex]This means that to convert hours to minutes, the multiplier is always 60.
The equation of a direct proportion is:
[tex]undefined[/tex]The values of events A, B, and C are provided. Compare the probabilityof event A occurring, given that event C occurred to the probability ofEvent B happening, given that event C occurred (Compare P(A/C) toP(BIC)] Which event is more likely?P(A) = 0.45P(B) = 0.30P(C) = 0.25
The conditional probability P(A/C) is given by
[tex]P(A|C)=\frac{P(A\cap C)}{P(C)}[/tex]If event A is independent to event C, we can write
[tex]P(A|C)=\frac{P(A)\cdot P(C)}{P(C)}=P(A)[/tex]Similary, if event B is independent to event C, we get
[tex]P(B|C)=\frac{P(B)\cdot P(C)}{P(C)}=P(B)[/tex]Then, by comparing both results we can see that event A is more likey than event B.
What is the value of x? 830 R 620 5х-130 6x – 360
Question:
Solution:
The entire circumference is equivalent to traveling 360 degrees. Therefore, we have the following equation:
[tex]83+62+(5x-13)+(6x-36)\text{ = 360}[/tex]this is equivalent to:
[tex]83+62-13-36+(5x+6x)\text{ = 360}[/tex]this is equivalent to:
[tex]96\text{ +11x = 360}[/tex]this is equivalent to:
[tex]11x\text{ = 360-96 = 297}[/tex]and solving for x, we obtain:
[tex]x\text{ = }\frac{264}{11}=\text{ 2}4[/tex]then, the correct answer is:
[tex]x\text{ = 2}4[/tex]Consider the following graph of two functions.(8-1-2)Step 3 of 4: Find (8.5(-2)Enable Zoom/Pan866) = -3010-35SG) = x + 3
The question requires that we evaluate the value of:
[tex](g\cdot f)(-2)[/tex]Recall that:
[tex]\left(g\cdot \:f\right)\left(x\right)=g\left(x\right)\cdot \:f\left(x\right)[/tex]Therefore, we have that:
[tex]\left(g\cdot\:f\right)\left(-2\right)=g\left(-2\right)\cdot\:f\left(-2\right)[/tex]We can get the values of g(-2) and f(-2) from the graph as shown below:
Therefore, we have:
[tex]\begin{gathered} g(-2)=5 \\ f(-2)=1 \end{gathered}[/tex]Hence, we can calculate the composite function to be:
[tex]\begin{gathered} (g\cdot f)(-2)=5\times1 \\ (g\cdot f)(-2)=5 \end{gathered}[/tex]Consider the following rational expression:2 – 2y / 2y - 2Step 1 of 2: Reduce the rational expression to its lowest terms.Answer
Factor out 2 on both numerator and denominator
[tex]\begin{gathered} \frac{2-2y}{2y-2} \\ =\frac{2(1-y)}{2(y-1)} \\ \\ \text{cancel out }2\text{ on both numerator and denominator} \\ =\frac{\cancel{2}(1-y)}{\cancel{2}(y-1)} \\ =\frac{(1-y)}{(y-1)} \\ \\ \text{factor out }-1\text{ on numerator},\text{ and rearrange to cancel out common binomial} \\ =\frac{(1-y)}{(y-1)} \\ =\frac{-1(-1+y)}{(y-1)} \\ =\frac{-1(y-1)}{(y-1)} \\ =\frac{-1\cancel{(y-1)}}{\cancel{(y-1)}} \\ =-1 \\ \\ \text{Therefore,} \\ \frac{2-2y}{2y-2}=-1 \end{gathered}[/tex]Part 2:
Since the given expression is in fraction, we cannot let the denominator equal to zero. Find values of y that makes the denominator by zero
[tex]\begin{gathered} \text{Denominator: }2y-2 \\ \\ \text{Equate to zero} \\ 2y-2=0 \\ 2y-2+2=0+2 \\ 2y\cancel{-2+2}=2 \\ \frac{2y}{2}=\frac{2}{2} \\ y=1 \\ \\ \text{If }y=1,\text{ the denominator }2y-2\text{ becomes zero therefore}, \\ y\neq1 \end{gathered}[/tex]To solve rational equation shown below, find the common denominator
Given:
[tex]\frac{3}{2x+1}=\frac{5}{4x+3}[/tex][tex]3(4x+3)=5(2x+1)[/tex][tex]12x+9=10x+5[/tex][tex]12x-10x=5-9[/tex][tex]2x=-4[/tex][tex]x=-\frac{4}{2}[/tex][tex]x=-2[/tex]According to the diagram, an 8-foot-tall statue casts a shadow on the ground that is 15 feet in length. Based on this information, which trigonometric ratio has the value 8/15 ?A. cos CB. tan BC. cos BD. tan C
the right optio is tan C because...
