solve the system by substitution and show all work:


2.5x-3y=-13

3.25x-y=-14

Answer:

Let x represents the number of apple tree and y represents the number of pear tree and z represents the number of cherry tree in an orchard.

From the given statement: The number of apple trees is 8 more than twice the number of pear trees.

⇒ [tex]x = 2y + 8[/tex]                         .....[1]

Also, It is given that the number of cherry and pear trees combined is 11 more than the number of apple trees.

⇒[tex]y + z = x + 11[/tex]                    ......[2]

The farmer plants 143 trees total.

⇒[tex]x +y +z =143[/tex]                        .....[3]

Substitute equation [2] into [3] we get;

[tex]x + x + 11 = 143[/tex]

Combine like terms;

[tex]2x +11 = 143[/tex]

Subtract 11 on both sides we get;

2x + 11 -11 =143 -11

Simplify:

2x = 132

Divide both sides by 2 we get;

x = 66

Substitute the value of x in equation [1];

66 = 2y + 8

Subtract 8 on both sides we get;

[tex]66 -8 =2y + 8 -8[/tex]

Simplify:

58 = 2y

Divide by 2 on both sides we get;

y = 29

Substitute the value of x and y in equation [3];

we have;

29 + 66 + z = 143

95 + z =143

Subtract 95 on both sides, we get;

95+ z -95 = 143- 95

Simplify:

z = 48

The framer plant in the orchard =  66 apple trees , 29 pear trees and 48 cherry trees

Answer:

B

Step-by-step explanation:

The measurement representing the largest volume among the options is D) 1.02 L, as it is larger than .99 L, 0.999 L and 0.998 L, which are the rest of the options converted into the same unit (liters).

In order to determine which of these measurements represents the largest volume, we need to make sure we're comparing them using the same units of measure. So, we'll convert everything to liters (L), as this is the most common unit among the options.

First of all, A) 999 milliliters (mL) is equal to 0.999 Liters (L) because 1 L = 1000 mL. B) .99L is just .99L. For C) 998 cubic centimeters (cm³), we need to know that 1 cm³ is equal to 1 mL, so 998 cm³ equals 0.998 L. Finally, D) 1.02 L is already in liters.

Looking at these conversions, D) 1.02 L represents the largest volume among the given choices.

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Angle G and Angle F are the same, which means that HF = GH

This means that x = 15

Answer:x=15

Step-by-step explanation:

Answer:

The combined speeds of the trains equals 800 miles per 4 hours or

200 miles per hour.

This averages out to 100 miles per hour for each train.  

Westbound train is 18 mph faster so  

109 mph = Westbound

91  mph = Eastbound

That seems to be right except trains speeds of 91 mph and 109 mph seem to be VERY fast.

Step-by-step explanation:

Answer:

13.863 years

Step-by-step explanation:

Initial deposit is $2,000.

The rate of interest is 5% compounded continuously.

The account balance of the savings account after t years by an exponential function:  

A(t) = $2,000 ∙ e^0.05t.

It says to find out the time when it takes for the initial deposit to double, i.e. A(t) = $4,000

Mathematically, we can set them equal and solve for t as follows:-

A(t) = $2,000 ∙ e^0.05t = $4,000.

e^(0.05t) = 4000/2000 = 2

0.05t Ln(e) = Ln(2)

t/20 = Ln(2)

t = 20 * Ln(2) = 13.86294361

So, it takes 13.863 years for the initial deposit to double.

Answer:

hope it hepls

Step-by-step explanation:

The factored form of the expression 18x - 498 when 18 is factored out is 'x - 27.67'

To factor out 18 from 18x-498, you divide each term in the expression by 18. That would look like this: 18x / 18 - 498 / 18. This simplifies to x - 27.67.

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To factor 18 out of 18x - 498, divide each term by 18. The factored form is 18(x - 27.67).

Factoring in mathematics involves breaking down an algebraic expression into its constituent factors.  Factoring is crucial for solving equations, simplifying expressions, and understanding the underlying structure of mathematical relationships.

To factor 18 out of 18x - 498, divide each term by 18:

18x / 18 = x

498 / 18 = 27.67

So, the factored form is: 18(x - 27.67)

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Answer:

The width is 32 inches

Step-by-step explanation:

Answer:

A geologist had to rocks on a scale that weighed 3.3 kg together the first rock was 0.3 of the total weight how much did each Rock weigh?

