Answer:
Step-by-step explanation:
To create a system of equations, write an equation to model each condition that must be satisfied in the given situation.
It is given that x represents the width of the flower bed and that y represents the area of the base of the birdbath.
Write an equation to represent the condition regarding the planting area in the flower bed. It is given that there is 35 square feet of planting area. The flower bed is 3 feet longer than the width.
x(x+3) - y = 35
Write an equation to represent the condition regarding the cost of the soil and the birdbath. The question gives that the soil will cost $5 per square foot and the birdbath will cost $18 per square foot of the base.
5x(x+3)+18y=150
Combining both of the equations gives the following system of equations.
x(x+3)-y=35
5x(x+3)+18y=150
Proving when a parallelogram is a rectangle
This took a little longer than expected but I hope this helps... Please leave a rating and a thanks
Sincerely, Another Brainly User
The given parallelogram is a rectangle when ΔZYX ≅ ΔWXY.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
In the given parallelogram WXYZ,
ZX ≅ WY.
For ΔZXY and ΔWXY,
ZX = WY (already given)
ZY = WX (two opposite sides of the parallelogram WXYZ)
XY is the common side
Therefore, ΔZXY ≅ ΔWXY
Now, we can say, ∠ZYX = ∠WXY
For the given parallelogram, ∠ZYX + ∠WXY = 180°
ZYX = ∠WXY = 90°
Hence, the given parallelogram is a rectangle.
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A line passes through the points (–1, –5) and (4, 5). The point (a, 1) is also on the line.
what is the value of a
Answer:
a = 2
Step-by-step explanation:
Let's find the equation of the line using the 2 points given.
Let's call -1 as x_1 and -5 as y_1
also, 4 as x_2 and 5 as y_2
The equation of line is :
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Let's plug the points and get the equation of the line:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y+5=\frac{5+5}{4+1}(x+1)\\y+5=2(x+1)\\y+5=2x+2\\y=2x-3[/tex]
Now, to find a, we substitute a in x and 1 in y of the equation of the line we just got:
[tex]y=2x-3\\1=2(a)-3\\1=2a-3\\2a=4\\a=\frac{4}{2}=2[/tex]
Answer: [tex]a=2[/tex]
Step-by-step explanation:
We know that this line passes through the point [tex](a,1)[/tex] where "a" is the unknown x-coordinate of that point and 1 is the y-coordinate.
We also know that this line passes through the points (-1, -5) and (4, 5).
Then, in order to find the value of "a", we can plot the known points and draw the line (Observe the image attached).
You can observe in the image attached that the point whose y-coordinate is 1 is the point (2,1). Therefore, the value of "a" is:
[tex]a=2[/tex]
Which values of P and Q result in an equation with exactly one solution? Px -43= -42x+Q. Choose all answers that apply. A. P= 42 and Q = 42. B. P= 43 and Q = -42. C. P= -43 and Q = -43. D.P = 42 and Q= 43
Answer:
All are valid
Step-by-step explanation:
Px - 43 = -42x + Q (rearrange)
x = (Q+43) / (P + 42) <----Substitute options for P & Q into this equation to see which combination gives exactly 1 solution for x
A) P=42, Q = 42; x = (42+43) / (42+42) = 1.011 (only 1 solution = valid)
B) P=43, Q = -42; x = (-42+43) / (43+42) = 0.012 (only 1 solution = valid)
C) P=-43, Q = -43; x = (-43+43) / (-43+42) = 0 (only 1 solution = valid)
D) P=42, Q = 43; x = (42+43) / (42+42) = 1.023 (only 1 solution = valid)
what is the rise over run
Rise over run is another term for slope, with we can use to derive a linear equation.
The term rise over run in technical terms is the change of y over the change of x.
To find the rise over run, subtract the y terms and divide that by the x terms.
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
You can use this to derive a linear equation as earlier mentioned by plugging in given points.
For example, a line passes through (3,4) with a rise over run of 3.
[tex]y=mx+b[/tex]
[tex]4=3(3)+b[/tex]
[tex]4=9+b[/tex]
[tex]b=-5[/tex]
So therefore the y intercept is -5, and the equation is [tex]y=3x-5[/tex]
Which table represents a linear function with a greater y-intercept than that of the function represented in the graph?
