Answer:
552.16 cm^3
Step-by-step explanation:
Just multiply the lenght together.
The volume of the rectangular prism is approximately 552.16 cubic cm.
To find the volume of a rectangular prism, you need to multiply its length, width, and height.
Given that the length is 14 cm, the width is 3.4 cm, and the height is 11.6 cm, we can calculate the volume as follows:
Volume of a rectangular prism = Length × Width × Height
Volume of a rectangular prism = 14 cm × 3.4 cm × 11.6 cm
Volume of a rectangular prism ≈ 552.16 cm³ (rounded to the nearest tenth)
Therefore, the volume of the rectangular prism is approximately 552.16 cubic cm.
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Three vertices of a rectangle are located at (1,4),(1,2), and (5,2).What are the coordinates of the fourth vertex of the rectangle.
It’ll be (5,4) because it’s on the same Y line (aka 4) just like (1,2) and (5,2).
The coordinates of the fourth vertex of the rectangle are (5, 4).
What is a rectangle?A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.
Given that, three vertices of a rectangle are located at (1,4), (1,2), and (5,2).
The intersection point of diagonals of rectangle is midpoint of each diagonal.
Let the fourth coordinate be (x, y). By the above property we get
Now, the midpoint of (1, 4) and (5, 2) is
[(1+5)/2, (4+2)/2] =(3, 3)
Thus, (3, 3) =[(x+1)/2, (y+2)/2]
3=(x+1)/2, 3=(y+2)/2
6=x+1, 6=y+2
x=5, y=4
Therefore, the coordinates of the fourth vertex of the rectangle are (5, 4).
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Three coins are tossed in succession. What is the probability of heads-tails-heads?
1/2
1/6
1/8
Answer:
1/8.
Step-by-step explanation:
The probability of of a head (and a tail) in one toss of a coin being obtained is 1/2.
Each toss is independent of the others so we multiply the probabilities.
So Prob(Head - tail - head) = 1/2*1/2*1/2 = 1/8.
Answer:
1/8.
Step-by-step explanation:
A box has a base of 12 inches by 12 inches and a height of 30 inches. What is the length of the interior diagonal of the box? Round to the nearest hundredth. Enter your answer in the box.
The sides of the box are 12in by 12in by 30in.
The interior diagonal =[12^2+12^2+30^2]0.5
=[144+144+900]^0.5
=1188^0.5
The final answer is 34.47in.
My deepest apology if this is not what you meant.
= 34.47in.
Answer:
34.47
Step-by-step explanation:
Jose can paint an entire house in seven hours and brandon can paint the same house in eight hours. Write an equation that can be used to find the time in hours, t, it would take jose and brandon to paint the house together. You do not need to solve the equation.
Answer:
t/8 + t/7 = 1
Step-by-step explanation:
Given in the question that,
time require for Jose to paint the house = 7 hours
time require for Brandon to paint the house = 8 hours
Suppose t means Full house painted.
To solve the question we have to figure out how much each of them can paint in ONE hour.7 hours----t
1 hour ---- t/7
8 hours----t
1 hour ---- t/8
Equationt/8 + t/7 = 1 (in one hour)
(7t + 8t)/8(7) = 1
15t/56 = 1
15t = 56
t = 56/15
t = 3.73 hours
What is the root of the polynomial equation x(x-2)(x+3)=18
Answer:
The root of the polynomial is 3
Step-by-step explanation:
To find the root of the polynomial x(x-2)(x+3)=18
We can use a graphing utility and the system of equations.
We can have the equations;
y = x(x-2)(x+3) ......(i)
Therefore, from the initial equation;
y = 18 ..................... (ii)
We can then plot the graph using the equations, and the x-coordinate of the point of intersection will be the root of the equation.
From the graph, the x-coordinate is 3, since the intersection point is (3,18).
Therefore; the root of the equation is 3.
Find the general solution of the given system. dx dt = 3x − y − z dy dt = x + y − z dz dt = x − y + z x(t), y(t), z(t) =
In matrix from, the system is
[tex]\dfrac{\mathrm d}{\mathrm dt}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}3&-1&-1\\1&1&-1\\1&-1&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}[/tex]
The coefficient matrix has eigenvalues [tex]\lambda[/tex] such that
[tex]\begin{vmatrix}3-\lambda&-1&-1\\1&1-\lambda&-1\\1&-1&1-\lambda\end{vmatrix}=-(\lambda-2)^2(\lambda-1)=0\implies\lambda=2_{(2)},\lambda=1[/tex]
(where the subscript denotes multiplicity of the eigenvalue).
