I believe the slope is negative. If it was positive then it would have been " / "
Answer:
C
Step-by-step explanation:
• A vertical line has an undefined slope
• A horizontal line has a slope of zero
• A line sloping downwards from left to right has a negative slope
• A line sloping upwards from left to right has a positive slope
-------------------------------------------------------------------
the line here slopes downwards from left to right and has a negative slope
What is the approximate total volume of the silo? use 3.14 for π and round the answer to the nearest tenth of a cubic meter. 37.1 m3 71.9 m3 116.5 m3 130.8 m3
The total volume of silo is = 116.5[tex]{~m}^{3}[/tex]
The correct option is C
What are the geometric figures?Any arrangement of points, lines, or planes constitutes a geometric figure. Depending on their dimensions, geometric figures can be categorized as either a space figure, a plane figure, a line, a line segment, a ray, or a point.
Any object's surface area is the space that the object's surface takes up on a specific area or region. Volume, however, refers to how much room a thing has.
Given data:
Radius =4.4/2
=2.2
height of cylinder = 6.2
to find :
total volume of silo = volume of cylinder + volume of hemisphere
[tex]\begin{aligned}&=\pi r^{2} h+\frac{2}{3} \pi r^{3} \\&=\pi r^{2}\left(h+\frac{2}{3} r\right) \\&=\frac{22}{7} \times(2.2)^{2}\left[6.2+\frac{2 \times 2.2}{3}\right]\end{aligned}[/tex]
= 116.5[tex]m^2[/tex]
The total volume of silo is = 116.5[tex]m^2[/tex]
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I understand that the question you are looking for is:
A grain silo is composed of a cylinder and a What is the approximate total volume of the silo? Use hemisphere. The diameter is 4.4 meters. The height of 3.41 for [tex]\pi[/tex] and round the answer to the nearest tenth of its cylindrical portion is 6.2 meters. a cubic meter.
a. 37.1[tex]m^2[/tex]
b. 71.9 [tex]m^2[/tex]
c.116.5 [tex]m^2[/tex]
d. 130.8[tex]m^2[/tex]
Find the surface area of the composite figure.
5 cm
6 cm
20 cm
4 cm
5 cm 4 cm
SA =
12 cm
-6 cm
[?] cm²
Step-by-step explanation:
we have 2 blocks, as the graphic shows.
the surface areas of both blocks are the sum of their 6 sides each.
the special thing about seeing them as "composite figure" is that 2 sides (one for each block) are partly or even completely blocking each other off from being seen, so these parts and whole side are not part of the combined surface area.
let's start with the large block :
it is 5cm × 6cm × 20cm.
its surface area is the sum of
top and bottom 5×6
front and back 20×5
left 20×6
visible right (20 - 12)×6 = 8×6
it is (20-12)cm long, because the short block
is 12cm high.
so, we have
2 times 5×6 =2×30 = 60 cm²
2 times 20×5 = 2×100 = 200 cm²
20×6 = 120 cm²
8×6 = 48 cm²
in total : 428 cm²
now the small block :
it is 4cm × 6cm × 12cm.
its surface area is the sum of
top and bottom 4×6
front and back 4×12
no left (completely covered by the large block)
right 6×12
so, we have
2 times 4×6 = 2×24 = 48 cm²
2 times 4×12 = 2×48 = 96 cm²
6×12 = 72 cm²
in total : 216 cm²
the complete surface area of the composite figure is
428 + 216 = 644 cm²
Please help!! due in 2 hours!!
Answer:
i think 80 copies
Step-by-step explanation:
PLS HELP IM SUPER STUCK AAA
Answer:
(15,0) , (0,6)
Step-by-step explanation:
Same concept as the previous 2 questions.
x-intercept is where the line touches the x-axis, and y = 0.
when y = 0,
12x + 30(0) = 180
12x = 180
x = [tex]\frac{180}{12}[/tex]
x = 15
Therefore the coordinates of the x-intercept is (15,0)
y-intercept is where the line touches the y-axis, and x = 0.
when x = 0,
12(0) + 30y = 180
30y = 180
y = [tex]\frac{180}{30}[/tex]
y = 6
Therefore the coordinates of the y-intercept is (0,6)
30 metres is percentage of 100 metres
Answer:
30%
Step-by-step explanation:
1) Based on the given conditions, formulate:
30 meters/100 meters
2) Calculate 30 meters/100 meters:
3/10
3) Convert to percentage:
- 3/10 x 10/10
- 3x10/10x10
30/100
30/100 = 30%
You’re done!