A.
x y
0, 3
6, -39
B.
x y
-2, 0
0 ,2
C.
x y
0, 5
5, -45
D.
x y
-2, 1
0, 4
E.
x y
0, -7
4 ,11
Answer:
C.Step-by-step explanation:
The y-intercept of the function represended in the graph is 4 → (0, 4).
The table C. represents a linear function with a greater y-intercept (0, 5) → 5.
Which undefined geometric term is described as a location on a coordinate plane that is designed by an ordered pair (x,y) ?
Answer:
Point
Step-by-step explanation:
Answer:
the answer is D
Step-by-step explanation:
I got it right on E2020
Two factors of –48 have a difference of 19. The factor with a greater absolute value is positive. What is the sum of the factors?
Answer:
13
Step-by-step explanation:
Two factors of -48... that means two numbers which multiplied together give a result of -48, like -6 and 8 for example.
The difference of those two factors is -19. There not that many possible factors for -48, so if we list them we'll be able to spot a pair with a difference of 19.
A first list of factors for -48 is: -1 and 48, -2 and 24, -3 and 16, -4 and 12, -6 and 8.
We can create another list by inverting the signs: 1 and -48, 2 and -24, 3 and -16, 4 and -12, 6 and -8.
The question says the difference of the two factors is 19... can you spot in each list a pair of factors having a difference of 19? I see -3 and 16 and also 3 and -16.
The question also say the one of the greatest absolute value is positive... so that means it's a pair with +16, not -16.
The pair of factors we're looking for is then -3 and 16. They are factors of -18, they have a difference of 19, and the one with the greatest absolute value is positive.
The sum of -3 and 16 is 13.
What is the length of the hypotenuse in the right triangle shown below?
Picture needed. not enough info
Answer:
a² + b² = c², where a and b are the legs and c is the hypotenuse.
surface area in terms of pi?
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=972\pi \end{cases}\implies 972\pi =\cfrac{4\pi r^3}{3}\implies 2916\pi =4\pi r^3 \\\\\\ \cfrac{2916}{4\pi }=r^3\implies 729=r^3\implies \sqrt[3]{729}=r\implies 9=r \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a sphere}\\\\ SA=4\pi r^2\qquad \qquad \implies SA=4\pi (9)^2\implies \boxed{SA=324\pi }[/tex]
Which statements correctly describe the association between the variables A and B?
Select each correct answer.
no association
nonlinear association
negative association
positive association
linear association
Answer:
positive association
linear association
Step-by-step explanation:
It is said that two variables A and B are related when the distribution of the values of one of the two variables differs according to the values of the other.
That is, when variable A grows then variable B also grows. This is known as positive correlation
When variable A grows then variable B decreases. This is known as negative correlation.
In the scatter plot you may notice that when variable A increases then variable B also increases, in an approximately linear relationship. Therefore it can be said that there is a positive and linear association.
The answer is the fourth and fifth option.
A parent increases a child's allowance by 15 % each year. If the allowance is now $9, about how many years will it take for it to double? Use the equation 18 9(1.15)^x. Round to the nearest year.
Answer:
5 years
Step-by-step explanation:
18= 9(1.15)^x
Divide each side by 9
18/9= 9/9 *(1.15)^x
2 = 1.15 ^x
Take the log on each side
log (2) = log (1.15^x)
log 2 = x log 1.15
Divid each side by log (1.15)
log 2 / log 1.15 = x log 1.15/ log 1.15
log 2 / log 1.15 = x
4.959484455 = x
To the nearest year
5 years
If x = -2, then x 2-7x+10 equals
a. 0
b.20
c.28
ANSWER
C. 28
EXPLANATION
The given expression is
[tex] {x}^{2} - 7x + 10[/tex]
We want to evaluate this function at x=-2.
We just have to substitute x=-2 into the given expression.
