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PolarNik [594]
3 years ago
6

The quotient of five times a number and 7 is no more than 10

Mathematics
2 answers:
Akimi4 [234]3 years ago
3 0
The sentence in numerical form is 5x/7≤10
to solve, multiply by 7
5x≤70
lastly, divide by 5
x≤14
KIM [24]3 years ago
3 0
14 is the answer okkkkkkkkkkkkkkkkkkkk
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What is the length of the hypotenuse in a right triangle with legs of length 7 and 24?
Fiesta28 [93]
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7² + 24² = c²

49 + 576 = c²

625 = c²

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25 = c

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3 years ago
Which of the following relationships represents a function?
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Answer: c

Step-by-step explanation:

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3 years ago
The following integral requires a preliminary step such as long division or a change of variables before using the method of par
shtirl [24]

Division yields

\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}

Now for partial fractions: you're looking for constants <em>a</em>, <em>b</em>, and <em>c</em> such that

\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}

\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a

which gives <em>a</em> + <em>b</em> = 2, <em>c</em> = 0, and 2<em>a</em> = -7, so that <em>a</em> = -7/2 and <em>b</em> = 11/2. Then

\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}

Now, in the integral we get

\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx

The first two terms are trivial to integrate. For the third, substitute <em>y</em> = <em>x</em> ² + 2 and d<em>y</em> = 2<em>x</em> d<em>x</em> to get

\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}

7 0
2 years ago
Maggy needs to ship watches for her boss. Maggy has 50 watches and 6 boxes. Each box must contain an equal number of watches. Ho
Xelga [282]
She’ll have 9 left over
7 0
3 years ago
Read 2 more answers
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). The vertex of a
dolphi86 [110]
Vertex form:
y-k=a(x-h)^2
h=-2,k=-20,y=-12 when x=0
thus;
-12+20=a(0+2)^2
8=4a
a=2
Equation:
y+20=2(x+2)^2
y+20=2(x^2+4x+4)
f(x)=2(x^2+4x+4)-20
f(x)=2x^2+8x+8-20
f(x)=2x^2+8x-20
4 0
4 years ago
Read 2 more answers
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