Answers
Answer:
No solution
Explanation:
Given the system
[tex]\begin{gathered} -x+2y=4 \\ y=\frac{1}{2}x+3 \end{gathered}[/tex]Graph the first equation -x+2y = 4.
Identify two points on the line. Plot and join them to get the graph of the line.
When x = 0, y =2. First point is (0, 2).
When y = 0, x = -4. Second point is (-4, 0).
Now, graph the second equation y= (1/2)x+3.
Identify two points on the line. Plot and join them to get the graph.
When x = 0, y = 3. First point is (0, 3).
When y = 0, x = -6. Second point is (-6, 0).
The graph of both lines are parallel, that is, not intersecting anywhere. Hence the system has no solution.
Related Questions
(4+3)²+5 what's the awnser
Answers
Solve;
[tex]\begin{gathered} (4+3)^2+5 \\ =(7)^2+5 \\ =49+5 \\ =54 \end{gathered}[/tex]-5|x+1|=10 solve for x
Answers
⇒This problem is an absolute value problem where in we know that whatever is in the absolute signs always will come out positive
⇒If we are to check carefully 10 is the product of -5 and a positive number |x+1| so it is NOT possible anywhere in MATHEMATICS that when you multiply a negative number by a positive number it is going to give you a positive number, There is no solution for this question since the product of a negative number and a positive number is negative the given equation cannot be solved.
GOODLUCK!!!!
Use the figure to find an exact value of the following trigonometric function.cos(2alphasymbol)
Answers
first, we need to compute the hypotenuse (c) of the triangle. Using the Pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=5^2+12^2 \\ c^2=25+144 \\ c=\sqrt[]{169} \\ c=13 \end{gathered}[/tex]By definition:
[tex]\cos (angle)=\frac{\text{adjacent side}}{hypotenuse}[/tex]Replacing with data:
[tex]\cos (\alpha)=\frac{5}{13}[/tex]Using the next identity:
[tex]\begin{gathered} \cos (2\alpha)=2\cos ^2(\alpha)-1 \\ \cos (2\alpha)=2(\frac{5}{13})^2-1 \\ \cos (2\alpha)=\frac{50}{169}^{}-1 \\ \cos (2\alpha)=-\frac{119}{169} \end{gathered}[/tex]POLESI Unit Fifty 11th graders were asked to select a favorite pattern out of 6 choices. The following display represents the choices of their favorite patterns. The counts have been recorded in the accompanying table according to the pattern and the number of students who selected that pattern. What is the missing value in the table? Color Pattern Frequency Blue on gray 4 Green 9 EE 14 Pink polka dots Purple Red and orange stripes 11 ? Yellow. 3 O A. 6 B. 9 O C. 8 D. 7 PREVIOUS
Answers
The frequency in the table represents the number of boxes coloured with a particular colour.
The number of red and orange stripes are 9.
Thus, the required missing value in the table is 9.
Christian is building a diorama of the ocean details of the weeks of different ocean animals this girl who did the alarm is 1 inch equals 2 feet how long is the actual shark and feet
Answers
From the table, we can see that the length of the shark is 4 inches.
And we have that the scale of the diorama is:
1 inch = 2 feet
Therefore:
[tex]4\times2=8[/tex]Answer: 8 feet
QueSUUl relp Heloise is drawing the design of the awning shown. The 2 triangular sections are identical isosceles triangles. Complete parts a and b. 3 ft 6 ft a. Write numbers in the boxes to show the missing dimensions. The number in the bottom left box is ft. The number in the middle box is ft. The number in the bottom right box is ft. (Type whole numbers or decimals.)
Answers
Answer:
a. The number in the bottom left box is 6 ft. The number in the middle box is 3 ft. The number in the bottom right box is 6 ft.
b. The total area of the awning is 54 ft²
Explanation:
An isosceles triangle is a triangle that has 2 equal sides.
So, the height and base of the triangles will be the same. It means that the number in the bottom left box is 6 ft and the number in the bottom right box is also 6 ft.
On the other hand, the number in the middlebox is the width of the rectangle, so it is 3 ft.
Then, the answers are:
The number in the bottom left box is 6 ft. The number in the middle box is 3 ft. The number in the bottom right box is 6 ft.
