Sylvie finds the solution to the system of equations by graphing.

y = A system of equations. y=2/3 x+1 and y=- 2/3x-1

Which graph shows the solution to Sylvie’s system of equations?

In algebra, "seven times a number" is written as 7x, which is the multiplication of seven instances of the symbol x.

An equation that includes constants, variables, and a few algebraic operations is said to be algebraic. A good example of an algebraic expression is 3x2 2xy + d. So, three different types of fundamental building blocks make up an algebraic expression: Coefficient (i.e. numbers) (i.e. numbers)

A seven-times-a-number is represented by multiplying it by seven or adding it to another integer (since this is an abbreviated successive addition ).

If x is any number, then it may be written as follows seven times: Algebraic expressions (numbers or letters) are linked by fundamental operations including addition, subtraction, multiplication, and division in mathematical language.

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Complete question -

Seven times a number in algebraic expression

Answer: y = -2x + 1

Step-by-step explanation:

The formula for slope-intercept form is y = mx + b. Keep y and x as the variables. Replace m with the slope, which can be found by doing rise/run, and replace b with the y-intercept. The y-intercept is the spot where the line intersects the y-axis.

Hope this helps! Have a great day! :)

Answer:

\(y =\frac{x}{4}\)

Step-by-step explanation:

We are given several functions, and we want to figure out which one is linear.

A linear function has both of its variables (x and y) with a power of 1. Variables with other powers do not mean that the function is linear.

Let's go through the list.

Starting with \(y=\frac{3}{x} -7\), we can see that x is in the denominator. If this is the case, it means that the power of x is -1.

Even though y has a power of 1, this is NOT linear, because x has a power of -1.

Now, with y=√x-2, this is also not linear. This is because √x = \(x^\frac{1}{2}\), even though y has a power of 1.

For x² - 1 = y, we can clearly see that x has a power of 2, while y has a power of 1. This means that the function is not linear.

This leaves us with \(y = \frac{x}{4}\). x is in a fraction, however it is not in the denominator. This means that the power of x in this function is 1. We can also see that the power of y in this function is 1.

This means that \(y=\frac{x}{4}\) is linear.

Answer:

We can use ratios for solve this problem

Cross multiply to get:

Lastly, divide both sides by 2 to isolate x

The line will be 1.25 inches

Hope this helps!

P.s. can I get Brainliest?

Answer:

2.191 · \(10^{-3}\)

Step-by-step explanation:

0.002191

2.191 · \(10^{-3}\)

Answer:

Area of the figure= area of the rectangle+ area of the semicircle

=(15×14)+(1/2)π(7)²=210+77=287 square unit

287 square unit is the right answer.

Remember:--- area of the rectangle

=(length×breadth)

and area of the semicircle=π(radius)²/2

Answer:

jk = 4

Step-by-step explanation:

it starts at -2x and then goes to 2 x so the equation is

so it's |2| +2 =jk

The probability that a randomly selected point within the square falls in the red shaded square is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it is 100% in percentage.

Probability = sample space /total outcome

sample space is the area of the red shaded square and the total outcome is the big square.

Area of red shaded square = 1 × 1 = 1unit²

area of the big square = 4 × 4 = 16 units²

Therefore the probability that a point selected falls on the red shaded square

= 1/16

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Carson's work is correct for solving the equations.

Given that;

Carson wants to solve this system of equations.

y = x² + 5x − 6

y = x − 1

Now, We can solve first equation as;

y = x² + 5x - 6

y = x² + 5x - 6 = 0

⇒ x = - 5 ± √5² - 4×1×- 6 / 2

⇒ x = - 5 ± √25 + 24 / 2

⇒ x = - 5 ± √49 / 2

⇒ x = - 5 ± 7/2

⇒ x = - 5 + 7 / 2

⇒ x = 2/2

⇒ x = 1

⇒ x = - 5 - 7 / 2

⇒ x = - 12 / 2

⇒ x = - 6

Hence, From (ii);

⇒ y = x - 1

At x = 1;

y = 1 - 1

y = 0

At x = - 6;

y = - 6 - 1

y = - 7

Hence, Carson's work is correct.

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A predicate nominative is a noun or a pronoun which follows the verb and describes the subject.

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Answer:

The answer is −6(10a−7)(a−10)

Step-by-step explanation:

1) Factor out the common term 6.

\( - 6( {10a}^{2} - 107a + 70)\)

2) Split the second term in 10a² - 107a + 70 into two terms.

