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Olin [163]
3 years ago
14

Gordon types 1,944 words in 27 minutes. Find the unit rate

Mathematics
2 answers:
Tomtit [17]3 years ago
7 0

Answer:

72 words per minute

Step-by-step explanation:

1,994 words = 27 minutes       original equation

1,994/27 = 27/27                      divide both sides by 27 to get 1 minute

72 words = 1 minute ; 72 words per minute

tester [92]3 years ago
3 0
The rate is 72, I hope it helps!!
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A student wants to construct the inscribed circle of a triangle. What is the first step he/she should take?
pantera1 [17]

The <em>correct answer</em> is:


d) Construct the angle bisector of each angle in the triangle


Explanation:


The incenter, or center of an inscribed circle, is the point where the angle bisectors of a triangle intersect. This means the first thing we will need to construct is the bisector of each angle of the triangle.

8 0
3 years ago
Read 2 more answers
Write the inequality!! Connie’s dog Fido weighs 35 pounds. Her vet placed Fido on a diet. What inequality can you write to find
Butoxors [25]

Answer:   \frac{35-28}{x} \leq 6

Step-by-step explanation:

Let x be the average number of pounds Fido must loss.

Since, the initial weight of Fido is 35 pounds.

And, After losing the weight, the new weight of Fido in pounds = 28 pounds.

Then the time taken for losing the weight

= \frac{\text{ The weight it losses}}{\text{ Average of losing weight per month}}

= \frac{35-28}{x}

According to the question,  it must lose weight within 6 months,

Thus,   \frac{35-28}{x}\leq 6

Which is the required inequality to find the average number of pounds per month.

By solving it we, get,    x\geq \frac{7}{6}

6 0
3 years ago
(a) Find a vector parallel to the line of intersection of the planes −4x+2y−z=1 and 3x−2y+2z=1.
valentinak56 [21]

Find the intersection of the two planes. Do this by solving for <em>z</em> in terms of <em>x</em> and <em>y </em>; then solve for <em>y</em> in terms of <em>x</em> ; then again for <em>z</em> but only in terms of <em>x</em>.

-4<em>x</em> + 2<em>y</em> - <em>z</em> = 1   ==>   <em>z</em> = -4<em>x</em> + 2<em>y</em> - 1

3<em>x</em> - 2<em>y</em> + 2<em>z</em> = 1   ==>   <em>z</em> = (1 - 3<em>x</em> + 2<em>y</em>)/2

==>   -4<em>x</em> + 2<em>y</em> - 1 = (1 - 3<em>x</em> + 2<em>y</em>)/2

==>   -8<em>x</em> + 4<em>y</em> - 2 = 1 - 3<em>x</em> + 2<em>y</em>

==>   -5<em>x</em> + 2<em>y</em> = 3

==>   <em>y</em> = (3 + 5<em>x</em>)/2

==>   <em>z</em> = -4<em>x</em> + 2 (3 + 5<em>x</em>)/2 - 1 = <em>x</em> + 2

So if we take <em>x</em> = <em>t</em>, the line of intersection is parameterized by

<em>r</em><em>(t)</em> = ⟨<em>t</em>, (3 + 5<em>t</em> )/2, 2 + <em>t</em>⟩

Just to not have to work with fractions, scale this by a factor of 2, so that

<em>r</em><em>(t)</em> = ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩

(a) The tangent vector to <em>r</em><em>(t)</em> is parallel to this line, so you can use

<em>v</em> = d<em>r</em>/d<em>t</em> = d/d<em>t</em> ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩ = ⟨2, 5, 2⟩

or any scalar multiple of this.

(b) (-1, -1, 1) indeed lies in both planes. Plug in <em>x</em> = -1, <em>y</em> = 1, and <em>z</em> = 1 to both plane equations to see this for yourself. We already found the parameterization for the intersection,

<em>r</em><em>(t)</em> = ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩

3 0
3 years ago
(ill give 25) let r be the region enclosed by the y-axis, the line y = 2, the line y = 3, and the curve =. a solid is generated
Nesterboy [21]
That’s a 70 degree angle
8 0
3 years ago
Hey friend please solve this question
Bas_tet [7]

yes and yes.

you're told ∠A=∠B. this means angle A and B are equal. so the value you get for cos A will be the same as the value you'll get for cos B

also, the value you get for tan A will be the same as the value you'll get for tan B


if that doesn't make sense you could also draw the triangle and solve for A and B.

you're told it's a right angled triangle meaning one of the angles = 90

you're told that C is that angle so if C is a right angle, angle C=90

the sum of all the angles in a triangle = 180

so angle A+ angle B + angle C = 180

angle A+ angle B + 90 = 180

angle A+ angle B = 180 - 90

angle A+ angle B = 90

  • A and B could be any value but you're told angle A = angle B

        angle A+ angle B = 90

        you can divide 90 by 2 because A and B are equal. that will give you 45 for A and 45 for B

or

  • angle A+ angle B = 90

        since angle A = angle B,

1. you can substitute angle A with angle B like this

  angle B+ angle B = 90

  2 angle B = 90

  angle B = 90/2

  angle B=45; ∴ angle A is also 45 ( because angle A= angle B)

2. or you could substitute angle B with angle A

   angle A+ angle A = 90

2 angle A = 90

  angle A = 90/2

  angle A =45; ∴ angle B is also 45 ( because angle A= angle B)


Now you know what A and B are,

sin A = sin 45; sin B = sin 45

sin 45 = sin 45

tan A = tan 45; tan B = tan 45

tan 45 = tan 45

7 0
3 years ago
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