Answer:
a=3
b=24
Step-by-step explanation:
If [tex]x^2+x-12[/tex] is a factor of [tex]x^3+ax^2-10x-b[/tex], then the factors of [tex]x^2+x-12[/tex] must also be factors of [tex]x^3+ax^2-10x-b[/tex].
So what are the factors of [tex]x^2+x-12[/tex]? Well the cool thing here is the coefficient of [tex]x^2[tex] is 1 so all we have to look for are two numbers that multiply to be -12 and add to be positive 1 which in this case is 4 and -3.
-12=4(-3) while 1=4+(-3).
So the factored form of [tex]x^2+x-12[/tex] is [tex](x+4)(x-3)[/tex].
The zeros of [tex]x^2+x-12[/tex] are therefore x=-4 and x=3. We know those are zeros of [tex]x^2+x-12[/tex] by the factor theorem.
So x=-4 and x=3 are also zeros of [tex]x^3+ax^2-10x-b[/tex] because we were told that [tex]x^2+x-12[/tex] was a factor of it.
This means that when we plug in -4, the result will be 0. It also means when we plug in 3, the result will be 0.
Let's do that.
[tex](-4)^3+a(-4)^2-10(-4)-b=0[/tex] Equation 1.
[tex](3)^3+a(3)^2-10(3)-b=0[/tex] Equation 2.
Let's simplify Equation 1 a little bit:
[tex](-4)^3+a(-4)^2-10(-4)-b=0[/tex]
[tex]-64+16a+40-b=0[/tex]
[tex]-24+16a-b=0[/tex]
[tex]16a-b=24[/tex]
Let's simplify Equation 2 a little bit:
[tex](3)^3+a(3)^2-10(3)-b=0[/tex]
[tex]27+9a-30-b=0[/tex]
[tex]-3+9a-b=0[/tex]
[tex]9a-b=3[/tex]
So we have a system of equations to solve:
16a-b=24
9a-b=3
---------- This is setup for elimination because the b's are the same. Let's subtract the equations.
16a-b=24
9a-b= 3
------------------Subtracting now!
7a =21
Divide both sides by 7:
a =3
Now use one the equations with a=3 to find b.
How about 9a-b=3 with a=3.
So plug in 3 for a.
9a-b=3
9(3)-b=3
27-b=3
Subtract 27 on both sides:
-b=-24
Multiply both sides by -1:
b=24
So a=3 and b=24
Two classes are planning to go on a field trip together. One clas with 18 students is being joined by 6 boys and 11 girls from another class, giving an overall ratio of boys to girls on the field trip of 2 to 3. Boys made up what proportion of the original class?
To find the proportion of boys in the original class, divide the number of boys by the total number of students in the class.
Explanation:To find the proportion of boys in the original class, we need to compare the number of boys in the original class to the total number of students in the original class.
The original class had 18 students, and it was joined by 6 boys from another class. This means there are now 18 + 6 = 24 boys on the field trip.
The overall ratio of boys to girls on the field trip is 2:3, which means for every 2 boys, there are 3 girls. If we have 24 boys, we can find the number of girls by dividing 24 by 2 and then multiplying by 3. This gives us (24/2) * 3 = 36 girls.
So, the original class had 24 boys and 36 girls. To find the proportion of boys in the original class, we divide the number of boys (24) by the total number of students (24 + 36 = 60). This gives us 24/60 = 0.4, or 40%.
Let y = safe load in pounds and x = length in feet of a horizontal beam. A constant of proportionality k exists such that Y=k/x If a beam can hold 2,000 pounds at 15 feet, what is the safe load if the length of the beam is 10 feet?
Answers: 300 pounds, 3,000 pounds, 20,000 pounds
Answer:
3000 pounds
Step-by-step explanation:
first sub in info to find k
2000=k/15 ; multiply both sides by 15 ; k=30000. if k is the constant, then to find the safe load (y) with the new beam (x), we input our new info into the equation.
y=30000/10 ; y=3000
Answer:
Safe load of the beam is 3000 pounds.
