Answer:
a = - 2, [tex]\frac{9}{4}[/tex] , b = 2, - [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
Since x = 1, y = 2 is a solution to the equations , then substitute these values into the 2 equations and solve for a and b
a + 2b = 2 → (1)
b + 2a² = 10 → (2)
In (1) subtract 2b from both sides
a = 2 - 2b → (3)
Substitute a = 2 - 2b into (2)
b + 2(2 - 2b)² = 10 ← expand parenthesis using FOIL
b + 2(4 - 8b + 4b²) = 10 ( simplify left side )
b + 8 - 16b + 8b² = 10 ( subtract 10 from both sides )
8b² - 15b - 2 = 0
Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term
product = 8 × - 2 = - 16 and sum = - 15
The factors are - 16 and + 1
Use these factors to split the b- term
8b² - 16b + b - 2 = 0 ( factor first/second and third/fourth terms )
8b(b - 2) + 1(b - 2) = 0 ← factor out (b - 2) from each term
(b - 2)(8b + 1) = 0
Equate each factor to zero and solve for b
b - 2 = 0 ⇒ b = 2
8b + 1 = 0 ⇒ 8b = - 1 ⇒ b = - [tex]\frac{1}{8}[/tex]
Substitute these values into (3) and evaluate for a
b = 2 ⇒ a = 2 - 2(2) = 2 - 4 = - 2
b = - [tex]\frac{1}{8}[/tex] ⇒ a = 2 - 2(- [tex]\frac{1}{8}[/tex] ) = 2 + [tex]\frac{1}{4}[/tex] = 2 [tex]\frac{1}{4}[/tex] = [tex]\frac{9}{4}[/tex]
The possible values of a and b are 8, -3 or 9/4 , -1/8 respectively.
What is an equation ?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equations are,
ax + by = 2 (1)
and bx + a²y = 10 (2)
Also, x = 1 and y = 2 are the solution of the equation,
Substitute x = 1 and y = 2in equation (1),
a(1) + b(2) = 2
a + 2b = 2 (3)
Further substitute x = 1 and y = 2 in equation (2),
b(1) + a²(2) = 10
2a² + b = 10 (4)
By solving equation (3) and (4),
The possible values of a are 8 and 9/4.
And possible value of b are -3 and -1/8.
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Write the inequality that represents the solution set to the given inequality below.
|x−3|<15
Group of answer choices
12 x>−18
−12>x>18
Answer:
-12 < x < 18
Step-by-step explanation:
x-3 < 15
x < 18
and
-x + 3 < 15
-x < 12
x > -12
A farmer decides to make three identical pens with 88 feet of fence. The pens will be next to each other sharing a fence and will be up against a barn. The barn side needs no fence. What dimensions for the total enclosure (rectangle including all pens) will make the area as large as possible?
Answer:
The long fence, AC = 44 feet
4 shorter segments at 11feet each = 44 feet
Area = 484 ft^2
Step-by-step explanation:
The three pens will share one fence section parallel to the barn, we'll call it AB. Each pen will need two side fence segments, from the front fence to the barn. We'll call those portions AC. We need four of them: two for the outer sides and two more to divide up the space equally among the three pens. The total area would be AB*AC.
We know that AC + 4AB = 88 feet.
or AC = (88feet - 4AB)
Area = AB(88feet - 4AB)
Area = 88AB - 4AB^2
To maximize the area, we can take the first derivative and set it equal to zero:
Area' = 88 - 8AB
0 = 88 - 8AB
AB = 11 feet
AC = (88 - 4AB)
AC = (88 - 44)
AC = 44 feet
The fours segments of fence:
AC + 4AB = 88 feet
(44) + 4(11 feet) = 88feet
Area = 44' x 11 ft' = 484 ft^2
--
△XYZ = △KLM,m
Find m
Answer:
<m is equal to the measure of <Z
_______________________________________
Hope this helps!!
Please tell me if I have made a mistake!!
I enjoy learning form them:)
What is the solution to the system of equations?
Answer:
a set of values for the variable that satisfy all the equations simultaneously.
Step-by-step explanation:
search it
what is the slope of the line tha passes through the points (4,-9) and (8,-3)
Gillian can jog 100 metres in 24 seconds. How long will it take her to jog 2 km?
