A mountain cabin on 1 acre of land costs 30,000 dollars. If the land cost 4 times as much as the cabin, what was the cost of each?

The amount of flour that Rosemary needs for the increased recipe of cookie is 138 2/3 batches.

The quantity of flour and sugar needed for a batch of cookie recipe are written as mixed numbers. A mixed number is a non-integer that consists of a whole number and a proper fraction. A proper fraction is a fraction where the numerator is smaller than the denominator.

In order to determine the quantity of flour that would be needed for 3 1/4 batches, multiply the amount of flour needed for one batch of cookie by the number of batches to be made.

Multiplication is the process that is used to determine the product of two or more numbers. The sign that represents multiplication is x.

Amount of flour needed for 3 1/4 batches = flour needed for one batch x number of batches

42 2/3 x 3 1/4

128 / 3 x 13/4 = 416 / 3  = 138 2/3 batches

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The distances of the ships makes a right angled triangle. Ship A sails at 25 mph in direction QP, towards north. Ship B sails at 14 mph in direction QR, towards east.

Therefore, the distance between the two ships at 1 P.M. would be the distance between PR.

Applying Pythagoras Theorem,

[tex]P^{2} +B^{2} = H^{2}[/tex]

[tex](PQ)^{2} + (QR)^{2} = (PR)^{2} \\PR= \sqrt{(PQ)^{2} + (PR)^{2} } \\= \sqrt{(25)^{2} + (14)^{2} } \\= \sqrt{821} mph[/tex]

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The first term of the geometric progression will be 128.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

Given that the common ratio of the geometric series is ( 1 / 4 ) and the sum of the first four terms is 170.

The first term of the geometric series will be calculated as:-

[tex]S_n = a_1\dfrac{(r^n-1)}{r-1}[/tex]

[tex]170 = a_1\dfrac{(\dfrac{1}{4}^4-1)}{\dfrac{1}{4}-1}[/tex]

a₁ = ( 170 x 64 ) / 85

a₁ = 2 x 64

a₁ = 128

Therefore, the first term of the geometric progression will be 128.

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The answer is 3.4

Because the 3 is in the tenths place. Since 6 is greater than 5 it gives 1 to the 3 which makes it a 4.

The cost of the 5 t-shirts in her currency of Krona is 608.313 Krona.

The formula for converting currencies is Original Currency / New Currency = Exchange Rate.

Given:

Cost of 7 t-shirts at a special deal = $97.93

Now, she wants to purchase 5 t-shirts for her family members at this special rate.

Total Cost of 5 shirts in dollars = (97.93 * 5)/7 = $69.95

The exchange rate of the currency is 1 U.S. Dollar = 8.6964 Krona

So, $69.95 = (69.95 * 8.6964)/1 = 608.313 Krona

Therefore, the cost of the 5 t-shirts in her currency of Krona is 608.313 Krona.

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Cube roots - The two numbers that are solutions to the equation x³ = 27 are +3 and -3.

What are cube roots?

A number's cube root is a quantity that, when multiplied by itself three or more times, returns the original quantity. The cube root of 27, represented as 327, for instance, is 3 because 3 x 3 x 3 = 27 = 33 when we multiply 3 by itself three times. As a result, we can state that the cube root yields a value that is essentially cubed. Here, 27 is referred to as the ideal cube. We may deduce what the cube's root is from the word "cube root." It denotes the integer that brought about the cube under the root. Typically, we use the prime factorization technique to determine the cubic root of perfect cubes. We can discover the importance of square root in a similar way.

We are given the equation,

[tex]x^{3}[/tex] = 27

taking cube root on both the sides to find the value of x,

we get,

x = ±[tex]\sqrt[3]{27}[/tex]

further solving,

x = ±3.

Hence the two solutions of the  x³ = 27 equation will be ±3 or +3 and -3.

Because 3x3x3 Equals 27, the cube root of 27 is 3.

Since 4x4x4 = 64, the cube root of 64 is also 4, and so on.

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Answer:

x=15, y=7

Step-by-step explanation:

Angles that form a linear pair are supplementary, so:

[tex]2(5x-5)+3x-5=180 \\ \\ 10x-10+3x-5=180 \\ \\ 13x-15=180 \\ \\ 13x=195 \\ \\ x=15 \\ \\ \\ \\ 5y+5+20y=180 \\ \\ 25y+5=180 \\ \\ 25y=175 \\ \\ y=7[/tex]

The number of weeks that they will they have same number of baseball cards is 5 weeks.