[tex]undefined[/tex]Find the volume of a candy corn, assume they are rectangular pyramids with a length of 8.2 mm, a width of 3.5 mm and a height of 20.1 mm
Given:
Lenght =8.2mm , width = 3.5mm and height = 20.1
The volume of pyramid is given by,
V=1/3 (base area) (height)
As it is rectangular pyramid,
first find area of reactangle . this will be base area for pyramid.
area of reactangle=lenght * weight
[tex]\begin{gathered} A=l\cdot w \\ =8.2\cdot3.5 \\ =28.7\text{ cm}^2 \end{gathered}[/tex]Volume is,
[tex]\begin{gathered} V=\frac{1}{3}\cdot A\cdot h \\ =\frac{1}{3}\cdot28.7\cdot20.1 \\ =192.29\text{ cm}^3 \end{gathered}[/tex]What is 5x2 (This is a joke)
Answer:
10 (duh)
Step-by-step explanation:
I just need the first one thanks
If the vector is pointing in the opposite direction of [-4,3], we can say it is pointing in the same direction of the vector [4,-3]. We just flipped the direction of the vector by changing the sign of the components.
We have now a vector that is pointing in the same direction of the vector we are looking for. Let's find the length of that vector to see how much it has to be scaled, or if it does not need to be scaled.
The length of the vector is calculated as the square root of the sum of the square of its components:
[tex]\text{Length}=\sqrt[]{x^2+y^2}[/tex]Then, the length of the vector is:
[tex]\begin{gathered} \text{Length}=\sqrt[]{4^2+(-3)^2}=\sqrt[]{16+9}=\sqrt[]{25} \\ \\ \text{Length}=5 \end{gathered}[/tex]Then the length of the vector [4,-3], which is pointing opposite to the vector [-4,3], happens to have a length of 5, then, that is the vector we were looking for. There is no need to scale it.
Then, the components of the vector are 4 and -3. [4,-3]
Write the equation of the line that is perpendicular to the line 8y−16=5x through the point (5,-5).A. y=5/8x+3B. y=−8/5x−3C. y=−8/5x+3D. y=8/5x+3
Given the equation of the line below,
[tex]8y-16=5x[/tex]If the line passes through the point,
[tex](5,-5)[/tex]Re-writing the eqaution of the line in slope intercept form,
[tex]\begin{gathered} 8y-16=5x \\ 8y=5x+16 \\ \text{Divide both sides by 8} \\ y=\frac{5x}{8}+\frac{16}{2} \\ y=\frac{5}{8}x+2 \end{gathered}[/tex]The slope of the perpendicular line is the negative reciprocal of the slope of the eqaution of the line in the slope-intercept form given above
The general form of the slope-intercept form of the equation of a straight line is,
[tex]\begin{gathered} y=mx+c \\ \text{Where m is the slope} \\ y=\frac{5}{8}x+2 \\ m=\frac{5}{8} \\ \text{Slope of the perpendicular line is} \\ m_1=-\frac{1}{m} \\ m_{1_{}}=-\frac{1}{\frac{5}{8}}=-1\times\frac{8}{5}=-\frac{8}{5} \end{gathered}[/tex]The formula to find the equation of a line with point (5, -5) below is,
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=m_1 \\ \text{Where} \\ (x_1,y_1)=(5,-5) \\ m_1=-\frac{8}{5} \end{gathered}[/tex]Substitute the values into the formula of the eqaution of a straight line,
