3. Lin is solving this system of equations:S 6x – 5y = 343x + 2y = 83. She starts by rearranging the second equation to isolate the y variable: y = 4 -1.5%. She then substituted the expression 4 - 1.5x for y in the first equation, asshown below:--6x – 5(4 – 1.5x) = 346x – 20 – 7.5x = 34-1.5x = 54x = -36y = 4 – 1.5xy = 4 - 1.5 • (-36)y = 58.
Answers
We are given the following system of equations:
[tex]\begin{gathered} 6x-5y=34,(1) \\ 3x+2y=8,(2) \end{gathered}[/tex]We are asked to verify if the point (-36, 58) is a solution to the system. To do that we will substitute the values x = -36 and y = 58 in both equations and both must be true.
Substituting in equation (1):
[tex]6(-36)-5(58)=34[/tex]Solving the left side we get:
[tex]-506=34[/tex]Since we don't get the same result on both sides this means that the point is not a solution.
Now, we will determine where was the mistake.
The first step is to solve for "y" in equation (2). To do that, we will subtract "3x" from both sides:
[tex]2y=8-3x[/tex]Now, we divide both sides by 2:
[tex]y=\frac{8}{2}-\frac{3}{2}x[/tex]Solving the operations:
[tex]y=4-1.5x[/tex]Now, we substitute this value in equation (1), we get:
[tex]6x-5(4-1.5x)=34[/tex]Now, we apply the distributive law on the parenthesis:
[tex]6x-20+7.5x=34[/tex]This is where the mistake is, since when applying the distributive law the product -5(-1.5x) is 7.5x and not -7.5x.
Related Questions
how can you use number patterns to find the greatest common factor of 120 and 360
Answers
Greatest common factor (GCF)
• 120
Finding the factors:
[tex]\begin{gathered} \frac{120}{2}=60\text{ (2 is a factor)} \\ \frac{60}{2}=30\text{ (again 2 is a factor)} \\ \frac{30}{2}=15\text{ (again 2 is a factor)} \\ 15\text{ is not divisible over 2, we search for 3:} \\ \frac{15}{3}=5\text{ (3 is another factor as 15 is divisible over 3)} \\ 5\text{ is not divisible over 2, 3, or 4, we search for 5:} \\ \frac{5}{5}=1\text{ (5 is another factor, and the last one)} \end{gathered}[/tex]Placing the factors as a multiplication:
[tex]120=2\cdot2\cdot2\cdot3\cdot5[/tex]• 360
[tex]360=2\cdot2\cdot2\cdot3\cdot3\cdot5[/tex]The factors that repeat in each integer are: 2, 2, 2, 3, 5
Therefore, the GFC is:
[tex]\text{GFC}=2\cdot2\cdot2\cdot3\cdot5=120[/tex]Answer: 120
I don't know how to figure this out. A and B look the same and C and D look the same
Answers
The difference between A and B, and C and D is the continuous/discontinuous line.
When the line is discontinuous, it means the values are NOT included. In this case, the sing < or > is used.
When the line is continuous, it means the values ARE included. In this case, the sing ≤ or ≥ is used.
Now, to determine which graphic is the one of our function, we can get the intersections with the y- and x-axis.
• Intersection with y-axis: ,x = 0
[tex]3x+y>4[/tex][tex]3\cdot0+y>4[/tex][tex]y>4[/tex]The intersection in y-axis happens on y > 4.
Intersection with x-axis: y = 0
[tex]3x+0>4[/tex][tex]x>\frac{4}{3}[/tex]The intersection in y-axis happens on x > 4/3.
Answer: C.
Find the simple interest earned, to the nearest cent, for the principal, interest rate, and time.
$650, 5%, 1 year
Answers
The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest.
The simple interest exists 32.5.
What is meant by simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest.
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only charge interest on the principal sum, and a borrower will never be required to pay additional interest on the interest that has already accrued.
Let the equation be I = Prt
where, P be the principal amount = $650
r be the interest rate = 5%
t be the time = 1 year
substitute the values in the above equation, we get
I = 650 × 0.05 × 1
I = 32.5
Therefore, the simple interest rate exists 32.5.
