The equation that models the height of the tent, h, in feet, with respect to the horizontal distance in feet from the left edge, d, is h = 1.5 d + h0.
The height of the tent is 22. 5 feet at a horizontal distance of 15 feet.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The height of the tent varies at a rate of 1. 5 feet with the horizontal distance from the left edge.
This can be written as -
h = 1.5 d, where d is the distance.
So, the equations that models the situation is -
h = 1.5 d + h0
The peak of the tent is at 30 feet and is at a horizontal distance of 20 feet from the left edge.
So, when d =20, then h =30.
Plugging the values in the equation -
30 = 1.5 (20) + h0
30 = 30 + h0
h0 = 0
The height of the tent is 22. 5 feet.
So, now h = 1.5 d and h = 22.5.
Equating these two -
22.5 = 1.5 d
d = 22.5/1.5
d = 15
Therefore, the distance value is obtained as 15 feet.
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For what value of k the given equation 4 K X² 2k 4 x+ 8k+ 1 0 is a perfect square?
For k=0 or k=3, the given equation will be a perfect square.
Note: we are taking the equation to be: (4−k) X^2+(2k+4) x+8k+1=0
Taking,
(4−k) X2+(2k+4) x+8k+1=0
Here, a=4+k, b=2k+4, c=8k+1
The given equation will be a perfect square, When D= 0
We know, D = b^2−4ac [A perfect square trinomial is an expression that can be generated from the square of a binomial equation. If an equation has the formula ax^2 + bx + c and meets the requirement b^2 = 4ac, it is referred to as a perfect square trinomial. The formula for the perfect square has the following variations: ax2 + 2abx + b2 = (ax + b). When b^2 = 4ac, we know that an equation is a perfect square.]
b2−4ac=0
(2k+4)2−4(4−k) (8k+1) =0
4k2+16+16k−4(32k−8k2+4−k) =0
K2+4+4k−32k+8k2−4+k=0
9k2−27k = 0
K2−3k = 0
k(k−3) =0
k=0 or k=3
Hence for k=0 or k=3, the given equation will be a perfect square.
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on the main floor of the Kodak halll at the easement they're the number of seats per row increase at a constant rate Steven counts 31 Seaton Rd. three and 37 Seaton Rd. six how many seats are there in a row 20
65 seats in 20th row.
What is direct proportion?Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. It is represented by the proportional symbol, ∝. In fact, the same symbol is used to represent inversely proportional, the matter of the fact that the other quantity is inverted here.
Given,
No. of seats in 3rd row = 31
No. of seats in 6th row = 37
Seats increase at a constant rate
Let k is the rate of increment.
Difference between no. of seats = k × difference between no. of rows
Difference of seats in 3rd and 6th rows = k difference between the no. of rows
37 - 31 = k ×(6-3)
6 = 3k
k = 2
Thus, we can determine
Difference between the no. of seats is twice the difference between the no. of rows.
Difference between 6th and 20th row = 14 rows
Hence the difference between number of seats = 2 × 14 = 28 seats.
No. of seats in 20th row = No. of seats in 6th row + 28 seats
No. of seats in 20th row = 37 + 28 = 65
Hence, there will be 65 seats in 20th row.
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Jane is making lunch for 12 people. she is serving hotdogs and plans on each person get eating two hotdogs. hotdog buns are sold in packages of eight. which expression can be used to find the number of packages she needs to buy?
He must purchase 3 packages of hot dogs and 2 packages of hot dog buns for a total of 24 hot dogs with buns if he doesn't want to have any leftover hot dogs or buns. You should be aware that students might respond with 24, which is the least common multiple of 8 and 12.
What are hot dog buns known as?The hot dog buns most frequently used in the American region of New England and its cuisine are New England-style hot dog buns, also referred to as New England hot dog buns or top-loading hot dog buns.
What does the slang term "hot dogs" mean?As you can see, "hot dog" is a versatile word that can be used as a noun, verb, adjective, or even as an exclamation.
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In order for a triangle to shrink in size but stay proportional to its original size, the scale factor, K, must be between
zero and what?
