[tex] \boxed{(x - a)(x - b) = 0}[/tex]
The equation above is the intercept form. Both a-term and b-term are the roots of equation.
[tex]x = - \frac{1}{3} \\ x = 5[/tex]
These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.
[tex](x + \frac{1}{3} )(x - 5) = 0[/tex]
Here we can convert the expression x+1/3 to this.
[tex]x + \frac{1}{3} = 0 \\ 3x + 1 = 0[/tex]
Rewrite the equation.
[tex](3x + 1)(x - 5) = 0[/tex]
Simplify by multiplying both expressions.
[tex]3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0[/tex]
Answer Check
Substitute the given roots in the equation.
[tex]3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0[/tex]
[tex]3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0[/tex]
The equation is true for both roots.
Answer
[tex] \large \boxed {3 {x}^{2} - 14x - 5 = 0}[/tex]
Solve this A tourist starts off from town A and travels for 50km on a bearing of N80°W to town B.At town B ,he continues for another 40kmbon a bearing of N20°E toC. How far is C from A?
Answer:
The point C is 12.68 km away from the point A on a bearing of S23.23°W.
Step-by-step explanation:
Given that AB is 50 km and BC is 40 km as shown in the figure.
From the figure, the length of x-component of AC = |AB sin 80° - BC cos 20°|
=|50 sin 80° - 40 cos 20°|=11.65 km
The length of y-component of AC = |AB cos 80° - BC sin 20°|
=|50 cos 80° - 40 sin 20°|= 5 km
tan[tex]\theta[/tex]= 5/11.65
[tex]\theta[/tex]=23.23°
AC= [tex]\sqrt{5^2+11.65^2}=12.68[/tex] km
Hence, the point C is 12.68 km away from the point A on a bearing of S23.23°W.
help me pls...
I will give 20 points and brainly
Answer:
[tex]1 \times { 10}^{ - 9} m[/tex]
Step-by-step explanation:
It can be written in scientific notation as [tex]1 \times { 10}^{ - 9} m[/tex],
Hope this helps u.... ^_^❤️Answer:
a) 1 nm = 0. 000 000 001 m
b) 1 nm = 1×10⁻⁹ m
Consider the system of linear equations.
2y =x+ 10
3y = 3x + 15
Which statements about the system are true? Check all
that apply.
-The system has one solution.
-The system graphs parallel lines.
-Both lines have the same slope.
-Both lines have the same y-intercept.
-The equations graph the same line.
-The solution is the intersection of the 2 lines.
Answer:
-The system has one solution
-Both lines have the same y-intercept
-The solution is the intersection of the 2 lines
Step-by-step explanation:
When you graph the two lines, you get the intersection at (0,5)
The slope of one line is 0.5 and the other is 1.
The lines are not parallel because they intersect, parallel lines would never intersect.
The equations do not graph the same line, they would be one on top of the other and have infinite solutions.
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y=1x-8
Step-by-step explanation:
the y intercept is the b in y=mx+b
Look at the image bel9w
Answer:
it's your answer
Step-by-step explanation:
60+5(6÷2)
60+30÷10
60+3
63
18+(10-6)square
18+(100-36)
18+64
82
Ryan is building a tree he use. It will take hours to complete. He can work on the tree
house hours each day. tow many days will it take Ryan to complete the tree
house?
Answer:
come have IT with me baby
Step-by-step explanation:
it will make us feel better
Solve the system of linear equations by elimination.
−2x+6y=−10
4x+3y=5
Answer: 2x+3y=5,4x+6y=10
Have a great day and remember to subscribe.!!
-Lilly Ketchmen
Answer:
x = 2 and y = -1
Step-by-step explanation:
simplify the first equation by dividing each term by -2
x - 3y = 5
now you can add this to 4x + 3y = 5 and the 'y-values' will be eliminated and you will have:
5x = 10
x = 2
substitute '2' for 'x' to solve for 'y':
-2(2) + 6y = -10
-4 + 6y = -10
6y = -6
y = -1
Given the following table, find the rate of change between 1-4) and 10).
