Answer:
x = - 90
Step-by-step explanation:
1 = 0.4x - 0.8x - 35 ( add 35 to both sides )
36 = - 0.4x ( divide both sides by - 0.4 )
- 90 = x
Reshma spends 1/4 of her pocket money on her comic books out of Rs 660.
What is the amount she spent on her comic books and what amount is left with her?
Answer step by step and give brief explanation for 20 points will also mark as brainliest
We need to know about fraction to solve this problem. The amount Reshma spent on comic books is Rs 165 and the amount that is left with her is Rs 495.
We can solve this problem by calculating what 1/4th of 660 will be. In this question we know that Reshma spends 1/4th of her pocket money on comic books out of Rs 660. We can think of 660 being divided in 4 parts equally and that Reshma spends one part of it. The amount that will be left with Reshma is the rest three parts.
Reshma spends= 1/4x660=165
Amount left= 660-165=495
Therefore the amount Reshma spends on comic books is Rs 165 and the amount that is left with her is Rs 495.
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Given y=x^2-2x-9 in standard form is y=(x+a)+b in vertexform, use completing the square to find a and b.
y = (x - 1)² - 10 is the vertex form of the equation y = x² - 2x - 9.
Given, y = x² - 2x - 9
The equation is already in standard form : y = ax² + bx + c
where a=1, b=-2 and c=-9 according to the equation y = x² - 2x - 9.
The vertex form of parabola is: y = a (x - h)² + k
The "a" in y = ax² + bx + c equation and the "a" in equation y = a (x - h)² + k are the same attributes of a parabola, therefore, substitute 1 for "a" in equation y = a (x - h)² + k: y = (x - h)² + k.
"h" is the x coordinate of the axis of the vertex: h = [tex]\frac{-b}{2a}[/tex]
Substitute in the values: h = - ( -2 ) ÷ 2(1)
∴ h = 1
Then, Substitute the value of h into the y = (x - h)² + k.
y = (x - 1)² + k.
Using the coordinates x and y from the above equations,
k = 1² - 2(1) - 9
k = 10
Now, Substitute the value of k into the equation y = (x - 1)² + k.
y = (x - 1)² - 10.
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(2x-4)²=2x(x-2)+48 solve this ecuation
Answer:
x = 2, 4
Step-by-step explanation:
[tex](2x-4)^2=2x(x-2)+48 \\ \\ 4x^2 - 16x+16=2x^2-4x+48 \\ \\ 2x^2-12x-32=0 \\ \\ x^2-6x-8=0 \\ \\ (x-2)(x-4)=0 \\ \\ x=2, 4[/tex]
Factor x2 – 3x – 28.
An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression a x squared + b x + c.
Identify the values that should be written to complete the X diagram.
On the top:
On the bottom:
On the sides:
–7 and 4
Rewrite the expression using the numbers on the sides of the X diagram.
Use double grouping to factor the four terms.
x2 – 3x – 28 =
Values needed to complete the X diagram are:
On top -28, On the bottom: -3 and On the sides: -7 and 4.
What do you mean by factorization?An algebraic expression is factorised when it is written as the product of its factors.
The given equation is :
F(x) = x²-3x-28
finding factors,
= x²-7x+4x-28
= x(x-7) +4(x-7)
= (x-7)(x+4)
Given general equation is ax²+bx+c,
on comparing with x²-3x-28
a = 1
b = -3
c = -28
ac = 1*(-28) = -28
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The graph of the function f(x) = –(x + 3)(x – 1) is shown below.
On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 1, 4), and goes through (1, 0).
Which statement about the function is true?
The function is positive for all real values of x where
x < –1.
The function is negative for all real values of x where
x < –3 and where x > 1.
The function is positive for all real values of x where
x > 0.
The function is negative for all real values of x where
x < –3 or x > –1.
The true statement about the function are;
⇒ The function is positive for all real values of x, where x < –1.
What is Function?
A relation between a set of inputs having one output each is called a function.
Given that;
The graph of the function;
f(x) = –(x + 3)(x – 1)
Now,
Graph of the function is shown in attached image.