Also, if you could label this brainliest that would be a great help!
Thanks xx
-Dante
Barrett works at an ice cream shop. the function f(x) represents the amount of money in dollars barrett earns per gallon of ice cream, where x is the number of gallons of ice cream he makes. the function g(x) represents the number of gallons of ice cream barrett makes per hour, where x is the number of hours he works. f(x) = 2x2 4 g(x) = the square root of three times x cubed find f(g(x)). f of g of x equals the square root of the quantity 6 times x to the fifth power plus 4 dollars over hour f of g of x equals the square root of the quantity 6 times x to the fifth power plus 4 gallons over hour f(g(x)) = 6x3 4 gallons over hour f(g(x)) = 6x3 4 dollars over hour
Amount of money earned per number of hours of work = [tex]f(g(x)) = 6x^{3} + 4[/tex]
What is a composite function?A composite function is generally a function that is written inside another function. Composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.To evaluate a composite function f(g(x)) at some x = a, first compute g(a) by substituting x = a in the function g(x). Then substitute g(a) into the function f(x) by substituting x = g(a). In the same way, we can calculate g(f(a)) as well.
Required calculation -
Amount of money (the earning) per unit x = [tex]f(x) = 2x^{2} + 4[/tex]
Number of gallons of ice cream that Barrett makes per hour, where x is the number of hours he works = [tex]g(x) = \sqrt{3x^{3}}[/tex]
we are to find the composite function [tex]f(g(x))[/tex]
Substituting g(x) into the x of f(x), we find:
[tex]f(g(x)) = 2(\sqrt{3x^{3} } )^{2} + 4\\\\= 2(3x^{3} ) + 4\\= 6 x^{3} + 4[/tex]
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Answer:
f(g(x)) = 6x3 + 4 dollars over hour
Step-by-step explanation:
if the mean of the frequency distribution below is 5.2 find y
class mark : 2,4,6,8
frequency: 4,y,6,5
20 points please help!!!!!
Answer:
a) Class A has the larger interquartile range.
b) Class A has the highest test score.
c) Class B has higher median test score.
d) Class B has smaller range of test score.
Step-by-step explanation:
a) Inter quartile range (IQR) = upper quartile - lower quartile
Class A: IQR = 79 - 65 = 14
Class B: IQR = 77 - 70 = 7
Class A has larger interquartile range.
b) Class A has the highest test score.
c) Median of class A = 70
Median of class B = 74
Class B has higher median test score.
d) Range is the difference between the highest and lowest score.
Range = highest score - lowest score
Range of Class A = 85 - 62 = 23
Range of class B = 79 - 68 = 11
Class B has smaller range of test score.
PLS HELP ASAP! Ty
Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6
Find (h-g)(2.1)
The function can be solved as follows:
(h - g)(2.1) = 3.51
How to solve a function?g(x) = 2x² + 3x - 9
h(x) = x² + 2x - 6
(h - g)(x) = h(x) - g(x)
(h - g)(x) = 2x² + 3x - 9 - ( x² + 2x - 6)
(h - g)(x) = 2x² + 3x - 9 - x² - 2x + 6
(h - g)(x) = 2x² - x² + 3x - 2x - 9 + 6
(h - g)(x) = x² + x - 3
Therefore,
(h - g)(2.1) = (2.1)² + (2.1) - 3
(h - g)(2.1) = 4.41 + 2.1 - 3
(h - g)(2.1) = 6.51 - 3
(h - g)(2.1) = 3.51
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Area=
Help me please!! Thanks so much-needed
First you have to figure out the side length of the triangle.
sin(60)= X/8
Let's call x the side length.
8 sin(60)=X
X=6.93
The multiply it by 4
The area is 27.72
PLS HELP IM STUCK PLS
Answer:
-4
Step-by-step explanation:
We are going to substitute 0 in for x and solve for y.
-2(0)+ 8y = -32 Anything times zero is zero
0 + 8 y = -32 Anything plus zero is itself.
