Solve these: state whether there is no solution, one solution specify it , or infinitely many Solutions.
Answers
Step 1:
Write the two systems of equations
y = 3x = 2
3x = y - 3
Step 2:
Substitute y from the first equation into the second equation
[tex]\begin{gathered} 3x\text{ = y - 3} \\ 3x\text{ = 3x + 2 - 3} \\ 3x\text{ - 3x = 2 - 3} \\ 0\text{ = 2 - 3} \\ 2\text{ = 3} \end{gathered}[/tex]Final answer
NO SOLUTION
Related Questions
Frank makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours
Answers
The equation will be
P = 8h
here, P = total pay
h= working hours.
A third friend wants to offer Rebecca andSteve some of the animal models she hasalready made. The model she has of thegiant squid is 5 inches tall. Using thesame scale (2 in:5ft), how tall would thegiant squid be in real life?
Answers
From the present question, it is said that the scale of a model is equal to:
[tex]e=\frac{2in}{5ft}[/tex]It means that the ratio of the size of the model and the real size of the giant squid must be always this same value. It was given that the size of the model is 5 in. Because we don't know the size of the real-life giant squid, we will use it as x. From this, we can write the following relation:
[tex]\frac{5in}{x}=\frac{2in}{5ft}[/tex]Now, we just need to isolate x in the present relation to find how tall would be a giant squid in real life.
[tex]\begin{gathered} \to2in\times x=5in\times5ft \\ x=\frac{5in\times5ft}{2in}=\frac{25}{2}ft=12.5ft \end{gathered}[/tex]From the solution developed above, we conclude that the real-life giant squid would be 12.5 ft tall.
Elijah is snorkeling above a shipwreck. The ship has an elevation of -105 feet. Elijah is snorkeling at 2/15 of the ship's elevation. What is Elijah's elevation?
Answers
Elijah's elevation when Elijah is snorkeling above a shipwreck is -14.
What is elevation?Elevation simply has to do with the height above sea level.
In this case, Elijah is snorkeling above a shipwreck and the ship has an elevation of -105 feet. Elijah is snorkeling at 2/15 of the ship's elevation.
Elijah's elevation will be:
= Fraction of his snorkeling × Ship's elevation
= 2/15 × (-105)
= -14
This shows the elevation of Elijah.
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Line Graph: This time you will not have the numbers on the x and y axis. You will need to decide which number to use (1, 2, 3... or 2,4,5.... Or 5, 10, 15...) 3: Creating Graphs Create a single line graph using the following table. Time goes on the x axis Rainfall goes on the y axis Make sure to do the following: Label the x and y axis Create a title 10 15 20 Time (minutes) 25 30 35 40 25 55 45 60 50 35 40 Speed (of car) (km/min)
Answers
Line Graph:
A line graph is used to show how the data points are changing with respect to time.
For Example:
A line graph may be used to show the average rainfall over the entire month.
For the given scenario we have,
X-axis = Time in minutes
Y-axis = Speed of car in km/min
Title of graph = Speed of Car Vs Time
Data points for time = 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
Data points for speed = 25, 30, 35, 40, 25, 55, 45, 60 50 35 40
This is how the line graph looks like.
It is showing the speed of the car in km/min over an interval of 60 minutes in steps of 5 minutes.n steps of
Procedure:
• Draw and label the x-axis and y-axis.
,• Label the data points on both axis.
,• Draw the data points.
,• Join the data points with a line.
,• We are done.
,•
Suppose it is believed that the probability a patient will recover from a disease following medication is 0.8. In a group of twenty such patients, the number who recover would have mean and variance respectively given by (to one decimal place):
Answers
Based on the number of patients and the probability that a patient will recover from the disease, the mean 16 patients would be and the variance would be 1.79
How to find out mean and the variance?The mean can be found by the formula:
= Number of patients in group x Probability that patient will recover
= 20 x 0.8
= 16 patients
The Variance is:
= Number of people x probability of recovery x (1 - probability of recover)
= 20 x 0.8 x (1 - 0.8)
= 3.2
So the standard deviation is:
= √3.2
= 1.79
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A rectangular garden has a walkway around it. The area of the garden is 2(4.5x +1.5). Thecombined area of the garden and the walkway is 3.5(8x + 4). Find the area of the walkway aroundthe garden as the sum of two terms.The area of the walkway around the garden is(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
DataL
garden area = 2(4.5x +1.5)
garden + walkway area = 3.5(8x + 4)
walkway area = ?
