[tex]\boxed{x\:=\:-8 }[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\purple{Step-by-step\:explanation}}{\purple{:}}}}}[/tex]
[tex]5x + 6 = 3x - 10[/tex]
[tex]➺ \: 5x - 3x = - 10 - 6[/tex]
[tex]➺ \: 2x = - 16[/tex]
[tex]➺ \: x = \frac{ - 16}{2} [/tex]
[tex]➺ \: x = - 8[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
[tex]5x + 6 = 3x - 10[/tex]
[tex]➼ \: 5 \times ( - 8 )+ 6 = 3 \times ( - 8) - 10[/tex]
[tex]➼ \: - 40 + 6 = - 24 - 10[/tex]
[tex]➼ \: - 34 = - 34[/tex]
[tex]➼ \: L.H.S.=R. H. S[/tex]
Hence verified.
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
Answer:
-8
Step-by-step explanation:
5x + 6 = 3x − 10
Subtract 3x from both sides:
5x + 6 - 3x = 3x - 10 - 3x
2x + 6 = -10
Subtract from 6 both sides:
2x + 6 - 6 = -10 - 6
2x = -16
Divide both sides by 2:
2x -16
____ = ____
2 2
-16
x = ____ (divide)
2
final answer: x = -8
I need help can someone please answer this for me
Explain why a + 2b = 110 in the triangle shown
Answer:
Step-by-step explanation:
According to the Triangle Angle-Sum Theorem, all the angles of a triangle have to add up to equal 180 degrees. For us, in our triangle:
a + 2b + 70 = 180 so
a + 2b = 180 -70 and
a + 2b = 110. That's why.
To find the quotient of 3 divided by 6/1
Answer:
1/3
Step-by-step explanation:
3÷6/1 is the same thing as 3÷6
and when reducing to the lowest term gives 1÷3 or 1/3
the window of a building 65m above the street level from this window ,a person looks across the street at a building and finds that the Angle of elevation of the top of the building is 72°and the angle of depression if the bottom of the building is 28° .if the street level is horizontal and the ground distance between the building is 80m.find to the nearest m the vertical heights of the building
not so sure about your question. please check.
I need help with this
Answer:
angle B is 38°
Step-by-step explanation:
all angles in a triangle has to equal 180°.
So first find the measurement of angle BAD. This is done by subtracting angle of CAD=46° from the total angle CAB=78° to get 32° for angle BAD. So if angle ADB is 110° and angle BAD is 32° which equals (110+32=) 142.
Then take 180 - 142 = 38°
Answer:
38
Step-by-step explanation:
We can see that A is equal to 78. We can also see that CAD is equal to 46. Therefore BAD is equal to 32. Add 32 and 110 together to get 142. Subtract 142 from 180 to get 38.
Hope that this helps!
Someone pls pls pls solve this!!!!!!! And pls explain how u solved it. I need this due rn ASAP!!!
35°..
can also be 145° but not in this case since the angle is less than 90°
Math, math,math, hate it all year long
Answer:
the answer is $50.00
Step-by-step explanation:
okay so first u gave to subtract $80.00 from $430 u will get $350.00 then divide it by 7 and then you will get your answer
Answer:
ok
Step-by-step explanation:
message
The drama club is running a lemonade stand to raise money for its new production. A local grocery store donated cans of lemonade and bottles of water. Cans of lemonade sell for $2.50 each and bottles of water sell for $1.25 each. The club needs to raise at least $600 to cover the cost of renting costumes. The students can accept a maximum of 460 cans and bottles.
Write a system of inequalities that can be used to represent this situation.