Now, the area of the awning can be calculated as the sum of the area of the isosceles triangles and the area of the rectangle.
The area of the triangles can be calculated as:
[tex]\text{Area Triangle = }\frac{Base\text{ }\times\text{ Height}}{2}[/tex]Where the base and the height are equal to 6 ft, so the area is:
[tex]\text{Area triangle = }\frac{6\text{ ft }\times\text{ 6 ft}}{2}=\frac{36ft^2}{2}=18ft^2[/tex]In the same way, the area of the rectangle is equal to:
Area Rectangle = Base x Height
Area Rectangle = 3 ft x 6 ft
Area Rectangle = 18 ft²
Finally, the total area of the awning is equal to:
Area = Area Rectangle + 2(Area Triangle)
Area = 18 ft² + 2(18 ft²)
Area = 18 ft² + 36 ft²
Area = 54 ft²
So, the total area of the awning is 54 ft²
A football team loses 8 yards on each of the 4 consecutive plays. Find the total change in yards from where the team started
Answers
EXPLANATION
We can get the total change in yards by multiplying the number of plays by the number of lost yards in a play.
The number of losses is negative.
-8 x 4 = -32
Taking the absolute value for both numbers:
|4| = |4|
|-8| = 8
Since -8 has the greater value, the answer is negative.
Build the rational expression into an equivalent rational expression with the indicated denominator.
Answers
Given:
[tex]\frac{m-3}{m+2}\text{ = }\frac{unknown}{m^2-m-6}[/tex]To find:
the numerator of the rational expression on the right
To determine the numerator, we need to factorise the denominator:
[tex]\begin{gathered} factors\text{ of -6 whose sum gives -1 are -3 and 2} \\ m^2\text{ - m -6 = m}^2\text{ - 3m + 2m - 6} \\ =\text{ m\lparen m - 3\rparen + 2\lparen m - 3\rparen} \\ =\text{ \lparen m + 2\rparen\lparen m - 3\rparen} \end{gathered}[/tex][tex]\begin{gathered} \frac{m-3}{m+2}\text{ = }\frac{unknown}{(m\text{ + 2\rparen\lparen m}-3)} \\ from\text{ the above, we see the denominator of the left side was multiplied by \lparen m -3\rparen to get} \\ the\text{ denominator on the right} \\ \\ So\text{ for the expression on the right to be equivalent to that on the left, } \\ \text{we will multiply the numerator on the left by \lparen m - 3\rparen} \end{gathered}[/tex][tex]\begin{gathered} denominator\text{ on the left = m + 2} \\ denominator\text{ on the right = \lparen m + 2\rparen\lparen m - 3\rparen} \\ \\ numerator\text{ on the left = m - 3} \\ numerator\text{ on the right = \lparen m - 3\rparen\lparen m - 3\rparen} \end{gathered}[/tex]Expanding the numerator on the right:
[tex]\begin{gathered} (m\text{ - 3\rparen\lparen m-3\rparen = m\lparen m - 3\rparen - 3\lparen m - 3\rparen} \\ =\text{ m}^2\text{ - 3m - 3m + 9} \\ =\text{ m}^2\text{ - 6m + 9} \end{gathered}[/tex]If the following series will continue in the same pattern. What is the next number in the series 1, 10, 7, 16 ?
Answers
Given:
The given series 1, 10, 7, 16, ... will continue in the same pattern.
Required:
We need to find the next number in the given series.
Explanation:
Consider the first two numbers.
10-1=9.
The second number is 9 more than the first number.
Consider the second and third numbers.
7-10=-3
The third number is 3 less than the second number.
Consider the third and fourth numbers.
16-7=9.
The fourth number is 9 greater than the third number.
So the pattern - add 9, subtract 3, add 9, and subtract 3.
So the fifth number is 16-3=13.
Final answer:
The next term is 13.
find the perimeter of the triangle whose vertices are (-7,-4), (1,11), and (-7,5). write the exact answer. do not round.
Answers
Answer:
36
Explanation:
Given the vertices of the triangle as A(-7, -4), B(1, 11), and C(-7, 5).
To be able to determine the perimeter of the triangle, we have to first find the distance between the vertices using the distance formula.
