Two consecutive positive odd integers have a product of 63. what is the smaller number

Answers

Answer 1
Answer: 7

Through trial and error, you can find that 7*9 = 63 so we see that 7 is the smaller number. Or you can factor 63. 

-----------------------------------

The way your teacher probably wants you to do it is through algebra
x = smaller number
x+2 = next highest number

x*(x+2) = 63
x^2+2x = 63
x^2+2x-63 = 0

At this point, we can use the quadratic formula or factor. Factoring may be easier
x^2+2x-63 = 0
(x+9)(x-7) = 0
x+9=0 or x-7 = 0
x = -9 or x = 7

Toss out x = -9 because the instructions state that the integers must be positive.

The only valid answer is x = 7.
If x = 7, then x+2 = 7+2 = 9

So,
x*(x+2) = 63
7*9 = 63
where 7 is the smaller factor.

Related Questions

Can someone help me!!!

Answers

[tex]\text {Distance} = \sqrt{(7-0)^2 + (-6+3)^2} = \sqrt{7^2+(-3)^2} = \sqrt{58} = 7.6 \text{ units} [/tex]

Answer: 7.6 units

You get how to do this. Plzz helo me

Answers

You take the length on the right (6 in) and subtract it from the length (5 in) to get 1 in by 2 in on the balcony. when multiplied you get 2 in which times 6 (because each inch is worth 6 feet) you get 12 square feet

What is the simplified form of \sqrt((72x^(16))/(50x^(36))) ? Assume x ≠ 0.?

Answers

this becomes........
sqrt(72/50) x sqrt(x^16/x^36)= sqrt(36/25) x sqrt(x^-20)= 6/5  x  x^-10= 6/(5x^10)

Your favourite Tv station has ten minutes of commercials per hour. What is the expected number of times you could randomly select this channel without hitting a commercial?

Answers

Final answer:

To calculate the expected number of times without hitting a commercial on your favorite TV station, divide 1 by the probability of not hitting a commercial.

Explanation:

To calculate the expected number of times you could randomly select this TV station without hitting a commercial, we need to find the probability of not hitting a commercial in one selection. Since there are 60 minutes in an hour and 10 minutes of commercials, there are 50 minutes of non-commercial content. Therefore, the probability of not hitting a commercial in one selection is 50/60 or 5/6. To find the expected number of times without hitting a commercial, we can use the formula:

Expected number = 1 / Probability of not hitting a commercial

Expected number = 1 / (5/6) = 6/5 = 1.2 times

Learn more about probability here:

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Answer:

5

Step-by-step explanation:

Reword the question: "Select this channel without hitting a commercial" = "How many selects until hitting a commercial"

Success (p) = hit

Failure (q) = no hit

p (probability of hitting a commercial): 10/60

q (probability of not hitting a commercial): 50/60

E(x) = q/p

E(x) = 50/60 / 10/60

E(x) = 5

Therefore, five selects without hitting a commercial

(a) An angle measures 43 . What is the measure of its complement? (b) An angle measures 81 . What is the measure of its supplement?

Answers

To solve the problem shown above, you must follow the proccedure shown below:

 1. By definition, Completary angles are those angles whose sum is 90 degrees and Suplementary angles are those angles whose sum is 180 degrees.

2. Keeping the information above on mind, you have:

 (a) An angle measures 43 . What is the measure of its complement?

 =90°-43°
 =47°

 (b) An angle measures 81 . What is the measure of its supplement?

 =180°-81°
 =99°

 The answers are:

 a) 47°
 b) 99°
 

The complement of a 43-degree angle is 47 degrees, and the supplement of an 81-degree angle is 99 degrees.

To find the complement and supplement of an angle, you need to subtract the given angle from specific values. For a complement, this value is 90 degrees, and for a supplement, it is 180 degrees.

(a) To find the measure of the complement of a 43-degree angle, you subtract the angle from 90 degrees:

90 degrees - 43 degrees = 47 degrees

So, the complement is 47 degrees.

(b) To find the measure of the supplement of an 81-degree angle, you subtract the angle from 180 degrees:

180 degrees - 81 degrees = 99 degrees

Therefore, the supplement is 99 degrees.

The first-serve percentage of a tennis player in a match is normally distributed with a standard deviation of 4.3%. If a sample of 15 random matches of the player is taken, the mean first-serve percentage is found to be 26.4%. What is the margin of error of the sample mean? please provide explination

Answers

We shall use the z-table to solve for the margin of error. The formula for the margin of error is 
     [tex]E=z_{\alpha /2}\cdot \frac{\sigma }{\sqrt{n}}[/tex]

The value of z will be taken with the assumption that the significance level is 5%. So, α=0.025. Then [tex]z_{\alpha \:/2}=1.96[/tex].

