Simplify the expression by combining like terms:

In a linear equation value of x and y  (x, y) = ( -2 , 6) when the graph of y=-3x and x=-2 intercept .

What in mathematics is a linear equation?

y= - 3x

Put x = -2 put in the equation

y = -3  * -2

y = 6

So, value of x and y  (x,y) = ( -2 , 6)

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Answer:

Step-by-step explanation:

Answer:

A . 6822 just divede 420 to 32 then times 562 tk 911

Answer:

[tex]2 \sqrt{3} [/tex]

Two numbers on the number line have an absolute value of 2.75 is -2.75 and 2.75

number line - A line on which numbers are marked at intervals and used to illustrate simple numerical operations.

absolute value - absolute value of real number is its distance from the zero.

The absolute value of 2.75 is 2.75 and the absolute value of -2.75 is 2.75

Two numbers on the number line have an absolute value of 2.75 is -2.75 and 2.75

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Answer:

[tex]x=\dfrac{1}{8}, \quad x=-2[/tex]

Step-by-step explanation:

Given equation:

[tex](8x+7)(x+1)=9[/tex]

Expand the brackets:

[tex]\implies 8x^2+15x+7=9[/tex]

Subtract 9 from both sides:

[tex]\implies 8x^2+15x+7-9=9-9[/tex]

Simplify:

[tex]\implies 8x^2+15x-2=0[/tex]

To factor a quadratic equation in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:

[tex]\implies ac=8 \cdot -2=-16[/tex]

[tex]\implies b=15[/tex]

Therefore, the two numbers are:  16 and -1.

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies 8x^2+16x-x-2=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 8x(x+2)-1(x+2)=0[/tex]

Factor out the common term (x + 2):

[tex]\implies (8x-1)(x+2)=0[/tex]

Apply the zero-product property:

[tex]\implies 8x-1=0 \implies x=\dfrac{1}{8}[/tex]

[tex]\implies x+2=0 \implies x=-2[/tex]

Therefore, the solutions to the given quadratic equation are:

[tex]x=\dfrac{1}{8}, \quad x=-2[/tex]

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Answer:

x = 1/8 (or) x = -2

Step-by-step explanation:

Now we have to,

→ solve the following quadratic equation.

Let's solve for quadratic equation,

→ (8x+7)(x+1) = 9

→ 8x² + 7x + 8x + 7 - 9

→ 8x² + 15x - 2

→ 8x² + 16x - x - 2

→ 8x(x + 2) - 1(x + 2)

→ (8x - 1)(x + 2)

→ x = 1/8 (or) x = -2

Hence, the solution is x = 1/8, -2.

The given equation 3y = -12x + 6 has infinitely many solutions.

The given equation 3y = -12x + 6 can be solved using the substitution method to determine whether this equation has no solution, 1 solution or infinitely many solutions.

Given equation,

3y = -12x + 6

Rearranging the terms of the equation, we get the value of y in terms of the variable x.

=> 3y = -12x + 6

=> y = -12x/3 + 6/3

=> y = -4x + 2

Next, we substitute this value of y in terms of the variable x in the original equation,

=> 3 ( -4x + 2 ) = -12x + 6

=> -12x + 6 = -12x + 6

=> -12x + 12x = 6 - 6

=> 0 = 0

From the obtained result, we can conclude that this system has infinitely many solutions. This implies, the lines are coincident and the system is consistent and dependent.

Therefore, it can be concluded that the given equation 3y = -12x + 6 has infinitely many solutions.

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Bacterial cell is smaller than the amoeba cell by 70 times or 7^ 10 times

What is mathematical expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

length of a bacterial cell = 5 x 10^-6 m

length of an amoeba cell = 3.5 x 10^-4 m

= 3.5 x 10^-4 x 100/100 m

= 350 x 10^-6 m

Now, comparing the length

= (350 x 10∧-6) / (5 x 10∧-6 )

= (350/5

= 70 times or 7^ 10 times

Therefore, bacterial cell is smaller than the amoeba cell by 70 times or 7^ 10 times

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The probability of color coming up the same for rolling two 20-sided dice is 129/400.

