Answers
slope of DE would be [tex]\( m_{DE} = \frac{(2c - b)}{(0 - (-a))} = \frac{(2c - b)}{a} \).[/tex]
slope of FG would be[tex]\( m_{FG} = \frac{(0 - c)}{(0 - (a+b))} = \frac{-c}{-(a+b)} = \frac{c}{a+b} \).[/tex]
To find the slope of line segments DE and FG from a trapezoid on a coordinate plane, we can follow these steps:
1. Identify the Coordinates of Endpoints:
- For DE, identify coordinates D and E.
- For FG, identify coordinates F and G.
2. Use the Slope Formula:
- The slope m of a line passing through two points [tex]\( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m = \frac{(y_2 - y_1)}{(x_2 - x_1)} \).[/tex]
3. Calculate the Slope for DE:
- Plug the coordinates of D and E into the slope formula.
4. Calculate the Slope for FG:
- Plug the coordinates of F and G into the slope formula.
Given the coordinates in the image, let's calculate the slopes for DE and FG:
For DE:
- Let's say D has coordinates (-a, b) and E has coordinates (0, 2c)
- The slope of DE would be [tex]\( m_{DE} = \frac{(2c - b)}{(0 - (-a))} = \frac{(2c - b)}{a} \).[/tex]
For FG:
- Let's say F has coordinates[tex]\( (a+b, c) \)[/tex] and G has coordinates (0, 0) .
- The slope of FG would be[tex]\( m_{FG} = \frac{(0 - c)}{(0 - (a+b))} = \frac{-c}{-(a+b)} = \frac{c}{a+b} \).[/tex]
Related Questions
Complete the table for the given rule y=x+3
Answers
Answer:
x= 1 when y =4 , x= 5 when y = 8 , x=2 when y = 5.
Step-by-step explanation:
y=x+3
Through this rule we have to find out the values of x when values of y are given:
y=x+3
y = 4
Substitute the value in the rule:
4=x+3
Combine the constants:
4-3=x
x= 1 when y =4
y=x+3
y = 8
8= x+3
Combine the constants:
8-3= x
5=x
x= 5 when y = 8
y=x+3
y = 5
5=x+3
Combine the constants:
5-3=x
2=x
x=2 when y = 5....
Help me please I’m losted
Answers
Answer:
[tex]\frac{50}{3}[/tex]
Step-by-step explanation:
Similar shapes have corresponding sides that are proportional.
So 20 corresponds to x (big to small).
So 12 corresponds to 10 (big to small).
Your information is already lined up for you to setup your proportion:
[tex]\frac{20}{12}=\frac{x}{10}[/tex]
Cross multiply:
[tex]20(10)=12(x)[/tex]
Simplify both sides:
[tex]200=12x[/tex]
Divide both sides by 12:
[tex]\frac{200}{12}=x[/tex]
Simplify by dividing top and bottom by 4:
[tex]\frac{50}{3}=x[/tex]
12. Determine the area of the given parallelogram with length 11 and altitude 5.
A. 55
B. 110
C. 27.5
D. 75
Answers
5times 11
55
What is the type of two-dimensional solid created by a vertical cross section of the cone that passes through the apex? What is the area of the cross section? triangle; area = 45 ft2 triangle; area = 90 ft2 circle; area = 36π ft2 circle; area = 144π ft2
Answers
Answer:
The answer is B on edge
Step-by-step explanation:
The area of the cross section is equal to 90 ft²
Looking at the diagram we would see that the two dimensional solid that passed the point is a triangle.
The formula for area of a triangle[tex]\frac{1}{2} bh[/tex]
Where b = bas
h = height
The radius of the cone = 6
The diameter of the cone = 2*radius
= 2*6
= 12
We have to put d = b = 12
When we put the values into the area of a triangle
= [tex]\frac{1}{2} 12*15\\\\= \frac{180}{2} \\\\= 90 ft^2[/tex]
The area of the cross section is therefore 90 ft²
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find the sum of these polynomials (x^2+x+9)+(7x^2+5)
Answers
Answer:
The correct option is A
Step-by-step explanation:
(x^2+x+9)+(7x^2+5)
Open the parenthesis:
=x²+x+9+7x²+5
Now add the like terms:
=8x²+x+14
Therefore the correct option is A...
