How do we add/subtract fractions and mixed fractions?
The addition and subtraction of fractions and mixed fractions can be done by finding the lowest common multiple (LCM) of the denominators before simplifying.
Addition and subtraction of fractionGiven 3 1/2 + 2 3/4
= 7/2 + 11/4
Find the LCM of both denominators= (14+11) / 4
= 25/4
= 6 1/4
Given 3 1/2 - 2 3/4
= 7/2 - 11/4
Find the LCM of both denominators
= (14-11) / 4
= 3/4
Therefore, the addition and subtraction of fractions and mixed fractions can be done by finding the lowest common multiple (LCM) of the denominators before simplifying.
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Three angles add up to 180 degrees, angle one has a measure of 8x+8, angle two has a measure of 8x+8 and angle three has a measure of 2x+8.
Given that the sum of the angles is 180 degrees, what is the measure of angle one? Round your answer to the hundredths place IE 79.50.
The first angle will be 77.33°.
How to calculate the angle?It should be noted that the total angles will be 180°.
This will be illustrated as:
8x + 8 + 8x + 8 + 2x + 8 = 180
18x + 24 = 180
18x = 180 - 24
18x = 156
x = 8.667
The first angle will be
= 8x +8
= 8(8.667) + 8
= 77.33°
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Negative eight times negative three
Answer:
24
Step-by-step explanation:
to solve this you should first write it out
-8 * -3
now multiply them
the negatives cancel each other out
so
you can just do 8 * 3
and get 24
An appliance store decreases the price of a 19-In television set 29% to a sale price of $442.69. What was the original price?
The original price is $623.51.
How to compute the price?Let the original price be represented by x.
Since the appliance store decreases the price of a 19-In television set 29%, that means the percentage of the sales price will be:
= 100 - 29
= 71%
Therefore, the original price will be:
= 71% of x = $442.69
0.71x = $442.69
x = $442.69/0.71
x = $623.51
The price is $623.51.
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What are all the roots, both real and nonreal, of the equation x4 + x2 = 4x2 + 4? Negative one-half, one-half, negative 2 i, 2 i. Negative one-half, one-half, negative i, i. Negative 1, 1, negative 2 i, 2 i. Negative 2, 2, negative i, i.
The roots of the function x⁴+ x² = 4 x² + 4 are ±2 or x = ±i.
What is a complex number?A Complex number is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a function as x⁴+ x² = 4 x² + 4
x⁴+ x² - 4 x² - 4 = 0
x⁴+ - 3 x² - 4 = 0
Assume u = x²
x⁴+ - 3 x² - 4 = 0
Now using the substitution u = x² , then
u² - 3u - 4= 0 ← in standard form
(u - 4)(u + 1) = 0 ← in factored form
Then equate each factor to zero and solve for u
u - 4 = 0 ⇒ u = 4
u + 1 = 0 ⇒ u = - 1
Then convert u back into terms of x
x² = 4 ( take square root of both sides )
x = ± 2
x² = - 1 ( take square root of both sides )
⇒ x = ±i
Thus, The roots of the function x⁴+ x² = 4 x² + 4 are ±2 or x = ±i.
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Hannah owns a food truck that sells tacos and burritos.She sells each tacos for $3.75 and each burritos for$7.75 . Hannah must sell no less than $430 worth of tacos and burritos each day
PLEASE HELP!!! DUE TMRW!!!
The values of the required parameters based on the analysis of the dataset are as follows;
X MIN = 0
X MAX = 2
X Scl = 0.5
Y MIN = 0
Y MAX = 110
Y Scl = 20
What is a dataset?A dataset is a presentation of a collection of data. In a tabular form, a dataset is arranged such that each column of the table presents the data of a specific variable.
The table of values in the question are presented as follows;
d [tex]{}[/tex] p
0 [tex]{}[/tex] 110
0.25 [tex]{}[/tex] 90
0.5 [tex]{}[/tex] 80
0.75 [tex]{}[/tex] 75
1 [tex]{}[/tex] [tex]{}[/tex] 75
1.25 [tex]{}[/tex] 40
1.5 [tex]{}[/tex] 40
1.75 [tex]{}[/tex] 10
2 [tex]{}[/tex] 0
Please find attached a plot of the data in the table presented in the question
X MIN is the minimum x-value obtained from the set of x-values, which is the minimum value of the domain of the data in the table.
