The consecutive integers are 12 , 13 ,14, and 15 .
Integers are real , rational numbers which are not fractions.Integers can be negative , positive or zero. Integers are represented on the number line . Integers are a subset of Real numbers.Of the four consecutive integers let us consider the smallest integer be x.
Therefore the other 3 integers are x+1 , x+2 and x+3 .
Therefore the sum of the integers are:
x +(x+1)+(x+2)+(x+3)=4x+6
The sum of the integers is given 54.
∴4x + 6 = 54
or, 4x = 54 - 6
or, 4x = 48
or, x = 48 ÷ 4
or, x = 12
Therefore the three other integers are 13,14 and 15.
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Scarlett made a scaled copy of the following quadrilateral. She used a scale factor greater than 1.
A
B
C
D
What could be the length of the side that corresponds with AD on the scaled copy of the
quadrilateral?
Answer:
Step-by-step explanation:
First of all AD is 9 units long. Anything less than or equal to 9 is not an answer because the scale factor is greater than 1. That means that anything over 9 will work.
So the answer must be 12 or 15 from those answers given.
Please help with problem 8
Answer:
The correct answer is A.
diary entry on 180 word about a sick friend 3 entrys
Factor each expression.
x²+x-6
After solving, the factors of equation x²+x-6 are:
(x-2) and (x+3)What is an equation, clearly?A mathematical statement made up of two characterizations joined by an equal sign is known as an equation.3x - 5 = 16 is an example of an equation.We get the value for the variable x as x = 7 after solving this equation.So,
Given the equation: x²+x-6
Then,
x²+x-6x²+x( - )-6x²+x(3-2)-6x²+3x-2x-6x(x+3)-2(x+3)Factors are: (x+3) and (x-2)
Therefore, after solving, the factors of equation x²+x-6 are:
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Choose all properties that were used to simplify the following problem:
[38 + 677] + (-38)
[677 + 38] + (-38)
677 + [38 + (-38)]
677 + 0
677
A.associative property of addition
B.distributive property
C.additive inverse
D.additive identity
E.commutative property of addition
The properties used to simplify the problem are associative property of addition, additive inverse, and additive identity.
Consider the given problem;
( 38 + 677 ) + ( - 38 )
The associative properties can be represented as:
( A + B ) + C = A + ( B + C )
Now, we need to check all the options to determine the properties used:
( 38 + 677 ) + ( - 38 ) = 38 + ( 677 - 38 )
( A + B ) + C = A + ( B + C )
Therefore, this is the associative property.
Now,
677 + 0 = 677
A + 0 = A
Thus, this is the additive identity.
Similarly,
677 + [ 38 + ( -38 ) ]
Here, 38 + ( -3 8 ) represents,
A + ( - A ) = 0.
Therefore, this is the additive inverse.
Thus, the properties used to simplify the problem are the associative property of addition, additive identity, and additive inverse properties.
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Solve each equation.
ln (x+2)- ln 4=3
After solving the given equation ln(x+2)-ln4=3, the value of [tex]x=e^{4 \ln +3}-2[/tex].
What exactly is an equation?An equation is a mathematical statement made up of two expressions joined by an equal sign.An example of an equation is 3x - 5 = 16.After solving this equation, we obtain the value of the variable x as x = 7.So,
Given equation: ln(x+2)-ln4=3Then,
ln(x+2)-ln4 = 3log(e)(x+2)-In4 = 3log(e)(x+2)-4In = 3[tex]x=e^{4 \ln +3}-2[/tex]Therefore, after solving the given equation ln(x+2)-ln4=3, the value of [tex]x=e^{4 \ln +3}-2[/tex].
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Given the expression -7x -1/6y +2z - xy+28 answer the questions below
A. how many terms are there? How did u find them
B. how many different variables are there list all of them.
C. what is the coefficient of the 4th term.
Answer:
A. 5 || how? uh counting; -7x -1/6y +2z -xy +28
B. 3 (2;x | 2;y | 1;z)
C. 28
Hope this helps!
--Blu
Translate each of the following verbal descriptions into an algebraic rule.The total cost of the order, t, is 11 dollars multiplied by the number of pizzas ordered, p.
The algebraic expression which correctly represents the verbal description; The total cost of the order, t, is 11 dollars multiplied by the number of pizzas ordered, p is; t = 11p.
Which algebraic expression correctly represents the verbal description as in the task content?It follows from the task content that the expression which correctly represents the verbal description be determined.
On this note, since total cost is; t and the number of pizzas ordered is; p.
The required expression is therefore;
t = 11 × p
t = 11p.
Ultimately, the verbal representation of the algebraic expression where total cost of the order, t, is 11 dollars and number of pizzas ordered, is p is given by t = 11p.