Let's determine the distance between A(-7, -4) and B(1, 11) as seen below;
[tex]\begin{gathered} AB=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}_{}_{} \\ =\sqrt[]{\lbrack1-(-7)\rbrack^2+\lbrack11-(-4)\rbrack^2} \\ =\sqrt[]{8^2+15^2} \\ =\sqrt[]{64+225} \\ =\sqrt[]{289} \\ =17 \end{gathered}[/tex]Let's also determine the distance between B(1, 11) and C(-7, 5);
[tex]\begin{gathered} BC=\sqrt[]{(-7-1)^2+(5-11)^2} \\ =\sqrt[]{(-8)^2+(-6)^2} \\ =\sqrt[]{64+36} \\ =\sqrt[]{100} \\ =10 \end{gathered}[/tex]Let's determine the distance between C(-7, 5) and A(-7, -4);
[tex]\begin{gathered} CA=\sqrt[]{\lbrack-7-(-7)\rbrack^2+(-4-5)} \\ =\sqrt[]{0^2+(-9)^2} \\ =\sqrt[]{81} \\ =9 \end{gathered}[/tex]To find the perimeter of the triangle, we'll add the distance between each vertex together;
[tex]\begin{gathered} Perimeter=AB+BC+CA \\ =17+10+9 \\ =36 \end{gathered}[/tex]Select the correct choice below and fill in any answer boxes in your choice.
Answers
The given equation is
[tex]x(5x-5)=(5x+9)(x-4)[/tex]We will simplify each side at first by multiply the brackets on the right side and multiply the common factor by the bracket on the left side
[tex]\begin{gathered} x(5x)-x(5)=(5x)(x)+5x(-4)+(9)(x)+(9)(-4) \\ 5x^2-5x=5x^2-20x+9x-36 \end{gathered}[/tex]Now, we will add the like terms on each side
[tex]\begin{gathered} 5x^2-5x=5x^2+(-20x+9x)-36 \\ 5x^2-5x=5x^2-11x-36 \end{gathered}[/tex]Subtract both sides by 5x^2
[tex]\begin{gathered} 5x^2-5x^2-5x=5x^2-5x^2-11x-36 \\ -5x=-11x-36 \end{gathered}[/tex]Add 11x to both sides
[tex]\begin{gathered} -5x+11x=-11x+11x-36 \\ 6x=-36 \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{6x}{6}=-\frac{36}{6} \\ x=-6 \end{gathered}[/tex]The solution set is {-6}
The answer is A
Given: BC = AD and BC || AD.Prove: ABECADEA.StepStatementReason1BCADBC | ADGiventryType of StatementBEDANote: AC and BD are segments
Answers
∆BEC =~ ∆ DEA
Then
Statements. Reason
BC=~ AD Given
BC || AD. A.S.A. (angle, side ,angle)
Proof by angle ,side ,angle. A.S.A
1. Parallel lines BC||AD,. Angle
2.BC=~ AD. Side
3. Both triangles ∆ BEC , ∆DEA, shares angle 180° -E
Segments AB, and DC, are congruent
If a, b, and care three different numbers, which of the following equations hasinfinitely many solutions?A. ax + b = ax + cB. ax + b = ax + bC. ax = bx + c
Answers
The equation has infinitely many solutions, if
The two sides are equal completely
Since ax + bx = ax + c
The two sides have the same terms of x, but a not equal C
Then this equation has no solution
A is not the answer
Since ax + b = ax + b
The two sides have the same term of x
The two sides have the same numerical terms
The two sides are equal completely
This equation has infinitely many solutions
B is the answe
Given the line with the equation y = 1/2x+1 ; determine the equation of the line that is perpendicular that goes through the point (1,-2)
Answers
C) y=-2x
1)Perpendicular lines have the slope equal to the reciprocal multiplied by -1 of the original line.