In order for a triangle to shrink in size but stay proportional to its original size, the scale factor, K, must be between zero and one.
What is scale factor?
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
In order for a triangle to shrink in size but stay proportional to its original size, the scale factor, K, must be between zero and 1.
The image is contracted if the scale factor is less than 1 (0< k <1).
The image is enlarged if the scale factor is more than 1 (k > 1).
The image remains the same if the scale factor is 1 (k = 1).
Hence, the scale factor k should be between 0 and 1.
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What is the degree of polynomial 2 y² Y³ 2y8?
The degree of the polynomial [tex]2yA^2yA^32y^8[/tex] is 15
A polynomial's degree is the sum of the degrees of its monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer.
The degree of a polynomial is the highest or largest power of a variable in a polynomial equation. The degree denotes the polynomial with the maximum exponential power (ignoring the coefficients).
Consider the following polynomial expression with two variables: [tex]x^3 + 6x^2y^4 + 3y^2+5[/tex]
The polynomial has a degree of 6.
This is because the exponent values of x and y in the second term of the algebraic formula, [tex]6x^2y^4[/tex], are 2 and 4, respectively. We get 6 when we sum the exponent values. As a result, the multivariable polynomial expression has a degree of 6.
As per question, polynomial is: [tex]2yA^2yA^32y^8[/tex]
The total sum of power is: 1+2+1+3+8=15
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homework i need to do pls help
Answer:
1.
(a) 4y
(b) 5w
(c) 6a
(d) 3s
(e) 2n
(f) 3g
(g) 2y
(h) 0
2.
(a) -2u
(b) -w
(c) -3a
(d) -7y
3.
(a) 7a+3b
(b) 12y+4h
(c) 2g+10a
(d) 15m+10p
(e) 10e+4
(f) 12+5a
Step-by-step explanation:
Don't be intimidated by the "letter" variables. It is really just simple addition and subtraction. Examples:
For Q1=
y + y + y + y = 4y because there are 4 y's, and since we don't know the values of the y, this is the farthest we can simplify it.
For Q2=
4u - 6u = -2u. Since these two numbers have the same variable, this is just a simple subtraction problem. 4 - 6 = -2.
For Q3=
3a + 2b + 4a + b = 7a + 3b.
Look for the numbers with the same variable. 3a and 4a both have a's, so we add the two and get 7a. 2b and b (b is the same thing as 1b) both have b's, so we add them and would get 3b.
Therefore, the answer is 7a + 3b.
I hope this helped! Good luck with future endeavors!!
Step-by-step explanation:
attached the answers below, hope that helps...
How to simplify the rational expression
Answer:
Factor the numerator and denominator and then divide out any common factors.
Step-by-step explanation:
Rewrite in simplest rational exponent form. Show each step of your process
The final answer is 4x, which is the simplest form of expression.
What is the rational exponent?
A rational exponent is an exponent that is in the form of a ratio of two integers, such as a/b where a and b are integers and b is not equal to zero.
To rewrite the expression in simplest rational exponent form, we can first simplify the radicals and then combine any like terms. Here are the steps to simplify the given expression:
4√x* √x = 4 * 1 √x * √x = 4 * x^(1/2) * x^(1/2) = 4 * x^( (1/2)+(1/2) ) = 4 * x^(1)
x^(1) = x
So, the expression in simplest rational exponent form is 4x
x * 4x = 4x
Notice that 4 and x are in the same radical which means 4 is a coefficient of x.
Therefore, 4√x * √x can be written as 4x, which is in the simplest form.
hence, the final answer is 4x, which is the simplest form of expression.
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Which can be the first step in finding the equation of the line that passes through the points (5.-4) and (-1,8) in
slope-intercept form?
In slope-intercept form, the equation of the line passing through the points (5.-4) and (-1,8) is y = -4x + 8 .
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter.
given
the points (5.-4) and (-1,8)
slope = [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
slope intercept form = y = mx + c
To find the equation of the line that passes through the points (5, -4) and (-1, 8),
The slope and the intercept by the slope intercept form = y = mx + c .