Answer:
A
Step-by-step explanation:
Point M is the midpoint of AB if the coordinates of A are (-3,6) and the coordinates of M are (-5,2) what are the coordinates of B ?
Please answer #5
Answers
Answer:
The coordinates of point B are (-7 , -2)
Step-by-step explanation:
* Lets explain how to solve the problem
- The mid-point (x , y) of the line whose endpoints are (x1 , y1) and
(x2 , y2) is [tex]x=\frac{x_{1}+x_{2}}{2},y=\frac{y_{1}+y_{2}}{2}[/tex]
∵ M is the midpoint of AB
∵ The coordinates of point A are (-3 , 6)
∵ The coordinates of point M are (-5 , 2)
- Let the coordinates of point A are (x1 , y1) , The coordinates of
point B are (x2 , y2) and The coordinates of point M are (x , y)
∴ x = -5 , x1 = -3 and y = 2 , y1 = 6
- Lets use the rule of the mid point to find x2 , y2
∵ [tex]-5=\frac{-3+x_{2}}{2}[/tex] ⇒ multiply both sides by 2
∴ [tex]-10=-3+x_{2}[/tex] ⇒ add 3 to both sides
∴ -7 = x2
∵ [tex]2=\frac{6+y_{2}}{2}[/tex] ⇒ multiply both sides by 2
∴ [tex]4=6+y_{2}[/tex] ⇒ subtract 6 from both sides
∴ -2 = y2
∵ The coordinates of point B are (x2 , y2)
∴ The coordinates of point B are (-7 , -2)
20 PTS! PLEASE HELP ME T^T!! Using complete sentences, explain which function has the greatest y-intercept.
Answers
Step-by-step explanation:
The y-intercept is the value of the function at x = 0.
f(0) = -3(0) + 2 = 2
g(0) = -3
h(0) = 4 sin(0 + π) + 3 = 3
h(x) has the greatest y-intercept.
Answer:
The y-intercept of functions f(x), g(x) and h(x) are 2,-3 and 3 respectively. Therefore the function h(x) has the greatest y-intercept.
Step-by-step explanation:
The given function is
[tex]f(x)=-3x+2[/tex]
Substitute x=0, to find the y-intercept of the function.
[tex]f(0)=-3(0)+2[/tex]
[tex]f(0)=0+2[/tex]
[tex]f(0)=2[/tex]
The y-intercept of the function f(x) is 2.
From the given graph it is clear that the graph of g(x) intersect the y-axis at y=-3.
Therefore the y-intercept of the function g(x) is -3.
The given function is
[tex]h(x)=4\sin (2x+\pi)+3[/tex]
Substitute x=0, to find the y-intercept of the function.
[tex]h(0)=4\sin (2(0)+\pi)+3[/tex]
[tex]h(0)=4\sin (0+\pi)+3[/tex]
[tex]h(0)=4\sin (\pi)+3[/tex]
[tex]h(0)=4(0)+3[/tex]
[tex]h(0)=3[/tex]
The y-intercept of the function h(x) is 3.
The y-intercept of functions f(x), g(x) and h(x) are 2,-3 and 3 respectively. Therefore the function h(x) has the greatest y-intercept.
which of the diagram below represents the contrapositive of the statement if it is an equilateral triangle,then it is an isosceles
Answers
The diagram that represents the contrapositive of the statement "If it is an equilateral triangle, then it is an isosceles triangle" is: B. Figure B.
In Mathematics, a conditional statement is a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, a conditional statement has the form "if P then Q."
P → Q
Where:
P and Q represent sentences or statements.
Generally speaking, the contrapositive of a conditional statement involves interchanging the hypothesis and conclusion, and negating both hypothesis and conclusion;
~Q → ~P
In this context, the contrapositive of the given statement "If it is an equilateral triangle, then it is an isosceles triangle" can be written as follows;
"If it is not an isosceles triangle, then it is not an equilateral triangle."
Therefore, only figure correctly represent the contrapositive of the statement.
