Lyanna opens a bank account with a deposit of $200. She earns 3%
interest per year. How much money will Lyanna have in her account after
the first year?

Answer:

x = 27, y = 6

Step-by-step explanation:

x - 2y = 15

x - 4y = 3 (rearranged the orginal equation)

  x - 2y = 15

-  x - 4y = 3

___________

2y = 12

y = 6

Plug this value in any original equation

x - 2(6) = 15

x = 27

x and y of the simultaneous equation are 27 and 6 respectively.

Given,

x - 2y = 15

x - 3 = 4y

Here,

Equations:

x - 2y = 15

Rearranged the original equation

x - 4y = 3

Now subtract both equations,

x - 2y = 15

x - 4y = 3

⇒2y = 12

y = 6

Plug this value in any original equation

x - 2(6) = 15

x = 27

Thus the solution of system of equation is x = 27 and y = 6.

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Answer:

A or 0.31 per bar

Step-by-step explanation:

To solve this problem we want to find the price of the singular bar and find the cheapest one. So we will divide the amount of bars by the total price, so option A will equal 0.31, option B will equal 0.34, option C will equal 0.33, and option D will equal 0.32. The cheapest per bar price would be a or 3 pack of granola bars for 0.93 cents.

Amy is correct, -7.1 is between -7 and -8.  

A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.

Two students were asked to graph a rational number -7.1.

Amy states that The number is between -8 and -7, but Laura states that the point is between -7 and -6.

In order to be in between -6 and -7, the number would have to be a decimal with a whole number of 6.

But -7.1 has a whole number of 7 then it is in between -7 and -8.

Thus, Amy is correct, -7.1 is between -7 and -8.  

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Answer:

Whole numbers

Explanation:

0 is a whole number, but not a natural number. Whole numbers include all natural numbers and 0.

The area of the logo using the length and the width is 162 cm²

Length of logo = 16 cm

Width of logo = 12 cm

Area of logo = length × width

= 16 cm × 12 cm

= 192 cm²

Therefore, the area of the logo using the length and the width is 162 cm²

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The graph second represents the line that is perpendicular to the line y = 4x - 2 option  (B) is correct.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The question is incomplete:

The complete question is:

Consider the equation y = 4x - 2 Which graph shows a line that is perpendicular to the line defined by the given equation?

Please refer to the attached picture.

The given line:

y = 4x - 2

The slope of the line m = 4

The slope of the line which is perpendicular to the above line:

M = -1/4 = -0.25

The graph second has a slope of -0.25

[tex]\rm y\ -2\ =\ \dfrac{\left(2-0.5\right)}{-4-2}\left(x+4\right)[/tex]

y - 2 = -0.25x - 1

y = -0.25x + 1

Thus, the graph second represents the line that is perpendicular to the line y = 4x - 2 option  (B) is correct.

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The measure of the side RS from the figure is 4.6 units

Midpoint theorem of a trapezium

The given figures are trapezoid. Given the following parameters

PQ = 4RS

We need to determine how PR is equivalent to 4.6

Since PQ = 18.4 from the diagram, hence;

18.4 = 4RS

RS = 18.4/4

RS = 4.6 units

Hence the measure of the side RS from the figure is 4.6 units

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Answer:

6.2172

Step-by-step explanation:

sin129=h/8

h=8(sin129)

8 x 0.77714596... =

6.2172

I just did it.

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. The height of the triangle is 6.2172 cm.

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

Sin(θ) = Perpendicular/Hypotenuse

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

In the given diagram let the centre of the circle be represented by O, while the point at which line segment h and the circle intersect be represented by B. Also, the point at which the 90° angle is formed is represented by A.

Now, in the ΔABO, for the ∠AOB, the sine ratio of the trigonometric function can be written as,

sin(θ) = perpendicular / Hypotenuse

sin(51°) = AB / OB

sin(51°) = h/ 8 cm

8cm × sin(51°) = h

h = 6.2172 cm

Hence, the height of the triangle is 6.2172 cm.

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The required value of  value of cospheta = √2/3​, here correct option is d) √2/3​.

The given equation is a Trignomatric Equation,
cos2pheta+cos^2pheta = 1

These are the equation which contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.



cos2pheta + cos^2pheta = 1
Now we know that,

[tex]cos2x[/tex] = [tex]cos^2x -1[/tex]

so, substituting  cos2pheta = 2cos^2pheta - 1
2cos^2pheta-1 + cos^2peta = 1
3cos^2peta = 2
cos^2pheta = 2/3
cospheta = √2/3​

Thus, the required value for the cospheta = √2/3​.

