Solve the system of equations algebraically and create a graphical model.
[tex]3x + 2y = 8 \\ x + 2y = 4[/tex]

The amount that was invested are at 3% = 400000, at 4% = 500000 and at 2% = 100000

We have x + y + z = 1000000

((1+0.03)x - x)+ ((1+0.04)y - y) + ((1 + 0.02)z-z) = 34000

4z + x + z = 1000000

((1+0.03)4z - 4z)+ ((1+0.04)y - y) + ((1 + 0.02)z-z) = 34000

((1+0.03)4z - 1)+ ((1+0.04)y - 1) + ((1 + 0.02)z-1) = 34000

12/100z + 4/100y +2/100z = 34000

2y + 7z = 1700000

-2y - 10z = -2000000

2y + 7z = 1700000

Solve through the use of the simultaneous linear equation

z = 100000

y = 500000

x = 400000

The amount that was invested are at 3% = 400000, at 4% = 500000 and at 2% = 100000

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Answer:F to the power of 2,N to the power of 2,—25,f to the power of 2

Step-by-step explanation: i really hope under stand

The possible formula for the polynomial in discuss whose roots are described as; having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is; P(x) = x^5 -5x⁴-6x³+18x².

The polynomial which is as described in the task content whose roots are as given can be written in its factorised form as follows;

P(x) = (x-3) (x-3) (x) (x) (x+1)

The expanded form is therefore;

P(x) = x^5 - 5x⁴- 6x³+ 18x².

Therefore, the polynomial having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is P(x) = x^5 - 5x⁴- 6x³+ 18x².

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Use the quotient and chain rules. If

[tex]y = \dfrac{\cos(2x)}{\tan(2x)}[/tex]

then the derivative is

[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) \frac d{dx}\cos(2x) - \cos(2x) \frac d{dx}\tan(2x)}{\tan^2(2x)}[/tex]

[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) (-\sin(2x)) \frac d{dx}(2x) - \cos(2x)\sec^2(2x) \frac d{dx}(2x)}{\tan^2(2x)}[/tex]

[tex]\dfrac{dy}{dx} = \dfrac{-2\sin(2x)\tan(2x) - 2 \sec(2x) }{\tan^2(2x)}[/tex]

and we can rewrite this by

• multiplying by [tex]\frac{\cos^2(2x)}{\cos^2(2x)}[/tex],

[tex]\dfrac{dy}{dx} = \dfrac{-2\sin^2(2x)\cos(2x) - 2 \cos(2x) }{\sin^2(2x)}[/tex]

• factorizing,

[tex]\dfrac{dy}{dx} = -\dfrac{2\cos(2x) \left(\sin^2(2x) + 1\right)}{\sin^2(2x)}[/tex]

etc

Answer:

6t tomato plants

Step-by-step explanation:

There are 6 rows, Tamala places t in each row. We multiply 6 by t.

If t were 5, the tomato plants would be 30 since we multiply the rows by the number of tomato plants

Answer:

6t

Step-by-step explanation:

number of rows × number of plants per row = total number of plants

6 × t = 6t

Answer: 6t

The function notation form of the given equation; y = -3x +3 as in the task content is; f(x) = -3(x) +3.

According to the task content, the equation given; y = -3x +3 is to be written in function notation.

Consequently, since the function expression given is linear in variable X, it follows that the required function notation is;

f(x) = -3x +3.

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Answer:

f(y-2)+f(4-y)=4

Step-by-step explanation:

Assume (let) x=y-2

So: y=x+2

f(y-2)+f(4-y)=f(x)+f(-x+2)=f(x)+f(2-x)

The value of that expression is 4 from the given.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

For two lines to be parallel, there should be angles that follow some specific properties that is usually observed with parallel lines.

We can clearly see that :

[tex] \qquad❖ \: \sf \: \angle7 \cong \angle16[/tex]

( by Alternate interior angle pair )

[tex] \qquad \large \sf {Conclusion} : [/tex]

Lines l and m are parallel to each other.

Answer:

12

Step-by-step explanation:

Here is what you have defined:

(36+ (18 x 6) ÷ 12

(36 + 108) / 12

144/12

12

The answer is -3.