Step-by-step explanation:
If a horizontal beam of x feet length can hold y pounds safe load, the expression that represents the relation between load and length of the beam is
y = [tex]\frac{k}{x}[/tex]
If y = 2000 pounds and x = 15 feet
then 2000 = [tex]\frac{k}{15}[/tex]
k = 15×2000 = 30000
Now we will calculate the safe load when beam is 10 feet long.
From the formula,
y = [tex]\frac{30000}{10}=3000[/tex] pounds
Therefore, safe load of the beam is 3000 pounds.
Two angles of a triangle have the same measure and the third one is 15 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.
The LARGEST angle has a measure of _____ degrees.
Answer:
70°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
let the equal angles be x then the third angle = x + 15
Sum the 3 angle and equate to 180
x + x + x + 15 = 180
3x + 15 = 180 ( subtract 15 from both sides )
3x = 165 ( divide both sides by 3 )
x = 55
Hence
The largest angle = x + 15 = 55 + 15 = 70°
2 + (-2 + 23) – Ӏ 8 - 9 Ӏ =
Answer:
Step-by-step explanation:
2+(-2+23)-/8-9/=
2+ 21- /-1/=
2+21-1=
2+20=
22
Please mark as brianliest! Hope this helps!
Answer:
Solution of the expression is 22.
Step-by-step explanation:
The given expression is 2 + (-2 + 23) – Ӏ 8 - 9 Ӏ
We have to solve this expression
2 + (-2 + 23) - | 8-9 |
= 2 + (21) - |-1 |
= 2 + 21 - 1 [Since absolute value of (-x) is x or |-x | = x ]
= 23 - 1
= 22
Solution of the expression is 22.
Two points are drawn on each side of a square with an area of 81 square units dividing the side into 3 congruent parts. Quarter-circle arcs connect the points on adjacent sides to create the figure shown. What is the length of the boundary of the bolded figure? Express your answer as a decimal to the nearest tenth.
Answer:
The length of the bold figure ABCDEFGH is 30.8 units
Step-by-step explanation:
* To solve the problem look to the attached figure
- There is a square of area 81 units²
∵ The area of the square = L² , where L is the length of the side of
the square
∵ The area of the square = 81 units²
∴ L² = 81 ⇒ take √ for both sides
∴ L = 9 units
- Two points are drawn on each side of a square dividing it into 3
congruent parts
∵ 9 ÷ 3 = 3
∴ The length of each part is 3 units
- Quarter-circle arcs connect the points on adjacent sides to create
the attached figure
∵ The radius of each quarter circle is 3 units
∵ The length of each side joining the two quarter circle is 3 units
∵ The figure ABCDEFGH consists of 4 quarters circle and 4 lines
- The length of the 4 quarters circle = the length of one circle
∵ The length of the circle is 2πr
∴ The length of the 4 quarters circle = 2 π (3) = 6π units
∵ The length of each line = 3 units
∴ The length of the figure = 6π + 4 × 3 = 30.8 units
* The length of the bold figure ABCDEFGH is 30.8 units
Answer:
30.8
Step-by-step explanation:
PLEASE HELP, I NEED TO BE HELPED WITH THESE QUESTIONS
Answer:
[tex](f+g)(x)=\sqrt{3x+7}+\sqrt{3x-7}[/tex]
[tex]f(g(x))=x+1[/tex]
[tex]f(x)=x+9 \text{ and } g(x)=\frac{4}{x^2}[/tex]
[tex]f^{-1}(x)=\frax{x+2}{3}[/tex]
Let me know if you have any questions about any of my work.
Step-by-step explanation:
You are given the following:
[tex]f(x)=\sqrt{3x+7} \text{ and } g(x)=\sqrt{3x-7}[/tex]
and asked to find [tex](f+g)(x) \text{ which means } f(x)+g(x)[/tex].