From the information given, Ty and Elijah each decide to collect baseball cards. It should take about Ty has 37 cards and Elijah has 42 cards to begin with. Ty decides to buy 4 more cards each week and Elijah decides to buy 3.

Therefore, the expression for Ty will be:

= 37 + 4x

The expression for Elijah will be:

= 42 + 3x

where x = number of cards

Therefore, this will be:

37 + 4x = 42 + 3x

4x - 3x = 42 - 37.

x = 5

The number of weeks is 5.

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Ty and Elijah each decide to collect baseball cards. Ty has 37 cards and Elijah has 42 cards to begin with. Ty decides to buy 4 more cards each week and Elijah decides to buy 3. In how many weeks will they have same number of baseball cards?

Hello!

To find f(12):

 ⇒ must plug in '12' into the x's position in the equation

  [tex]f(12)=-2(12) +1=-24+1=-23[/tex]

Hope that helps!

c = All real numbers are solutions.

How is the equation 8(c - 9) = 6(2c - 12) - 4c solved?

8(c - 9) = 6(2c - 12) - 4c

8c- 72 = 12c- 72- 4c

8c- 72 = 8c - 72

0=0

L.H.S = R.H.S

Both sides are equal and this stands true for all real number values as c.

For example:

Let c = 10

8(10) - 72= 8(10) - 72

8 = 8

L.H.S = R.H.S

What are real numbers?

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Answer: c x=3

Step-by-step explanation:

Simplify it you will get

2-x=x-4 then minus x and four so you will get

2x=6 divide

X=3

Answer:

False

Step-by-step explanation:

Scale copies are indicated by proportional changes in the lengths of the sides of a figure. in this image, we can see that the bottom side of the figure is different while the shorter segments on each figure are the same length. Because of this, the answer is False as they can not be scale copies.

well, the bill was $59.17, if we round it by the "tens", the closest to 59 is 60, since 59 is farther from 50 but closer to 60, so it rounds up to 60

[tex]50\stackrel{farther}{\rule[0.35em]{18em}{0.25pt}59.17}\stackrel{closer}{\rule[0.35em]{2em}{0.25pt}}60 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 60}}{\left( \cfrac{15}{100} \right)60}\implies 9[/tex]

The value of x that makes this equation (X-2)/2= (X+4)/4  to be true is 8.

An equation ca be described as the mathematical terms which can contains different digits as well we a as alphabet and it can simplified so that a particular expression or term can be found, in the given equation we were told to find the value of x by simplify the equation which is done below.

(X-2)/2= (X+4)/4

Then if we cross multiply we will have

(4x - 8) =(2x+8)

then we can simplify further and collect the like terms which is

2x=16

x=8

There, the correct option is B

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The inverse of the given function is f^-1(x)=  (x - 63) /14

A function's reverse function F is a function that reverses the action of f (sometimes known as the inverse of f). If the inverse of f exists, it is designated by f -1 and exists only if f is bijective. The graph of the inverse of a function shows the function and the inverse of the function, which are both plotted over the line y = x. This graph's line traverses the origin and has a slope value of 1.

The first step is to open the brackets

So now we get, f(x)= 14x - 63

Let f(x) be y so this  becomes y= 14x+ 63

Now interchange the variables and we will get

x= 14y+ 63

(x- 63)/14= y

Replace y by f^-1(x).

f^-1(x)= (x - 63) /14

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The value of y is +12 or -12 or y = ±12 if the quadratic equation is y² = 144 option (A) y = ±12 is correct.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

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

It is given that:

The quadratic equation is:

y² = 144

As we know, the polynomial equation is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

Taking square root on both sides:

y = ±√144

y = ±12

Thus, the value of y is +12 or -12 or y = ±12 if the quadratic equation is y² = 144 option (A) y = ±12 is correct.

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Using the given linear function, we have that:

a) The equation in standard form is: h - 3.34r - 81.2 = 0.

b) The intercepts are given as follows: h-intercept = 81.2, r-intercept = -24.31.

c) The predicted height is of 164.7 centimeters.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In standard format, the equation is given by:

y - mx - b = 0.

In which:

For this problem, the equation is:

h = 81.2 + 3.34r.

In standard format, the equation is:

h - 3.34r - 81.2 = 0.

From the equation, the h-intercept is of 81.2. To find the r-intercept, we have to solve for r when h = 0, hence:

3.34r + 81.2 = 0.