Complete Question:
Which of the diagrams below represents the contrapositive of the statement
"If it is an equilateral triangle, then it is an isosceles triangle"?
A. Figure A
B. Figure B
In an election 32 thousand people voted for Mayor Jackson. A total of 56 thousand people voted in the election. What is the ratio of the number of votes that were not for mayor Jackson to the total number of votes in simplest form?
Answers
Answer:
Ratio of the number of votes that were not for mayor Jackson to the total number of votes is 3:7
Step-by-step explanation:
Votes of Mayor Jackson = 32,000
Total Votes = 56,000
Votes not for Mayor Jackson = 56000 - 32000
Votes not for Mayor Jackson = 24000
ratio of the number of votes that were not for mayor Jackson to the total number of votes = Votes not for Mayor Jackson:Total Votes
= 24,000:56,000
=24:56 (divide numerator and denominator by 8)
=3:7
So, ratio of the number of votes that were not for mayor Jackson to the total number of votes is 3:7
Answer:
3 : 7
Step-by-step explanation:
It is given that,
In an election 32,000 people voted for Mayor Jackson
A total of 56,000 people voted in the election.
To find the ratio
Total number of people voted = 56000
Number of people voted for Mayor Jackson = 32000
Number of votes that were not for mayor Jackson = 56000 - 32000 = 24000
The ratio of the number of votes that were not for mayor Jackson to the total number of votes = 24000 : 56000
= 3 : 7
factor the given expression x squared + 16x +64
Answers
Answer:
(x + 8)^2.
Step-by-step explanation:
x^2 + 16x + 64
8 + 8 = 16 and 8^2 = 64 so the factors are
(x + 8)(x + 8) or (x + 8)^2
The square root of 64 is 8 and as you can see 2*8 is 16 so the middle also works out
(x+8)^2 is the answer
what is the equation of the following line written in slope intercept form? (-5,-1)
Answers
Answer:
[tex]\large\boxed{y=-\dfrac{2}{3}x-\dfrac{13}{3}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have two points (-5, -1) and (-2, -3).
Look at the picture.
Calculate the slope:
[tex]m=\dfrac{-3-(-1)}{-2-(-5)}=\dfrac{-2}{3}=-\dfrac{2}{3}[/tex]
Put it to the equation in slope-intercept form:
[tex]y=-\dfrac{2}{3}x+b[/tex]
We can't read the y-intercept from the graph. Therefore put the coordinates of the point (-5, -1) to the equation and calculate b:
[tex]-1=-\dfrac{2}{3}(-5)+b[/tex]
[tex]-1=\dfrac{10}{3}+b[/tex] subtract 10/3 from both sides
[tex]-\dfrac{3}{3}-\dfrac{10}{3}=b\to b=-\dfrac{13}{3}[/tex]
Finally:
[tex]y=-\dfrac{2}{3}x-\dfrac{13}{3}[/tex]
Figure ABCD is translated down by 6 units:
Which of the following best describes the sides of the transformed figure A'B'C'D'?
A'D' || A'B'
A'B' || B’C’
D’C’ || A'D'
A'D' || B’C’
Answers
Answer:
jjjjjj
Step-by-step explanation:
it would be the same as before because translated means it stays the same
一、225 + 4.8
I don’t understand it plz help
(And do it step by step...)
Answers
[tex]\bf -\sqrt{225}+4.8~~ \begin{cases} 225=&3\cdot 3\cdot 5\cdot 5\\ &3^2\cdot 5^2\\ &(3\cdot 5)^2\\ &15^2 \end{cases}\\\\\\ -\sqrt{15^2}+4.8\implies -15+4.8\implies -10.2[/tex]
what are the solutions to the quadratic equation x^2=7x+4
Answers
Answer:
x = 7/2 ±sqrt(65)/ 2
Step-by-step explanation:
x^2=7x+4
Subtract 7x from each side
x^2-7x=7x-7x+4
x^2 -7x =4
Complete the square
Take the coefficient of x and divide by 2
-7/2
Then square it
(-7/2)^2 = 49/4
Add this to each side
x^2 -7x +49/4 =4+49/4
(x-7/2)^2 = 4 +49/4
(x-7/2)^2 = 16/4 +49/4
(x-7/2)^2 =65/4
Take the square root of each side
sqrt((x-7/2)^2) =±sqrt(65/4)
x-7/2 = ±sqrt(65)/ sqrt(4)
x-7/2 = ±sqrt(65)/ 2
Add 7/2 to each side
x-7/2 +7/2=7/2 ±sqrt(65)/ 2
x = 7/2 ±sqrt(65)/ 2
The solutions to the quadratic equation x^2 = 7x + 4 are x = 3 and x = -7, found using the quadratic formula and verified by substitution into the original equation.