Answer:
8 minutes or 480 seconds
Step-by-step explanation:
1 km = 1000 m
100x20=2000
24 x 20 = 480
480/60 = 8
Answer:
Step-by-step explanation:
A pancake recipe calls for 4 eggs and 12 cups of flour. How many cups of flour would you need for a single egg?
Answer:
3
Step-by-step explanation:
i'd say 3
i divided 12 by 4 and then multiplied by one, since that is the amount of eggs we want
good luck! <3
Write the equation for the line in slope intercept form
Answer:
y = -x + 5
Step-by-step explanation:
lmk if you want an explanation
Archie and Michael are helping their friend George move the washers and dryers from his laundromat to a larger building. Archie's truck is carrying three washers and four dryers that have a combined mass of 1260 kg Michael's truck is carrying two washers and three dryers that have a combined mass of 880 kg.
How much does one of George's washers weigh?
Answer:
A
Step-by-step explanation:
Yes
Each batch of 24 cookies needs 2.25 cups of flour. If Stacy and her mom bake 3.5 batches, how much flour is
needed?
Show work !
Answer:
7 7/8 cups of flour
Step-by-step explanation:
2.25 times 3.5 equals 7.875
If you change something about an atom, you change the type of element it makes.
A. True
B. False
No links
Answer:
B
Step-by-step explanation:
Depends on what you change. If you change the number of electrons or neutrons, it will still be the same element. It will just become a charged ion or an isotope respectively. If you change the number of protons, it will become a different element.
Hope that helps
The point (-5,0) is plotted on a coordinate plane.
What is the point of reflection when (-5,0) is reflected across the y-axis?
A-(0,5)
B-(-5,0)
C-(0,-5)
D-(5,0)
[tex]\huge\boxed{Hello! :)}[/tex]
We plot the point (-5,0) on the coordinate plane.
Then, we reflect it over the y-axis.
Remember the rule:
If a point has coordinates (x, y), and the point is reflected over the y-axis, the new point's coordinates are: (-x,y)Let's use this rule now.
We reflect (-5,0) over the y-axis.
(-5,0)
The new point is: (5,0)
[tex]\huge\boxed{(5,0) \: is \: the \: answer. :)}[/tex]
(Option D)
[tex]\boxed{Felicitous\: Girlie\: here\: to\: help}[/tex]
the LCM and GCF of 66 and 101
Answer:
GCF: 1
LCM: 6,666
Step-by-step explanation:
I hope this helps!
21²/0.219 to 2 significant figures
what is 3x + 4y = 10
6x - 4y = 8
Answer:
x=2
y=1
Step-by-step explanation:
9x+0=18
so it's x=2
6=4y=10
so y=1
A triangle has two sides of length 2 and 18. What is the largest possible whole-number length for the third side?
Answer:
19
Step-by-step explanation:
Given 2 sides of a triangle then the third side x is
difference of 2 sides < x < sum of 2 sides , that is
18 - 2 < x < 18 + 2
16 < x < 20
Then the largest possible length of the third side is 19
What is the equation of a line perpendicular to minus x plus 2 equal y that intersects the line at open parentheses minus 1. 5 comma space 3. 5 close parentheses ?.
The required equation of a line perpendicular is y = x + 5
Given the equation y = -x + 2, the slope of the line is -1
The slope of the line perpendicular will be m -1/-1 = 1.Given the point (-1.5, 3.5)Substitute the slope and the point into the point-slope form of the equation expressed as:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-3.5=1(x-(-1.5))\\y-3.5=x+1.5\\y=x+1.5+3.5\\y=x+5[/tex]
Hence the required equation of a line perpendicular is y = x + 5
Learn more on equation of a line here: https://brainly.com/question/19417700
The diameter of the sun is about is about 1 390 000 km;
use scientific
notation to represent this diameter.
Answer:
1.39×10^6
Step-by-step explanation:
Hide 1 then count how many numbers are after it(6 numbers), that will be the power/exponent you will use
Please help
Me solve this ASAP
Answer:
i dont know it looks complicated
Step-by-step explanation:
copy paste then search it, you might find it.
what does x equals to if 3( x + 7 ) =57
3(x + 7) = 57 |÷3
x + 7 = 57/3
x + 7 = 19 |-7
x = 19 - 7
x = 12
Use the properties of operations to write an expression equivalent to 4x+1/2+2x-3. Please include explanations. Thanks!