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Answer:

a)

The GCF is 2k hence: 2k(2ck + 5k - 8c - 20)

b)

2k(2ck + 5k - 8c - 20)

After further factorization:

2k(k - 4)(2c + 5)

Answer:

83.97

Step-by-step equation:

Since there is 3 Bags of Dog food and each is 27.99, you want to multipy 27.99*3 to get your answer.

Answer:

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

Step-by-step explanation:

Perpendicular lines

Perpendicular lines have slopes whose product is -1.  In other words, to find a line that is perpendicular to a given line, the new line must have a that is the opposite reciprocal of the original line.

Passing through a point
Additionally, if a line contains a point, then the point must be a solution to the equation (meaning, when you plug in the "x" and "y", the equation must be true).

Finding our perpendicular line

Work on slope first

To find the slope of the original line, rewrite the original line in slope-intercept form: [tex]y=mx+b[/tex]

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

In this form, the slope is the number multiplied to the "x", so the original slope is -3/1.

Thus, the slope of the new perpendicular line will be the opposite reciprocal of -3/1 ... which is 1/3.

Writing what we do know about the new perpendicular line, we have [tex]y=\frac{1}{3}x+b[/tex]

Making sure it passes through the point
This new line is also supposed to contain the point (-3,-1), so (-3,-1) must be a solution to the equation, for whatever constant-value the "b" is.  To find out the "b", substitute the known quantities, and solve:

[tex]-1=\frac{1}{3} (-3)+b\\-1=-1+b\\(-1)+1=(-1+b)+1\\0=b[/tex]

Substituting this into our equation:

[tex]y=\frac{1}{3}x+(0)\\y=\frac{1}{3}x[/tex]

Conclusion

So, the equation for a line that is perpendicular to the original line [tex]y=6-3x[/tex], and that also passes through (-3,-1) is [tex]y=\frac{1}{3}x[/tex]

Trigonometry: Rounded to the nearest tenth of a foot, the answer is 15.2 feet.

Trigonometry is a branch of mathematics that studies the relationships between side lengths and angles of triangles. It is used to calculate unknown side lengths and angles of triangles when given other values, and to solve various problems in different fields such as engineering, navigation, astronomy, and physics.

The horizontal distance between the base of the ladder and the wall can be calculated using trigonometry.
The formula for finding the opposite side of a triangle (in this case, the horizontal distance) when given the angle and the adjacent side is: opposite side = adjacent side x tan (angle)
Therefore, the horizontal distance is 16 feet x tan(66°) = 15.2 feet.
Rounded to the nearest tenth of a foot, the answer is 15.2 feet.

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Answer:

54 degrees!

Step-by-step explanation:

its a right triangle so we know 2 out of the 3 angles

so 36 + 90 = 126

180 - 126 = 54!

hope this helps :)

Answer: 50m

Step-by-step explanation:

        The perimeter of the shape can be found by adding together all the lengths of the sides. See attached for my work.

[tex]\huge\textbf{Hey there!}[/tex]

[tex]\large\textbf{The missing number inside of the irregular figure is: \boxed{\bf9}}\\\large\textbf{because we had to do, 14 - 4, which gives you \underline{10}, then}\\\large\textbf{subtract 10 from another \underline{1}, \& that gives you you 9.}\\\large\textbf{The other missing number at the bottom: \boxed{\bf 7} because it measures}\\\large\textbf{the SAME length as the top number\large\textbf{Lastly, the last missing}}\\\large\textbf{number is \boxed{\bf4}.}[/tex]

[tex]\large\textbf{Now, let's solve for your perimeter of this irregular figure, }\\\large\textbf{shall we?}[/tex]

[tex]\large\textbf{14m + 9m + 7m + 7m + 4m +4m + 4m + 1m}[/tex]

[tex]\large\textbf{= 23m + 7m + 7m + 4m + 4m + 4m + 1m}[/tex]

[tex]\large\textbf{= 30m + 7m + 4m + 4m + 4m + 1m}[/tex]

[tex]\large\textbf{= 37m + 4m + 4m + 4m + 1m}[/tex]

