work out the value of each expression if x=4 and y=6
i 3x+9 ii 4x-y

Using linear equations, it is 3570metre  from the post office to the

library

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Length of each block=275 meter

let's Create a linear equation from this i.e. 275x where x=number of blocks.

No. of blocks from  post office to the library = 13 (x=13)

so, distance of  post office to the library= 275*13

                                                                    =3575meter

                                                        ≈3570 meter (round to nearest 10th)

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Answer:

I tried this but i got it wrong it is not b on the test thing

Step-by-step explanation:

oop

To find the constants m and b in the linear function f(x) = mx + b, we can use the given conditions f(7) = 9 and a slope of -3.

The value of f(7) represents the y-coordinate of the point on the line when x = 7. So, substituting x = 7 into the equation, we get 9 = 7m + b.

The slope of a linear function is given by the coefficient of x, which in this case is -3. So, we have m = -3.

Now, we can substitute the value of m into the equation obtained from f(7). We get 9 = 7(-3) + b, which simplifies to 9 = -21 + b.

Solving for b, we find b = 30.

Therefore, the constants for the linear function f(x) = mx + b that satisfy the given conditions are m = -3 and b = 30.

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The Outcome of event A and B is simply the intersection of both sets written as A ∩ B is; C: {seagull, crow}

From the image, we are given the animals namely; Pig, Penguin, Seagull, Tiger, Crow, Bat, Mosquito.

Now, these animals are classified as either a bird or can fly.

Animals that are birds are; Penguin, Seagull, Crow

Animals that can fly are; Seagull, Crow, Bat, Mosquito.

Now, we are told that;

Event A is the animal is a bird. Thus, the set notation that represents this event A is written as;

A = {Penguin, Seagull, Crow}

Event B is that the animal can fly and again the set notation that represents event B is written as;

B = {Seagull, Crow, Bat, Mosquito}

Now, Outcome of event A and B is simply the intersection of both sets. Thus; A ∩ B = {seagull, crow}

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Answer:

B

Step-by-step explanation:

It is B because:

21/5x+12-3+5/2x

21/5x+9+5/2x

u then find the lowest common multiple being 10x

42/10x+25/10x+90x/10x

67/10x+9

Answer:

-63

Step-by-step explanation:

\[x²-3x+18\]

discriminant=b²-4ac=(-3)²-4*1*18=9-72=-63

Answer:

\(\boxed {\boxed {\sf -63}}\)

Step-by-step explanation:

The discriminant is the portion of the Quadratic Formula that is under a square root. It helps us identify if a function has 2,1, or 0 solutions.

The quadratic formula is:

\({x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}\)

where the quadratic is: ax²+bx+c

The part under the square root is just:

\(b^2-4ac}\)

We are given the quadratic:

x² -3x+18

Therefore,

Substitute the values into the formula for the discriminant.

\((-3)^2-4(1)(18)}\)

Solve the exponent.

\(9-4(1)(18)}\)

Multiply.

\(9-72\)

Subtract

\(-63\)

Since the discriminant is negative, there are no real solutions. There are imaginary solutions though.

Answer:

Question 1 is false. The left side 28 does not equal on the right side 41, which means that the given statement is false.

Question 2 is false. The left side 0 does not equal to the right side 40, which means that the given statement is false.

Hope this helps :)

Answer:

a) 1.84m

b) 42.53°

Step-by-step explanation:

First, look though the diagram provided by the question.

And use the formula: \(\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}\)

Based on Additional Mathematics Form 4 (Dual Language Programme) KSSM from Malaysia

To find the length of AD

\(\frac{AD}{sin 67}=\frac{2}{sin 90}\)

\(AD=\frac{2}{sin 90} * sin 67\)

AD= 1.84 m

Find the angle C

\(\frac{sin 90}{2.5}=\frac{sin C}{1.84}\)

sin C=\(\frac{sin 90}{2.5} * 1.84\)

= 0.736

\(sin^{-1} (0.736)=47.39\) degree

So, we have the value of AD and the value of angle C. Now , we can solve the the angle of CAD.

Same as the first question use the formula of sine rule and you will get the answer.

\(\frac{sin 90}{2.5}=\frac{sin ACD}{1.69}\)

\(sinA = \frac{sin90}{2.5} * 1.69\)

=0.676

=42.53°

So, the answer of the angle of CAD is 42.53°

Check the answer:

90°+47.39°+42.53°

=179.92°

=180°(rounded off)(Proved)

That is all from me. I hope you will understand my solution.

The equation of the horizontal asymptote will be y = -2.