[tex]\lambda=2[/tex]:
[tex]\begin{bmatrix}1&-1&-1\\1&-1&-1\\1&-1&-1\end{bmatrix}\vec\eta_1=\vec0[/tex]
[tex]\implies\eta_{1,1}-\eta_{1,2}-\eta_{1,3}=0\implies\eta_{1,1}=\eta_{1,2}+\eta_{1,3}[/tex]
By picking [tex]\eta_{1,1}=1[/tex], we can then set [tex]\eta_{1,2}=1[/tex] and [tex]\eta_{1,3}=0[/tex], and vice versa, to find two corresponding eigenvectors,
[tex]\vec\eta_1=\begin{bmatrix}1\\1\\0\end{bmatrix},\vec\eta_2=\begin{bmatrix}1\\0\\1\end{bmatrix}[/tex]
[tex]\lambda=1[/tex]:
[tex]\begin{bmatrix}2&-1&-1\\1&0&-1\\1&-1&0\end{bmatrix}\vec\eta_3=\vec0[/tex]
[tex]\implies2\eta_{3,1}-\eta_{3,2}-\eta_{3,3}=0\implies2\eta_{3,1}=\eta_{3,2}+\eta_{3,3}[/tex]
We obtain [tex]\vec\eta_3[/tex] independent of [tex]\vec\eta_1,\vec\eta_2[/tex] by picking [tex]\eta_{3,2}=\eta_{3,3}=1[/tex], so that the third corresponding eigenvector is
[tex]\vec\eta_3=\begin{bmatrix}1\\1\\1\end{bmatrix}[/tex]
Then the general solution to this system is
[tex]\begin{bmatrix}x\\y\\z\end{bmatrix}=C_1e^{2t}\vec\eta_1+C_2te^{2t}\vec\eta_2+C_3e^t\vec\eta_3[/tex]
[tex]\begin{cases}x=C_1e^{2t}+C_2te^{2t}+C_3e^t\\y=C_1e^{2t}+C_3e^t\\z=C_2te^{2t}+C_3e^t\end{cases}[/tex]
To find the general solution of the given system of differential equations, we can solve each equation separately and obtain the general solution for x(t), y(t), and z(t).
Explanation:The given system of differential equations is:
dx/dt = 3x - y - z
dy/dt = x + y - z
dz/dt = x - y + z
To find the general solution, we can treat each equation separately.
For dx/dt = 3x - y - z, we can rewrite it as:
dx / (3x - y - z) = dt
Integrating both sides gives us:
ln|3x - y - z| = t + C1, where C1 is the constant of integration.
Exponentiating both sides gives us:
|3x - y - z| = e^(t+C1)
Since |3x - y - z| is always positive, we can remove the absolute value signs:
3x - y - z = e^(t+C1)
Now, we can solve the remaining two equations in a similar manner to find y(t) and z(t).
By solving the three equations, we can obtain the general solution for x(t), y(t), and z(t).
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There are 12 face cards in a deck of standard playing cards and 20 even numbered cards. if you draw one card and look at it. then replace it and then draw another card. what is the probability that you would draw a face card and then an even numbered card?
Answer:
[tex]\dfrac{9}{64}[/tex]
Step-by-step explanation:
There are 12 face cards in a deck of standard playing cards and 20 even numbered cards, in total 32 cards.
1. The probabilty that the first drawn card is face card is
[tex]p_1=\dfrac{12}{32}=\dfrac{3}{8}.[/tex]
2. The probabilty that the second drawn card is an even numbered card (even numbered cards are 6, 8, 10 - 12 in total, odd numbered cards are 7, 9 - 8 in total) is
[tex]p_2=\dfrac{12}{32}=\dfrac{3}{8}.[/tex]
3. The probability that the first drawn card is a face card and the second drawn card is an even numbered card is
[tex]p_1\cdot p_2=\dfrac{3}{8}\cdot \dfrac{3}{8}=\dfrac{9}{64}.[/tex]
If $315 is invested at an interest rate of 3% per year and is compounded continuously, how much will the investment be worth in 9 years? Use the continuous compound interest formula: A = Pert.
