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2 years ago

Help how do you solve this (step by step preferably please) 7^x5^y7^z

Mathematics

1 answer:

Sophie [7]2 years ago

7 0

Answer:

i realy try my best here it

Rewrite the equation as

Subtract

from both sides of the equation.

−

Divide each term by

and simplify.

Tap for more steps...

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Step-by-step explanation:

You might be interested in

Find the area of the following<br> kite:<br> A = [?] m²<br> 40 m<br> 16 m<br> 16 m<br> 6 m

Rama09 [41]

Answer:

$Area_{kite}=736m^2$

Step-by-step explanation:

There are a few methods to find the area of this figure:

1. kite area formula

2. 2 triangles (one top, one bottom)

3. 2 triangles (one left, one right)

4. 4 separate right triangles.

<h3><u>Option 1: The kite area formula</u></h3>

Recall the formula for area of a kite: $Area_{kite}=\frac{1}{2} d_{1}d_{2}$ where d1 and d2 are the lengths of the diagonals of the kite ("diagonals" are segments that connect non-adjacent vertices -- in a quadrilateral, vertices that are across from each other).

If you've forgotten why that is the formula for the area of a kite, observe the attached diagram: note that the kite (shaded in) is half of the area of the rectangle that surrounds the kite (visualize the 4 smaller rectangles, and observe that the shaded portion is half of each, and thus the area of the kite is half the area of the large rectangle).

The area of a rectangle is $Area_{rectangle}=bh$ , sometimes written as $Area_{rectangle}=bh$ , where w is the width, and h is the height of the rectangle.

In the diagram, notice that the width and height are each just the diagonals of the kite. So, the <u>Area of the kite</u> is <u>half of the area of that surrounding rectangle</u> ... the rectangle with sides the lengths of the kite's diagonals.Hence, $Area_{kite}=\frac{1}{2} d_{1}d_{2}$

For our situation, each of the diagonals is already broken up into two parts from the intersection of the diagonals. To find the full length of the diagonal, add each part together:

For the horizontal diagonal (which I'll call d1): $d_{1}=40m+6m=46m$

For the vertical diagonal (which I'll call d2): $d_{2}=16m+16m=32m$

Substituting back into the formula for the area of a kite:

$Area_{kite}=\frac{1}{2} d_{1}d_{2}\\Area_{kite}=\frac{1}{2} (46m)(32m)\\Area_{kite}=736m^2$

<h3><u /></h3><h3><u>Option 2: The sum of the parts (version 1)</u></h3>

If one doesn't remember the formula for the area of a kite, and can't remember how to build it, the given shape could be visualized as 2 separate triangles, the given shape could be visualized as 2 separate triangles (one on top; one on bottom).

Visualizing it in this way produces two congruent triangles. Since the upper and lower triangles are congruent, they have the same area, and thus the area of the kite is double the area of the upper triangle.

Recall the formula for area of a triangle: $Area_{triangle}=\frac{1}{2} bh$ where b is the base of a triangle, and h is the height of the triangle <em>(length of a perpendicular line segment between a point on the line containing the base, and the non-colinear vertex)</em>. Since all kites have diagonals that are perpendicular to each other (as already indicated in the diagram), the height is already given (16m).

The base of the upper triangle, is the sum of the two segments that compose it: $b=40m+6m=46m$

<u>Finding the Area of the upper triangle</u> $Area_{\text{upper }triangle}=\frac{1}{2} (46m)(16m) = 368m^2$

<u>Finding the Area of the kite</u>

$Area_{kite}=2*(368m^2)$

$Area_{kite}=736m^2$

<h3><u>Option 3: The sum of the parts (version 2)</u></h3>

The given shape could be visualized as 2 separate triangles (one on the left; one on the right). Each triangle has its own area, and the sum of both triangle areas is the area of the kite.

<em>Note: In this visualization, the two triangles are not congruent, so it is not possible to double one of their areas to find the area of the kite.</em>

The base of the left triangle is the vertical line segment the is the vertical diagonal of the kite. We'll need to add together the two segments that compose it: $b=16m+16m=32m$ . This is also the base of the triangle on the right.

<u>Finding the Area of left and right triangles</u>

$Area_{\text{left }triangle}=\frac{1}{2} (32m)(40m) = 640m^2$

The base of the right triangle is the same length as the left triangle: $Area_{\text{right }triangle}=\frac{1}{2} (32m)(6m) = 96m^2$

<u>Finding the Area of the kite</u>

$Area_{kite}=(640m^2)+(96m^2)$

$Area_{kite}=736m^2$

<h3><u>Option 4: The sum of the parts (version 3)</u></h3>

If you don't happen to see those composite triangles from option 2 or 3 when you're working this out on a particular problem, the given shape could be visualized as 4 separate right triangles, and we're still given enough information in this problem to solve it this way.

<u>Calculating the area of the 4 right triangles</u>

$Area_{\text{upper left }triangle}=\frac{1}{2} (40m)(16m) = 320m^2$

$Area_{\text{upper right }triangle}=\frac{1}{2} (6m)(16m) = 48m^2$

$Area_{\text{lower left }triangle}=\frac{1}{2} (40m)(16m) = 320m^2$

$Area_{\text{lower right }triangle}=\frac{1}{2} (6m)(16m) = 48m^2$

<u>Calculating the area of the kite</u>

$Area_{kite}=(320m^2)+(48m^2)+(320m^2)+(48m^2)$

$Area_{kite}=736m^2$

8 0

2 years ago

Express in the simplest form 777:147

Dvinal [7]

Answer:

your answer should be 37:7

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 777 and 147 is 21

Divide both terms by the GCF, 21:

777 ÷ 21 = 37

147 ÷ 21 = 7

The ratio 777 : 147 can be reduced to lowest terms by dividing both terms by the GCF = 21 :

777 : 147 = 37 : 7

Therefore:

777 : 147 = 37 : 7

3 0

3 years ago

Read 2 more answers

A water tank in the shape of a rectangular has a volume of 900 cubic feet. It is 15 feet

True [87]

The height of the water tank is 6.

L x W x H = V (volume)
15 x 10 x 6 = 900 cubic feet

6 0

2 years ago

Kenny has 51,400 in the bank. He eams $150 every week at his afterschool job. What is the rate of change for the scenario descri

vazorg [7]

Answer:

his pay check

Step-by-step explanation:

51,400+150 he would be adding more money

5 0

3 years ago

Given directed line segment AB determine point X on the graph such that X partions the segment A to B in a ratio of 1:4 and give

Viktor [21]

Answer:

The coordinates of point X that divides the line in 1:4 are: (3,8/5)

Step-by-step explanation:

When a point divides a line with coordinates (x1,y1) and (x2,y2) in ratio m:n,

the coordinates of point are given by:

$(x,y) = (\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n})$

Given points are:

(x1,y1) = (5,1)

(x2,y2) = (-5,4)

Putting the values in the formula

$X(x,y) = (\frac{(1)(-5)+(4)(5)}{1+4} , \frac{(1)(4)+(4)(1)}{1+4})\\= (\frac{-5+20}{5}, \frac{4+4}{5})\\=(\frac{15}{5}, \frac{8}{5})\\=(3,\frac{8}{5})$

Hence,

The coordinates of point X that divides the line in 1:4 are: (3,8/5)

8 0

3 years ago