Solve. Show work.
log3 5 + log3 x = log3 35

The cost of the hot dog and hamburger meals, given the amount bought by Mrs. Garcia and Mr. Clayton, are :

From Mrs. Garcia's purchase, we have:

2x + y = 18

And from Mr. Clayton's purchase, we have:

3x + 3y = 42

Use the substitution method to come up with the formula:

3x + 3(18 - 2x) = 42

-3x + 54 = 42

x = $ 4

Hamburgers would then cost:

2x + y = 18

2 ( 4 ) + y = 18

y = $ 10

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Answer:

800

Step-by-step explanation:

I am not so sure because you didn't explain the question well

The person who used more water was Sam and the person who's plant grew the least was Jessica.

The person who used more water in watering their plants is the person who used the most liters of water when they watered their plants. This person is Sam, who used 0. 89 liters of water on his plants every day.

Jessica on the other hand, water less at 0. 87 liters per day. As a result, Sam's plants grew the most was they grew 2. 35 feet, while Jessica's plants grew 2. 32 feet.

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The child's position after 90 seconds would be (0, -1).

The carousel revolves 360 degrees in one minute, which means it revolves 360/60 = 6 degrees per second.

After 90 seconds, the carousel would have revolved 90 * 6 = 540 degrees.

When the carousel revolves counterclockwise, the point (0, 1) would rotate to a new position by 540 degrees.

To find the new position, we can use the transformation:

540 - 360 = 180

hence the transformation is 180 degrees which is reflection across x axis

The rule for a reflection over the x -axis is (x, y) → (x, −y)

point (0, 1) → (0, −1)

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The measure of the angle mABF found using the corresponding angles theorem is mABC = 79°

Corresponding angles are angles that formed by a transversal and parallel lines, which are located in the same relative positions, with regards to the transversal and the parallel lines.

The specified information are;

Angle ∠ACD and angle ∠ABF are corresponding angles formed by a common transversal and two parallel lines.

The measure ∠ACD = 79°

According to the corresponding angles theorem, the corresponding angles formed by two parallel lines, and their common transversal are congruent, therefore;

∠ACD ≅ ∠ABF

The definition of congruency indicates that we get;

m∠ACD = m∠ABF

The substitution property of equality indicates that we get;

m∠ACD = 79° = m∠ABF

m∠ABF = 79°

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The correct statement regarding the solution to the equation 1/6(3x - 6) = 1/8(4x + 8) is given as follows:

Solving results in the statement -1 = 1, which is false. There is no solution.

The equation for this problem is given as follows:

1/6(3x - 6) = 1/8(4x + 8)

Applying the distributive property to each side of the equality, we have that:

0.5x - 1 = 0.5x + 1

Isolating the variable x, we have that:

0.5x - 0.5x = 1 + 1

0x = 2.

x = 2/0.

A division by zero is a false statement, hence the equation has no solution.

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Answer:

15/24

Step-by-step explanation:

(3a-3/4)

where a is 3/8,

we substitute the value of a;

(3(3/8)-3/4)

(9/8-3/4) =15/8

15/8 times 1/3 =15/24.

The volume of cone is gotten by dividing the volume of cylinder by 3.

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

The volume of a solid figure is the amount of space it occupies in three dimension.

The volume of a cylinder = π * radius² * height

The volume of a cone = (1/3) * π * radius² * height

Hence:

If the cone and cylinder have the same radius and height:

Volume of cone = (1/3) * volume of cylinder.

The volume of cone is one-third volume of cylinder.

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1) The value of x in the triangle is; x = 25

2) The measure of each interior angle is;

25°, 40° and 115°

Exterior angle = 65°

In a triangle, from the exterior angle property, we know that the exterior angle is always equal to the sum of the interior opposite angles. Thus, we say that any two triangles will be similar provided that their corresponding angles tend to be congruent and the length of their sides will be proportional.

