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svetoff [14.1K]

2 years ago

9

Renee is simplifying the expression (7) (13/29) (1/7).She recognizes that 7 and 1/7 are reciprocals, so she would like to find t

heir product before she multiplies by 13/29. Which property will allow Renee to do this without changing the value of the expression

2 answers:

Zepler [3.9K]2 years ago

7 0

Answer:

Multiplicative inverse property.

Step-by-step explanation:

∵ When a real number is multiplied by its inverse then the result is 1 ( multiplicative identity )

Also, for a real number a,

Representation of multiplicative inverse is $\frac{1}{a}$

Now, the multiplicative inverse of 7 = $\frac{1}{7}$

So,

$7\times \frac{1}{7}=1$

Hence, the required property is multiplicative inverse property.

astra-53 [7]2 years ago

5 0

Answer:

There's one important property which states that when a number is multiplied by its reciprocal, equals 1.

The commutative property of multiplication states that two or more numbers can be multiplied in any order, therefore, the expression: (7)×(13/29)×(1/7) can be changed to (7)×(1/7)×(13/29) and the result won't be altered.

Now, given that 7 and 1/7 are reciprocals, the result is 1. Therefore, the result of the multiplication equals (13/29)

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Mr. Johnson currently has a square garden. It is in his garden and into a range of 5 feet shorter than three times shorter than

Vlad [161]

Answer:

The Dimension of new garden is $25 \ feet\ \times 10\ feet.$

Step-by-step explanation:

Given:

Perimeter of new garden = 70 feet.

Let the length of the new garden be 'l'.

Also Let the width of the new garden be 'w'.

We need to find the dimension of new garden.

Now Given:

Length is 5 feet shorter than three times it width.

framing the equation we get;

$l =3w-5 \ \ \ \ equation\ 1$

Now we know that;

Perimeter of rectangle is equal to twice the sum of length and width.

framing in equation form we get;

$2(l+w)=70$

Now Diving both side by 2 using Division property of equality we get;

$\frac{2(l+w)}2=\frac{70}{2}\\\\l+w =35$

Now Substituting equation 1 in above equation we get;

$3w-5+w=35\\\\4w-5=35$

Adding both side by 5 Using Addition Property of equality we get'

$4w-5+5=35+5\\\\4w=40$

Now Diving both side by 4 using Division property of equality we get;

$\frac{4w}{4}=\frac{40}{4}\\\\w=10\ ft$

Now Substituting the value of 'w' in equation 1 we get;

$l =3w-5\\\\l =3\times10-5\\\\l = 30-5\\\\l= 25\ ft$

Hence The Dimension of new garden is $25 \ feet\ \times 10\ feet.$

3 0

2 years ago

In basketball there are three ways to score. 1 point for a free Throw, 2 points for a short field goal, and 3 points for a long

Free_Kalibri [48]

It says Dallas didn't make any free throws. It means there are short field goals (SFG) and long field goals (LFG) only.
Let's assume number of SFG = x
and number of LFG = y

Given that 2 points for a short field goal, and 3 points for a long field goal.
Total Score = 2x+3y
Also, Total score = 36 (given in the question)
So we have the equation
$2x + 3y = 36$
where x and y are integers.

when SFG=0, then x=0 and so 3y=36.
y=12 i.e. LFG = 12
So the extreme case is (0,12) i.e. SFG=0 and LFG=12.

Other cases would be integral vales of (x,y) which satisfy the equation 2x+3y=36.
So (3,10) , (6,8) , (9,6) , (12,4) , (15,2) , and (18,0) are other cases.

Hence final answers are (x,y) = (0,12) , (3,10) , (6,8) , (9,6) , (12,4) , (15,2) , and (18,0)

4 0

2 years ago

answer A radio station located 120 miles due east of Collinsville has a listening radius of 100 miles. A straight road joins Col

melamori03 [73]

Answer:

168.7602 miles

Step-by-step explanation:

One way to solve this problem is by using an equation that describes the listening radius of the station, and another for the road, then the points where this two-equation intersect each other will represent when the driver starts and stops listening to the station, and the distance between the points is the miles that the driver will receive the signal.

The equation for the listening radius (the radio station is at (0,0)):

$x^2+y^2=100^2$

The equation for the road that past through the points (-120,0) and (80,100) (Collinsville and Harmony respectively):

$m=\frac{y_2-y_1}{x_2-x_1} =\frac{100-0}{80-(-120)}=\frac{100}{200}=\frac{1}{2}$

$y-y_1=m(x-x_1)\\y-0=\frac{1}{2}(x-(-120))\\ y=\frac{1}{2}x+60$

Substitutes the value of y in the equation of the circle:

$x^2+(\frac{1}{2}x+60)^2=100^2\\x^2+\frac{1}{4} x^2+60x+3600=10000\\\frac{5}{4} x^2+60x+3600=10000\\\frac{5}{4} x^2+60x+3600-10000=0\\\frac{5}{4} x^2+60x-6400=0\\5 x^2+240x-25600=0\\x^2+48x-5120=0\\$

The formula to solve second-degree equations:

$x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac} }{2a} \\x_{1,2}=\frac{-48\pm\sqrt{48^2-4(1)(-5120)} }{2(1)}\\x_{1,2}=\frac{-48\pm\sqrt{2304+20480} }{2}\\x_{1,2}=\frac{-48\pm\sqrt{22784} }{2}\\x_{1,2}=\frac{-48\pm16\sqrt{89} }{2}\\x_{1,2}=-24\pm8\sqrt{89} \\x_1=-24+8\sqrt{89}\approx51.4718\\x_2=-24-8\sqrt{89}\approx-99.4718\\$

Using the values in x to find the values in y:

$y_1=\frac{1}{2}x_1+60\\y_1=\frac{1}{2}(-24+8\sqrt{89} )+60\\y_1=-12+4\sqrt{89}+60\\ y_1=48+4\sqrt{89}\approx85.7359$

$y_2=\frac{1}{2}x_2+60\\y_2=\frac{1}{2}(-24-8\sqrt{89} )+60\\y_1=-12-4\sqrt{89}+60\\ y_1=48-4\sqrt{89}\approx10.2641$

The distance between the points (51.4718,85.7359) and (-99.4718,10.2641) :

$d=\sqrt{(x_1 -x_2 )^2+(y_1 -y_2)^2} \\d=\sqrt{(-24+8\sqrt{89} -(-24-8\sqrt{89}) )^2+(48+4\sqrt{89} -(48-4\sqrt{89}) )^2}\\d=\sqrt{(-24+8\sqrt{89} +24+8\sqrt{89} )^2+(48+4\sqrt{89} -48+4\sqrt{89} )^2}\\d=\sqrt{(16\sqrt{89} )^2+(8\sqrt{89} )^2}\\d=\sqrt{22784+5696}\\d=\sqrt{28480}\\d=8\sqrt{445}\approx168.7602miles$

4 0

2 years ago

Each leg of a 45°-45°-90° triangle measures 14 cm. What is the length of the hypotenuse? 7 cm cm 14 cm cm

Mashutka [201]

Check the picture below.

8 0

2 years ago

Read 2 more answers

If Ethan takes out a $5,000 loan to buy a motorcycle and his payments are $168.45 a month for 36 months, how much money will he

Vilka [71]

Answer:

$1064.20

Step-by-step explanation:

36 payments of $168.45 have a total of $6064.20. The excess over the loan amount of $5000 is the interest paid:

$6064.20 -5000 = $1064.20 . . . . interest paid

4 0

2 years ago