By elimination, it means that we should apply algebraic operations so we find the value of one variable. So first, lets multiply the first equation by 5. We get
[tex]5\cdot(2x-3y)=5\cdot-5\text{ = 10x-15y = -25}[/tex]Now, lets multiply by 2 the second equation
[tex]2\cdot(5x+2y)\text{ = 16}\cdot2\text{ = 10x+4y=32}[/tex]With this two equations, lets subtract the second equation from the first equation
[tex]10x+4y-(10x-15y)\text{ = 32-(-25)}[/tex]We get
[tex]19y\text{ = 57}[/tex]If we divide y by 19 we get
[tex]y=\frac{57}{19}=3[/tex]Now, using this value in the second equation we get
[tex]5x+2\cdot3\text{ = 16 }=5x+6[/tex]If we subtract 6 on both sides, we get
[tex]16-6\text{ = 5x = 10}[/tex]Finally, we divide by 5 on both sides and we get
[tex]x=\frac{10}{5}=2[/tex]from the base of the tower, you meassure its shadow to be 17.25m.at same the time your shadoe is 0.21m.you are 1.68 tall.how tall ia the tower?(round to two decimal plaves if necessary)
The Solution:
Representing the given in a diagram, we have
By similarity theorem, we have that:
[tex]\frac{BA}{BT}=\frac{BC}{BD}[/tex]So,
[tex]\begin{gathered} BA=1.68m \\ BT=h=(1.68+x)m \\ BC=0.21m \\ BD=17.25m \end{gathered}[/tex]Substituting these values in the formula above, we get
[tex]\frac{1.68}{1.68+x}=\frac{0.21}{17.25}[/tex]Solving for x:
We shall cross multiply,
[tex]0.21(1.68+x)=1.68\times17.25[/tex][tex]0.3528+0.21x=28.98[/tex][tex]0.21x=28.98-0.3528=28.6272[/tex]Dividing both sides by o.21, we get
[tex]x=\frac{28.6272}{0.21}=136.32\text{ m}[/tex]The height of the tower is
[tex]h=1.68+x=1.68+136.32=138m[/tex]Therefore, the correct answer is 138 meters.
Points A(-2,-3),B(-2,4),and C(3,6) are three vertices of parallelogram ABCD. Opposite sides of a parallelogram have the same length. Draw the parallelogram in the coordinate plane and label the coordinates of the fourth point.
Given:
Points A(-2,-3),B(-2,4),and C(3,6) are three vertices of parallelogram ABCD.
As we know, the opposite sides of the parallelogram are parallel and congruent
To draw the parallelogram, we will draw the points and connect the sides
AB, AC, and BC
then, draw two lines parallel to AB from C and BC from A, the intersection will give the point D
The graph of the parallelogram will be as shown in the following picture
As shown the coordinates of the fourth point D = (3, -1)
I can send photo, which expressions are equivalent to 18x - 6? select all that apply
ANSWER:
The equivalent expressions are
[tex]\begin{gathered} 6\cdot(3x-1) \\ 2\cdot(9x-3) \\ 16.4x-6+1.6x \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]18x-6[/tex]If we factor we have:
[tex]\begin{gathered} 6\cdot(3x-1) \\ 2\cdot(9x-3) \end{gathered}[/tex]if we separate the value we have
[tex]16.4x-6+1.6x=18x-6[/tex]Using the data above, how many people would be expected to live in Japan if the proportion of people to square miles were the same in Japan as in the United States?
I NEED HELP WITH THIS TWO7) the shirt costs $25. the discount is 18% how many dollars is the discount? 8) 40% of 120 students passed the test. How many students passed?
If the shirt costs 25 and the discount is 18%, then the amount discounted is shown as follows;
[tex]\begin{gathered} \text{Cost}=25 \\ \text{Discount}=0.18 \\ \text{Discounted amount=25}\times0.18 \\ \text{Discounted amount=4.5} \end{gathered}[/tex]The discount is $4.5.
