9514 1404 393
Answer:
x = -5/2
Step-by-step explanation:
The equation ...
[tex]\dfrac{1}{4}x=-\dfrac{5}{8}[/tex]
is a "one-step" linear equation. It has a variable term on one side of the equal sign and a constant term on the other sided of the equal sign. It is solved by multiplying both sides of the equation by the reciprocal of the coefficient of the variable. The variable coefficient is 1/4, so you multiply by the reciprocal of that, 4. Multiplying by this value causes the coefficient of the variable to become the multiplicative identity element, 1. Both sides of the equation are multiplied by this value in accordance with the multiplication property of equality. That way, the variable value is not changed. Then the equation becomes ...
[tex]\dfrac{4}{4}x=-\dfrac{5\cdot4}{2\cdot4}\\\\x=-\dfrac{5}{2} \qquad\text{simplified}[/tex]
After simplifying the coefficient and the constant, the solution is found to be x = -5/2, or x = -2 1/2.
Your goal is to isolate the x. This is a multiplication problem, so use the inverse operation, which is division. Divide both sides of the equation by
1
4 by multiplying by the reciprocal, 4. (−
5
8)(4) is −
5
2. Use substitution to check the answer. x = −
5
2
how many numbers are in the first $20$ rows of pascal's triangle (from the $0$th row to the $19$th row)?
Numbers in the first 20 rows of pascal's triangle are 210
Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra.
We have been given that:
Numbers of rows = 20
Pascal's triangle formula
1 + 2 + 3 + ….+ 19 + 20 = n (n + 1) / 2
n=20
(20)×(21)/ 2 = 210
Pascal's triangle patterns is its symmetry. Observe that in any row, if we read the consecutive numbers from the left, we will obtain the same as if we read them from the right.
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the top of the john hancock building is a rectangle whose length is 60 ft more than the width. the perimeter is 520 feet. find the width and the length of the rectangle.
The length and width of rectangle is 160 feet and 100 feet.
The perimeter of the rectangle is calculated by the formula -
Perimeter = 2 × (length + width)
As per the given information, length = (60 + width)
Keep the values in formula to find the breadth of rectangle.
520 = 2 × (60 + width + width)
520 = 2 × (60 + 2 × width)
(60 + 2 × width) = [tex]\frac{520}{2}[/tex]
(60 + 2 × width) = 260
2 × width = 260 - 60
2 × width = 200
Width = [tex]\frac{200}{2}[/tex]
Width = 100 feet
Keep the value in formula to find the length of perimeter
520 = 2 × (length + width)
Length + 100 = [tex]\frac{520}{2}[/tex]
Length = 260 - 100
Length = 160 feet
Hence, the length and width of rectangle is 160 feet and 100 feet.
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What is an equation of the line that passes through the point (-4,5) and is perpendicular to the line 4x+y=7?
Answer:
y = [tex]\frac{1}{4}[/tex] x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
4x + y = 7 ( subtract 4x from both sides )
y = - 4x + 7 ← in slope- intercept form
with slope m = - 4
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex] , then
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute )- 4, 5 ) into the partial equation
5 = - 1 + c ⇒ c = 5 + 1 = 6
y = [tex]\frac{1}{4}[/tex] x + 6 ← equation of perpendicular line
if the mean of a set of 12 numbers is 13 , then the summer of the numbers is
Answer:
156, because the mean is 13, and the mean in equal to all of the numbers added up and divided by how many numbers there are.
If 1/2 cup of soup equals 120 milliliters, then how many milliliters are in 3 1/4 cups of soup?
If 1/2 cup of soup equals 120 milliliters, then there are 780 milliliters in
3 1/4 cups of soup.
A milliliter is a metric unit that is abbreviated as ml and is used to measure volumes for liquid and gas states. It is usually used to measure smaller volumes of liquids as it is equal to 1/1000 of a liter.
We can find the milliliters in 3 1/4 cups of soup as follows:
1/2 cup of soup = 120 milliliters
As 1/2 = 0.5
We can rewrite it as:
0.5 cup of soup = 120 milliliters
3 1/4 cups = 3.25 cups
Consider milliliters in 3 1/4 cups = x
Therefore,
0.5 cup = 120 ml
3.25 cups= x
Cross multiply to find x,
0.5 x = 120x3.25
0.5 x = 390
x= 390/0.5 = 780 milliliters
Hence it is found that 3 1/4 cups of soup is equal to 780 milliliters.