If you add those because we are asked to find f(x)+g(x) you get:
[tex]\sqrt{3x+7}+\sqrt{3x-7}[/tex]
----------------------------------------------------------
You are given the following:
[tex]f(x)=x^2+3 \text{ and } g(x)=\sqrt{x-2}[/tex]
and asked to find [tex]f(g(x))[/tex].
[tex]f(g(x))[/tex]
[tex]f(\sqrt{x-2})[/tex] I replaced g(x) with sqrt(x-2) because that is what it equals.
Now this last thing means to replace old input in x^2+3 with new input sqrt(x-2) giving us:
[tex](\sqrt{x-2})^2+3[/tex]
[tex]x-2+3[/tex]
[tex]x+1[/tex]
------------------------------------------------------------
We are given [tex]y=\frac{4}{x^2}+9[/tex] and asked to find g(x) and f(x) such that y=f(g(x)).
We have choices so let's use the choices:
Choice A:
[tex]f(g(x))[/tex]
[tex]f(\frac{4}{x^2}){/tex] I replace g(x) with 4/x^2:
[tex]\frac{4}{x^2}+9[/tex] I replaced the old input x with new input 4/x^2.
This was actually the desired result.
-----------------------------------------------------------
To find the inverse of f(x)=3x-2 or y=3x-2, your objective is to swap x and y and then remake y the subject.
y=3x-2
Swap x and y:
x=3y-2
Now solve for y.
Add 2 on both sides:
x+2=3y
Divide both sides by 3:
(x+2)/3=y
y=(x+2)/3
[tex]f^{-1}(x)=\frax{x+2}{3}[/tex]
Trey is a car salesman who earned a base pay of $47,300 and was paid
commission of 15% for each car he sold. If x represents total sales in dollars,
then which of the following equations best represents Trey's total pay in
dollars?
Answer:
Trey earns a base pay of $47,300 plus 15% for each car sold.
The equation that represets Trey's total pay in dollars is:
y = $47,300 + 0.15x
Where $47,300 represents the base pay, and 0.15x represents the money he earn for the total cars sold.
Answer:
[tex]y=47,300+0.15x[/tex]
Step-by-step explanation:
Let x represent total sales in dollars.
We have been given that Trey earns base pay of $47,300 and was paid commission of 15% for each car he sold.
Since Trey is paid 15% for each car he sold and total sales were x dollars, this means his commission would be 15% of x that is [tex]\frac{15}{100}x=0.15x[/tex].
The total salary of Trey would be base salary plus commission: [tex]y=47,300+0.15x[/tex]
Therefore, the equation [tex]y=47,300+0.15x[/tex] represents Trey's total pay in dollars.
Evaluate the expression
a-b/c*d
when a=48, b=18, c=3, and d=2
[tex]\huge{\boxed{36}}[/tex]
Substitute the values. [tex]48 - 18 \div 3 * 2[/tex]
Follow PEMDAS and multiply and divide first. [tex]48 - 6 * 2[/tex]
[tex]48 - 12[/tex]
Continue following PEMDAS and subtract. [tex]\boxed{36}[/tex]
Jade decided to rent movies for a movie marathon over the weekend. the function g(x) represents the amount of money spent in dollars where x is the number of movies. does a possible solution of 6.5,$ 17.50 make sense for this function. Explain your answer
A.yes the input is and output are both feasible
B. no the input is not feasible
C. no the output is not feasible
D. no neither the input nor output is feasible
kinda.
x = total of movies rented, INPUT
g(x) = total cost for all movies rented, OUTPUT.
the point of ( 6.5 , 17.50) means, that 6.5 movies were rented at a price of 17.50 total, that makes sense since 17.5 is more than 6.5 so the price is more than the quantity, however, whoever rents 6.5 movies? I mean, unless the movie store clerk gives you 6 movies and then cuts another with a chainsaw and gives you half of another.
so, the input is not too feasible, since no one rents 6.5 movies.