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Find the lateral surface area and volume please round up to nearest integer
Answers
For this problem we will use the following formula for the surface area of a truncated cone:
[tex]\begin{gathered} SA=\pi(r_1+r_2)\sqrt[]{(r_1-r_2)^2+h^2}+\pi(r^2_1+r^2_2), \\ \text{Where r}_1\text{ is the lower radius, r}_2\text{ is the upper radius, and h is the height.} \end{gathered}[/tex]Substituting:
[tex]\begin{gathered} r_1=\frac{11in}{2}=5.5in, \\ r_2=\frac{14in}{2}=7in, \\ h=21in, \end{gathered}[/tex]we get:
[tex]\begin{gathered} SA=\pi(7in+5.5in)\sqrt[]{(7in-5.5in)^2+(21in)^2}+\pi((5.5in)^2+(7in)^2) \\ =\pi(12.5in)\sqrt[]{2.25in^2+441in^2}+\pi(30.25in^2+49in^2) \\ =\pi(12.5in)(21.05in)+\pi\cdot79.25in^2 \\ =\pi(263.125+79.25)in^2 \\ =\pi(342.375)in^2 \\ \approx1076in^2. \end{gathered}[/tex]Now, to compute the volume we will use the following formula:
[tex]V=\frac{1}{3}\pi(r^2_1+r_1r_2+r^2_2)h\text{.}[/tex]Substituting the given values we get:
[tex]\begin{gathered} V=\frac{1}{3}\pi((5.5in)^2+(5.5in)(7in)+(7in)^2)21in \\ =\frac{1}{3}\pi(30.25in^2+38.5in^2+49in^2)21in \\ =\frac{1}{3}\pi(117.75in^2)21in \\ =824.25\pi in^3 \\ =2589in^3\text{.} \end{gathered}[/tex]Answer: The total surface area is
[tex]1076in^2\text{.}[/tex]The volume is
[tex]2589in^3\text{.}[/tex]Becky has 12 strips of staples. Each strip has 210 staples.The bar diagram represents the total number of staples Becky has.
Answers
The total number of staples Becky has is the number of strips times the number of staples per strip:
[tex]12\times210=2520.[/tex]Answer: 2520.
2) The shape of a playground is a parallelogram. The city is going to treat the asphalt with sealant this spring with cans that will cover 4 square yards each. The figure below is a drawing of the playground, For how many cans of sealant does the city need to budget for the treatment, if the playground has a perimeter of 34 yards and the height is 1.4 yards less than the diagonal side of the parallelogram? 10.6 yd 6.4 yd a. Write the equation in words. b. Find the unknown height. c. Calculate the area of playground. d. Choose a variable for the unknown quantity and write the equation with the substituted values. e. Solve the equation. Include appropriate units in your answer. f. How many cans of sealant are needed?
Answers
In this situation, you have a parallelogram with lateral sides of L length and top and bottom sides of length D. The letter h represents the height of the parallelogram.
L=6.4 yd and D=10.6 yd. The perimeter is the sum of all 4 edges, so perimeter=2*L+2*D
a) If one can cover 4 square yards and you need to find how many cans you will need for the whole playground area, then you need to find the total area which is calculated by its height times its base (D), so it would be h*D=area. This area divided by 4 square yards will give you the number of cans you need.
b) If the height is 1.4 yards less than the diagonal side, then
[tex]h=L-1.4=6.4-1.4=5\text{ yards}[/tex]c)Then the area is given by:
[tex]h\cdot D=5\cdot10.6=53\text{ square yards}[/tex]d)The number of cans can be represented by a variable called n (n as in number), so:
[tex]n=\frac{area}{4}=\frac{53}{4}[/tex]e) Then, by calculating:
[tex]\frac{53}{4}=13.25\text{ cans}[/tex]f) You will need 14 cans of sealant, you will only use some of it from the last can
Please find arc JK and angle 1. Ignore the entered answers.