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0.00015797 in scientific notations
Answer:
1.5797 x 10^-4
Step-by-step explanation:
What is the area of parallelogram ABCD with vertices A (2, 3), B (7, 3), C (8, -5), and D (3, -5)?
The area of the parallelogram ABCD with the vertices is 40 square units
What is the area of parallelogram ABCD with vertices?The vertices are given as
(2, 3), B (7, 3), C (8, -5), and D (3, -5)
From the graph, we have the following dimensions
Base = 5 units i.e. distance AB
Height = 8 units i.e. the distance between the parallel sides
The area of the parallelogram is then calculated as
Area = Base * Height
So, we have
Area = 5 * 8
Evaluate
Area = 40
Hence, the area of the parallelogram ABCD with the vertices is 40 square units
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. How many minutes will she need to finish labeling all books if she takes no breaks and labels 10 books per minute?
Answer:
(a) 75 minutes
(b) 50 minutes
Which expressions describe the end behaviors of the function f(x)=2^x+3. modeled by the graph attached to this. Choose all that are correct.
As x increases without bound, f(x) approaches zero.
As x decreases without bound, f(x) approaches zero.
As x decreases without bound, f(x) approaches the line y = 3.
As x increases without bound, f(x) increases without bound.
The graph of function f(x) = [tex]2^{x}[/tex] + 3 will be increases without bound As x increases without bound and As x decreases without bound, f(x) approaches the line y = 3 therefore option (C) and (D) will be correct.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
The graph is easy to understand behavior of the graph.
Given the function,
f(x) = [tex]2^{x}[/tex] + 3
At x = 0 → f(0) = 2⁰ + 3 = 3
This is an exponential function as shown below which will be increasing as x increase while it will gain the value y = 3 as x decrease.
Hence "The graph of function f(x) = [tex]2^{x}[/tex] + 3 will be increases without bound As x increases without bound and As x decreases without bound, f(x) approaches the line y = 3".
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8. Find the equation of the lines passing through the origin and (a) parallel (b) perpendicular to the lines represented by 6x² - 5xy + y2 + 5x - 2y + 1 = 0. .
Answer:
Hello,
Step-by-step explanation:
1. We must decompose the conic into 2 lines.
[tex]f(x,y)=x^2-5xy+y^2+5x-2y+1=0\\\\We\ are\ going\ to\ find\ the\ center\\\\\left\{\begin{array}{ccc}\dfrac{ \partial{f} }{\partial{x} }&=&12x-5y+5=0\\\\\dfrac{ \partial{f} }{\partial{y} }&=&-5x+2y-2=0\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}x=0\\y=1\\\end {array} \right.\\\\We\ must\ find\ an\ other\ point\ of\ f(x,y).\\\\if\ y=0\ then\ x=\dfrac{-1}{2} \ or\ x=\dfrac{-1}{3}[/tex]
The 2 lines are: 2x-y+1=0 and 3x-y+1=0
Paralleles are y=2x and y=3x
Perpendiculars are x+2y=0 and x+3x=0
Please someone answer this question points.
find all values of x in the interval [0, 2????] that satisfy the inequality. (enter your answer using interval notation.)
A component of the interval is x (π/4, 5π/4) when 5 sin(x) > 5 cos(x).
What does a math inequality mean?A relation in mathematics that compares two numbers or even other mathematical expressions in an unequal way is known as an inequality. When comparing two numbers on a number line, it is most frequently used to compare their sizes.
According to the given information:5 sin(x) > 5 cos(x)
To removing constant we divide both the side by 5:
5sin(x) > 5 cos(x)
sin(x) > cos(x)
sin x > cos x;
sin x = cos x; tan x = 1; x = π/4 or x = 5π/4
sin x > cos x for x ∈ (π/4, 5π/4)
A component of the interval is x (π/4, 5π/4) when 5 sin(x) > 5 cos(x).
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I understand that the question you are looking for is:
Find all values of x in the interval [0, 2] that satisfy the inequality. (Enter your answer using interval notation.) 5 sin(x) > 5 cos(x)
Which equation can be used to solve for x in the following diagram?