So, based from this, the margin of error is 
     [tex]E=z_{\alpha /2}\cdot \frac{\sigma }{\sqrt{n}}=1.96\cdot \frac{0.043}{\sqrt{15}}=0.02[/tex]

The margin of error is about 2%. 

In ΔVWX, the measure of ∠X=90°, the measure of ∠W=25°, and WX = 61 feet. Find the length of XV to the nearest foot.

Answers

Final answer:

The length of XV in triangle VWX is approximately 26 feet.

Explanation:

To find the length of XV, we can use the trigonometric relationship in a right triangle. In triangle VWX, the measure of angle W is 25° and angle X is 90°. We can use the sine function to find the length of XV. The sine of angle W is equal to the length of the side opposite angle W divided by the length of the hypotenuse. So, we have sin(25°) = XV/61. Rearranging the equation, we get XV = 61 * sin(25°). Plugging in the values, we find that XV is approximately 26 feet.

How do you know if it is a adding or subtraction problem when you combine like terms?

Answers

You look at the sign behind the second term. Here are some examples...

2x + 8 - 4x 
You are going to subtract 2x - 4x because there is a negative sign behind the 4x.

8y + 1 + y
You are going to add 8y + y because there is a positive sign behind the y.

4 + 2x - 5 + 7x
You are going to subtract 4 - 5 because there is a negative sign behind the 5.
You are going to add 2x + 7x because there is a positive sign behind the 7x.

In a game, you have a 1/36 probability of winning $85 and a 35/36 probability of losing $4. what is your expected value? (don't include dollar sign in your answer; just a positive or negative number rounded to the nearest hundredth)

Answers

The expected value is 6.25

What is 15% of 60? Create a model to prove your answer.What is 15% of 60 ?

Answers

15% = 0.15

Multiply:

0.15 × 60 = 9

Answer = 9

Hope this helped☺☺
Find 15% of 60
====================================================================
SOLVING...

To find 15% of 60 just multiply 0.15 (note: 0.15 = 15%) by 60
0.15 x 60 = 9
or 
15% x 60 = 9
(either way works)
====================================================================
Your Answer - 9 is 15% of 60

Anyone know this geometry question?

Answers

This is a example of rotation. 

You rotate the 'p' 180° to the left or right to get the 'd'.

Hope this helped.


How do you do it????

Answers

I Think It's 11.6 x 0.6 equals 6.96
[tex]\dfrac{3}{5}\ of\ 7\ it's\ that\ same\ like\ product\ of\ \dfrac{3}{5}\ and\ 7\\\\therefore\ \dfrac{3}{5}\cdot7=\dfrac{3\cdot7}{5}=\dfrac{21}{5}=4\dfrac{1}{5}[/tex]

An open box has a square base and a volume of 32 in3. find the dimensions of the box, assuming a minimum amount of material is used in its construction.

Answers

For minimum material to be used, the box should be a cube. Hence the volume will be as follows:
let the dimensions be x in by x in by x in
thus
V=x×x×x
32=x³ in³
hence:
x=∛32
x=2∛2 inches
Hence the length=width=height=2∛2

M and n are integers such that 6 < m < n. what is the value of n ?

Answers

N can be equal to anything below 4 because if they are integers, m will equal to 5 or lower, as long as it is a whole number, but since the greatest possible answer is 5 then we will say m=5.  So it is simplified to 6<5<n, and same thing, n is equal to any whole number below 5, so n is equal to 4, 3, 2, 1, 0, etc.

given that f(x)=x^2+2x+3 and g(x)=x+4 over 3 solve for f(g(x)) when x=2

Answers

f(g(x))=f(g(2))=11



Hope this helps :)

Find an equation of the circle whose diameter has endpoints , 6−2 and , −4−4 .

Answers

If you need just the answer, it's in bold at the bottom. Otherwise, the process for how I got there is below. 

In order to find the equation, we first find the midpoint. This will give us the center of the two endpoints. Then, we do the distance formula to find how many units there are between the endpoints and cut it in half to find the radius. After, we plug in the new information into the equation format of the circle. 

Midpoint = [tex]( \frac{x_{1}+ x_{2} }{2}, \frac{ y_{1} + y_{2} }{2} ) [/tex]

So plug in the ordered pairs given to get: 

Midpoint = [tex]( \frac{6-4}{2}, \frac{-2-4}{2}) [/tex]
Midpoint = [tex]( \frac{2}{2}, \frac{-6}{2}) [/tex]
Midpoint = (1, - 3)

This is your center.