8y = -32 Divide both sides by 8
y = -4
Consider the graph of the function f(x)=2^x which statements describe key features of function g if g(x)=3f(x)?
it's multiple choice, select all the correct answers:
y-intercept at (0,1)
y-intercept at (0,3)
horizontal asymptote of y=3
x-intercept at (3,0)
horizontal asymptote of y=0
no x-intercept
Answer:
A, C, D
Step-by-step explanation:
Select the correct answer from each drop-down menu.
The number of three-digit numbers with distinct digits that can be formed using the digits 1, 2, 3, 5, 8, and 9 Is
.The probability
that both the first digit and the last digit of the three-digit number are even numbers is
Reset
Next
Using it's concept, we have that the probability that both the first digit and the last digit of the three-digit number are even numbers is 2/27.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Considering that there are six numbers, out of which 4 are odd and 2 are even, we have that:
The first and last digits are even with 2/6 = 1/3 probability.The second digit is odd with 4/6 = 2/3 probability.Hence the desired probability is:
p = 1/3 x 2/3 x 1/3 = 2/27.
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PLS ANSWER ILL MARK U BRAINLIEST
Given the length of the two diagonals of the kite, the area of kite ABDC is 33 squared centimeters.
What is the area of kite ABDC?Formular for the area of a kite is expressed as;
A = pq/2
Where p and q are the two diagonals of the kite.
Given the data in the question;
Diagonal p = line BC = BM + MC = 3 + 3 = 6Diagonal q = line AD = AM + MDLine AM = ?Line MD = ?From the diagram, we can determine line AM and line MD using Pythagoras theorem.
c² = a² + b²
First, we find line AM
c² = a² + b²
5² = 3² + b²
25 = 9 + b²
b² = 25 - 9
b² = 16
b = √16
b = 4
Line AM = 4
Next, we determine Line MD
c² = a² + b²
(√58)² = 3² + b²
58 = 9 = b²
b² = 58 - 9
b² = 49
b = √49
b = 7
Line MD = 7
Now, we can find the area of the kite.
Diagonal p = BC = 6
Diagonal q = AD = AM + MD = 4 + 7 = 11
Area = pq/2
Area = [ 6 × 11 ]/2
Area = 66 / 2
Area = 33cm²
Given the length of the two diagonals of the kite, the area of kite ABDC is 33 squared centimeters.
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radians and degrees
180° irc =
[tex]\Large\texttt{Answer}[/tex]
[tex]180^\circ=\pi\:radians}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
⇨ For converting from degrees to radians, use this conversion factor:
[tex]\bf{\cfrac{\pi}{180}}[/tex]
⇨ Convert
[tex]\bf{\cfrac{180}{1}\times\cfrac{\pi}{180}}[/tex]
⇨ The 180s cancel out, and we have:
[tex]\pi[/tex]
Hence
[tex]\bf{180^\circ=\pi\:radians}[/tex]
Hope that helped
Find the polar equation of an ellipse with its focus at the pole and vertices at (−1,0) and (3,0).
The polar equation of an ellipse is [tex]r=-\frac{3}{1+2cos\theta}[/tex].
The vertices of ellipse are (−1,0) and (3,0).
The polar equation of an ellipse can be represented as
[tex]r=\frac{ep}{1+ecos\theta}[/tex]
where e is the eccentricity.
Eccentricity, e = [tex]\frac{c}{a}[/tex]
c is the distance from the center to the focus and a is the distance from the center to the vertex
[tex]c=\frac{3-(-1)}{2}[/tex]
⇒ [tex]c=\frac{4}{2}[/tex]
⇒ c = 2
[tex]a=\frac{3+(-1)}{2}[/tex]
⇒ [tex]a=\frac{2}{2}[/tex]
⇒ a = 1
Then, e = [tex]\frac{2}{1}[/tex]
⇒ e = 2
Now, the polar equation of an ellipse becomes as,
⇒ [tex]r=\frac{2p}{1+2cos\theta}[/tex] ------- (1)
Now plug in a vertex point such as (-1,0) and solve for p,
⇒ [tex]-1=\frac{2p}{1+2cos0}[/tex]
⇒ [tex]-1=\frac{2p}{1+2(1)}[/tex] [∵ cos 0 = 1]
⇒ [tex]-1=\frac{2p}{3}[/tex]
⇒ [tex]-3=2p[/tex]
⇒ [tex]p=-\frac{3}{2}[/tex]
Thus the polar equation of an ellipse (1) becomes as,
⇒ [tex]r=\frac{2(-\frac{3}{2} )}{1+2cos\theta}[/tex]
⇒ [tex]r=-\frac{3}{1+2cos\theta}[/tex]
Hence we can conclude that the polar equation of an ellipse is [tex]r=-\frac{3}{1+2cos\theta}[/tex].