The club sells 144 cans of lemonade. What is the least number of bottles of water that must be sold to cover the cost of renting costumes? Justify your answer
Answer:
Part A
x + y ≤ 460
2.5·x + 1.25·y ≥ 600
Part B
192 bottles
Step-by-step explanation:
The given parameters are;
The selling price of a can of lemonade = $2.50
The selling price for each bottle of water = $1.25
The amount the club needs to raise to cover the cost of renting costumes, A = $600
The maximum acceptable cans and bottles = 460
Part A
Let 'x', represent the number of cans of lemonade accepted by the students, and let 'y' represent the number of bottles of water accepted, we have;
The situation can be represented by the following system of inequalities
x + y ≤ 460
2.5·x + 1.25·y ≥ 600
Part B
The number of cans of lemonade sold, x = 144
Therefore, we have;
2.5 × 144 + 1.25·y ≥ 600
1.25·y ≥ 600 - 2.5 × 144 = 240
1.25·y ≥ 240
y ≥ 240/1.25 = 192
y ≥ 192
The least number of bottles of water that must be sold to cover the cost of renting costumes, y = 192 bottles
Solve the equation for all real solutions in simplest form.
2r^2 + 7r– 1 = -3r^2
Answer:
2r^2 + 3r^2 + 7r - 1 = 0
5r^2 + 7r - 1
Answer: 0.0833 or 83/1000
Hope this helps :)
Which ordered pair (a,b) is the solution to the given system?
Answer:
1,3 3,1
Step-by-step explanation:
Which is the graph of f(x) = (x + 3)(x - 2
Answer:
Step-by-step explanation:
f(x) = (x + 3)(x - 2) has two zeros: One stems from (x + 3) = 0 and is (-3, 0); the other stems from (x - 2) = 0 and is (2, 0).
The axis of symmetry is a vertical line located halfway between -3 and 2:
x = -1/2.
The graph opens up because the given (x + 3)(x - 2) has a positive leading coefficient (+1).
With this information we can eliminate the last two possible answers. Note that the x-intercepts of the first graph are -3 and 2, Thus, the first graph is the correct one.
The graphs below have the same shape. What is the equation of the graph of g(x)?
A. g(x) = (x-2)^2
B. g(x) = (x+2)^2
C. g(x) = x^2 - 2
D. g(x) = x^2 + 2
Answer:
Step-by-step explanation:
B. Because adding 2 moves you to the left when inside the parentheses.
Diego's family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5
gallons or less. Starting from a full tank, can Diego's family drive the car for 14 days without the warning light coming on? Explain or show your reasoning.
Question 6 Multiple Choice Worth 1 points)
(01.06 LC)
Solve x - 5y = 6 for x.
Answer:
x = 6+5y
Step-by-step explanation:
x - 5y = 6
Add 5y to each side
x - 5y+5y = 6+5y
x = 6+5y
Answer:
x = 6 + 5y
Step-by-step explanation:
x - 5y = 6
Solve for x.
x - 5y = 6
Add 5y to both side
x - 5y + 5y = 6 + 5y
x = 6 + 5y
(n+t) divided by 4 i need the answer please
Answer:
[tex]\frac{n+t}{4}[/tex]
Step-by-step explanation:
(n+t) divided by 4
The equation would be [tex]\frac{n+t}{4}[/tex]
Hope this helps
Answer:
(n+t)/4
Step-by-step explanation:
If y is 22.6 and c is 28.2, find b, rounded to the nearest tenth.
A company estimates that 1500 units of product will be sold at Rs.110 and 750 units at a price of Rs.125. Determine the demand function.