Which is a parabola, It goes through (- 3, 0), has a vertex at (- 1, 4), and goes through (1, 0).
Clearly, When x < -1
Take x = 0 < -1
The value of function;
f(x) = –(x + 3)(x – 1)
= - (0 + 3) (0 -1)
= -3 x -1
= 3
The function is positive.
Thus, The true statement about the function are;
⇒ The function is positive for all real values of x, where x < –1.
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75 [Chercher]
On considère l'expression suivante définie pour tout
ne Z par U(n)=n²+14n+33.
Résoudre U(n)=0.
Answer:
-11, -3
Step-by-step explanation:
[tex]n^2 + 14n+33=0 \\ \\ (n+11)(n+3)=0 \\ \\ n=-11, -3[/tex]
A conditional has a(n)? of true or false.
Answer:
The correct option is (b) truth value. If we are given two statements, the first statement is called the hypothesis and the second is its conclusion.
How many 1 3/5-inch-thick books can fit on a 1 4/12-inch-long bookshelf?
You can fit ? books on the bookshelf.
Using division we can calculate that 8 books can fit in the 14 inch long bookshelf .
Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number. Multiplication, addition, and subtraction make up the remaining operations.
One way to understand the division of two natural numbers is to tally the occasions in which one number is included within another. This number doesn't have to be an integer. For instance, each individual will receive 5 apples if 20 apples are spread evenly among 4 people.Both types of division are applied to various algebraic structures, or means of describing mathematical structure. These contain polynomial rings in a single indeterminate and are known as Euclidean domains. These are the cases where a defined Euclidean division (with remainder) exists.length of book shelf = 14 inch
length of each book = 1 3/5 inch = 1.6 inches
Number of books = 14 ÷ 1.6 = 8.75 books
Hence by division we get that 8 book can be put in the bookshelf.
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a whole number is more than 50. if this number is divided by 3, the remainder is 2. if it divided by 4, the remainder is 3. what is the smallest such whole number
The smallest such whole number is 11 which is, Which is divided by 3, the remainder is 2, f it, divided by 4, the remainder is 3
Let the number be x
Here we have to find the whole number which is Divided by 3,4 the remainder is 2,3 respectively,
x+(3–2)= x +1 is multiple of 3
Div by 4 remainder is
3x+(4–3) = x+1 is multiple of 4
So LCM of 3,4 is 3×4 = 12
Hence,x=12 –1 =11
The smallest such whole number is 11 which is divided by 3, the remainder is 2, if it divided by 4, the remainder is 3.
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What are precise definitions of perpendicular and parallel lines
Answer:
Perpendicular lines: Are lines that intersect at right angles (90°)
Parallel lines: Are lines which have no point of intersection.
Step-by-step explanation:
[tex]{}[/tex]
for the following exercises, find the lengths of the missing sides if side a is opposite angle a, side b is opposite angle b, and side c is the hypotenuse.
Using relations in a right triangle and the Pythagorean Theorem, it is found that the missing side lengths are as follows:
a = 14.4.c = 15.24.What are the relations in a right triangle?There are three relations in a right triangle, given as follows:
The sine of an angle of the triangle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle of the triangle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle of the triangle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.For this problem, we have that:
tan(A) = b/a.
Hence:
5/12 = 6/a
Applying cross multiplication, the side a is found as follows:
5a = 72
a = 72/5
a = 14.4.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
Hence the hypotenuse c is given as follows:
c² = 5² + 14.4²
c = sqrt(5² + 14.4²)
c = 15.24.
What is the missing information?For the triangle, we have that:
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Fill in: -5^2=____-5^2
The complete expression that fills the blank is -5^2 = 0 - 5^2
What are mathematical expressions?These are any statements that use variables, operators and coefficients as its representation
How to completely fill the blanks?The expression is given as
-5^2 = __-5^2
Represent the blank with x
So, we have the following expression
-5^2 = x - 5^2
Add 5^2 to both sides of the equation
So, we have
x = 5^2 - 5^2
Evaluate the difference
x = 0
This implies that -5^2 = __-5^2 gives -5^2 = 0 - 5^2
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Please help, I’ve been trying to do this for a couple of hours now but I can’t seem to figure it out.