If m = 4 and n = -7, we can evaluate the expression by substitution.

m + n

4 + (-7)

-3

❄ H there,

evaluate this expression by substituting the provided parameters –

[tex]\sf{m+n} \ | \ m=4 \ \& \ n=-7 \ | 4+(-7)=4-7=-3}[/tex]

That's it!

❄

Answer:

The Malaysia police departments statement was true, because 14/30 is extremely close to 54% (roughly 15.5/30).

Type: Probability

[tex]s(t) = 17699(1 .066) {}^{t} [/tex]

[tex]s(1) = 17699(1.066) = 18867.13 \\ s(2) = 17699(1.066) {}^{2} = 20112.36 \\ s(5) = 17699(1.066) {}^{5} = 24363.22 \\ s(10) = 17699(1.066) {}^{10} = 33536.73[/tex]

[tex]s(t) = 2 \times initial \: capital \: \\ s(t) = 2 \times 17699[/tex]

[tex]17699(1.066) {}^{t} = 2 (17699) \\ 1.066 {}^{t} = 2 \\ t = log¹°⁰⁶⁶(2) = 10.84511 \: years[/tex]

4. Compute the derivative.

[tex]y = 2x^2 - x - 1 \implies \dfrac{dy}{dx} = 4x - 1[/tex]

Find when the gradient is 7.

[tex]4x - 1 = 7 \implies 4x = 8 \implies x = 2[/tex]

Evaluate [tex]y[/tex] at this point.

[tex]y = 2\cdot2^2-2-1 = 5[/tex]

The point we want is then (2, 5).

5. The curve crosses the [tex]x[/tex]-axis when [tex]y=0[/tex]. We have

[tex]y = \dfrac{x - 4}x = 1 - \dfrac4x = 0 \implies \dfrac4x = 1 \implies x = 4[/tex]

Compute the derivative.

[tex]y = 1 - \dfrac4x \implies \dfrac{dy}{dx} = -\dfrac4{x^2}[/tex]

At the point we want, the gradient is

[tex]\dfrac{dy}{dx}\bigg|_{x=4} = -\dfrac4{4^2} = \boxed{-\dfrac14}[/tex]

6. The curve crosses the [tex]y[/tex]-axis when [tex]x=0[/tex]. Compute the derivative.

[tex]\dfrac{dy}{dx} = 3x^2 - 4x + 5[/tex]

When [tex]x=0[/tex], the gradient is

[tex]\dfrac{dy}{dx}\bigg|_{x=0} = 3\cdot0^2 - 4\cdot0 + 5 = \boxed{5}[/tex]

7. Set [tex]y=5[/tex] and solve for [tex]x[/tex]. The curve and line meet when

[tex]5 = 2x^2 + 7x - 4 \implies 2x^2 + 7x - 9 = (x - 1)(2x+9) = 0 \implies x=1 \text{ or } x = -\dfrac92[/tex]

Compute the derivative (for the curve) and evaluate it at these [tex]x[/tex] values.

[tex]\dfrac{dy}{dx} = 4x + 7[/tex]

[tex]\dfrac{dy}{dx}\bigg|_{x=1} = 4\cdot1+7 = \boxed{11}[/tex]

[tex]\dfrac{dy}{dx}\bigg|_{x=-9/2} = 4\cdot\left(-\dfrac92\right)+7=\boxed{-11}[/tex]

8. Compute the derivative.

[tex]y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b[/tex]

The gradient is 8 when [tex]x=2[/tex], so

[tex]2a\cdot2 + b = 8 \implies 4a + b = 8[/tex]

and the gradient is -10 when [tex]x=-1[/tex], so

[tex]2a\cdot(-1) + b = -10 \implies -2a + b = -10[/tex]

Solve for [tex]a[/tex] and [tex]b[/tex]. Eliminating [tex]b[/tex], we have

[tex](4a + b) - (-2a + b) = 8 - (-10) \implies 6a = 18 \implies \boxed{a=3}[/tex]

so that

[tex]4\cdot3+b = 8 \implies 12 + b = 8 \implies \boxed{b = -4}[/tex].

A statement correctly compares functions f and g is that: C. they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.

A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).