Answer:
d(x) = 6.68*x + 765
Step-by-step explanation:
The demand function is a linear function of the price, then:
demand function d(x), is an equation of the type:
d(x) = p*x + b
In that equation we have two parameters p and b
and we have two points of the straight line:
P ( 1500 ; 110 )
Q ( 750 ; 125 )
1500 = p*110 + b (1)
750 = p*125 + b (2)
Subtracting (1) - (2)
1500 - 750 = (110- 125 ) + b
750 + 15 = b
b = 765 intercept on y-axis
1500 = 110*p + 775
1500 - 765 = 110 *p
p = 735/110
p = 6.68
The equation of demand is:
d(x) = 6.68*x + 765
What is the equation of the parabola with focus (1/3, 2/3) and directrix y = 1/2pls help ill give points
Answer:
D. y = 3·x² - 2·x + 11/12
Step-by-step explanation:
The coordinates of the focus of the parabola, f = (1/3, 2/3)
The directrix of the parabola, y = 1/2
The standard form of the equation of a parabola is (x - h)² = 4·p·(y - k)
The coordinates focus = (h, k + p)
The y-coordinates of the directrix, y = k - p
By comparison, we have;
h = 1/3...(1)
k + p = 2/3...(2)
k - p = 1/2...(3)
Adding equation (3) to equation (2) gives;
k + p + (k - p) = k + k + p - p = 2·k = 2/3 + 1/2 = 7/6
k = (7/6)/2 = 7/12
k = 7/12
From equation (2), we get;
p = 2/3 - k
∴ p = 2/3 - 7/12 = 1/12
p = 1/12
The equation of the parabola is therefore;
(x - 1/3)² = 4·(1/12)·(y - 7/12) = y/3 - 7/36
y = 3 × ((x - 1/3)² + 7/36) = 3 × ((x² - 2·x/3 + 1/9) + 7/36) = 3·x² - 2·x + 11/12
y = 3·x² - 2·x + 11/12.
How do I find the area of the parallelogram?
Answer:
using trigonometry first find the height I mean the dotted line
then use the formular 1/2*h*(a+b)
where h is the height you just found
a is 10
b is 6
14. If I share 123 sweets equally among amongst 7 children, how many sweets will each child get?
……………………………………..
Answer:
No. of sweets = 123
No. of children = 7
then
sweets per children =123/7 =17. 57
Answer: =17.57
Step-by-step explanation:
Divide the no. of sweets by the no. of children
=123/7
=17.57
Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k.
A. 2
B. 3
C. 4
D. 5
Answer:
3
Step-by-step explanation:
The Duke Blue Devils basketball team plays home games at Cameron Indoor Stadium. The court is in the shape of a rectangle. If the length of the court is (5.8a+6.1b-3.6c) feet and the width of the court is (434b-235c) feet, then what is the perimeter of the court?
Answer:
11.6a + 880.2b - 477.2c
Step-by-step explanation:
Given:
length of the court = (5.8a+6.1b-3.6c) feet
width of the court = (434b-235c) feet
Since the court is said to be rectangular in shape :
The perimeter of a rectangle = 2(length + width)
Perimeter = 2(5.8a+6.1b-3.6c + 434b-235c)
Perimeter = 2(5.8a+6.1b+434b-3.6c-235c)
Perimeter = 2(5.8a + 440.1b - 238.6c)
Perimeter = 11.6a + 880.2b - 477.2c
A set of composite numbers less than 12 .express it in listing and set builder methods
Given:
A set of composite numbers less than 12.
To find:
The set by listing and set builder methods.
Solution:
Composite number: A positive integer is called a composite number if it has at least one divisor other than 1 and itself.
Composite numbers less than 12 are 4, 6, 8, 9, 10.
By using the listing method , the given set can be expression as:
Set = {4, 6, 8, 9, 10}
The numbers 4, 6, 8, 9, 10 are greater than 1, less than 12 and non prime numbers.
By using set builder method, the given set can be expression as:
Set = [tex]\{x|x\neq P,1<x<12\}[/tex]
Therefore, the list and set builder notation of the given set are {4, 6, 8, 9, 10} and [tex]\{x|x\neq P,1<x<12\}[/tex] respectively.
Please Help 50 points!!
A substance decays so that the amount A of the substance left at time t is given by:
Answer:
lol sorry for answer what's that
Please help me-
f(x) = x2. What is g(x)?
Answer:
D. g(x) = 3·x²
Step-by-step explanation:
The given parent function, f(x) = x²
The graph of the function, g(x) is narrower than the graph of the function f(x)
Therefore, the coefficient of the quadratic function is larger than 1
The given point on the parabola, g(x) = (1, 3)
Therefore. when x = 1, g(x) = 3
However, when x = 1, f(x) = 1
Therefore, given that g(x) = a·f(x), we get;
a = g(x)/(f(x)) = 3/1 = 3
g(x) = 3·x²
Which of the following is the solution to the inequality below?
