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kodGreya [7K]
2 years ago
8

Please solve these! Read the instructions too!

Mathematics
1 answer:
sleet_krkn [62]2 years ago
8 0
Just graph the coordinates
this picture is the different quadrants on the graph, whichever quadrant the coordinate is in, is what you put in the 2nd column
for example: (-2,-3) is in the 3rd quadrant
if its not in a quadrant its either on x or y axis, so its just on the line, and i assume you know which axis is which

for number 4. You just do subtraction, and then if its negative, it becomes positive since its asking for the absolute value
for example: |-24-11| > |-35| > 35

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What value does "h" have in this equation for this to be an infinite solutions equation. 6 (hx + 5) + 4 = -4(8 - 4(8 – 18x) 18x)
Sever21 [200]

We have the following:

6(hx+5)+4=-4(8-18x)+66

A system of linear equations has infinite solutions when the graphs are exactly the same line.

for this to happen, on both sides the value of x must be equal:

\begin{gathered} 6\cdot h=4\cdot18 \\ h=4\cdot\frac{18}{6} \\ h=12 \end{gathered}

replacing:

\begin{gathered} 6\cdot(12x+5)+4=-4\cdot(8-18x)+66 \\ 72x+30+4=-32+72x+66 \\ 7x+34=7x+34 \\ 0=0 \\ \text{true for all x} \end{gathered}

4 0
1 year ago
The growth rate of the sunflower from day 14 to day
nata0808 [166]

Option B) h = 4.5t – 27 is the equation of the straight line that best models the height h, in centimeters, of the sunflower t days after it begins to grow.

                     

From the above graph we can see that from day 14 to day 35 , it is a straight line.

And equation of a straight line is   y = mx + c  or   y – y1 = m(x – x1)

                               Where, m =slope of the line

                                             c = intercept

the equation can be rewritten as  h – h1  = m(t – t1)                    (1)

So, to find the equation of line , first we will calculate the slope of the line.

To find the slope : m = (h2 – h1 ) / (t2 – t1)                     (2)

From the graph and the table given, the coordinates (t1 , h1 ) and ( t2 , h2 ) are (14 , 36.6) and (35, 131) respectively.

Putting these values in equation (2), we get

                 m = (131 – 36.6)/(35 – 14)

                 m =  94.4/21

                 m  = 4.5

now to find the equation of line we put the values in equation (1), we get

h – 36.6 = 4.5(t – 14)

h – 36.6 = 4.5t – 63

h = 4.5t -63 + 36.6

h = 4.5t -27

Hence the equation of the line is ,   option B) h = 4.5t -27

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7 0
2 years ago
(PLESE HELP) Factor the following expression. Simplify your answer.
mars1129 [50]

The factor of the expression 5p(p + 2)^{\frac{2}{3} }  + 4(p + 2)^{\frac{1}{3} } is(p + 2)^{\frac{2}{3} } (5p^{3}  + 10p^{2}  + 20p + 4)

To answer the question, we need to know what factorization is

<h3>What is factorization?</h3>

Factorization is the process of breaking down an expressing into a simpler form containing its factors.

Since

5p(p + 2)^{\frac{2}{3} }  + 4(p + 2)^{\frac{1}{3} }

Since (p + 2)^{\frac{1}{3} } is common, we factor it out. So, we have

(p + 2)^{\frac{2}{3} } (5p(p + 2)^{2}  + 4)

Expanding the bracket, we have

(p + 2)^{\frac{2}{3} } (5p(p^{2}  + 2p + 4) + 4) = (p + 2)^{\frac{2}{3} } (5p^{3}  + 10p^{2}  + 20p + 4)

So, the factor of the expression 5p(p + 2)^{\frac{2}{3} }  + 4(p + 2)^{\frac{1}{3} } is(p + 2)^{\frac{2}{3} } (5p^{3}  + 10p^{2}  + 20p + 4)

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8 0
1 year ago
Type the correct answer in each box. Use numerals instead of words. Function g is a transformation of function f. Graph shows 2
yawa3891 [41]

An equation is formed of two equal expressions. The equation of function g(x) in terms of f(x) is g(x) = -3[f(x)].

<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given graph is the graph of an exponential function, the general equation of an exponential function is given by the y=aeᵇˣ. To get the function f(x) and g(x), you need to substitute the points in the given function and produce the equation of each function.

The equation for f(x) from the given graph can be written as,

f(x)=e^{(\ln2)x}-2

Now, similarly from the graph the function of g(x) can be written as,

g(x)=-3e^{(\ln2)x}+6

Further, the equation of function g(x) in terms of f(x) can be written as,

g(x) = -3[f(x)]

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4 0
2 years ago
The variable z is inversely proportional to x. When x is 16, z has the value 0.875. What is the value of z when x= 21?
ziro4ka [17]
For z and x to be inversely proportional, there must be some constant k such that

zx=k

Given that z=0.875 when x=16, it follows that

0.875\cdot16=k\implies k=14

Then when x=21, we have

21z=14\implies z=\dfrac{14}{21}=\approx0.667
8 0
3 years ago
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