An asymptote is a line that constantly reaches a given curve but does not touch at any infinite distance.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

From the graph, the horizontal asymptote is parallel to the x-axis and the equation of the horizontal asymptote is given as,

y = - 2

The equation of the horizontal asymptote will be y = -2.

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Answer:

B

Step-by-step explanation:

The triangle RUS is similar to RST. 9/sqrt(90)=y/(3+x) and y^2=x^2+81. Solving all this will give x=27 and y=9*sqrt(10)

Value of x is 27 and value of y is \(9\sqrt{10}\).

The angle addition postulate in geometry states that if we place two or more angles side by side such that they share a common vertex and a common arm between each pair of angles, then the sum of those angles will be equal to the total sum of the resulting angle.

X-value:

<RST = \(90^{0}\)

\(tan( < RSU)= \frac{\overline R \overline U}{\overline S \overline U}\)

\(tan( < RSU) = \frac{3}{9}\)

\(< RSU = 18.435^{0}\)

Angle addition postulate:

<RST = <RSU + <TSU

\(90^{0} =18.435^{0} + < TSU\)

\(< TSU =71.565^{0}\)

\(tan( < TSU) = \frac{\overline T \overline U }{\overline S \overline U}\)

\(tan(71.565^{0})=\frac{x}{9}\)

\(x=27\)

Y-value:

<RST = \(90^{0}\)

\(tan( < RSU)= \frac{\overline R \overline U}{\overline S \overline U}\)

\(tan( < RSU) = \frac{3}{9}\)

\(< RSU = 18.435^{0}\)

Angle addition postulate:

<RST = <RSU + <TSU

\(90^{0} =18.435^{0} + < TSU\)

\(< TSU =71.565^{0}\)

\(cos( < TSU) = \frac{\overline S \overline U }{\overline S \overline T}\)

\(cos(71.565^{0})=\frac{9}{y}\)

\(y=9\sqrt{10}\)

Value of x is 27 and value of y is \(9\sqrt{10}\).

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Answer:

3 shirts

Step-by-step explanation:

90 divided by 30 = 3

Therefore, with $90.00, Suzie can buy 3 shirts.

:)

Answer:

3 shirts

Step-by-step explanation:

$90/$30=3 shirts

Answer:  D.  y = -4x + 4

Step-by-step explanation:

Notice that the y-intercept is when x is zero and the x intercept is when y is 0.

and to write in the equation in slope intercept form , you will need the slope and the intercept.

We will use the y and x intercepts to find the slope, by find the difference in their y coordinates and dividing it by the difference in their x coordinates.

y intercept: ( 0,4)  

x intercept: (1,0)

y coordinates difference:  4 - 0 = 4

x coordinates difference:  0 - 1 = - 1  

Slope:  4/-1 =  -4  

Since the slope is -4 and the the y intercept is 4 , the equation will be

 y = -4x + 4

The curl and divergence of the given vector field can be determined by the following steps :

(a) The curl of the given vector field F(x, y, z) = 5eˣʸ sin(z)j + 4y tan⁻¹(x/z)k is:

curl F = ∇ × F = (∂F₃/∂y - ∂F₂/∂z)i + (∂F₁/∂z - ∂F₃/∂x)j + (∂F₂/∂x - ∂F₁/∂y)k.

Evaluating the partial derivatives, we have:

∂F₁/∂y = 5xeˣʸ sin(z),

∂F₂/∂z = 0,

∂F₃/∂x = 4y / (1 + (x/z)²),

∂F₃/∂y = 0,

∂F₁/∂z = 5eˣʸ cos(z),

∂F₂/∂x = 4y / (1 + (x/z)²).

Substituting these values into the curl equation, we get:

curl F = (0 - 0)i + (5xeˣʸ sin(z) - 4y / (1 + (x/z)²))j + (4y / (1 + (x/z)²) - 5eˣʸ cos(z))k.

(b) The divergence of the vector field F can be calculated as:

div F = ∇ · F = ∂F₁/∂x + ∂F₂/∂y + ∂F₃/∂z.

Evaluating the partial derivatives, we have:

∂F₁/∂x = 5yeˣʸ sin(z),

∂F₂/∂y = 0,

∂F₃/∂z = 5eˣʸ cos(z).

Substituting these values into the divergence equation, we get:

div F = 5yeˣʸ sin(z) + 0 + 5eˣʸ cos(z).

Therefore, the divergence of the vector field F is 5yeˣʸ sin(z) + 5eˣʸ cos(z).