Answer:
B. No the input is not feasible
because you cannot rent 6,5 movies :p
How do I solve this problem? Thanks!
Answer:
92
Step-by-step explanation:
87 + 91 + 92 = 270
270 / 3 = 90
What is the product?
(x^2-16)/(2x+8) x (x^3-2x^2+x)/(x^2+3x-4)
a. x(x-4)(x-1)/2(x+4)
b. x(x-1)/2
c. (x+4)(x-4)/2x(x-1)
d. (x-4)(x-1)/2x(x+4)
Answer:
Option A is correct.
Step-by-step explanation:
We need to find the product of
[tex]\frac{(x^2-16)}{(2x+8)} * \frac{(x^3-2x^2+x)}{(x^2+3x-4)}[/tex]
We know (a^2-b^2) = (a+b)(a-b)
so, (x^2-16) = (x)^2-(4)^2 = (x-4)(x+4)
2x+8 Taking 2 common from this term:
2x+8 = 2(x+4)
(x^3-2x^2+x) Taking x common from this term
x(x^2-2x+1) = x(x-1)^2 = x(x-1)(x-1)
(x^2+3x-4) factorizing this term
x^2+4x-x-4 = x(x+4)-1(x+4)
= (x-1)(x+4)
Now, Putting these simplified terms in the given equation:
[tex]\frac{(x-4)(x+4)}{2(x+4)}*\frac{x(x-1)(x-1)}{(x-1)(x+4)}[/tex]
Now cancelling the same terms that are in numerator and denominator
[tex]=\frac{(x-4)}{2}*\frac{x(x-1)}{(x+4)}\\=\frac{(x-4)(x)(x-1)}{2(x+4)}\\=\frac{x(x-4)(x-1)}{2(x+4)}[/tex]
So, Option A is correct.
Answer:
=x(x-4)(x-1)/2(x+4)
Step-by-step explanation:
=x^2-4^2/2(x+4) * x^3-2x^2+x/x^2+3x-4
=(x+4)(x-4)/2(x+4) * x(x^2-2x+1)/x^2+3x-4
Factor x^2-2x+1 using the perfect square root
=(x+4)(x-4)/2(x+4) * x(x-1)^2/x^2+3x-4
Factor x^2+3x-4 using AC method.
=(x+4)(x-4)/2(x+4) * x(x-1)^2/(x-1)(x+4)
Cancel the common factor of x+4 and x-1
=(x-4)/2(x+4) * x(x-1)/1
=(x-4)x(x-1)/2(x+4)
Reorder the terms
=x(x-4)(x-1)/2(x+4)
How do you solve 0.3r = 2.1
I know the answer I just need to show my work
Answer:
7
Step-by-step explanation:
0.3r = 2.1
r = 2.1 ÷ 0.3
r = 7
What is 72/5 in decimal form
Answer:
14.4
Step-by-step explanation:
72/5 in decimal form equals 14.4
[tex]\frac{72}{5}[/tex] in decimal form is 14.4
[tex]\frac{72}{5}[/tex] is the same as 72 ÷ 5
72 ÷ 5 = 14.4
All we have to do to turn this fraction into a decimal is divide the fractions numerator by its denominator and we will get our decimal.
alpha and beta are the zeros of the polynomial x^2 -(k +6)x +2(2k -1). Find the value of k if alpha + beta = 1/2 alpha beta(ITS URGENT)
Answer:
[tex]k=\frac{-11}{2}[/tex].
Step-by-step explanation:
We are given [tex]\alpha[/tex] and [tex]\beta[/tex] are zeros of the polynomial [tex]x^2-(k+6)x+2(2k-1)[/tex].
We want to find the value of [tex]k[/tex] if [tex]\alpha+\beta=\frac{1}{2}[/tex].
Lets use veita's formula.
