Given `lim_(x -> 2) 2x - 3 = 1`, use the formal definition of a limit to find the value of δ that corresponds to ε = 0.3.
A. 0.05
B. 0.15
C. 0.30
D. 0.50
Answer: B. 0.15
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What is the average rate of change of the function f(x) = x^2 – 2x + 4 over the interval –2 ≤ x ≤ 3?
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The rate of change of a function is the increase or decrease that a function experiences as the independent variable changes from one value to another.
The corresponding equation of the average rate of change is:
[tex]TVM(x_1,x_2)=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]In this case, x1 is 3 and x2 is 3
Remember that according to the notation of the limits, they take the values of 2 and 3.
Now, we solve f(3) and f(2)
[tex]\begin{gathered} f(3)=3^2-2\cdot(3)+4 \\ f(3)=9-6+4 \\ f(3)=7 \end{gathered}[/tex][tex]\begin{gathered} f(2)=2^2+2\cdot(2)+4 \\ f(2)=4-4+4 \\ f(2)=4 \end{gathered}[/tex]This way now we can replace the values in the TVM equation and I will solve this.
[tex]\begin{gathered} TVM(3,2)=\frac{7-4}{3-1_{}} \\ TVM(3,2)=\frac{3}{1}=3 \end{gathered}[/tex]In conclusion, the average rate of change of the function
How do I solve this I think I did it incorrectly
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Given:
The diameter of the circle = d = 14 cm
The radius of the circle = r = d/2 = 7 cm
The circumference is given by the formula: 2πr
so, the exact value = 2π * 7 = 14π cm
The approximated value to the nearest hundredth = 43.98 cm
The area of the circle is given by the formula: πr²
The exact value of the area = π * 7² = 49π cm²
The approximated value to the nearest hundredth = 153.94 cm²
11) The table below represents a linear equation. If the y-intercept is at point (0, b), what is the value of b?X-125Y-1817
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step 1
Find the slope of the linear equation
we take the points
(-1,-1) and (2,8)
so
m=(8+1)/(2+1)
m=9/3
m=3
step 2
Find the equation of the line in sloe intercept form
y=mx+b
we have
m=3
point (2,8)
substitute
8=3(2)+b
solve for b
8=6+b
b=2
the equation is
y=3x+2
and the value of b is 2
two gongs strike at intervals of 90 and 60 minutes respectively.At what time will they strike together again if they start simultaneously at 12 noon
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Both the gongs will strike together at 3 pm.
Given,
Two gongs strike at intervals 90 and 60 minutes respectively.
Use LCM to find at what time they will strike together
Using prime factorization:
LCM of (60,90)=[tex]2^2*3^2*5=4*9*5=180[/tex]
They will strike together after 180 minutes i.e. 3 hours
Hence, if they start simultaneously at 12 noon then they will strike together again at 3 pm
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Rewrite the expression with a positive rational exponent. Simplify, if possible.100-1/2
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We need that the 100 has a 2 in the denominator. To do this, we can multiply on top and bottom by 2:
[tex]100\cdot\frac{2}{2}=\frac{200}{2}[/tex]Now, we can make the subtraction:
[tex]\frac{200}{2}-\frac{1}{2}=\frac{199}{2}[/tex]The answer is 199/2
A factory makes candles. Each candle is in the shape of a triangular prism, as shown below. If the factory used 14,700 cm^3 of wax,how many candles did the factory make?
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Answer:
Explanation:
Step 1
First, we find the volume of one the triangular prism shaped candles.
The volume of a prism is calculated using the formula:
[tex]V=\text{ Cross-Sectional Area}\times\text{ Length}[/tex]The cross section of the prism is a triangle with:
• Base = 10cm
,• Height = 7cm
Length of the Prism = 6cm
Therefore:
[tex]\begin{gathered} V=\frac{1}{2}bh\times L \\ =\frac{1}{2}\times10\times7\times6 \\ =210\;cm^3 \end{gathered}[/tex]The volume of one of the candles is 210 cubic cm.
Step 2
Next, divide the volume of wax used by the factory by the volume of one candle.
[tex]\text{Number of candles made}=\frac{14700}{210}=70[/tex]If FG= 9x-2 and jk=3x+10, what value of x will make FG and JK congruent
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ANSWER
x = 2
EXPLANATION
If we want FG and JK to be congruent, then we have to see which value of x makes:
[tex]FG=JK[/tex]true.
f(x) = 8x⁵-7x⁴-73x³+23x²-20x-5÷8x+1
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f(x) = 8x⁵-7x⁴-73x³+23x²-20x-5÷8x+1
[tex]f\mleft(x\mright)=\frac{8x^{5}-7x^{4}-73x^{3}+23x^{2}-20x-5}{8x+1}[/tex]9 Is the sentence correct? Select Yes or No. A. O Yes O No 2 3 B. O Yes O No c. > O Yes O No D. too O Yes O No 8 E. O Yes O No F.
