Find three positive consecutive integers such that the product of the second integer and the third integer is 72
Answers
x---------> first positive integer
x+1------> second positive integer
x+2-----> third positive integer
we know that
(x+1)*(x+2)=72-------> x² +2x+x+2=72 -------> x² +3x-70=0
using a graph tool-------> I solve the quadratic equation
see the attached figure
the roots are
x1=-10
x2=7
the answer is
first positive integer is x=7
second positive integer is x+1=8
third positive integer is x+2=9
Let xbe a positive integer number. Then x, x+1 and x+2 are three positive consecutive integers (the first one is x, the second is x+1 and the third is x+2).
The product of the second integer and the third integer is (x+1)·(x+2) and is equal to 72. So you have the equation
[tex](x+1)\cdot (x+2)=72.[/tex]
Solve it:
[tex]x^2+2x+x+2=72,\\ \\x^2+3x+2-72=0,\\ \\x^2+3x-70=0,\\ \\D=3^2-4\cdot (-70)=9+280=289,\\ \\\sqrt{D}17,\\ \\x_1=\dfrac{-3-17}{2}=-10,\ x_2=\dfrac{-3+17}{2}=7.[/tex]
Solution [tex]x_1=-10[/tex] is extra because [tex]x_1[/tex] is negative.
Answer: three positive consecutive integers are 7, 8 and 9.
Related Questions
WXYZ is a square. If WT=3, find each measure
Answers
Hope this helps.
ZX
Solution:
The diagonals of a square are congruent, and bisect each other.
So, ZX = WY = 2(WT) = 6
In this exercise we have to use the knowledge of quadrilaterals to calculate the measures of each side of the square, in this way we can say that it will be valid:
[tex]ZX = WY = 6[/tex]
Given in the exercise that each the value of:
WT=3The diagonals of a square are congruent, and bisect each other, that will help to find:
[tex]WT=3\\ ZX = WY = 2(WT) = 6[/tex]
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Please help!! Show your work !!
Answers
34^2+41^2=X^2
1156+1681=x^2
2837=X^2
√2837=x
x=53.26 that are the distance from A to B
Add 34+ 41= 75
Subtract to find distance saved----------- 75-53.26= ANSWER: 21. 74 meters
Using the given equation find the missing coordinates of the points and then find the slope of the line for each equation y=3.5x+4; a(...; 5), b(10; ...)
Answers
A(2/7:5)
B(10:39)
The slope is 7/2.
The slope of the line y=3.5x+4 is 3.5, and the missing coordinates will be filled as a(0.28, 5) and b(10, 9)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given equation of line is y=3.5x+4
When we compare this with slope intercept form y=mx+b.
slope m=3.5
We need to find the value of x when y is 5
5=3.5x+4
1=3.5x
Divide both sides by 3.5
x=0.28
So a coordinates are (0.28, 5)
Now let us find y value when x is 10
y=3.5(10)+4
y=39
So b coordinates are (0.28, 39)
Hence, the slope of the line y=3.5x+4 is 3.5, and the missing coordinates will be filled as a(0.28, 5) and b(10, 9)
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How many pairs of parallel line segments are shown?
1. 8
2. 24
3. 4
4. 18
Answers
We then have as parallel edges:
AC and GE
CG and AE
CD and GH
AB and EF
BD and HF
DH and BF
CD and EF
GH and AB
Answer:
8 pairs of parallel lines
Answer: The correct answer is 8
Find the function p defined by a polynomial of degree 3 with real coefficients that satisfy the given condition. two of the zeros are 4 and 1+i
Answers
y = (x - 4)(x - i)(x + i)
y = (x - 4)(x^2 + 1)
y = x^3 - 4x^2 + x - 4
which statement can be proved if you are given that SK≌LR?
Answers
Answer:
C
Step-by-step explanation:
The correct answer is C.[tex]$\overline{SL}\cong\overline{KR}$[/tex]
Given that [tex]$\overline{SK}\cong\overline{LR}$[/tex] , we can see that triangle SKL is congruent to triangle LRP by the Side-Side-Side (SSS) congruence postulate. This means that all corresponding sides and angles of the two triangles are congruent.
Since [tex]$\overline{SK}\cong\overline{LR}$[/tex]is given, we know that [tex]$\overline{SL}\cong\overline{KR}$[/tex] must also be true. The other answer choices do not necessarily follow from the given information.