If 40% of students passed out of 120, then the number that passed is shown below;
[tex]\begin{gathered} Total\text{ number=120} \\ \text{Percentage that passed=0.40} \\ \text{Number that passed=120}\times0.40 \\ \text{Number that passed=48} \end{gathered}[/tex]The number of students that passed is 48
Answer: 7. $20.50 & 8. 48 students
Step-by-step explanation:
The line that passes through the points (3,0) and (-5,8) isA.)DecreasingB.)IncreasingC.)HorizontalD.)Vertical
The slope of a line
It is a parameter that can help us to know the behavior of a line, specifically if it's increasing, decreasing
how many 3/8 are in 3
We can see that there are 24/8 in 3 units, so we have then that there are 8 times 3/8 in 3 units.
So, the answer is there are 8 times.
volume= {1}{3} * \pi * r ^{2}* hHELPsolve for H
Explanation
[tex]Volume=\frac{1}{3}\pi r^2h[/tex]Step 1
multiply each side by 3
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ V\cdot3=\frac{1}{3}\pi r^2h\cdot3 \\ 3V=\pi r^2h \end{gathered}[/tex]Step 2
divide both sides by
[tex]\pi r^2[/tex][tex]\begin{gathered} 3V=\pi r^2h \\ \frac{3V}{\pi r^2}=\frac{\pi r^2\text{ h}}{\pi r^2} \\ h=\frac{3V}{\pi r^2} \end{gathered}[/tex]Find an equation of an ellipse satisfying the given conditions Vertices: (0 - 6) and (0.6) Length of minor axis: 8
As the given vertices are at a distance of 12 units:
As the major axis is vertical you have the next generall equation:
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]To find the center (h,k) of the ellipse use the coordinates of that vertices as follow:
[tex](\frac{0+0}{2},\frac{6-6}{2})=(0,0)[/tex]Now use the distance between those vertices to find a:
[tex]a=\frac{12}{2}=6[/tex]b is the distance of minor axis divided into 2:
[tex]b=\frac{4}{2}=2[/tex]Then, you get the next equation for the given ellipse:
[tex]\begin{gathered} \frac{(x-0)^2}{2^2}+\frac{(y-0)^2}{6^2}=1 \\ \\ \frac{x^2}{4}+\frac{y^2}{36}=1 \end{gathered}[/tex]A survey was given to a random sample of 1750 voters in the United States to askabout their preference for a presidential candidate. Of those surveyed, 28% of thepeople said they preferred Candidate A. Determine a 95% confidence interval for thepercentage of people who prefer Candidate A, rounding values to the nearest tenth.
A 95% confidence interval for the percentage of voters who choose Candidate A is (0.3,0.3).
Given that,
1750 American voters were chosen at random to participate in a poll on their presidential candidate preferences. 28% of those polled indicated they favored Candidate A.
We have to find determine a 95% confidence interval for the percentage of voters who choose Candidate A.
We have a sample size=1750
28% preferred candidate A.
Margin of error = Z[tex]\sqrt{P(1-P)/n}[/tex]
Where, z=1.96 at 95%
P=0.28
n=1750
ME = 1.96[tex]\sqrt{0.28(1-0.28)/1750}[/tex]
ME = 1.96[tex]\sqrt{0.28(0.72)/1750}[/tex]
ME = 1.96[tex]\sqrt{0.2016/1750}[/tex]
ME = 1.96[tex]\sqrt{0.000152}[/tex]
ME = 0.021
For confidence interval is
CI= 0.28±0.021
CI= (0.28+0.021,0.28-0.021)
CI = (0.301, 0.259)
For the nearest tenth,
CI = (0.3,0.3)
Therefore, A 95% confidence interval for the percentage of voters who choose Candidate A is (0.3,0.3).
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6. A basketball coach purchases bananas for the players on his team. Thetable shows total price in dollars. P. of n bananas. Which equation couldrepresent the total price in dollars for n bananas?number of bananastotal price in dollars74.13B47295.31105.90O P = 0.596O P = 5.90-0.59O P = 590//O Pan0.59
,Given the table of values we can find the equation that will represent the total price in dollars for the bannana by using the equation of a line.
