Find three consecutive odd integers with the sum of 51.

Answers

Answer 1

well.. hmmmm

bear in mind that, if you multiply any integer, odd or even, by 2, you get an even, no matter how you slice it and dice it, you always get an even number, 17 *2, 34*2, or whatever * 2, is always an EVEN integer.

you can always get an ODD integer, by simply adding or subtracting 1 from any even, say 4 - 1, or 4 + 1, is 3 and 5 respectively, both odd ones.

and you can always get another consecutive odd integer, by simply jumping 2 units from any odd, so 3, 5, 7, 9, 11 and so on, notice, you simply hop two spots from one, on either direction back or forth, and you get another ODD integer.

alrite, with that in mind, let's pick a reference value, say "a" is our reference integer.

so, 2*a or 2a, we know is an EVEN integer, however, we also know that 2a + 1 is an ODD integer, well, there you have it, our first odd integer is 2a + 1.

now, let's hop twice from there to get our second consecutive odd one, (2a + 1) + 2, or 2a + 3, now, let's hop again to get the next consecutive odd one, (2a + 3) + 2, or 2a + 5.

there you have it, our reference integer is "a", our odd integers are those.

alrite... now, we know their sum gives 51, alrite

[tex]\bf (2a + 1) + (2a + 3) + ( 2a + 5) = 51 \\\\\\ 2a + 1 + 2a + 3 + 2a + 5 = 51 \\\\\\ 2a + 2a + 2a +1 + 3 ++ 5 = 51\implies 6a+9=51\implies 6a=51-9 \\\\\\ 6a=42\implies a=\cfrac{42}{6}\implies \boxed{a=7}[/tex]

now, recall, "a" is only our reference integer, so... if you want to get the consecutive odd integers, well, they're just 2a + 1, 2a + 3 and 2a + 5, and since you already know what "a" is, well, just plug it in to get the integers.

Related Questions

Solve cos x +sqrt2 = -cos x for x over the interval (0,2pi) .

Answers

Final answer:

The equation cos x + sqrt(2) = -cos x is solved by combining like terms and isolating cos x, resulting in the solutions x = 3π/4 and 5π/4 over the interval (0,2π).

Explanation:

To solve the equation cos x + sqrt(2) = -cos x for x over the interval (0,2π), first combine like terms by adding cos x to both sides of the equation, resulting in:

2 cos x + sqrt(2) = 0

Isolate cos x by subtracting sqrt(2) from both sides:

2 cos x = -sqrt(2)

Divide both sides by 2 to solve for cos x:

cos x = -sqrt(2)/2

The value of cos x = -sqrt(2)/2 corresponds to angles in the second and third quadrants. So, the solutions for x in the interval (0,2π) are:

x = 3π/4, 5π/4

Which is a counterexample that disproves the conjecture? After completing several multiplication problems, a student concludes that the product of two binomials is always a trinomial.

Answers

When you make the product of a binomial of the kind x + a times other binomial that is of the kind x - a, you obtain another binomial (not a trinomial), so any example with that form will be a counterexample that disproves the conjecture:

(x + a) * (x - a) = x^2 - a^2

For example, (x +3) * (x - 3) = x^2 - 9. So, not always the product of two binomials is a trinomial.

Using the graph, find this information about the child’s movement in the vertical (y) direction:
1. the best trigonometric function to start with
2. the amplitude
3. the period
4. any horizontal displacement of the graph.
5. any vertical displacement of the graph.

Type your response here:

Answers

1. The sine and cosine function are sinusoidal waves such that they form waves when you graph them on a cartesian plane. The only difference between them is that the crest comes first followed by the trough in the sine function. The opposite is true for the cosine function. The graph in the picture is a sine function.