The complete question is: Which statement can be proved if you are given that SK≌LR?
What is the value of y if (4y + 8) - (7y - 12) = 11? (PLEASE ANSWER + 10 POINTS!!!!)?
Answers
(4y + 8) - (7y - 12) = 11 is 1(4y + 8) - 1(7y - 12) = 11
1(4y + 8) - 1(7y - 12) = 11 Given
4y + 8 - 7y + 12 = 11 Distribute the 1 and the -1
-3y + 20 = 11 Combine like terms
-3y = -9 Subtract 20 from both sides
y = 3 Divide both sides by -3
Answer:
y = 3
What is the simplified form of the quantity of x plus 5, all over the quantity of 9 − the quantity of x plus 4, all over the quantity of x plus 6?
Answers
Answer:
The answer above is the correct answer
What are the zeros of f(x) = 4x^2 - 12x + 8 (I need a clear explanation on how to solve it)
Answers
The zero of the quadratic function is therefore x = 1. Since both factors give the same zero, we have a repeated zero and f(x) only touches the x-axis at one point, x = 1.
The zeros of the quadratic function f(x) = 4x^2 - 12x + 8 are the values of x that make f(x) = 0. In this function, we can factor by finding two numbers that multiply to give the constant term (8 times 4, the coefficient of x^2) and add to give the coefficient of x (-12). Here, those numbers are -4 and -4, so we rewrite the middle term -12x as -4x - 4x, and factor by grouping:
4x^2 - 4x - 4x + 8 = 0
4x(x - 1) - 4(x - 1) = 0
(4x - 4)(x - 1) = 0
Now we have two factors equal to zero, which gives us two equations to solve:
4x - 4 = 0 or x - 1 = 0
x = 1
Part 1.] Identify the transformations that describe the graph of an odd function. Select all that apply.
reflection over the x-axis;
reflection over the y-axis;
reflection over the line y = x;
90° rotation around the origin;
180° rotation around the origin
Part 2.] Prove that if f(x) and g(x) are both even functions, then h(x) = f(x) + g(x) is an even function.
Answers
1) A odd function has the propriety f(-x)=-f(x)
Answer E
2)
if f(x) is even f(x)=f(-x)
if g(x) is even g(x)=g(-x)
h(x)=f(x)+g(x)=(f+g)(x)
h(-x)=(f+g)(-x)=f(-x)+g(-x)=f(x)+g(x)=(f+g)(x)=h(x)
h(x) is even
An urn contains six red balls, five black balls, and four green balls. If two balls are selected at random without replacement from the urn, what is the probability that a red ball and a black ball will be selected. Please explain how to do it
Answers
[tex]15\times14=210[/tex]
The favorable cases, number of possibilities:
[tex]6\times5=30[/tex]
Now we get the probability by dividing the above two numbers:
[tex] \frac{30}{210}=0.14 [/tex]
The probability that a red ball and a black ball is selected is 0.14.
Can someone plz explain Pythagoras theorem to me
Answers
So if the length of the hypotenuse = c units and the lengths of the 2 legs are a and b units The theorem says
c^2 = a^2 + b^2.
I assume you meant to say the Pythagorean Theorem. The Pythagorean Theorem is [tex] a^{2} + b^{2} = c^{2} [/tex] and it is used to find the length of a side of a triangle.
Hope this helps!
The ____ is the vertical number line on the coordinate grid
Answers
The y axis is the vertical number line on the coodinate grid.
Hope this helps!
I need help with this
Answers
17. 7^2 - 7 = 49-7 = 42
18. -9^2 - -9 = 81+9 = 90
19. 10(5) +4 = 54, 3*54 = 162
20. 3*5 = 15, 10(15) +4 = 154
Will FAN and MEDAL
A plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 7,600 feet, and the angles of elevation are given.
a. Find BC, the distance from Tower 2 to the plane, to the nearest foot.
b. Find CD, the height of the plane from the ground, to the nearest foot.