First thing you have to do is take 3.3 and multiply it by 0.3, that gives you 0.99. And just take the 0.99 and subtract 3.3 by 0.99. that gives you your ANSWER(2.31 kg) Hope that helps!

Step-by-step explanation:

To solve the problem, we first find the weight of the first rock by multiplying the total weight of the rocks by 0.3, then subtract the weight of the first rock from the total weight to find the weight of the second rock. The first rock weighs 0.99 kg and the second rock weighs 2.31 kg.

The problem involves understanding proportions since the first rock weighs 0.3 of the total weight. First, let us find the weight of the first rock. Multiply the total weight of the rocks, which is 3.3 kg, by 0.3 to find the weight of the first rock. That is 3.3 kg * 0.3 = 0.99 kg.

Next, subtract the weight of the first rock from the total weight to find the weight of the second rock. That is 3.3 kg - 0.99 kg = 2.31 kg. So, the first rock weighs 0.99 kg while the second rock weighs 2.31 kg.

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Answer:

First question answer: The limit is 69

Second question answer: The limit is 5

Step-by-step explanation:

For the first limit, plug in [tex]x=8[/tex] in the expression [tex](9x-3)[/tex], that's the answer for linear equations and limits.

So we have:

[tex]9x-3\\9(8)-3\\72-3\\69[/tex]

The answer is 69

For the second limit, if we do same thing as the first, we will get division by 0. Also indeterminate form, 0 divided by 0. Thus we would think that the limit does not exist. But if we do some algebra, we can easily simplify it and thus plug in the value [tex]x=1[/tex] into the simplified expression to get the correct answer. Shown below:

[tex]\frac{x^2+8x-9}{x^2-1}\\\frac{(x+9)(x-1)}{(x-1)(x+1)}\\\frac{x+9}{x+1}[/tex]

Now putting 1 in [tex]x[/tex] gives us the limit:

[tex]\frac{x+9}{x+1}\\\frac{1+9}{1+1}=\frac{10}{2}=5[/tex]

So the answer is 5

Answer:

105

Step-by-step explanation:

first, the printer print 15  (75/5) pages per minutes,

next, 7×15=105

Answer:

24

Step-by-step explanation:

39-5= 34, 34-5= 29, 29-5= 24

Answer:

3rd to last? 29

Step-by-step explanation:

Answer:

10.  1 right 2 acute 0 obtuse angles

11.   x=6

Step-by-step explanation:

10.  A triangle has 3 angles.

If it is a right triangle is has 1 right angle which is 90 degrees.

90 + x+y = 180  where x and y are the other 2 angles

Subtract 90 from both sides

x+y = 90

So the 2 angles that are left can only add to 90.

An obtuse angle is greater than 90 degrees, so we cannot have an obtuse angle.  Acute angles are less than 90 degrees.

A right angle is 90 degrees.  If one of the angles left is 90 degrees, the other one is zero, and that does not make a triangle.

So we must have 1 right angle and 2 acute angles  (no obtuse angles)

11.  Since the 2 sides are the same the triangle is isosceles.  That means the two angles have the same measurements.

90 + y+y = 180

y+y=90

2y = 90

y = 45

Each angle must equal 45 degrees

7x+3 = 45 degrees

Subtract 3 from each side

7x+3-3 =45-3

7x =42

Divide each side by 7

7x/7 =42/7

x =6

Answer:

(179.10 * 0.035) =6.2685    185.3685 = $196.32

Step-by-step explanation:

First we add 3.5% to the total.

Second we see that the total is over $125.01 thus we add another 10.95 and get 196.3185, rounded to 196.32

Answer:

Option C., $196.32 is the answer.

Step-by-step explanation:

Millicent filled out an order, worth of items = $179.10

The sales tax on that item = [tex]3\frac{1}{2}[/tex]% = 3.5%

total price of the item = 179.10 + ( 3.5% of 179.10)

179.10 + (0.035 × 179.10)

179.10 + 6.2685 = $185.3685 ≈ $185.37

Shipping and handling charges up to $125.01 and above is $10.95

Total price + shipping = 185.37 + 10.95 = $196.32

The total amount of her order is $196.32

for an experiment you need to dissolve 0.05 moles of NaCl in one liter of water. how much NaCl must you weigh out?

