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3 years ago

13

Given h(x) = -x + 5, find h(5).

2 answers:

BlackZzzverrR [31]3 years ago

8 0

Answer:

h(5) = 0

Step-by-step explanation:

1. Plug 5 into the equation

h(5) = - (5) + 5

2. Solve the equation

h(5) = -5+5

h(5) = 0

nekit [7.7K]3 years ago

4 0

Answer:

0

Step-by-step explanation:

h(x)=-x + 5

you input h(5) into where x is so then the equation would be

h(5)= -(5) + 5

you multiple the negative sign to the 5 in the parentheses

h(5)=-5 + 5

then you just solve

h(5)= 0

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Elena L [17]

Answer:

So I (3,0) becomes I' (1,3)

H (5,2) H' (1,1)

G (2,4) G' (2,1)

Step-by-step explanation:

So let's start with I, just count how many times you move to the left then how many times you move up.

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5 0

3 years ago

The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.

Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is $\dfrac{15}{2}.$

To find:

The sum of first six terms.

Solution:

We have,

$S_2=6$

$S_4=\dfrac{15}{2}$

Sum of first n terms of a GP is

$S_n=\dfrac{a(1-r^n)}{1-r}$ ...(i)

Putting n=2, we get

$S_2=\dfrac{a(1-r^2)}{1-r}$

$6=\dfrac{a(1-r)(1+r)}{1-r}$

$6=a(1+r)$ ...(ii)

Putting n=4, we get

$S_4=\dfrac{a(1-r^4)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}$

$\dfrac{15}{2}=6(1+r^2)$ (Using (ii))

Divide both sides by 6.

$\dfrac{15}{12}=(1+r^2)$

$\dfrac{5}{4}-1=r^2$

$\dfrac{5-4}{4}=r^2$

$\dfrac{1}{4}=r^2$

Taking square root on both sides, we get

$\pm \sqrt{\dfrac{1}{4}}=r$

$\pm \dfrac{1}{2}=r$

$\pm 0.5=r$

Case 1: If r is positive, then using (ii) we get

$6=a(1+0.5)$

$6=a(1.5)$

$\dfrac{6}{1.5}=a$

$4=a$

The sum of first 6 terms is

$S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}$

$S_6=\dfrac{4(1-0.015625)}{0.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Case 2: If r is negative, then using (ii) we get

$6=a(1-0.5)$

$6=a(0.5)$

$\dfrac{6}{0.5}=a$

$12=a$

The sum of first 6 terms is

$S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}$

$S_6=\dfrac{12(1-0.015625)}{1.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Therefore, the sum of the first six terms is 7.875.

5 0

3 years ago

Draw the graphs of the equations x – y = 1 and 2x + y = 8. Shade the area bounded by these two lines and y-axis. Also, determine

NikAS [45]

Answer:

Using Geometry to answer the question would be the simplest:

Step-by-step explanation:

Remembering the formula for the area of a triangle which is $A=\frac12bh$ . One can then tackle the question by doing the following:

Step 1 Find the y-intercepts

The y-intercepts are found by substituting in $x=0$ .

Which gives you this when you plug it into both equations:

$-y=1\\y=-1\\y=8$

So the y-intercepts for the graphs are $(0,-1)\\$ , and $(0,8)$ respectively.

Now one has to use elimination to solve the problems by adding up the equations we get:

$x-y=1\\2x+y=8\\3x=9\\x=3$

Now to solve for the y component substitute:

$2(3)+y=8\\y=2$

Therefore, the graphs intersect at the following:

$(3,2)$

Now we have our triangle which is accompanied by the graph.

now to solve it we must figure out how long the base is:

$b=8-(-1)\\b=9$

The height must also be accounted for which is the following:

$h=3$

Now the formula can be used:

$A=\frac12bh=\frac12(9)(3)=\frac{27}2\ \text{units}^2$

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3 years ago

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Which mountain range separates Georgia from Russia?<br>

agasfer [191]

Answer:

Step-by-step explanation:

The Caucasus Mountains

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4 years ago

1. (4x-3)(3x^2+8x-5)

lesya [120]

Here, you have to foil the equation.

Distribute 4x to all sides, then distribute the -3 to all sides. Next, combine like terms. If you do this, your answer will be

$12x^3+23x^2-44x+15$

6 0

4 years ago