1 .
a. Solve by elimination method.
x+y = 6 ; 2x - y = 3

b. Solve by substitution method.
2x - y = 7 , y = 3x

c. Solve
x^2 +(1 /16 ) = x / 2

2 . Factorize
a. a^2 - 2a - 2b - b^2
b. a^4 - 3a^2 + 1

​

Answer:

Translation

Step-by-step explanation:

Translation as the x and y are both being moved over the plane.

In order to make a the subject of this equation , we need to get a by itself .

The current equation is :

v = u + at

Subtract u on both sides :

v-u=at

Now, divide by t on both sides :

v-u/t=a

[tex]\boxed{\\\begin{minipage}{3cm}Equation \\ a=$\displaystyle\frac{v-u}{t} $ \\ \end{minipage}}[/tex]

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The inverse of the function is f ( x )⁻¹ = x + 4

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x - 4   be equation (1)

On simplifying , we get

The inverse of the function is given by replacing x with y

So , the value of the function is

y = x - 4

x = y + 4

On interchanging , we get

f ( x )⁻¹ = x + 4

Hence , the inverse is f ( x )⁻¹ = x + 4

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The interval of times which represents the middle 68% of Ryan's finishing times in the 400 meter race, using the empirical rule, is 74.5 seconds to 75.5 seconds.

According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.

[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%[/tex]

Here we had  where mean of distribution of X is [tex]\mu[/tex]  and standard deviation from mean of distribution of X is [tex]\sigma[/tex].

When Ryan runs the 400 meter dash, his finishing times are normally distributed with a mean of 75 seconds and a standard deviation of 0.5 seconds.

The interval of times that represents the middle 68% of his finishing times in the 400 meter race is,

[tex]P(75 - 0.5 < X < 75 + 0.5) = 68\%\\P(74.5 < X < 75.5) = 68\%[/tex]

Thus. the interval of times which represents the middle 68% of Ryan's finishing times in the 400 meter race, using the empirical rule, is 74.5 seconds to 75.5 seconds.

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Answer:

1 second

Step-by-step explanation:

[tex]s=-5\\u=0\\v=\\a=-10\\t=t[/tex]

[tex]\begin{aligned}\textsf{Using} \quad s & =ut+\dfrac12at^2\\ \implies -5 & =(0)t+\dfrac12(-10)t^2\\ -5 & = -5t^2\\ t^2& = 1\\ t & = \pm\sqrt{1}\\ t & = 1\: \sf s\end{aligned}[/tex]

[tex]5 \frac{1}{4} + 1 \frac{3}{8} [/tex]

Lets solve it

[tex]5 \frac{1}{4} + 1 \frac{3}{8} [/tex]

[tex] \frac{21}{4} + \frac{11}{8} [/tex]

Taking the LCM of both denominator which is 8

[tex] \frac{42 + 11}{8} [/tex]

[tex] \frac{53}{8} [/tex]

Hey ! there

Answer:

Step-by-step explanation:

In this question we are given with two whole fraction . And we are asked to simplify them by adding .

Solution : -

Step 1 : Converting the fractions into improper fraction :

[tex]\dashrightarrow \: \qquad \: \dfrac{21}{4} + \dfrac{11}{8} [/tex]

Step 2 : We know that L.C.M of 4 and 8 is 8. So,

[tex]\dashrightarrow \: \qquad \: \dfrac{42 + 11}{8} [/tex]

Step 3 : Adding 42and 11 :

[tex]\dashrightarrow \: \qquad \: \dfrac{53}{8} [/tex]

Step 4 : Converting it in form of whole fraction :

[tex]\dashrightarrow \: \qquad \blue{\underline{\boxed{\frak{ \:6 \dfrac{5}{8} }}}} \quad\bigstar[/tex]

Answer:

5

Step-by-step explanation:

ty

]

Answer:

This would be a statistical question.