Probability is defined as how likely something is to happen. For a single dice, getting a maroon, teal, and cyan have a probability of 4/20, 7/20, and 8/20, respectively.

Before solving the probability, we must identify whether the events are considered independent or dependent. Independent events are when the probability of an event happening does not affect the other's event probability of happening. A dependent event is when the probability of an event happening affects the other event. The rolling of dice is considered an independent event.  

For events that should occur together, the multiplication rule is used. To solve for the probability of two sides coming up the same, the formula below is used.

P (A and B) = P (A) * P (B)

P (red and red) = (4/20)*(4/20) = 1/25

P (teal and teal) = (7/20)*(7/20) = 49/400

P (cyan and cyan) = (8/20)*(8/20) = 4/25

Since no specific color was stated in the problem, the sum of the probability of each color coming up the same is determined.

P (color come up the same) = P (red and red) + P (teal and teal) + P (cyan and cyan)

P (color come up the same) = 1/25 + 49/400 + 4/25

P (color come up the same) = 129/400

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Step-by-step explanation:

x=total hours for wahing cars

y=total hours for walking dogs

1. 9x+8y=90 (total money)

2. x+y=11 (total hours)

=>8x+8y=88

=> 1-2

=> x=2

therefore y=9

The number of hours for Shandra working to wash car is 2 hours.

The number of hours for Shandra working to walking dogs is 9 hours.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Shandra is working two summer jobs, making $9 per hour washing cars and $8 per hour walking dogs.

Last week Shandra worked a total of 11 hours.

Total earned = $90

Now,

Total number of hours to wash car = x

Total number of hours to walk dogs = y

So, We can formulate;

⇒ 9x + 8y = $90  ... (I)

And, x + y = 11   .. (ii)

Solve equation (i) and (ii) we get;

x = 2 hours and y = 9 hours

So, The number of hours for Shandra working to wash car is 2 hours.

The number of hours for Shandra working to walking dogs is 9 hours.

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The difference between the speeds of the planets Neptune and Saturn is 9384 miles per hour.

The distance traveled in a unit of time is called speed. It refers to a thing's rate of movement. The scalar quantity known as speed is the velocity vector's magnitude. It has no clear direction. The formula for an object's general speed is [Speed = Distance Time]. M/s is the SI unit of speed.

The speed of an item, which is a scalar quantity in everyday usage and kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time.

Therefore, the difference between the speeds of the planets Neptune and Saturn will be:

= 21637 - 12253

= 9384 miles per hour.

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the dimensions of each rectangle is 72.

In geometry, a shape's perimeter is referred to as its total length. The perimeter of a form is determined by adding up the lengths of all of its sides and edges. Linear measurements like centimeters, meters, inches, and feet are used to indicate its dimensions.

EXPLANATION :

The length of a rectangle is 15 cm more than its width.

L - W = 15

Compared to the first rectangle, which has a circumference of 72 cm, the second is 2 cm smaller and 5 cm wider.

2(L-2) + 2(W+5) = 72

Simplify to get 36 L + W + 3 and 36 L + W, which equals 33 by multiplying L - 2 + W + 5 by 2.

Here, combine the two equations and apply elimination.

L - W = 15 \sL + W = 33

Using the initial length, L 2L = 48 L = 24 cm, we may find W = 24 - 15 W = 9 cm, so removing W. Second rectangle width: initial width 24 - 2 = 22 cm; second rectangle length: 9 + 5 = 14 cm.

Calculate the second rectangle's perimeter using the following equation: 2(22) + 2(14) = 44 + 28 = 72

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Answer:

-2/45

Step-by-step explanation:

Answer:

7.2

Step-by-step explanation:

The area of a rectangle is calculated by multiplying its width and length.

The length is already given as 13 cm and the area is given as 93.6 cm.

Now, to find the width we will divide the area by length:

93.6 ÷ 13 = 7.2

3230 kilograms of the soil supplement are required for the entire vineyard;

1 km = 1000 m = 10³ m

1 km² = 1000000 m² = 10⁶ m²

1 km² = 247 acres

1 kg = 1000 g;

A vineyard has 145 acres of Chardonnay grapes.