3.34r = -81.2

r = -81.2/3.34

r = -24.31.

For item c, the radius is given by r = 25, hence the height will be given as follows:

h = 81.2 + 3.34(25) = 164.7.

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LET US FIRST FIND m<FEG using sum of angles in a triangle

[tex]58 + 90 + < feg = 180 \\ < feg = 180 - 90 - 58 \\ < feg = 32[/tex]

NOW WE CAN SEE THAT <FEG +<E =180° BECAUSE THEY ARE ON A STRAIGHT LINE.

[tex] < feg + 4x = 180 \\ 32 + 4x = 180 \\ 4x = 180 - 32 \\ 4x = 148 \\ \frac{4x}{4} = \frac{148}{4} \\ x = 37[/tex]

THEREFORE x=37°

the slope of the line on the graph is 3 .

Slope is calculated by dividing the "vertical change" by the "horizontal change" between any two distinct points on a line. The ratio can alternatively be expressed as a quotient, which yields the same result for any two separate locations on the same line ("rise over run"). A negative "rise" indicates a falling line. A road surveyor may judge that the line is useful, or it may show up in a diagram of a road or a roof as a description or a design. The steepness, incline, or grade of a line can be measured using the slope's absolute value. A slope with a larger absolute value denotes a steeper line.

to find the slope of the graph we will take two points which lies on the same line i.e. they must be collinear .

the points i m choosing is (-2,0) and (-1,3)

now for finding the slope we will use the formula

m = (y2-y1)/(x2-x1)

m = (3 - 0 ) / (-1+2)

m = 3 / 1

m = 3

so the slope of the line on the graph is 3 .

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Using percentages we can conclude that the total commission the salesman gets is of $540.

So, the total commission:

5% of 10,000 -

8% of remaining (10,500 - 10,000 = 500) $500 -

Total commission: $500 + $40 = $540

Therefore, using percentages we can conclude that the total commission the salesman gets is of $540.

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Considering the numerical representation of integers with n bits, it is found that 8 bits would have to be set aside in order to store the number of high school students taking CS105 across the nation.

For this problem, we work with unsigned numbers, excluding negatives, as the number of students is a discrete amount that starts with 0 and increases by 1 for each new student.

For unsigned integers with n bits, we have that:

For this problem, we want to represent an amount of 220, hence the number of bits needed is found as follows:

2^n - 1 ≥ 220

2^n ≥ 221

log2(2^n) ≥ log(2)(221)

n ≥ 7.8.

The number of bits cannot be a decimal amount, hence n is rounded up, and thus, 8 bits are needed to represent the amount.

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The nonlinear system of the equation has two solutions as it intersects at two points.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

From the given figure we observe that the straight line intersects the parabolic curve at two distinct points, Therefore this nonlinear system of equation has two solutions.

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From the given graph, the numeric values of the expressions are given as follows:

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.

On the graph of the function, the equivalent to this is that we have to find where the x-axis has the value, and find the value of y for which the function passes through the y-axis.

From the graph, when x = -1, f(x) passes the point at y = 12, hence f(-1) = 12.

For the second item, applying the same logic, we have that:

Hence:

f(1) - g(1) = 10 - 2 = 8.

For the third item, we have to look at the graph of g(x), and find the value of x when y = 4, hence g(x) = 4 when x = 2.

For the fourth item, the functions intersect at point (3,8), hence f(x) = g(x) when x = 3.

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Based on the height climbed, and the yards climbed per feet, the distance west you would have moved from the foot of the hill is 66 yards

For every 2 feet that you climb higher, you would be moving about 11 yards to the west.

This means that the distance climbed is directly proportional to the number of yards to the west.

Every 2 feet that one climbs higher will meant they move 11 yards to the west so the yards to the west for 12 feet is:

=  12 / 2 x 11

= 6 x 11

= 66 yards

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An inequality to determine the rate of temperature decrease in degrees Celsius per day d, from Monday to Thursday is 30°c - 3d [tex]\leq[/tex] 20°c

Let's assume the constant rate of decreasing the temperature be d degree Celsius.

So, the total decrease in temperature in three days is 3d degree Celsius.

Given,

The temperature on Monday is 30° c

Then,

The temperature on Thursday (which is 3 days later) will be 30°c - 3d

Since the pool opens when the temperature is higher than 20°c,

The equation to determine the rate of temperature decrease in degrees Celsius per day will be 30°c - 3d [tex]\leq[/tex] 20°c

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