Is it possible for a system to have more than one solution? Explain your answer
Answers
recall that for a system of equations, where the graph of both equations intersect, is the solutions, check the picture below.
Related Questions
PLS HELP ME ANSWER THIS ASAP , I WILL GIVE EXTRA POINTS AND BRAINIEST.
Answers
+5.1 on both sides
a=6.8
-31=z+(-17)
+17 on both sides.
-14 = z
a = 1.7 + 5.1
a = 6.8
-31 = z + (-17)
-31 = z - 17
- 31 + 17 = z
z = -14
Which inequality represents all possible solutions of -7n < -14?
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If l = 65 cm and j = 33 cm, what is the length of k?
Answers
Answer:
The answer is 56 inches on Study Island.
Step-by-step explanation:
Is the expression 2f + 4f + 2 – 3 equivalent to 6f – 1? 6f – 1 evaluated at f = 9 is 53. 2f + 4f + 2 – 3 evaluated at f = 9 is also 53. 6f – 1 evaluated at f = 3 is 17. what is 2f + 4f + 2 – 3 evaluated at f = 3?
Answers
the expression 2f + 4f + 2 – 3-------> we can group it (2f+4f)+(2-3)
(2f+4f)+(2-3)=(6f-1)
therefore
the expression [2f + 4f + 2 – 3] is equivalent to [6f-1]
if the expression [6f-1] for f=3 is 17
then
the expression [2f + 4f + 2 – 3] for f=3 is also 17
let's check it
[2*3 + 4*3 + 2 – 3]--------> [6+12+2-3]=[20-3]=17------> is ok
Answer: 17
Step-by-step explanation:
The total area of the rectangular prism shown is 30 sq. ft. 50 sq. ft. 62 sq. ft.
Answers
The Surface area of rectangular prism is given by:
[tex] S.A = 2(wl + hl+ hw) [/tex]
where ,
w=width=2 ft
h=height=5 ft
l=length.=3 ft
Plugging these values in the formula,
[tex] S.A = 2(2*3 + 3*5+ 5*2) [/tex]
Answer : Surface Area =62 square feet.
A 45° sector in a circle has an area of 13.75π cm².
What is the area of the circle?
Use 3.14 for pi.
Enter your answer as a decimal in the box.
Answers
Number of sectors in a circle = 360°/45° = 8
Now multiply this number to 13.75[tex] \pi [/tex] to get the area of the circle.
[tex] \pi [/tex] = 3.14
Area of the circle = 8 * 13.75 * 3.14 = 345.4 [tex]c m^{3} [/tex]
Ans: 345.4 [tex]c m^{3} [/tex]
-i
Answer:
345.4
Step-by-step explanation:
I took the test
Find the percent change from the first value to the second. 36; 63
Answers
The percent change from 36 to 63 is calculated using the formula: [(New value - Original value) / Original value] x 100. The percent change in this case is 75%.
To find the percent change from the first value to the second, use the following formula:
Percentage change = [(New value - Original value) ÷ Original value] × 100
In this case, the original value is 36 and the new value is 63. So, the change in value is 63 - 36 = 27.
Next, divide the change by the original value: 27 ÷ 36 = 0.75.
To convert this to a percentage, multiply by 100: 0.75 × 100 = 75%.
Therefore, the percent change from 36 to 63 is 75%.
What are the solutions to the equation?
5w^2+10w=40
Enter your answers in the boxes.
w =
and
Answers
5w^2 + 10w - 40 = 0
Divide by 5 through ...
w^2 + 2w - 8 = 0
(w+4)(w-2) = 0
w = -4 or w = 2
Answer:
w= -4 and 2
Step-by-step explanation:
it's better to put it exactly how i wrote it to ensure you'll get it right ( -4 goes first then 2).
A car is traveling at a speed of 44 feet per second. What is the car’s speed in miles per hour? How many miles will the car travel in 4 hours? In your computations, use the fact that 1 mile is equal to 5280 feet. Do not round your answers
Answers
44 * 3600 = 158400 feet per hour
158400 / 5280 = 30 miles per hour
30 * 4 = 120 miles
Car travels at speed of 44 feet per second. Converted to miles per hour, it's 30 mph. In 4 hours, it travels 120 miles, using the conversion factor 1 mile = 5280 feet.
