3x + 8y = -18 -----------------------(1)
6x + 16 y = - 54 ---------------------------(2)
Using elimination method,
multiply equation (1) by 6 and equation (2) by 3
18x + 48y = -108 -----------------(3)
18 x + 48y = 162 -------------------(4)
From this, we can deduce that there is no solution to the system of equations
Given the following dataset, determine the mode 6056605570546055
Answer:
5
Step-by-step explanation:
put it in order
6056605570546055
and the one that appears the most is the mode
A piece of paper is folded into half repeatedly. The thickness of the paper in inches is modeled by the function y = 2x/1000, where x is the number of folds. How thick will the paper be if you could fold it 10 times?About an inchAbout 2 inchesAbout 3 inchesAbout 4 inches
Given: A piece of paper is folded into half repeatedly. The thickness of the paper in inches is modeled by the function y = 2x/1000, where x is the number of folds.
Required: To determine the thickness of the paper if the paper is folded 10 times.
Explanation: The thickness of the paper is given by the function
[tex]y=\frac{2x}{1000}[/tex]Here, x is the number of folds=10
Hence,
[tex]\begin{gathered} y=\frac{2\times10}{1000} \\ =0.02\text{ inches} \end{gathered}[/tex]Final Answer: After 10 folds, the thickness of the paper is 0.02 inches.
If d - 243 = 542, what does d-245 equal? CARA GOIECT CH 1UJAINRIகபட்ட RE Lien Answer: Your answer
Given the following expression:
[tex]d-243=542[/tex]if we add 243 on both sides of the equation we get the following:
[tex]\begin{gathered} d-243+243=542+243=785 \\ \Rightarrow d=785 \end{gathered}[/tex]thus, d = 785
a horse race has 14 entries and one person owns 2 of those horses. assuming that there are no ties, what is the probability that those two horses finish first and second (regardless of order)
Answer:
1/91
Explanation:
Number of entries in the horse race = 14
• The probability that one of those 2 horses will be first = 2/14
,• The probability that the second horse will be second = 1/13
Therefore:
[tex]\begin{gathered} P(\text{those two horses finish first and second)} \\ =\frac{2}{14}\times\frac{1}{13} \\ =\frac{1}{91} \end{gathered}[/tex]The probability is 1/91.
Given that the height of a trapezoid is 16 m and one base’s length is 25 m. Calculate the dimension of the other base of the trapezoid if its area is 352 m².
ANSWER:
19 m
STEP-BY-STEP EXPLANATION:
We have that the formula for the area of a trapezoid is the following:
[tex]A=\frac{B+b}{2}\cdot h[/tex]We substitute each value and calculate the length of the other base, like so:
[tex]\begin{gathered} 352=\frac{25+b}{2}\cdot16 \\ \\ 25+b=352\cdot\frac{2}{16}\frac{}{} \\ \\ b=44-25 \\ \\ b=19 \end{gathered}[/tex]The dimension of the other base of the trapezoid is 19 m
This graph shows the solution to which inequality?3.2)(-3,-5)O A. ys fx-2B. vfx-2O c. vfx-2OD. yzfx-2
First, find the equation of the line, given that the points (3,2) and (-3,-6) belong to that line. To do so, use the slope formula and then substitute the value of the slope and the coordinates of a point on the slope-point formula of a line:
[tex]y=m(x-x_0)+y_0[/tex]The slope of the line, is:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ =\frac{(2)-(-6)}{(3)-(-3)} \\ =\frac{2+6}{3+3} \\ =\frac{8}{6} \\ =\frac{4}{3} \end{gathered}[/tex]Therefore, the equation of a line (using the point (3,2)) is:
[tex]\begin{gathered} y=\frac{4}{3}(x-3)+2 \\ =\frac{4}{3}x-\frac{4}{3}\times3+2 \\ =\frac{4}{3}x-4+2 \\ =\frac{4}{3}x-2 \end{gathered}[/tex]Since the colored region on the coordinate plane is placed above the line
y=(4/3)x-2, then the equation of the inequality is:}
[tex]undefined[/tex]1 point Esther thinks she understands how to find the midpoint of a segment on a graph. "I always look for the middle of the line segment. But what should I do if the coordinates are not easy to graph?" she asks. Find the midpoint of KL if (2.125) and L(98, 15). *
In this case, we can write out the parameters
[tex]\begin{gathered} x_1=2,_{}y_1=125, \\ x_2=98,y_2=15 \end{gathered}[/tex]Thus, substitute the coordinates in the mid-point formula and simplify
[tex]\begin{gathered} x_m=\frac{98+2}{2}=\frac{100}{2}=50 \\ y_m=\frac{125+15}{2}=\frac{140}{2}=70 \end{gathered}[/tex]Hence, the coordinate of the mid-point is (50, 70)
2 dot plots. Both number lines go from 0 to 10. Plot 1 is titled fifth grade. There are 2 dots above 1, 3 above 2, 1 above 3, 4 above 4, 5 above 5, 5 above 6, 2 above 7, 2 above 8, 0 above 9, 0 above 10. Plot 2 is titled seventh grade. There are 2 dots above 0, 2 above 1, 3 above 2, 5 above 3, 5 above 4, 3 above 5, 3 above 6, 1 above 7, and 0 above 8, 9, and 10.
