The hypotenuse of right angle triangle is 13cm. If one of the other side of the triangle is 1cm shorter than the hypotenuse, calculate the third side of the triangle

Answer:

Steve got 32 points

Step-by-step explanation:

Take the total score and multiply by the percentage received

40 * 80%

Change to decimal form

40 * .80

32

Steve got 32 points

Answer:

See below.

Step-by-step explanation:

The domain of a function is simply the span of x-values the graph will encompass.

And the range of a function is simply the span of y-values the graph will encompass.

Since the function is a quadratic, the domain is all real numbers. From the graph, the graph will continue to expand left and right. Therefore, the domain is all real numbers.

In interval notation, this is:

[tex](-\infty,\infty)[/tex]

And in set notation, this is:

[tex]\{x|x\in\mathbb{R}\}[/tex]

For the range, notice that the graph is going downwards. In other words, the graph has a maximum value. From the graph, we can see that this maximum value is at y=-4. The graph never reaches any value above -4. Therefore, our range is all numbers equal to or less than -4.

In interval notation, this is:

[tex](-\infty,-4][/tex]

We use brackets because we include the -4 in the solution set.

Also, note that we write the infinity first because the smallest number should be on the left. [-4, -∞) would not be correct.

And in set notation, this is:

[tex]\{y|y\in\mathbb{R},y\leq 4}\}[/tex]

Answer:

Rational numbers are fractional numbers, whose numerator and denominator are integers and the denominator is ever zero.

Step-by-step explanation:

The sum of rational numbers gives a rational number;

   [tex]\frac{1}{3}[/tex]  + [tex]\frac{1}{3}[/tex] = [tex]\frac{2}{3}[/tex] , because the evaluation of the denominator always results to a non-zero integer.

The product of  [tex]\frac{1}{3}[/tex] x [tex]\frac{1}{3}[/tex] = [tex]\frac{1}{9}[/tex], which multiply both numerator and denominator to give integer numbers.

The sum and product of rational and irrational numbers are always irrational numbers, for instance,

           [tex]\frac{1}{3}[/tex] x 7 = 2.3 , which is a number which decimal points that can only be represented by the product irrational number and rational number , where 7 is an irrational number.

       [tex]\frac{1}{3}[/tex] + 7 =  7[tex]\frac{1}{3}[/tex] , which is a whole number and fractional number combined.

Answer:

x  = 7.45 inch for the maximum volume.

The area of the square = x² = 7.45² = 55.5025  inch²

Step-by-step explanation:

From the given information:

An open-top box is to be made from a 42-inch by 48-inch piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side.

The objective is to determine the length of the side x of the square cut out of each corner to get a box with the maximum volume

The volume of the box = l×b×h

The volume of the box = [tex](42 - 2x) \times (48-2x) \times (x)[/tex]

The volume of the box = [tex](2016 - 84x - 96x +4x^2)x[/tex]

The volume of the box = [tex](2016 -180x+4x^2)x[/tex]

The volume of the box = [tex](2016x -180x^2+4x^3)[/tex]

The volume of the box = [tex]4x^3 - 180x^2 +2016x[/tex]

For the maximum volume V' = 0

V' = [tex]12x^2 - 360x + 2016[/tex]

Using the quadratic formula; we have:

[tex]= \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

where;

a = 12 , b = -360 c = 2016

[tex]= \dfrac{-(-360) \pm \sqrt{(-360)^2 -4(12)(2016)}}{2(12)}[/tex]

[tex]= \dfrac{360 \pm \sqrt{129600 -96768}}{24}[/tex]

[tex]= \dfrac{360 \pm \sqrt{32832}}{24}[/tex]

[tex]= \dfrac{360 \pm 181.196}{24}[/tex]

[tex]= \dfrac{360 + 181.196}{24} \ \ \ OR \ \ \ \dfrac{360 - 181.196}{24}[/tex]

[tex]= \dfrac{541.196}{24} \ \ \ OR \ \ \ \dfrac{178.804}{24}[/tex]

[tex]= 22.55 \ \ \ OR \ \ \ 7.45[/tex]

For the maximum value , we check the points in the second derivative term

V'' = 24x - 360

V'' ( 22.55) = 24(22.55) - 360

V'' ( 22.55) = 541.2 - 360  

V'' ( 22.55) = 181.2   (minimum)

V'' ( 7.45) = 24(7.45) - 360

V'' ( 7.45) = 178.8 - 360  

V'' ( 7.45) = -181.2  < 0  (maximum)

Therefore, x  = 7.45 inch for the maximum volume.

