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2 years ago

Solve each word problem by setting up a system of equations.

Mathematics

1 answer:

Aleonysh [2.5K]2 years ago

6 0

X=2x(2y+3x) numbers

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Find the roots of h(t) = (139kt)^2 − 69t + 80

Sonbull [250]

Answer:

The positive value of $k$ will result in exactly one real root is approximately 0.028.

Step-by-step explanation:

Let $h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ , roots are those values of $t$ so that $h(t) = 0$ . That is:

$19321\cdot k^{2}\cdot t^{2}-69\cdot t + 80=0$ (1)

Roots are determined analytically by the Quadratic Formula:

$t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}$

$t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$

The smaller root is $t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ , and the larger root is $t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ .

$h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ has one real root when $\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0$ . Then, we solve the discriminant for $k$ :

$\frac{80\cdot k^{2}}{19321} = \frac{4761}{1493204164}$

$k \approx \pm 0.028$

The positive value of $k$ will result in exactly one real root is approximately 0.028.

7 0

2 years ago

a banner is made of a sqiare and a semocircle. the square has side lengths of 26 inches. one side of the square is also the diam

tamaranim1 [39]

ARea = area of square + area of semicircle

= 26^2 + 0.5pi(13)^2

= 941.46 square inches to nearest hundredth

8 0

2 years ago

Read 2 more answers

At what point do the lines y = 6x – 18 and<br> y=8x – 32 intersect?

anzhelika [568]

Answer:

(7, 24)

Step-by-step explanation:

Solve the system:

6x - 18 = 8x - 32

2x = 14

x = 7

y = 6(7) - 18

y = 24

4 0

2 years ago

that batch calls for 5 cups of flour and 4 teaspoons of vanilla if i use 6 teaspoons of vanilla how many cups will i need

Eva8 [605]

5 cups & 4 teaspoons
? cups & 6 teaspoons

2.5 cups is half of 5
2 is half of 4

you increased the recipe by 1/2

so for 6 teaspoons you will need 7.5 or 7 1/2 cups of flour b/c 5 + 2.5 = 7.5

ANSWER: 7 1/2

4 0

2 years ago

when you go to answer this, can someone please give me the steps on how to do it, because I think I'm doing it wrong

leva [86]

Answer:

TUA=123

Step-by-step explanation:

so first we find <TUS in terms of x

so 180-11x-2

178-11x

so now we can use the sum of a triangle's angles which is always 180 to find the angles in triangle TUS

178-11x+5x+10+58=180

178-6x=112

take 178 from both sides

-6x=-66

x=11

so we can do 11x11+2=TUA

TUA=123

6 0

2 years ago