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Anuta_ua [19.1K]

3 years ago

10

Dara has to solve 35 math problems for homework. She has completed 14 of them.what fraction of the problems does she have left t

o do?

1 answer:

RSB [31]3 years ago

6 0

Answer: 3/5

Step-by-step explanation: thats your answer.

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What is <br> 5(2x+1)=4-2(4x-5)

Butoxors [25]

Answer:

x=0.5

Step-by-step explanation:

4 0

3 years ago

Consider the parabola given by the equation: f(x) = 4x² - 6x - 8 Find the following for this parabola: A) The vertex: Preview B)

jeyben [28]

Answer:

The vertex: $(\frac{3}{4},-\frac{41}{4} )$

The vertical intercept is: $y=-8$

The coordinates of the two intercepts of the parabola are $(\frac{3+\sqrt{41} }{4} , 0)$ and $(\frac{3-\sqrt{41} }{4} , 0)$

Step-by-step explanation:

To find the vertex of the parabola $4x^2-6x-8$ you need to:

1. Find the coefficients <em>a</em>, <em>b</em>, and <em>c </em>of the parabola equation

<em> $a=4, b=-6, \:and \:c=-8$ </em>

2. You can apply this formula to find x-coordinate of the vertex

$x=-\frac{b}{2a}$ , so

$x=-\frac{-6}{2\cdot 4}\\x=\frac{3}{4}$

3. To find the y-coordinate of the vertex you use the parabola equation and x-coordinate of the vertex ( $f(-\frac{b}{2a})=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c$ )

$f(-\frac{b}{2a})=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c\\f(\frac{3}{4})=4\cdot (\frac{3}{4})^2-6\cdot (\frac{3}{4})-8\\y=\frac{-41}{4}$

To find the vertical intercept you need to evaluate x = 0 into the parabola equation

$f(x)=4x^2-6x-8\\f(0)=4(0)^2-6\cdot 0-0\\f(0)=-8$

To find the coordinates of the two intercepts of the parabola you need to solve the parabola by completing the square

$\mathrm{Add\:}8\mathrm{\:to\:both\:sides}$

$x^2-6x-8+8=0+8$

$\mathrm{Simplify}$

$4x^2-6x=8$

$\mathrm{Divide\:both\:sides\:by\:}4$

$\frac{4x^2-6x}{4}=\frac{8}{4}\\x^2-\frac{3x}{2}=2$

$\mathrm{Write\:equation\:in\:the\:form:\:\:}x^2+2ax+a^2=\left(x+a\right)^2$

$x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=2+\left(-\frac{3}{4}\right)^2\\x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=\frac{41}{16}$

$\left(x-\frac{3}{4}\right)^2=\frac{41}{16}$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

$x_1=\frac{\sqrt{41}+3}{4},\:x_2=\frac{-\sqrt{41}+3}{4}$

4 0

3 years ago

An organization has members who possess IQs in the top 4% of the population. If IQs are normally distributed, with a mean of 100

murzikaleks [220]

Answer:

The minimum IQ score will be "126".

Step-by-step explanation:

The given values are:

Mean

$\mu = 100$

Standard deviation

$\sigma=15$

Now,

⇒ $P(z>x)=4 \ percent \ i.e., 0.04$

⇒ $P(z>\frac{x- \mu}{\sigma} )=0.04$

⇒ $1-P(z \leq \frac{x-100}{15})=0.04$

⇒ $\frac{x-100}{15}=z0.96$

$=NORMDIS(z=0.96)$

$=1.751$

⇒ $x=100+15\times 1.751$

$=126.265 \ i.e., 126$

7 0

2 years ago

The sum of 20.7 and a number is 50.5. Which equation could you use to solve the problem? What should you do to each side of the

Arlecino [84]

Answer:

Equation to solve this: 50.5-20.7=a number

Answer: 29.8

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Draw the image of the figure after a rotation of 180° around O.

77julia77 [94]

Answer:

is there an image to go with this?

Step-by-step explanation:

3 0

3 years ago