Choose 1 answer:
A) 10x = 150
B) 10x + 90 = 180
C) 150 - 10x = 90
D) 10x + 150 = 180
PLEASE HELPP
Answer:
B
it is the right equation
pls help it's due for a grade
A party will have hexagonal tables placed together with space for one person on each open side:
n
12
a. Complete this table showing the number of people P (n) who can sit at n tables.
If n =12 then there are 50 person who can sit .
Hexagonal - In geometry, a hexagon is a closed two-dimensional six-sided polygon. It is made up of six line segments and six vertices that form six internal angles. The sum of all the internal angles of a hexagon is 720°.
Each table seats 4 people, which can be represented with n,plus two more people at either end of the set of tables. The table is hexagonal and so can seat 6 people. So, the given equation defines this situation.
The number of people who can sit at the tables increases by 4 each time a table is added
P=4n+2
the given equation to find the number of tables n.
P=4n+2
Where P = person
and n= no of tables .
given that
n=12
put value of n in equation to find the no. of person .
P = 4(12) +2
P = 48 +2
P = 50.
Hence,in this given seating arrangement 50 person can sit on 12 tables. .
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What does mx or mx = b mean in math pls explain from like your knowledge
Step-by-step explanation:
In the equation y = mx + b for a straight line, the number m is called the slope of the line. In the equation y = mx + b for a straight line, the. number b is called the y-intercept of the line.
the equation is -5 = -8+v/3 help
Step-by-step explanation:
could it be that the equation is rather
-5 = (-8 + v)/3
?
that is a huge difference ...
to solve such an equation we keep transforming it (every change we make we have to do on both sides of the equation to keep the equality), until we have only the variable on one side, and everything else (which is then the solution) on the other side.
1st step : we get rid of the "/3" by multiplying both sides by 3.
that gives us
-5×3 = ((-8 + v)/3)×3 via the multiplication property.
2nd step : we simplify
-15 = -8 + v
3rd step : we get rid of the -8 on the side of the variable by adding 8 to both sides.
that gives us
-15 + 8 = -8 + 8 + v via the addition property.
4th step : we combine like terms (or simplify, if we can use it a second time) :
-7 = 0 + v
-7 = v
that's it.
PLEASE HELP I WILL GIVE OUT BRAINLIST ONLY FOR THE RIGHT ANSWERS
The measure of angle 2 and angle3 are 133 ad 47 degrees respectively
Vertical angles and angle on a straight lineFrom the given diagram, the measure of angle 1 and 2 are congruent. (vertical angles)
Given he following parameters
m<1 = 133 degrees
Since m<1 = m<2, hence m<2 = 133 degrees
Also;
m<2 + m<3 = 180
133 + m<3 = 180
m<3 = 180 - 133
m<3 = 47 degrees
Hence the measure of angle 2 and angle3 are 133 ad 47 degrees respectively
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Please help as fast as you can!!!!
-2 1/3 - 1 3/4=
Write the answer as a fraction please!!
Answer:-41/4 try that
Carrie is packing her clothes in moving boxes that are in the shape of a cube. Each box has a volume of 3 cubic feet. The moving truck has shelves that are 12 inches in height. Will the moving boxes fit? Explain.
Yes, the moving boxes will fit in this volume.
What is volume ?The current volume of box :
Volume = height * width * depth
Volume = 12 * 9 * 2
Volume = 216 in³
New dimension :
Height and volume are the same
Width = 9 - 1 = 8
Depth = x
Volume = height * width * depth
216 = 12 * 8 * x
216 = 96x
x = 216 / 96
x = 2.25 inch
Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.
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What is the image of (8, -12) after a dilation by a scale factor of 1/4 centered at the origin?
Answer: (2, -3)
Step-by-step explanation:
To get these points, you just need to multiply the coordinates by 1/4, or divide by 4
question 11(multiple choice worth 5 points) (01.06 mc) the length of a blue whale is approximately 3 × 104 millimeters; the length of an otter is 2 × 103 millimeters. how many times longer is the blue whale than the otter? 1.5 2 10 15
Blue whale is 15 times longer than otter.
To find how many times the blue whale is longer than the otter, we will perform division. We will divide the length of blue whale by length of otter, which we will give us the desired result.
