8.a. Simplify: 10a+46-(3a+2b)​

Answer:

2x-y-1=0

Step-by-step explanation:

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Explanation:

Choice B has the GCF x we can factor out like so

10x^4-5x^3+70x^2+3x = x(10x^3-5x^2+70x+3)

Showing that choice B is not prime. If a polynomial can be factored, then we consider it not prime. It's analogous to saying a number like 15 isn't prime because 15 = 3*5, ie 15 can be factored into something that doesn't involve 1 as a factor.

In contrast, we consider 7 prime because even though 7 = 1*7, there aren't any other ways to write this integer as a factorization if we don't involve 1.

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Choice C is a similar story. This time we can factor out 3

3x^2 + 18y = 3(x^2 + 6y)

So we can rule this out as well.

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Choice D is a bit tricky, but we can use the difference of cubes factoring rule

a^3 - b^3 = (a-b)(a^2+ab+b^2)

where in this case a = x and b = 3y^2

Note how b^3 = (3y^2)^3 = 3^3*(y^2)^3 = 27y^(2*3) = 27y^6

All of this means choice D can be factored and it's not prime either.

------------------------------------

We've ruled out choices B through D. The answer must be choice A.

If you let w = x^2, then w^2 = x^4

The polynomial w^2+20w-100 is prime because setting it equal to zero and solving for w leads to irrational solutions. I'm assuming your teacher wants you to factor over the rational numbers.

Because w^2+20w-100 can't be factored over the rational numbers, neither can x^4+20x^2-100. This confirms that choice A is prime.

Answer:

0.75

Step-by-step explanation:

Given the table :

Number of sodas 24

28

32

36

Total Cost ($)

18

21

24

27

The rate of change :

Rate of change = Rise / Run

Rise = y2 - y1 ; Run = x2 - x1

From the table :

Take number of sodas as X - axis

Total cost as Y - axis

Taking the points :

(24, 18) ;(36, 27)

x1 = 24 ; x2 = 36

y1 = 18 ; y2 = 27

Rise = (y2 - y1) = (27 - 18) = 9

Run = (x2 - x1) = (36 - 24) = 12

Rate of change = 9 / 12 = 0.75

Answer:

[tex]\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta} = \frac{1}{\sin\theta} = \csc\theta[/tex]

Step-by-step explanation:

We have the expression:

[tex]\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta}[/tex]

And we want to write the expression in terms of sine and cosine and simplify.

Thus, let tanθ = sinθ / cosθ and secθ = 1 / cosθ. Substitute:

[tex]=\displaystyle \frac{\dfrac{\sin\theta}{\cos\theta}}{\dfrac{1}{\cos\theta}-\cos\theta}[/tex]

Multiply both layers by cosθ:

[tex]=\displaystyle \frac{\left(\dfrac{\sin\theta}{\cos\theta}\right)\cdot \cos\theta}{\left(\dfrac{1}{\cos\theta}-\cos\theta\right)\cdot \cos\theta}[/tex]

Distribute:

[tex]\displaystyle =\frac{\sin\theta}{1-\cos^2\theta}[/tex]

Recall from the Pythagorean Theorem that sin²θ + cos²θ = 1. Hence, 1 - cos²θ = sin²θ. Substitute and simplify:

[tex]\displaystyle =\frac{\sin\theta}{\sin^2\theta} \\ \\ =\frac{1}{\sin\theta}[/tex]

We can convert this to cosecant if we wish.

Answer:

a = 133 degrees

b = 78 degrees

Step-by-step explanation:

the top and bottom lines are parallel.

the two sidelines are lines that intercept the top and bottom lines.

as they intercept parallel lines, they actually must have the same angles with them.

so, the 47 degrees inner angle at the bottom line, must be also somewhere at the interception point with the top line. and right, it must be now mirrored the outward angle at the top line. and that means a (the inward angle at the top line) is also the outward angle at the bottom line.

the sum of inward and outward angles at a point must always be 180 degrees.

so, the outward angle of 47 = the inward angle a =

= 180 - 47 = 133 degrees.

similar in the other side.