Step 02:
walkway area:
walkway area = 3.5(8x + 4) - 2(4.5x +1.5)
= 28x + 14 - 9x - 3
= 19x + 11
The answer is:
The area of the walkway around the garden is 19x + 11
The length of a rectangle is given by a number, x (metres). The width is two metres longer than the length. The area of the rectangle is 120 m^2
Answers
metersGiven:
a.) The length of a rectangle is given by a number, x (meters).
b.) The width is two meters longer than the length.
c.) The area of the rectangle is 120 m^2.
Let's first recall the formula for getting the area of the triangle.
Area = L x W
Where,
L = Length
W = Width
The width is two meters longer than the length. Therefore, we can say that:
W = L + 2
Let's now determine the measure of the dimension of the rectangle:
Let,
x = length of the rectangle
We get,
[tex]\begin{gathered} \text{ A = L x W} \\ 120\text{ = L x (L + 2)} \\ 120=L^2\text{ + 2L} \\ L^2\text{ + 2L - 120 = 0} \\ (L\text{ - 10)(L + 12) = 0} \end{gathered}[/tex]Based on the relationships given, the Length of the rectangle has two possible measures.
L - 10 = 0
L = 10 m
L + 12 = 0
L = -12 m
Since a length must never be a negative value, the length of the rectangle must be 10 m.
For the width, we get:
W = L + 2 = 10 + 2 = 12 m
Summary:
Length = 10 m
Width = 12 m
For which value(s) of x will the rational expression below equal zero? Che all that apply. (x - 5)(x+2) x + 1 A.-5 B. 2 c. 1 1 D. -1 E. 5 F. -2
Answers
The rational expression we have is:
[tex]\frac{(x-5)(x+2)}{x+1}[/tex]For a rational expression to be equal to 0, the numerator of the expression has to be equal to 0.
The numerator is: (x-5)(x+2)
That has to be equal to 0:
[tex](x-5)(x+2)=0[/tex]Here, we apply the zero product property, which tells us that if a product is equal to 0, one of the two elements, or the two elements, are equal to 0:
[tex]\begin{gathered} x-5=0 \\ x+2=0 \end{gathered}[/tex]We solve the two equations, and get the two values that will make the rational equation equal to 0:
[tex]\begin{gathered} x=5 \\ x=-2 \end{gathered}[/tex]Answer:
E. 5
F. -2
What is 4527 written in scientific notation?A.4.527B.4.527 x 10*2C.4.527 x 10*3D.4.527 x 10*4
Answers
Solution
- The question would like us to convert the number 4527 to scientific notation.
- In order to write a number to its scientific notation, we need to follow these steps:
1. Move the decimal place to the right of the first digit of the number. Make sure you count each step as you move the decimal point from right to left or left to right.
2. The number of steps corresponds to the exponent of 10 that multiplies the decimal form of the original number.
- We can apply these steps to solve the question given as follows:
- Thus, we have that the scientific notation of the number 4527 is
[tex]4.527\times10^3[/tex]Final Answer
The scientific notation of the number 4527 is
[tex]4.527\times10^3\text{ (OPTION C)}[/tex]
Can you help me with question number 4 and double check all my other work. (I don’t really understand functions.)
Answers
SOLUTION
The relation is a function because each x-value has a unique y-value. That is each domain has only one image. Therefore, the relation is a function
How can use theorem 7-4 to find missing segments? (7-4 is similarity) :)
Answers
Given
AD = 6.4
BD = 3.6
Find
AC,BC and DC
Explanation
Using Pythogoras theorem in triangle ADC
[tex]AC^2=DC^2+6.4^2------(1)[/tex]Using PT in triangle BDC
[tex]BC^2=DC^2+3.6^2-------(2)[/tex]Adding equation (1) and (2)
[tex]\begin{gathered} AC^2+BC^2=DC^2+3.6^2+DC^2+6.4^2 \\ AC^2+BC^2=2DC^2+53.92 \end{gathered}[/tex]Using PT in triangle ABC
[tex]10^2=AC^2+BC^2[/tex]Equating above 2 equations
[tex]\begin{gathered} 100=2DC^2+53.92 \\ DC^2=23.04 \\ DC=4.8 \end{gathered}[/tex]Putting this value of DC in equation (2)
[tex]\begin{gathered} BC^2=4.8^2+3.6^2 \\ BC^2=23.04+12.96 \\ BC=6 \end{gathered}[/tex][tex]\begin{gathered} 10^2=AC^2+BC^2 \\ 100=AC^2+36 \\ AC=8 \end{gathered}[/tex]Final Answer
AC = 8
BC = 6
DC = 4.8
The coordinates of point F are (8,4) and the coordinates of point G are (-4,9). What is the slope of the line that is perpendicular to line FG. Enter the answer as a simplified fraction.
