The lengths of two sides of a triangle are 10 and 24, and the third side is x. How many whole number values are possible for x.

Answers

Answer 1

Answer:

[tex]20[/tex].

Step-by-step explanation:

In any triangle, the sum of the lengths of any two sides should be strictly greater than the length of the third side. For example, if the length of the three sides are [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex]:

[tex]a + b > c[/tex],

[tex]a + c > b[/tex], and

[tex]b + c > a[/tex].

In this question, the length of the sides are [tex]10[/tex], [tex]24[/tex], and [tex]x[/tex]. The length of these sides should satisfty the following inequalities:

[tex]10 + 24 > x[/tex],

[tex]10 + x > 24[/tex], and

[tex]24 + x > 10[/tex].

Since [tex]x > 0[/tex], the inequality [tex]24 + x > 10[/tex] is guarenteed to be satisfied.

Simplify [tex]10 + 24 > x[/tex] to obtain the inequality [tex]x < 35[/tex].

Similarly, simplify [tex]10 + x > 24[/tex] to obtain the inequality [tex]x > 14[/tex].

Since [tex]x[/tex] needs to be a whole number, the greatest [tex]x[/tex] that satisfies [tex]x < 35[/tex] would be [tex]34[/tex]. Similarly, the least [tex]x\![/tex] that satisfies [tex]x > 14[/tex] would be [tex]15[/tex]. Thus, [tex]x\!\![/tex] could be any whole number between [tex]15\![/tex] and [tex]34\![/tex] (inclusive.)

There are a total of [tex]34 - 15 + 1 = 20[/tex] distinct whole numbers between [tex]15[/tex] and [tex]34[/tex] (inclusive.) Thus, the number of possible whole number values for [tex]x[/tex] would be [tex]20[/tex].


Related Questions

what are two variables that might be positively related to academic success?

Answers

study habits and career goals/higher education goals

A bag contains seven red balls, five green balls, four yellow balls, and two black balls. A ball is picked at random
from the bag. What is the probability that the ball will NOT be black?


Answers

Answer:

50/50 chance a black ball will be picked

Which equation has the solution x = 2?

A. 2x - 3 = 19
B. 3 x + 2 = 8
C. 4x - 4 = -4
D. 5x + 1 = 10

Answers

Answer:

=> B. 3 x + 2 = 8

Step-by-step explanation:

=> 3x+2 = 8

=> 3(2) +2 = 8

=> 6+2 = 8

=> 8 = 8

(-3 + 3y = 9)(8x - 6y = -4)

Answers

Step-by-step explanation:

(3y=9+3)(8x-6y=-4)

(3y=12)(8x-6y=-4)

(y=12÷3)(8x-6y=-4)

(y=4)(8x-6y=-4)

Now putting the value of y in (8x-6y=-4)

8x-6*4=-4

8x-24=-4

8x=24-4

8x=20

x=20/8

x=5/2

1. Solve 2(x + 1)^2 = 18. What are the x-intercepts?

Answers

Answer:

The x-intercepts are [tex](2,0)[/tex] and [tex](-4,0)[/tex].

Step-by-step explanation:

We are given the equation

[tex]2(x+1)^2=18[/tex]

Begin by dividing both sides of the equation by 2:

[tex](x+1)^2=9[/tex]

Next, take the square root of both sides. Remember that there are two solutions to a square root, the positive and the negative root:

[tex]x+1=\pm3[/tex]

Split the equation into two based on the two solutions:

[tex]x+1=-3[/tex]

[tex]x+1=3[/tex]

Solve each equation by subtracting 1 from both sides:

[tex]x=-4\\ x=2[/tex]

Since the x-intercepts are the solutions to a quadratic, we know the solutions are (2,0) and (-4,0).

is 0.304 meters less than 1 meter

Answers

Answer:

yes!

Step-by-step explanation:

because it is 0.

if it is was 1.304, it would be more than 1 meter.

Hope this makes sense! If you have further questions, let me know!

- profparis

8. An angle that contains 126° 32' is a/an Angle

angle.

A. straight

B. obtuse

C. right

D. acute

Answers

Answer:

B.

Step-by-step explanation:

A straight angle is exactly 180°

An Obtuse angle is more than 90°, but less than 180.