[tex]\large\textbf{= 41m + 4m + 4m + 1m}[/tex]

[tex]\large\textbf{= 45m + 4m + 1m}[/tex]

[tex]\large\textbf{= 49m + 1m}[/tex]

[tex]\large\textbf{= 50m}[/tex]

[tex]\huge\textbf{Therefore, your answer is: \boxed{\mathsf{\mathsf{50m}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Let x be a multiple of 7

Three consecutive multiples of 7 are

[tex] \\ \large\blue\longrightarrow\rm \large \:x \: + \: (x \: + \: 7) + (x \: + \: 14) \: = \: 693[/tex]

[tex] \large\blue\longrightarrow \rm \large \:3x \: + \: 21 \: = \: 693[/tex]

[tex] \large\blue\longrightarrow \rm \large \:3x \: = \: 693 \: - \: 21[/tex]

[tex] \large\blue\longrightarrow \rm \large \:3x \: = \: 672[/tex]

Dividing both sides by 3 , we have

[tex]\large\blue\longrightarrow \rm \large \: \frac{3x}{3} \: = \: \frac{672}{3} \\ [/tex]

[tex]\large\blue\longrightarrow \rm \large \: \ \: \frac{ \cancel3x}{ \cancel3} \: = \: \frac{ \cancel{672} \: \: ^{ \red{224}} }{ \cancel3} \\ [/tex]

[tex]\large\blue\longrightarrow \rm \large \:x \: = \: 224 \\[/tex]

Three consecutive multiples of 7 are

The true statements are:

The lines are given as:

Lines mn, pq, mp, mn, nq and pq

From the question, the lines are either parallel lines or perpendicular lines

As a general rule,

Parallel lines have equal slope

This means that:

Lines mn and pq have the same slope

Assume two perpendicular lines have slopes m and n.

The relationship between their slopes is:

m * n = -1

This means that:

The product of the slopes of perpendicular lines mn and mp is -1

Hence, the true statements are (a) and (c)

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Complete question

Line mn is parallel to line pq, mp is perpendicular to mn, and nq is perpendicular to pq. consider each statement and determine whether it is true or false. circle the correct answer.

Pptions:

Answer:

Step-by-step explanation:

Ok so you are given the values of the slope-intercept form with m being the slope and b being the y-intercept. So since b is equal to -1 you want to plot a point at (0, -1) since that is the y-intercept (when x = 0). The next thing you want to do is look at the slope, which is essentially saying each time x increases by 5 the y-value decreases by 4 or in other words rise/run which is negative which is why you're going down. So from the point (0, -1) go forward 5 units and go down 4 units which should lead you to (5, -5) and the third point you can plot is by going backwards instead of forwards. So instead of every time x increases by 5 y decreases by 4 you're going to do the inverse. Every time x decreases by 5, y is going to increase by 4. So by doing this from the y-intercept (0, -1) you should go backwards 5 units and up 4 units which should lead you to (-5, 3). And then now just draw a line that goes through all those three points. Hope that helps :)

One possible answer is 120°

Answer:

While identity is true for all values of x, an equation may be true only for some values of x, or for no values of x. Examples: 2x + 6 = 4 is true when x = -1, but not when x = 0. The equation x + 5 = x is never true because a number is never equal to five more than itself.

Step-by-step explanation:

I hope this helps

The correct option of the function is C. (f+g)(x)= 6x^3 - 2x^2 + 4x - 8.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

f(x)= 3x^2 + 4x - 6

g(x)= 6x^3 - 5x^2 - 2

So,

(f + g)(x) = (3x^2 + 4x - 6) + (6x^3 - 5x^2 -2)

(f + g)(x) = 3x^2 + 4x - 6 + 6x^3 - 5x^2 - 2

Now, like terms and in order of exponent

(f + g)(x) = 6x^3 - 2x^2 + 4x - 8

Therefore, the correct option is C. (f+g)(x)= 6x^3 - 2x^2 + 4x - 8.

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Step-by-step explanation:

Given :

1- cosA = 1/2

or, CosA = 1 -1/2

Therefore ; CosA = 1/2 = b/h

According to the Pythagoras theorem,

P = root under h^2 - b^2

= root under (2)^2 - (1)^2

= root under 4 -1

= root 3

Again,

SinA = P/h

= root 3 / 2

Answer:

x=5

\

Step-by-step explanation:

Answer:

x = 0

Step-by-step explanation:

Line segment UV and line segment VW together form line segment UW.

