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2 years ago

4a² - 25? little help? Can you show me the steps to gets the answer? Thanks!

2 answers:

4 0

This is simply a difference of squares. To factor this, you simply take the square roots of the leading coefficient and the C term. Thus you get 2 and 5. As a pair of factors, it is simply (2a+5)(2a-5). If you actually need to solve this, you can set either the factors or the original equation equal to 0.

WARRIOR [948]2 years ago

4 0

4a² - 25

= (2a)² - 5²

= (2a+5)(2a-5) since a² -b² = (a+b)(a-b)

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A store sells almonds for $7 per pound, cashews for $10 per pound, and walnuts for $12 per pound. A customer buys 12 pounds of m

pshichka [43]

The complete question in the attached figure

Let
x-------------> pounds of almonds-------> ($7 per pound)
y-------------> pounds of cashews-------> ($10 per pound)
z-------------> pounds of walnuts-------> ($12 per pound)

we know that
x+y+z=12---------------> equation 1
7x+10y+12z=118---------> equation 2
z=2+y--------------------> equation 3

replacing equation 3 in 1 and 2
x+y+(2+y)=12----------> x+2y=10--------> equation 4
7x+10y+12*(2+y)=118--> 7x+10y+24+12y=118--> 7x+22y=94 --> equation 5

using a graph tool-----> to resolve the system of equations
see the attached figure

the solution is the point (4,3)
x=4
y=3
z=2+y-----> z=2+3-------->z=5

pounds of almonds are 4
pounds of cashews are 3
pounds of walnuts are 5

therefore

the answer is the option
a. The customer buys 1 more pound of walnuts than almonds and 1 more pound of almonds than cashews

7 0

2 years ago

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Find the lengths of the median o

nexus9112 [7]

Answer:

$5/2units\\$ .

$\sqrt{47/2}units \\$ .

$\sqrt{41/2}units\\$ .

Step-by-step explanation:

The given points are A(1,2,3), B(-2,0,5) and C(4,1,5). The triangle is represented in the attach file where the three possible median are length AE, BF, and CD. We determine the coordinate of point D,E and F using the midpoint equation which is for any point A(x,y,z) and point B(a,b,c), the midpoint D is determine by

$D=(\frac{x+a}{2},\frac{y+b}{2},\frac{z+c}{2})\\$ .

Hence going by the above formula we determine the coordinate of point D,E and F

$D=(\frac{-2+1}{2},\frac{0+2}{2},\frac{5+3}{2})\\$ .

$D=(\frac{-1}{2},1,4)\\$ .

point E

$E=(\frac{4-2}{2},\frac{1+0}{2},\frac{5+5}{2})\\$ .

$E=(1,\frac{1}{2},5)\\$ .

Point F

$F=(\frac{4+1}{2},\frac{1+2}{2},\frac{5+3}{2})\\$ .

$F=(\frac{5}{2},\frac{3}{2},4)\\$ .

To determine the length of each median line we use the formula for distance between two points which is express as

$AB=\sqrt{(y_{2}-y_{1} )^{2} +(x_{2}-x_{1} )^{2}+(z_{2}-z_{1} )^{2}} \\$ .

Using the above formula we determine the length of line AE,BF and CD.

$AE=\sqrt{(1-1 )^{2} +(1/2-2)^{2}+(5-3 )^{2}} \\$ .

$AE=\sqrt{0 +9/4+4} \\$ .

$AE=\sqrt{25/4} \\$ .

$AE=5/2units\\$ .

For point BF

$BF=\sqrt{(5/2+2 )^{2} +(3/2-0)^{2}+(4-5 )^{2}}\\$ .

$BF=\sqrt{81/4 +9/4+1} \\$ .

$BF=\sqrt{47/2} \\$ .

$BF=\sqrt{47/2}units \\$ .

For point CD

$CD=\sqrt{(-1/2-4 )^{2} +(1-1)^{2}+(4-5 )^{2}}\\$ .

$BF=\sqrt{81/4 +0+1} \\$ .

$BF=\sqrt{41/2} \\$ .

$BF=\sqrt{41/2}units\\$ .

7 0

2 years ago

Let h(x)=2x+5h(x)=2x+5h, left parenthesis, x, right parenthesis, equals, 2, x, plus, 5 and g(x)=8-3xg(x)=8−3xg, left parenthesis

BaLLatris [955]

The question is Let h(x)=2x+5 and g(x)=8-3x
what is the value of h(g(1.5))
the answer

h(g(1.5))= 2g(1.5)+5, and g(1.5)=8-3(1.5)=3.5, so
h(g(1.5))= 2(3.5)+5= 12
h(g(1.5))= 12

8 0

2 years ago

(-15,-6), (8,3) Find the slope of the line through each pair of points?

lukranit [14]

Slope is equal to the change in

over the change in

, or rise over run.

m = change in y / change in x

The change in

is equal to the difference in x-coordinates (also called run), and the change in

is equal to the difference in y-coordinates (also called rise).

m = y^2 - y^1 / x^2 x^1

Substitute in the values of

and

into the equation to find the slope.

−

(

−

)

−

(

−

)

Simplify.

Simplify the numerator.

Tap for more steps...

−

(

−

)

Simplify the denominator.

Multiply

−

Add

and

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8 0

2 years ago

Read 2 more answers

The radius of the large fish pond is 4 times the radius of the small fish pond.

Rom4ik [11]

Need the statements to answer don’t you

3 0

2 years ago