$206.23
$412.64
$2,343.56
$4,687.11
Answer:
[tex]\$412.64[/tex]
Step-by-step explanation:
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]t=9\ years\\ P=\$315\\ r=0.03[/tex]
substitute in the formula above
[tex]A=\$315(e)^{0.03*9}=\$412.64[/tex]
Answer: $412.64
Step-by-step explanation: you’re welcome :)
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Select Parameter or Statistic to classify each statement.
Answer:
Statistics;Parameter;Statistics;Parameter.Step-by-step explanation:
According to southeastern.edu,
parameters summarize data from an entire population, whereasstatistics summarize data from a sample of the population.The first statement is true for the sample "those surveyed" the population but not necessarily the entire population. Statistic.
The second statement implies that the soccer team is the population. All members of the population are surveyed. Parameter.
The third statement states that a sample of 100 of all swimming teams are surveyed. Statistic.
The fourth statement implies that the population is all members of the golf team, and that all members of the population are surveyed. Parameter.
In a sale normal prices are reduced by 10% Nathalie bought pair of shoes in the sale for ?54 what was the original price
Answer:
$59.4
Step-by-step explanation:
The original price of the shoes was £60 before the 10% discount was applied, resulting in a final price of £54.
1. First, let's denote the original price of the shoes as [tex]\( x \)[/tex] pounds.
2. Since Nathalie bought the shoes during the sale, she received a 10% discount.
3. Therefore, she paid 90% of the original price after the discount. This can be represented as [tex]\( 0.90x \)[/tex].
4. According to the given information, Nathalie paid £54 for the shoes. So, we can set up the equation:
[tex]\[ 0.90x = 54 \][/tex]
5. To find the original price [tex](\( x \))[/tex], we need to isolate it by dividing both sides of the equation by 0.90:
[tex]\[ x = \frac{54}{0.90} \][/tex]
6. Solving the equation gives us:
[tex]\[ x = 60 \][/tex]
7. Hence, the original price of the shoes was £60 before the 10% discount was applied.
The complete question is here:
In a sale, normal prices are reduced by 10% Nathalie bought a pair of shoes in the sale for £54. What was the original price of the shoes?
A function is in the form g(X) = ax^2 + d. If a is greater than 1 and d is negative, which could be the graph of g(x)?
Answer:
Option B
Step-by-step explanation:
Step-by-step explanation:
We have the function [tex]g(x)=ax^2 +d[/tex] then, by definition:
If [tex]0 <a <1[/tex] then the graph is compressed vertically by a factor a.
If [tex]|a| > 1[/tex] then the graph is stretched vertically by a factor a
If [tex]a <0[/tex] then the graph is reflected on the x axis.
If [tex]d> 0[/tex] the graph moves vertically upwards d units.
If [tex]d <0[/tex] the graph moves vertically down d units.
We know that:
[tex]a > 1[/tex] then the graph is stretched vertically by a factor a
and
[tex]d <0[/tex] the graph moves vertically down d units
The searched graph is stretched vertically and its vertex is displaced downwards
The answer is option B
Sarah, Natasha and Richard share some sweets in the ratio 4:5:3. Sarah gets 36 sweets. How many sweets are there altogether?
Answer:
108
Step-by-step explanation:
36÷4= 9
9 is the unit rate
5×9=45
Natasha has 45 sweets
3×9= 27
Richard has 27 sweets
36+ 45+ 27= 108
All together they have 108 sweets
In total, there are 108 sweets. This answer is derived by finding the value of one part of the ratio and then multiplying this by the sum of all parts of the ratio.
Explanation:The question is about the distribution of sweets among Sarah, Natasha and Richard in the ratio 4:5:3. You have been given that Sarah, represented by the first term of the ratio, gets 36 sweets. To find how many sweets there are altogether, we first need to determine the value of one part of the ratio.
In this case, if 4 parts are equivalent to 36 sweets, then one part is equivalent to 36 divided by 4 which equals 9 sweets.