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9 a) 1 /2 = 1/ 3 NO
b) 4/ 6 < 5/6 YES
c ) 5/ 6 > 5/8 YES
d) 4/8 < 7/8 YES
e) 3/3 = 3/ 8 NO
f) 1/4 < 3/4 YES
heights of men on a basketball team have a bell shaped distribution with the mean of 177 cm and a standard deviation if 5 cm. using the empirical rule, what is the approximate percentage of the men between 162 cm and 192 cm?
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The variable
X: height of a basketball team
This variable has a bell shaped distribution (Normal distribution) with mean μ=177cm and a standard deviation of δ=5cm
The empirical rule states that
68% of the distribution is within one standard deviation away from the mean
[tex]\begin{gathered} \mu\pm\sigma=0.68 \\ 177\pm5 \\ (172;182) \end{gathered}[/tex]95% of the distribution is within two standard deviations away from the mean
[tex]\begin{gathered} \mu\pm2\sigma=0.95 \\ 177\pm2\cdot5 \\ (167,187) \end{gathered}[/tex]99.7% of the distribution is within three standard deviations away from the mean
[tex]\begin{gathered} \mu\pm3\sigma=0.997 \\ 177\pm3\cdot5 \\ (162,192) \end{gathered}[/tex]So, following the empirical rule, 99.7% of the men are between 162 cm and 192 cm
which of the following expression has a coefficient of 10 and a constant of 5 10+5x. 10+5. 10 - 5. 10x+5
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the coefficient is the number that accompanies the variable, in this case it would be the number that accompanies the x
and a constant is a number without company
so, the expression is
[tex]10x+5[/tex]the last option
In 2009, Mariana paid $5,160 in federal income tax. In 2010, she paid 70% more than in 2009. How much did Mariana pay in 2010?
finishing. What is the percent of decrease in the number of finishers?
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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{70\% of 5160}}{\left( \cfrac{70}{100} \right)5160}\implies 3612~\hfill \underset{for~2010}{\stackrel{5160~~ + ~~3612}{\text{\LARGE 8772}}}[/tex]
Answer:
3,612
Step-by-step explanation:
70% of 5,160
0.70•5,160= 3612
Which equation represents a line which is parallel to the line by – 7x = 24?:A) y=7/6x+3B) y=6/7x-2C) y=-7/6x-1D)y=-6/7x+7
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We have the equation 6y-7x=24, and want to know what of the options represents a line parallel to that one.
First we need to write our equation in the form of the options:
[tex]\begin{gathered} 6y-7x=24 \\ 6y=7x+24 \\ y=\frac{7x+24}{6}=\frac{7x}{6}+\frac{24}{6} \\ y=\frac{7}{6}x+4 \end{gathered}[/tex]Now, we know that two lines are parallel if and only if they slopes are equal, so the slope of our line is 7/6 and the option that has the same slope is the option A.
So te correct answer is the option A
A third box is designed so that it is also a cube that has sides that are half of solid 1's. find the volume of solid 3. then find the ratio of the volume of solid 1 to the volume of solid 3. explain why the ratio is not 2 to 1
Answers
Given :
Solid 1:
The side of the cube is, a = 8 cm.
Solid 3:
The side of the cube is, b = 4 cm.
The volume of the third cube can be calculate as,
[tex]V=b^3=(4cm)^3=64cm^3[/tex]The volume of first cube is,
[tex]V^{\prime}=a^3=(8cm)^3=512cm^3[/tex]Thus, the ratio can be calculated as,
[tex]\frac{V^{\prime}}{V}=\frac{512}{64}=\frac{8}{1}[/tex]Thus the required ratio is 8:1.
Since the volume is proprtional to the cube of the side, the ratio will also be in the range of cube of the fractional difference between the sides.
help me on this math question! please
Answers
Answer:
X: -2, -1, 0, 1, 2
Y: -3, -1, 1, 3, 5
Step-by-step explanation:
A problem solver site says the table will look like this
the U.S senate has 100 members. there are 6 more democrats than republicans, with no other parties represented. how many memebr of each party were there in the senate
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The number of republicans and democrats will be 47 and 53 respectively.
Define equation.Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It shows that the expressions printed on the left and right sides have an equal relationship. In any mathematical equation, we have LHS = RHS (left hand side = right hand side). Equations can be solved to find the value of an unknown variable that represents an unknown quantity.