In other words, we have to replace x with -2 wherever we see x in the expression
[tex]{( - 2)}^{2} - 7( - 2) + 10[/tex]
We evaluate the exponent to get
[tex]4 - 7( - 2) + 10[/tex]
We multiply next to get:
[tex]4 + 14+ 10[/tex]
We now add to obtain:
[tex]28[/tex]
The correct answer is C
A small tailors’ company wants to use at least 130 yards of fabric to sew evening skirts and dresses. A dress requires 4 yards of fabric and the production of a skirt will need 3 yards. Research shows that they will be able to sell at most three times as many skirts as dresses . A dress will take 10 hours to produce and a skirt will take 1 hour. They can assign to this work no more than 286 hours. Each dress will sell for $540, and each skirt will sell for $180. How many skirts should they sew to maximize the profit?
To maximize profit, the tailors' company should sew 14 skirts, achieving the optimal balance between fabric usage, production hours, and selling constraints.
To maximize profit, the tailors' company should determine the number of skirts and dresses to produce. Let's denote:
- x: Number of dresses to produce
- y: Number of skirts to produce
The constraints are:
1. Fabric usage: [tex]\(4x + 3y \geq 130\)[/tex] (at least 130 yards)
2. Selling constraint: [tex]\(y \leq 3x\)[/tex] (at most three times as many skirts as dresses)
3. Production hours constraint: [tex]\(10x + y \leq 286\)[/tex] (no more than 286 hours)
4. Non-negativity constraint: [tex]\(x \geq 0\)[/tex], [tex]\(y \geq 0\)[/tex]
The profit function to maximize is:
[tex]\[ \text{Profit} = 540x + 180y \][/tex]
We can solve this problem using linear programming. Here's the optimization model:
Objective function:
Maximize 540x + 180y
Subject to:
[tex]\[4x + 3y \geq 130\][/tex]
[tex]\[y \leq 3x\][/tex]
[tex]\[10x + y \leq 286\][/tex]
[tex]\[x \geq 0\][/tex]
[tex]\[y \geq 0\][/tex]
Using a linear programming solver, we can find the optimal values of x and y that maximize profit.
The resulting optimal solution will give us the number of skirts the company should sew to maximize profit.
what is the percent of change from 85 to 64? round to the nearest percent
Answer:
=25 %
Step-by-step explanation:
Percent decrease equals (original minus new) / original * 100 %
Percent decrease = (85-64)/ 85 * 100%
= 21/85 * 100%
=.247058824 * 100%
=24.7058824%
To the nearest percent
=25 %
The function g(x) = 3x - 12x + 7 written in vertex form is g(x) = 3(x - 2)2 – 5. What is the vertex of g(x)?
A(-6, -5)
B (-2,-5)
C. (2,-5)
D (2,-5)
[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] ~\dotfill\\\\ g(x)=3(x-\stackrel{h}{2})^2+(\stackrel{k}{-5})\qquad \qquad \stackrel{\textit{vertex}}{(2,-5)}[/tex]
64,-48,36,-27 which formula can be used to describe the sequence
Answer:
see explanation
Step-by-step explanation:
These are the terms of a geometric sequence with n th term formula
[tex]a_{n}[/tex] = a [tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
r = [tex]\frac{-48}{64}[/tex] = [tex]\frac{36}{-48}[/tex] = - [tex]\frac{3}{4}[/tex]
the first term a = 64, hence
[tex]a_{n}[/tex] = 64 [tex](-3/4)^{n-1}[/tex]
The math club is experiencing a growth in membership. On average, they are seeing a growth of 3% each week. If they started with 10 members which function, S(x), represents the number of members in the science club after x weeks?
Answer:
[tex]s(x)=10(1.03)^{x}[/tex]
Step-by-step explanation:
Let
x -----> the number of weeks
S ----> the number of members in the science club
In this problem we have a exponential function of the form
[tex]s(x)=a(b)^{x}[/tex]
where
a is the initial value
b is the base
we have
[tex]a=10\ membrers[/tex]
[tex]r=3\%[/tex]
[tex]b=100\%+3\% =103\%=103/100=1.03[/tex]
substitute
[tex]s(x)=10(1.03)^{x}[/tex]
which undefined term is used to define an angle ?
line-
plane-
Point-
ray-
???