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The formula for finding slope is
m = (y2 - y1)/(x2 - x1)
y2 and y1 are the final and initial values of y
x2 and x1 are the final and initial values of x
From the given points ,
x1 = 8, y1 = 4
x2 = - 4, y2 = 9
m = (9 - 4)/(- 4 - 8) = 5/- 12 = - 5/12
Recall, if two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. The negative reciprocal of - 5/12 is 12/5
Thus, the slope of the perpendicular to line FG is 12/5
IF log x = 1/₂, find log (10x²)
Answers
Answer:
2
Step-by-step explanation:
log ab = log a + log b
Similarly,
log 10x² = log 10 + log x²
log a^b = b log a
Similarly,
log 10x² = 2 log x
= 2 * 1/2
= 2/2
= 1
Note :-
The value of log 10 = 1
Hence,
log 10x²
= log 10 + log x²
= 1 + 1
= 2
use the formula Sn to find the sum of the first five terms of the geometric sequence.
Answers
First, find the common ratio r:
-4/9 : 4/3 = -1/3
4/3 : -4 = -1/3
-4:12 = -1/3
r= -1/3
[tex]Sn=\frac{a(r^n-1)}{r-1}[/tex]Where:
a= first term = 12
n= number of terms = 5
Replacing:
[tex]Sn=\frac{12(-\frac{1^{}}{3}^5-1)}{-\frac{1}{3}-1}[/tex]Sn= 244/27 = 9 1/27
If 1 is added to a number and the sum is tripled, the result is 5 more than the number. Find the number
Answers
Answer;
[tex]n=1[/tex]Explanation;
Here, we want to get a number
Since the number is not known at the moment, we can start by identifying the number with an a;phabet
Let us call this n
If 1 is added to the number
mathematical representation;
[tex]1+n[/tex]And the sum is tripled;
[tex]3(1+n)[/tex]The result is 5 more than the number
5 more than the number is simply;
[tex]5+n[/tex]So, we equate this to what we had initially as follows;
[tex]5+n=3(1+n)[/tex]We can now solve this equation for n
[tex]\begin{gathered} 5+n=3+3n \\ 5-3=3n-n \\ 2n=2 \\ n=\frac{2}{2} \\ n=1 \end{gathered}[/tex]A number times the sum of 12 and 32 (write as an algebraic expression)
Answers
ANSWER
x(12 + 32)
EXPLANATION
Let x be 'the number'.
A number times... means 'a number multiplied by...'
The sum of 12 and 32 is (12 + 32)
The complete algebraic expression is x(12 + 32)
The safe load, L, of a wooden beam of width w, height h, and length l, supported at both ends, varies directly as the product of the width and the square of the height, and inversely as the length. A wooden beam 5 inches wide, 8 inches high, and 216 inches long can hold a load of 7670 pounds. What load would a beam 3 inches wide, 5 inches high, and 240 inches long of the same material, support? Round your answer to the nearest integer if necessary.
Answers
we know that
L=KW(h^2)/l
we have that
W=5 in
h=8 in
l=216 in
L=7670 pounds
step 1
Find the value of K (constant of proportionality)
substitute the given values in the equation
7670=K(5)(8^2)/216
7670=k(1.4815)
k=5,177.25
step 2
we have the equation
L=(5,177.25)W(h^2)/l
for
W=3 in
h=5 in
l=240 in
substitute in the equation and solve for L
L=(5,177.25)(3)(5^2)/240
L=1,617.89 pounds
Round your answer to the nearest integer
so
L=1,618 pounds
graph the inequality 3x+y<4
Answers
Subsituting (0,0) in the inequality,
[tex]\begin{gathered} 3\times0+0<4 \\ 0<4 \end{gathered}[/tex]Hence the line 3x+y=4, demarcating the plane contains the origin.
