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3 years ago

4(x-3)=5(x+1) solve the equation above for x

Mathematics

1 answer:

lesantik [10]3 years ago

6 0

First distribute: 4x-12=5x+5. subtract 4x on both sides: -12=x+5. Now subtract 5 from both sides. x=-17.

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Ron Co. sold sweatshirts ($20) and baseball caps ($10). If total sales were $2,860 and people bought 6 times as many sweatshirts

aksik [14]

Let the total number of sweatshirts sold be S and the total number of baseball caps sold be B
Total sales is the total number of sweatshirts sold times $20 plus the total number of baseball caps sold times 10.
Equation 1: 20S + 10B = 2860
people bought 6 times as many sweatshirts as caps. Which means the number of sweatshirts sold (S) is 6 times caps sold(B)
Equation 2: S = 6B --- substitute S in equation 1 with 6B
=> 20(6B) + 10B = 2860
=> 120B + 10B = 2860
=> 130B = 2860 --- divide both side by 130
=> B = 2860/130
=> B = 22 --- is the number of caps sold.
To find the number of sweatshirts sold we use equation 2
S = 6B --- but we know now B = 22
=> S = 6(22)
=> S = 132

therefore 132 sweatshirts sold and 22 baseball caps sold.

7 0

3 years ago

A customer buys a dress that has an original price of $38. The dress is discounted 25%. The customer pays 6% sales tax on the di

salantis [7]

Answer:

dress? or address?

Step-by-step explanation:

5 0

3 years ago

Is 0.0530 greater than 0.04?

SashulF [63]

Answer:

yes

Step-by-step explanation:

0.04 is equal to 0.0400

0.0530

0.0400

5 is higher than 4

5 0

3 years ago

Read 2 more answers

Find the point on the hyperbola xy= 8 that is closet to the point (3,0)

son4ous [18]

The distance $l$ between $(x, y)$ and $(3, 0)$ is:
$l=\sqrt{(0-y)^{2}+(3-x)^{2}}=\sqrt{y^{2}+(3-x)^{2}}$

Since the equation of the hyperbola is $xy=8$ , we can get $y$ by itself and end up with
$y=\frac{8}{x}$

which we can plug into our distance formula:
$l=\sqrt{(\frac{8}{x})^{2}+(3-x)^{2}}$

To make calculation easier, we'll square both sides:
$l^{2}=(\frac{8}{x})^2+(3-x)^{2}$
and create a new variable $m=l^{2}$ :
$m=(\frac{8}{x})^2+(3-x)^{2}$
$\rightarrow m=\frac{64}{x^{2}}+9-6x+x^{2}$

Differentiate both sides:
$\frac{dm}{dx}=-\frac{128}{x^{3}}-6+2x$
Minimum distance is achieved when $\frac{dm}{dx}=0$ :
$-\frac{128}{x^{3}}-6+2x=0$
$\rightarrow -128-6x^{3}+2x^{4}=0$
$\rightarrow 2(x^{4}-3x^{3}-64)=0$
$\rightarrow x^{4}-3x^{3}-64=0$

To find a value of $x$ , you can use methods like synthetic division and get the answer $x=4$

Plug into $xy=8$ :
$4y=8$
$\rightarrow y=2$

So the closest point on the hyperbola to $(3, 0)$ is $(4, 2)$

7 0

4 years ago

Using descartes' rule of signs to describe the roots of h(x)=4x^4-5x^3+2x^2-x+5, how many total roots must there be in this four

vlabodo [156]

H(x) = 4x⁴ - 5x³ + 2x² - x + 5

Take the coefficients, we have:

4 -5 2 -1 5

From the first coefficient to the second coefficient, there's a change of sign from positive to negative (positive four to negative five)

From the second coefficient to the third coefficient, there's a change of sign from negative to positive (negative five to positive two)

From the third coefficient to the fourth coefficient, there's a change of sign from positive to negative (positive two to negative one)

From the fourth coefficient to the fifth coefficient, there's a change of sign from negative to positive (negative one to positive five)

The changing of sign happened four times, and it means h(x) has four positive real zeros or less (even numbers of zeros), so h(x) could have either four or two real zeros.

The maximum number of solutions for a polynomial of degree four is four solution, so there are no negative zeros.

4 0

3 years ago