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The coordinates of A' and C' will not be the same. The perimeter and area of ΔA'B'C' will be the same. The measure of ∠B' and the slope of A'C' will be the same.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As per the given translation,

2 units down and 3 units right

The coordinate will change as,(x,y) → (x+3,y-2) so it will change.

The transformation consists only of linear transformation no rotation exists thus area and perimeter will remain the same.

The slope and angle are unchanged irrespective of any transformation.

Hence "A' and C' will not have the same coordinates. The boundaries and surface area of ΔA'B'C' will be identical. The slope of A'C' and the measure of ∠B will be equal.".

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Answer: -1

Step-by-step explanation:

Given by your question

2(3x-1)≥4x-6

Distributive property to take off the parentheses

2×3x-2×1≥4x-6

6x-2≥4x-6

Subtract 4x on both sides (Subtractive property of equality)

6x-2-4x≥4x-6-4x

2x-2≥-6

Add 2 on both sides (Addition property of equality)

2x-2+2≥-6+2

2x≥-4

Divide 2 on both sides (Division property of equality)

2/2 x≥-4/2

x≥-2

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

Looking at the options you've provided.

-10 INCORRECT, it is not greater or equal to -2

-5 INCORRECT, it is not greater or equal to -2

-3 INCORRECT, it is not greater or equal to -2

-1 CORRECT, it is greater than -2

Hope this helps!! :)

Please let me know if you have any question

x = - 1

2(3x – 1) ≥ 4x – 6

6x - 2 ≥ 4x - 6

6x - 4x ≥ 2 - 6

2x ≥ - 4

x ≥ - 2

x ∈ [ - 2 ; + oo )

x = - 1

Answer:

Step-by-step explanation:

Surface:

surface area = 2 ends + side

The ends are both a circle and they are identical.

area of a circle = \(\pi\)\(r^{2}\)

then  \(\pi\)\(7^{2}\) = 153.93804 \(cm^{2}\)

since there are two ends multiply the above by 2

2*153.93804 =307.87608 \(cm^{2}\)

the side is the length * height

length = perimeter of the circle , the perimeter of a circle is also the circumference.   circ = 2\(\pi\)r

circ = 2*\(\pi\)*7 = 53.407075

surface area of the side = 6* 53.407075=320.44245

add the two surfaces areas together :)

total surface area = 320.44245 + 307.87608 = 628.3185307 \(cm^{2}\)

Volume:

volume is the area of the end times the height

volume = circle area * height

volume = 153.93804 * 6

volume = 923.62824 \(cm^{3}\)

Answer:

58 more

Step-by-step explanation:

First solve both values

3/4 of (or x) 120 = 90

2/5 x 80 = 32

90 - 32 = 58

Answer:

It is C or 1/4

Sorry if wrong

The distance between the lines with the given equations is : 2.21 units.

We have the equation of line:

3x + y = 1

y + 6 = -3x

To find the distance between the lines.

Now, According to the question:

Convert both equations to slope-intercept form of y = mx + b:

3x + y = 1 ⇒ y = - 3x + 1

y + 6 = - 3x ⇒ y = - 3x - 6

And, we can see that both slopes are same.

So these are parallel lines, and the distance between parallel lines is:

We use the formula:

\(d = \frac{|b_1-b_2|}{\sqrt{1+m^2} }\)

where b₁, b₂ - y-intercepts, m- slope

Substitute the values and calculate them.

\(d = \frac{|1+6|}{\sqrt{1+(-3)^2} } =\frac{7}{\sqrt{10} }=2.21\)

Hence, The distance between the lines with the given equations is : 2.21 units.

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COMPLETE QUESTION:

Caitlyn recorded the height of each plant after she exposed each plant to a set amount of darkness daily. The scatterplot shows her results after 2 weeks of exposing each plant to the amount of darkness.

(Graph Below)

Which statement about the scatterplot is true?

A. The point (17, 12) could cause the description of the data set to be overstated.

B. The point (17, 12) could cause the description of the data set to be understated.

C. The point (17, 12) shows that there is no relationship between the number of hours of darkness and the height of the plant.

D. Although (17, 12) is an extreme value, it should be part of the description of the relationship between number of hours of darkness and the height of the plant.

Answer:

B. The point (17, 12) could cause the description of the data set to be understated.

Step-by-step explanation:

All other points on the scatter plot except point (17, 12), all follow a similar trend showing the negative relation between height of plants and darkness. If we are to consider just point (17, 12) alone when describing the data set, we might likely understate the relation between both variables.