Thus, the above graph gives the required region of inequality.
In parallelogram ABCD… Justify your answer with the applicable property.
Answers
Solution
For this case we have the following measures:
m <1= x+12
m < 2= 6x -18
We can set up both angles equal:
x +12 = 6x -18
Solving for x we have:
12+18 = 5x
5x = 30
x= 30/5= 6
Then the value of m< 2 is:
m< 2= 6*6 -18= 36-18= 18
the best second answer is:
If a quadrilateral is ||gram the opposite angles are congruent
What Is the inverse of.. (ignore pencil writing) -matrices- (there may be more than one answer
Answers
To find the inverse of the matrix, first let's find the determinant:
[tex]\begin{gathered} |A|\text{ = 3(2) - 5(1)} \\ |A|\text{ = 6 - 5} \\ |A|\text{ = 1} \end{gathered}[/tex]Then, we'll find the Adjunct of the matrix:
[tex]\begin{gathered} \begin{bmatrix}{3} & {5} & {} \\ {1} & {2} & {} \\ {} & {} & {}\end{bmatrix}\text{ : interchange }3\text{ and 2. negate 1 and 5} \\ \text{Adjunct = }\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex][tex]\begin{gathered} In\text{verse of the matrix = }\frac{1}{|A|}\times\text{ adjunct} \\ A^{-1}\text{ = }\frac{1}{1}(\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}) \\ A^{-1}\text{ =}\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}\text{ (option B)} \\ \end{gathered}[/tex]Solve T=C(8+AB) for A
Answers
If a price changes from $105,300 to $104,399 will that be a percentincrease or decrease?
Answers
If the price changes from $105,300 to $104,399, It means that there is a decrease in price.
Decrease = 105,300 - 104,399 = $901
The percentage decrease is gotten by dividing the decrease by the initial price and multiplying by 100. It becomes
[tex]\frac{901}{105300}\text{ }\times\text{ 100 = 0.8557\%}[/tex]By rounding up to the nearest whole number, it becomes 1%
The percent decrease is 1%
Which equation is equivalent to: 3r=78+14 ?A. −3r=−78+14B. 3r−14=78C. 3r=78−14D. −3r=78−14
Answers
3. Solve the system using elimination (not substitution or matrices). negative 2 x plus y minus 2 z equals negative 8A N D7 x plus y plus z equals negative 1A N D5 x plus 2 y minus z equals negative 91. If the system has a single solution, write the solution as an ordered triple, (x, y, z).2. If the system has infinite solutions, write the solutions IN TERMS OF z.The solution should look something like left parenthesis 3 minus 3 z comma space minus 1 plus 7 z comma space z right parenthesis but not like left parenthesis negative 6 plus 3 y comma space y comma space 2 minus 5 y right parenthesis or not like left parenthesis x comma space 3 plus 5 x comma space minus 1 plus 4 x right parenthesis. None of these are the solution, they are just examples of what the answer could look like and not look like.3. Be sure to show all appropriate work. Extraneous work may be counted against you. Your handwritten work should include the steps used to find the solution. You should label your steps with how you combined your equations, like 2E1+E3. Solutions with no work will receive no credit.