2. The amplitude is the measure from crest to crest, or from trough to trough. The amplitude in the graph is 1.5.

3. The period is the reciprocal of amplitude. Therefore,itis 1/1.5 or 2/3.

4. There is no horizontal displacement because the wave only moves in a vertical direction.

5. The vertical displacement is from crest to trough which is 1 unit.

Which equation is not equivalent to the formula m = ca?
A: [tex]c = \frac{m}{a} [/tex]
B: [tex]a = \frac{c}{m} [/tex]
C: [tex]a = \frac{m}{c} [/tex]
D: m = ac

Answers

m = ca

If we find a, we must do c = m/a and if we find c we must do a = m/c

The bigger measure over the known one.

Answer B

Answer:m=ca i remember my teacher telling me how to do this.

Step-by-step explanation:

Two containers, one for 3 liters and one for 5 liters, how would you measure 4 liters

Answers

Fill the 5-liter container, pour water from that into the 3 liter container until that is full, You will now have 2 liters left in the 5 liter container.

Empty the 3-liter container, and then transfer the 2 liters from the 5-liter container into it.

Now fill the 5-liter container again, then pour water carefully from the 5-liter container into the 3-liter container until it is full - exactly one more liter.

The 5-liter container now has 4 liters in it.

What is the equation of the line?

Answers

First find the slope of the line. Slope is defined as the change in y over the change in x.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Find two ordered pairs and plug them into the slope formula.

After looking at the graph, I found two points: (0, 1) and (4, 4)

[tex]\frac{4 - 1}{4 - 0} = \frac{3}{4}[/tex]

Now find where the line intersects the y-axis.

After looking at the graph, I found out that the line intercepts the y-axis at
(0, 1)

Now build the slope-intercept equation.

General form: y = mx + b
Where m is the slope and b the y-intercept

So, the answer is y = 3/4m + 1

The measure of an inscribed angle is 110°. What is the measure of the intercepted arc? 55° 110° 220°

Answers

the measurement of an inscribed angle is half of the measure of the intercepted arc.

the inscribed angle is 110 degrees, so we multiply 110 by 2.

110*2 = 220 degrees

The measure of the intercepted arc is 220 degrees

220° is the measure of the intercepted arc

Find the angle between the given vectors to the nearest tenth of a degree. u = <-5, 8>, v = <-4, 8>

Answers

Answer: 5.4 degrees

Step-by-step explanation:

look up online "how to find the angle between 2 vectors, and it'll show you how"

Parallel to the line 2x-3y=9 and having a y intercept of 3

Answers

Switch the signs which brings -2x+3y=-9

A surface on which all points are at the same potential is referred to as

Answers

equipotential, equi=equal

When a line has an undefined slope what will any two points on the line have in common

Answers

y-coordinate
Good luck and have a nice day.

I think it y or k coordinate most likely y coordinate

3. Simplify log3 20 - log3 5

Answers

[tex]\log_320-\log_35=\log_3\dfrac{20}{5}=\log_34[/tex]

Can you use the ASA Postulate or the AAS Theorem to prove the triangles congruent?

Answers

Answer:

ASA only

Step-by-step explanation:

Given is a picture of two triangles with one side and one angle congruent.

Comparison of these two triangles given

side = side

one angle = one angle (given)

Second angle = second angle (Vertically opposite angles)

Thus we find here that two angles and one corresponding side are congruent.

HEnce we say that these two triangles are congruent by ASA theorem

ASA theorem can be applied here because the equal side is between the two congruent angles.

Instead if the side is not between the congruent angles but corresponding side then we can only use AAS

SO here ASA is correct.

Answer:

ASA only

Step-by-step explanation:

We are given that two triangles in which

An angle of triangle is equal to its corresponding angle of second triangle.

One side of a triangle is equal to one side of other triangle.

ASA postulate: It states that two angles and included side of one triangle are congruent to its corresponding angles and corresponding side of other triangle , then the two triangles are congruent.

AAS postulate: It states that two angles and non- included side of one triangle are congruent to its corresponding two angles and its corresponding side of another triangle, then the triangles are congruent by AAS postulate.

