Work out the value of 4(2x+3y) when x=8 and y=-3

mrs jackson has $90.She spends 1/4 pf her money on food 1/2 of the remainder on clothes and she saves the rest. How many does sh

rodikova [14]

First you want to divide $90 by four. You want to take the answer and divide it by 2.

$90 / 4 = $22.5

22.5 / 2 = Mrs. Jackson saved $11.25.

7 0

2 years ago

A triangle is dilated by a scale factor of 1/5 and then rotated 90 degree clockwise about the origin. Why is the image similar t

yan [13]

Answers:
The corresponding angles of the triangles are congruent
The image is a reduction of the pre-image
Neither the dilation nor the rotation change the shape of the triangle

Explanation:
For shapes to be similar:
1- there should be a ratio between the sides
2- angles in first shape should be congruent to angles in second shape

Now, a scale factor of 0.2 means that the sides of the image are 0.2 of the length of the original shape. However, angles are not changes

Let's check the choices:
1- The corresponding sides of the triangles are congruent:
This option is incorrect as dilation changes the lengths of the sides

2- The corresponding angles of the triangles are congruent:
This option is correct as neither dilation nor rotation alters the measures of the angles

3- The corresponding sides of the image are 5 times as long as those of the pre-image:
This option is incorrect as the sides of the image are only 0.2 times as long as those of the pre-image

4- The image is a reduction of the pre-image:
This option is correct as the sides of the image are 0.2 times those of the pre-image which means that the shape is reduced

5- Neither the dilation nor the rotation change the shape of the triangle:
This option is correct as both dilation and rotation are rigid transformations that do not alter the shape of the triangle (a triangle remains a triangle only with different side lengths)

6- The rotation reduces the size of the triangle:
This option is incorrect as rotation does not alter the size of the shape. It only changes its position

Hope this helps :)

3 0

2 years ago

Read 2 more answers

Find the six trigonometric function values for angle ∅ where its adjacent side is -9 and its hypotenuse is 41. (Theta is located

arsen [322]

Check the picture below.

$\bf \textit{using the pythagorean theorem}
\\\\
c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b
\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}
\\\\\\
\sqrt{41^2-(-9)^2}=b\implies \sqrt{1681-81}=b\\\\\\ \sqrt{1600}=b\implies 40=b\\\\
-------------------------------$

$\bf sin(\theta )=\cfrac{\stackrel{opposite}{40}}{\stackrel{hypotenuse}{41}}\qquad~~ cos(\theta )=\cfrac{\stackrel{adjacent}{-9}}{\stackrel{hypotenuse}{41}}\qquad~~ tan(\theta )=\cfrac{\stackrel{opposite}{40}}{\stackrel{adjacent}{-9}}
\\\\\\
csc(\theta )=\cfrac{\stackrel{hypotenuse}{41}}{\stackrel{opposite}{40}}\qquad ~~sec(\theta )=\cfrac{\stackrel{hypotenuse}{41}}{\stackrel{adjacent}{-9}}\qquad ~~cot(\theta )=\cfrac{\stackrel{adjacent}{-9}}{\stackrel{opposite}{40}}$

3 0

2 years ago

Erin’s car uses 6 gallons of gas for every 138 miles she drives.which equation could be used to find how many gallons,g, Erin ne

gladu [14]

The equation that could be used to find how many gallons Erin would need to drive 92 miles is 92 = 23g (option c)

<h3>How many gallons is needed to drive 92 miles?</h3>

The first step is to determine the gallons needed to drive 1 mile. To do this, divide the 6 gallons by 138 miles. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.

Gallons needed for 1 mile = 6/138

In order to determine the gallons needed for 92 miles, multiply the ratio gotten in the previous step by 92

(6/138) x 92 = 4 gallons

The option that gives 4 gallons is : 92 = 23g

g = 92 / 32 = 4

To learn more about division, please check: brainly.com/question/13281206

#SPJ1

4 0

1 year ago

36, ___, ___, 32/3 is a geometric sequence, with some terms missing. First, please solve for "r", the common ratio between each

Ksju [112]

Answer: r = 2/3

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = 36

The 4th term is 32/3

n = 4

Therefore,

T4 = 32/3 = 36 × r^(4 - 1)

32/3 = 36 × r^3

Dividing both sides if the equation by 36, it becomes

32/3 × 1/36 = r^3

8/27 = r^3

Taking cube root of both sides of the equation, it becomes

(8/27)^1/3 = r^3 × 1/3

r = 2/3

3 0

2 years ago