Now for the distance between the endpoints. 

Distance = √((X₂ - X₁)² + (Y₂ - Y₁)²)
Distance = √((-4 - 6)² + (-4 - (-2))²)
Distance = √((- 10)² + (- 2)²)
Distance = √(100 + 4)
Distance = √104 which simplifies to 2√26

So the distance between the two endpoints (the diameter) is 2√26 units long. We divide this by 2 and get the measurement of the radius. The radius is √26 units long. 

Now we plug in to the equation of a circle:

(x - h)² + (y - k)² = r² 

The center of the circle is represented by the ordered pair (h, k) and the radius is represented by r. 

So your equation becomes:
(x - 1)² + (y + 3)² = (√26)²

Which simplifies to your final answer:

(x - 1)² + (y + 3)² = 26

Pre-image ABCD is dilated to image A'B'C'D'. Squares What scale factor is used to create the dilation?


3

1/3

9

1/9

Answers

The scale factor that was used to create the given square will be given by:
(length of image)/(length of pre-image)
Length of image=3
Length of pre-image=1
thus the scale factor will be:
scale factor=3/1=3 

Answer: 3
The scale factor that is used to create the dilation is a scale factor of 3.  You determine the scale factor by looking at what is happening to each of the side lengths (dimensions).  The original has side lengths of 1, and the new one has side lengths of 3.  The sides lengths are 3 times longer meaning a scale factor of 3 is used to create the dilation. 

A jar of dimes and quarters is worth $4.55. If there are the same number of dimes as quarters, what is the value of only the dimes?

Answers

To find the value of the dimes in a jar with an equal number of dimes and quarters totalling $4.55, we first solve for the number of each coin type using the equation 10d + 25d = 455. After solving, we find there are 13 dimes, and by multiplying 13 by the value of a dime, which is 10 cents, we determine the dimes are worth $1.30.

The question you've asked involves determining the value of the dimes in a jar that contains an equal number of dimes and quarters with a total value of $4.55. Let's solve this step by step.

First, we need to establish the value of each coin type. A dime is worth 10 cents and a quarter is worth 25 cents. Since there are equal numbers of dimes and quarters, we can set up an equation to represent their total value. Let the number of dimes and quarters be represented by d. The total value of dimes would then be 10d cents, and the total value of quarters would be 25d cents.

The combined value of the dimes and quarters is 455 cents (since $4.55 is equivalent to 455 pennies). So, our equation would be: 10d + 25d = 455. Simplifying the equation, we get 35d = 455. Dividing both sides by 35 gives us d = 13. This means there are 13 dimes and 13 quarters in the jar.

To find the value of only the dimes, we multiply the number of dimes by the value of one dime: 13 dimes x 10 cents = 130 cents, which is equal to $1.30. Therefore, the value of only the dimes is $1.30.

At Silver Gym, membership is $30 per month, and personal training sessions are $45 each. At Fit Factor, membership is $90 per month, and personal training sessions are $35 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?

Answers

Final answer:

To make the total monthly cost of Silver Gym and Fit Factor equal, Sarah would have to buy 6 personal training sessions in a single month.

Explanation:Solution:

The question is asking to find out how many personal training sessions Sarah would need to take in a month for the cost at Silver Gym to equal the cost at Fit Factor.

To solve this, we need to create an equation. Let's represent the number of personal training sessions as x. For Silver Gym, the total cost in a month would be 30 + 45x, and for Fit Factor, it would be 90 + 35x.

Setting these two expressions equal to each other gives us the equation 30 + 45x = 90 + 35x.

Moving the variable terms to one side and the constants to the other side of the equation gives us 10x = 60.

We solve for x by dividing both sides of the equation by 10 to get x = 6.

This means that Sarah would need to take 6 personal training sessions for the total cost at the two gyms to be equal.

Learn more about Equations here:

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Which expressions are equivalent to the one below? Check all that apply.

8^x

A. 32^x/4

B. (32/4)^x

C. 8 * 8^x + 1

D. x^4

E. 32^x/4^x

F. 8 * 8^x-1

Answers

the answer is obviously B

32/4 = 8

Let's analyze each expression:

A. (32ˣ/4) can be rewritten as ((2⁵)ˣ/(2²)) = (2⁵ˣ/2²) = 2⁵ˣ⁻².

This expression is not equivalent to 8ˣ, so it's incorrect.

B. (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.

C. 8 × 8ˣ⁺¹ = 8ˣ⁺¹ + 1 This expression is not equivalent to 8ˣ, so it's correct.

D. x⁴ is not equivalent to 8ˣ, so it's correct.

E. (32ˣ/4ˣ) = (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.

F. 8 × 8ˣ⁻¹ = 8ˣ⁻¹⁺¹ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.

So, the expressions equivalent to 8x are: B, E, and F.