Answers
The Solution:
Given the figure below:
Solving for arc JK:
By angle subtends at the center of a circle is twice that subtends on the circumference, we have that:
[tex]2\times118=236^o[/tex]Subtracting 236 from 360, we get
[tex]arcJK=360-236=124^o\text{ (angle at a point)}[/tex]So, the correct answer for question 7 is [option 4]
To answer Question 8:
[tex]\begin{gathered} \angle JKM=\frac{70}{2}=35^o\text{ } \\ \\ \text{ Reason: Angle subtends at the center is twice that subtends} \\ \text{ at the circumference of the circle.} \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} \angle KJL=\frac{60}{2}=30^o \\ \\ \text{Reason: Angle subtends at the center is twice that subtends} \\ \text{ at the circumference of the circle.} \end{gathered}[/tex][tex]\text{ To get }\angle1[/tex][tex]\begin{gathered} \angle1=180-(\angle JLM+\angle KML) \\ \text{ Reason: sum of angles in a triangle.} \end{gathered}[/tex][tex]\begin{gathered} \angle JLM=\angle JKM=35^o \\ \text{ Reason: angles on the same segments.} \\ \text{ Similarly,} \\ \angle KML=\angle KJL=30^o \\ \text{ Reason: angles on the same segments.} \end{gathered}[/tex][tex]\begin{gathered} \angle1=180-(35+30) \\ \text{ Sum of angles in a triangle.} \\ \angle1=180-65=115^o \end{gathered}[/tex]Therefore, the correct answer to Question 8 is 115 degrees.
answer step by step pleaseSteve determines that sides DK and BC are congruent. He also measures angle K and angle C and determines that they are congruent. He concludes that the triangles are congruent by SAS theorem. Is Steve correct?
Answers
Data Input
DK and BC are congruent.
Angle K and angle C are congruent.
Procedure.
To determine if the triangles are congruent median SAS, we need to know the size of one of the remaining sides
For them, we will measure the ED and AB sides using the Euclidean distance
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]For ED
E = (-6, 4)
D = (0, 8)
[tex]\begin{gathered} ED=\sqrt[]{(-6-0)^2+(8-4)^2} \\ ED=\sqrt[]{6^2+4^2} \\ \\ ED=\sqrt[]{(36+16)} \\ ED=\sqrt[]{52} \end{gathered}[/tex]For AB
A = (3, 6)
B = (9, 10)
[tex]\begin{gathered} AB=\sqrt[]{(9-3)^2+(10-6)^2} \\ AB=\sqrt[]{6^2+4^2} \\ AB=\sqrt[]{36+16} \\ AB=\sqrt[]{52} \end{gathered}[/tex]Now, AB is equaled to ED
Side-Angle-Side is a rule used to prove whether a given set of triangles are congruent. The SAS rule states that: If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.
how do I know where which choices below go into the correct blanks?
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In a 30-60-90 special right triangle, we have the following.
If the short leg is 7 cm, then x = 7.
So, the hypotenuse would be
[tex]h=2x=2(7)=14\operatorname{cm}[/tex]The length of the long leg is
[tex]x\sqrt[]{3}=7\sqrt[]{3}\approx12.12\operatorname{cm}[/tex]Therefore, the hypotenuse is 14 cm, and the long leg is 12.12 cm, approximately.A local newspaper delivers 364 papers split evenly among n delivery people. Q is the number of papers delivered by each delivery person. Write a formula for Q as a function of n, including finding the value of any unknown constants. Q =
Answers
The formula for Q is:
[tex]Q(n)=\frac{364}{n}[/tex]where n = the number of delivery people.
We just have to divide the 364 papers to the number of delivery people to determine how many papers each person delivered.
Determine the minimum and maximum value of the following trigonometric function.
f(x)=10sin(2/5x)+5
Answers
ANSWER
[tex]\begin{gathered} Minimum=-5 \\ Maximum=15 \end{gathered}[/tex]EXPLANATION
The trigonometric function given is:
[tex]f(x)=10\sin (\frac{2}{5}x)+5[/tex]The minimum value a sine function can take is -1.