Explanation
The equation of a line is given as
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}[/tex]We can then remodel the equation above to fit the given table of values. This would give;
[tex]\frac{p_2-p_1}{n_2-n_1}=\frac{p-p_1}{n-n_1}[/tex]Next, we will pick some random points to represent the variables in the equation
[tex]\begin{gathered} p_1=4.13;p_2=4.72 \\ n_1=7;n_2=8 \end{gathered}[/tex]Then we insert the variables into the formula.
[tex]\begin{gathered} \frac{4.72-4.13}{8-7}=\frac{p-4.13}{n-7} \\ \frac{0.59}{1}=\frac{p-4.13}{n-7} \\ p-4.13=0.59(n-7) \\ p-4.13=0.59n-4.13 \\ p=0.59n+4.13-4.13 \\ p=0.59n \end{gathered}[/tex]Answer: The equation is given as p = 0.59n
Alfred needs to buy small pumpkins that cost $2.75 each. The function he uses is ()=2.75. Use the function to determine the cost of 25 pumpkins.
From the question, we have a linear function for the cost of each pumpkin, and this function is:
[tex]f(x)=2.75x[/tex]As we can see, the cost for one pumpkin is:
[tex]f(1)=2.75(1)=\text{ \$2.75}[/tex]Now, to find the cost for 25 pumpkins, we need to substitute the value of x = 25 into the function, since this is a function that gives us the cost as a function of the number of pumpkins:
[tex]\begin{gathered} f(x)=2.75x \\ \\ f(25)=2.75(25)=68.75 \\ \\ f(25)=68.75 \\ \\ \end{gathered}[/tex]As we can see, we multiply 2.75 times 25, and we got 68.75.
Therefore, in summary, it will cost $68.75 for 25 pumpkins.
Write an nth term of arithmetic sequence -5,-2,1,4
Recall: Averaging Two NumbersMaddie earned an 88% on her first test and an 80% onyour second test. What is her average test score? (Note:Click on the little calculator icon above to pull up acalculator.)
We know that
• She earned an 88% on her first test.
,• She earned an 80% on her second test.
To know her average score, we just have to sum these percentages and divide them by 2, since they are just 2.
[tex]\bar{x}=\frac{88+80}{2}=\frac{168}{2}=84[/tex]Therefore, the average test score is 84%.Myra has a remote control toy boat.she runs the toy boat on a lake at a constant speed. The graph of a function representing the toy boats distance, y , in feet , from the shore of the lake after X seconds includes the points (1,8) and (1.5, 10.1)
Given
the constant speed.
the points 1 (1,8)
Point 2 (1.5, 10.1)
Procedure
y=mx+b
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{8-10.1}{1-1.5} \\ m=\frac{-2.1}{-0.5}=4.2 \end{gathered}[/tex][tex]\begin{gathered} y=mx+b \\ 8=4.2(1)+b \\ 8-4.2=b \\ 3.8=b \end{gathered}[/tex]the equation is: y=4.2x+3.8
The statements that are true are:
B. The rate of the change of the function is 4.2
D. The toy boat's speed on the lake is 4.2 feet per second
E. the toy boat is originally 3.8 feet from the shore of the lake
A jewelry salesperson earns 5 1/5 % commission on all sales. Today he sold $7,310 in jewelry. What is his total commission earned?
The total commission the salesperson earned is
The total commission salesperson earned is $394.5.
What is commission?
Commissions are a type of variable-pay compensation for provided services or sold goods. Commissions are a typical method of encouraging and rewarding salespeople. It is also possible to create commissions to promote particular sales behaviours. For instance, while offering significant reductions, commissions might be decreased.
Given: A jewelry salesperson earns 5 1/5 % commission on all sales. Today he sold $7,310 in jewelry.
We have to find the commission earned on $7310.