A right angle is 90°

An acute angle is less than 90°

Solve the following quadratic equation by factorin
x - 12x + 35 = 0
2
x? -
The solution set is {}.
(Simplify your answer. Type each solution only

Answers

Answer:

(x - 5)(x - 7x)

Step-by-step explanation:

x - 12x + 35 = 0

x - 12x + 35 = 0

x - 5x - 7x + 35= 0

x ( x - 5) -7x(x + 5)

(x - 5)(x - 7x)

If the cube shown above is sliced by a plane to create a triangle, which sets of vertices could the plane pass through?
A.
4, 5, and 7
1, 2, and 7
2, 3, and 7

B.
1, 3, and 4
2, 3, and 8
1, 3, and 7

C.
3, 5, and 8
1, 2, and 6
2, 4, and 7

D.
4, 5, and 7
1, 3, and 8
2, 4, and 7

Answers

Answer:

The correct answer is D.

4, 5, and 7

1, 3, and 8

2, 4, and 7.

Hope this helps you czn!!!!!

Thankyou For joining Brainly Community!!!!

Don't froget Mark me Brainleast!!!!

Answer: the correct answer is d .

4,5 and 7

1,3 and 8

2,4 and 7

Step-by-step explanation: I HOPE IT HELPS YOU BUDDY . PLEASE GIVE BRAINLIEST .THANKS .

Find the surface area.
9 in
7 in
16 in

Answers

❀ Explanation -:

In this question we are provided with the length breadth and height and we are asked to find the surface area of the figure.

[tex] \small\bf{ Length = 16 \: inches } \\ \small\bf{Breadth = 7 \: inches} \\ \small\bf{Height = \: 9 \: inches} [/tex]

We know,

[tex] \pink\star \: \large\boxed{ \pink{ \rm{ Surface \: area = 2(lb + bh + hl)}}}[/tex]

Substituting the values we get

Surface area = 2(16 × 7 + 7 × 9 + 9 × 16)

= 2(112 + 63 + 144)

= 2(319)

= 638

Surface area = 638 inches².

Hey !

Question :

Find the surface area of cuboid .

Given :

Length of Cuboid = 16 inches

Breadth of Cuboid = 7 inches

Height of Cuboid = 9 inches

To Find :

We have to find the surface area of given cuboid .

Concept :

The concept of this question belongs to surface areas of different three dimensional shapes . Whether they are cuboid , cube , cylinder , cone and many more .

Formula Used :

[tex] \boxed{\sf{ \pink{Surface \: Area \: of \: cuboid=} \pink{2(lw + wh + hl)}}}[/tex]

Where ,

l = length height of cuboid

w = width height of cuboid

h = height of cuboid

So Starting Our Solution :

Substituting value in formula ,

[tex] \longmapsto \: 2 ((16 \times 7) + (7 \times 9) + 9 \times 16)[/tex]

Now ,

[tex] \longmapsto \: 2(112 + 63 + 144)[/tex]

Adding the values which are inside bracket ,

[tex] \longmapsto \: 2(319)[/tex]

Now multiplying 319 by 2 ,

[tex] \longmapsto \: \bold{ 638 \: inches {}^{2} }[/tex]

Therefore ,

[tex] \boxed{ \sf \pink{Surface \: area \: of cuboid = 638 \: in {}^{2} }}[/tex]

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

#[tex] \rm{Keep \: Learning}[/tex]

Emily is 4 years Jacob's junior. Eight years ago. she was half Jacob's age. How old are they?

Answers

Answer:

Emily is now 12.

Jacob is now 16.

Step-by-step explanation:

since Emily is 4yrs younger than Jacob, let Jacob be x and Emily be (x - 4) yrs.

eight yrs ago: Emily is ( x-4-8) = ( x - 12)

Jacob is ( x - 8)

Emily was half Jacob's age: so, we have to balance the ages by either multiplying Emily's age by 2 or dividing Jacob's age by 2. ( I multiplied by 2)

2( x - 12) = x - 8

2x - 24 = x - 8............ Bring the like terms together and solve for x

x = 16, which is Jacob's current age

Emily ( x - 4) = 12 yrs

You make a shade of green icing using 2 drops of yellow food coloring for every 4 drops of blue. How many drops of blue food coloring would you need if you use 4 drops of yellow food coloring? how many drops of blue food coloring would u need if you use 4 drops of yellow food coloring ​

Answers

Answer:

8 drops of blue

Step-by-step explanation:

You doubled the yellow from 2 drops to four

  so double the blue from 4 to 8

The total price of 5 pounds of bananas was $1.95. What was the price per pound?