To solve the quadratic equation x^2 = 7x + 4, we first need to bring all terms to one side of the equation to get it into the standard form ax^2 + bx + c = 0. This gives us x^2 - 7x - 4 = 0. We can then apply the quadratic formula, which is x = (-b \/- sqrt(b^2 - 4ac)) / (2a), where a, b, and c are coefficients from the equation ax^2 + bx + c = 0.
For our equation, a = 1, b = -7, and c = -4. Substituting these values into the quadratic formula gives us two solutions, which result in x = 3 and x = -7 as the solutions to the problem. To verify these solutions, we can substitute them back into the original equation and confirm they satisfy the equation, thus proving they are correct.
In the diagram below, AB is parallel to CD. What is the value of y?
А. 50
B. 30
C. 150
D. 60
Answers
So, you will subtract 150 from 180.
180-150= 30.
Therefore, angle y is 30 degrees.
Hopefully, this helps!
The value of y = 30°
What is the property of alternating interior angle?When two parallel lines cut by a line, then their alternating interior angles will be same.By alternating interior property, alternate angle of 150° is equal to 150°.
Straight line has angle 180°
So, y + 150° = 180°
y = 30°
Hence the value of y = 30°
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Solve the inequality for x in terms of a. Ax - 8 less than or equal to 12
Answers
Answer:
[tex]\large\boxed{\left\{\begin{array}{ccc}x\leq\dfrac{20}{a}&\text{for}\ a>0\\\\x\geq\dfrac{20}{a}&\text{for}\ a<0\end{array}\right }[/tex]
Step-by-step explanation:
[tex]ax-8\leq12\qquad\text{add 8 to both sides}\\\\ax-8+8\leq12+8\\\\ax\leq20\qquad\text{divide both sides by}\ a\neq0\\\\(1)\ \text{if}\ a>0,\ \text{then:}\\\\x\leq\dfrac{20}{a}\\\\(2)\ \text{if}\ a<0,\ \text{then you must flip the sign of inequality:}\\\\x\geq\dfrac{20}{a}[/tex]
Final answer:
To solve the inequality Ax - 8 ≤ 12 for x in terms of a, add 8 to both sides to get Ax ≤ 20, and then divide by A (assuming A > 0) to find x ≤ 20/A.
Explanation:
To solve the inequality for x in terms of a, we start with the given inequality:
Ax - 8 ≤ 12.
First, we add 8 to both sides to isolate the term with x on one side:
Ax ≤ 20
Next, assuming A is not zero, we divide both sides by A to solve for x:
x ≤ 20 / A
This is the solution to the inequality, with the understanding that it only applies if A is positive, because if A were negative, we would need to reverse the inequality sign when dividing by A.
One solution to the problem below is 5. What is the other solution? c^2 - 25 = 0
Answers
Answer:
c = -5
Step-by-step explanation:
Plug in -5 to c in the equation:
c² - 25 = 0
(-5)² - 25 = 0
Simplify. First, solve the power, then solve the subtraction:
(-5)² - 25 = 0
(-5 * -5) - 25 = 0
(25) - 25 = 0
0 = 0 (True)
~
Answer:
c=-5
Step-by-step explanation:
c^2-25=0
I'm going to solve this by using square root after I get the square termed by itself.
[tex]c^2-25=0[/tex]
Add 25 on both sides:
[tex]c^2=25[/tex]
Square root both sides:
[tex]c=\pm \sqrt{25}[/tex]
[tex]c=\pm 5[/tex]
Check!