By that formula we have the following equations:
[tex]\alpha+\beta=\frac{-(-(k+6))}{1}[/tex] (-b/a where the quadratic is ax^2+bx+c)
[tex]\alpha \cdot \beta=\frac{2(2k-1)}{1}[/tex] (c/a)
Let's simplify those equations:
[tex]\alpha+\beta=k+6[/tex]
[tex]\alpha \cdot \beta=4k-2[/tex]
If [tex]\alpha+\beta=k+6[/tex] and [tex]\alpha+\beta=\frac{1}{2}[/tex], then [tex]k+6=\frac{1}{2}[/tex].
Let's solve this for k:
Subtract 6 on both sides:
[tex]k=\frac{1}{2}-6[/tex]
Find a common denominator:
[tex]k=\frac{1}{2}-\frac{12}{2}[/tex]
Simplify:
[tex]k=\frac{-11}{2}[/tex].
Someone help that is good in math
For this case we have:
[tex]x <2[/tex]Represents the solution of all strict minor numbers to 2.
[tex]x \geq2[/tex] Represents the solution of all numbers greater than or equal to 2.
The solution set, according to the figure, is given by the union of [tex]x <2[/tex] and [tex]x\geq2[/tex]. Thus, the complete solution is given by all the real numbers.
Answer:
Option D
what is 2% out of 3000
Answer:
It would be 60.
Answer:
Step-by-step explanation:
(3000×2)/100 = 6000/100 = 60
Tina's favorite shade of teal is made with 7 ounces of blue paint for every 5 ounces of green paint. Tyler's favorite shade of teal is made with 5 ounces of blue paint for every 7 ounces of green paint.
How does Tina's favorite shade of teal compare to Tyler's shade of teal?
A. Tina's favorite shade is more blue than Tyler's
B. Tina's favorite shade is greener than Tyler's
C. The two colors are the same
Answer:
A. Tina's favorite shade is more blue than Tyler's
Answer: The correct option is
(A) Tina's favorite shade is more blue than Tyler's.
Step-by-step explanation: Given that Tina's favorite shade of teal is made with 7 ounces of blue paint for every 5 ounces of green paint.
Tyler's favorite shade of teal is made with 5 ounces of blue paint for every 7 ounces of green paint.
We are to find how Tina's favorite shade of teal compare to Tyler's shade of teal.
The fraction of blue paint in Tina's favorite shade of teal is given by
[tex]F_{ti}=\dfrac{7}{7+5}=\dfrac{7}{12}[/tex]
and the fraction of blue paint in Tyler's favorite shade of teal is given by
[tex]F_{ty}=\dfrac{5}{7+5}=\dfrac{5}{12}[/tex]
We get
[tex]F_{ti}-F_{ty}=\dfrac{7}{12}-\dfrac{5}{12}=\dfrac{2}{12}=\dfrac{1}{6}>0\\\\\\\Rightarrow F_{ti}>F_{ty}.[/tex]
That is, the fraction of blue paint in Tina's favorite shade is more than the fraction of blue paint in Tyler's favorite shade.
Thus, Tina's favorite shade is more blue than Tyler's.
(A) is the correct option.
factor the expression 6g^3 + 8g^2 - 15g - 20
Answer:
(3g+4) (2g^2-5)
Step-by-step explanation:
6g^3 + 8g^2 - 15g - 20
Lets factor by grouping
Taking a 2 g^2 out of the first two terms and -5 out of the last two terms
2g^2 (3g+4) -5(3g+4)
Factoring out (3g+4)
(3g+4) (2g^2-5)
Answer:
The factors are (3g+4)(2g^2-5)....
Step-by-step explanation:
The expression is:
6g^3 + 8g^2 - 15g - 20
Make a group of the first two terms and last two terms:
(6g^3 + 8g^2) - (15g + 20)
Now factor out the common from each group:
2g^2(3g+4)-5(3g+4)
(3g+4)(2g^2-5)
Therefore the factors are (3g+4)(2g^2-5)....
