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Alborosie
3 years ago
8

Given that x:2=7:5 Calculate the value of x

Mathematics
1 answer:
Nataliya [291]3 years ago
8 0

Answer:

x=2.8≈3

Step-by-step explanation:

x:2=7:5

\frac{x}{2}=\frac{7}{5}

by cross-multiplication

x×5=2×7

5x=14

x=14/5

x=2.8≈3

i hope this will help you :)

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The difference between the roots of the equation 3x2+bx+10=0 is equal to 4 1 3 . find<br> b.
inna [77]
Given that the difference between the roots of the equation 3x^2+bx+10=0 is 4 \frac{1}{3} = \frac{13}{3}.

Recall that the sum of roots of a quadratic equation is given by - \frac{b}{a}.

Let the two roots of the equation be \alpha and \alpha + \frac{13}{3}, then 

\alpha + \alpha + \frac{13}{3} =2 \alpha + \frac{13}{3} =- \frac{b}{a} =- \frac{b}{3}  \\  \\ i.e.\ \ 2 \alpha + \frac{13}{3}=- \frac{b}{3} . . . (1)

Also recall that the product of the two roots of a quadratic equation is given by \frac{c}{a}, thus:

\alpha \left( \alpha + \frac{13}{3} \right)= \alpha ^2+ \frac{13}{3} \alpha = \frac{c}{a} = \frac{10}{3}  \\  \\ i.e.\ \ \alpha ^2+ \frac{13}{3} \alpha=\frac{10}{3} . . . (2)

From (1), we have:

2 \alpha =- \frac{b}{3} - \frac{13}{3}  \\  \\ \Rightarrow \alpha =- \frac{b}{6} - \frac{13}{6}

Substituting for alpha into (2), gives:

\left(- \frac{b}{6} - \frac{13}{6}\right)^2+ \frac{13}{3} \left(- \frac{b}{6} - \frac{13}{6}\right)= \frac{10}{3}  \\  \\ \Rightarrow \frac{b^2}{36} + \frac{13b}{18} + \frac{169}{36} - \frac{13b}{18} - \frac{169}{18} = \frac{10}{3}  \\  \\ \Rightarrow \frac{b^2}{36} - \frac{289}{36} =0 \\  \\ \Rightarrow \frac{b^2}{36} = \frac{289}{36}  \\  \\ \Rightarrow b^2=289 \\  \\ \Rightarrow b=\pm\sqrt{289}=\pm17
5 0
3 years ago
Emily has 300 books. if frank were to double the number of books that he now owns, he would still have fewer than Emily has
Alex_Xolod [135]
This statement is false. 
If he were to double the amount that Emily has to get franks, franks would have more. 
Look :)
Emily's = 300
Frank's = 300 x 2 = 600

now...
Emily's = 300
Frank's = 600

So frank has more! NOT fewer. 

8 0
3 years ago
Read 2 more answers
Solve each equation using the quadratic formula. Find the exact solution, then approximate the solution to the nearest hundredth
Anika [276]

Answer:

x_1=\frac{5+\sqrt{33}}{4}≈2.69

x_2=\frac{5-\sqrt{33}}{4}≈-0.19



Step-by-step explanation:

 To solve this problem you  must apply the proccedure shown below:

1. You have that the quadratic formula is:

x=\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}

2. To solve the quadratic equation you must substitute the values. So, you have that:

Rewrite the equation:

2x^{2}-5x-1=0

a=2\\b=-5\\c=-1

Then you have:

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3. Therefore, you obtain the following result:

x_1=\frac{5+\sqrt{33}}{4}≈2.69

x_2=\frac{5-\sqrt{33}}{4}≈-0.19


4 0
3 years ago
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N76 [4]
They are about 27 percent that are not seniors 
4 0
3 years ago
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A rectangular picture frame has a perimeter of 58 inches. The heigt of the frame is 18 inches. What is the width of the frame?
AleksandrR [38]
(18×2) + 2n=58
36+2n= 58
2n=58-36
2n= 22
n= 22÷2
n= 11
5 0
3 years ago
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