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Monica’s school band held a car wash to raise money for a trip to a parade in New York City. After washing 125 cars, they made $775 from a combination of $5.00 quick washes and $8.00 premium washes.
Let x represent the number of quick washes and let y represent the number of premium washes. Which system of linear equations represents the situation?
The system of linear equations represents the situation is;
x + y = 125
x + y = 1255x + 8y = 775
Simultaneous equationSimultaneous equation is an equation in two unknown values are being solved for at the same time.
let
number of quick washes = xnumber of premium washes = yx + y = 125
5x + 8y = 775
From equation (1)
x = 125 - y
5x + 8y = 775
5(125 - y) + 8y = 775
625 - 5y + 8y = 775
- 5y + 8y = 775 - 625
3y = 150
y = 150/3
y = 50
Substitute y = 50 intox + y = 125
x + 50 = 125
x = 125 - 50
x = 75
Therefore, the number of quick washes and premium washes Monica’s school band had is 75 and 50 respectively.
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Answer:
A. 5x + 8y = 775 and x + y =125
Step-by-step explanation:
The area of rectangle is (a²+69+8) sq- units find the length
and breadth of the
rectangle
Step-by-step explanation:
Area of rectangle= length × breadth
A= a²+6a+8
= a²+4a+2a+8
= a(a+4) + 2(a+4)
= (a+4)(a+2)
length= a+4
breadth= a+2
Jessica is a Custodian at an oracle Arena. She waxes 20m^2 of the floor in 3/5 of an hour. Jessica waxes the floor at a constant rate. How many square metres can she wax per hour?
Answer:
Step-by-step explanation:
Just multiply how much she waxes in 3/5 hour by 5/3. Answer is 100/3 or 33.33 sq. meters per hour
Select the correct answer. jackson is conducting an experiment for his physics class. he attaches a weight to the bottom of a metal spring. he then pulls the weight down so that it is a distance of 6 inches from its equilibrium position. jackson then releases the weight and finds that it takes 4 seconds for the spring to complete one oscillation. which function best models the position of the weight?
The function that best models the position of the weight is s(t) = 6cos (pi/2*t).
How to illustrate the function?From the information, we know that the spring is going to have a sin or a cos equation.
We have that the maximum distance of the spring is 6 inches and it is achieved at t=0. We have that the function is of the form 6sin(at+B).
We have that the period is 4 minutes and therefore that the time component in the equation needs to make a period (2pi) in 4 minutes.
In general, a=2pi/T where a is this coefficient, T is the period. Finally, for B, since sin(pi/2)=1, we have that B=pi/2 because when t=0, we have that 6sin(B)=6.
Substituting, we have s(t) = 6cos (pi/2*t).
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The function f(x) = x2 6x 3 is transformed such that g(x) = f(x − 2). find the vertex of g(x).
the vertex of the function g(x) = f(x 2) .
A quadratic equation's vertex form is defined.If a quadratic equation is expressed as the following
[tex]y=a(x-h)^{2}+k[/tex]
It is then said to be in vertex form. Because the vertex point (peak point) occurs on the graph of this equation, it is so named (h,k)
The parabola that the quadratic equation depicts has this point (h,k) as its vertex.
How may the given equation be changed to be in vertex form?We first remove the x squared coefficient, and then inside the bracket, we strive to create a condition that resembles a perfect square.