Thus;

x + 15 + 25 = 3x - 10

3x - x = 25 + 15 + 10

2x = 50

x = 50/2

x = 25

The measure of each interior angle is;

25°

25 + 15 = 40°

180 - (25 + 40) = 115°

Exterior angle = 180 - 115 = 65°

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The value of 30 dollars in British pounds is 24.3

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

We have to convert the 30 us dollars to the British pounds

The value of one dollar in pounds is 0.81

Now let us calculate for 30 dollars

30×0.81

24.3 pounds

Hence, the value of 30 dollars in British pounds is 24.3

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The  x = -1, 0, 1 and y = 1, 3, 5 represents a linear relationship that is also proportional.

Linear relationship is a statistical term used to describe a straight-line relationship between two variables.

A relationship is proportional if there is a constant of proportionality (k) such that for any x and y in the relationship, y = kx.

The table x = -1, 0, 1 and y = 1, 3, 5 represents a linear relationship that is proportional because we can see that for every increase in x by 1 unit, y increases by 2 units (the constant of proportionality).

This is a linear relationship because the values of x and y change in a consistent straight-line pattern.

Therefore, x = -1, 0, 1 and y = 1, 3, 5 represents a linear relationship that is also proportional.

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Answer:

A is the answer

Step-by-step explanation:

a. [tex]7[/tex]

b. [tex]2[/tex] and [tex]4x+1[/tex]; [tex]4[/tex] and [tex]x[/tex]

c. [tex]-3m+17[/tex]

d. Coefficient: [tex]4[/tex], [tex]11[/tex]; Term: [tex]4x^2, 11y, -37[/tex]; Constant: [tex]-37[/tex]; Variables: [tex]x, y[/tex]; Expression: [tex]4x^2 +11y-37[/tex]

e. Factors: [tex]-8, (m+n)[/tex]; Quotient: [tex]\frac{5-m}{n}[/tex]; Sum: [tex]m+n[/tex]; Product: [tex]8(m+n)[/tex]

A constant in the expression 3x²+7-2(4x + 1) is 7. The factors in 2(4x + 1) are 2 and (4x + 1), and the factors in 4x are 4 and x. An expression with a variable m, a coefficient -3, and a constant of 17 can be written as -3m + 17. In the expression 4x² + 11y - 37, the coefficient is 4, the term, expression, and the variables are defined, but there are no factors. In the expression m-2-8(m+n), m is a factor, 2 and 8 are factors, the quotient is (m + n), and the sum is (m - 2 - 8(m + n)).

a. A constant is a term that does not contain any variables. In the given expression, 7 is a constant.

b. The two factors in 2(4x + 1) are 2 and (4x + 1). In the expression 4x, the two factors are 4 and x.

c. An expression with a variable m, a coefficient -3, and a constant of 17 can be written as -3m + 17.

d. In the expression 4x² + 11y - 37, the coefficient is 4, the terms are 4x², 11y, and -37, there are two variables (x and y), and there are no factors.

e. In the expression m - 2 - 8(m + n), m is a factor, 2 and 8 are factors, the quotient is (m + n), and the sum is (m - 2 - 8(m + n)).

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If a large equilateral triangle pyramid stands in front of the city's cultural center. The time  it take the painter to paint 75% of the pyramid is 10.8 hours.

The area of the base is:

(1/2) * 40 * 40

= 800 square feet

The area of one lateral face is:

(1/2) * 50 * 40

= 1000 square feet

So, the total area of all four lateral faces is:

4 * 1000

= 4000 square feet

The total surface area of the pyramid is:

800 + 4000 = 4800 square feet

To paint 75% of the pyramid, the painter needs to paint:

0.75 * 4800

= 3600 square feet

Time it will take them is:

3600 / 100 * 18

= 648 minutes or 10.8 hours

Therefore painter will take approximately 648 minutes, or 10 hours and 48 minutes, to paint 75% of the pyramid.

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The lateral surface area of the pyramid is 200 square inches.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.

We know the lateral surface area of a pyramid is = (1/2)×P×h, where P is the perimeter of the base.

Given, Each side of the base of a square pyramid measures 10 inches.

So, The perimeter of the pyramid is 4×10 = 40 inches.

Therefore, The lateral surface area of the pyramid is = (1/2)×40×10.

= 200 square inches.