The slope is -4 and the intercept is 8.
In slope-intercept form, the equation of the line passing through the points (5.-4) and (-1,8) is y = -4x + 8 .
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Tyler drove 52\tfrac{1}{2}52
2
1
mile in 1\tfrac{2}{3}1
3
2
hour. If he drove at a contant rate, how far did he travel in one hour? Enter your anwer a a whole number, proper fraction, or mixed number in implet form
Tyler drove 40 miles in one hour.
To find how far Tyler drove in one hour, we need to divide the total distance he traveled (52 21/32 miles) by the total time it took him (1 2/3 hours). To do this, we first need to convert the time to a common denominator, which in this case is 32. We can convert 1 2/3 hours to 32/3 hours by multiplying the numerator and denominator of 2/3 by 32/32.
So, we have:
(52 21/32) miles / (32/3) hour = (52 21/32) miles * (3/32) hour
= (52 21/32) * (3/32)
= (52 213/3232)
= (52 63/32) miles/hour
= 40 miles/hour
So, Tyler drove 40 miles in one hour.
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HELP! (25 POINTS AND CROWN FOE THE RIGHT ANSWER!!)
What does =] mean in text?
It typically means that the person is being friendly and is in a good mood.The expression =] is often used as an emoticon to express friendliness, positivity, and happiness. It can be used as a stand-alone expression or as part of a longer sentence.
The expression =] is commonly used in text conversations as an emoticon to express friendliness, positivity, and happiness. It is typically used when a person wants to convey a feeling of warmth and good cheer. The expression can be used as a stand-alone expression or as part of a longer sentence. When used alone, it has a meaning similar to a smiley face and can be used to respond to a message in a positive way. When used as part of a longer sentence, it can be used to express a feeling of contentment. As an emoticon, it has no specific meaning, but it can be used to show that the person is in a positive and good mood. Using this expression can be a way to show that you are happy and in a friendly mood.
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[Please help me on this- I will give you brainlist!!]
Write the terms in standard form. Then state the degree of the polynomial and the leading coefficient (LC).
For the polynomial 9, 3x², 8x; the degree is 2 and the leading coefficient is 3
What is an equation?An equation is used to show the relationship between numbers and variables.
Polynomial is an expression composed of variables, constants and exponents using mathematical operations such as addition, subtraction, multiplication and division
The degree is the highest exponent of variable for the polynomial. The polynomial with degree of 2 is known as a quadratic polynomial
Given the polynomial:
9, 3x², 8x
Writing in standard form is done by rearranging from highest exponent of variable to least. This is:
3x², 8x, 9
Hence the degree is 2 and the leading coefficient is 3
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How do you find the sides of an acute triangle?
To find the missing side length of the acute angled triangle apply the cosine law as follow:
a² = b² + c² - 2bccosA
b² = a² + c² - 2accosB
c² = b² + a² - 2abcosC
As given in the question,
Given triangle is acute angled triangle.
Let us consider the measure of two sides and its included angle of the acute angled triangle is given.
Let the triangle be ABC,
Side opposite to ∠A, ∠B , and ∠C are a , b, and c respectively.
Apply cosine law to find the measure of the missing side in the acute angled triangle:
a² = b² + c² - 2bccosA
b² = a² + c² - 2accosB
c² = b² + a² - 2abcosC
Therefore, to get the measure of the missing side length in the acute angled triangle apply cosine law.
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I need help to get the answer
The length BC of the right triangle is 18 units.
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The length BC of the right triangle can be found as follows:
Therefore, using proportion because triangle ABC is similar to triangle BDC.
x / 36 = 9 / x
cross multiply
x × x = 36 × 9
x² = 324
square root both sides of the equation
x = √324
x = 18 units
Therefore,
BC = 18 units
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Marc's brownie pan, shown below, has a pair of parallel sides. Each day, Marc's family is going to eat 100 square centimeters of brownie from the pan. For how many days does Marc's family have brovnics before they run out? top:29 bottom: 41 side : 20
Determine how many square centimeters make up a square meter in order to determine how long Marc will have brownies before they run out.
