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3 years ago

Whats the algebraic expression of five less than two times a number is the same as 7?

1 answer:

3 0

Five less than (subtracting 5) two times a number (multiplying unknown number, x, by 2) is equal to 7. Thus, the algebraic expression would be:
2x - 5 = 7

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HELP HELP HELP HELP help help

SVETLANKA909090 [29]

Answer:

r = 6

Step-by-step explanation:

To get the value of r we will use the pythagoras theorem a shown;

PR² = QR² + PQ²

(4+r)² = 8² + r²

Expand

16+8r+r² = 64 + r²

16 + 8r = 64

8r = 64 - 16

8r = 48

r = 48/8

r = 6

Hence the value of r is 6

7 0

3 years ago

According to the empirical (69-95-99.7) rule, if a random variable z has a standard normal distribution, then approximately 95%

Dmitry_Shevchenko [17]

Using z-scores, it is found that the value of z is z = 1.96.

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

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula, which for a measure X, in a distribution with mean $\mu$ and standard deviation $\sigma$ , is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.
Each z-score has an associated p-value, which is the percentile.

The normal distribution is symmetric, which means that the middle 95% is between the <u>2.5th percentile and the 97.5th percentile</u>.
The 2.5th percentile is Z with a p-value of 0.025, thus Z = -1.96.
The 97.5th percentile is Z with a p-value of 0.975, thus Z = 1.96.
Thus, the value of Z is 1.96.

A similar problem is given at brainly.com/question/16965597

7 0

2 years ago

Zaheer, a boy of height 1.5m was watching the entire programme. Initially he observed the top of the flag pole at an angle of el

7nadin3 [17]

Answer:

15.2 m

Step-by-step explanation:

You need to draw a figure. Start by drawing a horizontal segment approximately 10 cm long; that is the ground. Label the left end point A and the right endpoint B. On the right endpoint, B, go up a short 1 cm vertically. That is 1.5 m, the height of Zaheer. Label that point C. Now from that point draw a horizontal line that ends up above point A. Label that point D. Now go back to point C. Draw a segment up to the left at a 30 deg angle with CD. End the segment vertically above point D. Label that point E. That is the top of the flagpole. Draw a vertical segment down from point E through point D ending at point A. Segment AE is the flagpole. Go back to point C. Move 3 cm to the left on segment CD, and draw a point there and label it F. That is where Zaheer moved to. Now connect point F to point E. That is a 45-deg elevation to point E, the top of the flagpole.

m<EFD = 45 deg

m<EFC = 135 deg

m<FEC = 15 deg

m<ECD = 30 deg

We now use the law of sines to find EC

(sin 15)/10 = (sin 135)/EC

EC = 27.32

Because of the 30-60-90 triangle, ED = EC/2

ED = 13.66

Now we add the height of Zaheer to find AE.

13.66 + 1.5 = 15.16

Answer: 15.2 m

7 0

3 years ago

Which function in vertex form is equivalent to f(x) = 4 + x2 – 2x?

Alexus [3.1K]

<h3>Answer:</h3>

option A

f(x) = (x – 1)2 + 3

<h3>Step-by-step explanation:</h3>

Given in the question a function,

f(x) = 4 + x² – 2x

Step 1

f(x) = 4 + x² – 2x

here a = 1

b = -2

c = 4

Step 2

x = -b/2a

h = -(-2)/2(1)

h = 2/2

h = 1

Step 3

Find k

k = 4 + 1² – 2(1)

k = 3

Step 4

To convert a quadratic from y = ax² + bx + c form to vertex form,

y = a(x - h)²+ k

y = 1(x - 1)² + 3

y = (x - 1)² + 3

6 0

3 years ago

(Geometry course question) Explain why it is not possible to construct an equilateral triangle that has

Nutka1998 [239]

Answer:

√3 is irrational

Step-by-step explanation:

The location of the third point of a triangle can be found using a rotation matrix to transform the coordinates of the given points.

<h3 /><h3>Location of point C</h3>

With reference to the attached figure, the slope of line AC is √3, an irrational number. This means the line AC <em>never passes through a point with integer coordinates</em>. (Any point with integer coordinates would be on a line with rational slope.)

<h3>Equilateral triangle</h3>

The line segments making up an equilateral triangle are separated by an angle of 60°. If two vertices are on grid squares, the third must be a rotation of one of them about the other through an angle of 60°. The rotation matrix is irrational, so the rotated point must have irrational coordinates.

The math of it is this. For rotation of (x, y) counterclockwise 60° about the origin, the transformation matrix is ...

$\left[\begin{array}{cc}\cos(60^\circ)&\sin(60^\circ)\\-\sin(60^\circ)&\cos(60^\circ)\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}x'\\y'\end{array}\right]$

Cos(60°) is rational, but sin(60°) is not. For any non-zero rational values of x and y, the sum ...

cos(60°)·x + sin(60°)·y

will be irrational.

As in the attached diagram, if one of the coordinates of the rotated point (B) is zero, then one of the coordinates of its image (C) will be rational. The other image point coordinate cannot be rational.

6 0

2 years ago