We need to know about quadratic equation to solve this problem. The other three consecutive odd integers that satisfy the conditions are 11, 13 and 15.
We need to consider three consecutive odd integers, odd integers are integers that are not divisible by 2. Odd and even integers occur alternately so the the difference between two consecutive odd integers is always 2. We will consider one odd integer x, the next odd iinteger will be x+2 and the third odd integer will be x+4. Therefore we have our three consecutive odd integers, x, x+2 and x+4. It is said that the square of the third integer is 65 less than the sum of the squares of the first two. We can write this relation as
[tex](x+4)^{2} +65=x^{2} +(x+2)^{2}[/tex]
We can solve this equation to get a quadratic equation, and then solve it for x
[tex]x^{2} +8x+16+65=x^{2} +x^{2} +4x+4\\x^{2} +4x-8x+4-16-65=0\\x^{2} -4x-77=0[/tex]
We will solve the above quadratic equation for x
[tex]x^{2} -4x-77=0\\x^{2} +7x-11x-77=0\\x(x+7)-11(x+7)=0\\(x+7)(x-11)=0\\[/tex]
Therefore we get two values for x -7 and 11, from the question we already know about -7, we will find the three odd integers from 11 now
So the other three consecutive odd integers that satisfy the given conditions are 11,13 and 15.
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Subtract the following polynomials, then place the answer in the proper location on the grid.
2x^2+5x-10
3x2 - x + 9
Answer:
[tex]-x^2+6x-19[/tex]
Step-by-step explanation:
Step one:
given
[tex]2x^2+5x-10\\\\3x^2 - x + 9[/tex]
we want to perform a subtraction operation
[tex]2x^2+5x-10-(3x^2 - x + 9)\\\\ 2x^2+5x-10-3x^2 + x - 9 \\\\[/tex]
collect like terms
[tex]2x^2-3x^2+5x+x-10-9\\\\-x^2+6x-19[/tex]
Use the percent formula, A = PB, where A is P percent of B, to answer the following question. What is 24% of 60?
It should be noted that 24 percent of 60 is 14.4.
How to calculate the percentage?The question is to calculate 24% of 60.
This will go thus:
= 24% × 60
= 24/100 × 60
= 0.24 × 60
= 14.4
Therefore, 24% of 60 is 14.4.
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PLEASE HELP? What is the graph form of them equation?
Find the scale factor of trapezoid QRST if it’s dilated to Q’R’S’T’. Type your result in the empty box provided below. HELPP PLEASE!!!!!!
Answer:
5 units
Step-by-step explanation:
its hard to tell but i think it dilated 5 units
We want to find the scale factor at which QRST is dilated to form Q'R'S'T'
We will find that the scale factor is 2.
In a general dilation, we will see that all the measures change in the same way, by the scale factor.
This means that:
QR*k = Q'R'
RS*k = R'S'
And so on, where k is the scale factor.
Then we can just find one of the equivalent measures in both trapezoids and find the value of k.
For example, we have:
Q'R' = 8
QR = 4
Replacing these on the above equation we get:
4*k = 8
k = 8/4 = 2
k = 2
The scale factor of dilation is 2.
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Please someone help me: Complete the reasons for the proof.
Given:
m ∠3 = m ∠4
To Prove:
∠1, ∠2 are supplementary
Step-by-step explanation:
1) given
2) 2 non - common sides in 1 ray
3) supplemental
5) opposite angles are congruent
Reasons:
(1) Given
(2) their 2 non-common sides in 1 ray
(3) definition of supplemental angles
(4) Substitution
(5) Opposite angles are congruent (equal)
(6) Substitution
(7) Definition of supplementary angles
The mean of four number is 30. if three of the numbers are 12, 50, and 48 what's the fourth number?
Answer:
if the mean of 4 numbers is 30 then that means that the total of all the numbers added together must add up to 120 (30 x 4)
then you subtract the three numbers that you have from the total
120-12-50-48 = 10
so the last number is 10
Step-by-step explanation:
Write equations for the vertical and horizontal lines passing through the point (-3,0).