Step-by-step explanation:

Answer:

d.  5490

Step-by-step explanation:

[tex]\begin{aligned}\displaystyle \sf \sum_{n=1}^{60} 3n & =3(1)+3(2)+3(3)+...+3(49)+3(50)\\ & = 3+6+9+...+147+150\end{aligned}[/tex]

Therefore, this is an arithmetic series with:

Sum of the first n terms of an arithmetic series:

[tex]S_n=\dfrac12n[2a+(n-1)d][/tex]

Therefore, the sum of the first 60 terms:

[tex]\begin{aligned}S_{60} &=\dfrac12(60)[2(3)+(60-1)3]\\ & =30[6+(59)3]\\ & = 30[6+177]\\ & = 30[183]\\ & = 5490 \end{aligned}[/tex]

Answer:

The answer is D) 5,490.

Step-by-step explanation:

please view the calculations section of this ans

The easiest way to determine the sine, cosine, and tangent of a number is to utilize the calculator, which we are asked to do.

cos (89) = 0.017

sin (17) = 0.29

tan (35) = 0.700

hope helpful ~

Based on the calculations, the chemical element (X) in this nuclear equation is equal to ²³⁵U₉₂.

An alpha decay refers to a type of nuclear reaction in which the atomic nucleus of a radioactive element emits an alpha particle (atom of helium), thereby, producing chemical elements with a different atomic nucleus.

In this exercise, we are given the following nuclear equation with an alpha decay:

²³⁹Pu₉₄  -----> X + ⁴He₂

For the superscript, we have:

239 - 4 = 235.

For the subscript, we have:

94 - 2 = 92.

Therefore, the chemical element (X) is equal to ²³⁵U₉₂.

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Answer:

its c

Step-by-step explanation:

trust

Answer:

4 ^3√7m^2

Step-by-step explanation:

^3√64×7m^2

^3√4^3×7m^3

^3√4^3 3^√7m^2

= 4^3√7m^2

Answer:

[tex] \boxed{ \tt = 4 \sqrt[3]{7m {}^{2} } }[/tex]

Step-by-step explanation:

Given,

[tex] \sqrt[3]{448m {}^{2} } [/tex]

Solution:

[tex] = \sqrt{4 {}^{3 } \times 7 \: m {}^{2} } [/tex]

[tex] \tt = 4 \sqrt[3]{7m {}^{2} } [/tex]

[tex] \rule{225pt}{2pt}[/tex]

Answer:

The boat is 26 mi far from dock .

Step-by-step explanation:

By using PGT

P²+B² = H²

=> 10² + 24² = c²

=> 100 + 576 = c²

=> 676 = c²

=> √676 = c

=> 26 = c

Answer:

26 miles

Step-by-step explanation:

We can use Pythagorean's Theorem for right triangles which states that:

[tex]a^2+b^2=c^2[/tex]

The values 'a' and 'b' are the shorter sides of the triangle, while the value 'c' is the longest side of the triangle. We are given the two shorter sides 'a' and 'b', so let's now find 'c':

[tex](24mi)^2+(10mi)^2=c^2[/tex]

[tex]576mi^2+100mi^2=c^2[/tex]

[tex]c^2=676mi^2[/tex]

[tex]c=\sqrt{676mi^2}[/tex]

[tex]c=26mi[/tex]

The unique triangles that can be formed with side lengths of 6.5 centimeters, 6 centimeters, and 2.5 centimeters is[tex]9.[/tex]

A triangle  can be referred to as a polygon with three edges and three vertices.

we can arrange length of one side of a unique triangle in 3 different ways.

Let x,y,z be the length of the three sides.

For triangles to be unique, length of one side can be arranged in 3 different ways.

Then, length of 6.5 cm can be at maximum three positions which is x,y,z.

The 2.5 cm lenght can appear to be at maximum three positions which is  x,y,z.This can as well be done for 6cm.

Therefore, total ways of making unique triangles[tex]= (3 + 3+ 3)= 9[/tex]

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Answer:

1

Step-by-step explanation:

Given:

What is the total number of unique triangles that can be formed with side lengths of 6.5 centimeters, 6 centimeters, and 2.5 centimeters?

​Solve:

Define:

What is a unique triangle?

Only one way to create triangle.

Are congruent which means same.