Given data -
Total number of members in U.S senate = 100
Let the number of republicans in U.S senate be x members
As republicans outnumber democrats by six,
Therefore, number of democrats = (x+6) members
According to the given data,
x + (x+6) = 100
2x + 6 = 100
2x = 94
x = 47
Number of members as a republicans will be 47.
Number of members as a democrats will be (100-47) = 53
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Max has 15-foot long piece of plastic pipe. He wants to cut it into four equivalent pieces to make corner flag poles for the soccer field. What should be the length of each flagpole that will be cut?
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Answer:
3.75 feet
Explanation:
To know the length of each flagpole, we need to divide 15 (the total length of the piece of plastic pipe) by 4 because he wants 4 pieces. Then:
15 ÷ 4 = 3.75 feet
Then, each flagpole should have a length of 3.75 feet.
(d) 8x + 3y = -45x + 2y = 6Solve the following simultaneous linear equation
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To solve the following simultaneous linear equation, we are going to solve for y on the first equation and replace it on the second as:
[tex]\begin{gathered} 8x+3y=-4 \\ 3y=-4-8x \\ y=\frac{-4-8x}{3} \\ y=\frac{-4}{3}-\frac{8x}{3} \end{gathered}[/tex]Replacing it on the second equation and solving for x, we get:
[tex]\begin{gathered} 5x+2y=6 \\ 5x+2(\frac{-4}{3}-\frac{8x}{3})=6 \\ 5x-\frac{8}{3}-\frac{16x}{3}=6 \\ 5x-\frac{16}{3}x=6+\frac{8}{3} \\ \frac{-1}{3}x=\frac{26}{3} \\ -x=26 \\ x=-26 \end{gathered}[/tex]Finally, replacing x on the first equation and solving for y, we get:
[tex]\begin{gathered} 8x+3y=-4 \\ 8(-26)+3y=-4 \\ 3y=-4+208 \\ 3y=204 \\ y=\frac{204}{3}=68 \end{gathered}[/tex]Answer: x = -26 and y = 68
To make subtraction of 5x - 16x/3, we can use the following equation:
[tex]\frac{a}{b}-\frac{c}{d}=\frac{a\cdot d-b\cdot c}{b\cdot d}[/tex][tex]\begin{gathered} 5x-\frac{16x}{3}=\frac{5x}{1}-\frac{16x}{3}=\frac{5x\cdot3-1\cdot16x}{1\cdot3}=\frac{15x-16x}{3}=\frac{-1x}{3} \\ \end{gathered}[/tex]ху Evaluate when x = 6 and y = 13. x + y
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EXPLANATION
When x=6 and y=13 x+y = 6 + 13 = 19
x + y = 19
what is 8 7/8+1/2 and what is 45.35 + 40 7/10
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8 7/8+1/2
1) We need to turn that Mixed number into an improper fraction, by keeping the denominator and multiplying it by the whole number, and then adding to the numerator of that Mixed Number:
[tex]8\frac{7}{8}=\frac{8\cdot8+7}{8}=\frac{71}{8}[/tex]2) Adding then:
[tex]\frac{71}{8}+\frac{1}{2}=\frac{8\colon8\times71+8\colon2\times1}{8}=\frac{71+4}{8}=\frac{75}{8}[/tex]Turning back to Mixed Number:
Dividing 75 by 8 and placing the quotient as the whole number, the divisor as the denominator, and the remainder as the numerator we have the mixed number back.
2)45.35 + 40 7/10
Rewriting 45.35 as a fraction:
[tex]\begin{gathered} 45.35\text{ =}\frac{4535}{100} \\ 40\frac{7}{10}+\frac{4535}{100} \\ \frac{407}{10}+\frac{4535}{100} \\ \frac{4070+4535}{100} \\ \frac{8605}{100} \\ \frac{1721}{20} \end{gathered}[/tex]Note that we've rewritten as fractions, and then turned them into improper ones, added them, and then simplified.
3) Hence, the answer is
[tex]\begin{gathered} a)9\frac{3}{8}\text{ or }\frac{75}{8} \\ b)\text{ }\frac{1721}{20} \end{gathered}[/tex]How is this equation true?4/4 * x/1 + 1/4 = 4x/4 + 1/4 = 4x+1/4
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Given
[tex]\frac{4}{4}*\frac{x}{1}+\frac{1}{4}[/tex]Simplify as shown below,
[tex]\begin{gathered} \frac{4}{4}*\frac{x}{1}+\frac{1}{4}=\frac{4*x}{4*1}+\frac{1}{4} \\ =\frac{4x}{4}+\frac{1}{4} \\ =\frac{4}{4}*x+\frac{1}{4} \\ =1*x+\frac{1}{4} \\ =x+\frac{1}{4} \end{gathered}[/tex]If the initial equation is correct, the last equality in the question tab is incorrect. The simplification is x+1/4, not 4x+1/4.