In Mathematics, there are different types of functions and these include the following;

Function g is represented by the following table and a line representing these data is plotted in the graph that is shown in the image attached below.

x          -1   0   1    2   3   4

g(x)     24  6   0  -2  

Based on the line, we can logically deduce the following points:

This ultimately implies that, a statement correctly compares functions f and g is that both functions have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.

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Answer:

  1.6 times   or   60% more than

Step-by-step explanation:

The question seems to be asking about the growth factor in the given exponential function.

A generic exponential function will have the form ...

  quantity = (initial value) × (growth factor)^(number of intervals)

Comparing this form to the given formula ...

  f(x) = 58 × 1.6^x

we see the "growth factor" is 1.6. This is the multiplier from one interval (year) to the next.

Each year the expected number of birds is 1.6 times the number the year before.

__

Additional comment

A growth factor is sometimes expressed in terms of a growth rate, usually a percentage.

  growth factor = 1 + growth rate

  1.6 = 1 + 0.60 = 1 + 60%

The growth rate of this bird population is 60% per year. Each year, the population is 60% more than the year before.

Answer: 1.6

Step-by-step explanation:

The correct option regarding the domain and the range of the function f(x)=[tex]a^{x+g} +k[/tex] is given by that the domain is (-∞,∞) and the range of the function is (k,∞).

Given a function f(x)=[tex]a^{x+g} +k[/tex].

We are told to find the domain and range of the function.

The domain is basically the values which we enters in a function.

The range is basically the values which we are getting by entering some values in the function.

An exponential function is given in the function which has no restrictions hence the domain is  (-∞,∞).The range depends on the vertical shift given by k. Hence the range of function is (k,∞).

Hence the correct option regarding the domain and the range of the function f(x)=[tex]a^{x+g} +k[/tex] is given by that the domain is (-∞,∞) and the range of the function is (k,∞).

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The equation of the line passing through the point (-5, -7) with a slope of 2/5 is y = (2/5)x - 5.

To find the equation of a line, we can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁),

where (x₁, y₁) is the given point on the line and m is the slope.

In this case, the given point is (-5, -7) and the slope is 2/5. Substituting these values into the equation, we have:

y - (-7) = (2/5)(x - (-5)).

Simplifying further:

y + 7 = (2/5)(x + 5).

Distributing the 2/5:

y + 7 = (2/5)x + 2.

Subtracting 7 from both sides:

y = (2/5)x - 5.

Therefore, the equation of the line passing through the point (-5, -7) with a slope of 2/5 is y = (2/5)x - 5.

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Answer:

C

Step-by-step explanation:

This is a translation 5 units left and 5 units dowh.

Here, the translation is [tex]T < 5,-5 >[/tex].

Here, the translation is given as: [tex]y=2(x-5)+5\longrightarrow y=2(x-0)+0[/tex].

i.e. [tex]y=2(x-5)+5\longrightarrow y=2(x-5+5)+(5-5)[/tex].

So, the graph of [tex]y[/tex] moves 5 units to the right and (-5) units to the up i.e., 5 units to the down.

Therefore, here, the translation is [tex]T < 5,-5 >[/tex].

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Given that the pieces of steel rods comes in bundles, the mechanist will require 13 bundles of steel rods to get the 98 pieces of steel rod he needs.

Given the data in the question;

To determine the bundle of steel required, let y represent the bundle.

Since;

1 bundle = 8 piece

y bundle = 98 piece

We cross multiply

y bundle × 8 piece = 1 bundle × 98 piece

y = ( 1 bundle × 98 piece ) / ( bundle ×  8 piece  )

y = 98 pieces / 8 piece

y = 12.25 ≈ 13

Given that the pieces of steel rods comes in bundles, the mechanist will require 13 bundles of steel rods to get the 98 pieces of steel rod he needs.

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The shapes that have less than 3 lines of symmetry are Isosceles trapezoid and Isosceles triangle

The shapes are given as:

The lines of symmetry are the lines that, when the shape is rotated through this line, the shape remains the same

As a general rule:

An Isosceles trapezoid and an Isosceles triangle have two lines of symmetry

Hence, the shapes that have less than 3 lines of symmetry are Isosceles trapezoid and Isosceles triangle

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Answer:

an angle bisector

Step-by-step explanation:

This is showing the construction of the bisector of ∠LNM

Answer:

42

Step-by-step explanation:

similar triangles

24/x = (24+8)/x+14

that looks complicated so we do

8/24 = 14/x

or

24/8 = x/14

3 = x/14

x = 3*14

x = 42

we test it with the first equation

24/42 = 32/56

simplify

4/7 = 4/7

true so 42 is correct

Answer:

472.19

Step-by-step explanation:

$472.19 weekly

Thus the required weekly installment is $402.30 for 25 years.