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Find all solutions to 8x³-10x² - 21x + 18 = 0 if x= 2 is one solution.
According to the given cubic equation 8x³-10x² - 21x + 18 = 0 the other value of x will be 4.
How does one solve a three-degree equation?Traditionally, a cubic problem can be solved by converting it to a quadratic equation and then solving it using factoring or the quadratic formula. A cubic equation, like a quadratic equation, has three roots.
What is the simplest method for solving a cubic equation?The typical strategy for solving a cubic problem is to convert it to a quadratic equation and then solve the quadratic using the standard methods, either factoring or using the formula. All of them are cubic equations. A cubic equation, like a quadratic equation, may have two or three real roots.
According to the given data:8x³-10x² - 21x + 18 = 0
x= 2
substituting the value in the equation we get:
8x³-10x² - 21x + 18 = 0
8(2)³-10(2)² - 21(2) + 18 = 0
68 - 40 - 42 + 18 = 0
4 = 0
According to the given equation 8x³-10x² - 21x + 18 = 0 the other value of x will be 4.
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ojos del salado is the highest mountain in chile, with a peak at about 6900 meters above sea level. The atacama trench, just off th coast of peru and chile,is about 8100 meters below sea level (at its lowest point.) What is the difference in elevations between Mount Ojos del salado and the atacama trench.
The difference in elevations between Mount Ojos del salado and the atacama trench is 15000 meters
From the question, we are to calculate the difference in elevations between Mount Ojos del salado and the atacama trench
From the given information,
"Ojos del salado is the highest mountain in Chile, with a peak at about 6900 meters above sea level"
and
"The atacama trench, just off the coast of Peru and Chile, is about 8100 meters below sea level"
Thus,
With respect to the sea level,
The elevation of Mount Ojos del salado is 6900 meters
and
The elevation of the atacama trench is -8100 meters
Then,
The difference in elevation between Mount Ojos del salado and the atacama trench is 6900 - (-8100) meters
6900 - (-8100)
= 6900 + 8100
= 15000 meters
Hence, the difference in elevations between Mount Ojos del salado and the atacama trench is 15000 meters
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90+x+67+35=180
Step by step please if someone could help
Answer:
[tex] \sf{x=−12}[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
90+x+67+35=180
Step 1: Simplify both sides of the equation.
90+x+67+35=180
(x)+(90+67+35)=180(Combine Like Terms)
x+192=180
x+192=180
Step 2: Subtract 192 from both sides.
x+192−192=180−192
x=−12
what is the change in temperature between 24 Celsius and 15 Celsius
Answer:
It got colder by 9 degrees
Step-by-step explanation:
A fire is steadily burning at a temperature of 600 degrees F. If the fire is no longer maintained, the temperature drops 20 F every half hour. After how many hours will the fire be out?
When the fire is steadily burning at a temperature of 600 degrees, the number of hours needed to run out is 30 hours.
How to illustrate the information?From the information, the fire is steadily burning at a temperature of 600 degrees F and t was stated that the fire is no longer maintained, the temperature drops 20 F every half hour.
Therefore, the appropriate expression to solve the information will be:
Let the number if hours be h
600 - (20 × h) = 0
600 - 20h = 0
20h = 600
Divide
h = 600 / 20
h = 30
Therefore, when the fire is steadily burning at a temperature of 600 degrees, the number of hours needed to run out is 30 hours.
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How is solving a square root equation similar to solving an absolute value equation? How is it different?
The absolute value will always be a positive number while solving an equation that does not involve an absolute value could be any number.
The absolute value of a number n, written |n|, can be described
geometrically as the distance of n from 0 on the number line.
For instance, |42| = 42 and |–42| = 42. Both 42 and –42 are 42 units
from zero.
Algebraically, the absolute value of a number can be defined
piecewise as follows.
|x| = {
x, for x ≥ 0
–x, for x < 0
Examine the definition carefully. Because –x is the opposite of x,
–x is positive when x is negative. For instance, |–7.4| = –(–7.4) = 7.4.
Thus |x| are |–x| are never negative, and, in fact, |x| = |–x|.
On many graphing utilities, spreadsheets, and CAS, the absolute–
the value function is denoted abs. For example, abs(x–3) = |x–3|.
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How does the multiplicity of a zero determine the behavior of the graph at that zero?
Select answers form the drop-down menus to correctly complete the statements.
A seventh degree polynomial function has zeros of −6 (multiplicity of 2), 0, 1 (multiplicity of 3), and 4.
The graph of the function
Choose...
the x-axis at −6.
The graph of the function
Choose...
the x-axis at 0.
The graph of the function
Choose...
the x-axis at 1.
The graph of the function
Choose...
the x-axis at 4.