The dot plot shows the number of hours, to the nearest hour, that a sample of 5th graders and 7th graders spend watching television each week. What are the mean and median?
The 5th-grade mean is
.
The 7th-grade mean is
.
The 5th-grade median is
.
The 7th-grade median is
.
The mean of the 5th grade students is 4.67
The mean of the 7th grade students is 3.46
The median of the 5th grade students is 5
The median of the 7th grade students is 3.5
What are the mean and median?A dot plot is a graph used to represent a dataset. A dot plot is made up of a number line and dots. The dots in the dot plot represent the frequency of the data. The greater the frequency of a data, the greater the number of dots.
Mean is the average of a dataset. It is determined by adding all the numbers in the dataset together and dividing it by the total numbers in the dataset.
Mean = sum of numbers / total numbers in the dataset
Mean of the 5th grade students = ( 1 + 1 + 2 + 2 + 2 + 3 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 6 + 7 + 7 + 8 + 8 ) / 24
112 / 24 = 4.67
Mean of the 7th grade students = ( 0, 0, 1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7) / 24
83 / 24 = 3.46
Median is the number that is in the middle of a dataset.
Median = (n + 1) / 2
Median of the 5th grade students = (24 + 1) / 2 = 12.5 terms = 5
Median of the 7th grade students = (24 + 1) / 2 = 12.5 term = (3 + 4) / 2 = 3.5.
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Question 7, pre calc, include the answer in bold please. I have bad WiFi so please finish question if I get disconnected so I can see it, thanks
Given the following function
[tex]f(x)=x^4-x^3+7x^2-9x-18[/tex]We want to find its roots. Since we already know that (x + 1) and (x - 2) are factors of this polynomial, we can divide our polynomial by those factors and factorize the result to get the other roots.
Let's start by dividing by the first factor
[tex]\frac{x^4-x^3+7x^2-9x-18}{x+1}[/tex]To divide a polynomial by other, we start by dividing the leading term of the dividend by the leading term of the divisor(this will be the first term of our result)
[tex]\frac{x^4}{x}=x^3[/tex]Then, we ultiply it by the divisor
[tex]x^3(x+1)=x^4+x^3[/tex]Subtracting this result from the dividend, we have
[tex](x^4-x^3+7x^2-9x-18)-(x^4+x^3)=-2x^3+7x^2-9x-18[/tex]This means that our division is
[tex]\frac{x^4-x^3+7x^2-9x-18}{x+1}=x^3+\frac{-2x^3+7x^2-9x-18}{x+1}[/tex]Repeating the whole process of division with the second term, we have
[tex]\begin{gathered} x^3+\frac{-2x^3+7x^2-9x-18}{x+1}=x^3-2x^2+\frac{9x^2-9x-18}{x+1} \\ \Rightarrow\frac{x^4-x^3+7x^2-9x-18}{x+1}=x^3-2x^2+9x-18 \end{gathered}[/tex]From this result, we can rewrite our function as
[tex]x^4-x^3+7x^2-9x-18=(x+1)(x^3-2x^2+9x-18)[/tex]Repeating this same process with the other know factor, the other division we have to solve is
[tex]\frac{(x^3-2x^2+9x-18)}{x-2}=x^2+9[/tex]Then, our function is
[tex]f(x)=(x^4-x^3+7x^2-9x-18)=(x+1)(x-2)(x^2+9)[/tex]Then, to find the roots we need to solve the following equation
[tex](x+1)(x-2)(x^2+9)=0[/tex]Since we have a product of 3 terms, the result will be zero if and only if one of the terms is zero. This means that the roots can be found by assuming each one is zero. The solutions for this equation are the same solutions for the following system
[tex]\begin{cases}x+1=0 \\ x-2=0 \\ x^2+9=0\end{cases}\Rightarrow\begin{cases}x=-1 \\ x=2 \\ x=\pm\sqrt[]{-9}=\pm3i\end{cases}[/tex]And those are the roots for our function. x = -1, 2, +-3i.
