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3 years ago

betty has 15 less than triple the number of points that jennie has. Write an expression to find how many points betty 1. has??

Mathematics

2 answers:

Dmitry [639]3 years ago

6 0

3x-15

.........................................................................

Troyanec [42]3 years ago

4 0

3x - 15

less than or more than trick-------> the number before those words should be the second number in the equation

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If a sequence of 8 consecutive odd integers with increasing values has 9 as its seventh term. What is the sum of the terms of th

klemol [59]

Answer:

$Sum = 32$

Step-by-step explanation:

Given

Sequence = Consecutive Odds

$T_7 = 9$

Required

The sum of the terms

A sequence of odd number has a difference of 2. So, the sequence is represented as:

$S = \{-3,-1,1,3,5,7,9,11\}$

Add up all terms in the sequence

$Sum = -3-1+1+3+5+7+9+11$

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3 years ago

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S_A_V [24]

Answer:

f(g(x))=16x^2+6x-4

Step-by-step explanation:

f(g(x))=4(2x)^2 +3(2x)-4

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2 years ago

Consider the following equation. f(x, y) = y3/x, P(1, 2), u = 1 3 2i + 5 j (a) Find the gradient of f. ∇f(x, y) = Correct: Your

BaLLatris [955]

$f(x,y)=\dfrac{y^3}x$

a. The gradient is

$\nabla f(x,y)=\dfrac{\partial f}{\partial x}\,\vec\imath+\dfrac{\partial f}{\partial y}\,\vec\jmath$

$\boxed{\nabla f(x,y)=-\dfrac{y^3}{x^2}\,\vec\imath+\dfrac{3y^2}x\,\vec\jmath}$

b. The gradient at point P(1, 2) is

$\boxed{\nabla f(1,2)=-8\,\vec\imath+12\,\vec\jmath}$

c. The derivative of $f$ at P in the direction of $\vec u$ is

$D_{\vec u}f(1,2)=\nabla f(1,2)\cdot\dfrac{\vec u}{\|\vec u\|}$

It looks like

$\vec u=\dfrac{13}2\,\vec\imath+5\,\vec\jmath$

so that

$\|\vec u\|=\sqrt{\left(\dfrac{13}2\right)^2+5^2}=\dfrac{\sqrt{269}}2$

Then

$D_{\vec u}f(1,2)=\dfrac{\left(-8\,\vec\imath+12\,\vec\jmath\right)\cdot\left(\frac{13}2\,\vec\imath+5\,\vec\jmath\right)}{\frac{\sqrt{269}}2}$

$\boxed{D_{\vec u}f(1,2)=\dfrac{16}{\sqrt{269}}}$

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3 years ago

Find the perimeter and area

stepladder [879]

Answer:

32 times square root of 3. is the perimeter, area is 48 times square root of 3

Step-by-step explanation:

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3 years ago

Which is the completely factored from of xy^3-x^3y

Oksanka [162]

Answer:

$xy(y+x)(y-x)$

Step-by-step explanation:

To factor the expression, remove the greatest common factor or GCF from each term. Both terms share in common xy. The expression becomes:

$xy^3-x^3y\\xy(y^2-x^2)$

What remains in the parenthesis is a different of perfect squares. Factor the difference of perfect squares into two binomials of the form (x+a)(x-a) where a is the square root of $(x^2-a^2)$ .

So the expression becomes:

$xy(y^2-x^2)\\xy(y+x)(y-x)$

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3 years ago