The area of the square = x² = 7.45² = 55.5025  inch²

The maximum volume of a box is the highest volume the box can take.

The side length that ensures maximum volume is 22.55 inches or 7.45 inches.

The dimension of the plastic is:

[tex]\mathbf{Length = 42}[/tex]

[tex]\mathbf{Width = 48}[/tex]

Assume the side length cut-out is x

So, the dimension of the box is:

[tex]\mathbf{Length = 42 - 2x}[/tex]

[tex]\mathbf{Width = 48 - 2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

So, the volume of the box is:

[tex]\mathbf{Volume = Length \times Width \times Height}[/tex]

This gives;

[tex]\mathbf{Volume = (42 - 2x) \times (48 - 2x) \times x}[/tex]

Expand

[tex]\mathbf{Volume = (42 - 2x) \times (48x - 2x^2)}[/tex]

Expand

[tex]\mathbf{Volume = 2016x - 96x^2 - 84x^2 + 4x^3}[/tex]

Differentiate

[tex]\mathbf{V' = 2016 - 192x - 168x + 12x^2}[/tex]

[tex]\mathbf{V' = 2016 -360x + 12x^2}[/tex]

Rewrite as:

[tex]\mathbf{V' = 12x^2 -360x + 2016}[/tex]

Set to 0

[tex]\mathbf{12x^2 -360x + 2016 = 0}[/tex]

Divide through by 12

[tex]\mathbf{x^2 -30x + 168 = 0}[/tex]

Using a calculator, the values of x are:

[tex]\mathbf{x = 22.55\ or\ x = 7.45}[/tex] ------ approximated to 2 decimal places

Hence, the side length that ensures maximum volume is 22.55 inches or 7.45 inches.

Read more about maximizing volumes at:

https://brainly.com/question/11599887

Answer:

the price of the vanilla flavored coffee per pound is $8.50

the price of the espresso flavored coffee per pound is $9.00

Step-by-step explanation:

Let's give letters to the unknowns, so we can generate equations easily:

cost of espresso coffee beans per pound:  "E"

cost of vanilla flavored coffee beans per pound : "V"

Now, the first statement:

18 pounds of E plus 17 pounds of V cost $306.50, can be written as:

18 E + 17 V = 306.5

The second statement:

19 pounds of E plus 15 pounds of V cost $298.50, can be written as:

19 E + 15 V = 298.5

Now, in order to solve this system of linear equations we can use substitution for example:

E = (306.5 -17 V)/18

and use this expression to substitute for E in the second equation:

19  (306.5 - 17 V)/ 18 + 15 V = 298.5

multiplying by 18 on both sides to eliminate denominators, we get:

19 (306.5 - 17 V) + 270 V = 5373

5823.5 - 323 V +270 V = 5373

5823.5 - 53 V = 5373

5823.5 - 5373 = 53 V

450.5 = 53 V

V = 8.5

Therefore the price of the vanilla flavored coffee per pound is $8.50

Now we use this found value in the substitution equation:

E = (306.5 -17 V)/18

E = (306.5 - 17 (8.5))/18

E = 9

Therefore the price of the espresso flavored coffee per pound is $9.00

Answer:

Binomial Distribution

Step-by-step explanation:

Unlike the normal or Gaussian probability distribution, the binomial distribution gives a curve representing the coefficient of the outcomes of every item in a sample or population.

the formula is ;

             mean ( υ ) = n x p

where p is the probability and n is the population.