Here, [tex]5\frac{1}{5} = \frac{(5)(5)+2}{5} =\frac{27}{5}[/tex]
5 1/5% = 27/5%
Today he sold $7310 in Jwellary.
So, the commission is,
[tex]\frac{(7310)(27)}{(5)(100)} = 394.5[/tex]
Hence, the total commission of $7310 is $394.5.
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A bank features a savings account that has an annual percentage rate of 4.1 % with interestcompounded monthly. Zach deposits $3,000 into the account.How much money will Zach have in the account in 1 year?Answer = $Round answer to the nearest penny.What is the annual percentage yield (APY) for the savings account?%. Round to the nearest hundredth of a percent.APY=
It is given that the amount invested is $3000 with an interest rate of 4.1% compounded monthly.
It is required to find the amount in 1 year and the annual percentage yield.
The formula for Compound Interest is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
• A= final amount
,• P= amount invested initially
,• r= interest rate
,• n= number of times interest is compounded in a year
,• t= number of years
Substitute P=3000, r=4.1%=0.041, n=12 (compounded monthly), and t=1 into the formula:
[tex]A=3000(1+\frac{0.041}{12})^{12(1)}\approx\$3125.34[/tex]The formula for the Annual Percentage Yield is given as:
[tex]APY=(1+\frac{r}{n})^n-1[/tex]Substitute r=0.041, n=12 into the formula:
[tex]APY=(1+\frac{0.041}{12})^{12}-1\approx0.0418=4.18\%[/tex]Answers:
Amount = $3125.34
APY = 4.18%
The organizer of a conference is selecting workshops to include. She will select from 3 workshops about anthropology and 10 workshops about psychology. In how many ways can she select 7 workshops if 2 or fewer must be about anthropology?
give the following from the question:
the organizer will select from 3 workshop about anthropology and 10 workshops about psychology.
we were asked in how many ways she can select 7 workshops if 2 or fewer must be anthropology
so,
If 2 or fewer must be anthropology,
Then tha means it is either she selects 2 from anthropology and 5 from psychology or 1 from anthropology and 6 from psycology.
that is:
= 3C2 x 10C5 or 3C1 x 10C6
= 3!/(3-2)!2! x 10!/(10-5)!5! + 3!/(3-1)!1! x 10!/(10-6)!6!
= 3x2!/2! x 10x9x8x7x6x5!/5!5! + 3x2!/2! x 10x9x8x7x6!/4!6!
= 3 x 252 + 3 x 210
= 756 + 630
= 1,386 ways
The ways she can select 7 workshops if 2 or fewer must be about anthroplogy is 1,386 ways
A rectangle or televisions length is 3 inches more than twice its width the perimeter of the television is 144 inches what is the width of the television
The width of the television is 23 in.
What is rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles. The opposite sides of a rectangle are equal and parallel.
Given that, A television's length is 3 inches more than twice its width the perimeter of the television is 144 inches
Perimeter of a rectangle = 2(length+width)
According to question,
l = 3+2w
Therefore,
Perimeter = 2(w + 3+2w) = 144
3w + 3 = 72
3w = 69
w = 23
Hence, The width of the television is 23 in.
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Which of the following choices best describes the expression 2/3 (3/4x - 3/2)A: equivalent to 1/2x - 1B: equivalent to x - 1/2C: not equivalent to 1/2x - 1 or x - 1/2
distributing:
[tex]\begin{gathered} \frac{2}{3}\cdot\frac{3}{4}x-\frac{2}{3}\cdot\frac{3}{2}= \\ =\frac{1}{2}x-1 \end{gathered}[/tex]the expression is equivalent to 1/2x - 1
A company is making building blocks. What is the length of each side of the block? V=1 ft3 The length of each side is
The length of the block = 1ft.
The volume of the length of the side of blocks = 1ft^3
The 3 on the one feet means raised to power 3.