Need help with finding the vertex and the Y intercept of the quadratic function and use them to graph the function for number 21
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EXPLANATION
Given the function y=-2x^2 -12x -5
[tex]\mathrm{The\: vertex\: of\: an\: up-down\: facing\: parabola\: of\: the\: form}\: y=ax^2+bx+c\: \mathrm{is}\: x_v=-\frac{b}{2a}[/tex][tex]\mathrm{The\: parabola\: params\: are\colon}[/tex][tex]a=-2,\: b=-12,\: c=-5[/tex][tex]x_v=-\frac{b}{2a}[/tex][tex]x_v=-\frac{\left(-12\right)}{2\left(-2\right)}[/tex][tex]\mathrm{Simplify}\colon[/tex][tex]x_v=-3[/tex]Plug in x_v=-3 to find the y_v value:
[tex]y_v=-2\mleft(-3\mright)^2-12\mleft(-3\mright)-5[/tex]Computing the powers and multiplying terms:
[tex]y_v=-18+36-5[/tex]Adding and subtracting numbers:
[tex]y_{v\text{ }}=13[/tex]Therefore, the parabola vertex is:
(-3,13)
Now, we need to compute the y-intercept
[tex]y\mathrm{-intercept\: is\: the\: point\: on\: the\: graph\: where\: }x=0[/tex][tex]\mathrm{Apply\: rule}\: 0^a=0[/tex][tex]0^2=0[/tex][tex]y=-2\cdot\: 0-12\cdot\: 0-5[/tex]Multiplying numbers:
[tex]y=-5[/tex]The y-intercept is at (0,-5)
In conclusion, the graph of the function is as follows:
Divide.
-10/25 8/10
What is the quotient?
Enter your answer as a simplified fraction in the box.
Answers
Answer:
-10/25÷8/10
-10/25×10/8
-100/25(8)
-100/200
-1/2
Hope this is right!!
Answer:
-1/2
Step-by-step explanation:
change the sign from divide to multiply: -10/25 X 8/10
flip the second fraction: -10/25 X 10/8
simplify the expression: -10 divide 5/ 25 divide 5 x 10 divide 2/ 8 divide 2
cancel out greatest factor: -2/5 x 5/4
simplify: - 2 /4
answer: - 1/2
Which equation represents a line which is parallel to the y-axis?a) x=4yb) x=1/4yc) x=3d) y=-6
Answers
The graph of x = 3 is a line parallel to the y-axis, which passes through the point (3, 0). This means that x = 3 for every value of y.
What is the intensity of an earthquake in Hawaii
which measured 3.92 on the richter scale?
Use the formula M = log(i/s)
S= 1 micron
- 7,943 microns
- 6904 microns
- 8318 microns
- 2818 microns
Answers
8318 microns is the intensity of an earthquake in Hawaii.
What is Richter scale?The Richter scale was originally developed to measure the magnitude of moderate earthquakes (magnitude 3 to magnitude 7) by assigning numbers so that the magnitude of one earthquake can be compared to another. This scale was developed for the Southern California earthquake recorded by the Wood He Anderson seismograph whose epicenter was less than 600 km (373 mi) from the seismometer location. However, today's seismometers can be calibrated to calculate the Richter magnitude, and modern methods of measuring earthquake magnitude are designed to give results consistent with those measured using the Richter scale. Developed.
The magnitude of an earthquake is determined using the logarithm of the amplitude (height) of the largest seismic wave, calibrated to scale by the seismograph.
Using the formula,
[tex]M = log \frac{i}{s}\\ 3.92 = log\frac{i}{1 micron} \\10^3.92 = \frac{i}{s} \\i = 8318[/tex]
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7. Elena wanted to find the slope and y-intercept of the graph of 25x – 20y = 100. Shedecided to put the equation in slope-intercept form first. Here is her work:-25x - 20y = 10020y = 100 - 25x5y = 5 - 2x-4She concluded that the slope isand the y-intercept is (0,5).a. What was Elena's mistake?b. What are the slope and y-intercept of the line? Explain or show your reasoning.