[tex](5)^2-25=0 \text{ and } (-5)^2-25=0[/tex]
A system of two equations is shown below. What will you need to multiply the top equation by in order to solve this system using the elimination method?
X+2y=11
6x+4y=34
A.6
B.2
C.-2
D.-4
Answers
For this case we have the following system equations:
[tex]x + 2y = 11\\6x + 4y = 34[/tex]
To use the elimination method we must multiply the first by -2. So:
[tex]-2x-4y = -22\\6x + 4y = 34[/tex]
In this way, if we add the equations, the variable y is eliminated.
Answer:
-2
Option C
On the provided graph, select the locations of the x-intercepts of the following polynomial function. x^3-7x^2-26x+72
Answers
Answer:
The x-intercepts are the points (-4,0). (2,0) and (9,0)
The location of the x-intercepts in the attached figure
Step-by-step explanation:
we know that
The x-intercepts of a function are the values of x when the value of the function is equal to zero
we have
[tex]f(x)=x^{3}-7x^{2}-26x+72[/tex]
using a graphing tool
The x-intercepts are the points (-4,0). (2,0) and (9,0)
see the attached figure
Answer:
(-4,0), (2,0), (9,0)
Step-by-step explanation:
Correct on Plato
The expression on the left side of an equation is shown below.
-4(x-2)+5x=0
If the equation has no solution, which expression can be written in the box on the other side of the equation?
1)2(x + 4) - x
2)x+8
3)4(x + 2) - 5x
4)x
Answers
Answer:
4) x
Step-by-step explanation:
The expression on the left side simplifies to:
-4(x - 2) + 5x =
= -4x + 8 + 5x
= x + 8
To have an equation with no solution, you need the same x term on the right side but a different constant term. The x term on the left side is x. You need x on the right side but with a constant term different than 8.
Answer: 4) x
Answer:
D) x
Step-by-step explanation:
When simplified, the answer will result to a=b which means that it has no solution
If Jackie were to paint her living room alone, it would take 8 hours. Her sister Patricia could do the job in 9 hours. How long would it take them working together? If needed, submit your answer as a fraction reduced to lowest terms.
Answers
Answer:
(72/17) hours
Step-by-step explanation:
Time Jackie would take alone , J = 8 hrs
Time Patricia would take alone , P = 9 hrs
Let the time they will take together be T
use the formula for shared unit rate
[tex]\frac{1}{T}[/tex] = [tex]\frac{1}{J}[/tex] + [tex]\frac{1}{P}[/tex]
[tex]\frac{1}{T}[/tex] = [tex]\frac{1}{8}[/tex] + [tex]\frac{1}{9}[/tex]
[tex]\frac{1}{T}[/tex] = [tex]\frac{17}{72}[/tex]
T = [tex]\frac{72}{17}[/tex] hours (or 4.24 hours)
It takes them to work together for 4 hours and 14 minutes.
Ratio and proportionA ratio is an ordered pair of numbers a and b, written as a/b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
Given
Jackie was to paint her living room alone. It would take 8 hours.
Her sister Patricia could do the job in 9 hours.
To findHow long would it take them to work together?
How to get the solution?We know the work is inversely proportional to the time. And formula we have
[tex]\rm \dfrac{1}{T_f} = \dfrac{1}{T_1} +\dfrac{1}{T_2}[/tex]
We have
[tex]\rm T_1 = 8, \ \ \ and\ \ T_2 = 9[/tex]
Then by the formula.
[tex]\rm \dfrac{1}{T_f} = \dfrac{1}{8} +\dfrac{1}{9}\\\\\rm \dfrac{1}{T_f} = \dfrac{8+9}{8*9} \\\\\rm \dfrac{1}{T_f} = \dfrac{17}{72} \\\\T_f \ = \dfrac{72}{17}\\\\T_f \ = 4.24[/tex]
Then the time 4.24 will be 4 hours and 14 minutes.
Thus, it takes them to work together for 4 hours and 14 minutes.
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One carton of eggs contains 12 eggs.
Write an equation that can be used to find the number of eggs e in any number of cartons c.
e = 120
c= 12e
e=c+12
e=C +12
Answers
Answer:
it may be e=c+12
Step-by-step explanation:
common sense
For this case we have:
e: Variable representing the number of eggs
c: Variable representing the number of cartons of eggs.