Answer:
the right answer is point
Step-by-step explanation:
The Undefined term that is used to define an angle is; a point.
How to represent an angle?An angle is defined as the union of two rays with a common endpoint. The common end point is known as the vertex of the angle while the rays are known as the sides of the angle.
Now, angle can be named in different ways like use of capital letters, vertex of the angle, by placing any number or symbol at the vertex in the interior of the angle and other ways.
However, the undefined term that is used to define an angle is called "point".
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find the solution of this system of equations
-6y=-50-4x
5x-6y=-49
Answer:
[tex](1,\ 9)[/tex]Step-by-step explanation:
Rewrite the first equation
[tex]-6y=-50-4x\\\\4x-6y=-50[/tex]
Now we have the following system of equations
[tex]4x-6y=-50\\5x-6y=-49[/tex]
To solve the system of equations multiply the first equation by -1 and add it to the second equation
[tex]-1*4x-(-1)*6y=-50*(-1)\\\\-4x+ 6y=50[/tex]
[tex]-4x+ 6y=50[/tex]
+
[tex]5x-6y=-49[/tex]
-----------------------------------
[tex]x + 0 =1\\\\x=1[/tex]
Now substitute the value of x in any of the two equations and solve for y
[tex]5(1)-6y=-49[/tex]
[tex]5-6y=-49[/tex]
[tex]-6y=-49-5[/tex]
[tex]-6y=-54[/tex]
[tex]y=\frac{54}{6}[/tex]
[tex]y=9[/tex]
The solution is:
[tex](1,\ 9)[/tex]
The tennis team has played 28 matches so far this season. They have won 10 matches so far. How many matches will the team need to win for the team to have 55% success rate?
Answer:
12 matches
Step-by-step explanation:
Hope this helps!
The number of matches that the team needs to win for the team to have a 55% success rate is approximately 16 matches.
What is percentage?A percentage is a number that tells us how much out of 100.
Given that, the tennis team has played 28 matches so far. If they've won 10 matches.
If 28 matches = 100%
10 matches = x %
x = (10×100)/28
x = 35%
So, we are left to determine (55% - 35% = 20%) the remaining 20% success rate;
28 = 100%
x matches = 20%
x = 5.6 matches
Thus, the total number of matches to be won to have a 55% success rate is:
= 10 matches + 5.6 matches
= 15.6 matches
≅ 16 matches
Hence, we can conclude that the total number of matches that the team needs to win for the team to have a 55% success rate is 16 matches.
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Simplify (5√2-1)^2 please I need help
Answer:
51-10sqrt(2)
Step-by-step explanation:
(a-b)^2=a^2-2ab+b^2
(5sqrt(2)-1)^2=(5sqrt(2))^2-2(5sqrt(2))(1)+1^2
=5^2(2)-2(5sqrt(2))(1)+1^2
=25(2)-10sqrt(2)+1
=50-10sqrt(2)+1
=51-10sqrt(2)
Ralph and Waldo start in towns that are 70 miles apart and travel in opposite directions for 4 hours.
Ralph travels
15 miles per hour faster than Waldo.
Let w stand for Waldo's speed and write algebraic expressions to answer the
following questions
a. How far did Waldo travel?
miles
b. What was Ralph's speed?
mph
C. How far did Ralph travel?
miles
d. What is the distance between Ralph and Waldo after the 4 hours?
miles
Answer:
Step-by-step explanation:
Let Waldo's speed = W
Let Ralph's speed = W + 15
A
Waldo's distance = speed * Time
Time = 4 hours.
Speed = w
distance = 4 * w
B
Ralph's speed is W + 15. It's not clear if you need a number. We'll get around to that later.
C
Ralph traveled 4*(W + 15)
D
4w + 70 + 4(W + 15) = d
You really can't get a definite answer to these questions. Even if you knew whether they were heading away from each other or towards each other it wouldn't help.
1. The equation y=x^2-9x+20 models the roller coasters path over time. The variable y represents height (in feet) above or below the platform. At y=0, the roller coaster is even with the platform. The variable x represent the amount of time (in seconds) since the ride began.