UV + VW = UW

(5 + x) + (6) = (2x + 11)

5 + x + 6 = 2x + 11

x + 11 = 2x + 11

x + 11 - 11 = 2x + 11 - 11

x = 2x

x - x = 2x - x

0 = x

You can also verify the result by substituting x with our result 0.

5 + x + 6 = 2x + 11

5 + (0) + 6 = 2(0) + 11

11 + 0 = 0 + 11

11 = 11

Left side of the equation is the same as the right side of the equation, therefore the result x = 0 is correct.

Answer: [tex]\angle STU=34^{\circ}, \angle TVW=116^{\circ}[/tex]

Step-by-step explanation:

By the alternate interior angles theorem,

[tex]3x+4=2x+14\\\\x+4=14\\\\x=10\\\\\implies \angle STU=3(10)+4=\boxed{34^{\circ}}[/tex]

By the alternate interior angles theorem, [tex]\angle UTV=82^{\circ}[/tex], and we also know that [tex]\angle TUV=34^{\circ}[/tex].

Thus, by the exterior angle theorem,

[tex]\angle TVW=82+34=\boxed{116^{\circ}}[/tex]

The equation that represents this number sentence is 1/5n - 3 = 28

Let the unknown number be "n". One-fifth of a number is expressed as 1/5n

Three less than one-fifth of a number is expressed as 1/5n - 3

Finally, if three less than one-fifth of a number is equal to 28, then the final expression will be 1/5n - 3 = 28

The equation that represents this number sentence is 1/5n - 3 = 28

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Answer:

450 N

Step-by-step explanation:

Since you have the VOLUME and the HEIGHT of the prism, you can calculate the AREA of the prism base :

 18 m^3 / 3 m =   6 m^2    area

Now you are given  pressure = force / area

                                      75 n/m^2 =  force / 6 m^2

        6 *75 = force = 450 N

Answer:

450 newtons

Step-by-step explanation:

To solve for the force, we first need to find the area. (Force = Pressure × Area)

[tex]Area = \frac{volume}{height} = \frac{18m^{3} }{3m} = 6m^{2}[/tex]

Now we just substitute this number into [tex]Force = Pressure * Area[/tex] and get that [tex]Force = 75newtons/m^{2} * 6m^{2} = 450 newtons[/tex]

(p.s. Units are very important! This question doesn't require any unit

conversions, but others might.)

The respective missing proofs are; Alternate interior; Transitive property; Converse alternate interior angles theore

We are given that;

∠T ≅ ∠V and ST || UV

From images seen online, the first missing proof is Alternate Interior angles because they are formed when a transversal intersects two coplanar lines.

The second missing proof is Transitive property because angles are congruent to the same angle.

The last missing proof is  Converse alternate interior angles theorem

because two lines are intersected by a transversal forming congruent alternate interior angles, then the lines are parallel.

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Answer:

Given: ∠T ≅ ∠V; ST || UV

Prove: TU || VW

4 connected lines are shown. A line from point S goes slightly down and to the left to point T to form S T. A line from point T goes slightly down and to the right to point U to form T U. A line from point U goes slightly down and to the left to point V to form U T. A line goes slightly down and to the right to point W to form point W.

Complete the two-column proof.

♣ =

✔ alternate interior angles theorem

♦ =

✔ transitive property

♠ =

✔ converse alternate interior angles theorem

Step-by-step explanation:

The function is h(t) =  7/4 cos π/3 t + 9/4,

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

As, h(t) =  x cos π/3 t +y

when t= 0, h(t) = 4

when t= 3, h(t) = 0.5

So,

x cos π/3 *0 +y=4

x cos π/3 *3 +y=0.5

and, x+ y = 4,   -x+ y =0.5

Now,

2y= 4.5

y= 9/4

and, x= 4-9/4= 7/4.

Hence, h(t) =  7/4 cos π/3 t + 9/4

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Answer:got it right

h(t)=1.75, cos(1/3), + 2.25

Step-by-step explanation:

Answer:

[tex]x^{-\frac{2}{7} }[/tex]

Step-by-step explanation:

→ Add the powers together

[tex]x^{\frac{3}{7} {-\frac{5}{7} }[/tex]

→ Simplify

[tex]x^{-\frac{2}{7} }[/tex]