So, if in each carton there are 12 eggs we can write the following equation:
[tex]e = 12c[/tex]
Answer:
The equation is: [tex]e = 12c[/tex]
In 1928, when the high jump was first introduced as a women's sport at the Olympic Games, the winning jump
for women was 70.0 inches, while the winning jump for men was 86.5 inches. Since then, the winning jump for
women has increased by about 0.48% per year, while the winning jump for men has increased at a slower rate,
0.4%. If these rates continue, when will the winning jump for women be higher than the winning jump for men?
after 110 years
after 248 years
after 265 years
after 270 years
Answers
Answer:
D) After 270 years
Answer:
Step-by-step explanation:
Given that in 1928, f(x) = the winning jump
for women was 70.0 inches and g(x) = the winning jump for men was 86.5 inches.
Increase = 0.48% for women and 0.4% for men
i.e. after x years [tex]f(x) =70(1.0048)^x \\\\g(x) = 86.5(1.004)^x[/tex]
Let us find when these two values would be equal.
That is at point of intersection
Solving we get x =244 years
Hence approximately after 248 years women will exceed men.
Which of the following terms best describes a condition in which a quantity
decreases at a rate that is proportional to the current value of the quantity?
O
A. Exponential growth
O
B. Positive slope
O
C. Negative slope
O
D. Exponential decay
Answers
Answer:
C- Negative Slope
This is because it you stated it is decreasing and it is proportional.
Negative slope best describes a condition in which a quantity decreases at a rate that is proportional to the current value of the quantity .
What is slope?The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.
What are types of slope?Depending upon the relationship between the two variables x and y and thus the value of the gradient or slope of the line obtained.
There are 4 different types of slopes, given as,
Positive slope: indicates that while moving from left to right in the coordinate plane, the line rises, which also signifies that when x increases, so do y.Negative slope : indicates that while moving from left to right in the coordinate plane, the line falls, which also signifies that when x increases, y decreases.Zero slope : the rise is zero, and thus applying the rise over run formula we get the slope of the line as zero.Undefined Slope: The slope of a vertical line is undefined.According to the question
A quantity decreases at a rate that is proportional to the current value of the quantity
As,
Slope decreases i.e when x increases, y decreases.
and the rate at which it is decreasing is proportional to the current value of the quantity .
Therefore ,
It best describes the negative slope .
Hence, the Negative slope best describes a condition in which a quantity decreases at a rate that is proportional to the current value of the quantity .
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Choose the equation that represents the line that passes through the point (−1, 6) and has a slope of −3.
Answers
Answer:
y = - 3x + 3
Step-by-step explanation:
The equation of a line in slope intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 3, hence
y = - 3x + c ← is the partial equation of the line
To find c substitute (- 1, 6 ) into the partial equation
6 = 3 + c ⇒ c = 6 - 3 = 3
y = - 3x + 3 ← equation of line
Answer: A
Step-by-step explanation:
FLVS Question, the answer is A !!
A new coffee shop can hold no more than 50 seats. The owner wants at least 20 of the seats to be stools and the remaining seats to be recliners. If x is the number of stools and y is the number of recliners, which graph represents the solution to the system of inequalities? x + y ≤ 50 x ≥ 20
Answers
The system of inequalities x + y ≤ 50 and x ≥ 20 can be graphically represented as two intersecting regions in a two-dimensional space, showing the possible combinations of stools (x) and recliners (y) the new coffee shop could have.
Explanation:The subject of the question is a system of inequalities which is a common topic in high school level algebra. In this case, the system of inequalities presented is x + y ≤ 50 and x ≥ 20, where 'x' represents the number of stools and 'y' represents the number of recliners in the new coffee shop.
In order to represent this system graphically, firstly, we draw two lines that correspond to the equations x + y = 50 and x = 20. The area of intersection between the two regions defined by these lines represents the solution to the system of inequalities.
For the inequality x + y ≤ 50, we shade the area below the line because the sign is 'less than or equal to', and for x ≥ 20, we shade to the right because of the 'greater than or equal to' sign. The overlap region satisfies both inequalities and represents the possible combinations of stools and recliners the coffee shop can have according to the owner's preferences.