How to calculate a square meter?We must first determine the number of square centimeters in a square meter in order to determine how many days Marc has left of brownies before they run out. A square meter has 3.6 square meters in it.
Because of this, Marc has access to brownies for 3.6 days until they are finished.
Knowing the dimensions of a square or rectangle will allow you to compute its square meters. Also known as the shape's area, this term is used. Length times width equals m2, which is the formula used to calculate square meters. As an illustration, if your square is 3 meters long and 2 meters wide, 3 x 2 equals 6 meters2.
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In what quadrant does 2/3 lie?
The point (2, 3) lies in the first quadrant.
Quadrant
The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes.
These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the (x; y) coordinates are I (+; +), II (−; +), III (−; −), and IV (+; −).
Cartesian system
The Cartesian coordinate system uses a horizontal axis that is called the x-axis and a vertical axis called the y-axis. Equations for lines in this system will have both the x and y variable.
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26 °
100°
X=
help anyone ?
Answer:
Step-by-step explanation:
26° + 100°
= 126°
360° - 126°
234°
7. Mai and Tyler are selling items to earn money for their elementary school. The school
earns w dollars for every wreath sold and p dollars for every potted plant sold. Mai
sells 14 wreaths and 3 potted plants and the school earns $70.50. Tyler sells 10
wreaths and 7 potted plants and the school earns $62.50.
This situation is represented by this system of equations:
[ 14w + 3p = 70.50
10w+7p = 62.50
Explain why it makes sense in this situation that the solution of this system is also a
solution to 4w + (-4p) = 8.00.
On solving the provided question we can say that - her in the equation 14w + 3p = 70.50 and 10w+7p = 62.50 , w = 12; p = 18
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
[tex]14w + 3p = 70.50 \\[/tex]
10w+7p = 62.50 ,
[tex]w = 12\\[/tex]
p = 18
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How many solutions do the pair of linear equations 3x 2y 5 and 2x 3y 7 have?
The pair of linear equations 3x + 2y = 5 and 2x + 3y = 7 has no solution.
To solve these equations, we will use the method of elimination.
We start by multiplying the first equation by 2:
6x + 4y = 10
Now we add both equations together:
6x + 4y + 2x + 3y = 10 + 7
Combining like terms, we have:
8x + 7y = 17
We can now solve for x by dividing both sides by 8:
x = 17/8
Now we can substitute this value of x into either of the original equations to solve for y:
3(17/8) + 2y = 5
51/8 + 2y = 5
2y = 5 - 51/8
2y = -41/8
y = -41/16
However, this value for y is not a real number, so there is no solution for the pair of linear equations.
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A sample of size 95 will be drawn from a population with mean 25 and standard deviation 13. Find the probability that will be between 22 and 27.
1.3338 is the likelihood, The probability of anything occurring is known as probability.
How are probabilities calculated?The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.
The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.
Explanation:
Mean (m) = 25
The standard deviation is 13
Sample size (n) is 95.
Chance that x will fall between 22 and 27.
Zscore = x - mean / s / n
If x = 22, Zscore is equal to (22 - 25) / (13/95).
For x = 27, Zscore is equal to (27 - 25) / (13/95) / n = 13 / 95, which is 1.3338.
1.3338 is the likelihood.
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A plane flew 390 nautical miles in 45 min. Find its average speed in knots ( nautical miles per hour)
Answer:
Step-by-step explanation:
1.change minutes to hours,45 minutes is [tex]\frac{3}{4}[/tex] hours
2.then use 390÷ [tex]\frac{3}{4}[/tex]=390·[tex]\frac{4}{3}[/tex]=130·4=520 nautical per hour
One angle of a triangle measures 45°. The other two angles are in a ratio of 7:20. What are the measures of those two angles?