2) As the given line is y = 1/2x + 1 and the point that is intercepted by (1,-2) we can state the following
Original line:
Slope m = 1/2
Point
Perpendicular line
slope = -2
Let's plug into the slope-intercept formula the given point, to find b the linear coefficient
y=mx +b
-2=-2(1) +b
-2 =-2 +b
-2+2=b
b=0
So the function is, y=-2x
Writing a Proportion The recipe for beef stew calls for 1/4 teaspoon of pepper for every 3 potatoes. If 9 potatoes are used, how much pepper is needed? Which proportion represents this problem? 9 3 II 3 3
Answers
Writing a Proportion The recipe for beef stew calls for 1/4 teaspoon of pepper for every 3 potatoes. If 9 potatoes are used, how much pepper is needed? Which proportion represents this problem? 9 3 II 3 3
we know that
1/4 teaspoon of pepper for every 3 potatoes.
so
For 9 potatoes
Multiply the recipe by 3
(1/4)3 teaspoon of pepper --------> 3(3) potatoes
3/4 teaspoon of pepper ------> 9 potatoes
therefore
the answer is 3/4 teaspoon of pepper
Part b
Granola bars are on sale for $0.50 each. If Brad paid $5 for granola bars, write and solve a multiplication equation to find how many bars he bought.
Answers
Let n be the number of Granola bars purchased with the $5 bill:
C(n) = 0.5n, where C = cost of n Granola bars.
With a $5 bill, one can purchase:
C(n) = 0.5n
5 = 0.5n
Divide both sides by 0.5:
[tex]\begin{gathered} \frac{5}{0.5}=\frac{0.5n}{0.5} \\ 10\text{ = n} \end{gathered}[/tex]So the linear function is function C(n) = 0.5n and a $5 bill can purchase 10 Granola bars.
/ 0.50 /0.50
x = 10
He can buy 10 bars.
whats 19.64 as fraction?
Answers
491/25
Explanation:To convert 19.64 to farction, we need to know the number of decimal numbers after the point. We have two numbers after the point. This represents hundred. Hence, we would be dividing by 100.
[tex]19.64\text{ = }\frac{1964}{100}[/tex]We can write in the lowest form:
[tex]\begin{gathered} \text{Divide the numerator and denominator by 4} \\ 19.64\text{ = }\frac{1964\div4}{100\div4} \\ 19.64\text{ = }\frac{491}{25} \end{gathered}[/tex]given a line segment with endpoint a(16,8) and b(1,3) what are the coordinate of the line segment partitioned two-fifths from A to B
Answers
Answer:
(10, 6)
Explanation:
The x and y coordinates of a point (x, y) that partitioned a segment that goes from (x1, y1) to (x2, y2) by fraction of m/n are calculated as:
[tex]\begin{gathered} x-\text{coordinate = }\frac{m}{n}(x_2-x_1)+x_1 \\ y-\text{coordinate}=\frac{m}{n}(y_2-y_1)+y_1 \end{gathered}[/tex]So, replacing (x1, y1) by A(16, 8), (x2, y2) by B(1, 3), and the fraction m/n by 2/5, we get
[tex]\begin{gathered} x-\text{coordinate = }\frac{2}{5}(1-16)+16=\frac{2}{5}(-15)+16=-6+16=10 \\ y-\text{coordinate}=\frac{2}{5}(3-8)+8=\frac{2}{5}(-5)+8=6 \end{gathered}[/tex]Therefore, the coordinate of the point that divided the segments into 2/5 is (10, 6).
complete the sequence 128,64,a3,16,8,a6,2
Answers
Answer:
128, 64, 32, 16, 8, 4,2
Explanation:
Each next term in the sequence is half of the previous term.
For example,
[tex]64=\frac{128}{2}[/tex][tex]8=\frac{16}{2}[/tex]In a similar fashion, the a_3 term is 1/2 the previous term:
[tex]a_3=\frac{64}{2}[/tex][tex]a_3=32.[/tex]And similarly, a_6 is
[tex]a_6=\frac{8}{2}[/tex][tex]a_6=4[/tex]Hence, the complete sequence with a_3 = 32 and a_6 = 4 is 128, 64, 32, 16, 8, 4,2
which equation represents a line on a coordinate plane that passes though the point (-1,1) and is parallel to the line 3x-2y=16?
Answers
Given equation of the parallel line:
3x - 2y = 16
The line passes through the point: (-1, 1)
Parallel lines have the same slope.
Let's rewrite the equation of the parallel line in slope intercetpt form:
y = mx + b
Where m is the slope and b is the y-intercept.
