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3 years ago

Four times a number +3 is the same as 5+ the number

Mathematics

2 answers:

solmaris [256]3 years ago

6 0

Four times a number +3 is the same as 5+ the number

Now writing in numerical form

4x + 3 = 5 + x

yarga [219]3 years ago

4 0

x=2/3

4x+3=5+x

4(2/3)+3=5+2/3

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What is the perimeter of triangle PQR? Show your work.

zubka84 [21]

You know that the two triangles are congruent because two sides and one angle are congruent.

According to CPCTC, corresponding parts of congruent triangles are congruent, which means that PR and SU are equal.

3y-2=y+4
3y=y+6
2y=6
y=3

3(3)-2=9-2=7

7+4+6=17

The perimeter is 17 feet.

Hope this helps!

6 0

2 years ago

If logb2=x and logb3=y, evaluate the following in terms of x and y:

Alja [10]

$log_b{162} = x + 4y\\\\log_b324 = 2x+4y\\\\log_b\frac{8}{9} = 3x-2y\\\\\frac{log_b27}{log_b16} = 3y-4x$

Solution:

Given that,

$log_b2 = x\\\\log_b3 = y --------(i)$

Use the following log rules

Rule 1: $log_b(ac) = log_ba + log_bc$

Rule 2: $log_b\frac{a}{c} = log_ba - log_bc$

Rule 3: $log_ba^c = clog_ba$

$a) log_b{162}$

Break 162 down to primes:

$162 = 2^1 \times 3^4$

$log_b{162} =log_b 2^1. 3^4\\\\By\ rule\ 1\\\\ log_b{162} = log_b 2^1 +log_b 3^4\\\\By\ rule\ 3\\\\1log_b2 + 4log_b3\\\\1x+4y\\\\x+4y$

Thus we get,

$log_b162 = x + 4y$

$b) log_b 324$

Break 324 down to primes:

$324 = 2^2 \times 3^4$

$log_b324 = log_b 2^2.3^4\\\\By\ rule\ 1\\\\log_b324 = log_b2^2 + log_b3^4\\\\By\ rule\ 3\\\\log_b324 = 2log_b2 + 4log_b3\\\\From\ (i)\\\\log_b324 = 2x + 4y$

$c) log_b\frac{8}{9}$

By rule 2

$log_b\frac{8}{9} = log_b8 - log_b9\\\\log_b\frac{8}{9} = log_b 2^3 - log_b3^2\\\\By\ rule\ 3\\\\log_b\frac{8}{9} = 3 log_b2 - 2log_b3\\\\From\ (i)\\\\log_b\frac{8}{9} = 3x - 2y$

$d) \frac{log_b27}{log_b16}$

By rule 2

$\frac{log_b27}{log_b16} = log_b27 - log_b16\\\\ \frac{log_b27}{log_b16} = log_b3^3 - log_b2^4\\\\By\ rule\ 2\\\\ \frac{log_b27}{log_b16} = 3log_b3 - 4log_b2 \\\\From\ (i)\\\\\frac{log_b27}{log_b16} = 3y - 4x$

Thus the given are evaluated in terms of x and y

3 0

2 years ago

Find the midsegment of triangle ABC so that it is parallel to side BC and label it as segment EG on the graph coordinate of E: _

Sholpan [36]

Answer:

Coordinate of E: (-2,3) Coordinate of G: (2.5, 1.5)

Step-by-step explanation:

You first have to find the midpoints of AC and AB.

AC X coordinate:

X1+X2/2

Substitute the x points of AC in

1+(-5)/2=-2

AC Y coordinate:

Y1+Y2/2=3

Substitute the y points of AC in

5+1/2=3

You do the same thing with the AB line. I am pretty sure this works and I hope this helps!

5 0

2 years ago

What is 2x-64<108 If you answer this I will give you a total of 23 points!

alexandr1967 [171]

Answer:

2x-64<108

One solution was found :

x < 86

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

2*x-64-(108)<0

Step by step solution :

Step 1 :

Pulling out like terms :

1.1 Pull out like factors :

2x - 172 = 2 • (x - 86)

Equation at the end of step 1 :

Step 2 :

2.1 Divide both sides by 2

Solve Basic Inequality :

2.2 Add 86 to both sides

x < 86

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