х
-4 -2 0 2 4
f) -2 -1 0 1 2
Answer:
1/2Step-by-step explanation:
As per given table there are pairs:
(-4, -2), (-2, -1), (0, 0), (2, 1), (4, 2)This is line passing through the origin and the equation is:
f(x) = 1/2xRate of change is the slope 1/2, which is same over any interval
Ben is making a chart in which he is listing the masses of different planetary bodies. He plans to write the masses in scientific notation. Convert the values in scientific notation to standard notation.
The mass of Ganymede is 1.48E23, or
, kilograms.
The mass of Pandora is 2.20E17, or
, kilograms.
Answer:
1.48E23 in standard notation is 148,000,000,000,000,000,000,000 and 2.20E17 is 220,000,000,000,000,000
Answer:
1.48E23 in standard notation is 148,000,000,000,000,000,000,000 and 2.20E17 is 220,000,000,000,000,000
Step-by-step explanation:
Evaluate the expression 3(9 - 16)
Answer:
Just use the distributive property.
3 times 9 is 27, and -16 times 3 is -48.
This means your expression comes out to be:
27-48
Solve that, and you get -21
If the correlation coefficient between two variables is .90, what percent of the variance is explained by this correlation
Answer: 81% of the variance in dependent variable is explained by this correlation .
Step-by-step explanation:
For X = Independent variable and Y=dependent variable,
If r= correlation coefficient , then we say [tex]r^2[/tex] of the variance in Y is explained by Variable X.
Given: r= 0.90
[tex](0.90)^2= 0.81[/tex]
So, 81% of the variance in dependent variable is explained by this correlation .
In AEFG, EF = 44 centimeters and FG = 12 centimeters. Which of the following best describes the possible length, in centimeters, of
AO 44
B. O 32
CO 12
D. 32 < EG < 44
Answer:
The best inequality describes the possible length of EG is 32 < EG < 56 ⇒ B
Step-by-step explanation:
In any triangle
The sum of the lengths of any two sides must be greater than the length of the third sideThe length of any side is greater than the difference between the lengths of the other two sidesIn Δ EFG
∵ EF = 44 cm
∵ FG = 12 cm
→ Find their sum and difference
∴ The sum of their length = 44 + 12 = 56 cm
∴ The difference between their length = 44 - 12 = 32 cm
→ By using the rule above
∵ EG is the third side
∴ EG < 56
∴ EG > 32
→ Write them in one inequality
∴ 32 < EG < 56
∴ The best inequality describes the possible length of EG is 32 < EG < 56
0.625 divided by 0.56
Answer:
1.116071429
Step-by-step explanation:
This is an irrational number, but if you round it, it should be about 1 or 1.12. You can put this in the calculator btw :)
IM GOING TO START CRYING PLEASE HELP ME THIS IS SO HARD
Answer: what is
Step-by-step explanation:
Answer:
there is nothing ................
People most likely need to take out a mortgage when they
a) have bad credit.
b) are making a large purchase.
c) are spending less than $1,000.
d) have legal problems.
FIRST ANSWER GETS BRAINLIEST ;)
Answer:
a or c
Step-by-step explanation:
Which of the following equations represents a proportional relationship?
a
y = 5x
b
y = x + 1/2
c
y = 1/2 x + 5
d
y = 5/x
Answer:
(a)
Step-by-step explanation:
The equation representing a proportional relationship is
y = kx ← k is the constant of proportion
The only equation fitting this description is (a) y = 5x
Find the value of x in the triangle shown below.
X=____
Please help!!
Answer:
62
Step-by-step explanation:
the sum of all angles in a triangle should be 180°
180-56= 124
124÷2= 62
x= 62
Answer:
The sum of the interior angles of a triangle is 180°.
Two sides of the triangle is same, so the their corresponding angles will also be same.
[tex]x + x + 56 = 180 \\ 2x = 180 - 56 \\ 2x = 124 \\ \boxed{x = 62°}[/tex]
62° is the right answer.Find the 94th term of the arithmetic sequence -26,-37,-48,...
