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3 years ago

Q.16 please With steps

Mathematics

1 answer:

blsea [12.9K]3 years ago

8 0

The equations

$2x^2+9x-5=0$

and

$2\left(t-\dfrac12\right)^2+9\left(t-\dfrac12\right)-5=0$

are really the same, we're just setting $x=t-\dfrac12$ , or $t=x+\dfrac12$ .

$2x^2+9x-5=(2x-1)(x+5)=0\implies x=\dfrac12,x=-5$

So we get

$t=\dfrac12+\dfrac12=1,t=-5+\dfrac12=-\dfrac92$

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Find the sum. <br> (- 7/2 z + 4) + (1/5 z - 15)<br> HELPPP

Nonamiya [84]

Answer:

-33/10z - 11

Step-by-step explanation:

since all of these terms are being added, there are no need for the parenthesis

-7/2z +4 + 1/5z -15

add like terms (to add the fractions, convert them to a common denominator)

-7/2z + 4 + 1/5z - 15

-35/10z + 2/10z - 11

-33/10z - 11

8 0

2 years ago

27 solid iron spheres, each of radius 'xcm'ate melted to form a sphere with radius 'ycm',find the ratio x:y

r-ruslan [8.4K]

Answer:3:1

Step-by-step explanation:

Given

There are 27 solid spheres of radius x cm

The volume of a sphere is $\frac{4}{3}\pi r^3$

The volume of 27 old spheres is the same as the volume of a new sphere

The volume of the old spheres is

$V_o=\dfrac{4}{3}\pi x^3$

The volume of a new sphere is

$V_n=\dfrac{4}{3}\pi y^3$

Now, $V_o=V_n$

$\Rightarrow 27\times \dfrac{4}{3}\pi x^3=\dfrac{4}{3}\pi y^3\\\\\Rightarrow (\dfrac{x}{y})^3=27\\\\\Rightarrow \dfrac{x}{y}=3$

7 0

2 years ago

To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equati

murzikaleks [220]

Answer:

$x-4y+4=0$

$f(x)=\sqrt x$ and x=4

Step-by-step explanation:

We are given that a curve

$y=\sqrt x$

We have to find the equation of tangent at point (4,2) on the given curve.

Let y=f(x)

Differentiate w.r.t x

$f'(x)=\frac{dy}{dx}=\frac{1}{2\sqrt x}$

By using the formula $\frac{d(\sqrt x)}{dx}=\frac{1}{2\sqrt x}$

Substitute x=4

Slope of tangent

$m=f'(x)=\frac{1}{2\sqrt 4}=\frac{1}{2\times 2}=\frac{1}{4}$

In given question

$m=\lim_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}$

$\frac{1}{4}=\lim_{x\rightarrow 4}\frac{f(x)-f(4)}{x-4}$

By comparing we get a=4

Point-slope form

$y-y_1=m(x-x_1)$

Using the formula

The equation of tangent at point (4,2)

$y-2=\frac{1}{4}(x-4)$

$4y-8=x-4$

$x-4y-4+8=0$

$x-4y+4=0$

8 0

3 years ago

the correlation between two variables related to the same sample is a scaled quantitative measure. what is used to scale this me

Doss [256]

The correct option is the standard deviations of the variables.

What is correlation?

Any statistical relationship between two random variables or bivariate data, whether causal or not, is referred to in statistics as correlation or dependence.

Correlation is a term used to describe the linear relationship between two entities. When using a correlation tool, the variables must be present in quantities of two or more to test their relationship (degree of association).

In order to scale the measurement between two variables connected to a similar sample, the standard deviation measures dispersion.

The variables' standard deviations are the best choice as a result.

Option involving the standard errors of the variables is incorrect because standard error, which stands for standard deviation, determines the relationship between dependent and independent variables.

Option involving the coefficients of variation of two variables is incorrect because the coefficient expressing standard deviation and mean ratio determines how much variation there is.

Option The means of the variables are incorrect because they are not a scale for determining the correlation between two variables.

Hence, the correct option is the standard deviations of the variables.

To know more about correlation, click on the link

brainly.com/question/2088651

#SPJ4

Complete question:

The correlation between two variables related to the same sample is a scaled quantitative measure. What is used to scale this measurement?

- the standard deviations of the variables

- the standard errors of the variables

- the coefficients of variation of the two variables

- the means of the variables

6 0

1 year ago

What is x+y=8 and 5x+3y=34 graphed on the same graph

expeople1 [14]

To help you graph this, get y alone in both equations. If you don't have a graphing calculator, use the Desmos graphing calculator online.

So, you will end up graphing this:
y=8-x
y=(34/3)-(5/3)x

They will meet at (5,3)

8 0

3 years ago