If $3700 is invested at a rate of 2.4% that is compounded annually, how much will it be worth after 4 years?​

Answer:

tanD =4/7

Step-by-step explanation:

tanD = P/B

Where P=4 and B=7

So;

tanD=4/7

to get the equation of any straight line, we simply need two points off of it, let's use the ones provided in the picture below.

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{-7}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{7}{2}}(x-\stackrel{x_1}{1}) \\\\\\ y-4=-\cfrac{7}{2}x+\cfrac{7}{2}\implies y=-\cfrac{7}{2}x+\cfrac{7}{2}+4\implies y=-\cfrac{7}{2}x+\cfrac{15}{2}[/tex]

The correct statement about the center of both box plots is: the median for Town A, 30° is greater median for Town B, 25°

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile.

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Answer:

C: y = 8x^2 + 10.

Step-by-step explanation:

It looks close to being a parabola so I think it is probably a function in x^2.

Try 8x^2 + 10

Checking against the plot

When x = 5 , y = 8(5)^2 + 10 = 210 , and on graph its 200

Calculating y for other values:

When x = 7, y = 8(7)^2 + 10 = 402, and on graph y =  400.

When x = 11, y = 978 , and on graph  =  1000.

When x = 17, y = 2322, and on graph y = about 2350.

Answer:

(x+5) (x+5)

Step-by-step explanation:

it's just (x+5)^2 twice

The expression E(p) represents the elasticity at point p and by putting the known data we can find the value of elasticity.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a demand function:

q=0. 6(3800-p²)

Differentiate with respect to p:

[tex]\rm \dfrac{dq}{dp} = -1.2p[/tex]

We know the elasticity:

[tex]\rm E(p) = \dfrac{dq}{dp}\times\dfrac{p}{q}[/tex]

[tex]\rm E(p) =-1.2p \times\dfrac{p}{0.6(3800-p^2)}[/tex]

[tex]\rm E(p) = -\dfrac{2p^2}{(3800-p^2)}[/tex]

Here the data for p and q are not given, but we can find any value using the above expression by putting the known data.

Thus, the expression E(p) represents the elasticity at point p and by putting the known data we can find the value of elasticity.

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(-5,6)

Step-by-step explanation:

Step-by-step explanation:

remember a few things :

a × -1 = -a

-a × -1 = a

-1 × -1 = 1

1 × a = a

therefore,

-1 × -1 × a = 1 × a = a

and finally

c × (a + b) = c×a + c×b

so, we can say

(1 - 5) = -1 × -1 × (1 - 5) =

= -1 × (-1×1 + -1×-5) = -1 × (-1 + 5) =

= -1 × (5 - 1) = -(5 - 1)

The ratio of Nathan's nickels to dimes to quarters is 4 : 4 : 17.

Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value(s).

The ratio = 8 : 8 : 34 = 4 : 4 : 17

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im not sure I'd need to see the figure

Answer:

Step-by-step explanation:

V=14h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4aBase sidebBase sidecBase sidehHeight

Step-by-step explanation:

1) x+6 =4

x. =4-6

x. =-2

2) x-(-4) =-6

x+ 4. =-6

x. =-6-4

x. =-10

3)2(x-1)=-200

2x-2 =-200

2x. = -200+2

2x. = -198

x. = -198/2

x. = -99

4)2x+(-3) =-23

2x-3. =-23

2x. =-23+3

2x. =-20

x. =-20/2

x. = -10

Answer:

its the Pentagon, the other shaps have 2 lines if symmetry

The correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle are (6,6√3, 12).

A triangle has three angles of 30-60 and 90 degrees in which the two sides are perpendicular to each other.

The three sides of the triangle will be calculated by applying the Pythagorean theorem:-

The sum of the square sides will be equal to the square of the third side.

For sides  (6,6√3, 12)

12² = 6² + (6√3)²

144 = 36 + (36 x 3)

144 = 36 + 108

144 = 144

Therefore the correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle (6,6√3, 12).