Answer:
[tex]6x -2\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]4x + \frac{1}{2} + 2x - 3[/tex] Addition of like terms
[tex]6x + \frac{1}{2} - 3[/tex] Addition of content terms
[tex]6x -2\frac{1}{2}[/tex]
ASAP help 50 points Please hurry
Answer:
Step-by-step explanation:
Y=7
Let it be x
[tex]\\ \sf\longmapsto \dfrac{150}{x}=\dfrac{150+150}{280}[/tex]
[tex]\\ \sf\longmapsto \dfrac{150}{x}=\dfrac{300}{280}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{x}=\dfrac{2}{280}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{x}=\dfrac{1}{140}[/tex]
[tex]\\ \sf\longmapsto x=140ft[/tex]
can somebody help me
Jason has $45.00. He wants to buy equal numbers of soft drinks and sandwiches. A soft drink costs $0.79. A sandwich costs $2.49.
Part A
How much does a sandwich and drink cost together?
$
Part B
How many can he buy with $45.00?
soft drinks and
sandwiches
Part C
How much change will Jason get?
$
Answer:
Step-by-step explanation:
How much does a sandwich and drink cost together?
($0.79 + $2.49) = $3.28
How many can he buy with $45.00?
$45/$3.28 = 13.72 or 13 sandwich/soda combos.
13 soft drinks and
13 sandwiches
How much change will Jason get?
$45 - 13($3.28) = $2.36
A 14-oz iced tea at a certain restaurant has 140 calories. How many calories are there in a 22-oz iced tea?
Answer:
220 calories
Step-by-step explanation:
Cross multiply and then divide:
[tex]\frac{14}{22}= \frac{140}{x}[/tex]
140 x 22 = 3080
3080 / 14 = 220
Find the missing base.
Write your answer as a whole number.
?^2=36
Answer:
6
Step-by-step explanation:
6^2 = 36
hope this helps! :D
have a miraculous day!! <3
please help i'm stuck and it's a unit test if correct i will give brainiest
Which inequality represents this statement?
A number is no more than 5.
a. n≥5
b. n<5
c. n>5
d. n≤5
Answer:
d. n≤5
Step-by-step explanation:
This is the answer
Answer:
D) n≤5
Step-by-step explanation:
No more than 5 means that the number cannot exceed 5, but it's ok to have any number less than 5 or equal to 5. So, this means that D is correct.
Plz help brainiest to the correct answer!
#1
Current temperature=0°C
Temperature before 1 hour
[tex]\\ \sf{:}\dashrightarrow 0+3°C=3°C[/tex]
#2
Temperature before 3h
[tex]\\ \sf{:}\dashrightarrow 0+3(3)=0+9=9°C[/tex]
#3
Temperature before 4.5h
[tex]\\ \sf{:}\dashrightarrow 0+4.5(3)=13.5°C[/tex]
A carton of a orange juice is in the sahpe of a cuboid. It has a height of 20cm lenght of 12cm and depth of 8cm. The depth of the orange juice is 6cm.the carton is turned so that it stands the shaded face.Work out the depth of the orange juice.
Answer:
4cm
Step-by-step explanation:
The area of the base will be doubled 60[tex]cm^{2}[/tex] to 120[tex]cm^{2}[/tex]
Company A: A 2-column table with 5 rows. The first column is labeled hours with entries 5, 12, 20, 29, 42. The second column is labeled earnings (dollar sign) with entries 340, 404, 460, 530, 630. Company B: A 2-column table with 5 rows. The first column is labeled hours with entries 4, 9, 20, 32, 39. The second column is labeled earnings (dollar sign) with entries 125, 234, 450, 668, 828. If Amelia wants to make the maximum amount of money working only 22 hours per week, which company should she work for? Explain your answer. Company A: Using linear regression models from both data sets, she determines that it pays about $14 more. Company A: Using quadratic regression models from both data sets, she determines that it pays about $5 more. Company B: Using linear regression models from both data sets, she determines that it pays about $10 more. Company B: Using exponential regression models from both data sets, she determines that it pays about $8 more.
Answer:
86 & tends to increase
Step-by-step explanation:
Goodluck :)
Answer:
Company B: Using linear regression models from both data sets, she determines that it pays about $10 more.
Step-by-step explanation:
C/3