Now, performing calculation as per the above statements -
Number of times longer length = [tex]\frac{3*10^{4} }{2*10^{3} }[/tex]
Performing division of numbers. Also, as we know, on division the exponents are subtracted. Hence, subtracting the exponents to get the desired result.
Number of times longer length = 1.5*[tex]10^{4-3}[/tex]
The result will be -
Number of times longer length = 1.5*10
Performing multiplication -
Number of times longer length = 15
Hence, we get that blue whale is 15 times longer than otter.
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Simplify the difference.
One rectangle has an area of ((7x² - 4x +12) ft². A second rectangle has an area of
(4x² + 2x − 1) ft².
How many more square feet is the first rectangle ?
O 3x² - 2x + 11
O 11x² - 6x + 11
O 3x²- 6x + 13
O-4x²-5x-9
Answer:
The first rectangle is 3x² - 6x + 13 more square feet then the second rectangle
Step-by-step explanation:
A rule for subtracting polynomials
Keep the first term the same Change the subtraction sign to addition Change the sign for every termSteps
Keep the polynomial 7x²- 4x + 12 the same Change the subtraction sign to addition Change the sign for every term 4x² + 2x - 1 becomes -4x² - 2x + 13At the end of the expression is (7x²- 4x + 12) + -4x² - 2x + 1
At this point you combine like terms like you do with adding polynomials so ( 7x² + (-4x²) is 3x², (-4x) + (-2x) is (-6x), and 12 + 1 is 13) so the final answer would be 3x²-6x+13
grafica
[tex]5y-15=-4x[/tex]
El grafico de la ecuación lineal se puede ver en la imagen al final.
¿Como graficar la ecuación lineal?En este caso queremos graficar la ecuación lineal:
5y - 15 = -4x
Para ello debemos encontrar dos puntos en la linea, y para hacer eso podemos evaluar en dos valores de x.
Sí x = 0 obtenemos:
5y - 15 = -4*0
5y = 15
y = 15/5 = 3
Sí x= 5 obtenemos:
5y - 15 = -4*5
5y = -20 + 15
5y = -5
y = -5/-5 = -1
Entonces solo tenemos los dos puntos (0, 3) y (5, 1), ahora debemos graficar estos en un eje de coordenadas y trazar una linea que pase por ambos, como en el ejemplo de abajo.
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which expression simplifies to 41? choose all that apply! question 14 options: 10 2³ ∙ 4 - 1 10 2³ ∙ (4 - 1) (10 2³) ∙ 4 - 1 10 (2³ ∙ 4) - 1
The expressions that simplifies to 41 are:
a) 10 + 2³ * 4 - 1
d) 10 + (2³ * 4) - 1
Information about the problem:
a) 10 + 2³ * 4 - 1
b) 10 + 2³ * (4 - 1)
c) (10 + 2³) * 4 - 1
d) 10 + (2³ * 4) - 1
We solve the equations respecting the level of hierarchy:
First the operations in parentheses, then brackets and finally braces.Of the arithmetic operations, first the multiplication and divisions and then the additions and subtractions.a) 10 + 2³ * 4 - 1
10 + 8*4 - 1
10 + 32 - 1
42 - 1
41 (it applies)
b) 10 + 2³ * (4 - 1)
10 + 8 * (3)
10 + 24
34 (it doesn't applies)
c) (10 + 2³) * 4 - 1
(10 + 8) * 4 - 1
18*4 - 1
72 - 1
71 (it doesn't applies)
d) 10 + (2³ * 4) - 1
10 + (8*4) - 1
10 + 32 -1
42 - 1
41 (it applies)
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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14.2 in scientific notation
Answer: 1.42 x 10^1
Step-by-step explanation:
Answer: 1.42x10
Step-by-step explanation:
karen earn $10 per hour. she wants to go to a concert on saturday and the price of the ticket is $75, but her friend sold her a ticket for $50. if karen had to take 4 hours off of work to attend the concert, what was her total cost for going to the concert?
The total cost for going to the concert = $90.
What is opportunity cost?The loss of value or benefit that'd result from engaging in a particular activity option in comparison to engaging in such an alternative activity which offers a higher come back on value or benefit is referred to as opportunity cost. The value of the best alternative picked during the decision-making process is provided.