So, 1ft raised to power 3:
[tex]1ft^3\text{ = 1ft }\times\text{ 1ft }\times\text{ 1ft}[/tex]To get the length, we would assume the block is a cube
The volume of a cube = length^3
1 ft^3 = length^3
[tex]\begin{gathered} \text{cube root both sides:} \\ \sqrt[3]{1ft^3}\text{ = }\sqrt[3]{length^3} \\ \text{length = }\sqrt[3]{(1\text{ft}}\times1ft\times1ft) \\ \text{length = 1ft} \end{gathered}[/tex]Hence, the length of the block = 1ft.
The figure below is an isosceles trapezoid:KLIK = 12x - 34IL = 4x - 10X =Blank 1:
From the definition, it must have symmetry in the present figure. It seems to be a vertical line going through the middle of the drawing. From this, we can say that:
[tex]\begin{gathered} IK=JL \\ 12x-34=4x-10 \end{gathered}[/tex]Now, we can solve it.
[tex]\begin{gathered} 12x-34=4x-10 \\ 12x-4x=34-10 \\ 8x=24 \\ x=\frac{24}{8} \\ x=3 \end{gathered}[/tex]The coordinates below represents points that were translated.Match the coordinates with the correct algebraic representations
R(1, 8) >> R'(10, -10) ........(x+9, y-18)
V(-2, -10) >> V'(5, -3).......(x+7, x+7)
U(3, -9) >> U'(10, -16).......(x+7, y-7)
T(-4, 7) >> T'(-11, 14)..........(x -7, y+7)
Explanations:When a pont A(x, y) is translated by a in the x-axis, and b in the y-axis, the new point becomes A'(x+a, y+b)
For the expression R(1, 8) >> R'(10, -10)
The coordinates of R' ae formed using the expression (x+9, y-18)
For the expression V(-2, -10) >> V'(5, -3)
The coordinates of V' are formed by using the expression (x+7, x+7)
For the expression U(3, -9) >> U'(10, -16)
The coordinates U' are formed by using the expression (x+7, y-7)
For the expression T(-4, 7) >> T'(-11, 14)
The coordinates T' are formed by using the expression (x -7, y+7)
Donna earns a commission. She makes 3.5% of the amount she sells. Yesterday she sold a $800 recliner. How much was her commission.
Amount sold = $800
Commission = 3.5%
To calculate the commission amount, multiply $800 by the commission percentage in decimal form (divided by 100)
800 x (3.5/100)= 800 x 0.035 = $28
Bobs car rental is offering a special of 40$ a day for a seden as long as you purchase the car damage protection insurance for 20$
In this case, we have a proportional relationship, since the cost varies directly with the days, this means that as x increases, y increases, and as x decreases, y decreases. A proportional relationship has the form:
y=kx
Where k is the constant of proportionality.
The ratio between them (x and y) is always the same, in this case, the ratio or constant of proportionality is 40, since each day the rent cost increases $40, then:
Constant of proportionality = 40 , replacing 40 for k into the above equation, we get:
equation: y = 40x
We can use this equation to find some pair of values (x,y) to fill the table, like this:
For x equals 2:
y= 40*2 = 80
For x equals 3:
y= 40*3 = 120
For x equals 4:
y=40*4 = 160
For x equals 5:
y=40*5=200
Then, we can fill the table as follows:
We can also use these data to graph the relationship, by taking the point (5,200) and joining it to the origin, we get:
Henry started the school year with 3 packages of pencils. He used 4 pencils each week. If a school year is 36 weeks, during which week will he run out of pencils?
We know that
• Henry started with 3 packages of pencils.
,• He used 4 pencils each week.
,• The school year is 36 weeks.