To find the car's speed in miles per hour, you can use the conversion factor:
1 mile = 5280 feet
So, first, we need to convert the car's speed from feet per second to miles per hour.
Find out how many feet the car travels in an hour, and then we'll convert that to miles:
1 hour = 60 minutes
1 minute = 60 seconds
So, in 1 hour, there are 60 minutes × 60 seconds = 3600 seconds.
Now, if the car is traveling at a speed of 44 feet per second, in 1 hour, it would travel:
44 feet/second × 3600 seconds/hour = 158,400 feet/hour
Now, convert this to miles:
158,400 feet/hour / 5280 feet/mile = 30 miles/hour
So, the car's speed is 30 miles per hour.
To find out how many miles the car will travel in 4 hours at this speed:
4 hours × 30 miles/hour = 120 miles
The car will travel 120 miles in 4 hours.
Therefore, speed of the car is 30 miles/hour and it travels 120 miles in 4 hours.
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Emily added 5 grams of water into 20 grams of 50% salt solution.
She made ___ grams of ___% salt solution.
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She made ___25___ grams of ___40___% salt solution
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The given info "20 grams of 50% salt solution" tells us that we have 10 grams of pure salt
Since 50% of 20 = 0.50*20 = 10
Put another way, we have 10 grams of pure salt out of 20 total so 10/20 = 0.50 = 50% salt solution
The 20 grams of solution updates to 25 grams of solution when we add the 5 grams of water
We don't add any salt, assuming this water is fresh water
So we still have 10 grams of pure salt out of 25 grams now
10/25 = 2/5 = 0.40 = 40% is the new salt concentration
The explicit rule for a sequence is
an=17−5n .
What is the recursive rule for the sequence?
can you explain also
Answers
[tex]a_n=a_1+d(n-1)[/tex], where a₁ is the first term of the sequence and d is the common difference. Since we have [tex]a_n=17-5n[/tex], we know that n is multiplied by 5. That means that d must be 5, since that is the only thing that n gets multiplied in our general form. This gives us:
[tex]a_n=a_1+5(n-1) \\ \\a_n=a_1+5*n-5*1 \\ \\a_n=a_1+5n-5[/tex]
We know that we add something to 5n and then subtract 5 to get 17. Cancelling this process, we can add 5 to 17 to get 22. This gives us
[tex]a_n=22+5(n-1)[/tex]
We know that our first term, a₁, is 22 and our common difference, d, is 5.
The general form of a recursive formula for an arithmetic sequence is
[tex]a_n=a_n_-_1+d[/tex], where d is the common difference and [tex]a_n_-_1[/tex] is the previous term. We know that d is 5, so our recursive formula is
[tex]a_n=a_n_-_1+5[/tex]
Angle 2 and angle 3 are vertical angles. true or false
Answers
Answer: If you don't know the answer don't put one down but i do believe the answer is false.
Step-by-step explanation:
The statement 'Angle 2 and Angle 3 are vertical angles' can be true depending on their position, as vertical angles are those directly opposite from each other at the intersection of two lines.
Explanation:The question is asking about vertical angles. Vertical angles are pairs of non-adjacent angles formed when two lines intersect. This means they are the angles that are directly opposite from each other where the two lines intersect. So if Angle 2 and Angle 3 are directly opposite each other at the point where two lines cross, then they are indeed vertical angles. So, the statement 'Angle 2 and Angle 3 are vertical angles' can be true depending on their placed positions.
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Isaac is on the 4th floor of a building. If he rides an elevator up 7 floors, what floor will he be on?
What integer represents the floor Isaac is starting on?
What integer represents how many floors the elevator will rise?
What floor will the elevator stop at?
Answers
1) if Isaac is on the 4th floor and goes up 7, that is 4 + 7= 11. So he is on the 11th floor.