Answers

Answer:

Well you divide the total of 1.95/5

.39 cent

Answer:

you would need to do 1.95/5 and that equals 39 cents so your answer would be .39

A pair of equations is shown below:

y = 7x − 9
y = 3x − 1

Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)

Part B: What is the solution to the pair of equations? (4 points)

Answers

If you graph y=7x-9 and y=3x-1 the two lines will intersect at one point.  That is how you graphically "solve" the system of equations.

Both of these lines are of the form y=mx+b where m is the slope and b is the y-intercept.

So for y=7x-9, the slope is 7 and the y-intercept is -9

For  y=3x-1, the slope is 3 and the y-intercept is -1

....

The solution for this system occurs when both coordinates are equal to each other so we can say:

7x-9=3x-1  subtract 3x from both sides

4x-9=-1  add 9 to both sides

4x=8  divide both sides by 4

x=2, making y=3x-1 become:

y=3(2)-1=6-1=5, so the solution to the system of equations is:

(2,5)

Answer:

Part A: If you graph the pair of equations shown above both lines will intersect at one point and that is how you would solve the system of equations graphically. The y intercept and slope for each equation would be for y = 7x − 9 it would have a slope of 7 and y intercept of -9 and y = 3x − 1 would have a slope of 3 and y intercept of -1.

Part B:The solution to the pair of equations is (2,5)

The line L passes through the points (5, -5) and (1, 2).
Find the gradient of line L.

Answers

gradient of L = -7/4

Explanation:

[tex]\sf gradient = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

Insert the following values.

[tex]\rightarrow \sf \dfrac{2-(-5)}{1-5}[/tex]

[tex]\rightarrow \sf \dfrac{7}{-4}[/tex]

[tex]\rightarrow \sf -\dfrac{7}{4}[/tex]

hello!

Use the slope formula:-

(the slope is the same as the gradient)

[tex]\sf{\displaystyle\frac{y2-y1}{x2-x1} }[/tex]

[tex]\sf{\displaystyle\frac{2-(-5)}{1-5}}[/tex]

[tex]\sf{\displaystyle\frac{2+5}{-4} }=\frac{7}{-4} ={\boxed{-\frac{7}{4} }}\leftarrow\sf{slope~of~line~L}}}[/tex]

note:-

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

In preparation for an earnings report, a large retailer wants to estimate p= the proportion of annual sales

that occur during the month of December. A SRS of sales from last year revealed that 37 of

the randomly selected sales occurred during the month December out of 161 sales.

Answers

Using the z-distribution, it is found that the 95% confidence interval for the proportion of sales that occured in December is (0.1648, 0.2948).

What is a confidence interval of proportions?

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The sample size and the estimate are given by:

[tex]n = 161, \pi = \frac{37}{161} = 0.2298[/tex]

Hence:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2298 - 1.96\sqrt{\frac{0.2298(0.7702)}{161}} = 0.1648[/tex]

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2298 + 1.96\sqrt{\frac{0.2298(0.7702)}{161}} = 0.2948[/tex]

The 95% confidence interval for the proportion of sales that occured in December is (0.1648, 0.2948).

More can be learned about the z-distribution at https://brainly.com/question/25890103


There were 57 cars in a parking lot at 9:00 AM and 36 different cars at 8:00 PM.
How many cars were there all together?
21 cars
83 cars
93 cars
97 cars

Answers

Answer:

C. 93 cars

Step-by-step explanation:

57 cars + 36 cars = 93 cars

Which distribution has the greatest spread? A. distribution 1 B. distribution 2 C. distribution 3 D. distribution 4

Answers

Answer:

D I think so

Step-by-step explanation:

HOPE IT HELPS

1 3/5 gallons of gasoline were used to drive 25 1/2 miles. How many miles per gallons did the car get?​

Answers

Answer:

15.9375

Step-by-step explanation:

Just divide the number of miles over the number of gallons.