The graph shows a dilation of trapezoid TRAP with respect to the origin which statements are true about the figures select three
A dilation means an elongation of the sides of a figure
So in a dilation the sides are bigger than at the original figure
A key formula for found dilation is Pithagoras theorem
For calculate T'R'
T'R' is the exact diagonal of OT' and OR', that means
OT' + OR' = T'R' in vectorial sum
OT'^ 2 + OR'^ 2 = T'R'^2. In numerical sum
So then T'R'^2 = 5^2 + 5^2 = 50.
and T'R'= √50
Now find TR to find the factor of dilation that is
T'R'/TR
Find the volume of 12 cm
Answer:
1728 cm ^ 3.
Step-by-step explanation:
we are given 12 cm
As we know formula of volume of cube = s ^3 ( side * side * side ) So = 12 * 12* 12 = 1728 cm ^ 3.
Find the Volume cylinder (8cm) (12cm) h = 8cm r = 12cm h = 8 cm r = 12 cm. The volume of a cylinder is equal to the area of the base πr2 π r 2 times the height. π⋅(radius)2 ⋅(height) π ⋅ ( r a d i u s) 2 ⋅ ( h e i g h t) Substitute the values of the radius r = 12 r = 12 and height h = 8 h = 8 into the formula to find the volume of the cylinder
P.s hopes this helps
Find the volume of a cylinder and cinema given the following dimensions
Given:
The radius , r=20 ft.
The height , h=23 ft.
The volume of the cylinder can be calculated as,
[tex]\begin{gathered} V=\pi r^2h \\ =\pi\times20^2\times23 \\ =28902.65ft^2 \end{gathered}[/tex]Therefore, the volume of the cylinder is 28902.65 sq.ft.
The volume of the cone can be calculated as,
[tex]\begin{gathered} V=\frac{1}{3}\pi\times r^2h \\ =\frac{1}{3}\pi\times20^2\times23 \\ =9634.22ft^2 \end{gathered}[/tex]Therefore, the volume of the cone is 9634.22 sq.ft.
please show and explain this please
only answer ;( c.
Step-by-step explanation:
so hope it help
6+[(-9)+(-1)] what does this equal
-4
Explanation:
6+[(-9)+(-1)]
Open the bracket:
6 + (-9) + (-1)
Note: Multiplication of opposite signs give a negative number.
6 - 9 - 1
= 6 - 10
= -4
Question 5 of 40Roxanne likes to fish. She estimates that 30% of the fish shecatches are trout, 20% are bass, and 10% are perch. Shedesigns a simulation.
30% are trout, 20% are bass, 10% are perch
what is the chance that one of the next 4 is a bass
20% are bass
100 - 20 = 80
0.8^4 = 0.4096
1 - 0.4096 = 0.5904
of the 20 simulation results, 12 had bass
12/20 = 0.6
B) 60% estimate
59.04% actual
use a combination of inverse operations to solve the following equations.2(x-1) = -6
Given the following question:
[tex]2(x-1)=-6[/tex][tex]\begin{gathered} 2(x-1)=-6 \\ \text{ Divide by two} \\ -6\div2=-3 \\ \frac{2(x-1)}{2}=(x-1) \\ (x-1)=-3 \\ -1+1=0 \\ -3+1=-2 \\ x=-2 \end{gathered}[/tex]Your answer is x = -2.
1 a) is the above sequence arithmetic? Justify your answer. b) Write the explicit formula for the above sequence. c) Find the 18th term.
First, we count the number of boxes.
We have: 4,8,12,16
(a)Now:
• 8-4=4
,• 12-8=4
,• 16-12=4
Since the difference is the same, the sequence is an arithmetic sequence.
(b)In the sequence
First term, a =4
Common difference, d=4
The nth term of an arithmetic sequence is:
[tex]\begin{gathered} U_n=a+(n-1)d \\ =4+4(n-1) \\ =4+4n-4 \\ =4n \end{gathered}[/tex]The explicit formula for the above sequence, f(n)= 4n.
(c)18th term
f(18)= 4 x 18
=72
The 18th term is 72.
Jenelle invests $8,000 at 3% simple interest for 48 years. How much is in the account at the end ofthe 48 year period? Round your answer to the nearest cent.Answer: $Submit Question
Given
Principal = $8,000
Rate = 3%
Time = 48 years
Find
Amount at the end of the 48 years
Explanation
Amount = Simple interest + Principal
Simple Interest is given by
[tex]S.I=\frac{P\times R\times T}{100}[/tex]now substitute the values ,
[tex]\begin{gathered} S.I=\frac{8000\times3\times48}{100} \\ \\ S.I=11520 \end{gathered}[/tex]amount = 11,520 + 8000 = $19,520.00
Final Answer
Therefore , the amount at the end of the 48 years will be $19,520.00
Mrs. Maria's Market buys 75% of eggs from farm A and the rest from farm B. Of the eggs from A,8% are green, and of those from B, 3% are green. If an egg is chosen at random and found to begreen, what is the probability that the egg is from farm B? Enter your answer as a decimal numberrounded to TWO digits after the decimal point.