Now, to find the total sweets, we need to sum all parts of the ratio which is 4 parts for Sarah, 5 parts for Natasha and 3 parts for Richard. Total parts = 4 + 5 + 3 = 12. This total is then multiplied by the value of one part of the ratio. Here, total sweets = 12 parts * 9 sweets = 108 sweets.
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Which row of the input/output table is incorrect?
y = 2x - 3
x y
Row A 3 3
Row B 5 7
Row C 7 11
Row D 10 15
Row A
Row B
Row C
Row D
Row A: x = 3
y = 2x - 3
y = 2(3) - 3 = 3 This is correct
Row B: x = 5
y = 2x - 3
y = 2(5) - 3 = 7 This is correct
Row C: x = 7
y = 2x - 3
y = 2(7) - 3 = 11 this is correct
Row D: x = 10
y = 2x - 3
y = 2(10) - 3 = 17 THIS IS INCORRECT, SO ROW D
Answer:
Road D
Step-by-step explanation:
Which function best fits the following points?
A. Exponential
B. Quadratic
C. Linear
D. None of the above
Answer:
Option B. Quadratic
Step-by-step explanation:
In a regression model, the value of [tex]r ^ 2[/tex] tells us how accurately the model fits the data.
That closer the value of [tex]r ^ 2[/tex] of 1 is, better is the model.
This can be used to compare what type of model is most convenient to use in some cases.
In this problem the attached table shows a comparison of the value of [tex]r ^ 2[/tex] for 3 models
Linear
Quadratic
Exponential
Note that the value of [tex]r ^ 2[/tex] that is closest to 1 is that which corresponds to the quadratic model.
[tex]r ^ 2 = 0.89[/tex]
Therefore the function that best fits the points is the quadratic
The side of a square garden is 12 meters and the total length of the wire brought for fencing the garden is 19 m. Will the wire length be sufficient to fence garden
Answer:
No
Step-by-step explanation:
If its a square garden then that means all 4 sides are 12 meters so 12 times 4 equals 48. This meaning you need 48 meters of wire to wire the entire fence garden.
Answer:
no
Step-by-step explanation:
if the garden is to be fence on all 4 sides then the total length of wire needed is 48 meters as 12*4=48 so since 19<48 it will not be enough
Please answer this question only if you know it! 30 points and brainliest!
5 out of 20 people said that they like the new packaging of Toasty Toasts.
Please help me with these questions
Thank u
Answer:
4(a + b)^2
p = 6/5 or 1.2
Step-by-step explanation:
Question One
z = a^2 + b^2
y = ab
4z = 4*a^2 + 4*b^2
8y = 8*ab
=================
4z + 8y = 4a^2 + 8ab + 4b^2
4z + 8y = 4(a^2 + 2ab + b^2)
4z + 8y = 4(a + b)^2
Question Two
2(p + 1) + 8(p - 1) = 5p
2p + 2 + 8p - 8 = 5p
2p + 8p + 2 - 8 = 5p
10*p - 6 = 5p
10*p = 5p + 6
10p - 5p = 6
5p = 6
p = 6/5 or 1.2
Kristin bought eight boxes.A week later half of all her boxes were destroyed in a fire.There are now only 17 boxes left.With how many did she start
Answer:
She started with 26 boxes.
Step-by-step explanation:
She started with x boxes. Then she bought 8 more boxes. Now she had x + 8 boxes. Then half the boxes were destroyed, so she has the other half of the boxes. Half of the boxes is (x + 8)/2. She has now 17 boxes, so (x + 8)/2 = 17.
(x + 8)/2 = 17
Multiply both sides by 2.
x + 8 = 34
Subtract 8 from both sides.
x = 26
She started with 26 boxes.
In the commutative property, order does not matter. However, this is not true when it comes to__ & __problems where order does matter.
In the commutative property, order does not matter for addition and multiplication. However, this is not true when it comes to subtraction and division problems, where order does matter.
The commutative property states that:
a + b = b + a (addition)
a × b = b × a (multiplication)
However, this does not apply to:
a - b ≠ b - a (subtraction)
a ÷ b ≠ b ÷ a (division)
In subtraction and division, the order of the operands matters, and changing the order can result in different values.
PLEASE HELP 50 points!!!!trapezoid ABCD is similar to trapezoid EFGH. What is the value of s?