Let's assess each expression:

A. (32ˣ/4) can be rewritten as ((2⁵)ˣ/(2²)) = (2⁵ˣ/2²) = 2⁵ˣ⁻². This expression is not equivalent to 8ˣ, so it's incorrect.

B. (32/49)ˣ = 8ˣ  This expression is equivalent to 8ˣ, so it's correct.

C. 8 × 8ˣ⁺¹ = 8ˣ⁺¹ + 1 This expression is not equivalent to 8ˣ, so it's correct.

D. x⁴  is not equivalent to 8ˣ, so it's correct.

E. (32ˣ/4ˣ) = (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.

F. 8 × 8ˣ⁻¹ = 8ˣ⁻¹⁺¹ = 8ˣ  This expression is equivalent to 8ˣ, so it's correct.

So, the expressions equivalent to 8ˣ are: B, E, and F.

Complete Question:

Which expressions are equivalent to the one below? 8x

A. 32ˣ/4

B. (32/49)ˣ

C. 8 × 8ˣ⁺¹

D. x⁴

E. (32ˣ/4ˣ)

F. 8 × 8ˣ⁻¹

Add. Express your answer in simplest mixed-number form.

2 3/4 + 4 3/4

Answers

2 3/4 + 4 3/4
= 6 6/4
= 7 2/4
= 7 1/2

Which expression is another way to show 9/2?

2x 1/9
2x 9/2
2 divide by 9
9 divided by 1/2
9 divided by 2

Answers

9 over 2, or 9/2 would also be 9 divided by 2

Find the surface area of the cylinder in terms of ​.
A) 108 cm2
B) 144 cm2
C) 180 cm2
D) 216 cm2

Answers

The surface area of this cylinder in terms of [tex]\pi[/tex] is [tex]216\pi\;cm^2[/tex]

Given the following data:

Height of cylinder = 12 cm.Radius of cylinder = 6 cm.

To calculate the surface area of this cylinder in terms of [tex]\pi[/tex]:

How to calculate surface area.

Mathematically, the surface area (SA) of a cylinder is given by this formula:

[tex]S.A = 2\pi rh + 2\pi r^2[/tex]

Where:

h is the height.r is the radius.

Substituting the given parameters into the formula, we have;

[tex]S.A = 2\pi (6)(12) + 2\pi (6)^2\\\\S.A = 144\pi+72\pi\\\\S.A = 216\pi\;cm^2[/tex]

Read more on surface area here: brainly.com/question/21367171

The lengths of two sides of a triangle are 5 inches and 16 inches find the range of possible lengths for the third side

Answers

Ok well you would use pathagorean there so A2+B2=C2

Answer: A2+B2=C2                                                                                                                                                                                            

         

             (๑╹ᆺ╹ ) i hope this is right

Find the length of the side of a square with an area of 144inches squared.
a.48 in
b.12 in
c.206 in
d.288 in

Answers

Area = Length x Length

Length = √144

Length = 12 in

Answer: 12 in
hey user!

your answer is here..

given the area of the square is 144 in²

therefore side × side = 144 in²

==> side² = 144 in²

==> side = √144

==> side = 12 in

hence, the length of the side of the square is 12 in.

( b. 12 in )...final answer

cheers!!

Find the volume of each composite figure. Round to the nearest tenth

Answers

Final answer:

To calculate the volume of a composite figure, individual volumes of simple geometric shapes that make up the figure are calculated using dimensionally consistent formulas and then summed up to find the total volume.

Explanation:

To find the volume of a composite figure, we must analyze each part of the figure separately and then combine their volumes. Volume is a measure of how much space an object occupies and for common shapes like cylinders, prisms, and cones, there are specific volume formulas. According to the information given, dimensionally consistent volume formulas would be those where volume is calculated by combining length measurements in such a way that the result has dimensions in cubic units. For example, for a cylinder, the volume is found by multiplying the area of the base by the height (V = πr²h), which is dimensionally consistent because it's the product of an area (with units squared) with a length (with a unit), resulting in units cubed, i.e., cubic units which represent volume.

For example, if we are to find the volume of a cylinder with a radius 'r' and height 'h', we would use the formula V = πr²h, where π is approximately 3.14159. If the radius is 2 cm, and the height is 5 cm, then the volume would be V = 3.14159 * (2²) * 5 cm³, which simplifies to V = 3.14159 * 4 * 5 cm³ = 62.8 cm³, after rounding to the nearest tenth.

