In triangle PQR, the measure of angle P=53degrees, PQ=7.4, and PR=9.6. what is the measure of angle R to the nearest degree?

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

Identify the properties of equality needed to isolate a varaible and solve a given equation. Use the drop-down menus to show you

Anna71 [15]

Answer:

If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal. When you solve an equation, you find the value of the variable that makes the equation true. In order to solve the equation, you isolate the variable.

4 0

2 years ago

Alexander is a stockbroker he earns 11% commission each week last week he sold $7,200 worth of stocks how much money did he make

AlekseyPX

Answer:

Last week Alexander earned $792 in commissions.

Step-by-step explanation:

Giving the following information:

Commission= 11%

Sales= $7,200

T<u>o calculate the total commission, we need to use the following formula:</u>

Total commission= commission rate*sales

Total commission= 0.11*7,200

Total commission= $792

Last week Alexander earned $792 in commissions.

3 0

2 years ago

Gelatin Methacryloyl Hydrogels in the Absence of a Crosslinker as 3D Glioblastoma Multiforme (GBM)-Mimetic Microenvironment

scoray [572]

For the eradication of malignancies like the aggressive type of human brain tumour known as glioblastoma multiforme (GBM), 3D platforms are crucial for tracking tumour growth and assessing treatment candidates.

<h3>What is Glioblastoma Multiforme (GBM)?</h3>

Glioblastoma (GBM), commonly known as a grade IV astrocytoma, is an aggressive brain tumour that grows quickly. The local brain tissue gets invaded, but it typically does not spread to distant organs. GBMs can develop from lower-grade astrocytomas or develop from new brain tumours.

Some characteristics of GBM are-

We explore cellular behavior, expression profiles of malignancy, and apoptosis-related genes within this novel network using suspension and spheroid-based models of GBM.
In-depth research is also done on the sensitivity to the anticancer medication Digitoxigenin.
According to the research, GelMA hydrogels contain high levels of prosurvival Bcl-2 gene expression and sparse or spheroid U373 cells, which have much lower expressions of apoptosis-activating genes like Bad, Puma, and Caspase-3.
The up regulation of matrix-metalloproteinase genes within GelMA suggests that gels have a beneficial effect on the extracellular remodelling of cancer cells.
Through the investigation of 3D malignant cancer cell behavior, this special photo curable gelatin shows significant promise for the practical translation of cancer research and, consequently, for more effective treatment techniques for GBM.

To know more about brain tumour, here

brainly.com/question/13606763

#SPJ4

4 0

2 years ago

***no links please***

prisoha [69]

Answer:

3(pi)

Step-by-step explanation:

8.33 (repeating 33) is 8.333333...

3(pi) = 9.42477796...

17/2 = 8.5

sqrt(64) = 8

Answer: 3(pi)

4 0

3 years ago

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