Answer:
x = -3
y = 0
Step-by-step explanation:
What is the image of (-3, -5) after a reflection over the x-axis
Answer:
(3,-5)
Step-by-step explanation:
I'm pretty sure sorry if I'm wrong
(7-6)•w
simplify the variable expression
Answer:
7w-6w
Step-by-step explanation:
I think this is what your asking for. If it is, you distribute the w
Answer:
w
Step-by-step explanation:
You complete the subtraction in the parentheses first, then multiple that by w. So:
(7-6) x w
(7-6) = 1
1 x w = w
help me lol
50 points for whoever answers correctly
Answer:
C
Step-by-step explanation:
You want to choose the number line graph that appropriately represents the inequality 0 < x ≤ 26.
Graphing inequalitiesThe given compound inequality is conveniently written with the "arrows" pointing to the left. This means the lower limit of the variable is on the left side of the inequality, just as it is on the left end of the number line graph.
The inequality symbols used are "less than" (<) and "less than or equal to" (≤). The "less than" symbol is represented on a number line graph by an open circle. The "less than or equal to" symbol is represented by a filled dot on the number line.
This means you are looking for a graph that has an open circle on the left end of a solid line, and a filled dot on the right end. Only graphs B and C have finite-length lines, and only graph C has a filled dot at the right end.
Car seatsIn English, the word "between" often implies "and including" when it is describing an interval between two limits. Here, you are given 3 car seat specifications:
A: 0 < x ≤ 26 . . . . . up to 26 lbsB: 18 ≤ x ≤ 35 . . . . . between 18 and 35 poundsC: 26 ≤ x ≤ 75 . . . . . between 26 and 76 poundsThe seats appropriate for a 33-lb child would be seats B and C, because 33 is included in each of those intervals.
Solve for x for the triangle
Answer:
(appx) 4.3
Step-by-step explanation:
[tex] \sin(64) = \frac{x}{10} [/tex]
[tex] = > 0.43 = \frac{x}{10} [/tex]
[tex] = > x = 4.3[/tex]
If a student is taking classes, math, English, P.E., history, biology and Spanish, then what is the chance that the student will take math period? Assume that there are six periods in one day.
10%
17%
25%
60%
Answer:
60%
Step-by-step explanation: i hope this heple
\
Juanita makes $26 an hour at work. She has to take time off work to purchase her skirt, so each hour away from work costs her $26 in lost income. Assume that returning to work takes Juanita the same amount of time as getting to a store and that it takes her 30 minutes to shop. As you answer
the following questions, ignore the cost of gasoline and depreciation of her car when traveling.
Answer: Local Department Store: $6.5, $118.5
Across Town: $13, $102
Neighboring City: $26, $96
Step-by-step explanation:
Local Department Store: 1 hr=60 min.
60/15=4
26/4=$6.5
112+6.5=$118.5
Across Town: 60/30=2
26/2=$13
89+13=$102
Neighboring City: 60/60=1
26/1=$26
70+26=$96
9 - (-4)=?
What does that equal to?
Answer:
= 13
Step-by-step explanation:
When you are subtracting a negative both the subtraction sign and the negative cancel out. This makes it so that you are adding them together.
Answer:
the answer is 13
Step-by-step explanation:
This is because when you subtract a positive by a negative if the positive is larger it will be considered the same as addition
If there are four quarters in a dollar, which expression correctly shows how you might figure out how many quarters are in $9.25
pls help me show my work and the answer :( tysm!!!
Answer:
37
Step-by-step explanation:
4(9) + 1 = 37
Answer:
There are 37 quarters in $9.25
Step-by-step explanation:
.25 x 37 = 9.25
or
.25 +.25+.25+.25+.25+.25+.25+.25+.25+.25+.25+.25+.25+.25+.25+.25+.25+.25+.25+.25+.25+.25+....till 37
Angles that form a linear pair
add up to [?]°
Answer:
180°
Step-by-step explanation:
Two adjacent angles whose sum add up to 180°are called Linear pair. The uncommon arms of two adjacent angles form a straight line.
Evaluate the numerical expression: 44
The second 4 is an exponent
its 256.............................
Use the number line to identify the least value, first quartile, median, third quartile, and greatest value of the data.
Ages of teachers (in years): 30, 62, 26, 35, 45, 22, 49, 32, 28, 50, 42, 35
Answer: least value - 22
first quartile - 29
median - 35
third quartile - 47
greatest value - 62
Step-by-step explanation:
Burj Khalifa in Dubai is the tallest building in the world, standing at 828 meters. An adjacent
building, 100 meters away, stands at 550 meters tall. What is the angle of depression from Burj
Khalifa to the adjacent building?