So, this is what we have:
[tex]$f(x)=x^{2}+6 x+3$\\$g(x)=f(x-2)$[/tex]
Thus, we obtain:
[tex]\begin{aligned}&g(x)=f(x-2) \\&g(x)=(x-2)^{2}+6(x-2)+3 \\&g(x)=x^{2}-4 x+4+6 x-12+3 \\&g(x)=x^{2}+2 x-5\end{aligned}[/tex]
Vertex form transformation of g(x):
[tex]\begin{aligned}&g(x)=x^{2}+2 x-5 \\&g(x)=x^{2}+2 x+1-1-5 \\&g(x)=(x+1)^{2}-9 \\&g(x)=(x-(-1))^{2}-6 \\&g(x)=(x-(-1))^{2}+(-6)\end{aligned}[/tex]
By comparing this[tex]a(x-h)^{2}+k[/tex] to, we obtain the coordinates of the vertex of the graph of g(x) as (h,k) = (-1,-6), as shown below.
As a result, the vertex of the function g(x) = f(x 2) .
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find all the frist differnce and explian your answer
Answer: No this is not a linear function as the y values have different first differences.
Step-by-step explanation:
First we look at the x values. We start off and look at the second x value and subtract the first x value from it (That would be 1-0) and that equals to 1. Then we look at the third x value and subtract the second x value from it (2-1) and that equals to 1. Then we look at the fourth x value and subtract the third x value from it (That would be 3-2) and that is 1. Next we look at the fifth x value and subtract the fourth x value from it (That would be 4-3) and that is 1.
Now we look at the y values and do the same thing as with the x values. We start off and look at the second y value and subtract the first y value from it (That would be 1-0) and that equals to 1. Then we look at the third y value and subtract the second y value from it (4-1) and that equals to 3. Then we look at the fourth y value and subtract the third y value from it (That would be 9-4) and that is 5. Next we look at the fifth y value and subtract the fourth y value from it (That would be 16-9) and that is 7.
Even though the x values all have the same first differences, the y values do not and so this cannot be a linear function.
I hope this helps. Tell me if something doesn't make sense.
Answer:
No, it is a quadratic relation.
Step-by-step explanation:
Work out the first differences between the given y-values:
[tex]0 \underset{+1}{\longrightarrow} 1 \underset{+3}{\longrightarrow} 4 \underset{+5}{\longrightarrow} 9 \underset{+7}{\longrightarrow} 16[/tex]
As the first differences are not the same, this is not a linear relation.
Work out the second differences:
[tex]1 \underset{+2}{\longrightarrow} 3\underset{+2}{\longrightarrow}5\underset{+2}{\longrightarrow}7[/tex]
As the second differences are the same, the relation is quadratic and will contain an x² term. The coefficient of x² is always half of the second difference. As the second difference is 2, the coefficient of x² is one.
[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}x & 0 & 1 & 2 & 3 & 4\\\cline{1-6}x^2 & 0 & 1 & 4 & 9 & 16\\\cline{1-6}\end{array}[/tex]
Comparing x² with the given y-values, we can see that no further operation is needed. Therefore, the relation is quadratic and the equation is [tex]y=x^2[/tex].
A line passes through the point (7, 3. and has a slope of 2. Write an equation for this line.
Answer:
y = 2x - 11.
Step-by-step explanation:
Use the point-slope form of the straight line.
y - y1 = m(x - x1) where m = slope and (x1, y1) is the given point.
Here m = 2 and (x1, y1) = (7,3) so the equation is:
y - 3 = 2(x - 7)
y - 3 = 2x - 14
y = 2x - 11
The Data
Decorative glass pebbles are often used in vases for their appearance, and to have their weight stabilize the vase. The table below gives the total weight of a vase full of uniform glass pebbles.
TABLE OF DATA ATTACHED BELOW*
The Analysis
1- Using the table of data above, determine if this relationship is linear or not. Explain how you know.
2-Write an equation that best represents this relationship:
Explain how you reach your answer and show your work below.
3- Graph the data on the grid to the right, label both axes, and label it Line 1.
4-
a) What is the meaning of the initial value in this scenario?
b) What is the meaning of the slope in this scenario?
5- How would the graph AND equation change if a Styrofoam cup is used to collect the data, instead of a glass vase? Explain your reasoning.
6- Based on your equation in question #2, how much will 112 pebbles weigh with the vase?
7- If the total weight is 504 g, how many pebbles are in the vase?