From the table in the question; X MIN = 0
X MAX is the maximum x-value obtained from the set of x-values of the data in the table, which is also the maximum x-value of the range of input values in the table.
The maximum x-value in the table, X MAX = 2
X scl is the scale the specification of the distance between consecutive tick marks on the x-axis.
The distance between tick marks on the x-axis of the attached graph, X Scl = 0.5
Y MIN is the minimum y-value obtained from the set of y-values, which is the minimum value of the range of the data presented in the table
The Y MIN obtained from the table is 0
Y MAX is the maximum y-value obtained from the y-values of the data in the table, which is the maximum value of the range of the data in the table
The maximum y-value, Y MAX = 110
Y Scl is the distance between consecutive tick marks on the y-axis of the graph of the data
The Y Scl of the y-axis of the attached graph Y Scl = 20
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(100 POINTS!) Evaluate each expression given that the variables have the following values: (image below)
One pizza will feed 4 people. How many pizzas are needed for 36 people?
pizzas
Answer:
9 Pizzas
Step-by-step explanation:
calculate the VAT charged on this amount R1599.00(VAT included)
Answer:
VAT = R239.85
Step-by-step explanation:
VAT = 15%
15/100 = 0.15
R1599 × 0.15 = 239.85
VAT = R239.85
How do I answer this
Answer:
[tex]m∠1 = 64°[/tex]
[tex]m∠2 = 26°[/tex]
[tex]m∠3 = 36°[/tex]
Step-by-step explanation:
[tex]m∠1→75° + 41° + m∠1 = 180° \\ m∠1 = 180 - 116[/tex]
[tex]m∠1 = 64°[/tex]
[tex]m∠2→64° + m∠2 = 90° \\ m∠2 = 90 - 64[/tex]
[tex]m∠2 = 26°[/tex]
[tex]m∠3→m∠3 + 54° = 90° \\ m∠3 = 90 - 54[/tex]
[tex]m∠ 3 = 36°[/tex]
(15 POINTS)
Find the value of x for which a||b.
2x+27=n and 3x-27 also = n
(please also explain your answer, thank u)
A recipe for cookies calls for 3 cups of flour for every 4 cups of oatmeal. how much floir is needed for a big batch of cookies that uses 16 cups of oatmeal?
The flour that is needed for a big batch of cookies that uses 16 cups of oatmeal will be 12 cups of flour.
How to calculate the value?From the information, it was stated that the recipe for cookies calls for 3 cups of flour for every 4 cups of oatmeal.
Therefore, the flour that is needed for a big batch of cookies that uses 16 cups of oatmeal will be:
= 3/4 × 16
= 12
Therefore, the flour that is needed for a big batch of cookies that uses 16 cups of oatmeal will be 12 cups of flour.
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HELP
Graph the following system of inequalities on the coordinate plane. You will need to explain your
work. Each correct line graphed WITH the correct explanation and shading is worth 2 points.
> − −
+ ≤
> −
See attachment for the graphs of the inequalities
How to graph the system of inequalities?To do this, we analyze and plot each inequality at a time
Having said that, we have
Inequality 1: y > -3x - 2
Here, we have
y > -3x - 2
The inequality > implies that the right-hand side of the origin will be shaded
Also, it means that the line of the inequality will be a dotted line
Inequality 2: 4x + 5y ≤ 20
Here, we have
4x + 5y ≤ 20
The inequality ≤ implies that the left-hand side of the origin will be shaded
Also, it means that the line of the inequality will be a closed line
Inequality 3: y > -4
Here, we have
y > -4
The inequality > implies that the upper part of the origin will be shaded
Also, it means that the line of the inequality will be a dashed line
See attachment for the graphs of the inequalities
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PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: [tex]3^{14}[/tex]
Step-by-step explanation:
[tex]\frac{3^{9} }{3^{-5} }[/tex]
Properties of exponents (negative exponent) says that a term can be moved from the numerator to the denominator and vice versa by flipping the sign.