The tables show a Linear function that represents your earnings y in dollars after x working hours
(Picture below)
What is the totals earnings for the 6th hour?
$
What is your hourly wage?
$
Answer:
total earnings at 6th hour: 111
hourly wage (slope): 18.5
Step-by-step explanation:
A linear function has a linear relationship, which essentially states as x increases by one, the y-value increases by some constant amount yielding a straight line.
The slope, or how much the y-value changes as x changes by 1 is generally written as: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We can choose any two points and this should yield the slope of the function, but it's a lot easier to choose y-values that are only separated by an x-value of one.
Let's say: [tex](x_1, y_1)=(4,\ 74)\text{ and }(x_2,y_2)=(5,\ 92.50)[/tex]
If we plug the values into the slope formula we just get: [tex]\frac{92.50-74}{5-4}=\frac{92.50-74}{1}=92.50-74[/tex]
And this makes sense, since by definition of a slope, it's just the change in y over change in x. This is equivalent to how much the y-value changes as x increases by one, so if we select two values with a difference of one in their x-values, the slope just turns out to be the difference between the two numbers.
Simplifying our expression we get: [tex]92.50-74=18.5[/tex]
This slope in this context represents how earnings increases as the hour increases, or in other words the hourly wage.
To calculate the earnings of the 6th hour we can just use the definition of a slope. From the x-value 5 to the x-value 6, the y-value should simply increase 18.5
So adding 18.5 to the y-value at x=5 we get: [tex]92.5+18.5=111[/tex]
what is the fastest way to find the radius of a circle that's daimeter is 679.756
Answer:
divide it in half it would be 339.878
Step-by-step explanation:
radius is half of a diameter
Hello
By definition:
⇒ the diameter of a circle is twice the length of the radius of the circle
Thus if the diameter is 679.756:
[tex]\text{radius} = \dfrac{679.756}{2} = 339.878[/tex]
Hope that helps!
Solve the following inequality:
3r-13>14
could I have a demonstration of how it worked out
Answer:
r>9
Step-by-step explanation:
3r-13+13>14+13
3r>27
3r/3>27/3
r>9
Answer:
r > 9
Step-by-step explanation:
Hello!
Treat inequality as an equal sign. The only rule is that when you divide or multiply by a negative number, flip the sign.
Solve for r3r - 13 > 143r > 27r > 9The solution is true for any value of r greater than 9.
The Mississippi river flows at a rate of 1 7⁄8 miles per hour. If
Marco floats down the river in a boat for 5 1⁄6 hours, how far will
he float?
I don't know how to do this :(
465/48
Step-by-step explanation:
1 ⅞ miles × 5⅙ = 465/48
________ _______
1 hour × 5⅙ = 5⅙ hours
Giving anyone that gets it right 100 points!
Six cantaloupes are cut up and served into thirty-two equal portions for a catering event. Which of the following shows the amount of cantaloupe in each portion?
A. 0.1875
_
B. 0.1875
C. 0.533
_
D. 0.53
Answer: pretty sure its B
hope this helps :)
←++
2. The 7th grade class plans to collect at least 600 pairs of socks for people in need. So far, 135
pairs have been collected. How many pairs of socks does the class need to collect over the
next 5 days?
34 = -w/7 solve for w
Answer: w = -238
Step-by-step explanation:
[tex]34=\frac{-w}{7}[/tex]
Switch sides
[tex]\frac{-w}{7} =34[/tex]
Multiply both sides by 7
[tex]\frac{7\left(-w\right)}{7} =34\cdot \:7[/tex]
Simplify
-w = 238
Divide both sides by -1
[tex]\frac{-w}{-1}=\frac{238}{-1}[/tex]
Simplify
w = -238
If I made any mistakes, please let me know!
I hope this helped :)
Simplify the expression.