PLEASE HELP ME 20 POINTS !! tyvm
ASAP
Answer:
[tex]\large\boxed{m\angle S=78^o}[/tex]
Step-by-step explanation:
[tex]\text{If}\ \triangle MNP\cong\triangle QST,\ \text{then corresponding angles}\\\text{and corresponging sides are congruent.}\\\\\angle M\cong\angle Q\\\angle N\cong\angle S\\\angle P\cong\angle\\\\m\angle N=78^o,\ \text{therefore}\ m\angle S=78^o[/tex]
If h(x) = (fog) (x) and h(x) = 4 square root x+7, find g(x) if f(x) = 4 square root x+ 1
Answer:
[tex]g(x)=x+6[/tex] is the answer
given
[tex]h(x)=4\sqrt{x+7}[/tex] and [tex]f(x)=4\sqrt{x+1}[/tex].
Step-by-step explanation:
[tex]h(x)=(f \circ g)(x)[/tex]
[tex]h(x)=f(g(x))[/tex]
Inputting the given function for h(x) into the above:
[tex]4\sqrt{x+7}=f(g(x))[/tex]
Now we are plugging in g(x) for x in the expression for f which is [tex]4\sqrt{x+1}[/tex] which gives us [tex]4\sqrt{g(x)+1}[/tex]:
[tex]4\sqrt{x+7}=4\sqrt{g(x)+1}[/tex]
We want to solve this for g(x).
If you don't like the looks of g(x) (if you think it is too daunting to look at), replace it with u and solve for u.
[tex]4\sqrt{x+7}=4\sqrt{u+1}[/tex]
Divide both sides by 4:
[tex]\sqrt{x+7}=\sqrt{u+1}[/tex]
Square both sides:
[tex]x+7=u+1[/tex]
Subtract 1 on both sides:
[tex]x+7-1=u[/tex]
Simplify left hand side:
[tex]x+6=u[/tex]
[tex]u=x+6[/tex]
Remember u was g(x) so you just found g(x) so congratulations.
[tex]g(x)=x+6[/tex].
Let's check it:
[tex](f \circ g)(x)[/tex]
[tex]f(g(x))[/tex]
[tex]f(x+6)[/tex] I replace g(x) with x+6 since g(x)=x+6.
[tex]4\sqrt{(x+6)+1}[/tex] I replace x in f with (x+6).
[tex]4\sqrt{x+6+1}[/tex]
[tex]4\sqrt{x+7}[/tex]
[tex]h(x)[/tex]
The check is done. We have that [tex](f \circ g)(x)=h(x)[/tex].
18. One biker rode at an average speed of 10.1 kilometers per hour. How far did
bikes
he ride in 5 hours?
Answer:
50.5 km
Step-by-step explanation:
If speed=distance/time, then distance=time*speed.
So we have the time and the speed to find the distance.
We just need to multiply 5 hours and 10.1 km/hour.
distance=(5 hours)(10.1 km/hour)
The time unit cancels and you are just left with the distance unit.
distance=50.5 km
Answer:50.5 km
Step-by-step explanation:
What theorem or postulate can be used to justify that AHIG EAFIE?
A. SAS
B. ASA
C. AAS
D. SSS
Answer:
ASA
Step-by-step explanation:
There is an included side in between both angles in each triangle.
I hope this helps you out, and as always, I am joyous to assist anyone at any time.
solve the following system of equations
2x – 3y = 6
4x+2y=4
Answer:
[tex]\boxed{(\frac{3}{2} ,-1)}[/tex]
Step-by-step explanation:
[tex]\left \{ {{2x-3y=6} \atop {4x+2y=4}} \right.[/tex]
It seems this system of equations would be solved easier using the elimination method (the x and y values are lined up).
Multiply everything in the first equation by -2 (we want the 4x to be able to cancel out with a -4x).
[tex]2x-3y=6 \rightarrow -4x+6y=-12[/tex]
Now line up the equations (they are already lined up - convenient) and add them from top to bottom.