We have:
[tex]\begin{gathered} 3x-2y=16 \\ \\ \text{Subtract 3x from both sides:} \\ -3x+3x-2y=-3x+16 \\ \\ -2y=-3x+16 \\ \\ \text{Divide all terms by -2:} \\ \frac{-2y}{-2}=\frac{-3x}{-2}+\frac{16}{2} \\ \\ y=\frac{3}{2}x+8 \end{gathered}[/tex]The slope is 3/2
Substitute 3/2 for m in the slope intercept form.
[tex]y=\frac{3}{2}x+b[/tex]To solve for the y-intercept, b, since the line passes through (-1, 1), substitute -1 for x and 1 for y:
[tex]\begin{gathered} y=\frac{3}{2}x+b \\ \\ 1=\frac{3}{2}(-1)+b \\ \\ 1=-\frac{3}{2}+b \\ \\ \text{Multiply all terms by 2:} \\ 1(2)=-\frac{3}{2}\ast2+2(b) \\ \\ 2=-3+2b \\ \\ \text{Add 3 to both sides:} \\ 3+2=-3+3+2b \\ \\ 5=2b \\ \\ \text{Divide both sides by 2:} \\ \frac{5}{2}=\frac{2b}{2} \\ \\ \frac{5}{2}=b \\ \\ b=\frac{5}{2} \end{gathered}[/tex]The y-intercept, b is 5/2
Therefore, the equation that represents the line is:
[tex]y=\frac{3}{2}x+\frac{5}{2}[/tex]ANSWER:
[tex]y=\frac{3}{2}x+\frac{5}{2}[/tex]quadrilateral DEFG has vertices at D(3,4), E(8,6), F(9,9), and G(4,7). Prove that defg is a parallelogram.
Answers
I'll graph it
From the graph we can observe that it is a parallelogram, let's calculate the distance between the vertex to know if it is a parallelogram.
[tex]\begin{gathered} \text{distance DE = }\sqrt[]{(8-3)^2+(6-4)^2} \\ \text{ = }\sqrt[]{(5)^2+(2)^2} \\ \text{ = }\sqrt[]{25\text{ + 4}} \\ \text{ = }\sqrt[]{29} \\ dis\tan ce\text{ DG = }\sqrt[]{(4-3)^2+(7-4)^2} \\ \text{ = }\sqrt[]{(1)^2+(3)^2} \\ \text{ = }\sqrt[]{1\text{ + 9}} \\ \text{ = }\sqrt[]{10} \\ \text{distance EF = }\sqrt[]{(9-8)^2+(9-6)^2} \\ \text{ = }\sqrt[]{(1)^2+(3)^2} \\ \text{ = }\sqrt[]{1\text{ + 9}} \\ \text{ = }\sqrt[]{10} \\ \text{distance GF = }\sqrt[]{(9-4)^2+(9-7)^2} \\ \text{ = }\sqrt[]{(5)^2+(2)^2} \\ \text{ = }\sqrt[]{25\text{ + 4}} \\ \text{ = }\sqrt[]{29} \end{gathered}[/tex]Conclusion: it is a parallelogram because DE = GF
and DG = EF
Simplify each ratioA) 39:52B) 44:77C) 45:81
Answers
A) 3:4
B) 4:7
C) 5:9
To solve this, we need to find the Greatest Common Divisor (GDC) of each pair of numbers.
For pair A)
Factors:
39 => 1, 3 13, 39
52 => 1, 2, 4, 13, 26, 52
The GCD is 13. Then divide both numbers by the GCD:
39/13 = 3
52/13 = 4
The SImplified ratio is 3:4
For B)
Factors:
44 => 1, 2, 4, 11, 22, 44
77 => 1, 7, 11, 77
Then divide by GCD, in this case, 11:
44/11 = 4
77/11 = 7
44:77 => 4:7
For c)
Factors:
45 => 1, 3, 5, 9, 15, 45
81 => 1, 3, 9, 27, 81
The GCD is 9. Then
45/9 = 5
81/9 = 9
The ratio is 45:81 => 5:9
What vocabulary term best defines Ray ED and ray EF
Answers
Answer:
C. Opposite Rays
Explanation:
By definition, two rays are opposite rays, if they have the same endpoint and their union is a line.