The probability density function which generates the probability curve;

           Binomial Distribution function= f( k, n, p ) = [tex]\frac{n!}{k!(n-k)}[/tex] [tex]P^{k}[/tex][tex](1- P)^{(n -k)}[/tex]

Answer:

Moshe made $1875 and Jamal made $5625

Step-by-step explanation:

divide it in half, then divde Moshe's half in half because he only made half as much,

hope this helps and remember to mark brainliest

Moshe furnishes $5000 and Jamal furnishes $2500 of the capital. Computed by solving the linear equation x + x/2 = 7500, where x is the capital furnished by Moshe.

Linear equations are an equation involving constants and variables, where variables are raised to a power of not greater than 1.

We are informed that Jamal and Moshe starts a business with a capital of $7500. Also, we are informed that Jamal furnishes half as much capital as Moshe does.

We will try to make a linear equation and solve for it to find the capital furnished by each of them.

Let the capital furnished by Moshe be $x.

Jamal furnishes half as much capital as Moshe does.

∴ Capital furnished by Jamal = 1/2 of Moshe's capital = 1/2 of $x.

∴ Jamal's capital + Moshe's capital = Total capital furnished

We know the total capital is $7500.

∴ Our linear equation is: 1/2 of $x + $x = $7500.

Now we solve this equation in the following ways:

or, (1/2)*x + x = 7500

or, x/2 + x = 7500

or, (x + 2x)/2 = 7500

or, 3x/2 = 7500

or, x = (7500*2)/3 = 15000/3 = 5000.

∴ x = 5000.

∴ Moshe's share = $x = $5000

Jamal's share = 1/2 of $x = 1/2 of $5000 = $2500.

∴ Moshe furnishes $5000 and Jamal furnishes $2500 of the capital. Computed by solving the linear equation x + x/2 = 7500, where x is the capital furnished by Moshe.

Learn more about linear equations at

https://brainly.com/question/1682776

#SPJ2

Answer:

done same as before put value and do process like simplify

Answer:

Step-by-step explanation:

First you have to change your fraction:

Change 7/4 into a mixed number

7/4 = 1  3/4

Then you 'guestamate' about 3/4 of the distance between 1 and 2 and mark your point. Like this:

Hope this helps

The number is expressed as the equation A = 7/4 or A = 1.75

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 7/4   be equation (1)

On simplifying the equation , we get

A = 1.75

Now , the number 1.75 lies on the positive side of the number line and is between 1 and 2

So , the number 1.75 lies between 1 < 1.75 < 2

Hence , the number is A = 1.75

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

Answer:

C.  1.11

Step-by-step explanation:

Ball: f(x) = 24 − 16x^2

Balloon: g(x) = 4x

4x = 24 - 16x^2

16x^2 + 4x - 24 = 0

4x^2 + x - 6 = 0

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] x = \dfrac{-1 \pm \sqrt{1^2 - 4(4)(-6)}}{2(4)} [/tex]

[tex] x = \dfrac{-1 \pm \sqrt{1 + 96}}{8} [/tex]

[tex] x = \dfrac{-1 \pm \sqrt{97}}{8} [/tex]

[tex] x = \dfrac{-1 + \sqrt{97}}{8} [/tex]   or   [tex] x = \dfrac{-1 - \sqrt{97}}{8} [/tex]

We discard the negative solution.

[tex] x = 1.11 [/tex]

Answer: C.  1.11

Answer:

The correct option is x = 5

Please find the attached graph of the function

Step-by-step explanation:

The given functions are;

1) f(x) = -x² + 4·x + 12

2) g(x) = x + 2

The table of values are therefore;

x,        f(x),      g(x)

-7,       -65,     -5

-6,       -48,     -4

-5,       -33,     -3

-4,       -20,     -2

-3,        -9,      -1

-2,        0,        0

-1,         7,         1

0,        12,        2

1,        15,         3

2,       16,         4

3,       15,         5

4,       12,         6

5,        7,          7

6,       0,           8

Therefore the solution to the equation f(x) = g(x), occurs at x = -2 and x = 5, where  f(x) = g(x) = 0 and 7 respectively

To verify, we have;

Equating the two functions gives;

f(x) = g(x)

-x² + 4·x + 12 = x + 2

-x² + 4·x + 12 - (x + 2) = 0

-x² + 3·x + 10  = 0

(x + 2)(x - 5) = 0

x = 5 or -2

The correct option is x = 5.