102 is the inward angle.

the outward angle of that is 180 - 102 = 78 degrees.

and that is also the inward angle b.

b = 78 degrees

Answer:

57

Step-by-step explanation:

Answer: 40

Step-by-step explanation:

If you cut 20 lemons by half and then cut half of these halves by half, then 80  lemon parts we have

A division is a process of splitting a specific amount into equal parts.

Given that 20 lemons are cut by half.

cut half of these halves by half.

We need to find how many lemon parts will you have.

Let us consider a lemon whic is 1

Now let us make it half 1/1/2=2

Now each part is divided to half =2/(1/2)=4

So for one lemon it has 4 parts.

Now let us find for 20 lemons.

Multiply 20 with 4

20×4

80 parts

Hence, If you cut 20 lemons by half and then cut half of these halves by half, then 80  lemon parts will you have

To learn more on Division click:

https://brainly.com/question/21416852

#SPJ5

Answer:

The last table (the bottom one)

Step-by-step explanation:

The ingredients having the same ratio means that, for every number of servings, we should have:

Y/X = constant.

So, for the first table when we have 1 serving, the quotient is:

Y/X = 2/1 = 2

when we have two servings:

Y/X = 3/2 = 1.5

The ratios are different.

Then this is not the correct option.

For the second table, when we have 1 serving the ratio is:

Y/X = 2/1 = 2

when we have two servings:

Y/X = 4/2 = 2

when we have 3 servings:

Y/X = 8/3 = 2.66

This is not the correct option.

For the third table:

1 serving:

Y/X = 2/1 = 2

2 sevings

Y/X = 3/2 = 1.5

This is not the correct option.

fourth table:

1 serving:

Y/X = 2/1 = 2

2 servings

Y/X = 4/2 = 2

3 servings

Y/X = 8/4 = 2

Here we can see that the ratio is always the same, then the ratio remains constant.

This is the table that shows a possible ratio for ingredients X and Y,

We have that

x - 3y = 12 and -x + y = 4

We add the 2 equations together

x - 3y + (-x + y) = 16

-> -2y = 16

-> y = -8 (1)

We plug y = -8 into -x + y =4

-> -x - 8 = 4

-> -x = 12

-> x = - 12 (2)

From (1) and (2) we could conclude that the answer is B

Answer:

Step-by-step explanation:

Coordinates of the vertices of ΔABC,

A(-6, -1), B(-3, -3), C(-1, -2)

Step - 1

Rule for the translation of a point (x, y) by 'h' units right and 'k' units upwards,

A(x, y) → A(x + h, y + k)

If ΔABC is translated by 5 units right and 2 units up, image points will be,

A(-6, -1) → H(-6 + 5, -1 + 2)

            → H(-1, 1)

B(-3, -3) → J(-3 + 5, -3 + 2)

             → J(2, -1)  

C(-1, -2) → K(-1 + 5, -2 + 2)

            → K(4, 0)

Step - 2

If the image triangle HJK is reflected across a line [tex]y=-x[/tex], rule for the reflection will be,

H(x, y) → A'(-y, -x)

By this rule,

H(-1, 1) → A'(-1, 1)

J(2, -1) → B'(1, -2)

K(4, 0) → C'(0, -4)

Step - 3

Rule for the rotation of a point 270° counterclockwise about the origin,

A'(x, y) → A"(y, -x)

By this rule, image points of ΔA'B'C' will be,

A'(-1, 1) → A"(1, 1)

B'(1, -2) → B"(-2, -1)

C'(0, -4) → C"(-4, 0)

Now we can graph the image triangle A"B"C".

Answer:

(∠ABC) 108 (for all)

(∠ACB) 27 (for all)

(∠CAB) 45 (for all)

Step-by-step explanation:

Answer:

slope= difference in y ÷difference in x

=y-y1÷x-x1

=-3-(-1)÷-3-1

=-3+1÷-3-1

=-2÷-4

=1/2

Step-by-step explanation:

hope this is helpful

Y2 -Y1 ÷ X2-X1

-1 - 1 ÷ -3 - -3= 0.5 or 1/2

Answer:

12,-2

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

the angles on top of a line (or below a line) sum up to 180 degrees, as a line stands in that regard for a flip from left to right - which is a half circle or 180 degrees.

therefore, the sum of both angles must be 180.

