Answer:
y = 14/3 and 2
x = -13/3 and 1
(-13/3, 14/3) and (1, 2)
Step-by-step explanation:
[tex]x + 2y = 5 - - - (a) \\ {x}^{2} - {y}^{2} = - 3 - - - (b)[/tex]
for equation (a)
make x the subject of the formular:
[tex]x = 5 - 2y - - - (c)[/tex]
for equation (b)
[tex] {x}^{2} - {y}^{2} = - 3[/tex]
substitute for x as 5 - 2y in equation (b):
[tex] {(5 - 2y)}^{2} - {y}^{2} = - 3 \\ (25 - 20y + 4 {y}^{2} ) - {y}^{2} = - 3 \\ 25 - 20y + 3 {y}^{2} = - 3 \\ {3y}^{2} - 20y + 28 = 0 \\ (3y - 14)(y - 2) = 0[/tex]
therefore,
[tex]y = \frac{14}{3} \: \: and \: \: 2[/tex]
substitute for all values of y in equation (c):
for y = 14/3:
[tex]x = 5 - 2( \frac{14}{3} ) \\ \\ x = 5 - \frac{28}{3} \\ \\ x = - \frac{13}{3} [/tex]
for y = 2:
[tex]x = 5 - 2(2) \\ x = 5 - 4 \\ x = 1[/tex]
Answer:
(1, 2)
(-13/3, 14/3).
Step-by-step explanation:
x + 2y = 5
x² - y² = -3
From the first equation x = 5 - 2y
Substitute for y in the second equation:
(5 - 2y)^2 - y^2 = -3
25 + 4y^2 - 20y - y^2 = -3
3y^2 - 20y + 28 = 0
Factoring:-
(3y - 14(y - 2) = 0
y = 2, 14/3.
So when y = 2, x = 5 - 2(2) = 1.
When y = 14/3, x = 5 - 2(14/3) = -13/3.
Checking the results in the second equation:
(1, 2):-
1^2 - 2^2 = -3 Correct.
(-13/3, 14/3):-
(-13/3)^2 - (14/3)^2 = -3 Correct.
What numbers are 3 units from -2 on a number line?
A number line ranging from negative 10 to positive 10
Select from the drop-down menus to correctly complete the statements.
______is 3 units left from -2 on a number line.
______- is 3 units right from -2 on a number line.
The answers are
-1
-5
1
5
please hurry
Answer:
___-5___is 3 units left from -2 on a number line.
___1___- is 3 units right from -2 on a number line
Multiply. Write your answer as a fraction in simplest form. −1/4×(−4/3)=
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given
- [tex]\frac{1}{4}[/tex] × - [tex]\frac{4}{3}[/tex] ( negative times negative = positive )
= [tex]\frac{1}{4}[/tex] × [tex]\frac{4}{3}[/tex] ( cancel the 4 on the numerator and denominator )
= [tex]\frac{1}{3}[/tex]
Help me with this math question plss
Answer:
C. 8/17
Step-by-step explanation:
PM = 16+14 = 30 cm
KP= LN = 16×tan45° = 16×1 = 16cm
by using pythagorean theorem, we find :
KM² = PM²+KP²
= 30²+16²
= 900+256
= 1156
=> KM =√1156 = 34cm
so, cos theta = KP/KM = 16/34 = 8/17
5. Classify the number 15.
O Whole, integer, rational, real
Integer, rational, real
O Natural, whole, integer, rational, real
O rational, real
Answer:
O Natural, whole, integer, rational, real
Step-by-step explanation:
it can be expressed as a fraction of 45/3, which means that it is rational.
it is a whole number because it does not contain a fraction or decimal.
it is a real number because it is a number we normally use such as 1, -0.1, 3/4, etc
it is a natural number because it is a positive integer.
and it is an integer because it does not contain a decimal.
Answer: Natural, whole, integer, rational, real
Find type of angle and solve for x.Please help.
Step-by-step explanation:
72° and a° is the angle of a straight line so
a+72°=180
a=180-72
a=108°
By using alternate exterior angle definition:
7x+24=180
7x=108-24
7x=84
x=84/7
x=12
A cookie company expanded its standard package of 36 cookies to include 4 extra cookies of a brand new flavor. If all of the cookies from an expanded package were put in a container and one were selected at random, what is the probability that it will be a cookie of the new flavor?