Answer:

C. x=5

Step-by-step explanation:

Please see attachments. You'll see that at the x=5 y will equal 7.

Hope this helps!

Answer:

21.37 days.

Step-by-step explanation:

Step 1

Find the total amount Nancy is paying for her iPhone

Cost of the phone = $899

Tax = 8.50%

Amount paid for tax = 8.5% × 899

= 8.5/100 × 899

= $76.415

Total amount Nancy is paying = Tax + Cost of the phone

= $76.415 + $899

= $975.415

Step 2

We are told in the question that Nancy had already saved $78

Hence, Totally amount left for Nancy to buy her iPhone = $975.415 - $78

= $897.415

Step 3

Nancy works at a car wash and earns $42 every day.

The number of days left for her to work in the car wash in order to buy her phone is calculated as:

$42 = 1 day

$897.415 = x days

Cross Multiply

= $42 × x = $897.415 × 1 day

x = $897.415/$42

x = 21.36702381 days.

Approximately, x = 21.37 days

Therefore, Nancy has to work for 21.37 days at the car wash to have enough money for her iphone

Answer:

[tex]\huge \boxed{\mathrm{500 \ miles}}[/tex]

Step-by-step explanation:

A right triangle is formed.

300 miles and 400 miles are the legs of the triangle.

We can apply Pythagorean theorem.

[tex]c=\sqrt{300^2 +400^2 }[/tex]

[tex]c=\sqrt{90000 +160000}[/tex]

[tex]c=\sqrt{250000}[/tex]

[tex]c=500[/tex]

Answer:

15 minutes

Step-by-step explanation:

First, the motorcycle goes at a speed of 40 km/hr.

The question asks for how long it would take to travel 10 km.

Well, there are 60 minutes in an hour, since we will be translating into minutes.

Also, 10 km is 1/4 of 40 km, so it would make sense that the time length would be 1/4 of an hour as well.

1/4 of 60 minutes is 15 minutes.  So it takes 15 minutes for the motorcycle to travel 10 km.

Now, if all this wordy stuff is too much to comprehend, you can also solve using proportional relationships.

[tex]\frac{40km}{60min}=\frac{10km}{xmin}[/tex]

Now cross multiply:

[tex]40km*xmin=10km*60min\\40x=600[/tex]

Divide both sides by 40:

[tex]\frac{40x}{40}=\frac{600}{40}\\x=15[/tex]

Again, this shows that it wouls take 15 minutes for the motorcycle to travel 10 km.

Answer:

(-infinity, 20)

Step-by-step explanation:

the lower bound is negative infinity because no lower bound was given. The higher bound is 20, and it has a parentathesis because it is less than.

Answer:

200 meters per minute

Step-by-step explanation:

12/60 since hr into minutes

0.2 x 1000 since km and meters

Answer:

(1, 6).

Step-by-step explanation:

The reflection of  the x coordinate of (1, 2) creates a point with y -coordinate

-1 - 3 = -4 while the x-coordinate  remains 1.

The point (1, -4) is now reflected about  y = 1, so  -4 translates to 1 + 5 = 6. and x stays at 1.

Answer is (1, 6).

Answer:

Step-by-step explanation:

hello :

2x²+x-1=2  means : 2x²+x-3=0

a=2  b= 1  c= -3

the solutios are :   x1 and x2 when the product is : x1×x2 = c/a  

let x1 = -3/2  you have : (-3/2)×x2 = -3/2   so x2 = (-3/2)/(-3/2) = 1  

The solutions to the equation 2x²+x-1=2 are x=-3/2 or x= 1

Answer:

Associative Property of Mulitplication

Step-by-step explanation:

The associative property of multiplication states that if all the operations are multiplication, then one can group and add them in whatever order they prefer.