Answers
Part A) Find BC, the distance from Tower 2 to the plane, to the nearest foot.
in the triangle ACD
sin16=CD/(7600+BD)--------> CD=sin16*(7600+BD)---------> equation 1
in the triangle BCD
sin24=CD/BD-----------> CD=sin24*BD---------------> equation 2
equation 1=equation 2
sin16*(7600+BD)=sin24*BD-----> sin16*7600+sin16*BD=sin24*BD
sin24*BD-sin16*BD=sin16*7600----> BD=[sin16*7600]/[sin24-sin16]
BD=15979 ft
in the triangle BCD
cos24=BD/BC---------> BC=BD/cos24-------> 15979/cos24-------> 17491
BC=17491 ft
the answer part 1) BC is 17491 ft
Part 2) Find CD, the height of the plane from the ground, to the nearest foot.
CD=sin24*BD ( remember equation 2)
BD=15979 ft
CD=sin24*15979 -----------> CD=6499 ft
the answer part 2) CD is 6499 ft
Choose the situation that represents a function. The number of raisins in an oatmeal raisin cookie is a function of the diameter of the cookie. The inches of rainfall is a function of the day’s average temperature. The time it takes to cook a turkey is a function of the turkey’s weight. The number of sit-ups a student can do in a minute is a function of the student’s age.
Answers
In a function, there is an input and there is an output. The idea of a function is that each individual input is changed into an output.
The time it takes to cook a turkey depends on the size of the turkey.
Smaller turkeys would take less time to cook and larger turkeys would take longer to cook.
So if you start with the turkeys weight, you could determine how long it would need to cook. This is an example of a function.
The time it takes to cook a turkey is a function of the turkey’s weight. Then the correct option is C.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
Choose the situation that represents a function.
An intake and an outlet are both present in a function. Each unique supply is converted into a result as per the concept of a function.
The amount of the turkey determines how long it will take to cook.
Oversized turkeys will take longer to prepare than smaller turkeys, and vice versa.
The time it takes to cook a turkey is a function of the turkey’s weight.
Then the correct option is C.
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Which of the functions below is the inverse of the logarithm function?
Linear function
Exponential function
Rational function
Radical function
Answers
Answer:
Option 2 - Exponential function
Step-by-step explanation:
To find : Which of the functions below is the inverse of the logarithm function?
Solution :
The inverse of a logarithmic function is an exponential function.
As by property of logarithmic,
[tex]y=\log_b(x)\\\Rightarrow x=y^b[/tex]
For example -
Taking log function,
[tex]y=\log_2 x[/tex]
Applying property it convert into exponential function,
[tex]x=2^y[/tex]
The graphs of the logarithmic function and the exponential function are mirror images of one another.
Therefore, Option 2 is correct.
Paul has a tack stuck in his four-wheeler tire. If the tire has a diameter of 36 inches, how far does the tack travel in 62° of rotation?
A. 31π
B. 18π
C. 31 pi over 5
D. 31 pi over 90,
Answers
C. 31 pi over 5
~sbcardinals :)
hello there
your answer would be
C, 31 pi over 5
hope it helps
thank you
best regards Queen Z
If A(0, 0), B(3, 3), C(9, 3), and D(6, 0) are the vertices of a quadrilateral, do the points form a parallelogram? Justify your answer.
A. Yes, it is a parallelogram because the slope of segment AB equals the slope of segment DC, which equals 1, and AB = DC = square root of 18.
B. Yes, it is a parallelogram because the slope of segment AB equals the slope of segment DC, which equals −1, and AD = CD = 3 units.
C. Yes, it is a parallelogram because the midpoint of the diagonals of segment AC and segment BD is (4.4, 1.5).
D. No, it is not a parallelogram because the slope of segment AB = 1 and the slope of segment DC = −1.
Answers
it's a parallelogram but I'm not completely sure about the answer
I think that C is the correct answer
the picture can help you to find the answer.
hope this helps
How many hours of training would you need to have a salary of $1,265? 20 points
Hours of Training / Monthly Salary
10 1250
20 1400
30 1550
40 1700
50 1850
60 2000
70 2150
Answers
[tex] \frac{1250}{10 } = \frac{1265}{x} [/tex]
solve for x
1250x=12650
[tex]12650 \div 1250 = x[/tex]
x=10.12 hours
Is 5,783 − -500,500 positive or negative?
Answers
*positive (minus) a negative equals a positive*.
It has always stayed in my mind ever sense.
And because of this, I could be able to help you on this question.