10x - 20 + 6x + 8 = 180

16x -12 = 180

16x = 192

x = 12

Answer : - 4 + 3 = - 1

- 2 + 3 = 1

By half gives - 1/2 and 1/2

So midpoint (-1/2, 1/2)

Answer:

$52,500

$152,500

Step-by-step explanation:

$100,000 * .105 = $10500

Answer:

y = -x - 6

Step-by-step explanation:

Parallel lines have same slope

y = -x + 9   {y = mx  + c}

m = -1  

(x₁, y₁) = (7 , -13)

Equation: y - y₁ = m(x -x₁)

y - [-13] = -1(x -7)

y+ 13 = -x + 7

    y = - x + 7 - 13

y = -x - 6

Answer:

Step-by-step explanation:

(3,9)

9514 1404 393

Answer:

  -2/3

Step-by-step explanation:

  2^a = 0.5 = 2^-1   ⇒   a = -1

  5^b = 125 = 5^3   ⇒   b = 3

Then the expression a^b  +b^a is ...

  a^b +b^a = (-1)^3 +3^(-1) = -1 +1/3 = -2/3

Given:

The dotted boundary line passes through the points (-3,-8), (1,-2) and (9,10).

Above line is shaded.

To find:

The inequality for the given graph.

Solution:

Consider any two points on the line. Let the two points are (1,-2) and (9,10). So, the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-(-2)=\dfrac{10-(-2)}{9-1}(x-1)[/tex]

[tex]y+2=\dfrac{10+2}{8}(x-1)[/tex]

[tex]y+2=\dfrac{12}{8}(x-1)[/tex]

[tex]y+2=\dfrac{3}{2}(x-1)[/tex]

Multiply both sides by 2.

[tex]2(y+2)=3(x-1)[/tex]

[tex]2y+4=3x-3[/tex]

[tex]2y-3x=-3-4[/tex]

[tex]-3x+2y=-7[/tex]

Above line is shaded and the boundary line is a dotted line. So, the sign of inequality must be >.

[tex]-3x+2y>-7[/tex]

This inequality is not in the equations. So, multiply both sides by -1 and change the inequality sign.

[tex](-3x+2y)(-1)<-7(-1)[/tex]

[tex]3x-2y<7[/tex]

Therefore, the correct option is D.

Answer:

[tex]x = 0.143[/tex]

[tex]P(High\ |\ Cancer) = 0.215[/tex]

Not independent

Step-by-step explanation:

Given

See attachment for proper table

Solving (a): The missing probability

First, we add up the given probabilities

[tex]Sum = 0.242+0.047+0.079+0.391+0.098[/tex]

[tex]Sum = 0.857[/tex]

The total probability must add up to 1.

If the missing probability is x, then:

[tex]x + 0.857 = 1[/tex]

Collect like terms

[tex]x = -0.857 + 1[/tex]

[tex]x = 0.143[/tex]

Solving (b): P(High | Cancer)

This is calculated as:

[tex]P(High\ |\ Cancer) = \frac{n(High\ n\ Cancer)}{n(Cancer)}[/tex]

So, we have:

[tex]P(High\ |\ Cancer) = \frac{0.079}{0.242+0.047+0.079}[/tex]

[tex]P(High\ |\ Cancer) = \frac{0.079}{0.368}[/tex]

[tex]P(High\ |\ Cancer) = 0.215[/tex]

Solving (c): P(Leukemia) independent of P(High Wiring)

From the attached table

[tex]P(Leukemia\ n\ High\ Wiring) = 0.242[/tex]

[tex]P(Leukemia) = 0.242 + 0.391 =0.633[/tex]

[tex]P(High\ Wiring) = 0.242+0.047+0.079=0.368[/tex]

If both events are independent, then:

[tex]P(Leukemia\ n\ High\ Wiring) = P(Leukemia) * P(High\ Wiring)[/tex]

[tex]0.242 = 0.633 * 0.368[/tex]

[tex]0.242 \ne 0.232[/tex]

Since the above is an inequality, then the events are not independent

Answer:

m∠B =  

✔ 101

°

m∠C =  

✔ 79

°

m∠D =  

✔ 101

°

Step-by-step explanation:

Answer:

The answer above is right!