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Answer:

x ≈ 8.7

Step-by-step explanation:

given 2 secants from an external point to the circle, then

the product of the external part of one secant and the entire secant is equal to the product of the external part of the other secant and the entire secant , that is

6(6 + x) = 4(4 + 18) ← distribute parenthesis on both sides

36 + 6x = 4 × 22 = 88 ( subtract 36 from both sides )

6x = 52 (divide both sides by 6 )

x ≈ 8.7 ( to the nearest tenth )

(x+8/3)²+y²=1

(x+8/3)²+y²+0²+2×0y=1

(x+8/3)²+(y+0)²=(V1)²

->center: C(8/3,0)

-> radius: V1

Answer:

28 students

Step-by-step explanation:

7 times 4 = 28

there are are seven students in 4 teams, so that means there are 4 groups of seven, and you multiply them together to get how many students in the class

Answer:

28

Keyword(s):

divided, four, 7, per team, how many

Step-by-step explanation:

7 × 4 = 28

Answer:9

Step-by-step explanation:

Use the pythagorean theorem. [tex]a^{2}+b^{2}=c^{2}[/tex]

We know both a and c, so it becomes

[tex]4^{2}+b^{2}=\sqrt{97}^{2}[/tex]=

16+b^2=97=

97-16=b^2=

81=b^2=

9=b

Deductive Reasoning is the practice of arriving at a mathematical conclusion by simply analyzing the facts using the knowledge of the related concepts.

Looing at ΔOAB and ΔOEF

It is clear that

OB = OF (O is the midpoint)

∠OBA = ∠OFE = 90°

Therefore

∠AOB = ∠EOF (Vertically Opposite Angles)

⇒ ΔOAB ≅ ΔOEF and

∠ A ≅ ∠E.

QED

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Answer:

The quadratic equation 3x² - 12x + 9 = 0 has two real roots when solved:

x₁ = 1 and x₂ = 3

Step-by-step explanation:

✍ An equation of type ax² + bx + c = 0, can be solved, for example, using the quadratic formula:

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

either

[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{\Delta} }{2a} }[/tex]

where

[tex]\bf{\Delta=b^{2}-4ac }[/tex]

Identify the coefficients

a = 3, b = -12 and c = 9

Calculate the discriminant value

Δ = b² - 4ac

Δ = (-12)² - 4.3.9 = 144 - 12.9

Δ = 144 - 108 = 36

Enter the values of a, b and the discriminant value in the quadratic formula

[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{\Delta } }{2a} }[/tex]

[tex]\boldsymbol{x=\dfrac{-(-12\pm\sqrt{36} }{2\cdot3 } }[/tex]

[tex]\boldsymbol{x=\dfrac{(12\pm\sqrt{36} }{6 } \ ==== > \ (Solution \ general) }[/tex]

As we can see above, the discriminant (Δ) of this equation is positive (Δ> 0) which means that there are two real roots (two solutions), x₁ and x₂.

[tex]\boldsymbol{x_{1}=\dfrac{-12-\sqrt{36} }{6}=\dfrac{12-6}{6}=\dfrac{6}{6}=1 \ === > (First \ solution) }[/tex]

To find x₁, just choose the positive sign before the square root. Later,

[tex]\boldsymbol{x_{1}=\dfrac{12+\sqrt{36} }{6}=\dfrac{12+6}{6}=\dfrac{18}{6}=3 \ === > (Second \ solution) }[/tex]

The recorded angle measurements of ∠BAC and ∠CAD could be 110° and 70°, vice versa.

Supplementary angles are a pair of angles that always sum up to 180°. These angles can either;

Adjacent supplementary are angles with a common vertex and arm.

Non- adjacent supplementary angles are angles without a common vertex or arm.

∠BAC and ∠CAD are adjacent supplementary angles because they have a common vertex, A, and a common arm AC.

They add up to 180°.

∠ BAC = 110° and ∠CAD = 70°

Hence, the angles could be 110° and 70°.

Note, this is an overview as the question is not complete.

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Answer: When the two angles are supplementary, m∠BAC = m∠CAD = 90° and m∠DAB = 180°.

Step-by-step explanation: Edmentum Answer

Answer:

Area of Circle  = 346.5 cm².