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For the given triangles ΔABC ≈ ΔXYZ, the length of the side AB is, 24

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"

Given that,

One triangle, ΔABC

Another triangle , which is ΔXYZ

Triangle ΔABC and ΔXYZ similar,

So, we can say ΔABC ≈ ΔXYZ

And it is known that

for similar triangles, ratio of lengths of sides are equal for similar triangles

so, AB/BC = XY/ZY

⇒   X/18   =  16/12

⇒   X   =  24

Hence, the value of x is 24

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Answer:

2

Step-by-step explanation:

3.6 / 1.8 = 2.

Answer:

The answer is 2

Step-by-step explanation:

The differentiation of the equation will be (dy/dx) = - x² / y². Then the correct option is D.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

The equation is given below.

x³ + y³ = 1

Differentiate the equation with respect to 'x'. Then we have

(d/dx) (x³ + y³) = d/dx (1)

3x² + 3y² (dy/dx) = 0

x² + y² (dy/dx) = 0

y² (dy/dx) = - x²

(dy/dx) = - x² / y²

The differentiation of the equation will be (dy/dx) = - x² / y². Then the correct option is D.

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Answer: 1st friend = 13333 x 6

2nd friend = 13333 x 2

3rd friend = 13333

(this is rounded off the actual amount of 1 unit is 13333.3333333)

Step-by-step explanation:

1st friend = 6 units

2nd friend =2 units

3rd friend =1 unit

6+2+1 = 9

120000 divided 9 = 13333

1st friend = 13333 x 6

2nd friend = 13333 x 2

3rd friend = 13333

a. Perimeter = 72 yd

b. Area = 640 yd².

a. To find the perimeter of the compound figure, we need to add the lengths of all four sides together.

The perimeter is equal to 16 yd + 32 yd + 16 yd + 8 yd = 72 yd.

b. To find the area of the compound figure, we need to separate the figure into two separate shapes and find the area of each.

The figure can be separated into a 16 yd by 32 yd rectangle and a 8 yd by 16 yd rectangle.

The area of the 16 yd by 32 yd rectangle is 16 yd x 32 yd = 512 yd² and the area of the 8 yd by 16 yd rectangle is 8 yd x 16 yd = 128 yd². The total area is 512 yd² + 128 yd² = 640 yd².

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The probability of passing if the minimum passing grade is 70 %

is  0.3074.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

A quiz consists of 20 multiple-choice questions, each with 4 possible answers.

now,

n = 20, the number of questions

p = 1/4= 0.25, the probability of making a correct guess

q = 1 - p = 0.75, the probability of making an incorrect guess.

Expected success  = 70% or 7 of 10.

From the binomial distribution,

P(7of 10) = ₁₀C7 p^7q^3

               =120×0.000061×0.42

               =0.3074

Hence, the Answer: 0.3074.

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We are given two triangles ABC and DEF... it is given that they are similar and we know that when 2 triangles are similar the ratio of their corresponding sides are equal... Here, the corresponding sides are AB/DE and BC/EF but maryam has taken the wrong ratio.. Maryam has taken AB/EF and BC/DE...

AB/DE = BC/EF

x/18 = 16/12

x/18 = 4/3

3x = 72

x = 24m

The production level that achieves a marginal cost of $0.50/L is 1875 litres.

To find the average cost of producing 625 L of maple syrup, we need to find the total cost of producing that amount, and then divide by the number of litres. The total cost can be found using the cost function:

C(x) = 75(√x - 10)

C(625) = 75(√625 - 10) = 75(25 - 10) = 75(15) = 1125

The average cost per litre is the total cost divided by the number of litres:

Average cost = Total cost / Number of litres = 1125 / 625 = 1.8

b. The marginal cost is the derivative of the cost function:

C'(x) = 75(1/(2√x))

C'(1225) = 75(1/(2√1225)) = 75(1/(35)) = 75/35 = 2.14

c. To find the production level at which the marginal cost is $0.50/L, we set the derivative equal to 0.50 and solve for x:

0.50 = 75(1/(2√x))

0.50 * 2√x / 75 = 1

√x = 75 / (2 * 0.50)

x = (75 / (2 * 0.50))^2

x = 1875

So the production level that achieves a marginal cost of $0.50/L is 1875 litres.