Answer:
1/9 probability
Step-by-step explanation:
The total cookies are 36 and the new flavors are 4, if you simplify 4/36, it equals 1/9
identity the value for a, b, and c.
2x^2=-7x-9
(Please help) Solve.
-4+4(-8+2n) = -37+8n
Answer:
No solutions for n
Step-by-step explanation:
Distribute the 4 to the -8 and the 2n
-4 + 4*-8 + 4*2n = -37 + 8n
Multiply
-4 - 32 + 8n = -37 + 8n
Subtract 8n on both sides
-4 - 32 = -37
Subtract on the left
-36 = -37
No solutions because -36 does not equal -37
Answer:
No solution
Step-by-step explanation:
-4 + 4(-8 + 2n) = -37 + 8n
-4 - 32 + 8n = -37 + 8n
-36 + 8n = -37 + 8n
8n - 8n = -37 + 36
0 = -1
Since 0 does not equal 1, this is a “No Solution”
What is the solution to the equation 1/4x - 1/8 = 7/8 + 1/2x ?
A. x = -5
B. x = -4
C. x = 4
D. x = 5
Hey there! I'm happy to help!
We want to get all of the variables on the left side and all of the numbers on the right side. This will allow our variable to be isolated so we can see what it is equal to.
1/4x - 1/8 = 7/8 + 1/2x
We add 1/8 to both sides.
1/4x=1+1/2x
We subtract 1/2x from both sides.
-1/4x=1
We divide both sides by -1/4 (same thing as multiplying -4).
B. x=-4
Have a wonderful day and keep on learning! :D
Help please.
Simplify: 5i/ 3 + 2i
Answer:
10+15i/13
Step-by-step explanation:
This question is about complex numbers.
so,
in this type of questions we have to multiply this fraction by the conjugate of the denominator
conjugate of the denominator is 3-2i
1) 5i(3-2i)/(3+2i)(3-2i)
2) 15i-10i^2/9-4i^2 ( we know that i^2 = -1 )
3) 15i+10/9+4
4) 15i+10 / 13
How many solutions are there to the equation below?
9x + 16 = 4x
A. infinitely many
B. 1
C. 0
Step-by-step explanation:
Infinitely many solutions are there....
hope it helps
Round
63.999
to two decimal places?
Answer:
64.00
Step-by-step explanation:
64.00 is the correct answer.
63.999 rounded to 2 decimal places is 64.00
What is the 5 rounding rule?In rounding off numbers, if the first figure dropped is 5, and all the figures following the five are zero or if there are no figures after the 5, then the last figure kept should be increased by 1 if that last figure is odd.
For example, if only two decimals are to be kept, then 6.755000 becomes 6.76.
Learn more about rounding off here https://brainly.com/question/10679598
#SPJ2
Can you answer this, please?
Answer: C) 3
Explanation:
The degree of a single variable polynomial is the largest exponent, which in this case is 3.
Which expression represents the number of sides in the polygon for the nth member of the sequence?
A) n+2
B) 2n + 1
C) 4n-3
D) 3n+2
Answer:
The answer is n+2.Step-by-step explanation:
I hope U like my answer and my answer helped U....Answer:
n+2 represemts the number of sides in the polygon for the nth member of the sequence
The product of 4 and a number x
Answer:
you can`t multiply an integer with a variable unless the variable represents something
ex: if x = 10 then the product of 4 and x is 40
Answer:
4x
Step-by-step explanation:
'Product' refers to multiplication.
What is the smallest integer greater than the square root of 325
Answer:
19
Step-by-step explanation:
√325 ≈ 18.02
The next greatest integer is 19.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Jocelyn is going to the amusement park, where she has to pay a set price of admission
and another price for tickets to go on each of the rides. The total amount of money
Jocelyn will spend is given by the equation y 3.5x + 28, where y represents the
total amount of money, in dollars and cents, and x represents the number of rides
Jocelyn goes on. What could the number 28 represent in the equation?
HELP ASAP will give BRAINLIEST
Hey there! I'm happy to help!