As you may know the word "Unique"

which means : original and unique designs

So without even solving we can see that there is only "One" way .

Kavinsky

System of equations are equations that is more than one and have two or more unknowns. The solution to the given system of equation is expressed as (0, 2)

System of equations are equations that is more than one and have two or more unknowns.

Given the simultaneous equation

m + 4n = 8

m = n - 2

Substitute equation 2 into 1 to have:

n - 2 + 4n = 8

5n - 2  = 8

5n = 10

n = 2

Recall that m = n - 2

m = 2 - 2

m = 0

Hence the solution to the given system of equation is expressed as (0, 2)

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Answer:

y=40/183x

Step-by-step explanation:

y = Rise/Run multiplied plus y intercept by x or Y= mx + b

There is no b

m = 40/183

Y = 40/183x

Answer:

He was 11

Step-by-step explanation:

if Camila was 4 years younger than her brother and she was seven. That means he is 4 years older than her. so 7+4=11

Answer:

Assuming that the circle bissects the triangles equal sides at their midpoints, the ratio of the larger to smaller triangle should be close to 1/3

Answer:

1 time they will only cross 1 time

Answer:

one, in a linear equation a line will only cross the x-axis and y-axis once.

Answer:

what is it asking?

Step-by-step explanation:

if its how many cubes it needs for it to fill up its 9

There are 20853 ways are there to select the 4 leaders so that either Natasha and Rodrigo are both selected or Natasha and Rodrigo are both not selected.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items.  

The number of the possible ways will be calculated by:

[tex]=2 ^{28}C_2+^{28}C_4[/tex]

[tex]=\dfrac{28\times 27}{2}+\dfrac{28\times 27\times 26\times 25}{4\times 3\times 2}[/tex]

[tex]=756+28853[/tex]

[tex]=21231[/tex]

Hence there are 20853 ways are there to select the 4 leaders so that either Natasha and Rodrigo are both selected or Natasha and Rodrigo are both not selected.

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Answer:

the numbers are -5 and 3

Step-by-step explanation:

First of all, the question is asking you to find the values of x from the given inequalities.

-8x -19<21 and 3x - 4 < 5

group all liked terms, in other words, make x and its coefficient stand alone.

-8x < 21 + 19 and 3x < 5 + 4

-19 became +19 because it crossed the sign <, also -4 became +4 because it crossed the sign <.

so we get

-8x < 40 and 3x < 9

we divide each "x" by its coefficient

[tex] \frac{ - 8x}{ - 8} < \frac{40}{ - 8} \: and \: \frac{3x}{3} < \frac{9}{3} [/tex]

then we get

x < -5 and x < 3

but x is positive so it's greater than -5 so we get

x > -5 and x < 3

A = -4

B = -1

C = 3

hope this helped!

#1

Slope:-

Equation in point slope form

Shading done to right means towards origin

So

shading is towards origin

The inequality is

Dashed line given so we remain it <

#2

Slope:-

Equation in point slope form

Put (0,0)

The inequality is(solid line given)

Graph attached

Answer:

c and b was right for me

Step-by-step explanation:

Answer: is 832cm

Step-by-step explanation:

Answer:

4^4=4*4*4*16*16=256

Step-by-step explanation:

Answer:

4^4 =16

Step-by-step explanation:

4^4 = 4 · 4

they are both the same thing

4 + 4+4+4 = 16

Answer:

Given a figure that is broken into a rectangle and triangle.

The dimensions of the rectangle are:

Base : 5 ft

Height : 1/3 ft

The dimensions of the triangle are :

Base : 3 upon 2/3 ft

Height : 2 ft

The area of the figure calculated below :-

Area of rectangle + Area of triangle

Area of rectangle + Area of triangleLB + 1/2BH

(5×1/3) + (1/3+3upon2/3×2)

The result is simplified below :-

5/3+11/3

5+11/3

16/3 ft

51/3 ft square.

The area of the figure is 5 and one third square feet.

Answer:

5 1/3

Step-by-step explanation:

Answer:

y = negative 5 x + 4

Step-by-step explanation:

Hope it helps you in your learning process