So,
[tex]\frac{1}{3^{-5} } =3^{5}[/tex]
Properties of exponents (Product Rule) also say that
[tex]a^{x} *a^{y} = a^{x+y}[/tex]
So,
[tex]3^9*3^5=3^{9+5} =3^{14}[/tex]
Another way to solve this is simply using the Properties of exponents (Quotient Rule) which states
[tex]a^{x} /a^{y} =a^{x-y}[/tex]
So,
[tex]\frac{3^{9} }{3^{-5} }=3^{9-(-5)} =3^{14}[/tex]
Feng says that the set of ordered pairs {(0, 1), (3, 2), (3, -5), (5, 4)} represents a function. Determine whether his statement is true or false. Select the correct answer and justification. Multiple choice question. cross out A) True; every element of the domain is paired with an element of the range. cross out B) True; each relation is written as an ordered pair. cross out C) False; one element of the domain, 3, is paired with two different elements in the range, –5 and 2. cross out D) False; one element of the range, 3, is paired with two different elements in the domain, –5 and 2.
Answer:
It's C, a function cannot have an x paired with 2 different y's
Carol buys last year's best-selling novel, in hardcover, for $25.50. This is with a 15% discount from the original price. What was the original price of the novel?
Answer:
$30.00
Step-by-step explanation:
$25.50 = y(1 - 0.15)
$25.50 = y(0.85)
($25.50) / (0.85) = y
y = $30
Answer:
$30
Step-by-step explanation:
let x = the original price
x - .15x = 25.50
The original price - .15 of the original price is 25.25
.85x = 25.25 Divide both sides by .85
x = 30
Check:
30 - .15(30) = 25.25
30 - 4.50 = 25.25
25.25 = 25.25
Practice Another
A city lot has the shape of a right triangle whose hypotenuse is 4 ft longer than one of the other sides. The perimeter of the lot is 440 ft. How long is each side of the lot?
short leg
ft
long leg
ft
hypotenuse
ft
Short leg:___________ft
Long Leg:___________ft
Hypotenuse:___________ft
The length of each sides of the right triangle are as follows:
short leg = 27 ftlong leg = 90 fthypotenuse = 94 ftHow to find the sides of a right triangle?The shape of the city lot is a right triangle.
The hypotenuse side is 4 ft longer than one of the other side.
The perimeter of the lot is 440 ft.
Therefore, using Pythagoras theorem,
let
x = the other side
y = the second leg
x² + y² = (x + 4)²
x² + y² = (x + 4)(x + 4)
x² + y² = x² + 4x + 4x + 16
x² + y² = x² + 8x + 16
y² = 8x + 16
Hence,
x + x + 4 + y = 440
2x + y + 4 = 440
2x + y = 436
2x + y = 436
y = 436 - 2x
y² = 8x + 16
(436 - 2x)(436 - 2x) = 8x + 16
190096 - 872x - 872x - 4x² = 8x + 16
190096 - 1744x - 4x² = 8x + 16
4x² + 1752x -190080 = 0
4(x² + 438x - 47520) = 0
x² + 438x - 47520 = 0
Therefore,
x = 90 and x = - 528
Therefore, the hypotenuse side is 94 ft.
94² - 90² = y²
y = √8836 - 8100
y = √736
y = 27.1293199325
y = 27 ft
Therefore, the short leg, long leg and hypotenuse are 27 ft, 90 ft and 94 ft.
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Write an equation of a line passing through
the point (-1, 2) that is parallel to the line
y = -4x + 5
y + 1/4x - 9/4 is an equation of a line passing through the point (-1, 2) that is parallel to the line y = -4x + 5
In an equation, parallel lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.
Here given that y = -4x + 5
Here -4 is the slope and 5 is the y-intercept
To find a parallel line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.
y - y₁ = m(x - x₁)
We have, m = 1/4, x₁ = -1 and y₁ = 2
y - 2 = 1/4(x - (-1))
y - 2 = 1/4(x + 1)
y - 2 = 1/4x + 1/4
y + 1/4x - 9/4
What is point-slope formula?
