Solve the following quadratic-linear system of equations.

exis [7]

Answer:

Part 1) The length of the longest side of ∆ABC is 4 units

Part 2) The ratio of the area of ∆ABC to the area of ∆DEF is $\frac{1}{100}$

Step-by-step explanation:

Part 1) Find the length of the longest side of ∆ABC

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

The ratio of its perimeters is equal to the scale factor

Let

z ----> the scale factor

x ----> the length of the longest side of ∆ABC

y ----> the length of the longest side of ∆DEF

so

$z=\frac{x}{y}$

we have

$z=\frac{1}{10}$

$y=40\ units$

substitute

$\frac{1}{10}=\frac{x}{40}$

solve for x

$x=(40)\frac{1}{10}$

$x=4\ units$

therefore

The length of the longest side of ∆ABC is 4 units

Part 2) Find the ratio of the area of ∆ABC to the area of ∆DEF

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x ----> the area of ∆ABC

y ----> the area of ∆DEF

$z^{2}=\frac{x}{y}$

we have

$z=\frac{1}{10}$

so

$z^2=(\frac{1}{10})^2$

$z^2=\frac{1}{100}$

therefore

The ratio of the area of ∆ABC to the area of ∆DEF is $\frac{1}{100}$

3 0

3 years ago

you can spend at most $20 on tomatoes and red peppers for a soup. tomatoes cost $2.50 per pound and red peppers cost $4 per poun

Ber [7]

Answer-

$\boxed{\boxed{2.50x+4y\leq 20}}$

Solution-

The total money that you have or maximum amount that you can spend = $20

Let's assume,

x = Number of tomatoes bought

y = Number of red peppers bought

Price of tomatoes per pound = $2.50

Price of red peppers per pound = $4

Hence,

Total cost of tomatoes = $2.5x

Total cost of red peppers = $4y

As you can spend at most (any amount less than or equal to) $20, so

$2.5x+4y\leq 20$

Taking a point as origin (0, 0) and then putting it in the equation,

$\Rightarrow 2.5(0)+4(0)\leq 20\\\\\Rightarrow 0\leq 20$

As this satisfies, so the shaded region will be towards that point i.e origin

From the graph, the two solutions that are on the boundary line are (8, 0), (5, 0)

6 0

3 years ago

4# is a two digit number ,where # represents the digit at ones place . 7999 ÷ 4# lies between ---------

Hitman42 [59]

Answer:

$7999 \div 4\#$ lies between 163.245 and 199.975

Step-by-step explanation:

Given

2 digit = 4#

Required

The range of $7999 \div 4\#$

Let

$\# = 0$ --- the smallest possible value of #

So:

$7999 \div 40 = 199.975$

Let

$\# = 9$ --- the largest possible value of #

So:

$7999 \div 49 = 163.245$

Hence, $7999 \div 4\#$  lies between 163.245 and 199.975

4 0

3 years ago

20 POINTS!!! belongs to a: pyramid cube rectangular prism triangular prism

Klio2033 [76]

The middle row is long on one side and short in the other side which is the shape of a rectangle.

The net is a rectangular prism

8 0

3 years ago

Plz, answer this question plz!

Dominik [7]

Actual Answer:

A (I THINK )

Answer:

There is a hack in forms that forms gives u the answer hold ctrl + u, and scrool to the bottom he read the part with the question and there will be an answer.

Mark as brainliest if im right good luck!!

3 0

3 years ago

Read 2 more answers