145 acres = 145/247 km²

                = 0.587 km²

A particular soil supplement requires 5.50 grams for every square meter of vineyard.

1 km² requires = 5.5 × 10³ kg

145 acres requires = 0.587 × 5.5 × 10³ kg = 3230 kg;

An annual percentage rate is expressed as an hobby charge. It calculates what percentage of the major you will pay every year by using taking things inclusive of month-to-month bills under consideration. APR is also the annual rate of interest paid on investments without accounting for the compounding of interest within that year.

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the answer of all the 5 expressions is given as : 0, 14, 49, -49, -14 respectively.

What is mathematic expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here the given expression are :

1)  |-7| - 7 :

now, here considering the modulus value of -7 as 7 that is positive only :

 |-7| - 7 = 7-7 = 0

2) 2|-7| = 2x 7

   2|-7| = 14

3) (-7)² = -7 x -7 = 49

4) -7² = -(7 x 7) = -49

5) -7 -|-7| = -7 - 7 = -14

it should be noted that we have considered only positive value of modulus function only.

Therefore, the answer of all the 5 expressions is given above.

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Answer:

(-5,4)

Step-by-step explanation:

when the coordinate is reflection it stays the same number but is change to  the opposite (-/+)

reflecting over the y-axis flip the X coordinate (-5,4)

reflecting over the x-axis flip the Y coordinate (5,-4)

Answer:

1.66...

Step-by-step explanation:

5/3=

5 * 1/3=

5 * 0.33...=1.66...   ==> with bar on top of the 6

A semicircle is a one-dimensional locus of points that forms half of a circle.

The area of the semicircle is 10796.9 square feet.

A semicircle is a one-dimensional locus of points that forms half of a circle.

Its area is half the area of a circle.

We have,

The radius of the semicircle is 23 feet.

The figure is given below.

The area of a semicircle is given by:

= πr² / 2

r = radius

π = 22/7 = 3.14

So,

The area of the semicircle tunnel:

= (3.14 x 23 x 23) / 2

= 10796.89

Rounding to the nearest tenth.

= 10796.9 square feet

Thus the area of the semicircle is 10796.9 square feet.

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The ending balance based on the information given will be $2000.

From the information, it was stated that there are 2 checks for $500 and 2 bills for $2000 with $5000.

It should be noted that bill is a expense and will be deducted.

This will be illustrated as:

= $5000 + (2 × $500) - (2 × $2000)

= $5000 + $1000 - $4000

= $2000

Therefore, the ending balance based on the information given will be $2000.

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Answer: $1.05

Step-by-step explanation:

March has 31 days

Hence,

[tex]\displaystyle\\32.55:31=\\\\32\frac{55}{100}*\frac{1}{31} =\\\\32\frac{11}{20} *\frac{1}{31} =\\\\\frac{(32)(20)+11}{(20)(31)} =\\\\\frac{640+11}{620} =\\\\\frac{651}{620}=[/tex]

$1.05

Answer:

c

Step-by-step explanation:

The number of solutions of the equation [tex]5x^2+7x-4=0[/tex] is 2. Option (c) is correct.

Further explanation:

The Fundamental Theorem of Algebra states that the polynomial has n roots if the degree of the polynomial is n.

The polynomial function has n roots or zeroes.

Given:

The equation is [tex]f(x)=5x^2-7x-4=0[/tex]

According to the Fundamental Theorem of Algebra the function has 2 roots

Solve the above equation to obtain the zeros.

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-7\pm \sqrt{7^2-4\cdot \:5\left(-4\right)}}{2\cdot \:5}[/tex]

[tex]\sqrt{7^2-4\cdot \:5\left(-4\right)}[/tex]

[tex]=\sqrt{129}[/tex]

[tex]x_1=\frac{-7+\sqrt{129}}{2\cdot \:5},\:x_2=\frac{-7-\sqrt{129}}{2\cdot \:5}[/tex]

so, x has 2 solutions

Answer:

options c

Step-by-step explanation:

I hope it's helpful for you to

Answer:

t = nRT/M + 5ab/M

Step-by-step explanation:

I'm going to assume that the t and T are seperate variables.

basically all you have to do is isolate t by dividing each side with factors that do not contain the t

The expression that represents the age of the oldest child is x +5

Integers are whole number and can be negative or positive. For instance, 1,2, 3, -5 are al integers.