2.9 i just took the test

To find the amount of NaCl required, multiply the number of moles by the molar mass of NaCl. Hence, you need approximately 2.922 g of NaCl to get 0.05 moles.

To find out how much NaCl you would need to weigh out, we need to convert moles to grams using the molar mass of NaCl. Knowing that the molar mass of NaCl is 58.44 g/mol, we could get the mass by multiplying the number of moles by the molar mass.

So, it would be 0.05 moles * 58.44 g/mol = 2.922 g of NaCl. You would need to weigh out approximately 2.922 grams of NaCl (assuming precision up to three decimal places) to get the required 0.05 moles needed for the experiment.

This is a typical example of applying concepts of molality and molarity in chemical solutions, where you need to accurately determine the amount of solute to use to achieve a precise molar concentration.

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Answer:

A

Step-by-step explanation:

To find the number of real roots for a quadratic, we apply the discriminate. The discriminate is the inside portion of the square root from the quadratic formula.

a. [tex]x^2-6x+12=0[/tex] where a=1, b=-6, and c=12

    [tex]b^2-4ac=(-6)^2-4(1)(12)=36-48=-12<0)[/tex] has no real roots

b. [tex]x^2-25=0[/tex] where a=1, b=0, and c=-25

    [tex]b^2-4ac=(0)^2-4(1)(-25)=0+100=100>0)[/tex] has 2 real roots

c. [tex]x^2+11x=0[/tex] where a=1, b=11, and c=0

    [tex]b^2-4ac=(11)^2-4(1)(0)=121-0=-121>0)[/tex] has 2 real roots

d. [tex]x^2+12x+11=0[/tex] where a=1, b=12, and c=11

    [tex]b^2-4ac=(12)^2-4(1)(11)=144-44=100>0)[/tex] has 2 real roots

Answer:

False

Step-by-step explanation:

If the value is a root of the polynomial, then the remainder will be 0. This means that the root as a factor will multiply to make the polynomial.

Answer: A and B

pi/3 and 2pi/3

=========================================

Work Shown:

2*sin(x) - sqrt(3) = 0

2sin(x) = sqrt(3)

sin(x) = sqrt(3)/2

Using the unit circle, we see that sin(theta) is equal to sqrt(3)/2 when theta is theta = pi/3 in quadrant I, and when theta = 2pi/3 in quadrant II.

So sin(pi/3) = sqrt(3)/2 and sin(2pi/3) = sqrt(3)/2

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

You can check these answers by replacing x with the value in question and seeing if you get zero. Make sure your calculator is in radian mode

Plug in x = pi/3

2*sin(x) - sqrt(3) = 0

2*sin(pi/3) - sqrt(3) = 0

0 = 0 .................... this is a true equation, x = pi/3 is confirmed as a solution

Plug in x = 2pi/3

2*sin(x) - sqrt(3) = 0

2*sin(2pi/3) - sqrt(3) = 0

0 = 0 .................... true equation, x = 2pi/3 is confirmed as a solution

Plug in x = 4pi/3

2*sin(x) - sqrt(3) = 0

2*sin(4pi/3) - sqrt(3) = 0

-3.4641016 = 0 ............ false equation, x = 4pi/3 is a nonsolution

Plug in x = 5pi/3

2*sin(x) - sqrt(3) = 0

2*sin(5pi/3) - sqrt(3) = 0

-3.4641016 = 0 ............ false equation, x = 5pi/3 is a nonsolution

Final answer:

To solve the trigonometric equation 2 sin x - √(3) = 0 within the interval 0 ≤ x < 2π, we find that sin x = √(3)/2 at x = π/3 and 2π/3, which are the correct answer choices.

Explanation:

To solve for x in the given trigonometric equation 2 sin x - √(3) = 0, we first isolate the sine function by adding √3 to both sides and then divide by 2, giving us sin x = √(3)/2. Now, we seek the angles x within the interval 0 ≤ x < 2π (where π is pi) that satisfy this equation. We know that sin x is √(3)/2 at the angles π/3 and 2π/3 in the first and second quadrants, respectively. These are the two angles where the sine function takes the value of √(3)/2 between 0 and 2π. Therefore, the correct answer choices are π/3 and 2π/3.