2) the integer representing the floor he is starting on is 4 because that is the whole number associated with "4th."
3) the integer representing how many floors he will rise is 7.
4) the elevator will stop at 11.
Hope this helps! :)
Answer:
1. 4
2. 7
3. 11
Step-by-step explanation:
Just did the assignment.
An aquarium is 18 in. high, 12 in. wide, and 24 in. long. How much water can the aquarium hold? (V = lwh)
Answers
Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm, is a right triangle?
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Answer:
Let first side= 5 cm
second side= 12 cm
third side = 13 cm
To prove this triangle to be right angle triangle, we need to prove Pythagoras Theorem
[tex]5^{2}[/tex]=25
[tex]12^{2}[/tex]=144
[tex]13^{2}[/tex]=169
169= 25+144
169=169
According to Pythagoras theorem ,
[tex]p^{2}[/tex]+[tex]b^{2}[/tex]=[tex]h^{2}[/tex]
since, it follows Pythagoras theorem,
Hence, it is a Right angle Triangle
WZ←→− is tangent to circle O at point B.
What is the measure of ∠OBZ?
80º
90º
160º
180º
Answers
WZ is tangent to circle O at point B. The measure of [tex]\angle OBZ[/tex] is [tex]90^{\circ}[/tex].
Given,line wz is tangent to circle O at point B.
We have to find out the measure of [tex]\angle OBZ[/tex].
What is a tangent?A tangent to a circle is a straight line which touches the circle at only one point. This point is called the point of Tangency.
The tangent to a circle is perpendicular to the radius at the point of tangency.
Here in circle O, WZ is the tangent which touches the circle at point B,
so B is the point of tangency and the [tex]\angle OBZ[/tex] is [tex]90^{\circ}[/tex].
Hence the correct option is B. [tex]90^{\circ}[/tex]
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The number of cents per kilometer it costs to drive a car depends on how fast you drive it. At low speeds the cost is high because the engine operates inefficiently. At high speeds the cost is high because the engine must overcome high wind resistance. At moderate speeds the cost reaches a minimum. Assume that the number of cents per kilometer varies quadratically with the number of kilometers per hour.
A) Suppose that it costs 28,21, and 16 cents per kilometer to drive at 10,20,and 30 kph,respectively. Write the particular function to represent this situation.
B)How much would it cost to drive at 150 kph?
C) Between what two speeds must you drive to keep your cost at no more than 13 cents per kilometer?
C)Is it possible to spend only 10 cents per kilometer?
D) What is the optimum speed and how much per kilometer will it cost? What part of the function represents this function?
Answers
Using the form of a quadratic equation f(x) = ax^2 + bx + c, we can derive an equation for each of three given points (10,20,30 kph and their corresponding costs). Solving these simultaneously we would get the particular equation representing the situation. We could then apply this to calculate costs at various speeds including checking if it is possible to spend only 10 cents/km, determining an optimal speed range for a 13 cents/km cost, and finding the optimal speed and cost per km.
Explanation:To write a particular function that represents this scenario, we can set up three equations using the general form of a quadratic equation, which is f(x) = ax^2 + bx + c. In this case, our x-values are the speeds (10, 20, and 30 kph) and our f(x) values are the corresponding costs (28, 21, and 16 cents/km).
Substitute these values into the equation f(x) = ax^2 + bx + c, we get three equations:
100a + 10b + c = 28
400a + 20b + c = 21
900a + 30b + c = 16
By solving the system of equations, we could find the values of a, b and c. Then we would substitute the speed into the function to calculate the cost at 150 kph, and to find the speed range for a cost of 13 cents/km and check if it is possible to spend only 10 cents/km. Finally, the optimal speed and cost per km would be represented by the minimum point of the function, which in the case of a parabola occurs at x = -b/2a.
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Given △ABC where A(2, 3), B(5, 8), C(8, 3), RS is the midsegment parallel to AC, ST is the midsegment parallel to AB, and RT is the midsegment parallel to BC, determine if the statements are true or false.