Find the volume of the oblique rectangular prism below. Round your answer to the
nearest tenth if
necessary.
1100
1115
1120
1135

Answers

Answer:

1100 units³

First calculate the Base Area:

parallelogram area:

Base * Height

11 * 10

110 units²

Volume:

Base Area * Length

110 * 10

1100 units³

Answer:

volume = 1100 cm³

Step-by-step explanation:

[tex]\textsf{Volume of an oblique rectangular prism}=l \cdot w \cdot h[/tex]

where:

[tex]l[/tex] is the base length[tex]w[/tex] is the base width[tex]h[/tex] is the height perpendicular to the base

Given:

[tex]l[/tex] = 11 cm[tex]w[/tex] = 10 cm[tex]h[/tex] = 10 cm

Substituting the given values into the formula:

[tex]\implies \textsf{Volume}=11 \cdot 10 \cdot 10 = 1100\: \sf cm^3[/tex]

PLEASE HELP PLEASE PLEASE HELP

Answers

Answer: Choice D

Reason:

Choices A through C all result in 8/3 = 2.667 approximately

In contrast, choice D becomes 2/3 + 4/3 = (2+4)/3 = 6/3 = 2; showing that choice D is not equivalent to choices A through C.

Convert the binary number 1101001 to decimal.

Answers

Answer:

105

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

Decimal calculation steps
(1101001)₂ = (1 × 2⁶) + (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰) = (105)₁₀

HELLLPPLPPPP MUDDLE SCHOOLLL!!!!

Answers

Answer:

D.

Thats what gauth.math said

A perimeter of a square field is 200, what is the area of that field?

Answers

Answer:

2500

Step-by-step explanation:

The perimeter is given by the formula :

P = 4L  (L is length)

We rearrange the equation to get L as the subject:

L = P÷4

L = 200÷4

L = 50

The area of a square is given by the formula :

A = L²

A = 50²

A = 2500

A simple random sample of 49 8th graders at a large suburban middle school indicated that 89% are involved in some type of after school activity. Find the 95% confidence interval that estimates the proportion of them that are involved in an after school activity.

A. [0.722], [0.978]
B. [0.802], [0.978]
C. [0.702], [0.928]
D. [0.802], [0.778]
E. [0.852], [0.857]
F. None of the above

Answers

Answer:

B. [0.802], [0.978]

Step-by-step explanation:

n=49

p=.89

confidence level of 95% has a z value of 1.960

z*= 1.960

z*=qnorm(1.95/2)

p+/-z* multiplied by sqrt[ P * ( 1 - P ) / n ]

p+/-z*times(√(p)(1-p)/n)

.89+/-1.960* (square root of (.89)(.11)/49))

calculatornetconfidenceintervalcalculatorhtml

mathuheducathyMath2311TestsTest2032311PT3helppdf

For which values of x is the expression undefined x-8/x-5

Answers

Answer:

(x+10 (3x-45) is the answer of the question so easy

Answer:

x = 5

Step-by-step explanation:

Any number over 0 is undefined. Given that, the values of x that make this expression undefined make the denominator equal to 0

x - 5 = 0

x = 5

I hope this helps!

consecutive integers differ by, such as 15 and

Answers

Answer:

integers are not fractions so there you go

Which of these inequalities means that
18 is greater than three times a number?

Answers

hello!

Let's write this verbal phrase as an inequality.

First of all, let the number be n.

"three times n" can be written like so:-

[tex]\pmb{3n}[/tex]

Now, 18 is greater than 3n:-

[tex]\pmb{18 > 3n}[/tex]

Which means 3n is less than 18:-

[tex]\bigstar{\boxed{\pmb{3n < 18}}}[/tex]

note:-

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)

Find the surface area of the prism. Write your answer as a fraction or mixed number
2/3ft
2/3ft
2/3ft

Answers

12.94 is the total surface area lateral surface area 8.94 bottom surface area is 4

Which answer is $734,596 rounded to the nearest thousand??

1) 734,500

2)734,600

3)735,000

4)734,000

Thank you so much

Answers

Answer:

2

Step-by-step explanation:

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