[tex]\left \{ {{-4x+6y=-12} \atop {4x+2y=4}} \right.[/tex]
The -4x and 4x are opposites, so they cancel out.
Adding 6y and 2y gives you 8y, and adding -12 and 4 gives you -8.
[tex]8y=-8[/tex]
Divide both sides by 8.
[tex]y=-1[/tex]
Since you have the y-value you can substitute this in to the second (or first equation, it doesn't necessarily matter) equation.
[tex]4x +2(-1)=4[/tex]
Simplify.
[tex]4x -2=4[/tex]
Add 2 to both sides.
[tex]4x=6[/tex]
Divide both sides by 4.
[tex]x=\frac{6}{4} \rightarrow\frac{3}{2}[/tex]
The final answer is [tex]x=\frac{3}{2} ,~y=-1[/tex].
[tex](\frac{3}{2} ,-1)[/tex]
Find the area of the parallelogram whose three of the vertices are (1, -2), (2, 3) and (-3, 2) in order. Also find its fourth vertex .
do it
like this
i have done by coordinates of geometry
Answer:
Area = 24 square unit,
Fourth vertex = (-4, -3)
Step-by-step explanation:
Suppose we have a parallelogram ABCD,
Having vertex A(1, -2), B(2, 3), and C(-3, 2),
Let D(x,y) be the fourth vertex of the parallelogram,
∵ The diagonals of a parallelogram bisect each other,
Thus, the midpoint of AC = midpoint of BD
[tex](\frac{1-3}{2}, \frac{-2+2}{2})=(\frac{2+x}{2}, \frac{3+y}{2})[/tex]
[tex](\frac{-2}{2}, 0)=(\frac{2+x}{2}, \frac{3+y}{2})[/tex]
By comparing,
[tex]-2=2+x\implies x=-4[/tex]
[tex]3+y=0\implies y = -3[/tex]
Thus, the fourth vertex is (-4, -3),
Now, the area of the parallelogram ABCD = 2 × area of triangle ABC (Because both diagonals divide the parallelogram in two equal triangles)
Area of a triangle having vertex [tex](x_1, y_1)[/tex], [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] is,
[tex]A=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
So, the area of triangle ABC
[tex]A=\frac{1}{2}|(1(3-2)+2(2+2)-3(-2-3)}|[/tex]
[tex]=\frac{1}{2}(1+8+15)[/tex]
[tex]=\frac{1}{2}\times 24[/tex]
[tex]=12\text{ square unit}[/tex]
Hence, the area of the parallelogram ABCD = 2 × 12 = 24 square unit.
2x + y = 8 x + y = 4 The lines whose equations are given intersect at (4, 0) (0, 4) all points on the line
Answer:
(4,0)
Step-by-step explanation:
Plug them into see:
Check (4,0)
In order for the lines to intersect at (4,0) it must be on both lines.
2(4)+0=8 is true because it is saying 8=8
4+0=4 is true because 4=4
So (4,0) is a intersection point.
Check (0,4)
2(0)+4=8 is not true because it is saying 4=8
0+4=4 is true so it's on this line while not on the other line.
So (0,4) is not an interestion point for the mentioned lines.
Well all points can't be on the line since (0,4) is not on both lines but just one of them.
We could have solve this out instead plugging in but the problem gave us the option here with the choices.
The system of linear equations given intersects at the point (4, 0), and since these equations represent distinct lines, they only intersect at this single point.
The question involves solving a system of linear equations to find the point of intersection. The system given is:
2x + y = 8x + y = 4Let's solve the equations step by step:
Subtract the second equation from the first to eliminate y, getting 2x - x + y - y = 8 - 4, which simplifies to x = 4.Substitute x = 4 into the second equation: 4 + y = 4, solving for y, which gives y = 0.Therefore, the lines intersect at the point (4, 0).
To determine whether the lines intersect at all points on a line, note that these equations represent distinct lines with different slopes, meaning they only intersect at one point, facing the choice given, (4, 0) is correct.