32m
3.2m
0.8m
8m
You can set up a proportion based on the information you know. There are several ways to do this but here's one: [tex]\frac{8}{4} = \frac{s}{16}[/tex] because the 8 corresponds to the 4 and the s correspnds to the 16. Cross multiply to get 8 * 16 = 4s → 128 = 4s → 32 = s so the value of s is 32m
The value of s is 32 m.
Similar TrapezoidsSimilar trapezoids are trapezoids whose sides are in a ratio. the ratio is known as the scaled factor.
Scale factorA scale factor is a factor by which the image is been enlarged. for example, the scale factor of 10 means each side will be multiplied by 10, resulting in a figure that is 10 times the real figure.
As given to us, ABCD is similar to trapezoid EFGH. therefore, the sides of the trapezoid are in a ratio.
Thus we can write,
[tex]\bold{\dfrac{EH}{AD}=\dfrac{GH}{CD}}[/tex]
substituting the values we get,
[tex]\bold{\dfrac{s}{16}=\dfrac{8}{4}}[/tex]
[tex]\bold{s=\dfrac{8\times 16}{4}=32}[/tex]
Hence, the value of s is 32 m.
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Pls pls pls help me on this math! Will mark brainliest
Answer:
The volume of the prism is [tex]16.65\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the triangular prism is equal to
[tex]V=BH[/tex]
where
B is the area of the triangular base
H is the height of the prism
Remember that
In a right triangle 45°-45°-90°
The measures of the legs are equal
The area B is equal to
[tex]B=\frac{1}{2}(3)(3)=4.5\ in^{2}[/tex]
[tex]H=3.7\ in[/tex]
substitute in the formula
[tex]V=(4.5)(3.7)=16.65\ in^{3}[/tex]
Answer:
16.65
Step-by-step explanation:
Mary covered her kitchen floor with 10 tiles. The floor measures 6 feet long by 5 feet wide. The tiles are each 3 feet long and w feet wide. Write an equation to represent each situation
Answer:
Step-by-step explanation:
Some foundation pieces:
Floor is 30 ft^2
tiles are 3w
Equation:
30=(3w)*10
3=3w
1=w
Now that you know that w has to 1 you can write the formula 30=(3w)×10
What is the surface area of the rectangular prism below?
A. 496 units^2
B. 248 units^2
C. 490 units^2
D. 980 units^2
Answer:
The correct answer is option C. 490 units ²
Step-by-step explanation:
Area of cuboid = 2(lb + bh + lh)
From the figure we can see that a rectangular prism.
To find the surface area of prism
Here l = 14 units
b = 7 units and h = 7 units
Surface area = 2((14 * 7) + (7 * 7) + (14 * 7))
= 490 units ²
Answer:
490 units squared
Step-by-step explanation:
Using point slope form write the equation of the line that passes through the point (-1/2, 1/2) and has a slope of -1
Answer: [tex]y-\frac{1}{2}=-(x+\frac{1}{2})[/tex]
Step-by-step explanation:
The point-slope form of the equation of the line is:
[tex]y-y_1=m(x-x_1)[/tex]
Where "m" is the slope of the line and [tex](x_1,y_1)[/tex] is a point of the line.
You know the value of the slope and you also know a point of the line, then you need to substitute values into [tex]y-y_1=m(x-x_1)[/tex].
Therefore, you get that the equation of this line in point-slope form is:
[tex]y-\frac{1}{2}=-1(x-(-\frac{1}{2})\\\\y-\frac{1}{2}=-(x+\frac{1}{2})[/tex]
Answer:
y = -x
Step-by-step explanation:
Given in the question,
co-ordinate(-1/2 , 1/2)
gradient of the line = -1
Standard equation form of a straight line
y - y1 = m(x - x1)here y1 = 1/2
x1 = -1/2
m = -1
Plug values in the equation
y - 1/2 = -1(x + 1/2)
y -1/2 = -x - 1/2
y = -x
Which algebraic expression is a trinomial? x3 + x2 – 2x3 – x2 4x3 + x2 – x6 – x +
ANSWER
D.
[tex] {x}^{6} - x + \sqrt{6} [/tex]
EXPLANATION
A trinomial is a simplified polynomial with three terms.
The first option is not a polynomial because of the presence of √x.