What makes the opportunity cost significant?We can select the best option out of all the options available with the aid of the idea of opportunity cost. It helps us use all of our resources as skillfully and productively as possible in order to maximize our financial gains.
According to the given data:For her part-time job, Karen receives a $10 hourly wage. The cost of the concert ticket after the discount is $50, so she decided to go.
It will cost money to take four hours off work. $10 x 4
=$40
Opportunity costs of going to the concert = $50 + $40
= $90
It is evident that the opportunity cost will be $90.
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I understand that the question you are looking for is:
Karen earn $10 per hour. she wants to go to a concert on Saturday and the price of the ticket is $75, but her friend sold her a ticket for $50. if Karen had to take 4 hours off of work to attend the concert ,What was her opportunity cost of attending the concert?
a.$40
b.$50
c.$75
d.$90
hint: since there are 100 terms in the sum, it isn’t a good idea to write them all out and add. use the formula for the sum of terms of a geometric sequence. leave the answer with exponents rather than using a calculator to try to get a decimal approximation of the answer.
Final answer obtained is 2/3
What is a geometric sequence?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio. For instance, the geometric progression 2, 6, 18, 54, etc. has a common ratio of 3. Similar to that, the geometric series 10, 5, 2.5, 1.25,... has a common ratio of 1/2.
Powers [tex]r^{k}[/tex] of a given non-zero number r, like [tex]2^{k}[/tex] and [tex]3^{k}[/tex], are examples of a geometric sequence. A geometric sequence's basic structure is
[tex]ar,ar^{2},ar^{3}.ar^{4},-----[/tex]
where a is not equal to 0 is a scale factor that is equal to the initial value of the series and r is not equal to 0 is the common ratio.
A series is a sum, whereas a progression is a sequence. This is the difference between the two.
∑[tex]_{i=0}^{n}[/tex] [tex]ar^{i}=\frac{a(1+r^{n+1})}{1-r}[/tex]
We see that n= 99, r= -1/2, a=1
∑[tex]_{i=0}^{99}[/tex] [tex](\frac{-1}{2}) i=[/tex] [tex]\frac{1-(\frac{-1}{2})^{99+1} }{1-\frac{1}{2} }=\frac{1-(\frac{-1}{2})^{100} }{1+\frac{1}{2} }=\frac{1-\frac{1}{2}^{100} }{\frac{3}{2} }[/tex]
[tex]=\frac{\frac{2^{100}}{2^{100}} -\frac{1}{2^{100}} }{\frac{3}{2} } =\frac{2*(2^{100}-1)}{3*2^{100}}[/tex]
[tex]\frac{2*(2^{100}-1)}{3*2^{100}}[/tex]
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A jeweler has 5 rings, each weighing 12 g, made of an alloy of 5% silver and 95% gold. She decides to melt down the rings and add enough silver to reduce the gold content to 75%. How much silver should she add?.
The amount of silver that should be added is 48% . A jeweler is said to have 5 rings that weigh 12 g apiece and are composed of an alloy of 20% silver and 80% gold.
What are linear equations?
An equation between two variables that, when plotted on a graph, produces a straight line.
The material will weigh 12 × 5 = 60 grams after melting all 5 rings.
The alloy's 20% silver and 80% gold content have been disclosed to us. Let's further say that the melted material receives an additional x grams of silver, resulting in a composition of 64% gold and 36% silver.
Thus, we can construct the following equation:
Amount of gold before = Amount of gold after mixing
So the equation we get
80% of 60 grams =64% of (X + 60) gram
0.80 × 60 = 0.64 (x + 60)
48 = 0.64x + 38.4
0.64x = 9.6
x = 9.6/0.64
x = 15
So
Amount of silver that needed to be added
= 0.64(15 + 60)
= 0.64(75)
= 48%
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Please help me I dont understand this! its due soon by the end on class omg!
The number of people who would prefer Choco chocolate chip is 120.
How many people would prefer Choco chocolate chip?
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
In order to determine the number of people who would prefer Choco chocolate chip , multiply the given ratio of people who prefer Choco chocolate chip by the total number of people in the group.
The number of people who would prefer Choco chocolate chip = (ratio of people who prefer choco / sum of ratios) x number of people
(3/5) x 200 = 120
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