Given,
The family borrowed $400,000 from the bank to purchase a new home.
the bank charges 3.8% interest per year, compounded weekly, it will take 25 years to pay off the loan. How much will each weekly payment to be determined?

Statistics is the study of mathematics that deals with relations between comprehensive data.

The principle amount to refund = 400,000
Let the principle amount for weekly = P
Rate per year = 3.8%
Tenure = 25 year
For weekly installments,
52 Weeks in a year
Tenure = 25/52

Now,
[tex]Amount = P(1-(1+r)^{-tn})/i\\400000 = P (1-(1+0.038/52)^{-25*52}) / (0.038/52)\\400000 * 0.038/52 = P(1-(52.038)^{-25*52})\\292.30 = P(1-(1.001)^{-1300})\\292.30 = P(1-0.273)\\292.30=P * 0.727\\P = 402.30[/tex]

Thus the required weekly installment is $402.30 for 25 years.

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Answer:

2

Step-by-step explanation:

Substitute:

2(1)(3)+2 / 2(1)(3)-2 =

6 + 2 / 6 - 2 =

8 / 4 =

2.

Hey there!

2ab + 2 / 2ab - 2

= 2(1)(3) + 2 / 2(1)(3) - 2

= 2(3) + 2 / 2(3) - 2

= 6 + 2 / 6 - 2

= 8 / 4

= 2

Therefore, your answer should be: 2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The value of  values of t for which the ball's height is 7 meters then is 4.79secs.

Velocity can be regarded as a vector measurement of the rate as well as direction of motion.

It is the the speed at which something moves in one direction and with the given velocity, the time as well as the distance can be calculated as :

Given:

h=2+25t-5t^2

But h=7

Then 2+25t-5t^2=7

-5t^2++25t +2-7=0

-5t^2+25t -5=0

we can then factorize as :

-5(t^2+5t -1)=0

Solving the equation using quadratic formula, the the roots of equations are: 4.79  and -5.0

The value of  values of t for which the ball's height is 7 meters then is 4.79secs.

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COMPLETE QUESTION :

A ball is thrown from an initial height of 2 meters with an initial upward velocity of 25 m/s . The ball's height h (in meters) after t seconds is given by the following. h=2+25t-5t^2

Find all values of t for which the ball's height is 7 meters.

Round your answer(s) to the nearest hundredth.

The odds against selecting a red marble is =2/11

The number of marbles which were red = 9

The number of marbles which were blue = 2

The total amount of marbles in the Box = 11

When one marble is picked at random from the box, the odds against selecting a red marble can be gotten through the blue marble.

That is, the number of blue marble/ total marble

= 2/11

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Step-by-step explanation:

The heaviest legal bowling ball weighs 16 pounds. The lightest weight you can usually find at most bowling alleys is six pounds.

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Answer:

8+8+12+5= 33

Step-by-step explanation:

8+8+12+5=33

In mathematics a linear inequality is an inequality involving a linear function. A linear inequality contains one of the inequality symbols.​< is less than > is greater than ≤ is less than or equal to ≥ is greater than or equal to ≠ is not equal to.

Let's find the critical points of the inequality.

x² − 9x −(−8) = − 8 −(−8) (Subtract -8 from both sides)

(x − 1)(x − 8) = 0 (Factor left side of equation)

x − 1 = 0 or x − 8 = 0 (Set factors equal to 0)

x < 1 (Doesn't work in original inequality)

1 < x < 8 (Works in original inequality)

x > 8 (Doesn't work in original inequality)

The third option is the correct one.

Answer:

The milk would be 60 ml and the topping would be 30 ml

Step-by-step explanation:

If there are 2 parts milk and 1 part toppings that would be a total of 3 (2+1 =3)  So we are looking for 2/3 of 90 and 1/3 of 90.