Answers
Given the system of equation
[tex]\begin{gathered} -2x+y-2z=-8\ldots\ldots\ldots\text{.}(1) \\ 7x+y+z=-1\ldots\ldots\ldots\text{..}(2) \\ 5x+2y-z=-9\ldots\ldots\ldots\text{.}(3) \end{gathered}[/tex]step 1: Make z the subject of the formula in equations (2)
[tex]z=-1-7x-y\ldots\ldots\ldots(2)[/tex]step 2: Substitute the value of z obtained into equation (1)
10
step 3: Substitute the value of z obtained in step 1 into equation (3)
[tex]\begin{gathered} 5x+2y-(-1-7x-y)=-9 \\ 5x+2y+1+7x+y=-9 \\ 12x+3y=-10\ldots\ldots\ldots\text{.}(5) \end{gathered}[/tex]step 4: Solve equations (4) and (5) simultaneously,
[tex]\begin{gathered} 12x+3y=-10\ldots\ldots\ldots\text{.}(4) \\ 12x+3y=-10\ldots\ldots\ldots\text{.}(5) \\ \text{subtract equation (5) from (4)} \\ (12x-12x)+(3y-3y)=-10-(-8) \\ 0\text{ + 0 = }-10+10 \\ 0=0 \end{gathered}[/tex]Therefore, the system has infinite solutions
The solution in terms of z is
[tex]\begin{gathered} x=-\frac{1}{3}z+\frac{7}{9} \\ y=\frac{4}{3}z-\frac{58}{9} \\ z=z \end{gathered}[/tex]which ordered pair is a solution of the equation 7x−5=4y−6?PLEASE HURRY THIS IS DUE NOW A. only (2,4)B. only (3,6)C. both A and BD. neither A or B
Answers
To answer this question, we can take the coordinates (2, 4), and (3, 6) and substitute each of them in the given equation. Then, we can determine which of these ordered pairs is a solution of the equation 7x - 5 = 4y - 6. Then, we have:
1. Case: Ordered pair (2, 4):
[tex]7\cdot(2)-5=4\cdot(4)-6\Rightarrow14-5=16-6\Rightarrow9\ne10[/tex]This ordered pair is NOT a solution.
2. Case: Ordered pair (3, 6):
[tex]7\cdot(3)-5=4\cdot(6)-6\Rightarrow21-5=24-6\Rightarrow16\ne18[/tex]This ordered pair is NOT a solution.
Therefore, neither the ordered pair (2, 4) nor (3, 6) are solutions to the given equation (Option D).
Which equation is the best approximation of the trend line
Answers
approximatesThe equation of a line is given by
[tex]\begin{gathered} y=mx+c \\ m=\frac{change\text{ in y}}{change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \end{gathered}[/tex]Taking two points from the line of best fit
Point A(14,200) and Point B (18,400)
[tex]\begin{gathered} x_1=14;y_1=200;x_2=18;y_2=400 \\ \frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \\ \frac{400-200}{18-14}=\frac{y-200}{x-14} \\ \frac{200}{4}=\frac{y-200}{x-14} \\ \frac{50}{1}=\frac{y-200}{x-14} \\ y-200=50(x-14) \\ y-200=50x-700 \\ y=50x-700+200 \\ y=50x-500 \end{gathered}[/tex]Hence, the equation that best approximate the trend line is y=50x-500
Fill in the blank with the correct inequality symbol. State which property of inequalities is being utilized.If x-8>10, then x_18.
Answers
GIVEN
The inequality:
[tex]x-8>10[/tex]SOLUTION
The inequality is to be solved.
Add 8 to both sides of the inequality. This follows the Addition Property of Inequalities:
[tex]if\text{ }xTherefore:[tex]\begin{gathered} x-8+8>10+8 \\ x>18 \end{gathered}[/tex]ANSWER
[tex]x>18[/tex]What is the position of see on the number line belowWrite your answer as a fraction or mixed number
Answers
Answer:
1/3
Explanation:
We can see that from 0 to 1 the number line is divided into 6 parts and the point is right after the second part. Therefore, the fraction that represents point C is 2/6
This fraction is also equal to 1/3 because we can divide the line from 0 to 1 into 3 parts and take the first. The point will be at the exact same position of C.
Therefore, the answer is:
1/3
Bella drove her car 81 km and used 9 liters of fuel. She wants to know how many kilometers (x) she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate.
Answers
Find the proportion between liters of fuel
that is find 22/9 = 2.444
thats how much liters have more to consume
now multiply 2.444 by 81 , the kilometers she has drived
It gives as result 2.444 x 81 = 198 kilometers
A hummingbird's brain has a weight of approximately 2.94 x 10- ounces. An elephant's brain has a weight ofapproximately 1.76 x 102 ounces.Approximately how many times heavier is the elephant's brain than the hummingbird's brain?A) 60B) 600C) 6,000D) 60,000
Answers
Given the information on the problem,we have to divide the weight of the elephant's brain by the weight of the bird's brain, then, using the rules of exponents, we have the following:
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