Therefore, the statement that is true about the scatter plot is "B. The point (17, 12) could cause the description of the data set to be understated."

The statement (B) the point (17, 12) could cause the description of the data set to be understated is correct.

Scatter plots are graphs that represent individual points of data and are labelled with quantitative values on both the co-ordinate axes, meaning that there is only one projection on the x-axis and one projection on the y-axis for each point.

We have the scatter plot shown in the picture.

As we can see in the scatter plot, there is a point (17, 12) which is not follow the trend like other points follows.

We can say about the data set, we might likely understate the relation between both variables.

Thus, the statement (B) the point (17, 12) could cause the description of the data set to be understated is correct.

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Answer: 3.078139077

Step-by-step explanation:

Use the 1st digit 2 from dividend 2367800.

Since 2 is less than 769231, use the next digit 3 from dividend 2367800 and add 0 to the quotient.

Use the 2nd digit 3 from dividend 2367800.

Since 23 is less than 769231, use the next digit 6 from dividend 2367800 and add 0 to the quotient.

Use the 3rd digit 6 from dividend 2367800

Since 236 is less than 769231, use the next digit 7 from dividend 2367800 and add 0 to the quotient.

Use the 4th digit 7 from dividend 2367800.

Since 2367 is less than 769231, use the next digit 8 from dividend 2367800 and add 0 to the quotient.

Use the 5th digit 8 from dividend 2367800.

Since 23678 is less than 769231, use the next digit 0 from dividend 2367800 and add 0 to the quotient.

Use the 6th digit 0 from dividend 2367800.

Since 236780 is less than 769231, use the next digit 0 from dividend 2367800 and add 0 to the quotient.

Use the 7th digit 0 from dividend 2367800.

Find closest multiple of 769231 to 2367800. We see that 3×769231=2307693 is the nearest. Now subtract 2307693 from 2367800 to get reminder 60107.

Add 3 to quotient.

Quotient: 3

Reminder: 60107

It's not as difficult as it looks.

✨

Answer:

In short, the multiplicative identity is the number 1, because for any other number x, 1*x = x. So, the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity,

Answer: Any number to the power of zero would be 1

Answer:

Step-by-step explanation:

The area of a rectangle is length time width.

A=LW

In this case,

A=32x^2+12

W=4x

Solve for L

L=A/W

Substitute

L=(32x^2+12)/4x

L=(8x^2+3)/x

After 21 years, the amount in the account would be approximately $2160 to the nearest dollar.

To find out how much money would be in the account after 21 years, we can use the concept of compound interest.

Given that the money in the account doubles every 9 years, we can calculate the number of doubling periods within 21 years:

Number of doubling periods = 21 years / 9 years = 2.333 (approximately)

Since we can't have a fraction of a doubling period, we need to consider that there are 2 doubling periods within 21 years.

Now, let's calculate the final amount in the account using the formula for compound interest:

Final amount = Initial amount * (1 + interest rate)^(number of doubling periods)

In this case, the initial amount is $540 and the interest rate is 100% because the money doubles. The number of doubling periods is 2.

Final amount = $540 * (1 + 1)^(2)

Final amount = $540 * (2)^2

Final amount = $540 * 4

Final amount = $2160

Therefore, after 21 years, the amount in the account would be approximately $2160 to the nearest dollar.

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Answer:

7.3

Step-by-step explanation:

The relation that is able to model the decay is given as N = 690e^-0.04r. The quarterly rate of change is 0.21%.

We know that the term radioactivity has to do with the fact that the object is able to undergo the process of a spontaneous disintegration. The implication of this is that the element is going to be gradually be transformed into a different element and this is going to occur at a given rate which we have called the decay constant for the reaction.

We know that element X is a radioactive isotope such that its mass decreases by 4% every year then an experiment starts out with 690 grams of Element X.

It follows that;

Initial amount of X No = 690 g

Decay rate of X (r) = 0.04

Time taken for decay = t

Amount of X at time t = N

The model now becomes;

N = 690e^-0.04r

The  quarterly rate of change is obtained from;

A(t) = (1- 0.04)Ao

= 0.96 Ao

0.96Ao = Ao(1 - r)^30

0.94 = (1 - r)^30

30√0.94  = (1 - r)

r = -0.0021 or -0.21%

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Answer:

yes

Step-by-step explanation:

it is possible to be an isoscelize triangle

pls mark brainliest

Answer:

I think yes

Step-by-step explanation:

because the two sides that are bigger can be the ones with the lenght of 8

and the one in the bottom can be the one with the lenght 1

hope this helps <33

have a nice day :)