\( - 6( {10a}^{2} - 7a - 100a + 70)\)

3) Factor out common terms in the first two terms, then in the last two terms.

\( - 6(a(10a - 7) - 10(10a - 7))\)

4) Factor out the common term 10a - 7.

\( - 6( 10a - 7)(a - 10\)

Therefor, the answer is -6 ( 10a - 7) (a - 10).

Answer: Area of Cylinder = 753.982

Step-by-step explanation:

Given:

h = 7 cm

r = 8cm

Formula for cylinder:

A = (Perimeter of base) x height + 2 (Area of Base)

Breakdown:

Perimeter of base = 2\(\pi r\)

Perimeter of base = 2 \(\pi\) (8)

Perimeter of base = 50.2655

Area of Base = \(\pi r^{2}\)

Area of Base = \(\pi 8^{2}\)

Area of Base = 201.0619

Area of Cylinder = (Perimeter of base) x height + 2 (Area of Base)

Area of Cylinder = (50.2655)(7) +2(201.0619)

Area of Cylinder = 753.982

The probability of landing on purple to the nearest hundredth: 0.15

The total number of spins is 84, and the probability of landing on purple is 13/84 = 0.15476.

Rounding to the nearest hundredth, this is 0.15.

Elaborating:

Number of times the spinner landed on purple: 13

Total number of spins: 84

Probability of landing on purple: (13/84) = 0.15476

Probability of landing on purple to the nearest hundredth: 0.15

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The Complete Question

A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:

Spinner Results

Color Frequency

Red 18

Blue 15

Green 20

Yellow 18

Purple 13

Based on these results, express the probability that the next spin will land on purple as a decimal to the nearest hundredth.

The customer gets 5.66 hours of bike per dollar

At Hoffman's bike, it cost $17 to rent a bike for 3 hours

The number of hours gotten from the bike per dollar can be calculated as follows

17= 3
1= x

Cross multiply both sides

3x= 17

x= 17/3

x= 5.66

Hence it will cost the customer 5.66 hours to rent the bike for one dollar

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Answer:

a

  \(df = 24.32\)

b

 \(df = 30.10\)

c

 \(df = 30.7\)

d

\(df = 25.5\)

Step-by-step explanation:

Generally degree of freedom is mathematically represented as

          \(df = \frac{ [\frac{ s^2_i }{m} + \frac{ s^2_j }{n} ]^2 }{ \frac{ [ \frac{s^2_i}{m} ]^2 }{m-1 } +\frac{ [ \frac{s^2_j}{n} ]^2 }{n-1 } }\)

Considering a

         a) m = 12, n = 15, s1 = 4.0, s2 = 6.0

           \(df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{15} ]^2 }{ \frac{ [ \frac{4^2}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{15} ]^2 }{15-1 } }\)

         \(df = 24.32\)

Considering b

       (b) m = 12, n = 21, s1 = 4.0, s2 = 6.0

          \(df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{4^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }\)

        \(df = 30.10\)

Considering c

      (c) m = 12, n = 21, s1 = 3.0, s2 = 6.0

           \(df = \frac{ [\frac{ 3^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{3^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }\)

           \(df = 30.7\)

Considering c

        (d) m = 10, n = 24, s1 = 4.0, s2 = 6.0

                \(df = \frac{ [\frac{ 4^2 }{10} + \frac{ 6^2 }{24} ]^2 }{ \frac{ [ \frac{4^2}{10} ]^2 }{10-1 } +\frac{ [ \frac{6^2}{24} ]^2 }{24-1 } }\)

               \(df = 25.5\)

The limit of the given function as x approaches 1 is 0.

To find the limit of the given function as x approaches 1, we need to evaluate the expression by substituting x = 1. Let's break it down step by step:

1. Begin by substituting x = 1 into the numerator:

\(\[12\sin\left(\frac{\pi}{2}\cdot 1\right)\ln(1) = 12\sin\left(\frac{\pi}{2}\right)\ln(1) = 12(1)\cdot 0 = 0\]\)

2. Now, substitute x = 1 into the denominator:

(1³ + 5)(1 - 1) = 6(0) = 0

3. Finally, divide the numerator by the denominator:

0/0

The result is an indeterminate form of 0/0, which means further analysis is required to determine the limit. To evaluate this limit, we can apply L'Hôpital's rule, which states that if we have an indeterminate form 0/0, we can take the derivative of the numerator and denominator and then evaluate the limit again. Applying L'Hôpital's rule:

4. Take the derivative of the numerator:

\(\[\frac{d}{dx}\left(12\sin\left(\frac{\pi}{2}x\right)\ln(x)\right) = 12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{x} + \frac{\sin\left(\frac{\pi}{2}x\right)\ln(x)}{x}\right)\]\)

5. Take the derivative of the denominator:

\(\[\frac{d}{dx}\left((x^3 + 5)(x - 1)\right) = \frac{d}{dx}\left(x^4 - x^3 + 5x - 5\right) = 4x^3 - 3x^2 + 5\]\)

6. Substitute x = 1 into the derivatives:

Numerator: \(\[12\left(\cos\left(\frac{\pi}{2}\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{1} + \sin\left(\frac{\pi}{2}\right) \cdot \frac{\ln(1)}{1}\right) = 0\]\)

Denominator: 4(1)³ - 3(1)² + 5 = 4 - 3 + 5 = 6

7. Now, reevaluate the limit using the derivatives:

lim as x approaches 1 of \(\[\frac{{12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{{-1}}{{x}} + \sin\left(\frac{\pi}{2}x\right) \cdot \frac{{\ln(x)}}{{x}}\right)}}{{4x^3 - 3x^2 + 5}}\]\)

= 0 / 6

= 0

Therefore, the limit of the given function as x approaches 1 is 0.

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Answer:

18

Step-by-step explanation:

since U is the midpoint of QT, QT = 2(QU)

similarly, QS = 2 (QR)

because QR is parallel to QS and QU is parallel to QT, triangle QUR is similar to triangle QTS. therefore, the scaling factor between QT/QU and QS/QR is equal to the scaling factor between RU and ST.

therefore,

ST  = 2(RU)

36 = 2(RU)

18 =RU

Answer:

I got 4ab

Step-by-step explanation:

that's what I got, hope ot helps

Answer:

0

Step-by-step explanation:

(2ab-2ab)+(-a+a)=0

Answer:

Each sock is $2.75

Step-by-step explanation:

Divide $11.00 by 4 (socks)

Which would be $11/4

which is: $2.75

$7500 is the  amount invested in the 5% bonds

Let's call the principals (pre-profit amounts) of the 5% profit bonds F and the 12% profit bonds T.

The profit from the 5% bonds would thus be 0.05 * F, and the profit from the 12% bonds 0.12 * T

Then we have two equations, for two unknowns:

0.12 * T = 0.05 * F + 885  

T + F = 18000 (as the total amount invested into both those bonds is 18000)

Then T = (0.05 * F + 885) / 0.12 = 5/12 * F + 7375

Subtracting (T+F) from both sides, except on the other side (where the non-variable number is), we're going to subtract (T+F) by subtracting 18000. This will just give us a single equation in terms of one variable (F)

T - (T+F) = (5/12)*F + 7375 - 18000

-F = (5/12)*F - 10625

Let's solve for F by adding F to both sides of the last equation, getting us:

-F + F = 0 = 17/12 * F - 10625

This means 17/12 * F = 10625

F = 12/17 * 10625 = $7500

Hence the amount invested in the 5% bonds (before profit) is $7500

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Answer:

Pie heysgeusuwhueywgyssyywyw

Answer:

Area=length×width

=12m×15m

=180m

so,the area is 180.

hope it helps!

Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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Answer:

y = -5/2x

Step-by-step explanation:

Perpendicular = opposite sign and reciprocal slope

-5/2x

y = -5/2x

Answer:

Answer is 48

Step-by-step explanation:

cross-sectional area = 12*4 =48

Answer:

Area = 615.44cm²

Step-by-step e explanation:

Area of a circle = πr²

where π = 3.14

r = 14cm

Area = πr²

area= 3.14 * (14)²

area= 3.14*(196)

Area = 3.14*196

Area =615.44cm²

To the nearest hundredth

Area = 615.44cm²

Answer:

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

Step-by-step explanation:

In order for two lines to be parallel they must have the same slope. In other words the m constant in the line equation needs to match

\(y = mx + b\)

This means for the equation we're trying to find, we already know m. It's just -1/2 since that's the slope of the line it needs to be parallel to.

Next, let's find the constant b. We know the slope, and we know it goes through points (-4, 1), so let's plug this into our equation

\(y = -\frac{1}{2}x + b\\1 = - \frac{1}{2}\times{-4} + b\\1 = 2 + b\\b = -1\)

Now that we have both constants, we know the equation of the line.

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

To convince yourself this is correct, let's plot these two lines.