Answer: -997
Step-by-step explanation:
It keeps going down by 11 so it becomes -11. Then multiply that by 93 and you get 1,023 then add 26 to that to get the answer.
Does anyone knows how to solve thiss
Is this shape a regular polygon
jesus joseph maryian christ, what is this math problem ? 25 points
Answer:
1,075,920,000,000 km³
if P=(-3,4), find: Ry-axis (P)
Answer:
(3,4)
Step-by-step explanation:
what is the answer to 72.8+164.02+174.01
Answer:410.83
Step-by-step explanation:
Just add, its easy
Answer:
410.83
Step-by-step explanation:
Hope this helps!!!
I do not understand this. Can you please explain.
Answer:
E
Step-by-step explanation
y^(3/5) = [tex]\sqrt[5]{y{3}}[/tex]
y^(-3/5) = 1/[tex]\sqrt[5]{y{3}}[/tex]
Each time Miranda goes to the store she plans to spend \$7$7dollar sign, 7, and each time Savannah goes to the store she plans to spend \$9$9dollar sign, 9. A few weeks from now, Miranda and Savannah are surprised to find out that they have spent the exact same total amount of money at the store. What is the least possible number of times that Miranda has been to the store
Answer:
9 visits
Step-by-step explanation:
Given that:
Amount spent by Miranda per visit = $7
Amount spent by Savanah per visit = $9
To obtain the least number of visits by Miranda ;
We obtain the L. C. M of 7 and 9, the. Divide by the amount she spends per visit ;
Multiples of :
7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77
9 = 9, 18, 27, 36, 45, 54, 63, 72, 81
Hence, lowest common multiple of 7 and 9 is 63 ;
Hence, least possible. Number of visits by Miranda is ; 63 / 7 = 9 visits
what is the value of -6-(x+3)y when x = -5 and y = 2????
Answer:
-2
Step-by-step explanation:
Answer: -2
Step-by-step explanation:
Substitute -5 for x and 2 for y in the expression, which gives -6 minus the quantity -5+3, all divided by 2.
Then, use the order of operations to simplify the numerator of the expression. Finally, simplify the fraction, which gives -2. So, when x equals -5 and y equals 2, the expression is equal to -2.
Cory has a sister named Jessica. Jessica is 7
years older than twice Cory's age. Write an
expression that represents the relationship of
Jessica's age in terms of Cory's age, c.
Answer:
2c+7
Step-by-step explanation:
Jessica is 7 more than 2x Cory's age.
Given that Cory is c years old,
then Jessica is
2c+7
I hope this helps! :)
Tyrone is designing a new recycling
program for a school. Tyrone charges the
school $1125 for 9 hours of consulting
work. His rate is constant.
Answer:
125$ per hour
Step-by-step explanation:
Answer: 125 dollars per hour
Step-by-step explanation:
1125 / 9 = 125
Solve for X and solve for Y?
Answer:
[tex] x=3\sqrt 5\\[/tex]
[tex]y = \sqrt {126}[/tex]
Step-by-step explanation:
By geometric mean property:
[tex]x = \sqrt{9 \times 5} = \sqrt{45} = 3 \sqrt{5} \\ \\ by \: pythagoras \: theorem \\ \\ {y}^{2} = {9}^{2} + {x}^{2} \\ \\ {y}^{2} = {9}^{2} + {(3 \sqrt{5}) }^{2} \\ \\ {y}^{2} = 81 + 45 \\ \\ {y}^{2} = 126 \\ \\ y = \sqrt{126} [/tex]
I'm so confused
At the beginning of the school year, the number of students in the band was the same as the number of students in the choir. Throughout the school year, the number of students in the band decreased by 8, and the number of students in the choir decreased by 4. At the end of the school year, the number of students in the choir was 25% more than the number of students in the band. How many students were in the band at the beginning of the school year?
At the beginning of the school year, _________ students were in the band
Answer: 16............................
Answer:
16
Step-by-step explanation:
4=25%