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Answer:

d. x = 7

Step-by-step explanation:

[tex]\frac{32}{8} = \frac{28}{x}[/tex]

Cross multiply, the denominator "8" is multiplied by numerator "28", while the numerator "32" is multiplied by denominator "x":

8 * 28 = 224

32 * x = 32x

[tex]32x = 224[/tex]

Divide both sides by 32:

[tex]\frac{32}{32} = \frac{224}{32}[/tex]

[x = 7]

The Stafford loan will have a higher balance of $114.84 at the time of repayment.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

The formula for compound interest compounded monthly is

A = P(1 + (r/12)/100)¹²ⁿ.

So, For Unsubsidized Stafford Loan,

A = 4980(1 + (6.25)/12/100)¹⁸.     (12 times 1.5 years two semesters and 6  

                                                                                                           months)                                                                                                                    

A = 4980(1 + 0.0052)¹⁸.

A = 4980(1.0052)¹⁸.

A = $5467.

So, Unsubsidized Stafford Loan will give a higher balance.

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Answer: The Stafford loan will have a higher balance by $114.84 at the time of repayment.

Step-by-step explanation:

Answer:

The slope of the line is -5/7

Step-by-step explanation:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{4-(-3)}=\frac{-5}{4+3}=-\frac{5}{7}[/tex]

1) Maeve needs to earn $140 each weekend to get at least $1,250, using a linear inequality.

2) The graph on a number line that solves her problem is number line D, showing Maaeve's earnings per weekend.

A linear inequality is a first-order term inequality that compares two values by the inequality symbols such as, '<', '>', '≤', '≠' or '≥'

In a linear inequality, m is the slope and b is the y-intercept with the x-intercept.

The amount Maeve currently has = $130

The number of weekends for the summer = 8

The least amount she wants to earn ≥ $1,250

130 + 8x ≥ 1,250

8x ≥ 1,250 130

8x ≥ 1,120

x ≥ 140

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The percent of people satisfied with the survey is 55%

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given that, in a survey of 1,600 people who owned a certain type of​ car, 880 said they would buy that type of car again, we need to find what percent of the people surveyed were satisfied with the​ car,

The percent of people satisfied with the survey = 880 / 1600 × 100

= 55%

Hence, the percent of people satisfied with the survey is 55%

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The height of the tree given the ratio of the hikers shadow to the tree's shadow is 21.85 meters

Tree's shadow = 25.3 meters

Hikers shadow= 2.2 meters

Tree's height= x

Hiker's height= 1.9 meters

Equate the ratio of tree's to hikers

25.3 : 2.2 = x : 1.9

25.3/2.2 = x / 1.9

cross product

25.3 × 1.9 = x × 2.2

48.07 = 2.2x

divide both sides by 2.2

x = 48.07 / 2.2

x = 21.85 meters

Ultimately, the tree's height is given by 21.85 meters

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If the customer's water bill was $24.79, 4500 gallons of water were used by the general public as a result.

Quantity and their permutations, theorems and surrounding structures, figures and their locales, and venues where they can found are all parts of the mathematics course of study. The interaction of both a group of values, each of which produce a collective agreements, is referred to as a "function." A utility is a linkage between and outputs where each input produces a single, unique result. Every action has a region but a codomain, often termed as a scope. F is frequently utilised denote formulas (x). An x is the input. In light of the following criteria, there are four primary categories of functions that are available: on functions, yet another functions, so several operations, within functions, and then on functions.

given

(A) given that 7.5 falls between 5 and 8,

As a result, in order to determine C(7.5), we must utilize the definition of C(g) for 5 g 8

Considering that C(g) = 3.75(g - 5) + 19.16, 5 g > 8

calculating g = 7.5

C(7.5) = 3.75(7.5 – 5) + 19.16 = 28.535

Water usage is represented by g, and C(g) provides the cost (before taxes) for that.

In other words, the cost to the citizen before taxes for 7500 gallons of water use will be 28.535.

(B) We must apply the definition of C(g) for g > 8 because 8.2 > 8.

C(g) = 5.33(g – 8) + 30.14, g > 8

So, C(8.2) = 31.206

C(g) = $17.52

C(g) has a value of 19.16 30.14.

If the customer's water bill was $24.79, 4500 gallons of water were used by the general public as a result.

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