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3 years ago

In a painting, The Great Pyramid of Giza is 45 centimeters tall.

Mathematics

1 answer:

777dan777 [17]3 years ago

6 0

Answer:

The scale is: 1 cm = 3.26 meter

Step-by-step explanation:

Given

Height of Pyramid in Painting = $H_p = 45 cm$

Actual Height of Pyramid = $H_a = 146.5m$

In order to find the scale, we can find the ratio between actual height and height in painting.

The ratio can be found by dividing the actual height by height in painting

$Scale = \frac{H_a}{H_p}\\= \frac{146.5}{45}\\=3.25555 m/cm$

Rounding off to nearest hundredth

= 3.26

This means that the scale is:

1 cm = 3.26 meter

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Show work please<br> \sqrt(x+12)-\sqrt(2x+1)=1

Nesterboy [21]

Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

Square both sides:

$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

$\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}$

Only $x=4$ works when plugged in the original equation. Therefore, $x=24$ is extraneous and the only solution is $\boxed{x=4}$

4 0

2 years ago

Question text<br><br>If x − 2 = 1/3, then what is the value of x to the power of 2 − 4x + 4?

TiliK225 [7]

Answer: 1/9

Step-by-step explanation:

6 0

3 years ago

Sarah Rhodes prepared one gallon of hot

makvit [3.9K]

1 gallon = 128 ounces

Divide total ounces by ounces per cup:

128 / 4 = 32

She had 32 servings

8 0

2 years ago

A skirt originally cost $10. How much will it cost if you sell it in Amazon with 25% mark-up price

san4es73 [151]

Answer:

$20.40

Step-by-step explanation:

20% off means that the new price of the skirt will be 80% of the original price:

$30(100% – 20%) = $30(80%)

Converting the percent to a decimal gives:

$30(0.8) = $24.00

There is an additional 15% off the sale price of $24.00, so the final price is 85% of the sale price:

$24(100% – 15%) = $24(85%)

Again converting the percent to a decimal gives:

$24(0.85) = $20.40

5 0

3 years ago

The product of nine and a number is added to six the result is 24 what is the number

Andru [333]

Hello!

We can make an equation based on what we know

The product of 9 and a number is

9 * x

Added to six

9 * x + 6

Gives the result of 24

9 * x + 6 = 24

Now you solve it algebraically

Subtract 6 from both sides

9 * x = 18

Divide both sides by 9

x = 2

The answer is 2

Hope this helps!

8 0

3 years ago