Answer:
Approximately 70 degrees
Step-by-step explanation:
If we make a right triangle connecting the two buildings, we get a triangle with height 278m and length 100m
We can connect these two values to the theta by using the inverse tan formula
arctan(278/100) = 70.21572110836 degrees.
The angle of depression is approximately 70 degrees
Can anyone help with this question on laws of exponents?
Write your own situation about the inequality below. 10 x + 20 ≤ 150
Answer:
k
Step-by-step explanation:
10)×20+21-150
you will end up getting your answers
I want you to just do the easy bit
the calculations if that's alright
The graph of y= 8x² + 7x - 5/5x² + 2x + 6 has a horizontal asymptote with equation (enter the equation of the horizontal asymptote)
The horizontal asymptote of the rational function y = (8 · x² + 7 · x - 5) / (5 · x² + 2 · x + 6) is y = 8 / 5.
How to determine the equation of a horizontal asymptote
A horizontal asymptote of a rational function is an horizontal line equations to which the rational function tends to when x tends to the infinite. The horizontal asymptote exists whether the lead grade of the numerator is not greater than the lead grade of the denominator.
Now we proceed to find the value of the horizontal function by using limit properties for rational functions:
y = 8 / 5
The horizontal asymptote of the rational function y = (8 · x² + 7 · x - 5) / (5 · x² + 2 · x + 6) is y = 8 / 5.
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A wall clock is generally a more precise tool for measuring a length of time than a stopwatch.
True
or
False
Answer:
False
Step-by-step explanation:
86.04005 is written in words as
Answer: eighty six point zero four zero zero five. OR eighty six and four thousand five, hundred thousandths
Step-by-step explanation:
the place value answer is a little confusing but its correct i believe
what is 7 7/8 dvided by 3 1/8 mixed numbers
Answer:
2.52
Step-by-step explanation:
Answer:
2.52
Step-by-step explanation:
To solve an equation you use the_____________ operation
Answer:
order of
Step-by-step explanation:
You have already saved $55. You earn $9 per hour babysitting. You are saving for a camera that costs $199. Write and solve an inequality represents the possible numbers you need to work to buy the camera.
49 students are enrolled in health and 21 students are not what percentage of students in the school are in rolled in Health 
Answer:
im pretty sure its 30%. because 70% are in heath. so 30% of the students arent. i think... hope this helped.
Step-by-step explanation:
Answer:
i'm pretty sure its 30%.
Step-by-step explanation:
because 70% are in heath. so 30% of the students arent. i think... hope this helped.
Select all the expressions which have 3 as the greatest common factor of the terms.
b + 3 + 6c
27n + 66p
38 – 9j + 6k
12x + 75y + 21
–32 – 24z
Answer:
27n+66p and 12x+75y+21
Step-by-step explanation:
The greatest common factor is 3 for 27n + 66p and 12x + 75y + 21.
What are Factors?Factors of a number or an algebraic expression are the numbers or expressions which divides the given number evenly.
For example, 10 = 2 × 5
So we can say that 2 and 5 are factors of 10.
Greatest common factor of two numbers or expressions, as the name suggests is the greatest of all the common factors of the given numbers or expressions.
Consider 27n + 66p
Factors of 27n are 1, 3, 9 and 27
Factors of 66p are 1, 2, 3, 6, 11, 22, 33 and 66
Greatest common factor of both = 3
Consider 12x + 75y + 21.
Common factors of three of them are 1 and 3.
Greatest common factor is 3.
Hence the expression with greatest common factor as 3 are 27n + 66p and 12x + 75y + 21.
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Brandon is going to invest in an account paying an interest rate of 5% compounded quarterly. How much would Brandon need to invest, to the nearest dollar, for the value of the account to reach $490 in 16 years?
Answer:
Brandon wants $490 in 16 years by investing "x" dollars in an account that pays 5% compounded quarterly. How much is "x"?
Principal = Total / [ (1 + (r/n) )^ n * years]
n = 4 (for compounded quarterly)
Principal = 490 / [ (1. + (.05/4)) ^ 4 * 16]
Principal = 490 / [ (1.0125)^ 64]
Principal = 490 / 2.2145324106
Principal = 221.2656710971
So, if we invested 221.27 for 16 years at 5% compounded quarterly interest, we would have a total of $490.00
Step-by-step explanation:
Answer:
221
Step-by-step explanation:
I just know