You can use the point-slope form calculator to determine the equation of a line given its slope and a point on the line. You will soon understand what the point-slope form equation is and how it differs from the slope-intercept form equation.
The point-slope formula is expressed as
y - y₁ = m(x - x₁)
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Find the edge length of the cube.
Answer:
The volume of a cube is the edge length cubed (S^3)
To find the edge length when the volume is known find the cubic root of the volume.
Step-by-step explanation:
Edge = ∛1/27
Edge = 1/3 ft.
Marci needs to rent a storage unit. She needs to determine the volume of the storage unit to decide if the storage unit is big enough to hold her things. If the storage unit is 8 ft high, what is the volume of the storage unit?
WILL GIVE BRAINLY
A.
176 ft3
B.
136 ft3
C.
192 ft3
D.
144 ft3
When the storage unit is 8 ft high, the volume of the storage unit is C. 192ft³
How to calculate the volume?To determine the volume, V,
= Area of the rectangle ABCG + Area of the rectangle CDEF
Area of the rectangle ABCG =2 x 2 = 4 square feet.
Area of the rectangle CDEF = 6 x 3 = 18 square feet.
So, the area of the base ABCDEFG, A = 18+4 = 22 square feet.
The given height, h= 8 feet
Volume = 22 x 8 = 192 cubic feet.
Therefore, it should be noted that when the storage unit is 8 ft high, the volume of the storage unit is 192ft
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What is the standard form of 2y =6x + 4
Answer: solve for x
x=[tex]\frac{y-2}{3}[/tex]
solve for y
y=3x+2
Step-by-step explanation:
solve for x
2y=6x+4
Swap sides so that all variable terms are on the left hand side.
6x+4=2y
Subtract 4 from both sides.
6x=2y−4
Divide both sides by 6.
6
6x
Dividing by 6 undoes the multiplication by 6.
[tex]x=\frac{2y-4}{6}[/tex]
Divide −4+2y by 6.
x=[tex]\frac{y-2}{3}[/tex]
solve for y
2y=6x+4
The equation is in standard form.
2y=6x+4
Divide both sides by 2.
[tex]\frac{2y+2}{2} =\frac{6x+4}{2}[/tex]
Dividing by 2 undoes the multiplication by 2.
[tex]y=\frac{6x+4}{2}[/tex]
Divide 6x+4 by 2.
y=3x+2
Use the following information to find
x . Write the value of the variable.
B is between A and C
AB=4x-7
BC=20x-5 and
AB=BC
Using the given information, the value of the variable x is equal to -0.125.
The given question can easily be solved using the constraints given in the question. It is given that B is between A and C. Also, the given question is in the form of Linear equation in one variable. Linear equation in one variable is the one which is of the form ax+b=0 where a and b are real numbers and x is the variable.
So, this implies that AB+BC=AC
Also, AB=4x-7 and BC=20x-5 and it is given that AB=BC
Thus, this implies that:
AB=BC
4x-7=20x-5
Taking 20x from Right hand side to Left hand side and -7 from Left hand side to Right hand side.
4x-20x=-5+7
-16x=2
x=-2/16
=>x=-1/8
=>x=-0.125
Thus, the value of x is equal to -0.125.
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alan invests £1000 in a bank account with an interest rate of r% per year. after one year the value of the account is £1025.
calculate r.
Bank account with an interest rate of r% per year = 2.5%
Simple Interest :
Simple interest paid or received over a certain period is a fixed percentage of the principal amount.
Simple Interest=P×[tex]\frac{r}{100} }[/tex]×T
where:
P=Principal
r= interest rate on a certain period
T= Time
Given :
Principal(P)= £1000
Time (T)= 1 Year
Find :
the interest rate per year = r%
Now,
Interest earned on account = £1025 - £1000
Simple Interest= £ 25
Simple Interest=P×[tex]\frac{r}{100}[/tex]×T
25= 1000×[tex]\frac{r}{100}[/tex]×1
25×100=1000r
2500=1000r
[tex]\frac{2500}{1000} =r\\\frac{25}{10} =r\\\frac{5}{2} =r\\2.5=r[/tex]
r= 2.5%
the interest rate of r% per year. after one year the value of the account=2.5%
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Please help meeee it'll be great if you guys do.