The graph at:
x=-6,-4→intersects directly
x=0→passes through
x=1→tangent
At different x-intercepts, graphs exhibit varying behaviours. On occasions, the graph will intercept the x-axis and cross it. On occasions, the graph will contact the x-axis and then deviate from it. The graphs contact or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities. Higher even powers, such as 4, 6, and 8, will still cause the graph to contact and deviate from the x-axis, but as even power increases, the graph will appear flatter as it does so.The graph will still cross through the x-axis for higher odd powers like 5, 7, and 9, but for each rising odd power, the graph as it approaches and departs the x-axis, it seems flatter.
The zeros of a polynomial function of seventh degree are -6, 4, 1(multiplicity of 2) and 0(multiplicity of 3).The graph will intersect directly at x = -6 and x = 4.Since x = 0 has an odd multiplicity > 1, the graph will "pass through while hugging" at this point (this will always be the case with an odd multiplicity > 1).The graph will always be tangent with an even multiplicity because we have an even multiplicity at x = 1.∴x=-6,-4→intersects directly
x=0→passes through
x=1→tangent
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When would an ordinary annuity consisting of quarterly pay- ments of $500 at 6% compounded quarterly be worth more than a principal of $5,000 invested at 4% simple interest?
Firstly we will convert the percent R into a decimal value r. For that, we will divide with a hundred,
r = R/100
r = 6/100
r = 0.06 rate per year,
Then solve the equation for A
A = P(1 + r/n) ^ nt
A = 500.00(1 + 0.06/12) ^ (12 x 10)
A = 500.00(1 + 0.005)^ 120
A = $909.70
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $500.00 at a rate of 6% per year compounded 12 times per year over ten years, is $909.70.
I = A - P = $2,000.00
Equation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 4%/100 = 0.04 per year.
Solving our equation:
A = 5000(1 + (0.04 × 10)) = 7000
A = $7,000.00
The total amount accrued, principal plus interest, from simple interest on a principal of $5,000.00 at a rate of 4% per year for ten years is $7,000.00.
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Using the change of base formula, what is the value of x for which log₉x=log₃5 ?
The value of x using the change of base formula of logarithm is 25.
What are the various properties of the logarithm?
Out of several properties of logarithms, some of the main properties are given below:
Product Rule
log (ab) = log a + log b
Change of base
log ₇ x = log x / log 7
Power Rule
log a² = 2 log a
Quotient Rule
log (a / b) = log a - log b
Solving the given equation by using the change of base formula
We are given a logarithmic expression: log ₉ x = log ₃ 5
Using properties of the logarithm, we have
log x / log 9 = log 5 / log 3
log x = (log 5 × log 9) / log 3
= (log 5 × 2 log 3) / log 3
= 2 × log 5
= log 5²
log x = log 5²
Applying exponent both sides, we get,
x = 25
Hence, the value of x is 25.
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Using the quadratic formula, solve 0 = 2x²-14x +9 Give each of your answers to 2 d.p.
help please
Answer:
x=6.28 0r 0.72
Step-by-step explanation:
The explanation is in the image
What polynomial must be added to -5c² - 3+ 4c in order to get a sum of -2c²-c+1?
Answer: 3c^2 +4 -5c
Step-by-step explanation:
-2c^2 -c +1 -(-5c^2 -3 +4c)
3c^2 +4 -5c
Solve each equation for θ with 0 ≤ θ <2 π.
cotθ=-10
Answer:
0 with 0 2 pi cot0=-10 am not sure what It is
What does |-5| + |7| equal?
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Remember that we're using absolute values. A negative number plus a positive number is the same as a positive number subtracted by another positive number.
what is the equation of this parabola??
The equation of the parabola in vertex form is y = - (1 / 4) · x².
How to derive the equation of the parabola
In this problem we find a parabola whose axis of symmetry is on the y-axis and the directrix is above the parabola, which means that the least distance between the vertex and the directrix is negative. The equation of the parabola in vertex form is described below:
4 · p · (y - k) = (x - h)²
Where:
p - Least distance of the vertex from the directrix.(h, k) - Coordinates of the vertex.If we know that p = - 1 and (h, k) = (0, 0), then the equation of this parabola is:
4 · (- 1) · y = x²
- 4 · y = x²
y = - (1 / 4) · x²
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Julie is a member of a swim club. The swim club
charges a monthly fee of $15 plus $0.50 per hour
to use the pool. Julie spent $35 in August to use
the pool. How many hours did Julie use the pool
in August?
Answer: 40 hours
Step-by-step explanation:
As stated in the question the total amount spent in the month of august is $35.
First of all you have to subtract 15 out of the entire amount spent so that you can start calculating how many hours did Julie use the pool.