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which ordered pair is a solution to the inequality 3x - 4y < 16 ?
Answers
Answer:
C.
Step-by-step explanation:
You are given 3x-4y<16 and we want to see which of the ordered pairs is a solution.
These ordered pairs are assumed to be in the form (x,y).
A. (0,-4) ?
3x-4y<16 with (x=0,y=-4)
3(0)-4(-4)<16
0+16<16
16<16 is not true so (0,-4) is not a solution of the given inequality.
B. (4,-1)?
3x-4y<16 with (x=4,y=-1)
3(4)-4(-1)<16
12+4<16
16<16 is not true so (4,-1) is not a solution of the given inequality.
C. (-3,-3)?
3x-4y<16 with (x=-3,y=-3)
3(-3)-4(-3)<16
-9+12<16
3<16 is true so (-3,-3) is a solution to the given inequality.
D. (2,-3)?
3x-4y<16 with (x=2,y=-3)
3(2)-4(-3)<16
6+12<16
18<16 is false so (2,-3) is not a solution to the given inequality.
Use the discriminant to determine what type of roots the equations will have, and categorize the equations according to their roots.
two distinct roots, One repeated root, two complex roots
x^2 − 4x + 2 = 0
5x^2 − 2x + 3 = 0
2x^2 + x − 6 = 0
13x^2 − 4 = 0
x^2 − 6x + 9 = 0
x^2 − 8x + 16 = 0
4x^2 + 11 = 0
Answers
Final answer:
The discriminant of a quadratic equation informs us about the nature of its roots. By calculating the discriminant for each given equation, we categorize them accordingly: equations with discriminant greater than zero have two distinct real roots, equal to zero have one repeated real root, and less than zero have two complex roots.
Explanation:
The discriminant of a quadratic equation ax² + bx + c = 0 is given by the expression b² - 4ac. The value of the discriminant determines the nature of the roots of the equation. To find the type of roots for each given equation:
x² − 4x + 2: The discriminant is (-4)² - 4(1)(2) = 16 - 8 = 8, which is greater than zero, so this equation has two distinct real roots.
5x² − 2x + 3: The discriminant is (-2)² - 4(5)(3) = 4 - 60 = -56, which is less than zero, indicating two complex roots.
2x² + x − 6: The discriminant is (1)² - 4(2)(-6) = 1 + 48 = 49, also greater than zero, leading to two distinct real roots.
13x² − 4 = 0 has a discriminant equivalent to that for x² − 4/13 = 0, which is 0² - 4(1)(-4/13) = 16/13, which is greater than zero, so this equation will have two distinct real roots.
x² − 6x + 9: The discriminant is (-6)² - 4(1)(9) = 36 - 36 = 0, indicating one repeated root.
x² − 8x + 16: The discriminant is (-8)² - 4(1)(16) = 64 - 64 = 0, which means this equation has one repeated root.
4x² + 11 = 0 has a discriminant equivalent to that for x² + 11/4 = 0, which is 0² - 4(1)(11/4) = -11, less than zero, thus resulting in two complex roots.
Through the method of using the discriminant, we can determine the types of roots each quadratic equation will have.
Evaluate -7a – 2b, if a = -1 and b = 2
Answers
Answer:
3
Step-by-step explanation:
Plug in the values for a and b= -7(-1)-2(2)
Multiply= 7-4
Subtract= 3
Hope this helps ^-^
Answer:
3
Step-by-step explanation:
We'd just substitute the value provided to us with the variable.
-7(-1) - 2(2)
-7 * -1 = 7
-2(2) = -4
7-4 = 3
Our answer is 3
The domain of the following relation: R: {(-4,8),(8,10),(5,4),(1,6),(5,-9) } is
Answers
Answer:
{-4, 8, 5, 1, 5}
Step-by-step explanation:
In a set of ordered pairs, the domain is the set of the first number in every pair.
If the set of ordered pairs is {(-4,8), (8,10), (5,4), (1,6), (5,-9)},
the domain is { -4, 8, 5, 1, 5}