The second option is not a trinomial because it has only two terms.
The third option is not a polynomial because of the presence of
[tex] \frac{1}{x} [/tex]
The last option:
[tex] {x}^{6} - x + \sqrt{6} [/tex]
This is trinomial because it has three terms and cannot be simplified further.
There is not fractional exponent.
Answer:
x^8 - x + √6
Step-by-step explanation:
The fourth expression is a trinomial (a polynomial with three terms). The term √6 is acceptable because it's a constant; it's the coefficient of x^0.
What is the sum of 2 / 3x^2 +12x and 8 / c. Need steps
Answer:
[tex]\frac{2c}{3x^2c}+ \frac{36x^3c}{3x^2c} +\frac{24x^2}{3x^2c} [\tex]
Step-by-step explanation:
We need to find sum of 2 / 3x^2 +12x and 8 / c
So, solving:
[tex](\frac{2}{3x^2} + 12 x ) +\frac{8}{c}[/tex]
Taking LCM of 3x^2 and 1 i.e. 3x^2
[tex]=(\frac{2 + 12 x(3x^2)}{3x^2} ) +\frac{8}{c}\\=(\frac{2 + 36x^3}{3x^2} ) +\frac{8}{c}\\=\frac{2 + 36x^3}{3x^2} +\frac{8}{c}\\LCM \,\, 36x^2 c\\=\frac{(2 + 36x^3)c + 8(3x^2)}{3x^2c}\\=\frac{2c + 36x^3c + 24x^2}{3x^2c}\\= \frac{2c}{3x^2c}+ \frac{36x^3c}{3x^2c} +\frac{24x^2}{3x^2c}[/tex]
50 POINTS!!! Which of the following expressions are equivalent to 2/x^8-y^8
Answer:
it's A&B
Step-by-step explanation:
Answer:
[tex]\large \boxed{\mathrm{\bold{A.} } \ \frac{2}{x^4-y^4} \cdot \frac{1}{x^4 +y^4}} \\\\\\ \large \boxed{\mathrm{\bold{B.} } \ \frac{2}{(x^4)^2 -(y^4)^2 } }[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{2}{x^8-y^8 }[/tex]
Factor the denominator.
[tex]\displaystyle \frac{2}{(x^4)^2 -(y^4)^2 }[/tex]
[tex]\displaystyle \frac{2}{(x^4-y^4)^2 }[/tex]
[tex]\displaystyle \frac{2}{(x^4-y^4)(x^4 +y^4) }[/tex]
Split the fraction into two fractions.
[tex]\displaystyle \frac{2}{x^4-y^4} \cdot \frac{1}{x^4 +y^4}[/tex]
sophie makes necklaces by stringing different color beads each necklaces is 15 inches long sophie has 66 inch length of bead string how many necklaces can she make
(I think) you just divide the length of the bead string the the inches of the beads
(Which equals 4.4 so when simplified is 4)
The linear parent function f(x) = x is transformed to g(x) = 1/3x-5. Which statement correctly compares the graphs of the functions?
Answer:
A
Step-by-step explanation:
The graph of the parent function f(x)=x is the straight line that passes trough the origin and is the bisector of first and third coordinate quadrants (red line in attached diagram).
The graph of the function g(x)=1/3x-5 is the straight line that passes through the point (0,-5) and is less steep (because the slope 1/3 is less than the slope 1). This line is blue line in attached diagram.
So, correct option is option A
A playground has two sides that each measure 70 feet and two sides that each measure 50 feet. Name the quadrilaterals that describe the shape of a playground with these dimensions. Select all that apply. A.Parallelogram B.Square C.Rectangle D.Kite E.Trapezoid
Answer:
The possible shapes of the playground should be: parallelogram, rectangle, and kite because all of these shapes have 2 pairs of equal sides, and also the question didn't specify if the sides are opposite to each other or not so kite is also a possible option.
The quadrilaterals that describe the shape of a playground with these dimensions will be Rectangle.
What is a rectangle?A rectangle is a quadrilateral with four sides and the two opposite sides are equal and parallel the two sides are also perpendicular to each other.
It is given in the question that a playground has two sides that each measure 70 feet and two sides that each measure 50 feet.
So it is clear that the two sides are equal and parallel to the shape of the playground will be rectangular.
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