The question tells us that m∠JKL is 54. We see from the diagram that this is the combination of the angles m∠JKM and m∠MKL. So, we can combine their values, which are equal to 54 to find x.
13x+1+5x+4=54
We combine like terms
18x+5=54
We subtract 5 from both sides.
18x=49
We divide both sides by 18.
x=2.7222222....
Now, we want to find the measure of m∠MKL. We plug our x value into the value of this angle and evaluate.
5(2.722....)+4=17.61111....... or 17 11/18.
Have a wonderful day and keep on learning! :D
Solve the equation shown. 12+3/5x-4=29
Answer:
35
Step-by-step explanation:
12+3/5x=33
3/5x=21
x=21×5/3
x=35
Answer:
[tex]12 + \frac{3}{5} x -4 = 29[/tex]
x = 35
1) 3/5 x = 21
3x = 105
x = 35
Step-by-step explanation:
Determine the product of the binomial 6x−2 and the trinomial 3x2−5x−1.
Answer:
6(x-2)
Step-by-step explanation:
because x and 2 are taken as common by us
solve the following vertically opposite angle
Step-by-step explanation:
[tex]thank \: you[/tex]
Answer:
y = 20
BRAINLIEST, PLEASE!
Step-by-step explanation:
y = 20 (vertical angles are equivalent, and the opposite angle, which is vertical, is 20.)
Find the 68th multiple of 89, if the 69th multiple is 6141.
Answer:
6141 - 89 = The 68th multiple (6052)
A tree casts a shadow of 45 feet. If the angle of elevation to the top of the tree is 50º,
how tall is the tree?
Answer:
95
Step-by-step explanation:
add 50,45
The longer base of an isosceles trapezoid measures 23 ft. The nonparallel sides measure 9 ft, and the base angles measure 80°. Find the length of a diagonal.
Answer:
Hi,
Step-by-step explanation:
Using Al's kashi theorem,
diag²=9²+23²-2*9*23*cos(80°)=538,109654....
diag=23,197190... (ft)
PLEASE PLEASE TRANSLATING A SENTENCE INTO AN EQUATION
The difference of Jose's age and 21 is 58
Use the variable j to represent Jose's age.
Answer:
j - 21 = 58
Step-by-step explanation:
happy to help if you have any others i can help you
Answer:
j - 21 = 58
Step-by-step explanation:
Can someone show me how to factor this please?
Answer:
[tex]\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}[/tex]
Step-by-step explanation:
We want to solve the equation:
[tex]2\sin ^2 \theta + 3\sin \theta + 1 = 0[/tex]
In the interval [0, 2π).
Notice that this is in quadratic form. Namely, by letting u = sin(θ), we acquire:
[tex]\displaystyle 2u^2 + 3u + 1 = 0[/tex]
Factor:
[tex]\displaystyle (2u+1)(u+1) = 0[/tex]
By the Zero Product Property:
[tex]\displaystyle 2u + 1 = 0\text{ or } u + 1 = 0[/tex]
Solve for each case:
[tex]\displaystyle u = -\frac{1}{2} \text{ or } u = -1[/tex]
Back-substitute:
[tex]\displaystyle \sin \theta = -\frac{1}{2} \text{ or } \sin \theta =-1[/tex]
Use the Unit Circle. Hence, our three solutions in the interval [0, 2π) are:
[tex]\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}[/tex]
A(-2,3)
Triangle ABC has vertices at A(-2,3), B(-3,6), and
C(2,-1) Is triangle ABC a night triangle? If so, which
angle is the night angle?
O No, the triangle has no right angles.
O Yes, the right angle is angle A
O Yes, the right angle is angle B
O Yes, the right angle is angle C
VA
C (2-1)
B (-3,-6)
second choice i’m prolly wrong
Mr. Jones took a survey of college students and found that 60 out of 64 students
are liberal arts majors. If a college has 7505 students, what is the expected
number of students who are liberal arts majors?
Pringle's variety pack 18 cups for $6.48 cost per cup
Answer:
0.36
Step-by-step explanation:
Please help me with this problem
[tex] \sqrt{11} \: lies \: between \: 3 \: and \: 4[/tex]
Answer:
Lies between 3&4
See THE IMAGE FOR SOLUTION
