Given the rule: y is 5 more than x, when x=5 what is the value of y?

Use the zero product property to find the solutions to the equation 6x2 – 5x = 56.

jasenka [17]

Hello,

6x²-5x-56=0
==>6x²-21x+16x-56=0
==>3x(2x-7)+8(2x-7)=0
==>(2x-7)(3x+8)=0
==>x=7/2 or x= -8/3

7 0

2 years ago

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If f (x) = -2x-3 and g (x) =x^2+5x find g (2) -f(3)

sammy [17]

G(2)=2^2 +5(2)=14
f(3)=-2(3)-3=-9

g(2)-f(3)=14-(-9)=14+9=23

4 0

3 years ago

Nick is making bread dough. The recipe requires 3/4 cup of flour and 1 1/8 teaspoon of salt. Nick wants to make the recipe using

madam [21]

Answer:

$1\dfrac{1}{2}$ teaspoon of salt is required

Step-by-step explanation:

The recipe requires 3/4 cup of flour and Nick wants to make the recipe using 1 cup of flour.

The recipe requires 1 1/8 teaspoon of salt and Nick wants to know how much salt he heeds.

Consider short description:

3/4 cup of flour - 1 cup of flour,

1 1/8 teaspoon of salt - x teaspoon of salt.

Mathematically, you can wrte a proportion:

$\dfrac{\frac{3}{4}}{1\frac{1}{8}}=\dfrac{1}{x}.$

Then

$\dfrac{3}{4}\cdot x=1\cdot 1\dfrac{1}{8},\\ \\\dfrac{3x}{4}=\dfrac{9}{8},\\ \\3x\cdot 8=4\cdot 9,\\ \\24x=36,\\ \\x=\dfrac{36}{24}=\dfrac{3}{2}=1\dfrac{1}{2}.$

3 0

3 years ago

The population of bacteria in an

horsena [70]

Answer:

5

Step-by-step explanation:

5 makes sense since the period of time this takes place is 5 days. therefore [?] should be 5

3 0

2 years ago

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A long jumper lifts off 3 m after starting his run, and lands 6 m later. When he is 8 m from the start line, he is 5 cm above an

slega [8]

Answer:

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2}+12\cdot x -27$ .

Step-by-step explanation:

Mathematically, we know that parabolas are second-order polynomials and every second-order polynomials, also known as quadratic functions, can be constructed by knowing three different points of the curve. The standard form of the parabola is:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Horizontal distance from the start line, measured in meters.

$y$ - Height of the long jumper, measured in meters.

$a$ , $b$ , $c$ - Polynomial constants, measured in $\frac{1}{m}$ , dimensionless and meters, respectively.

If we know that $(x_{1},y_{1}) = (3\,m, 0\,m)$ , $(x_{2},y_{2}) = (8\,m, 0.05\,m)$ and $(x_{3}, y_{3}) = (9\,m, 0\,m)$ , this system of linear equations is presented below:

$9\cdot a + 3\cdot b + c = 0$ (Eq. 1)

$81\cdot a + 9\cdot b + c = 0$ (Eq. 2)

$64\cdot a + 8\cdot b + c = 0.05$ (Eq. 3)

The coefficients of the polynomial are, respectively:

$a = -\frac{1}{100}$ , $b = \frac{3}{25}$ , $c = -\frac{27}{100}$

The equation of the parabola that models the path of the long jumper through the air is $y' = -\frac{1}{100}\cdot x^{2}+\frac{3}{25}\cdot x -\frac{27}{100}$ .

But we need $y$ measured in centimeters, then, we use the following conversion:

$y = 100\cdot y'$

Then, we get that:

$y = -x^{2}+12\cdot x -27$

Where $x$ and $y$ are measured in meters and centimeters, respectively.

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2}+12\cdot x -27$ .

4 0

2 years ago