In triangle AOB and COD

[tex]\angle AOB= \angle COD[/tex] (Vertical angles are equal )

[tex]\angle ABO=\angle CDO[/tex] ( Given )

[tex]OB=OD[/tex] (Given )

[tex]\triangle AOB\cong \triangle COD[/tex] ( ASA Postulate )

Answer: ASA only

Evaluate f(x) when x=9

Answers

if x = 9 then f(x) = 12

answer
12

that is in the range 9≤x<13

f(x) in that range is equal to 12

so f(9)=12

Can someone help me

Answers

2.89-2.84 = 0.05 cent increase

0.05/2.84 = 0.0176

0.0176 = 1.8% increase

price increase = (new number - original number) / original number....* 100
= (2.89 - 2.84) / 2.84...* 100
= 0.05 / 2.84....* 100
= 0.0176 ...* 100
= 1.76 rounds to 1.8% <===

HELP! Type the correct answer in each box. Use numerals instead of words, if necessary, use / for the fractions bar(s)

Answers

The piecewise function is:

[tex]\[ f(x) = \begin{cases} 4 & \text{if } -1 \leq x \leq 1 \\ x - 1 & \text{if } 3 \leq x \leq 5 \end{cases} \][/tex]

To determine the piecewise function represented by the given coordinates, let's examine the points and their corresponding intervals.

The coordinates are (-1, 4), (1, 4), (3, 2), and (5, 4).

The points (-1, 4) and (1, 4) have the same y-coordinate, indicating that on the interval [tex]\(-1 \leq x \leq 1\)[/tex], the function has a constant value of 4. Therefore, the piecewise function for this interval is f(x) = 4 for [tex]\(-1 \leq x \leq 1\).[/tex]

The points (3, 2) and (5, 4) indicate that on the interval [tex]\(3 \leq x \leq 5\)[/tex], the function is a line passing through these two points. We can find the slope (m) and y-intercept (b) for this line.

[tex]\[ m = \frac{\text{change in } y}{\text{change in } x} = \frac{4 - 2}{5 - 3} = \frac{2}{2} = 1 \][/tex]

Using the point (3, 2), we can find the y-intercept:

2 = 1(3) + b

b = -1

Therefore, the equation for the line on the interval [tex]\(3 \leq x \leq 5\) is \(f(x) = x - 1\) for \(3 \leq x \leq 5\).[/tex]

Putting it all together, the piecewise function is:

[tex]\[ f(x) = \begin{cases} 4 & \text{if } -1 \leq x \leq 1 \\ x - 1 & \text{if } 3 \leq x \leq 5 \end{cases} \][/tex]

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Quadrilateral ABCD is a parallelogram. , bisects , and . What is the best name for quadrilateral ABCD?

A.

rectangle

C.

isosceles trapezoid

B.

rhombus

Answers

C. Isosceles trapezoid

Solve the quadratic equation by completing the square.

x^2-10x+15=0

First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.

Form:
( x + _ )^2 = _
or
( x - _ )^2 = _

Solution:
x = _

^ Please use the template above to answer ^

Answers

Final answer:

To solve the quadratic equation x^2 - 10x + 15 = 0 by completing the square, we manipulate it to the form (x - 5)^2 = 10, then solve for x to get two solutions: x = 8.16 and x = 1.84.

Explanation:

To solve the quadratic equation by completing the square, we need to manipulate the equation x^2 - 10x + 15 = 0 so it takes the form of (x - a)^2 = b, where a is half of the coefficient of x, and b is a constant.

First, we move the constant to the other side of the equation:

x^2 - 10x = -15

Next, we find the value that completes the square. This value is (10/2)^2 = 25.

Adding 25 to both sides, we get:

x^2 - 10x + 25 = 25 - 15

Now the equation is a perfect square:

(x - 5)^2 = 10

To find the solution for x, we take the square root of both sides:

x - 5 = ±10√10

x = 5 ± √10

Thus, the solutions rounded to the nearest hundredth are:

x = 5 + √10 ≈ 8.16

x = 5 - √10 ≈ 1.84

The complete answer in the template is:

Form:
( x - 5 )^2 = 10
Solution:
x = 8.16, 1.84

I need help with #18 c-i

Answers

c - one is -4 due to that when y=0 the x coordinate shows -4, the other is when 4-x^2=0, and the square root of 4 is 2

d - x intercepts

e - it's 4 due to that 4 is shown where x=0 on the graph

f - y intercept

g - Since x>0, we do 4-x^2. x=1, and 1^2=1, so 4-1=3. 1 is x and 3 is f(x), or y, so the coordinates are (1,3)

h - Since it's <0, -1+4=3, and since 3 is the output the coordinates are (-1,3)

i - Since -3 <0, we do -3+4=1

Find the greatest common factor of the following monomials 28g5h2 12g6h5
Also explain step by step how to solve these problems please

Answers

28g^5h^2 and 12g^6h^5

first, we find the GCF of the coefficients 28 and 12. What is the highest number that will go into both 28 and 12 evenly ? That number is going to be 4.

now, we look at our variables....to find the GCF of the variables, pick the lowest exponent.
another words, the lowest exponent of ur variable h is h^2...and the lowest exponent of ur variable g is g^5

therefore, the GCF of these monomials is : 4h^2g^5

If four times a number plus 3 is 11, what is the number

Answers

4x + 3 = 11
4x = 11 -3
4x = 8
x =8/4
x =2

answer
the number is 2

4x + 3 = 11
4x = 11-3 = 8
x = 2

number is 2

Find the exact values of sin A and cos A. Write fractions in lowest terms. A right triangle ABC is shown. Leg AC has length 15, leg BC has length 20, and hypotenuse AB has length 25.

Answers

sin A = opposite / hypotenuse = BC/AB = 20/25 = 4/5

cos A = adjacent / hypotenuse = AC/AB = 15/25 = 3/5

In the right triangle with sides 15, 20, and 25, the exact values of sin A and cos A are 4/5 and 3/5, respectively.

In the right triangle ABC, we can use the given side lengths to find the trigonometric ratios for angle A. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AB) is equal to the sum of the squares of the lengths of the legs (AC and BC).

Let's denote the angle A as angle A:

Find sin A:

sin A = (opposite / hypotenuse) = BC / AB = 20 / 25 = 4/5.

Find cos A:

cos A = (adjacent / hypotenuse) = AC / AB = 15 / 25 = 3/5.

So, the exact values are sin A = 4/5 and cos A = 3/5.

In summary, in the right triangle ABC with side lengths AC = 15, BC = 20, and AB = 25, the exact values of sin A and cos A are 4/5 and 3/5, respectively.

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The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6.
Applying Newton's cooling model, the temperature of the tea after 2 hours will be ___
ºF. round to the nearest integer.

Answers

Newton's Law of Cooling states that the change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature over time.

Therefore when expressed mathematically, this is equivalent to:

dT = - k (T – Ts) dt

dT / (T – Ts) = - k dt

Integrating:

ln [(T2– Ts) / (T1– Ts)] = - k (t2 – t1)

Before we plug in the values, let us first convert the temperatures into absolute values R (rankine) by adding 460.

R = ˚F + 460

T1 = 200 + 460 = 660 R

Ts = 70 + 460 = 530 R

ln [(T2– 530) / (660 – 530)] = - 0.6 (2 - 0)

T2 = 569.16 R

T2 = 109 ºF

Answer: After 2 hours, it will be 109 ºF

Answer:

109 degrees

Step-by-step explanation:

A gardener has 27 pansies and 36 daisies. He plants an equal number of each type of flower in each row.What is the greatest possible number of pansies in each row?

Answers

There are 27 pansies.
The factors of 27 are (3,9)
Therefore,
Either (a) plant 3 pansies in 9 rows, or
(b) plant 9 pansies in 3 rows.

There are 36 daisies.
The factors of 36 are (3,12), (6,6) or (9,4).
Therefore
Either (a) plant 3 daisies in 12 rows, or
(b) plant 12 daisies in 3 rows, or
(c) plant 6 daisies in 6 rows, or
(d) plant 9 daisies in 4 rows, or
(e) plant 4 daisies in 9 rows.