Select True or False for each statemen
Answers
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]. Using the coordinates of A and B, we have:
[tex]R=(\frac{5+2}{2},\frac{8+3}{2}) \\R=(\frac{7}{2},\frac{11}{2}) \\R=(3.5, 5.5)[/tex]. Similarly, S is the midpoint of BC:
[tex]S=(\frac{5+8}{2},\frac{8+3}{2}) \\S=(\frac{13}{2},\frac{11}{2}) \\S=(6.5, 5.5)[/tex].
Since ST is a midsegment parallel to AB, then T must be a midpoint of AC:
[tex]T=(\frac{2+8}{2},\frac{3+3}{2}) \\T=(\frac{10}{2},\frac{6}{2}) \\T=(5,3)[/tex].
Now that we have the coordinates of each point we can find the length of each segment using the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For ST:
[tex]d=\sqrt{(6.5-5)^2+(5.5-3)^2} \\=\sqrt{(1.5)^2+(2.5)^2} \\=\sqrt{2.25+6.25 \\=\sqrt{8.5}=2.9 \neq 4[/tex]
For RT:
[tex]d=\sqrt{(3.5-5)^2+(5.5-3)^2} \\=\sqrt{(-1.5)^2+(2.5)^2} \\=\sqrt{2.25+6.25} \\=\sqrt{8.5}=2.9 \neq 5[/tex]
For RS:
[tex]d=\sqrt{(3.5-6.5)^2+(5.5-5.5)^2} \\=\sqrt{(-3)^2+(0)^2} \\=\sqrt{9+0}=\sqrt{9}=3[/tex]
Type the domain and range values for the corresponding variables that make these relations inverses of each other. a = b = c = d = e =
Answers
B) -2.6
C) 1.7
D) 4.4
E) 1
HELP! This circle graph shows the results of a survey that asked people to identify their favorite type of music. What percent of people chose rock or country as their favorite type of music? 9% 35% 45% 55%
A circle graph with 5 sections. The first section is labeled Rock 27 percent. The second section is labeled Hip Hop 28 percent. The third section is labeled Jazz 19 percent. The fourth section is labeled Country 18 percent. The fifth section is labeled Other 14 percent.
Answers
The percentage that choose rock or country is 45%
From the circle graph, we have the following parameters:
Rock = 27%.
Hip Hop = 28%
Jazz = 19%.
Country = 18%
Other = 14%
The percentage that choose rock or country is then calculated as:
Rock or Country = 27% + 18%
Rock or Country = 45%
Hence, the percentage that choose rock or country is 45%
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Please Hurry, I really need help! A cylinder has a height of 6" and the circumference of its base is 16π".
Find the volume of the cylinder. (P.S There is no picture of the cylinder)
96π cubic inches
192π cubic inches
384π cubic inches
Answers
Circumference is 2*pi*r
16pi=2pir
r=8
v=pi*8^2*6
v=384pi cubic inches
Height of cylinder = 6 inch
Circumference of base = 16 π inch
Volume of cylinder = πr^2h
Radius =?
Circumference of circle = 2πr
2πr= 16π
2r= 16
r= 16/2
r= 8 inch
Volume= π×8×8×6
Volume= 384π cubic inches
Hope it helps...!!!
helpppppppppppppppppppp
Answers
either x = 5 or x = -1 (second option)
Explanation:
We are asked to use the u substitution. This means that we will assume that:
u = x - 3
Substitute in the given expression:
u^2 + 2u - 8 = 0
(u-2)(u+4) = 0
either u = 2
or u = -4
Now, we have:
u = x- 3
at u = 2:
x - 3 = 2
x = 2 + 3 = 5
at u = -4:
x - 3 = -4
x = -4 + 3 = -1
Hope this helps :)
Using substitution we have:
u = x-3
We rewrite:
(u) ^ 2 + 2 (u) -8 = 0
We are looking for roots:
u1 = 2
u2 = -4
We return the change:
u1 = 2 = x-3
x1 = 3 + 2 = 5
u2 = -4 = x-3
x2 = -4 + 3 = -1
Answer:
x1 = 5
x2 = -1
(option2)
The simplest form of square root of eighty can be written as a times square root of b, where a
Answers
a = 4
b = 5 I'm guessing.
Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let x represent the length of each of the equal pieces of yarn that Julie decides to cut. What is the equation that can be used to determine the total length of all of the yarn that she ends up cutting, y? Is the graph of the equation continuous or discrete?
Answers
It is discrete...
The answer would be: D). y=4x+7.75; continuous. Let me know if this is right!
While in europe, if you drive 107 km per day, how much money would you spend on gas in one week if gas costs 1.10 euros per liter and your car's gas mileage is 42.0 mi/gal ? assume that 1euro=1.26dollars?
Answers
Answer:
The money spend on gas in one week = 46.13 Euro
The money spend on gas in one week = $58.12
Step-by-step explanation:
1 week = 7 days
You drive 107 km per day.
Kilometer driven for 7 days = 7 *107 = 749 kilometers.
Now let's convert kilometers to miles.
1 mile = 1.60934 kilometers
We have to divide 749 km by 1.60934.
So, 749 km = 465.41 miles.
Car mileage is 42 miles / gallon.
We need to find the number of gallons of gas needed to travel 465.41 miles.
So, we have to divide 465.41 miles by 42.
The number of gallons of gasoline needed = [tex]\frac{465.41}{42} = 11.08 gallons[/tex]
cost of 1 .10 Euros per liter.
Now we have to convert 11.08 gallons to liters.
1 gallon = 3.78541 liters.
So we have to multiply 11.08 by 3.78541
11.08 gallons = 41.94 liters.
Now to find the cost, we need to multiply 41.94 liters by 1.10 Euro.
The money spend on gas in one week = 46.13 Euro
To convert the cost in dollars.
1 euro = 1.26
We need to multiply 46.13 by 1.26
The money spend on gas in one week = $58.12
Let f(x)=3x and g(x)=x^2+5. Perform function operation g(x)/f(x). State the domain.
Answers
f(x)=3x
g(x)=x²+5
g(x)/f(x)=[x²+5]/[3x]
that new function will exist for all real numbers except the value of zero, value for which it becomes indefinite
the domain is the interval (-∞,0) U (0,∞)
using a graph tool
see the attached figure
Helppppppp!!!!!!!!!!!!!!!!!!
Answers
Interior angles of triangles add to equal 180 degrees, so you can set up an equation to find m<2:
180 = 115 + 50 + x
180 = 165 + x
15 = x
Answer:
The measure of angle 2 is 15 degrees.
Find the distance between the points given.
(-3, -6) and (3, 2)
4
10
√52
Answers
Quadrilateral ABCD is inscribed in this circle. What is the measure of ∠A ? Enter your answer in the box.
Answers
180 - 43 = 137
:)
Answer: The answer is 137°.
Step-by-step explanation: Given that the quadrilateral ABCD is inscribed in a circle, where measure of angle C is 43°. We are to find the measure of ∠A.
Since the quadrilateral ABCD is inscribed in a circle, so it will be a cyclic quadrilateral. Also, the sum of opposite angles of a cyclic quadrilateral is 180°.
Therefore, we have
[tex]\angle A+\angle C=180^\circ\\\\\Rightarrow \angle A+43^\circ=180^\circ\\\\\Rightarrow \angle A=180^\circ-43^\circ\\\\\Rightarrow \angle A=137^\circ.[/tex]
Thus, the required answer is 137°.
Which description is correct for the polynomial 4x² +3x +5?
cubic binomial
cubic trinomial
quartic monomial
quadratic trinomial
Answers
The answer is: D)quadratic trinomial
The solution is Option D.
The quadratic trinomial is given by A = 4x² + 3x + 5
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 4x² + 3x + 5 be equation (1)
On simplifying the equation , we get
There are 3 terms on the equations , so it is a trinomial
And , since the variable is x² , it is a quadratic equation
Therefore , the equation A is quadratic trinomial
Hence , the equation is quadratic trinomial
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