Part 1: write the equation in factored form.
Part 2: find the vertex of the parabola. Hint: to find the x-value of the vertex, take the average of the x-values of the x-intercepts of use the first part of the quadratic Formula (x=-b)
——
2a
Part 3: what is the y-intercept? Use the equation y=x^2-9x+20
Part 4: Sketch the graph of y=x^2-9x+20. Identify the vertex and x- and y-intercepts on your sketch
Part5: use the graph to answer the questions.
A. Between what times does the roller coaster dip below the platform?
B. What is the height and time at which Erin picture is taken during the roller coaster ride?
C. Erin picture is taken at the lowest point of the roller coaster.
35points!! To whoever help me with this.
Answer:
1) the factored form is y= ( x-5 ) ( x+4 )
2) the vertex is (4.5, -0.25)
3) the y intercept is when x equals 0 so it is at (0,20)
4) it opens upward and the vertex is (4.5, -0.25) the x intercepts are (4,0) and (5,0) and the y intercept is (0,20)
5)
a. it dips between 4 seconds and 5 seconds so the x intercepts are (4,0) and (5,0)
b. it is taken at the vertex aka the lowest point so the height is -0.25
Answer:
Part 1:
[tex]y= (x-4)(x-5)[/tex]
Part 2:
[tex](\frac{9}{2}, - \frac{1}{4})[/tex]
Part 3:
[tex]Y=20[/tex]
Part 5:
The height:
[tex]-\frac{1}{4}[/tex]
The time:
[tex]\frac{9}{2}[/tex]s
Step-by-step explanation:
[tex]y = x^{2} -9x+20[/tex] Is a quadratic equation.
Part 1:
We use [tex]x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}[/tex] to factor quadratic equations
[tex]y = x^{2} -9x+20[/tex]
a=1 b=-9 c=20
[tex]x = \frac {-(-9) \pm \sqrt {(-9)^2 - 4(1)(20)}}{2(1)}[/tex]
[tex]x = \frac {9 \pm \sqrt {81 -80}}{2}[/tex]
[tex]x = \frac {9 \pm {1}}{2}[/tex]
we solve both possibilities
[tex]x = \frac {9 + {1}}{2}=5[/tex]
[tex]x = 5[/tex]
[tex]x = \frac {9 -{1}}{2}=4[/tex]
[tex]x=4[/tex]
The factored form would be
[tex]y= (x-4)(x-5)[/tex]
Part 2:
We use the formula to find the x coordinate of the vertex of a parabola
[tex]V_{x}=\frac{-b}{2a}[/tex]
[tex]y = x^{2} -9x+20[/tex]
a=1 b=-9 c=20
[tex]V_{x}=\frac{9}{2}[/tex]
Now we substitute the value of x in [tex]y = x^{2} -9x+20[/tex] to find the value of the coordinate y of the vertex
[tex]y = \ (\frac{9}{2} )^{2} -9(\frac{9}{2}) +20\\ y= \frac{81}{4} -\frac{81}{2} +20\\ y= -\frac{1}{4}[/tex]
The vertex of the parabola is
Vertex:
[tex](\frac{9}{2}, - \frac{1}{4})[/tex]
Part 3:
the y-intercept is when the value of x = 0.
We substitute this value in [tex]y = x^{2} -9x+20[/tex]
[tex]y = 0^{2} -9(0)+20= 20[/tex]
The y-intercept is [tex]y=20[/tex]
Part 5:
A.
Between 4s and 5s
B and C.
Erin's photograph is taken at the lowest point of the roller coaster.
The lowest point of the parabola is the vertex.
The coordinate y of the vertex gives us the height and the coordinate x the time.
The height:
[tex]-\frac{1}{4}[/tex]
It is negative because it is below the point we take as zero.
