[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"d" proportional to }t^2}{ {\Large \begin{array}{llll} d=kt^2 \end{array}}}\qquad \textit{we also know that} \begin{cases} d=80\\ t=4 \end{cases}\implies 80=k(4)^2 \\\\\\ \cfrac{80}{4^2}=k\implies 5=k\hspace{15em}\boxed{d=5t^2} \\\\\\ \textit{when t = 8, what is "d"?}\qquad d=5(8)^2\implies d=640~in[/tex]
A salesman sellls a car for $10,500. If he paid a commission of 5% for the first $10,000 and 8% on the remainder, what’s the total commission
Using percentages we can conclude that the total commission the salesman gets is of $540.
What is the percentage?A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a part per hundred. Per 100 is what the word percent means. By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%.So, the total commission:
5% of 10,000 -
10,000/100 × 5 = $5008% of remaining (10,500 - 10,000 = 500) $500 -
500/100 × 8 = $40Total commission: $500 + $40 = $540
Therefore, using percentages we can conclude that the total commission the salesman gets is of $540.
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Since three bits can be used to represent numbers between 0 and 7, we could use three bits to store the size of most families. Three bits wouldn’t be sufficient to store the number of students in a typical discussion section as they run anywhere from 15 to 25 students and three bits can only store numbers from 0 to 7.
How many binary digits would we need to set aside in order to store the number of high school students taking CS105 across the nation (we have 220 high school students in total)?
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.
What is the range of the binary representation of unsigned numbers with n bits?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:
The minimum value that can be represented is: 0.The maximum value that can be represented is: 2^n - 1.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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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.
The number of weeks that they will they have same number of baseball cards is 5 weeks.
How to illustrate the information?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?
Evaluate the equation
f(n) = -2n + 1
ƒ (12) =
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!
Select the correct answer.
What is the solution for x in the equation?
1/2+³/2= = x - 4
O A.
OB.
O c.
= -3
I = //
x = 3
OD. I =
-1/3
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
The swimming pool is open when the temperature is higher than 20C. Lahey tried to swim Monday and Thursday(which was 3 days later). The pool was open on Monday, but it was closed on Thursday. The high temperature was 30C on Monday, but decreased at a constant rate in the next 3 days.
WRITE an inequality to determine the rate of temperature decreased in degrees Celsius per day d, from Monday to Thursday.
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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On the east side of Holly Hill, you climb 2 feet higher for every 11 yards you climb toward the west. If you climb the hill to a height of 12 feet, how far west have you moved from the foot of the hill?
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
How to find the distance moved?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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If I move up to 8 and then move down to 8 what can you tell me about my ending position please help me
Help me with this question pleaseeeeeee
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.
3.3615 rounded to the nearest tenth
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.
Determine the values of y in the equation y2 = 144.
a. y = ±12
b. y = ±72
c. y = 12
d. y = 72
The value of y is +12 or -12 or y = ±12 if the quadratic equation is y² = 144 option (A) y = ±12 is correct.
What is a quadratic equation?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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4. 8(c - 9) = 6(2c - 12) - 4c
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?
Real numbers are the values of continuous quantities that can be used to indicate distances along lines It is a quantity that can be represented as an infinite decimal expansion.Real numbers can be pictured as points on the number line or real line, which is an indefinitely long line where the points corresponding to integers are evenly spaced. While both the set of all natural numbers and the set of all real numbers are infinite sets, the set of all real numbers is uncountable in the sense that there cannot be a one-to-one function from the real numbers to the natural numbers.To learn more about real numbers, refer:
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Select the TWO numbers that are solutions to the equation x³ = 27.
□A√27
□ C √27
□D 27³
DE 9
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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Distance between two ships two ships leave the same port at noon. ship a sails north at 25 mph, and ship b sails east at 14 mph. how fast is the distance between them changing at 1 p.m.?
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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classify the equation 10x+22x-5=8(4x+7)?as having one solution,no solution,or infinite many solutions
Find the value of r so that the line that passes through each pair of points has the given slope:
(r, -2) (10, 1) and the slope of the line is 1/4
Question 2(Multiple Choice Worth 4 points)
(01.02 MC)
A foreign exchange student from Denmark would like to buy gifts for her family. She finds a special deal, 7 t-shirts for $97.93, that
she would like to purchase for her family. However, her family only consists of 5 people. If she wants to purchase 5 t-shirts for her
family members at that special rate, what would be the cost of these t-shirts in her currency of Krona? (Currency conversion rate is 1
U.S. Dollar = 8.6964 Krona)
O 121.663 Krona
O 13.99 Krona
608.313 Krona
2
69.95 Krona
The cost of the 5 t-shirts in her currency of Krona is 608.313 Krona.
How do you make a currency conversion?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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Which box-and-whisker plot represents this data: 6, 7, 9, 9, 20, 22, 26, 28, 29, 30?
The Last box-and-whisker plot represents the data 6, 7, 9, 9, 20, 22, 26, 28, 29, 30.
What is the box-and-whisker plot?A box and whisker plot is a visual representation of variance in a set of data. The majority of the time, a histogram analysis gives an adequate display, but a box and whisker plot can add more detail while enabling the display of various sets of data on the same graph.It divides the data into five numerical categories: minimum, first quartile (Q1), median, third quartile (Q3), and "maximum." You can learn more about your outliers' values from it.The box-and-whisker plot and the box-and-whisker diagram are other names for a box plot that also includes lines (referred to as whiskers) extending from the box to indicate variability outside the top and lower quartiles.To learn more about box-and-whisker plot sums, refer
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Hey hon yybhy just got off work
The common ratio of a geometric series is \dfrac14
4
1
start fraction, 1, divided by, 4, end fraction and the sum of the first 444 terms is 170170170.
What is the first term of the series?
The first term of the geometric progression will be 128.
What is geometric progression?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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If f(x) = 7(2x - 9), find f^-1(x).
The inverse of the given function is f^-1(x)= (x - 63) /14
What is an inverse?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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if the sum of a number and two is doubled, the result is nine less than the number. find the number
What is the value of x?
A. x = 32
B. x = 37
C.x = 58
D. x = 148
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 height of a woman can be predicted by the equation h = 81.2 +3.34r, where his her height in centimeters and ris
the length of her radius bone in centimeters.
a. Write the equation in standard form.
h=
b. Find the r- and h-intercepts. Round to the nearest hundredth.
h-intercept =
r-intercept =
c. Use the function to find the approximate height of a woman to the nearest centimeter whose radius bone is 25 centimeters long.
cm
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.
What is a linear function?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:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).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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What value of x makes this equation true?
X/2-2= X/4+4
A. 4
B. 8
C. 16
D. 24
Please help me :'(
The value of x that makes this equation (X-2)/2= (X+4)/4 to be true is 8.
What is an equation?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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What is the slope of the line?
the slope of the line on the graph is 3 .
What is slope of a line ?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.
Calculationto 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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Rosemary is using the cookie recipe that cause 42 2/ 3rd cups of flour and 1 7/8 cups of sugar for each batch. She decides to increase the recipe so she can make three 1/4 batches of cookies to serve at her. Pick me how much flour does rosemary need for the increased recipe?
The amount of flour that Rosemary needs for the increased recipe of cookie is 138 2/3 batches.
How much flour is needed?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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How
many solutions does this nonlinear system of equations have?
The nonlinear system of the equation has two solutions as it intersects at two points.
What is the graphical solution of a system of equations?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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Estimate a 15% tip on a dinner bill of 59.17 by first rounding the bill amount to the nearest ten dollars.
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]
i need help on this, thanks
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]