8- Your friend Wilma shares her analysis of similar data about pebbles and a vase, but her equation is W = 10p + 80.
a) Graph it on the same grid as question #3. Label it Line 2.
b)What are the coordinates of the point of intersection?
c)What does it mean in this scenario?
9- Write a SIMPLIFIED algebraic expression to represent the area of the following trapezoid. Show all your work.
(Hint: area of a trapezoid = [tex]\frac{h(a+b)}{2}[/tex])
TRAPEZOID ATTACHED BELOW*
10- Tanya is 12 years older than Leah. Three years ago, Tanya was five times as old as Leah. What is the age of Tanya and Leah now?
I NEED IT TODAY PLESE!
With the aid of the attached diagrams in the question, we have;
1- Linear relation
2- W = 8•P + 80
3- Please find attached the graph created using a graphing calculator.
4- a) The initial value is the mass of the vase
b) The slope is the mass of each pebble
5- The initial value is lesser than 80
6- 1.2 kilograms
7- 53 pebbles
8- a)
b) (0, 80)
c) The masses are the same
9- Trapezoid area, A = 14•x² - 4•x
10- Tanya and Leah are 18 and 6 years old respectively
How can the table and diagram be analyzed?1- The relationship between two variables (x and y) is linear if the difference between the terms of the x-values and the terms of the y-values are both constant.
From the table we have;
The difference between consecutive terms of the x-values is constant and equal to 10The difference between consecutive terms of the y-values is constant and equal to 80The relationship between the x and y-values in the table is therefore;
A linear relationship2. The slope, m, of the linear function is found as follows;
m = (360 - 280)/(30 - 20) = 8
The equation is therefore;
W - 360 = 8•(P - 30)
W = 8•P - 240 + 360 = 8•P + 80
The equation is; W = 8•P + 803. Please find attached the graph drawn with a graphing calculator.
4. The initial value is the output variable (W-value) when the input variable (P-value) is zero.
Therefore;
y = 8×0 + 80 = 80
a) The initial value indicates when the input, P-value is zero, which gives the mass of the vases
b) The slope indicates the number of times an additional pebble increases the weight of the vase and pebble, which is the mass of one pebble
5- A styrofoam cup is lighter than a glass cup, therefore, the initial value, which is the constant term, c, reduces.
The change is that, the initial value reduces and becomes less than 806- The weight, W, of 112 pebbles is therefore;
W = 10 × 112 + 80 = 1,200
The weight of 112 pebbles is 1,200 g, which is 1.2 kg.7- 504 = 8•P + 80
Which gives;
504 - 80 = 8•P
P = 424 ÷ 8 = 53
The number of pebbles in the vase when it weighs 504 g. is 53 pebbles8- Wilma's equation is; W = 10•P + 80
a) Please find the second graph showing the graphs of the two equations combined.
b) The point of intersection is given by the relation 10•P + 80 = 8•P + 80
2•P = 0
P = 0
Therefore, at the point of intersection, W = 80
The coordinates of the point of intersection is therefore;
(0, 80)c) The point of intersection means that the weight of Wilma's vase and the vase in question 1 are the same.
9. The area of the trapezoid, A, can be expressed as follows;
A = 4•x × ((2•x + 5)+(5•x - 7))/2
A = 2•x × (7•x - 2) = 14•x² - 4•x
Area of the trapezoid = 14•x² - 4•x10. Let T represent Tanya's age now and let L represent Leah's current age, we have;
T = L + 12
T - 3 = (L - 3) × 5
Solving gives;
L + 12 - 3 = (L - 3) × 5 (Substitution property)
L + 9 = 5•L - 15
4•L = 9 + 15 = 24
L = 24 ÷ 4 = 6
Leah's age now, L = 6 yearsT = L + 12
Therefore;
T = 6 + 12 = 18
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3. The diagram on the right shows the pattern drawn on a Cartesian plane. The final line on the plan is parallel to the y-axis and passes through x = -10. Find the sum of the length of the overall pattern.