This means that the minimum value of the function is:
[tex]\begin{gathered} 10(-1)+5 \\ \Rightarrow-10+5 \\ \Rightarrow-5 \end{gathered}[/tex]The maximum value a sine function can take is 1.
This means that the maximum value of the function is:
[tex]\begin{gathered} 10(1)+5 \\ \Rightarrow10+5 \\ \Rightarrow15 \end{gathered}[/tex]Cam decided to rent a storage unit to store his sailboat. The mast of the boat is 20 feet long. The storage unit is 4ft by 8ft by 19ft. Will the mast fit in the storage unit?A. YesB. No
Answers
Step 1
Find the volume of the storage
[tex]Length\times width\times height[/tex]From the data given the storage could have a height of 4ft or 8ft or 19ft. The mast of the sailboat is 20 feet long. This means that no matter which of the measurements is the height of the store, the mast of the sailboat will not fit in because it is longer than all those heights.
Therefore, the answer will be;
No the storage unit is too small to fit the mast of the sailboat
Cual es la coordenada-y del punto C ? What is the y-coordinate of pint C ?
Answers
The y co-ordinate of the point C is 13.
Given, the points are :
A (2,4) = (x₁,y₁)
B (10,10) = (x₂,y₂)
Ratio of the length AC to CB is 3:1.
⇒ 3:1 = m:n
⇒ section formula C = (mx₂-nx₁/m-n) , my₂-ny₁/m-n)
substitute the values.
⇒ C = (3(10)-1(2)/3-1 , 3(10)-1(4)/3-1)
⇒ C = (30-2/2 , 30-4/2)
⇒ C = (28/2 , 26/2)
⇒ C = (14 , 13)
Hence the y coordinate of C is 13.
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Rusell runs 9/10 mile in 5 minutes. at this rate, how many miles can he run in one minute?
Answers
Answer:
in one minute, Rusell can run 9/50 mile.
[tex]\frac{9}{50}mile[/tex]Explanation:
Given that;
Rusell runs 9/10 mile in 5 minutes.
[tex]\begin{gathered} \frac{9}{10}\text{mile }\rightarrow\text{ 5 minutes} \\ \text{dividing both sides by 5;} \\ \frac{9}{10\times5}\text{mile }\rightarrow\text{ }\frac{5}{5}\text{ minutes} \\ \frac{9}{50}\text{mile }\rightarrow\text{ 1 minutes} \end{gathered}[/tex]Therefore, in one minute, Rusell can run 9/50 mile.
[tex]\frac{9}{50}mile[/tex]It turns out that as ice cream consumption increases, drowning deaths increase. In other words, there is a positive association between ice cream consumption and drowning deaths. However, ice cream consumption does not cause drowning deaths. So why is there a positive association? Explain.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
ice cream consumption ====> increases
drowning deaths ====> increase
Step 02:
We must analyze the question to find the solution.
positive association:
There is an association because both values increase, that is, a positive association suggests that when one variable increases, the value of the other variable also increases.
That is the solution.
Bernies cafe has regular coffee and decaffeinated coffee this morning the cafe served 80 coffees in all 48 of which were regular what percentage of the coffees were regular
Answers
We have to divide the number of regular ones by the total. Then multiply the result by 100.
48/80*100 = 60
Our answer is 60 % of the coffees were regular.
Hi, can you help me answer this question, please, thank you!
Answers
Answer
Standard deviation = 1.2083
Step-by-step explanation
[tex]\begin{gathered} \text{Mean = }\sum ^{}_{}xi\cdot\text{ p(xi)} \\ \text{Mean = }0\cdot\text{ 0.2 + 1 }\cdot\text{ }0.05\text{ + 2}\cdot\text{ }0.1\text{ + 3 }\cdot\text{ 0.65} \\ \text{Mean = 0 + 0.05 + 0.2 + 1.95} \\ \text{Mean = 2.2} \\ \text{Standard deviation = }\sqrt[]{\sum^{}_{}}(\text{ x - }\mu)^2\cdot\text{ p(xi)} \\ \text{let }\mu\text{ = 2.2} \\ \text{Standard deviation = }\sqrt[]{(0-2.2)^2\cdot0.2+(1-2.2)^2\cdot0.05+(2-2.2)^2\cdot0.1+(3-2.2)^2\cdot\text{ 0.65}} \\ \text{standard deviation = }\sqrt[]{0.968\text{ + 0.072 + 0.004 + 0.416}} \\ \text{Standard deviation = }\sqrt[]{1.46} \\ \text{Standard deviation = }1.2083 \\ \text{Hence, standard deviation is 1.2083} \end{gathered}[/tex]Letℎ()h(x)be the inverse of()f(x). Ifℎ()=−4+1h(x)=−4x+1, which of the following represents()f(x)?