3(−6+2 ÷ 4) - 72²
If Roni and Allie work together to mow the field, what part of the field would Roni mow?
about 0.52 of the field
about 0.64 of the field
about 0.71 of the field
about 0.87 of the field
If Roni has a riding lawn mower and can mow the field in 30 minutes and Allie is pushing a lawn mower and can mow the field in 75 minutes. If Roni and Allie work together to mow the field, about 0.71 of the field will Roni mow.
Time taken by Roni to mow the field = 30 minutes
Time taken by Allie to mow the field = 75 minutes
Work done by the Roni = x/30
Word done by Allie = x/75
Then they are working together
x/30 + x/70 = 1
Solve the equation
[tex]\frac{70x+30x}{2100}=1[/tex]
70x+30x = 2100
100x = 2100
x = 2100/100
x = 21
Then, the work done by Roni = x/30
= 21/30
= 0.70
Hence, if Roni has a riding lawn mower and can mow the field in 30 minutes and Allie is pushing a lawn mower and can mow the field in 75 minutes. If Roni and Allie work together to mow the field, about 0.71 of the field will Roni mow.
The complete question is
Roni and Allie are mowing the grass at the soccer field. Roni has a riding lawn mower and can mow the field in 30 minutes. Allie is pushing a lawn mower and can mow the field in 75 minutes. If Roni and Allie work together to mow the field, what part of the field would Roni mow?
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After how much time to the nearest minute Will the cost of plan a be equal to the cost of plan b
Let
y ----> total charge in a month
x ----> number of minutes
so
Plan A
y=0.21x+11
Plan B
y=0.10x+20
Equate both equations
0.21x+11=0.10x+20
solve for x
0.21x-0.10x=20-11
0.11x=9
x=9/0.11
x=81.82 minutes
Convert to hours and minutes
81.82 minutes=60+21.82=1 hour 22 min
therefore
the answer is option APLEASE HELP!!!
A system of linear inequalities is graphed below.
What are the linear inequalities for the system? Show your work, or explain your answer.
Answer:
System of linear inequalities is x - y + 1 < 0 and x + 2y +6 < 0
Step-by-step explanation:
Given:
The dotted line has two points as (-1,0) and (0,1).The solid line also has two points as (-6,0) and (0,-3).To Find:
Linear inequality for the system.Formula used:
Equation of a line passing through point (x1, y1) and (x2, y2) is given by (y-y1) = (y2-y1)/(x2-x1) * (x-x1)According to question, we have
Inequality for dotted line :
(y-1) > (0-1)/(-1-0) * (x-0)
y - 1 > x
x - y + 1 < 0...(1)
Inequality for solid line:
(y-(-3)) < (0-(-3))/(-6-0) * (x-0)
y + 3 < -x/2
x + 2y +6 < 0...(2)
Using (1) and (2), we get
System of linear inequalities is x - y + 1 < 0 and x + 2y +6 < 0.
A graph (not shown) of the selling prices of homes in a certain city for the month of April reveals that the distribution is skewed to the left. Which of the following statements is the most reasonable conclusion about the selling prices based on the graph?
Responses
The mean is greater than the median.
The mean is greater than the median.
The median is the average of the first quartile and the third quartile.
The median is the average of the first quartile and the third quartile.
There are fewer selling prices between the first quartile and the median than there are between the median and the third quartile.
There are fewer selling prices between the first quartile and the median than there are between the median and the third quartile.
There are more selling prices that are less than the mean than selling prices that are greater than the mean.
There are more selling prices that are less than the mean than selling prices that are greater than the mean.
The value of maximum minus third quartile is less than the value of first quartile minus minimum.
The statement which is the most reasonable conclusion about the selling prices based on the graph is that: E. the value of maximum minus third quartile is less than the value of first quartile minus minimum.
What is a box and whisker plot?A box and whisker plot is also referred to as boxplot and it can be defined as a type of graph that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread. Also, the five-number summary include the following:
Minimum (Min).First quartile (Q₁) or lower quartile.Median (Med).Third quartile (Q₃) or upper quartile.Maximum (Max).In Mathematics, the value of maximum minus third quartile (Max - Q₃) is generally less than value of first quartile minus minimum (Q₁ - Min). Mathematically, this can be represented by this expression:
Data value = (Max - Q₃) < (Q₁ - Min)
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A wall in Marcus's bedroom is 8 feet high and 18 feet long. If he paints of the wall blue, how many square feet will be
blue?