This would be known to be a "positive".
As we mentioned above, (+)-(-)= (++).
Your answer: Positive.
we know that
A positive number minus a negative number is equal a positive number
so
we have
[tex]5,783-(-500,500)=5,783+500,500=506,283[/tex]
therefore
the answer is
A positive number
Each test grade in Sara's science class counts for 1/6 of the final grade. The final exam counts for 1/2. Sara's test scores are 72, 84, and 90. Her final exam score is 90.
What is Sara's final grade for the class?
A) 83
B) 86
C) 87
D) 89,
Answers
Andrea recorded the points she scored in her last eight basketball games. What is the mean absolute deviation of the scores
28,32,47,16,40, 35,38,54
Answers
The attached work shows how to find the MAD (mean absolute deviation).
Here are the steps:
1. Find the mean of the data. 2. Find the difference between the mean and the data values. 3. Find the average of these differences.
Consider the function y = 1.05(x/12), which represents the growth of capital in a bank account.
The annual interest is __%,
a. 12
b. 105
c. 1.05
d. 5
and the bank compounds the interest__ .
a. annually
b. continuously
c. daily
d. monthly
The balance of the account will grow __ .
a. logarithmically
b. exponentially
c. asymptotically
d. linearly
Answers
2) is D
3)is D
Answer:
The annual interest is,
Option d is correct
5%
The bank compounds the interest_
Option a is correct.
Annually.
The balance of the account will grow,
Option b is correct
exponentially
Step-by-step explanation:
Exponential growth function is given by:
[tex]y=(1+r)^x[/tex] .....[1]
where,
r is the annual interest in decimal
x is the number of periods.
As per the statement:
Consider the function:
[tex]y=(1.05)^{\frac{x}{12}}[/tex] where, x represents the time in months.
On comparing with [1] we have;
[tex]1+r = 1.05[/tex]
Subtract 1 from both sides we have;
r = 0.05 = 5%
The annual interest is, 5%
and
the bank compounds the interest annually.
The balance of the account will grow exponentially
geometry easyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Answers
The 1st selection in the 4th panel is appropriate.
___
* The figure is not necessarily a trapezoid if the diagonals do not bisect each other. It can be any quadrilateral with at least one pair of non-parallel opposite sides, a kite, for example.
Tom caught 4 fish and his son caught 12 fish.
The number of fish that Tom caught was what percent of the number of fish that his son caught?
Answers
To solve this problem, we need to divide 4 by 12.
4 ÷ 12 = 1/3
1/3 = 33.33%
Hope this helps!
(50 PTS) NEED HELP FAST ILL MARK BRAINLIEST AND RATE 5 STARS AND SAY THANK YOU
A tournament organizer recorded the number of people in different age groups who participated in the archery tournament. He then created the following histogram:Which of the following statements best compares the height of the bars of the histogram?
A.) There are more participants in the 20–39 age group than in the 0–19 and 60–79 groups combined.
B.) There are more participants in the 20–39 age group than in the 40–59 and 0–19 groups combined.
C.) There are twice as many participants in the 40–59 age group than in the 60–79 age group.
D.) There are twice as many participants in the 0–19 age group than in the 60–79 age group.
Answers
Answer:
d
blessed have one
What number belongs in the blank space in the formula??
Answers
The formula is An=An-1+d
Can someone graph it for me and answer a or b???
Answers
simplify 6/x-6+3x/x+5-1/(x-6)(x+5)
Answers
To simplify a complex algebraic expression, you handle fractions first by bringing them to a common denominator. However, the resources provided seem misplaced as they pertain to calculus rules and Chemistry, which are not relevant to this algebra question.
Explanation:The student's question is asking to simplify a complex algebraic expression: 6/x-6+3x/x+5-1/(x-6)(x+5). To simplify such an expression, it's best to deal with fractions first. Note that the given expression can also be expressed as three separate fractions summed together, i.e., (6/x-6) + (3x/x+5) - [1/(x-6)(x+5)]. Dealing with fractions in simplification, we combine them to a common denominator and rationalize the numerator and denominator. After that, simplify the resulting expression. However, with provided reference, it seems that there is a misunderstanding or a misplacement of information because resources given are about calculus rules and Chemistry which are not relevant in simplifying this algebraic expression.
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