Hope this helps!  Tell me if I'm wrong!

Answer:

I have not J.H.S 3 , because the questions look like some J.H.S 3 ,so please I am very sorry that I can't help u in this questions . Thanks

Answer:

a) 22:53

b)213 min

Step-by-step explanation:

c) 10 17 + 4 = 14 17

she has 2 minutes to spare

Answer:

she has 2 minutes to spare

Step-by-step explanation:

================================================

Explanation:

The arc measures of 60 and x average to the angle 70, which is the the angle formed between the intersecting chords

70 = (60+x)/2

70*2 = 60+x

140 = x+60

x+60 = 140

x = 140-60

x = 80

The full 360 degree circle has the arc measures of 60, 79, x = 80, and w, where we don't know w yet. But we can add the four pieces of the circle to get 360

60+79+x+w = 360

60+79+80+w = 360

w+219 = 360

w = 360-219

w = 141

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

Or you could find angle z first

z+70 = 180

z = 180-70

z = 110

Then use the averaging technique done at the start of this problem

z = (79+w)/2

110 = (79+w)/2

2*110 = w+79

220 = w+79

w+79 = 220

w = 220-79

w = 141

Answer:

5/8

Decimal Form: 0.625

​​

Step-by-step explanation:

Cancel 6.

−5×-5/8*1/5

cancel 5

-  -5/8

Move the negative sign to the left.

-  (-5/8)

remove parentheses

answer is 5/8

hope i helped

-lvr

Answer:

  27/10

Step-by-step explanation:

A calculator can tell you the fraction value is 2.7. As the ratio of integers, this is ...

  108/40 = 27/10

Answer:

  each of the 12 turns is 150°

Step-by-step explanation:

If we number the points of the star 1–12, in order for the star to be symmetrical, each point must connect to two points symmetrically located around the centerline.

That is, point 1 may connect to points {2, 12} or {3, 11} or {4, 10}, or {5, 9} or {6, 8} or {7, 7}. For each of these connections, the angle made at the point of the "star" is, respectively, 150°, 120°, 90°, 60°, 30° or 0°. For these angles, the figure obtained will be ...

  150° - dodecagon, a 12-sided figure

  120° - hexagon

  90° - square

  60° - equilateral triangle

  30° - 12-pointed star

  0° - straight line

The two 12-pointed figures are shown in the attachment.

__

We suspect the star you're interested in is the one with points that are 30°. In order to have that point angle, the spider must make a turn of 180° -30° = 150°.

The spider will make 12 turns of 150°, for a total of 1800°, for a total of 5 full turns of 360°.

Answer:

Move the spide by 100 units and then turn the spider by 150 degrees. Repeat until you complete the star.

Step-by-step explanation:

people above are correct! I'm just making the steps as clear as possible for those who need it :)

Answer:

Step-by-step explanation:

Answer:

2.6305

Step-by-step explanation:

Answer:

3/8 or a a decimal 0.375

Answer:

C: (-5, 1)

Step-by-step explanation:

If you put the equation in a graphing calculator and examine all the points, C is the only one not on the line.

Answer:

Step-by-step explanation:

Length ( L ) = 8 cm

Perimeter of square = 4 L

( where L is the side of the square )

Plug the value of length

⇒[tex] \sf{4 \times 8}[/tex]

Multiply the numbers

⇒[tex] \sf{32 }[/tex] cm

Hope I helped!

Best regards!

Answer:

[tex]\huge \boxed{\mathrm{32 \ cm}}[/tex]

Step-by-step explanation:

The formula to calculate the perimeter of a square is given as:

[tex]\sf Perimeter = 4 \times side \ length[/tex]

The side length of the square is 8 centimeters.

[tex]P=4 \times 8[/tex]

Solve for the perimeter.

[tex]P=32[/tex]

The perimeter of the square is 32 centimeters.