infinitely many solutions
Example
Simplify left side using distributive property to 6x+16. Combine like terms (2x and 4x) on the right side to 6x+16. Both sides simplify to the same expression (left side = right side) so there are infinitely many solutions. You can plug in any real number for x and the left side will always equal the right side.
Consider the point \left(x,y\right)(x,y) in the coordinate plane.
What is the rule for translating the point 5 units down?
1. (x,y−5)
2. (x,y+5)
3. (x+5,y)
4. (x−5,y)
Answer:
The first option
Step-by-step explanation:
(100 POINTS!) Evaluate each expression given that the variables have the following values: (image below)
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]
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]
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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(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)
the day of the month
a) interval
b)ordinal
c) nominal
d) ratio
?
The day of the month is nominal (option c).
What is nominal data?Nominal data is data that can be labelled or classified into mutually exclusive categories within a variable. A nominal variable is a categorical variable that is qualitative.
A ratio scale is quantitative. A ratio scale is a variable with a true zero. An example is weight. An interval variable is a variable where each value is measured along a scale. An example of an interval variable is credit score.
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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.
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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Stephan monthly pay stub indicates that his monthly gross income is 3800 however 800 is withheld for income and social security taxes and 200 is withheld for his health and disability insurance how much is Stephan’s Disposable income
Step-by-step explanation:
3800 is the general amount, but before he can touch it, 800 and 200 are taken away from it for the described purposes.
so, what is left is
3800 - 800 - 200 = 2800
this is then the real amount he can do something with.
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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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
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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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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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
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
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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A town's population has been growing linearly. In 2003, the population was 59,000
and the population has been growing by 1,700 people each year. Let P represent the
population, and the number of years after 2003.
Answer
59,000+1,700=60,000
Step-by-step explanation:
The price of a McChicken sandwich at McDonald's was $1.00 in 2018, and the sandwich
is now $2.44 in 2022. Find the percent increase of the sandwich that occurred from
2018 to 2022. (Round to the nearest whole percent)
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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*100 POINTS!* Answer fast
Answer:
[tex](x-6)^2=-1[/tex]
Step-by-step explanation:
Given equation:
[tex]-6x^2+64x-222=-8x[/tex]
When completing the square, first move the terms in x to the left and the constant to the right of the equation:
[tex]\implies -6x^2+64x-222=-8x[/tex]
[tex]\implies -6x^2+64x-222+222=-8x+222[/tex]
[tex]\implies -6x^2+64x=-8x+222[/tex]
[tex]\implies -6x^2+64x+8x=-8x+222+8x[/tex]
[tex]\implies -6x^2+72x=222[/tex]
Factor out the leading coefficient -6 from the left side, then divide both sides by -6:
[tex]\implies -6(x^2-12x)=222[/tex]
[tex]\implies \dfrac{-6(x^2-12x)}{-6}=\dfrac{222}{-6}[/tex]
[tex]\implies x^2-12x=-37[/tex]
Add the square of half the coefficient of the term in x to both sides, forming a perfect square trinomial on the left side:
[tex]\implies x^2-12x+\left(\dfrac{-12}{2}\right)^2=-37+\left(\dfrac{-12}{2}\right)^2[/tex]
[tex]\implies x^2-12x+\left(-6\right)^2=-37+\left(-6\right)^2[/tex]
[tex]\implies x^2-12x+36=-37+36[/tex]
[tex]\implies x^2-12x+36=-1[/tex]
Factor the perfect square trinomial on the left side:
[tex]\implies (x-6)^2=-1[/tex]
To solve:
[tex]\implies \sqrt{(x-6)^2}=\sqrt{-1}[/tex]
[tex]\implies x-6=\pm i[/tex]
[tex]\implies x-6+6=\pm i+6[/tex]
[tex]\implies x=6 \pm i[/tex]
Therefore, the solutions are:
[tex]x=6+i, \quad x=6-i[/tex]
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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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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Select correct answer from the drop-down menu. Charlie stands at point while holding the control line attached to a model airplane. The plane travels 120 feet counterclockwise from point to point . About how long is the control line? A circle with center point A. C and B are points on the circle. A line connects AC and AB. The angle of A is 80 degrees. The control line is about feet long.
The 120 feet point to point displacement and the 80° angle formed at the vertex A by the control line, AC = AB, Charlie is holding, gives the length of the control line as about 93 feet.
How can the length of the control line be calculated?The given parameters are;
The distance (displacement) traveled by the plane = 120 feet (point to point)
The points on the circle, flown by the model plane = C and B
The center of the circle = A
The angle formed by AC and AB = 80°
Required;
The length of the control line.
Solution:
The control line in the description of the diagram is the line AC or AB
Therefore;
AC = AB
Taking the points C and B as the point the plane flew through, we have;
BC = 120 feet
Which gives
‹ABC = ‹ACB = (180° - 80°)/2 = 50°
From the law of sines, we have;
BC/(sin(A)) = AC/(sin(‹ABC))Which gives;
120/(sin(80°)) = AC/(sin(50°))
AC = 120×(sin(50°))/(sin(80°)) ≈ 93
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Answer:
The control line is about 86 feet long.
Hope this helps!
Step-by-step explanation:
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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PLS HELP! 50 points!
Xin has a dimes and y nickels. She has a maximum of 18 coins worth a minimum of $1.10 combined. Solve this system of inequalities graphically and determine one possible solution.
The x and y nickels and a dime. She has up to 18 coins totaling a minimum of $1.10 in value. In the graphically representation we can see the line intersect each other at point (12,6).
Given that,
The x and y nickels and a dime. She has up to 18 coins totaling a minimum of $1.10 in value.
We have to create a graphic representation of this inequality system and choose a potential resolution.
x + y ≤18----->equation(1)
Amount in pennies: 5x+10y≥110------>equation(2)
solves by eq2 - 5×eq(1)
5x+10y - 5(x+y) = 120 - 5×18
5x + 10y -5x-5y = 120 - 90
5y = 30
y=6
Then x=12
Therefore, x=12, y=6 is the point where two lines converge.
In the graphically representation we can see the equation (1) line and equation (2) line intersect each other at point (12,6).
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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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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
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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