The correct answers are:

First box: option C. 101

Second box: option B. 79

Third box: option C. 101

Step-by-step explanation:

Just got it right on edge - Hope it helps :)

Brainliest would be greatly appreciated :D

Answer:

well your answer should be "F"

Step-by-step explanation:

we have

Y<-2x+10  -----> inequality A

The solution of the inequality A is the shaded area below the dashed line

Y = -2x+10

The y-intercept of the dashed line is (0,10)

The x-intercept of the dashed line is (5,0)

Y<1/2x-2 ----> inequality B  

The solution of the inequality B is the shaded area below the dashed line

Y= 1/2x-2

The y-intercept of the dashed line is (0,-2)

The x-intercept of the dashed line is (4,0)

The solution of the system of inequalities is the shaded area between the two dashed lines

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area of the solution

therefore

The solution are the points

E, F and G

i hope this helps

Answer:

2. x=4

3. y= -7

4. y = -7

5. w = 0

Step-by-step explanation:

2.

4x-15=1

4x=16

x=4

3.

2y+3= -11

2y=-14

y= -7

4.

2y+7= -7

2y = -14

y = -7

5.

3w+3=3

3w = 0

w = 0

Answer:

Step-by-step explanation:

Answer:

Domain = ( -∞ , ∞ )

Range = ( ∞ , ∞ )

Step-by-step explanation:

A function is given to us and we need to find the domain and range of the given function .

The function :-

[tex]\rm \implies y = \dfrac{1}{4}x - 6 [/tex]

Definitions :-

In this case, there is no real number that makes the expression undefined. Therefore the domain will be :-

Domain :-

[tex]\rm Domain = ( -\infty , \infty ) [/tex]

or

[tex]\rm Domain = \{ x | x \in \mathbb{R} \}[/tex]

Range :-

[tex]\rm Range = ( -\infty , \infty ) [/tex]

or

[tex]\rm Range = \{ y | y \in \mathbb{R}\} [/tex]

Answer:

Create a table or a graph of the function. The domain represents all input values and the range represents all output values. The domain and range contain all real numbers.

Step-by-step explanation:

When a pair of parallel lines is intersected by a transversal, then

Interior opposite angles are equal.

So, (3x + 4)° = 115°

=> 3x + 4 = 115

=> 3x = 115 - 4

=> 3x = 111

=> x = 111/3

=> x = 37

Answer:

37

Step-by-step explanation:

So, if you got two parallel line, which are crossed by another line, the conterminal angles are gonna be as big as each other.

what we get outta this explanation is

3X+4=115===> 3X=111===> X=37

Answer:

The last one is the answer

Answer: For each hour that Michelle drove, she travelled an additional 50 miles.

Step-by-step explanation:

Test each option to see its accuracy

Calculate the slope:

[tex](x_{1}, y_{1}) = (7, 0)\\(x_{2}, y_{2}) = (0, 350)\\ \\\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{350-0}{0-7} =\frac{350}{-7} =-50[/tex]

This means that Michelle drove 50 miles per hour.

The other three options are wrong because if you bring in:

into your function- y = -50x + 350, you would not get the stated miles.

[tex]\displaystyle\bf 1) \ if\ y=152 \Longrightarrow x=30+152=182 \\\\2) \ if \ y =200 \Longrightarrow x=200+30=230\\\\3) \ if \ y=80 \Longrightarrow x=30+80=110\\\\4) \ if \ y=4 \Longrightarrow x=4+30=34 \\\\5)\ if \ y=8 \Longrightarrow x=30+8=38[/tex]