[tex]\begin{gathered} \frac{y-(-5)}{x-5}=-\frac{8}{5} \\ \frac{y+5}{x-5}=-\frac{8}{5} \\ \text{Crossmultiply} \\ 5(y+5)=-8(x-5) \\ 5y+25=-8x+40 \\ \text{Collect like terms} \\ 5y=-8x+40-25 \\ 5y=-8x+15 \\ \text{Divide both sides by 5} \\ \frac{5y}{5}=-\frac{8}{5}x+\frac{15}{5} \\ y=-\frac{8}{5}x+3 \end{gathered}[/tex]Hence, the right option is C
Question 7b: Let g(x) be a polynomial function. Name all horizontal andvertical intercepts of the graphsg(x) = (x - 1)2 (x + 2)Horizontal intercepts: 1, -2; vertical intercepts: 2Horizontal intercepts: 2, vertical intercepts: 1,-2Horizontal intercepts: -1, 2, vertical intercepts: 4Horizontal intercepts: 4, vertical intercepts: -1,2
The given function is expressed as
g(x) = (x - 1)^2(x + 1)
It can be written as
y = (x - 1)^2(x + 1)
The horizontal intercept is also known as the x intercept. The x intercept is the value of x when y = 0
If we substitute y = 0 into the function, it becomes
0 = (x - 1)^2(x + 2)
This means that
(x - 1)^2 = 0 and x + 2 = 0
For (x - 1)^2 = 0, if we take the square root of both sides, it becomes
x - 1 = 0
x = 1
For x + 2 = 0,
x = - 2
Thus, the horizontal intercepts are 1 and - 2
The vertical intercept is also known as the y intercept. The y intercept is the value of y when x = 0
If we substitute x = 0 into the function, it becomes
y = (0 - 1)^2(0 + 2)
y = (- 1)^2(2)
y = 1 * 2 = 2
Thus, the vertical intercept is 2
Thus, the correct option is
Horizontal intercepts: 1, -2; vertical intercepts: 2
which expression is equivalent to 7y + 7y?
Evaluate the value of expression.
[tex]7y+7y=14y[/tex]So answer is 14y.
The question is in the image. Answer question 20 only.
To convert radians to degrees we use the formula:
[tex]\theta\cdot\frac{180}{\pi}[/tex]In this case the angle is 12 radians, then we have:
[tex]12\cdot\frac{180\degree}{\pi}=687.55[/tex]Therefore, the angle in degrees is 687.55°
how much time has elapse? 3:00 A.M to 7:14 A.M
To know how much time has elapsed from 3:00 A.M. to 7:14 A.M., we subtract the hours with the hours and the minutes with the minutes,
[tex]\begin{gathered} \text{Hours,} \\ 7h-3h=4h \\ \text{ Minutes,} \\ 14\min -0\min =14\min \end{gathered}[/tex]So, the time that has elapsed is 4 hours 14 minutes.
Write an equation for the line that contains (-32, -12) and is perpendicularto the graph -8x + 10y = 40Can anyone that KNOWS the answer help?
The first step is finding the slope of the equation -8x + 10y = 40.
To do so, let's put this equation in the slope-intercept form: y = mx + b, where m is the slope.
So we have:
[tex]\begin{gathered} -8x+10y=40 \\ -4x+5y=20 \\ 5y=4x+20 \\ y=\frac{4}{5}x+4 \end{gathered}[/tex]Then, since the line we want is perpendicular to this given line, their slopes have the following relation:
[tex]m_2=-\frac{1}{m_1}[/tex]So, calculating the slope of the line, we have:
[tex]m_2=-\frac{1}{\frac{4}{5}}=-\frac{5}{4}[/tex]Finally, our equation has the point (-32, -12) as a solution, so we have:
[tex]\begin{gathered} y=mx+b \\ y=-\frac{5}{4}x+b \\ -12=-\frac{5}{4}\cdot(-32)+b \\ -12=-5\cdot(-8)+b \\ -12=40+b \\ b=-12-40 \\ b=-52 \end{gathered}[/tex]So our equation is y = (-5/4)x - 52