Which two operations are needed to write the expression that represents "eight more than the product of a number and
two"?
Answer:
Addition and Multiplication
Step-by-step explanation:
The keywords more than in this case means "addition", and the keyphrase product of a number and two means "multiplication". Here is what your expression should look like:
2n + 8
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If sin A = 3/5 and the cosA =4/5 then what is tan A
Answer:
Tan A = 3/4
Step-by-step explanation:
sin A = y/r
Cos A = x/r
Tan A = y/x
Answer:
3/4
Step-by-step explanation:
sin A = 3/5
cosA =4/5
We know that tan A = sin A / cos A
= 3/5 / 4/5
= 3/5 * 5/4
= 3/4
Consider the equation (x^m)=(x^13)^5 x(x^-8)^-5
The value of m is
A. 15
B. 28
C. 35
D. 70
Answer:
m = 106Step-by-step explanation:
[tex]x^m=(x^{13})^5x(x^{-8})^{-5}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\x^m=(x^{(13)(5)})x(x^{(-8)(-5)})\\\\x^m=(x^{65})x^1(x^{40})\qquad\text{use} \ a^na^m=a^{n+m}\\\\x^m=x^{65+1+40}\\\\x^m=x^{106}\Rightarrow m=106[/tex]
I ONLY HAVE TILL TONIGHT PLZ SAVE ME I WILL MARK YOU THE BRAINLEST IF YOU ANSWER MY FULL QUESTION
Answer:
This graph is a not a Function because it doesn't pass the vertical line test. The opened and closed circles are not in relation to the y-value and the x-value. This function also doesn't corresponds to one another, which messes up the domain and range.
Step-by-step explanation:
The average NBA ticket price for the 2018-2019 season is up 14.01% from the average ticket price of $78 during the 2015-2016 season. what is the average ticket price in 2018-2019? Round to the nearest penny.
The average ticket price in 2018-2019 by calculating increase and add it to previous year ticket price and rounded it to the nearest penny is $88.93
Given that the average NBA ticket price for the 2018-2019 season is up 14.01% from the average ticket price of $78 during the 2015-2016 season.
To find the average ticket price in 2018-2019 by calculating increase and add it to previous year ticket price and rounded it to the nearest penny.
Step 1: Find the increase ticket price by multiplying the increase % with the previous ticket price:
Increase ticket price = increase % x previous ticket price
Plugging the given data:
Increase ticket price = 14.01 % x 78
Convert percent into decimal:
Increase ticket price = 0.1401 x 78
On multiplying gives:
Increase ticket price = $10.9278
Step 2: Find the average ticket price in 2018-2019 by add it to previous year ticket price :
average ticket price= previous ticket price +Increase ticket price
Plugging the given data:
average ticket price=78 + 10.9278
On adding gives:
average ticket price=88.9278
Round to the nearest penny
average ticket price = $88.93
Therefore, the average ticket price in 2018-2019 by calculating increase and add it to previous year ticket price and rounded it to the nearest penny is $88.93
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Final answer:
The average NBA ticket price for the 2018-2019 season, based on a 14.01% increase from the 2015-2016 average of $78, is approximately $88.93 after rounding to the nearest penny.
Explanation:
To calculate the average NBA ticket price in the 2018-2019 season, we can use the percentage increase from the 2015-2016 season ticket price. We start with the average ticket price of $78 during the 2015-2016 season. According to the question, the ticket prices have increased by 14.01%. This percentage needs to be converted into a decimal (by dividing by 100) and then multiplied by the original average price to find the increase amount.
The calculation for the increase amount will be:
Convert the percentage increase into a decimal: 14.01% ÷ 100 = 0.1401.
Multiply this decimal by the original average price: 0.1401 × $78 = $10.9278.
Add this increase to the original average price to get the new average price: $78 + $10.9278 = $88.9278.
When we round this to the nearest penny, the new average ticket price for the 2018-2019 season is approximately $88.93.