prove that the value of the expression (125^2+25^2)(5^2–1) is divisible by 3

Answer:

y = -2/5 or y = 1

Step-by-step explanation:

5y^2 - 2 = 3y

5y^2 - 3y - 2 = 0

(5y + 2)(y - 1)

5y + 2 = 0 or y - 1 = 0

5y = -2 or y = 1

y = -2/5 or y = 1

Answer:

y = -2/5 or y = 1

Step-by-step explanation:

5y²-2 = 3y

Add -3y on both sides

5y²- 3y -2 = 0

Factorize.

(5y + 2)(y-1) = 0

(5y+2) = 0

Subtract 2 on both sides.

5y = -2

Divide 5 into both sides.

y = -2/5

(y - 1) = 0

Add 1 on both sides.

y = 1

Answer:

y = -1/2x + 1

Step-by-step explanation:

Step 1: Find slope

m = (2-4)/(-2+6) = 1/2

Step 2: Find y-intercept

y = -1/2x + b

2 = -1/2(-2) + b

2 = 1 + b

b = 1

Step 3: Write it all together

y = -1/2x + 1

And we have our final answer!

Answer:

The answer would be just about 61% or 9/14

Step-by-step explanation:

So, it would be a 71% chance to get 1 green out of the bag, but then you have to keep that green out, which then lowers the chances of getting another green out of the bag, then you have to combine the percentages, and then that is the final percentage.

The probability of getting 2 greens is 5/31

Probability is the likelihood or chance that an event will occur. It is expressed as:

Probability = Expected outcome/Total outcome

Given that a bag is filled with 4 blue, 3 red and 5 green marbles, the total outcome is expressed as:

If green is picked at first, the probability of selecting a green is  5/12

The probability of getting 2 greens = 5/12 × 4/11

The probability of getting 2 greens = 20/132

The probability of getting 2 greens = 5/31

Hence the probability of getting 2 greens is 5/31

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Answer:

C(-1) = -5.

Step-by-step explanation:

C(x) = -4x² + 4x + 3

Plug in -1 for x to solve for C(-1):

C(-1) = -4(-1)² + 4(-1) + 3

Simplify:

C(-1) = -4 + (-4) + 3

C(-1) = -5

Answer:

C(-1)= -5

Step-by-step explanation:

This question asks us to find C(-1). We know what C(x) is, it is:

[tex]C(x)=-4x^{2} +4x+3[/tex]

Therefore, we must substitute -1 in for every x to find C(-1).

[tex]C(-1)=-4(-1)^{2} +4(-1)+3[/tex]

Now, solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

First, evaluate the exponent.

-1^2=-1*-1=1

[tex]C(-1)=-4(1) +4(-1)+3[/tex]

Next, multiply -4 and 1.

[tex]C(-1)=-4+4(-1)+3[/tex]

Multiply 4 and -1 again.

[tex]C(-1)=-4+ -4 + 3[/tex]

Add the numbers together.

[tex]C(-1)=-8+3[/tex]

[tex]C(-1)=-5[/tex]

Answer:

x = 2

y = 1

z = 3

Step-by-step explanation:

Okay, we know y=z-x.

Let's plug in that y-value into the first equation: x + 2 (z - x) -z =1

Simplify that down to x +2z -2x -z = 1

Equation 1 becomes -x + z = 1

Let's plug it into equation 3 and solve to get: 2x - (z - x) +3z = 12

Equation 3 becomes 3x + 2z = 12

Now let's use system of equations for those two equations we just found

3x + 2z = 12

-2x + 2z = 2 ------> multiplied this by 2 to simplify

subtract, and you 5x = 10, x = 2

Use x = 2 and solve for the other variables using the same method (try this on your own!) to get y = 1 and z = 3

Answer:

y° = 110°

z° = 26°

Step-by-step explanation:

Looking at the above geometry, we have two parallel lines , m and m

We have been asked to solve for y° and z°

Step 1

We solve for y°

On line n , we have can see that 70° and y° are CONSECUTIVE INTERIOR ANGLES

It is important to note that THE SUM OF TWO CONSECUTIVE INTERIOR ANGLES = 180°

Hence,

70° + y° = 180°

y° = 180° - 70°

y° = 110°

Step 2

Solve for z°

Looking at the geometric diagram we can see that

y° and (6z - 46) ° are ALTERNATE INTERIOR ANGLES

This means

y° = (6z - 46) °

In step 1 , we have already solved for y°

y° = 110°

Hence,

110° = (6z - 46) °

110° = 6z° - 46°

collect like terms

110° + 46° = 6z°

156° = 6z°

Divide both sides by 6

156°/6 = z°

z° = 26°

Therefore, the value y = 110° and the value of z = 26°

Answer:

[tex]3y + x = -6[/tex]

Step-by-step explanation:

Given

y = 3x + 1

Required

Equation of line that passes through (12,-6) and is perpendicular to y = 3x + 1

First, the slope of the line has to be calculated;

Th slope of a line is the coefficient of x in its linear equation;

This implies that the slope of y = 3x + 1 is 3

Having calculated the slope of the first line;

The relationship between both lines are perpendicularity; this implies that [tex]m_1 * m_2 = -1[/tex]

Where m_1 = 3 and m_2 is the slope of the secodnd line

[tex]m_1 * m_2 = -1[/tex] becomes

[tex]3 * m_2 = -1[/tex]

Divide both sides by 3

[tex]\frac{3 *m_2}{m_2} = \frac{-1}{3}[/tex]

[tex]m_2 = \frac{-1}{3}[/tex]

The equation of the line can be calculated using the folloing formula

[tex]m = \frac{y - y_1}{x - x_1}[/tex]

Where [tex](x_1, y_1) = (12,-6)[/tex] and [tex]m_2 = \frac{-1}{3}[/tex]

The equation becomes

[tex]\frac{-1}{3} = \frac{y -- 6}{x - 12}[/tex]

[tex]\frac{-1}{3} = \frac{y + 6}{x - 12}[/tex]

Cross multiply

[tex]-(x - 12)= 3(y + 6)[/tex]

[tex]-x + 12=3y + 18[/tex]

Collect like terms

[tex]12 - 18 = 3y +x[/tex]

[tex]-6 = 3y + x[/tex]

[tex]3y + x = -6[/tex]

Answer:

[tex](x-2)^2+(y+4)^2=34[/tex]

Step-by-step explanation:

The standard form for the equation of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex], where h is the x coordinate of the center of the circle, k is the y coordinate, and r is the radius. Since you already know the coordinates of the center of the circle, all you need to do is find the radius. Using the distance formula:

[tex]r=\sqrt{(7-2)^2+(-1-(-4))^2}=\sqrt{5^2+3^2}=\sqrt{25+9}=\sqrt{34}[/tex]

The equation of the circle is therefore:

[tex](x-2)^2+(y+4)^2=34[/tex]

Hope this helps!

Answer:

4 pizzas = $9

1 pizza= $9 ÷ 4

= $2.25

12 pizzas = 12 × $2.25

= $ 27

Answer:

73.72 ft Squared

Step-by-step explanation:

First you need to find the area of the rectangle the area of rectangle is 8x10=80. Then You take that 80=3.14x2. then you find the area by dividing it. so...

1.) 80=3.14x2

3.14x2=6.28       80=6.28              (Then you divide 6.28 by 80)

                             80    80                  

The sporting goods store receives the shipment of 124 golf bags in total.

Let us assume that the number of full-sized bags = X

Then the number of collapsible golf bags = 124 - X

Cost of each full sized bags = $38.50

Cost of each collapsible bags = $22.50

Total cost of the 124 bags received by the sporting goods store = $3430

Then

(38.50)X + (124 - X)22.50 = 3430

(38.50X - 22.50X) + 2790 = 3430

16X = 3430 - 2790

16X = 640

X = 640/16

  = 40

So the number of full-sized golf bags received = 40

Then the number of collapsible golf bags received = 124 - 40

                                                                                = 84

Answer:

Choice D

Step-by-step explanation:

After writing the data down seperate the values according to the x-axis on the graphs. You will find that 6 people chose between 0 to 3, 4 people chose between 4 to 7, 3 people chose between 8 to 11 and 2 people chose between 12 to 15.

