If the expression 4x+3 is equal to 1 for some value of x what is the expression 4x+8 equal to for the same value of x

A positive real number is 2 less than another. When 4 times the larger is added to the square of the smaller, the result is 49.

Kobotan [32]

Answer:

The numbers are

$-2+3\sqrt{5}$ and $3\sqrt{5}$

Step-by-step explanation:

Let

x -----> the smaller positive real number

y -----> the larger positive real number

we know that

A positive real number is 2 less than another

so

$x=y-2$

$y=x+2$ ----> equation A

When 4 times the larger is added to the square of the smaller, the result is 49

so

$4y+x^2=49$ ----> equation B

substitute equation A in equation B

$4(x+2)+x^2=49$

solve for x

$x^2+4x-41=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^2+4x-41=0$

so

$a=1\\b=4\\c=-41$

substitute in the formula

$x=\frac{-4\pm\sqrt{4^{2}-4(1)(-41)}} {2(1)}$

$x=\frac{-4\pm\sqrt{180}} {2}$

$x=\frac{-4\pm6\sqrt{5}} {2}$

$x=-2\pm3\sqrt{5}$

so

The positive real number is

$x=-2+3\sqrt{5}$

Find the value of y

$y=x+2$

$y=-2+3\sqrt{5}+2$

$y=3\sqrt{5}$

6 0

3 years ago

Please help me answer #4, #5 and #6

Salsk061 [2.6K]

Answer:

4). The Washington Monument is 169.2-m tall.

Step-by-step explanation:

4). We know this because...

person 1.8 0.7

---------- = ----- = -------

Wash. x 65.8

We then know to cross-multiply to get:

1.8(65.8) = 0.7x

Which simplifies down to:

118.44 = 0.7x

x = 169.2

Answer:

5). The pond is 180ft wide.

Step-by-step explanation:

5). We know this because...

90 120

----- = -------

135 x

We then know to cross-multiply to get:

90x = 120(135)

Which simplifies down to:

90x = 16200

x = 180

Answer:

6). The height of the clock tower is 13ft 9in.

Step-by-step explanation:

6). We know this because...

person 5.5 4

---------- = -------- = -----

clock x 10

We then know to cross-multiply to get:

5.5(10) = 4x

Which simplifies down to:

55 = 4x

x = 13.75 (13 ft 9 in)

7 0

2 years ago

In anova, by dividing the mean square between groups by the mean square within groups, a(n) _____ statistic is computed.group of

jek_recluse [69]

In anova, by dividing the mean square between groups by the mean square within groups, a(n) Analysis of variance statistic is computed.

What is Analysis of variance ?

With the help of the statistical analysis approach known as ANOVA, apparent aggregate variability within a data set is explained by separating systematic components from random factors.
Systematic influences, but not random ones, statistically affect the data set that is being presented.

What are some instances where ANOVA has been applied?

An ANOVA demonstrates the link between the dependent variable and the level of the independent variable.
For illustration: In order to determine whether there is a difference in the number of hours of sleep each night as your independent variable, you divide the groups into low, medium, and high social media use categories.

Learn more about Analysis of variance

brainly.com/question/28274784

#SPJ4

4 0

1 year ago

How would you round 95687 to the nearest thousand?

andre [41]

Answer:

96,000

Step-by-step explanation:

To round to the nearest thousand, we need to look at the digit in the hundreds place, which is 6. Since 6 > 5, we know that we need to round up (because 6 is closer to 10 than it is to 0). Currently, the number is 95 thousand so when rounding up, the answer will be 96,000.

5 0

3 years ago

riel wants to use squares to tile a floor that measures 240 cm by 300 cm what is the length of the largest square he can use

Alexxx [7]

<span>So, what you want is the biggest square that can evenly tile a space 240*300. The biggest possible number that can divide 240 and 300. Does that ring any bells? Maybe you should divide 240 and 300</span>

4 0

3 years ago