Fractions cannot be an integers. From the question, we are told that the ages of the three children are three consecutive even integer. If the  youngest child is represented by x + 3, the the others will be determine by simply adding 1 to each term

Middle child = x + 3 + 1

Middle child = x + 4

Oldest child = x + 4 + 1

Oldest child = x + 5

Hence the expression that represents the age of the oldest child is x +5

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The width of the schoolyard in the drawing is 45 millimeter.

In the given statement is ,

kirk made a scale drawing of the elementary school. the scale of the drawing was 3 millimeters : 4 meters. if the actual width of the schoolyard is 60 meters.

To find the how wide is the schoolyard in the drawing

Now, According to the question:

and, Based on the given condition

Let width of the schoolyard in the drawing be x

So, 3 : 4 = x : 60

[If b/a = d/c, ad = bc]  

3/4 = x/60

3 x 60 = 4x

x = 180/4

x = 45 millimeters

Hence, The width of the schoolyard in the drawing is 45 millimeter.

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The relation between the linear and recursive functions are given as follows:

A linear function is modeled according to the following rule:

f(x) = mx + b

In which:

Considering the concepts of a linear function, the recursive function is given as follows:

The linear function with first term -1 and slope -1 is given by:

f(n) = -n.

Hence:

f(n) = -n < - > {-1,-2,-3,-4...}, where f(1) = 1 and f(n + 1) = f(n - 1) - 1 for n > 1.

The linear function with first term -1 and slope 2 is given by:

f(n) = 2n - 3

Hence:

f(n) = 2n - 3 < - > {-1,1,3,5...}, where f(1) = -1 and f(n + 1) = f(n - 1) + 2 for n > 1.

The linear function with first term 4 and slope -1 is given by:

f(n) = -n + 5

Hence:

f(n) = -n + 5 < - > {4,3,2,1...}, where f(1) = 4 and f(n + 1) = f(n - 1) - 1 for n > 1.

The linear function with first term 4 and slope 2 is given by:

f(n) = 2n + 2

Hence:

f(n) = 2n + 2 < - > {4,6,8,10...}, where f(1) = 4 and f(n + 1) = f(n - 1) + 2 for n > 1.

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Answer:hi how are you

Step-by-step explanation:

In a line segment DF with point e somewhere on the line, ef = 16 and ed = 3.

We have given a line segment  DF  with a point e on the line segment

We have been informed that ef = 16 and DF = 19

We know that

⇒ DF = ed + ef

⇒ ed = DF - ef

         = 19 - 16

         = 3 units

This line segment has two ends with defined lengths, A and B. This line segment's length is equal to the distance between its ends, A and B.

A line segment is hence a section or component of a line with two endpoints. A line segment, unlike a line, has a set length.

Measuring the length of a line segment can be done using either metric measurements, such as millimeters or centimeters, or conventional measurements, such as feet or inches.

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Full question

Point e is on line segment DF given ef =16 and DF=19. Find ed.

Answer:

50mm

Step-by-step explanation:

From the smaller to the larger:

Let s + the scale factor

3s = 10  Divide both sides by 3

s = [tex]\frac{10}{3}[/tex]

15[tex](\frac{10}{3})[/tex] = [tex]\frac{150}{3}[/tex] = 50

Answer:
Midpoint = (-0.5, 1)

Step-by-step explanation:

Midpoint formula is (x1 + x2)/2, (y1 + y2)

Lets plug that into the formula.

-4 + 3 = -1

x = -1/2 or -0.5


-1 + 3 = 2

2/2 = 1

y = 1

Final Answer: (-0.5, 1) or (-1/2, 1)