Area of square = 272.25 cm ² .

Step-by-step explanation:

So , 2πR = 66

2 × 22 / 7 × R = 66

R comes out is 21/2 cm .

Area of Circle = 22/7 × 21/2 × 21/2 = 33×21/2

= 693 / 2 = 346.5 cm².

If bent into the shape of a square ;

4 a = 66

a = 33/2 . ( Side of a square )

Area of square = a ² = 33×33/4 = 1089/4

= 272.25 cm ² .

Using a dot plot, it is found that the number of dots of each point are given as follows:

The dot plot shows the number of times each measure appears in the data-set.

In this problem, one measure has a value of 1/8, hence:

The value [tex]\frac{1}{8}[/tex] will have one dot above it.

Two measures have a value of 1/4, hence:

The value [tex]\frac{1}{4}[/tex] will have two dots above it.

Three measures have a value of 3/8, hence:

The value [tex]\frac{3}{8}[/tex] will have three dots above it.

Five measures have a value of 1/2, hence:

The value [tex]\frac{1}{2}[/tex] will have five dots above it.

Two measures have a value of 5/8, hence:

The value [tex]\frac{5}{8}[/tex] will have two dots above it.

Three measures have a value of 3/4, hence:

The value [tex]\frac{3}{4}[/tex] will have three dots above it.

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Answer:

1 2 3 5 2 3

Step-by-step explanation:

Answer: y - 17 = -2(x-7)

Step-by-step explanation:

point-slope form: y - y1 = m(x - x1)

m = y2-y1/x2-x1

   = 9+17/-6-7

   = 26/-13

   = -2

y1 = -17

x1 = 7

y - 17 = -2(x-7)

The equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y =  -2x - 3

The general equation of a straight line is-

y = mx + c

where, m is the gradient and is given by y₂ - y₁/x₂ - x₁

and, c is the value where the line cuts y-axis.

Now it is given that the line passes through points (−6,9) and (7,−17)

Therefore we have,

x₁ = -6, y₁ = 9, x₂ = 7, y₂ = -17

So, the slope m of the line is given as,

m = (y₂ - y₁)/(x₂ - x₁)

Put the values,

m = (-17 - 9)/(7 - (-6))

m = -26/7+6

m = -26/13

m = -2

Thus, the equation parallel to the line will be given as:

y - y₁ =  m(x - x₁)

y - 9 =  -2{x - (-6)}

y - 9 =  -2(x + 6)

y =  -2x - 12 + 9

y =  -2x - 3

Thus, the equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y =  -2x - 3

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[tex]x^2-x-42=0\\x^2+6x-7x-42=0\\x(x+6)-7(x+6)=0\\(x-7)(x+6)=0\\x=7 \vee x=-6[/tex]

Answer:

The roots are 7 and -6.

Keys:

When you see a ± in a quadratic equation, you will have multiple solutions; more than one.

Step-by-step explanation:

solve the main expression

[tex]x^2-x-42=0\\x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-42\right)}}{2\cdot \:1}\\\rightarrow \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-42\right)}\\=\sqrt{\left(-1\right)^2+4\cdot \:1\cdot \:42}\\\rightarrow \left(-1\right)^2\\=1^2\\=1\\\rightarrow 4\cdot \:1\cdot \:42\\=168\\=\sqrt{1+168}\\=\sqrt{169}\\=\sqrt{13^2}\\=13\\x_{1,\:2}=\frac{-\left(-1\right)\pm \:13}{2\cdot \:1}[/tex]

solve for x₁

[tex]\frac{-\left(-1\right)+13}{2\cdot \:1}\\=\frac{1+13}{2\cdot \:1}\\=\frac{14}{2\cdot \:1}\\=\frac{14}{2}\\=7[/tex]

solve for x₂

[tex]\frac{-\left(-1\right)-13}{2\cdot \:1}\\=\frac{1-13}{2\cdot \:1}\\=\frac{-12}{2\cdot \:1}\\=\frac{-12}{2}\\=-\frac{12}{2}\\=-6[/tex]

Answer:

y=15 is the answers for the question

Step-by-step explanation:

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