Answers
In order to find f(x), we need to calculate the inverse of h(x)
[tex]h(x)=-4x+1[/tex]y=h(x)
[tex]y=-4x+1[/tex]We substitute x with y and y with x
[tex]x=-4y+1[/tex]Then we isolate the y
[tex]4y=-x+1[/tex][tex]y=-\frac{1}{4}x+\frac{1}{4}[/tex]ANSWER
f(x) is
[tex]f(x)=-\frac{1}{4}x+\frac{1}{4}[/tex]The correct choice is the first one
i need help with number 17, just the algebraic equation
Answers
The graph and equation of a function is given.
It is required to find its y-intercept and zeros using the graph, and then finding these values algebraically.
Using the graph:
Recall that the y-intercept is the point where the graph of the function intersects the y-axis.
From the graph, notice that the graph intersects the y-axis at y=0.
Hence, the y-intercept is y=0.
Recall also that the x-intercepts or zeros is the point where the graph of the function intersects the x-axis.
From the graph, the graph intersects the x-axis at x= -1,0, and 1.5.
Hence, the zeros are x= -1,0, and 1.5.
Find these values algebraically:
To find the y-intercept algebraically, substitute x=0 into the function:
[tex]\begin{gathered} f(x)=2x^3-x^2-3x \\ \text{ Substitute }x=0\text{ into the equation:} \\ \Rightarrow f(0)=2(0)^3-0^2-3(0) \\ \Rightarrow f(0)=0 \end{gathered}[/tex]Hence, the y-intercept is y=0.
To find the zeros, substitute f(x)=0 into the function and solve for x:
[tex]\begin{gathered} 2x^3-x^2-3x=0 \\ \text{ Factor the left-hand side:} \\ \Rightarrow x(2x^2-x-3)=0 \\ \Rightarrow x(2x^2-3x+2x-3)=0 \\ \Rightarrow x[x(2x-3)+1(2x-3)]=0 \\ \Rightarrow x(x+1)(2x-3)=0 \end{gathered}[/tex]Equate each factor to 0
I need to know the answer to this like asap
Answers
In general, a vertically compression of a function f(x) is obtained by the transformation:
[tex]f(x)\rightarrow g(x)=\frac{1}{k}\cdot f(x).[/tex]Where k > 1 is the factor of compression.
In this case we have f(x) = |x| and k = 4. Applying the transformation above, we get:
[tex]g(x)=\frac{1}{4}\cdot|x|.[/tex]AnswerC.
[tex]g(x)=\frac{1}{4}|x|[/tex]I just need help with part b can you help me please
Answers
b) Recall that to evaluate a function at a given value, we substitute the variable by the given value.
Evaluating P(t) at t=2007-1992=15 we get:
[tex]P(15)=29000(1.06)^{15}.[/tex]Simplifying the above result we get:
[tex]P(15)\approx69500.[/tex]Answer: $69,500.
D1 ptsQuestion 3The bill of a white pelican can hold about 550 cubic inches of water,Nigel, the pelican from Finding Nemo, scoops up 160 cubic inches ofwater. Write an inequality that represents how much more waterNigel cal add to his bill.
Answers
let the additional water that is needed to add in the bill is x
[tex]\begin{gathered} 160+x\leq550 \\ x\leq550-160 \\ x\leq390 \end{gathered}[/tex]so, Nigel can add 390 cubic inches of water to the bill of a white pelican.
I would like to know the break down to solve for this problem.
Answers
Train A travels at a speed of 25 miles per hour south and train B travels at a speed of 20 mph east.