O 77
O 72 1/15
O 154
O 144 1/15
The blue portion of the wall in Marcus's bedroom is discovered to be 144(1/15) or 9.6 square feet in size.
How do you calculate the area of a wall?Use the standard formula of Length x Width = Area to calculate the area of a wall.
What is the area of a wall measured in square meters?Because square feet is the most commonly used measurement in the world when it comes to wall sizes, the measurement unit will have an impact on how you calculate square footage.
It is given that a wall in Marcus's bedroom is 8 feet high and 18 feet long.
So, the area of a wall = 8 × 18
= 144
Further, 1/15 portion is painted with blue color.
So, the portion that is painted with blue = 144 × 1/15
= 9.6
Therefore, the area of the wall in Marcus's bedroom that is painted with blue color is found to be 144(1/15) or 9.6 square feet.
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Let a = $125.36, b = $729.35, c = $49.53, d =$500, f =$3.50, p =$1,450, and w =
$60.
Answer:
a = $125.36, b = $729.35, c = $49.53, d =$500, f =$3.50, p =$1,450, and w =
$60
Step-by-step explanation:
SOMEONE please please pleaseee help me out...
Graph the lines in standard form.
A graph of the linear equation (3x + 2y = 6) in standard form is shown in the image attached below.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In Mathematics, the graph of any proportional relationship such as a linear equation is characterized by a straight line as shown in the image attached below.
Next, we would rewrite the linear equation in standard form as follows:
3x + 2y = 6
2y = 3x + 6
Dividing all through by 2, we have:
2y/2 = 3x/2 + 6/2
y = 3x/2 + 3
In conclusion, a graph which represents the linear equation (y = 3x/2 + 3) shows a proportional relationship between the value of x and y.
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Find a function of the form y=Asin(kx)+C or y=Acos(kx)+C whose graph matches the function shown below:
The sinusoidal function that matches the graph given is:
g(x) = 4cos((π/7)x) - 2.
What is the cosine function?The cosine function is defined as follows:
g(x) = acos(bx)+d.
The coefficients have these following roles:
a: amplitude.b: The period is of 2π/b.d: vertical shift.For this problem, we use a cosine function because the function is not zero at the origin, while for the sine it is.
From the graph of this function, the maximum value is of 2, while the minimum value is of -6, hence the amplitude is found as follows:
2a = 8 (difference between these values).
a = 4.
Then:
g(x) = 4cos(bx) + d.
A function with amplitude of 4 should oscillate between -4 and 4, while this one oscillates between -6 and 2, meaning that it was shifted 2 units down, hence d = -2 and:
g(x) = 4cos(bx) - 2.
The period is of 14 units, hence:
2π/b = 14
14b = 2π
b = π/7
Hence the function is:
g(x) = 4cos((π/7)x) - 2.
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Amol drives his truck at an average speed of 50 km/h. He leaves at 07 00 and arrives at 11 15. Calculate the distance he drives.
Answer:
209km/h
Step-by-step explanation:
4hrs 15mins was the time.
4hrs x 50km/h = 200km/h
15 percent of 60: how many minutes is in an hour, is 9.
Hence, The answer would be 209km/h.
At what speed should you enter an expressway? Question 1 options: 70mph 35mph the prevailing 10 miles below the freeway traffic
At a speed of 10 mph below the freeway traffic one should enter the expressway.
The speed of an object, also known as v in kinematics, is a scalar quantity that depends on the magnitude of the change in that object's position over time or the magnitude of the change in that object's position per unit of time.
The instantaneous speed serves as the upper bound of the average speed as the duration of the time period gets closer to 0. The average speed of an object over a given period is calculated by dividing its total distance traveled over that time by its duration. Velocity and speed are not the same thing.Now of the given options since the respective speeds on various expressways are different it is tangible than to enter an expressway one must use less speed than the speed of the traffic on the expressway.
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