(35-15) = 20 (divide the answer with 0.50)
(20/0.50) = 40 (We have to divide to get the amount of hours she spent in pool)
A cargo plane flew to the maintenance facility and back. It took one hour less time
The time it took to fly through ah fro is 21 hours
x=21 hrs
This is further explained below.
How many hours did the trip take?Generally, A cargo aircraft traveled to the repair facility and returned again, and the flight there took an hour less of its total time than the flight back did.
The voyage there had an average speed of 220 miles per hour, whereas the return back had an average speed of 200 miles per hour. I was wondering how many hours the journey took.
Generally, the equation for the distance is mathematically given as
Dist = speed * time
Therefore
Dist to = dist back
220t = 200(t+1)
220t = 200t + 200
220t - 200 = 200
20t = 200
t = 200/20
t = 10 hrs to
Considering for hours back
10 + 1 = 11 hrs back
Total hrs: 10 + 11 = 21 hrs for the round trip
In conclusion, The trip took
21 hrs
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CQ
a cargo plane flew to the maintenance facility and back it took one hour less time to get there than it did to get back. the average speed on the trip there was 220mph the average speed on the way back was 200mph how many hours did the trip take
Simplify (h³)^7
Please
Answer:
[tex]\sf \bf h^{21}[/tex]
Step-by-step explanation:
Exponent law:We have to multiply the powers.
[tex]\sf \boxed{\bf (a^m)^n=a^{m*n}}[/tex]
[tex]\sf (h^3)^7=h^{3*7}[/tex]
[tex]\sf = h^{21}[/tex]
PLEASE HELP I’LL GIVE BRAINLIEST!!!!
Which equation represents the line through (0, 0) and (4, 7)
A. y = 7/4x
B. y = 4/7x
C. y = 7x
D. y = 4x
Answer:
A) [tex]y = \frac74x[/tex]
Step-by-step explanation:
Since the equation's graph passes through the origin, its [tex]c[/tex] value is equal to 0, and, therefore, you will only need to find the slope as the equation is of the template [tex]y = mx[/tex] where [tex]m[/tex] is the slope.
To find the slope, you can substitute the coordinates of the given points into the formula for a line's slope: [tex]y = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]y = \frac{7 - 0}{4 - 0} \to \frac74[/tex]
Therefore, the line's equation is [tex]y = \frac74x[/tex]
an oil tank is being filled at a constant rate of .2 feet per minute. After 15 minutes the tank is 6 feet deep. Write an equation that can be used to determine the amount of oil in the tank at any time.
The equation that represent amount of oil in the tank at x minutes is
6- 0.2t
What is an equation?A mathematical statement that shows that two mathematical expressions are equal.
Given:
rate of filling the tank = 0.2 feet/ minute
After 15 minutes,
height = 6 feet
let the time take be x minutes
So, the equation that represent amount of oil in the tank at x minutes.
=6- 0.2t
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i need help on this 4−d<4+d
For all the values of 'd' the expression 4-d will be less than 4+d.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
Given that 4−d < 4+d. The inequality expression will be solved as:-
4−d < 4+d
4 - 1 < 4 + 1
3 < 5
4 - 2 < 4 + 2
2 < 6
It is concluded that for all the values of d in the given expression the portion 4 - d will be less than 4 + d.
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The vertices of a quadrilateral are A(−5, 3), B(2, 2), C(4,−3), and D(−2,−2). Find the slope of each side.
The sole of AB = 1/7, BC = -5/2, CD= -1/6, DA= -5/3
Here we have to find the slope of the side of the quadrilateral
The formula of the slope between A(x1, y1), B (x2, y2)
slope = (y2 - y1)/( x2- x1)
Slope of AB , where A = (-5, 3), B = (2,2)
AB = (2-3)/ ( 3- (-5))
= 1/ 8
Slope of BC, where B= (2,2 ), C = (4, -3)
BC = (-3 -2)/ (4-2)
= -5/2
Slope of CD, where C= (4,-3), D=(-2,-2)
CD = (-2-(-3))/ (-2-4)
= 1/ (-6)
=-1/6
Slope of DA , where D=(-2,-2), A=(-5,3)
DA= (3-(-2))/(-5-(-2))
= (3+2)/(-5+2)
= 5/-3
=-5/3
Therefore the slope of AB, BC, CD, DA = 1/7, -5/2, -1/6, -5/3 respectively.
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(-3 1/3 n +1/6) + (1 3/6n - 3/12 )
- 2/6n-1/12
-29/6 n + 1/12
-11/6n - 1/12
- 11/6n+5/12
(-3 1/4d +3/5) -2 7/8 d +7 /10
Answer:
[tex]\frac{4080n+1585d-188}{240}[/tex]
Step-by-step explanation:
I simplified it to the best possible state