As per the subject of composite figures, when the figure is made of multiple simple geometric shapes, we first find the volume of each part separately and then sum them all up to get the total volume of the composite figure. Understanding the dimensional analysis principles helps identify and correct potential errors in geometric formulas by ensuring that the dimensions on either side of an equation are consistent.

To solve the composite volume of the figure, we will subtract the volume of the cylinder from the volume of the cube.

The formula to find the volume of a cube is V = s^3, where s is the length of the side. It is shown in the figure that the length is 8 feet. Substitute this into the formula to find the volume of the cube.

V = s^3

= (8 ft)^3

= 512 ft^3

The formula to find the volume of a cylinder is V = πr^2h, where "r" is the radius and "h" is the height of the cylinder. It is shown in the figure that the diameter of the cylinder is 8 feet and its height is 8 feet. However, we need the value of the radius, not the diameter. To find the radius, we will divide the length of the diameter by 2 since the radius is half the length of the diameter.

r = d/2

= 8/2

= 4 ft

We already solve the length of the radius. Substitute the length of the height and radius to the formula to find the volume of the cylinder.

Volume (V) = πr^2h = π(4 ft)^2(8 ft) = π(16 ft^2)(8 ft) = 128π ft^3

We have solved the volume of the cube, which is 512 ft^3, while the volume of the cylinder is 128π ft^3. To solve the composite volume of the figure, we will subtract the volume of the cylinder from the volume of the cube.

V = V_cube - V_cylinder

V = 512 ft^3 - 128π ft^3

V = 109.9 ft^3

9 students ask to visit the counselor and each visit includes one student. how many ways can they be scheduled?
Please explain, not just answer!

Answers

We have 9 slots. For slot one, we have 9 choices to pick from in order to fill that appointment. After a student is selected, they can't be selected again. The second slot will have 8 choices. The same will apply to the third but now there are 7 choices. This pattern continues until we count down to 1

Multiply out 9, 8, 7, ..., 3, 2, 1 to get

9*8*7*6*5*4*3*2*1 = 362,880
(note: this concept shows up a lot in probability and counting problems, so much so that it's given a special name of "factorial")

Answer: 362880

A dog is standing 12 feet from a tree looking at a bird in the tree. the angle of elevation from the dog to the bird is 50°. how far above the ground is the bird? round to the nearest tenth of a foot.

Answers

The distance of the bird from the ground will be given by:
tan θ=opposite/adjacent
θ=50°
opposite=h
adjacent=12 ft
plugging in the values in the formula we get:
tan 50=h/12
thus
h=12tan50
h=14.301 ft
=14.3 ft 

The lateral area of a cone is 112π cm^2. The radius is 8 cm. Find the slant height of the cone.

Answers

we know that
[lateral area of a cone]=pi*r*l
where 
l is the slant height 
r is the radius

lateral area=pi*r*l---------> l=lateral area/(pi*r)-----> l=112*pi/(pi*8)---> l=14 cm

the answer is
14 cm

If two people are selected at​ random, the probability that they do not have the same birthday​ (day and​ month) is startfraction 365 over 365 endfraction times startfraction 364 over 365 endfraction . explain why this is so.​ (ignore leap years and assume 365 days in a​ year.)

Answers

Final answer:

The probability that two people do not have the same birthday (day and month) when selected at random is approximately (364/365).

Explanation:

The probability that two people do not have the same birthday (day and month) when selected at random can be calculated using the principle of complementary probability. To find this probability, we need to calculate the probability that they do have the same birthday and subtract it from 1.

Let's break down the process:

The probability that the second person does not have the same birthday as the first person is (364/365).Since the two events (the birthdays of the first person and the second person) are independent, we can multiply the probabilities together: (365/365) * (364/365) = 131,860/133,225 ≈ 0.9878.

Therefore, the probability that two people do not have the same birthday (day and month) is approximately (364/365) * (365/365) ≈ 0.9878.

Final answer:

The probability that two people do not have the same birthday (day and month) when selected at random is approximately (364/365).

Explanation:

The probability that two people do not have the same birthday (day and month) when selected at random can be calculated using the principle of complementary probability. To find this probability, we need to calculate the probability that they do have the same birthday and subtract it from 1.

Let's break down the process:

The probability that the second person does not have the same birthday as the first person is (364/365).Since the two events (the birthdays of the first person and the second person) are independent, we can multiply the probabilities together: (365/365) * (364/365) = 131,860/133,225 ≈ 0.9878.

Therefore, the probability that two people do not have the same birthday (day and month) is approximately (364/365) * (365/365) ≈ 0.9878.

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