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Lostsunrise [7]

3 years ago

8

Julian has 56 books. He arranges them in 7 groups. Write an expression that could be used to find the number of books in each gr

oup.

1 answer:

myrzilka [38]3 years ago

5 0

56 divided by 7 = how many books in each group

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Using the converse of Pythagorean Theorem and the law of sines and cosines solve the word problem.

Helga [31]

Answer:

It's the law of cosines

Step-by-step explanation:

law of cosines states that $c^{2} =a^{2} +b^{2} -2ab (cos(\alpha ))$

so we know that a = 7, b = 4, and alpha would be 135 degrees, so just plugging it in gets us 49+16-2*7*4*(-0.707) = 65 + 39.59 = 104.59

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3 years ago

True or False: A millisecond is a millionth of a second.

lesya692 [45]

Answer:

False

Step-by-step explanation:

a millisecond (ms or msec) is one thousandth of a second

7 0

3 years ago

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Given that F(x) = x2 + 2, evaluate F(1) + F(5).

gavmur [86]

Answer:

F(1)+F(5)= 30

Step-by-step explanation:

F(1)=1^2+2=1+2=3

F(5)=5^2+2=25+2=27

27+3=30

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3 years ago

Question 2 (5 points)<br> What is the value of x?<br> HELP ASAP

Anton [14]

Step-by-step explanation:

$In \: \triangle HDT, \: BM || DT.. (given) \\ \\ \therefore \: \frac{HM}{MT} = \frac{ HB}{ BD} \\ (by \: basic \: proportionality \: theorem) \\ \therefore \: \frac{6}{x} = \frac{9}{15} \\ \\ \therefore \: x= \frac{15 \times 6}{9} \\ \\ \therefore \: x= \frac{90}{9} \\ \\ \therefore \: x= 10 \\ \\$

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3 years ago

Find the volume and area for the objects shown and answer Question

klio [65]

Step-by-step explanation:

You must write formulas regarding the volume and surface area of the given solids.

$\bold{\#1\ Rectangular\ prism:}\\\\V=lwh\\SA=2lw+2lh+2wh=2(lw+lh+wh)\\\\\bold{\#2\ Cylinder:}\\\\V=\pi r^2h\\SA=2\pi r^2+2\pi rh=2\pir(r+h)\\\\\bold{\#3\ Sphere:}\\\\V=\dfrac{4}{3}\pi r^3\\SA=4\pi r^2$

$\bold{\#4\ Cone:}\\\\V=\dfrac{1}{3}\pi r^2h\\\\\text{we need calculate the length of a slant length}\ l\\\text{use the Pythagorean theorem:}\\\\l^2=r^2+h^2\to l=\sqrt{r^2+h^2}\\\\SA=\pi r^2+\pi rl=\pi r^2+\pi r\sqrt{r^2+h^2}=\pi r(r+\sqrt{r^2+h^2})\\\\\bold{\#5\ Rectangular\ Pyramid:}\\\\V=\dfrac{1}{3}lwh\\\\$

$\\\text{we need to calculate the height of two different side walls}\ h_1\ \text{and}\ h_2\\\text{use the Pythagorean theorem:}\\\\h_1^2=\left(\dfrac{l}{2}\right)^2+h^2\to h_1=\sqrt{\left(\dfrac{l}{2}\right)^2+h^2}=\sqrt{\dfrac{l^2}{4}+h^2}=\sqrt{\dfrac{l^2}{4}+\dfrac{4h^2}{4}}\\\\h_1=\sqrt{\dfrac{l^2+4h^2}{4}}=\dfrac{\sqrt{l^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{l^2+4h^2}}{2}$

$\\\\h_2^2=\left(\dfrac{w}{2}\right)^2+h^2\to h_2=\sqrt{\left(\dfrac{w}{2}\right)^2+h^2}=\sqrt{\dfrac{w^2}{4}+h^2}=\sqrt{\dfrac{w^2}{4}+\dfrac{4h^2}{4}}\\\\h_2=\sqrt{\dfrac{w^2+4h^2}{4}}=\dfrac{\sqrt{w^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{w^2+4h^2}}{2}$

$SA=lw+2\cdot\dfrac{lh_1}{2}+2\cdot\dfrac{wh_2}{2}\\\\SA=lw+2\!\!\!\!\diagup\cdot\dfrac{l\cdot\frac{\sqrt{l^2+4h^2}}{2}}{2\!\!\!\!\diagup}+2\!\!\!\!\diagup\cdot\dfrac{w\cdot\frac{\sqrt{w^2+4h^2}}{2}}{2\!\!\!\!\diagup}\\\\SA=lw+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw}{2}+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw+l\sqrt{l^2+4h^2}+w\sqrt{w^2+4h^2}}{2}$

6 0

3 years ago