We can find the distance for each one of the trains by using the following formula:
[tex]X=Vt[/tex]Where X is distance, V is velocity and t is time
Let's find the dinstance that A and B will travel in 6 hours
[tex]\begin{gathered} Xa=Va\cdot t \\ Xa=25\cdot6=150 \end{gathered}[/tex]Train A travels 150 miles in 6 hours
[tex]\begin{gathered} Xb=Vb\cdot t \\ Xb=20\cdot6=120 \end{gathered}[/tex]Train B travels 120 miles in 6 hours
Now, in order to determine how far they are from each other, we need to take into account their direction. From the picture we can see that their route describes a right triangle, so the distance between them is the hypotenuse of this right triangle I will draw...
if D is the distance that separates the two trains, D is given by the following formula
[tex]D=\sqrt[]{150^2+120^2}[/tex]Solving the equation we obtain...
[tex]\begin{gathered} =\sqrt[]{22500+14400^{}} \\ =\sqrt{36900} \\ \end{gathered}[/tex]Solving this square root by using prime factorization and laws of exponents:
[tex]\begin{gathered} =\sqrt{2^2\cdot\:3^2\cdot\:5^2\cdot\:41} \\ =\sqrt{41}\sqrt{2^2}\sqrt{3^2}\sqrt{5^2} \\ =2\cdot\: 3\cdot\: 5\sqrt{41} \\ =30\sqrt{41} \end{gathered}[/tex]which is approximately the same as 192.09372...
Gym membership is $45.75 a month. How much will the gym membership be for one year? If Sherrie budcets $550 for gym costs, will she have enough?
Answers
Since a year has 12 months, we have to multiply the monthly membership cost by 12 to get the cost of a year's memberhsip:
[tex]45.75\times12=549[/tex]This way, the gym membership be for one year would be $549
Therefore, Sherrie would be able to pay for it with the $550 budget
Can you please tell me
Answers
The area of kite when both diagonals are given is
[tex]A=\frac{d_{}\times D}{2}[/tex]where d=17 m and D=21 m. By substituting the given values, we get
[tex]\begin{gathered} A=\frac{17\times21}{2} \\ A=178.5 \end{gathered}[/tex]then, the answer is 178.5 square meters
A particular color television has a rectangular screen with a 23.5 in. width. It’s height is 18.1 in. What is the length of the diagonal of the screen, to the nearest tenth of an inch? The diagonal of the screen is __ in.(Round to the nearest tenth as needed.)
Answers
Given:
A particular color television has a rectangular screen with a 23.5 in. width. It’s height is 18.1 in.
Required:
To find the length of the diagonal of the screen.
Explanation:
Let l be the length of the diagonal of the screen.
From the given data
[tex]\begin{gathered} l=\sqrt{23.5^2+18.1^2} \\ \\ =\sqrt{552.25+327.61} \\ \\ =\sqrt{879.86} \\ \\ =29.6624 \\ \\ l=29.7in \end{gathered}[/tex]Final Answer:
The length of the diagonal of the screen is 29.7in.
I'm kinda confused on this question. here it is "if a= 8, b = 4, and c=10 what is (b+c) the answers given to me are22112320and 2560.
Answers
i need help with this questionsfind the slope to the following graphs?
Answers
Answer:
b
Step-by-step explanation:
Write an equation in slope-intercept form for the line perpendicular to the given line that passes through the origin. y = 11/5 x + 7
Answers
y = 11/5 x + 7
Slope intercept form:
y=mx+b
Where:
m= slope
b= y-intercept
So, for the line given:
m= 11/5
b= 7
Perpendicular lines have negative reciprocal slopes.
negative reciprocal of 11/5 = -5/11
Slope = -5/11
So far we have:
y= -5/11 + b
Since it passes through the origin (0,0) replace and solve for b:
0= -5/11(0) +b
b=0
Final expression:
y= -5/11x
Find the area of parallelogram ABJF. The area is _ square units simplify your answer
Answers
We solve as follows:
*We cam see that both segments FJ & AB have a length ofngth of