The sum of the length of the overall pattern in the given cartesian coordinate is calculated as; 44
How to find the lengths of a cartesian?We are told that The final line on the plan is parallel to the y-axis and passes through x = -10
Now, looking at the pattern, the lengths of each side are as follows;
1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5
Thus, the sum of the length of the overall pattern is calculated as;
1.5 + 2 + 2.5 + 3 + 3.5 + 4 + 4.5 + 5 + 5.5 + 6 + 6.5 = 44
Therefore we can conclude from all the deductions and calculations above that the sum of the length of the overall pattern in the given cartesian coordinate is calculated to be; 44
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Given f of x is equal to the quantity 8x plus 1 end quantity divided by the quantity 2x minus 9 end quantity, what is the end behavior of the function?
Answer:
Step-by-step explanation:
Equation
f(x) = (8x + 1) / (2x + 9)
Notice the brackets. They are necessary to show what comes before the division sign, and what comes after.
Behavior
The best way to state the behavior is to get something like a graphing program to show you what the curve looks like -- where it's critical points are for example. I use Desmos for this kind of question, Just do a search for Desmos and bookmark it. You will use it quite often.
So you want to know the behavior.
Right Curve
Crosses the x axis at (-0.125, 0)
Crosses the y axis at (0,0,111)
The right curve has a domain of -∞ < x < ∞
The right curve has a range of -∞ < x < ∞
The range is going to have to go out quite a ways before you see any dramatic decrease in the way it is drawn.
Left Curve.
The right hand curve never crosses either the x or y axis. Nor does it just touch the x or y axis.
The domain is -∞ <x < 0
The range is 0<x<∞
What is the equation of the line that passes through the point (-5, -3) and has a
slope of -3?
Answer: y=-3m+13
Step-by-step explanation:
y=mx+c
m is the gradient
y=-3x+c
We know one point
-2=3(-5)+c
Solve for c
-2=-15+c
13=c
y=-3m+13
What is the area of the following polygon?
I have tried 24, 25 and 26 and none of worked and I am at a loss.
The area of the polygon is 25.5 square units
How to determine the area of the polygon?From the figure, we have the following coordinates
A = (-2, 1)
B = (3, 2)
C = (5, -3)
D = (-1, -3)
The area of the polygon is then calculated as:
A = 0.5 * |(x1y2 - x2y1) + (x2y3 - x3y2) + (x3y4 - x4y3) + (x4y1 - x1y4)|
Substitute the known values in the above equation
Area = 0.5 * |(-2 * 2 - 3 * 1) + (3 * -3 - 5 * 2) + (5 * -3 + 1 * -3) + (-1 * 1 + 2 * -3)|
Evaluate the sum of products
Area = 0.5 * |-51|
Remove the absolute bracket
Area = 0.5 * 51
Evaluate the product
Area = 25.5
Hence, the area of the polygon is 25.5 square units
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A man gets Rs. 40 for everyday he works, but is fined Rs. 10 for everyday he is absent If he got Rs. 700 at the end of 30 days. How many days he was absent from the work?
Answer:
50 days
Step-by-step explanation:
40×300=1200
1200-700
500
so 1 day is 10 . 50 days is 500
The number of days he was absent from work will be 50 days
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a man gets Rs. 40 for every day he works, but is fined Rs. 10 for every day he is absent If he got Rs. 700 at the end of 30 days.
The number of days he was absent from work will be calculated as below:-
40×300 = 1200
= 1200-700
= 500
1 day is 10 then 50 days is 500. Therefore, the number of days he was absent from work will be 50 days
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Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°
Prove: △HKJ ~ △LNP
Triangles H K J and L N P are shown. Triangle L N P is smaller and to the right of triangle H K J.
Statement Reason
1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. given
2. m∠H + m∠J + m∠K = 180° 2. ?
3. 30° + 50° + m∠K = 180° 3. substitution property
4. 80° + m∠K = 180° 4. addition
5. m∠K = 100° 5. subtraction property of equality
6. m∠J = m∠P; m∠K = m∠N 6. substitution
7. ∠J ≅ ∠P; ∠K ≅ ∠N 7. if angles are equal then they are congruent
8. △HKJ ~ △LNP 8. AA similarity theorem
Which reason is missing in step 2?
CPCTC
definition of supplementary angles
triangle parts relationship theorem
triangle angle sum theorem
Answer:
triangle angle sum theorem
Step-by-step explanation:
The missing statement is one that justifies the sum of the angles in a triangle being 180°.
That justification is provided by the ...
triangle angle sum theorem