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The slope-intercept form for an equation of a line looks like this:
[tex]y=mx+b[/tex]Where m is the slope and (0,b) the y-intercept. Let's take the equation given by the question, operate and write it in slope-intercept form and see which was Elena's mistake. So we have:
[tex]25x-20y=100[/tex]We can substract 25x from both sides:
[tex]\begin{gathered} 25x-20y-25x=100-25x \\ -20y=100-25x \end{gathered}[/tex]Here we can see Elena's mistake. Instead of the equation I just wrote she got:
[tex]20y=100-25x[/tex]This doesn't have the negative sign in 20y. This was her mistake and answer to part a.
Now let's continue, we can divide both sides by -20:
[tex]\begin{gathered} -\frac{20y}{-20}=\frac{100-25x}{-20} \\ y=-\frac{100}{20}+\frac{25}{20}x \\ y=\frac{5}{4}x-5 \end{gathered}[/tex]Which means that the slope is 5/4 and the y-intercept is (0,-5).
Which of the following lines is NOT parallel toy = 3x + 4?
Answers
We are to look for lines that are not parallel to y=3x + 4
Comparing the above equation with y=mx + b, the slope(m) = 3
Equations of lines are said to be parallel, if they have the same slope
So, we need to re-write each equation in the slope-intercept form to see which is NOT parallel to the given equation
OPTION A
3y - 9x - 6 = 0
[tex]y=\frac{9x}{3}+\frac{6}{3}[/tex][tex]y=3x+2[/tex]slope = 3 which implies. it is parallel to the given equation
OPTION B
-2y + 6x + 4 = 0
[tex]2y=6x+4[/tex]Divide through by 2
[tex]y=3x\text{ + 2}[/tex]slope = 3 which implies the line is parallel to the given line
OPTION C
2y - 6x - 4 = 0
[tex]2y=6x\text{ + 4}[/tex]Divide through the equation by 2
[tex]y=3x\text{ + 2}[/tex]slope = 3 which implies the line is parallel to the given line
OPTION D
2y - 4x - 8 = 0
[tex]2y=4x\text{ + 8}[/tex]Divide through the equation by 2
[tex]y=2x\text{ + 4}[/tex]slope = 2, which means tthe line is NOT parallel to the given line.
Therefore, the line which is NOT parallel to y=3x+ 4 is D. 2y - 4x - 8 = 0
Which of the following Platonic solids is made from squares? Check all thatapply.A. icosahedronB. cubec. tetrahedronD. octahedronE, hexahedronF. dodecahedron
Answers
From the information on platonic solids, we can say that cube is the only platonic solid that is made from squares. Thus, option B is correct.
Platonic solids, also referred to as regular solids or regular polyhedrons, are the types of solids that have identical faces composed of congruent regular convex polygons.
A platonic solid can be defined as a 3D shape where each face is similar to a regular polygon and consists of same number of faces that meet at each vertex of the polygon.
There are 5 different types of platonic solids that are -
Tetrahedron - A tetrahedron is referred to as a triangular pyramid in geometry. The tetrahedron comprises of 4 triangular faces, 6 straight edges, and 4 vertex corners.Cube - A cube can be defined as 3D solid object with 6 square faces and consists of the sides that are of the same length. The cube is also called as a regular hexahedron which is a box-shaped solid with 6 equivalent square faces.Octahedron - An octahedron is in fact, a polyhedron consisting of 8 faces, 12 edges, and 6 vertices and at each of the vertices, the 4 edges coincide. The faces of an octahedron are shaped in the form of an equilateral triangle.Dodecahedron - A dodecahedron is referred to as a platonic solid comprising of 12 sides and 12 pentagonal faces. Icosahedron - An icosahedron is a platonic solid with 20 faces, 30 edges, and 12 vertices. The shape of an icosahedron consists of equilateral triangle faces.Thus, from the above information on platonic solids, we can say that cube is the only platonic solid that is made from squares. Thus, option B is correct.
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For 97.1 seconds, a remote-controlled helicopter flew at an altitude of 3 meters and a constant velocity of 19.0 meters per second to the west. During this time, how far did the helicopter fly?
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The relationship between time, distance and velocity is:
[tex]v=\frac{d}{t}[/tex]In this case, we need to find the distance, d
We can solve for d:
[tex]v=\frac{d}{t}\Rightarrow d=v\cdot t[/tex]The velocity of flight is v = 19 m/s and the time of flight is t = 97.1s
Then:
[tex]d=19\frac{m}{s}\cdot97s[/tex][tex]d=1844.9m[/tex]The answer is 1844.9m
To get the 10% discount, a shopper must spend no less than $400.Use d to represent the spending (in dollars) of a shopper who gets the discount.
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d represents the amount spent by a shopper who gets the discount.
The expression for d would be
[tex]d\text{ }\ge400[/tex]d is greater than or equal to 400I’m done answering. Do you understand my explanation?