Assuming that each package of pencils has 8, he would have
[tex]3\cdot8=24[/tex]Henry has 24 pencils in total. But he uses 4 pencils each week, so let's divide
[tex]\frac{24}{4}=6[/tex]Therefore, Henry will run out of pencils in week 6.[tex]7x(x + 4) = [/tex]simplify
Given expression:
[tex]=\text{ 7x(x + 4)}[/tex]Expanding:
[tex]\begin{gathered} =\text{ 7x }\times\text{ x + 7x }\times\text{ 4} \\ =\text{ 7 }\times\text{ x }\times\text{ x + 7 }\times\text{ x }\times\text{ 4} \\ =\text{ 7 }\times x^2\text{ + 7 }\times\text{ 4 }\times\text{ x} \end{gathered}[/tex]Simplifying the expression:
[tex]\begin{gathered} =7\times x^2\text{ + }28\times x \\ =7x^2\text{ + 28x} \end{gathered}[/tex]Answer:
[tex]7x^2\text{ + 28x}[/tex]Convert the following unit areas as indicated. Choose the right answe Area Conversion Number Table English Area Conversion Number Metric Area Square Miles Square Miles Acres Acres Square Yards Square Feet Square Inches 2.59 259 4.05 x 10-3 4.05 x 10-1 8.36 x 10-1 9.29 x 10-2 6.45 Square Kilometers Hectares Square Kilometers Hectares Square Meters Square Meters Square Centimeters 50 in.2 to cm2
Answer:
322.5 square centimeters
Explanation:
To convert from square inches to square centimeters, we need to multiply the number by the conversion factor 6.45, so 50 in² are equivalent to:
50 in² x 6.45 = 322.5 cm²
Therefore, the answer is 322.5 square centimeters.
1. An equation is shown below. 60 10 100 = Determine the value of the missing numerator. Your answer
m = 6
Explanations:The given equation is:
[tex]\frac{m}{10}=\text{ }\frac{60}{100}[/tex]Cross multiply:
100m = 60 x 10
100m = 600
Divide both sides by 100
[tex]\begin{gathered} \frac{100m}{100}=\text{ }\frac{600}{100} \\ m\text{ = 6} \end{gathered}[/tex]The missing numerator is 6
de a and perform the symmetry lest on each of the following is. eld plerd Find the in 16 r2 + 25y2 = 400 A00 (c) r2 + 4y2 = 4 (e) 4x2 + y2 = 64 (B) 9x² + 4y2 = 36 (b) 25x+6y (d) 4x + y = A () Ay? (h) 7x + y - 112 Graph the vertices, foci, endpoints of the minor axis, and endpoints of the latera recta, then draw AB is a chord of the partial ellipse with equation f(x) = ba? - x'. (a) 576x2 + 625y2 = 360,000, A (15,f(15)), B(20, f(20)) (b) 49x 2 + 625y2 = 30,625, A (15, f(15)), B(20,f(20)) – x. Find the length of AB using
The given ellipse is
[tex]576x^2+625y^2=360,000[/tex]Where A(15, f(15)), B(20, f(20)).
First, we find f(15) and f(20) by evaluating the given expression
[tex]\begin{gathered} f(15)=576(15)^2+625y^2=360,000 \\ 576\cdot225+625y^2=360,000 \\ 129,600+625y^2=360,000 \\ 625y^2=360,000-129,600 \\ 625y^2=230,400 \\ y^2=\frac{230,400}{625} \\ y^2=368.64 \\ y=\sqrt[]{368.64} \\ y=19.2 \end{gathered}[/tex]We use the same process to find f(20).
[tex]\begin{gathered} f(20)=576(20)^2+625y^2=360,000 \\ 576\cdot400+625y^2=360,000 \\ 625y^2=360,000-230,400 \\ x^2=\frac{129,600}{576} \\ x=\sqrt[]{225}=15 \\ \end{gathered}[/tex]So, the points are A(15, 19.2) and B(20, 15). To find the distance between these points, we have to use the distance formula
[tex]\begin{gathered} d_{AB}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d_{AB}=\sqrt[]{(20-15)^2+(15-19.2)^2} \\ d_{AB}=\sqrt[]{5^2+(-4.2)^2}=\sqrt[]{25+17.64}=\sqrt[]{42.64} \\ d_{AB}\approx6.5 \end{gathered}[/tex]Hence, the length of AB is around 6.5 units.