0.12
Explanations:What is probability?Probability is the likelihood or chance that an event will occur. It ca be expressed as:
[tex]Probability=\frac{n(E)}{n(S)}[/tex]where:
n(E) is the expected event
n(S) is the total sample space
If Mrs. Maria's Market buys 75% of eggs from farm A and the rest from farm B, the percentage amount of egg bought from B will be 25% (100-75)
n(S) = 25%
If 3% of the eggs from B are green, hence n(E) = 3%
Determine the required probability
Pr(egg is from farm B) = n(E)/n(S)
Pr(egg is from farm B) = 3/25 = 0.12
Hence the probability that the egg is from farm B is 0.12
Enter the equation for the graph.АА- 112y = [?] cos([ ]x)Enter
A cosine function has the form.
[tex]y=A\cos (Bx)[/tex]Where A refers to the changes of the y-coordinate along the curve, that is, the amplitude. And B refers to the period, that is, the repetition period of the curve.
According to the graph, the amplitude is 1, so A = 1.
Notice that from 0 to 2(pi) the function completes two cycles, which means B = 3.
Therefore, the function is [tex]y=1\cdot\cos (3x)[/tex]HELP HELP! PLEASE, MY MOM WANT ME TO BE DONE!
From least to greatest, we have:
2 to 3, 3:4, and 7/8
Explanation:Given the following:
7/8, 2 to 3, and 3:4
The least is 2 to 3, followed by 3:4, then 7/8
Given f(x)=3x+2 find f(-4)
Step-by-step explanation:
i think it will satisfied you
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Andre drew a plan of a courtyard at a scale of 1 to 60. On his drawing, one side of the courtyard is 2.75 inches. What is the actual measurement of that side of the courtyard? Show your work.
Okay, here we have this:
Considering that the scale is of 1 to 60, we obtain the following:
2.75 inches * 60 =165.
Use compatible numbers to determine if 455+ 229 is more than 650
Step 1
compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally.
Step 2
Math problem
455 + 229
Compatible numbers
455 + 225 = 680
680 is close to 455+229 = 684
Step 3:
Hence
By compatible numbers, 455 + 229 is more than 650.
How do you write 6 tens + 4 ones + 5 tenths + 2 hundredths + 8 thousandths
Answer:64.528 is the decimal
Step-by-step explanation:
Ashley watches a giant that has 16 equally spread seats. Identify w.
The angle formed outside the circle by the intersection of a tangent and a secant is equal to half of the difference of the intercepted arcs. The bigger arc is 180º, because the starting point of the secant and the starting point of the tangent are precisely on the opposite position of each other(we can see that by counting the same amount of seats between them on both sides). The smaller arc is equal to 90º, therefore
[tex]w^o=\frac{1}{2}(180^o-90^o)=45^o[/tex]P(-3,-5) and Q(1.–3) represent points in a coordinate plane. Find the midpoint of Pe.
By formula,
Midpoint between two points PQ =
[tex](\frac{x_2+x_1}{2},\text{ }\frac{y_2+y_1}{2})[/tex][tex]\begin{gathered} (\frac{1+-3}{2},\text{ }\frac{-3+\text{ -5}}{2}) \\ \\ \frac{-2}{2},\text{ }\frac{-8}{2}\text{ = (-1,-4)} \\ \\ \end{gathered}[/tex]So, (-1,-4) (option 3)
Helppppppppppppppppppp
Perpendicular line are reciprocals
slope of the original line = -1/9
slope of the perpendicular line = 9
Suppose Yolanda places $9000 in an account that pays 8% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding. (a) Find the amount in the account at the end of 1 year. $ (b) Find the amount in the account at the end of 2 years. $0 X S
Compound interest - The amount in the account at the end of 1st year is $9720 and The amount in the account at the end of 2nd years is $10497.6
What is compound interest?
The interest earned on savings that is calculated using both the initial principal and the interest accrued over time is known as compound interest. It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a sum more quickly than simple interest, which is only calculated on the principal sum. Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
We are given that the principal amount is $9000
An the interest is 8%
Hence after 1 year the amount will be
[tex]A=9000(1+0.08)\\A=9000(1.08)\\A=9720\\[/tex]
After 1 year the amount becomes $9720
Now After 2 years we will get interest on $9720
Hence the amount after 2 years will be
[tex]B=9720(1+0.08)\\B=9720(1.08)\\B=10497.6[/tex]
Therefore the amount after 2 years is $10497.6
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7(x+2)=
4(x+4)=
9(x+6)=
Answer:
Step-by-step explanation:
7(x+2) = 7x+14
7(x+2)=7x+7 times 2
4(x+4)= 4x+16
4 times x = 4x
4 times 4 = 16
= 4x+16
9(x+6) = 9x+54
9 times x = 9x
9 times 6 = 54
= 9x+54