-6(4 - x) S-4(x + 1)
O A. x210
O B. x5 10
O C.x22
O D. x52
Answer:
x≤2
Step-by-step explanation:
-6(4 - x) ≤-4(x + 1)
Distribute
-24 +6x≤ -4x-4
Add 4x to each side
-24 +6x+4x≤-4x-4+4x
-24 +10x≤ -4
add 24 to each side
-24+10x+24≤-4+24
10x≤20
Divide by 10
10x/10 ≤20/10
x≤2
Answer:
D. x ≤ 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
-6(4 - x) ≤ -4(x + 1)
Step 2: Solve for x
[Distributive Property] Distribute -6: -24 + 6x ≤ -4(x + 1)[Distributive Property] Distribute -4: -24 + 6x ≤ -4x - 4[Addition Property of Equality] Add 4x on both sides: -24 + 10x ≤ -4[Addition Property of Equality] Add 24 on both sides: 10x ≤ 20[Division Property of Equality] Divide 10 on both sides: x ≤ 2Suppose that the regression equation y = 16.99 + 0.32 x1 + 0.41 x2 + 5.31 x3 predicts an adult's height (y) given the individual's mother's height (x1), his or her father's height (x2), and whether the individual is male (x3 = 1) or female (x3 = 0). All heights are measured in inches. In this equation, the coefficient of ______ means that ______. x1; if two individuals have mothers whose heights differ by 0.32 inch, then the individuals' heights will differ by 1 inch. x1; if two individuals have mothers whose heights differ by 0.5 inch, then the individuals' heights will differ by 0.32 inch. x2; if two individuals have fathers whose heights differ by 1 inch, then the individuals' heights will differ by 0.41 inches. x2; if two individuals have mothers whose heights differ by 1 inch, then the individuals' heights will differ by 0.41 inches. x3; a brother is expected to be 5.31 inches taller than his sister
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Given equation:
[tex]\to y = 16.99 + 0.32 x_1 + 0.41 x_2 + 5.31 x_3[/tex]
Predicts a height [tex](y)[/tex]of adults provided the height of the mother [tex](x_1)[/tex], the height [tex](x_2)[/tex] of a father but if the person is male [tex](x_3 = 1)[/tex] or female [tex](x_3 = 0)[/tex].
The factor[tex]x_1 = 0.32[/tex] is an increase in the kid's length even as the mother increases by one inch.
Likewise, the coefficient [tex]x_2 = 0.42[/tex] was its rise in child length as just a result of the increase of one inch in dad.
The coefficient [tex]x_3 = 5.31[/tex] is an increase of a child's height cos of the male as opposed to that same female.
i'll mark brainliest !!!!!!!!!!
Amar wants to make lemonade for a birthday party. He wants to mix 12 tablespoons of sugar in water. He only has a teaspoon which needs to be used 4 times to be equivalent to one tablespoon. At this rate, how many teaspoons of sugar will Amar need to make the lemonade?
HOW MANY TEASPOONS OF SUGAR WILL AMAR NEED TO MAKE LEMONADE !?
Answer:
Amar will need 48 teaspoons of sugar to make lemonade
Step-by-step explanation:
If u need 4 teaspoons to make one tablespoon, then you just can do
4 x 1 = 4
so, having that now you can do
4 x 2 = 8
there you get 8 teaspoons
Now you do
4 X 12 = 48
Need help with this question
Answer:
don't know about this question
Which of the following functions represent exponential decay and has a y-
intercept of 2?
O y = {(0.85)*
O y = (2)*+2
O y = 4 (2)*
O y = 2(3)*
Answer:
Non of the given options
A function that represent an exponential decay and 2 as the y-intercept is y = 0.85ˣ + 1
Step-by-step explanation:
An exponential decay function is a function that reduces in magnitude at a constant percentage rate, r (< 1)
An exponential decay can be represented by the formula, y = a·(1 - r)ˣ
Therefore, the growth factor, (1 - r) = b is less than 1 for an exponential decay
Therefore the function that represent an exponential decay is y = 0.85ˣ, while a function that represent an exponential decay and has a y-intercept of 2 is y = 0.85ˣ + 1. therefore, non of the options