The first letter in the name of a ray refers to its endpoint; the second refers to the name of any other point on the ray.
• The endpoint of ray ED is E.
,• The endpoint of ray EF is E.
Thus, they have the same endpoint.
Next, joining the two rays forms line DF.
Thus, rays ED and EF are Opposite Rays.
Can you help me with questions C how much would that cost?What did you have to assume to get that answer? Explain in words: type the number you assume here (number only for grading purposes)
Answers
Explanation:
To know what is the cost to travel 380 miles, we need to know the cost of one gallon of fuel. So, let's assume that this cost is $3.8 per gallon.
Since 380 miles spent 20 gallons of fuel, the cost is
C = 20 gallons x $3.8 = $76
Answers:
Therefore, the answers are:
How much would that cost: $76
What did you have to assume to get the answer: The cost of one gallon of fuel
Type the number you assumed here: 3.8
use the grouping method to express the polynomial below as a product of its factors. write each factor as a polynomial in descending order x(10x-9)+11(10x-9)
Answers
Express the polynomial given as a product of its factors;
[tex]\begin{gathered} x(10x-9)+11(10x-9) \\ =(x+11)(10x-9) \end{gathered}[/tex]The commonn factor is
[tex](10x-9)[/tex]Factor this out and you'll be left with
[tex]x+11[/tex]If A and B are independent events, what can we say about P(A|B)?
Answers
Solution:
Independent events are those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.
This indicates that The probability of A won't be affected by the probability of B
HENCE,
The final answer is
[tex]P(A|B)=P(A)[/tex]The fourth OPTION is the right answer
If DBC = 90° what is the relationship between AD and CD?
Answers
If DBC = 90° what is the relationship between AD and CD?
_____________________________________
Answer
AD=CD
_____________________________________
The sum of supplementary angles is 180º
If ∠ DBC = 90°
∠ DBC = 90° so then ∠ DBA = 90º
DB is the same for the two triangles
and AB = BC
By the side angle side congruence theorem, we can conclude AD=CD
is 17 an integer number
Answers
The answer is YES.
17 is an integer number.
Any number which is a whole number, either positive or negative and must not not include fractions
Complete the table for the following functiony=(1/3)^x*imageGraph the function and describe what the graph looks like.A. Increases in Quadrant Ib. Increases from left to rightc. Decreases from left to rightd. Decreases in Quadrant III
Answers
Given:-
[tex]y=(\frac{1}{3})^x[/tex]To graph the image.
So now we find the values of y when the value of x is -3,-2,-1,0,1,2,3.
When x is -3. we get,
[tex]\begin{gathered} y=(\frac{1}{3})^{-3} \\ y=(3)^3 \\ y=27 \end{gathered}[/tex]So the required value is 27.
when x is -2. we get,
[tex]\begin{gathered} y=(\frac{1}{3})^{-2} \\ y=(3)^2 \\ y=9 \end{gathered}[/tex]So the required value is 9.
When x is -1. we get,
[tex]\begin{gathered} y=(\frac{1}{3})^{-1} \\ y=(3)^1 \\ y=3 \end{gathered}[/tex]So the required value is 3.
When x is 0. we get,
[tex]\begin{gathered} y=(\frac{1}{3})^0 \\ y=0 \end{gathered}[/tex]So the required value is 0.
When x is 1. we get,
[tex]\begin{gathered} y=(\frac{1}{3})^1 \\ y=\frac{1}{3} \end{gathered}[/tex]So the required value is 1/3.
When x is 2. we get,
[tex]\begin{gathered} y=(\frac{1}{3})^2 \\ y=\frac{1}{9} \end{gathered}[/tex]So the required value is 1/9.
When x is 3. we get,
[tex]\begin{gathered} y=(\frac{1}{3})^3 \\ y=\frac{1}{27} \end{gathered}[/tex]So the required value is 1/27.
So the graph looks like,
This is the graph and it decreases from left to right.
Which unit would you most likely use to measure the capacity of a mug? Teaspoons Quarts Fluid Ounces Done My l
Answers
According to the size, it would be fluid ounces.