The equation of the CD in slope-intercept form is: C. y = -4x + 2.
How to Write an Equation in Slope-intercept Form?The equation of a line in slope-intercept form can be written as y = mx + b. In this form, m represents the slope and b represents the y-intercept.
The slopes of lines that are parallel are equal, while the slopes of the lines that are perpendicular to each other are negative reciprocals of each other.
The slope (m) of the graph y = 1/4x - 3 is 1/4. Since AB of rectangle ABCD is perpendicular to the graph, then the slope (m) of AB would be the negative reciprocal of 1/4 which is: -4.
Also, since CD is parallel to AB, they would have the same slope, m = -4.
To find the equation of CD that is parallel to AB, substitute m = -4 and (a, b) = (-1, 6) into y - b = m(x - a):
y - 6 = -4(x - (-1))
y - 6 = -4(x + 1)
y - 6 = -4x - 4
y = -4x - 4 + 6
y = -4x + 2
Therefore, the equation of the CD in slope-intercept form is: C. y = -4x + 2.
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The average rate of change of
f from x =2 to x =5
is _________ -5/4 is incorrect
Answer:
-1 or -3/3
Step-by-step explanation:
Average rate of change = slope
x = 2 x = 5
(2,3) (5,0)
Slope formula: y₂-y₁/x₂-x₁
(0-3)/(5-2) = -3/3 or -1
A men’s dress shirt costs $45, but it is $8.1 off today. What is the percentage saved if the customer purchases the shirt today? What percentage of the original price is the sale price? What percent discount is offered on the shirt?
The percentage saved if the customer purchases the shirt today will be 18%.
The percentage of the original price which is the sale price will be 82%.
The percent discount offered on the shirt is 18%.
How to calculate the percentage?From the information, the men’s dress shirt costs $45, but it is $8.1 off today, the percentage saved if the customer purchases the shirt today will be:
= Amount off / Cost × 100
= 8.1/45 × 100
= 18%
The percentage of the original price that is the sale price will be:
= ($45 - $8.1) / $45 × 100
= 36.9/45 × 100
= 82%
The percent discount offered on the shirt is 18%.
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The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $6 and each adult ticket sells for $9. There was a total of $747 in revenue from the sale of 98 total tickets. Write a system of equations that could be used to determine the number of student tickets sold and the number of adult tickets sold. Define the variables that you use to write the system.
Answer:
x + y = 989x + 6y = 747==============================
Let the number of adult tickets be x and student tickets be y.
Set equationsNumber of tickets:Adult tickets + student tickets = 98x + y = 98Amount of revenue:Total of adult tickets = 9x, total of student tickets = 6y9x + 6y = 747What is the solution to r/-3 = 12? A. r=-36 B. r= -4 C. r=4 D. r=36 (1 point)
Usted arrienda un local de su propiedad por un valor mensual de $1´600.000 y decide ahorrar
durante dos años este ingreso. Determine el valor acumulado en su cuenta de ahorros al finalizar
los dos años, si la tasa de interés que reconoce la entidad financiera por estos ahorros es 5,25%
efectiva semestral.
Usando la fórmula del valor futuro, se encuentra que el valor acumulado en su cuenta al final de los dos años es de $110,615.
¿Cuál es la fórmula del valor futuro?La formula es dada por:
[tex]V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right][/tex]
En que:
P es el pagamiento.n es el numero de pagamientos.r es la taja de interés.En este problema, hay que:
El valor mensual es de $1,600, por eso P = 1600.La taja de interés es semestral, asi r = 0.0525/2 = 0.02625.Al largo de los dos años, há 12 x 2 = 24 pagamientos, por eso n = 24.Así:
[tex]V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right][/tex]
[tex]V(24) = 1600\left[\frac{(1 + 0.02625)^{23}}{0.02625}\right][/tex]
V(24) = $110,615.
El valor acumulado en su cuenta al final de los dos años es de $110,615.
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