It is important to consider that the sine function is positive in the first and second quadrants, and given the range for x, we don't need to consider the third or fourth quadrants where sine is negative. Additionally, the angles 4π/3 and 5π/3 correspond to a negative value of the sine function, thus they do not satisfy the equation.

Answer: The correct option is D.

Step-by-step explanation: We are given a linear equation:

[tex]m\times 5=30[/tex]

To calculate the value of , we need to separate m from the constant '5' which is done when 5 goes to the other side of the equation and gets divided there:

[tex]m=\frac{30}{5}\\\\m=6[/tex]

Conclusion: Hence, the value of m is 6 for the given equation.

Answer:

The surface area is 162 yards

Step-by-step explanation:

A = 2(w l + h l + h w)

A = 2(7 (3) + 6 (3) + 6 (7))

7 x 3 = 21

6 x 3 = 18

6 x 7 = 42

21 + 18 +42 = 81

81 x 2 = 162

Answer:

Either 177 or 188 buttons

Step-by-step explanation:

2134/12=177.83

Lisa can place 177 buttons into each jar when she distributes 2,134 buttons equally among 12 jars.

To determine the number of buttons Lisa can distribute into each jar, we perform a simple division: dividing her total button count, 2,134, by the number of jars, which is 12. This calculation results in approximately 177.83 buttons per jar. However, since you can't have a fraction of a button, we must round down to the nearest whole number, which is 177. Consequently, each jar will be filled with exactly 177 buttons. This fair distribution ensures that all 12 jars are equally supplied, making it practical and straightforward for Lisa to organize her collection.

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Answer:

D) 154 feet

Step-by-step explanation:

The angle is less than 45°, so you know the distance will be more than 89 feet. There is only one choice in that range.

_____

The mnemonic SOH CAH TOA reminds you ...

... Tan = Opposite/Adjacent

so ...

... tan(30°) = (89 ft)/(distance to boat)

Then ...

... distance to boat = (89 ft)/tan(30°) ≈ 154 ft

Answer:

i took a long time figuring it out lol but here it is let me know if you got them all correct

Step-by-step explanation:

A) 3.6 × 10^(-1)   B) 3.1 × 10^(6)  C) 5.3 × 10^(-6)  D) 4.2 × 10^(-1)

Answer: s = 324/4 = 81 yards

Answer:

s=81 yards

Step-by-step explanation:

Answer:

100 degrees

Step-by-step explanation:

Remark

The endpoints of the smaller diagonal of a kite, intersect the vertexes of 2 equal angles. Put in simpler language, if x is at the top of the kite and x is the vertex of the larger angle between the top and bottom angles, then the other two angles (left and right) are equal.

In still simpler language. <W = <Y

Equation

<X + <W + <Z + <Y = 360               All quadrilaterals have 360 degrees for their interior angles.

Givens

Solution

Answer

Answer:

100

Step-by-step explanation:

Angle ZWX and angle ZYX are congruent.

360 = 120 + 4x + 10x + 10x

360 = 120 + 24x

240 = 24x

10 = x

The measure of angle ZYX is equal to 10(10) = 100°

Final answer:

The rate of the boat is 7 mph and the rate of the current is 3 mph.

Explanation:

To find the rate of the current in this problem, we can use the equation:

Rate of downstream trip = Rate of boat + Rate of current

Rate of upstream trip = Rate of boat - Rate of current

Let's assign variables to the rate of the boat and the rate of the current. Let B represent the rate of the boat and C represent the rate of the current.

From the information given, we know that:

40 miles = (B + C) x 4 hours

40 miles = (B - C) x 10 hours

Now we can solve these equations to find B and C. Let's start by simplifying the equations:

40 = 4B + 4C

40 = 10B - 10C

Divide both sides of the equations by 4 and 10 respectively:

10 = B + C

4 = B - C

Add the two equations together:

10 + 4 = 2B

14 = 2B

Divide both sides by 2:

7 = B

Substitute the value of B back into one of the equations to solve for C:

10 = 7 + C

Subtract 7 from both sides:

3 = C

Therefore, the rate of the boat is 7 mph and the rate of the current is 3 mph.