Answer:

x = 2±3sqrt(3)

Step-by-step explanation:

(x-2)^2/3=9

Multiply each side by 3

(x-2)^2/3 *3=9*3

(x-2)^2=27

Take the square root of each side

sqrt( (x-2)^2)=±sqrt(27)

x-2 = ±3sqrt(3)

Add 2 to each side

x = 2±3sqrt(3)

Answer:

The value of expression remains the same

Step-by-step explanation:

Let the given function be f(y), where

[tex]f(y) = \frac{3y}{2y}[/tex]

Lets put different values of y to finds its effect on the function

f(y) = 3y/2y

Let y = 1

f(1) = 3(1)/2(1) = 3/2

Let y = 2

f(2) = 3(2)/2(2) = 6/4 = 3/2

Let y = 3

f(3) = 3(3)/2(3) = 9/6 = 3/2

Let y = 10

f(4) = 3(10)/2(10) = 30/20 = 3/2

As we can see, no matter whatever value of y we put in the expression, the result is always the same i,e 3/2

Hence,

The value of expression remains the same

Answer:

2625

Step-by-step explanation:

First let's see all the possible combinations.

(Even=E, Odd= O)

1) EEEO

2) EEOE

3) EOEE

4) OEEE

5) EEEE

Now let's see what E and O possibly could be

E = 0, 2, 4, 5, 6 and 8 (5)

O = 1, 3, 5, 7, 9 (5)

Now we are just simply gonna multiply

1) EEEO = 4*5*5*5

2) EEOE = 4*5*5*5

3) EOEE = 4*5*5*5

4) OEEE = 5*5*5*5

5) EEEE = 4*5*5*5

The even contains a 0, so you can't put 0 in, so (5-1=4), there are only 4 digits for the even.

500 times 4 = 2000

5⁴ = 625

2000+625= 2625

Answer:

x= -132

Step-by-step explanation:

Answer:

[tex]x=-132[/tex]

Step-by-step explanation:

[tex]\frac{x}{11}=-12\\ \\x=-12*11\\\\x=-132[/tex]

Answer:

C 2:1

Step-by-step explanation:

10 is double 5

and 2 is double 1

Answer:

C 2:1

Step-by-step explanation:

this is the answer

Answer:

using the equation of the line y = mx + b

m= slope

b = y intercept

y= - 1.5x - 4 m = -1.5 b = -4

y = -3x + 4 m = -3 b = 4

y = 3x m = 3 b = 0

y = 1.5x - 7 m = 1.5 b = -7

y = 7 m = 0 b = 7

Hope this helps.

Answer:

y=3x goes with m=3, b=0

y=7 goes with m=0, b=7

y=-3x+4 goes with m=-3, b=4

y=1.5x-7 goes with m=1.5, b=-7

y=-1.5x-4 goes with m=-1.5, b=-4

Step-by-step explanation:

The b represents the y- intercept in a graph (where the line crosses the y axis). The m represents the slope of the line. You can find the slope by taking the rise of the graph and dividing it by the run (rise/run). If you get the numbers in the equation form y=mx+b, then you just take the information they give you out of the equation.

Answer:

Brainleist!

Step-by-step explanation:

10^x = 0.1

x =log(0.1)

Decimal Form:  x=−1

Answer:

B) Acute triangle

Step-by-step explanation:

In acute triangles, all of the angles are less than 90°. This is true for this triangle :)

I hope this helps!!

Answer:

B) Acute triangle

Step-by-step explanation:

All the angles are less than 90 degrees so all the angles are acute

Answer:

x = -3 and x= 3

Step-by-step explanation:

Answer:

The probability that 6 out of the next 8 individuals in his community are in favor of the president.

