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Alexandra [31]
3 years ago
10

Y = x^2+ 7x - 5 can be written in the form y = (x + a)^2+b

Mathematics
1 answer:
BARSIC [14]3 years ago
8 0

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = (x - h)² + k (h, k) are the coordinates of the vertex

Given y = x² + 7x - 5

To express in vertex form use the method of completing the square

add/subtract ( half the coefficient of the x- term )²

y = x² + 2( \frac{7}{2} )x +\frac{49}{4} - \frac{49}{4} - 5

y = (x + \frac{7}{2} )² - \frac{49}{4} - \frac{20}{4}

y = (x + \frac{7}{2} )² - \frac{69}{4}

Hence

a = \frac{7}{2} and b = - \frac{69}{4}

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Triangle ABC is a scaled copy of triangle DEF. Side AB measures 12
Dima020 [189]

Answer:

1. The scale factor here is 1.5

2. The scale factor here is 2/3

Step-by-step explanation:

Here, we shall be dealing with scales of triangles.

we have two triangles;

ABC and DEF

longest sides are in the ratio;

12 : 8

1. What scale factor translates DEF to ABC?

The ratio of the length can be beaten down to 3:2

So therefore, we can see that by multiplying the sides of of DEF by 1.5, we can arrive at the sides of ABC

So the scale factor here is 1.5

2. This is like the other way round of what we have above.

By multiplying the sides of ABC by 2/3, we shall have the sides of DEF

4 0
3 years ago
Alice has 12 more trees in her garden than Stephen has. After Stephen planted 10 more trees and Alice dug out 4, together they h
Dafna1 [17]

Answer:

Stephen has 9 trees

Alice has 21 trees

Step-by-step explanation:

<u>At the beginning:</u>

Stephen = x trees

Alice = x + 12 trees

<u>At the end:</u>

Alice = (x + 12) - 4 trees

Stephen = x + 10 trees

Total = 36

Then

((x+12)-4)+(x+10)=36\\ \\(x+12-4)+(x+10)=36\\ \\(x+8)+(x+10)=36\\ \\x+8+x+10=36\\ \\2x+18=36\\ \\2x+18-18=36-18\\ \\2x=18\\ \\x=9

Stephen - 9 trees

Alice - 9 + 12 = 21 trees

8 0
3 years ago
Read 2 more answers
20 men decided to complete a work in 30 days. but after 6 days 8 men left now in how many day the work will be completed​
Serga [27]

First, we convert it into a unit like this

20 workers × 30 days = 600 units work

After leaving the 5 workers, we have 35 days to complete the work.

In 35 days only 15 workers will do the work.

So the work completed in 35 days by 15 workers = 35 ×15 =525 units

Remaining unit = 600 -525 =75 units

This unit would do by 5 workers in (75/5) = 15 days.

So after 15 days, 5 workers should leave the job.

6 0
2 years ago
Questions and Answers<br>1.<br>A is 40% of B. what percentages<br>Discuss<br>A<br>6090<br>B.​
ratelena [41]

Answer:

yeah thats right good job keep up the good work and keep doing ur thing good job

Step-by-step explanation:

5 0
2 years ago
Cuánto es la mitad de cinco octavos
shutvik [7]
Mitad de \frac{5}{8}'s
Multiplicar \frac{5}{8} por \frac{1}{2}
(\frac{5}{8})  (\frac{1}{2}) =  \frac{(5)(1)}{(8)(2)} =  \frac{5}{16}
4 0
3 years ago
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