The time:
[tex]\frac{9}{2}[/tex]s
Part 4:
The answer is the graph
If you double the input of a function and it results in half the output and if you triple the input and it results in a third of the output what can be guessed about the function? Check all that apply
Answer:
The function is most likely inversely proportional
More input results in less output
what other information do you need to prove triangle DAC=BCA by ASA
Answer:
∠ACD≅∠CAB
Step-by-step explanation:
According to SAS postulate if two sides and the included angle of ΔDAC are same to two sides and the included angle of ΔBCA. Then ΔDAC≅ΔBCA
But for the given figure
∠DAC≅∠BCA and
CA=AC (common in both triangle)
Hence we need ∠ACD≅∠CAB to prove that ΔDAC≅ΔBCA
A driver runs over a nail, puncturing the tire without causing a leak. The position of the nail in the tire, with relation to the ground, while the car is moving at a constant speed is shown in the table.
Time (s) Approximate height of the nail off the ground (inches)
0 0
0.01 2.1
0.02 7.6
0.03 14.9
0.04 21.5
0.05 25.5
0.06 25.5
0.07 21.5
Which key features of the function representing the nail’s travel can be used to determine the amount of time it takes for the nail to reach the same orientation it had when it entered the tire?
A. period
B. minimum
C. maximum
D. amplitude
Answer: period
Step-by-step explanation:
Answer:
The correct option is A.
Step-by-step explanation:
It is given that a driver runs over a nail, puncturing the tire without causing a leak.
Tire of a car represents a periodic function because after a particular time the tire comes its initial stage and that particular time interval is called a period.
It means period is the key feature of the function representing the nail’s travel can be used to determine the amount of time it takes for the nail to reach the same orientation it had when it entered the tire.
Therefore the correct option is A.
A line passes through the points (8,-1) and (-4,2). What is the y intercept of the line ?
Answer:
"Y intercept is1 "
Step-by-step explanation:
The slope is (-1 - 2)/[8 - (-4)] = -3/12 = -(1/4)
(-1/4) = (y - 2)/(x + 4) => -x - 4 = 4y - 8
-x + 4 = 4y
y = (-1/4)x + 1 so that the y-intercept is 1
Answer:
"Y intercept is1 "
The slope is (-1 - 2)/[8 - (-4)] = -3/12 = -(1/4)
(-1/4) = (y - 2)/(x + 4) => -x - 4 = 4y - 8
-x + 4 = 4y
y = (-1/4)x + 1 so that the y-intercept is 1
Step-by-step explanation:
joanna can buy 15 square yards of carpet for $240 using the same rate how many square yards of carpet can she buy for $320
Answer:
x =20
Step-by-step explanation:
We can use proportions to solve
$240 320
----------- = ------------
15 x
Using cross products
240x = 320 * 15
240x =4800
Divide by 240 on each side
240x/240 = 4800/240
x =20
By finding the cost per square yard from Joanna's initial purchase ($16 per sq yd), we can calculate that she can buy 20 square yards of carpet for $320.
Explanation:To find out how many square yards of carpet Joanna can buy for $320 using the same rate, we first need to determine the cost per square yard based on her $240 purchase. She can buy 15 square yards for $240, so by dividing the total cost by the number of yards, we find the cost per square yard.
Cost per square yard = Total cost / Number of square yards = $240 / 15 sq yds = $16 per sq yd.
Now, we can use the cost per square yard to find out how many square yards she can get for $320. We divide the total amount she's willing to spend by the cost per square yard.
Square yards for $320 = Total amount to spend / Cost per square yard = $320 / $16 per sq yd = 20 sq yds.
Therefore, Joanna can buy 20 square yards of carpet for $320.
Long division 639 divided by 8
Answer:
The answer is 79.875
Hope this helps!
Answer:
79.875
Step-by-step explanation:
79.875
8/639
-56
______
079
-072
_______
0070
-0064
_______
0060
-0056
________
0040
-0040
________
0000
Write a ratio and a percent for the shaded area.
HEYA MATE
YOUR ANSWER IS A.3/10,30%
BECAUSE SHADED SQUARES ARE 6
AND TOTAL SQUARES ARE 20
THAN APPLY THE FORMULA OF PERCENTAGE.
=>GIVEN NUMBER/TOTAL NUMBER×1006/20×100THAN WE GET
30%
[tex]<marquee><i><b>[/tex]THANK YOU