P( X=6) = 0.070 or 7 percentage

Step-by-step explanation:

Step(i):-

Given data the researcher has obtained data that states that 45% of citizens are in favor of the president

probability of success  'p' = 45% or 0.45

                                       q = 1-0.45 = 0.55

Given random sample size 'n' = 8

Let 'X' be the random variable

let 'X' = 6

[tex]P(X=r) = n_{C_{r} } (p)^{r} (q)^{n-r}[/tex]

The probability that 6 out of the next 8 individuals in his community are in favor of the president.

[tex]P(X=6) = 8_{C_{6} } (0.45)^{6} (0.55)^{8-6}[/tex]

[tex]8_{C_{6} } = \frac{8!}{(8-6)!6!} = \frac{8 X 7 X 6!}{2 X 1 X 6!} =\frac{8 X 7}{2 x1} = 28[/tex]

P( X=6) = 28 × 0.00830 ×0.3025

P( X=6) = 0.070

Conclusion:-

The probability that 6 out of the next 8 individuals in his community are in favor of the president.

P( X=6) = 0.070 or 7 percentage

Answer:

28

Step-by-step explanation:

The rational expression that has a value of 1 when x =-1 would be; D 2x²/ (x + 3).

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol.

We need to determine the expression that has a value of 1 when x =-1

Let's consider the rational expression of the option D;

2x²/ (x + 3)

Now substitute the value x = -1 in the given expression

2x²/ (x + 3)

2(-1)²/ (-1 + 3)

= 2/ 2

= 1

Hence, the required rational expression is D 2x²/ (x + 3).

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Answer:

115° and 245°

Step-by-step explanation:

Given

cos x = - 0.4226

Since cos x < 0 then x is an angle in the second / third quadrants, thus

x =  (0.4226) = 65° ← related acute angle , thus

x = 180° - 65° = 115° ← angle in second quadrant

x = 180° + 65° = 245° ← angle in third quadrant

Answer:

[tex]x=\{44\º, 317\º\}[/tex]

Step-by-step explanation:

The interval given is [tex](0, 360\º) \text{ or } (0, 2\pi)[/tex]

In exercises of this kind I usually use

[tex]\cos \left(x\right)=a\quad \Rightarrow \quad \:x=\arccos \left(a\right)+360\º n, n \in \mathbb{Z}[/tex]

[tex]\quad \:x=\arccos \left( 0.7252\right)+360\º n, n \in \mathbb{Z}[/tex]

And [tex]\arccos \left( 0.7252\right) \approx 43.5^{\circ \:}[/tex]

But once we have the solution for cos in two different quadrants, I mean, Quadrant I and Quadrant IV angle.

To the nearest degree, we have

[tex]x=\{44\º, 317\º\}[/tex]

Answer:

Volume of cuboid = length × width × height

length = 20cm

width = 8cm

height = 15cm

Volume = 20cm × 8cm × 15cm

= 2400cm³

Volume of the cuboid is 2400cm²

Hope this helps.

Answer:

2,400cm³

Step-by-step explanation:

FORMULA FOR VOLUME OF A CUBOID= L×B×H

WHERE L IS LENGTH = 20cm

B IS BREADTH = 15cm

H IS HEIGHT=8cm

:• VOLUME= 20cm ×15cm × 8cm

= 2,400cm³

Answer: 34.27 sq. mm.

Step-by-step explanation:

Area of a triangle = hb / 2

= 8 x 4 / 2

= 32 / 2 = 16 mm

Area of the circle = πr^2

= π x 4^2

= 50 27 sq. mm.

Area of the shaded part

= 50.27 - 16

= 34.27 sq. mm

Answer: the answer is c, 34.24 mm

Step-by-step explanation: I just did the test

Answer: A

Step-by-step explanation:

This is because  diagonals of a rhombus are perpendicular not congruent, ]

Pependicular means at an angle of 90°

If this helped please mark brainliest

Answer:

Slope = 32+5/-21+55

= 37 / 34

Hope this helps

Answer:

The graph shows 2 outliers. The scatter plot consist on a straight pattern. As seen, only 2 points are not within the straight line. We can conclude that only two points are outliers. =

Answer:

2

Step-by-step explanation:

Two points: (1,9) and (10,7)