Because each row has an equal number of pansies and daisies, the only common arrangements are
(a) 9 pansies and 12 daisies in 3 rows, or
(b) 3 pansies and 4 daisies in 9 rows.

To have the greatest number of daisies in each row means planting 9 pansies and 12 daisies in 3 rows.

Answer:
The greatest number of pansies per row is 9.
Plant 9 pansies and 12 daisies in 3 rows.

Determine the common ratio and find the next three terms of the geometric sequence.

3/4,3/10,3/25,...

Answers

to find the common ratio, divide the 2nd term by the 1st term
(3/10) / (3/4) = 3/10 * 4/3 = 12/30 = 2/5 <==

In a geometric sequence, the next term is found by multiplying the term by the common ratio.
3/25 * 2/5 = 6/125 <==
6/125 * 2/5 = 12/625 <==
12/625 * 2/5 = 24/3125 <==

The next three terms of the sequence are 6/125, 12/625 and 24/3125

Geometric sequence

The nth term of a geometric sequence is given as:

Tn = ar^n-1

Given the geometric sequence

3/4,3/10,3/25,...

Find the common ratio

r = 3/10 * 4/3

r = 2/5

Find the 4th, 5th and 6th terms

T4 = (3/4)(2/5)^3
T4 = 3/4 * 8/125
T4 = 6/125

T5 = (3/4)(2/5)^4
T5 = 3/4 * 16/625
T5 = 12/625

T6 = (3/4)(2/5)^5
T6 = 3/4 * 32/3125
T6 = 24/3125

Hence the next three terms of the sequence are 6/125, 12/625 and 24/3125

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Three out of four students in a school said they would vote for nuncio for class president. Predict how many of the 340 students would vote for nuncio

Answers

3/4 = x / 340....3 to 4 students = x to 340 students
cross multiply
(4)(x) = (3)(340)
4x = 1020
x = 1020/4
x = 255 <==

or this way.....

3 out of 4 students.....3/4 = 75%
so 75% of 340 = 0.75(340) = 255 <=

A line passes through the point (-8,3) and has a slope of 5/4.

Write an equation in slope-intercept form for this line.

Answers

y = mx + b
3 = 5/4(-8) + b
3 = -10 + b
b= 13

equation

y = 5/4x + 13

y - y1 = m(x - x1)
y - 3 = (5/4) ( x + 8)
y - 3 = 5/4x + 10
add 3 to both sides
y = 5/4 x + 13

Use Gauss-Jordan elimination to solve the following linear system: 5x – 2y = –2 –x + 4y = 4 A. (–6,–5) B. (2,0) C. (0,1) D. (–1,0)

Answers

Im pretty sure its A.

The answer is C.(0,1)

5x - 2y = -2 -x + 4y = 4

5(0) - 2(1) = -2 -(0) + 4(1) = 4

The variable Z is inversely proportional to X. When X is 6, Z has the value 2. What is the value of z . When x = 13
Round to at least the thousandths place if needed.

Answers

Given that z is inversely proportional to x, then:
z α 1/x
hence;
z=k/x
where:
k is the constant of proportionality;
when x=6, z=2
therefore;
2=k/6
hence;
k=2*6=12

Therefore:
z=12/x
the value of z when x=13 will be:
z=12/13
the answer is 12/13

In the diagram below, what is the approximate length of the minor arc ?

Answers

arc length = given angle/360 x 2 x PI x radius

120/450 x 2 x 3.14 x 23 = 48.17

round to 48 cm

Answer:

Option A is correct

the approximate length of the minor arc is, 48 cm

Step-by-step explanation:

Length of an arc is given by:

[tex]l = r \theta[/tex] .....[1]

here r is the radius of the circle from the center and [tex]\theta[/tex] is the angle in radian.

From the given figure, we have;

r = 23 cm

Use conversion:

1 degree = 0.0174533 radian

then

120 degree = 2.094396

[tex]\theta = 2.094396[/tex] radian.

Substitute these in [1] we have;

[tex]l = 23 \cdot 2.094396 = 48.171108[/tex] cm

Therefore, the approximate length of the minor arc is, 48 cm

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