Answer:
35° and 100°
Step-by-step explanation:
The total angle of a triangle = 180°
The total angle of two angles = 180° - 45° = 135°
One part of the ratio = 135° : (20 + 7) = 5°
The smaller angle = 5° x 7 = 35°
The bigger angle = 5° x 20 = 100°
Answer:
35° and 100°
Step-by-step explanation:
the sum of the 3 angles in a triangle is 180°
the ratio of 2 angles is 7 : 20 = 7x : 20x ( x is a multiplier )
equate the sum to the 3 angles to 180 and solve for x
45 + 7x + 20x = 180
45 + 27x = 180 ( subtract 45 from both sides )
27x = 135 ( divide both sides by 27 )
x = 5
Then
7x = 7 × 5 = 35
20x = 20 × 5 = 100
the measure of the 2 angles is 35° and 100°
The mean length of 10 childrens' index finger is 6.8cm.
The mean length of 7 adults' index finger is 12.8cm.
What is the mean length (rounded to 2 DP) of these 17 people's index finger?
Answer:
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Step-by-step explanation:
PLEASE HELP: Given AC and BD bisect each other, prove that ΔABX≅ΔCDX using the SAS congruence theorem. ??
The ∆ABX and ∆CDX formed after the mutual bisection of AC and BD each other at point X are congruent i.e ΔABX ≅ ΔCDX, by SAS congruance theorem.
SAS congruence theorem: "SAS " stands for "Side-Angle-Side". If there is two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are said to be congruent. We have , A Quadrilateral ABCD, such that AC and BD bisect each other at point X. After bisection there is formed 4 triangles. We have to show ΔABX ≅ ΔCDX by SAS Congruance Rule. Now, as we know that bisect point divides the sides into two equal parts, i.e, AX = CX and DX = BX. So, in ΔABX and ΔCDX
AX = CX ( since X is bisecter point )BX = DX ( from bisection )m∠AXB = m∠CXD ( corresponding angles)As we see ∠AXB is angle in between to two sied AX and BX . Similarly, ∠CXD is in between CX and DX . So, by using SAS congruance theorem ∆ABX is congruent to ∆CDX i.e., ΔABX ≅ ΔCDX.
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Tara rocc mos
her home to a restaurant and ate lunch. She wen continued along the same road to a movie theater to see a movie. Finally, she returned home on the same road after the movie. Tara's distance from home during the 4 hours she was out is shown in the graph above. How many total miles did she ride her bicycle?
A)
5
B) 10
C) 16
D) 20
You can ride in many places, so be sure to look for hazards that could cause injury or other risks while bicycling.
How many miles is a lot to cycle?The number of miles you can cycle in a single day is unlimited. It depends on your level of fitness, your exercise regimen, and the distance you cycle. Starting out, 10 kilometres per day is OK.
If you're an experienced cyclist who can pedal 25–30 miles every day, 45 miles is a realistic limit. You can ride a certain bike trail. By riding a bike to work, you can get in shape. If you've never rode a bike before, start out slowly. If you ride your bike for at least three miles every day, you might be able to travel further.
You may be able to make the most of your speed sensor’s accuracy, depending on how accurate it is. You need to know exactly how much effort you put in during your rides.
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if you shift the linear parent function, f(x)=x, left 14 units, what is the equation of the new function
Answer: This is a horizontal translation so, the equation is f(x) = (x + 5). Whenever you translate to the right it is negative
Step-by-step explanation:
Ryan has a points card for a movie theater. He receives 85 rewards points just for signing up. He earns 7.5 points for each visit to the movie theater. He needs 160 points for a free movie ticket. Write and solve an equation which can be used to determine vv, the number of visits Ryan must make to earn a free movie ticket.
Answer:
85+7.5v=160
7.5v=160-85
7.5v=75
V=75/7.5
V=10
Ryan would need to take 10 visits to get a free ticket.
`y=7/(1,000)-(9x)/8` whats the y incercept
for each mentor artist, write an equation and a graph showing the proportional relationship between the art sold and your total commission.
Sara's pieces of art sell for $25 each your commission is 60%
Ravi's pieces of art sell for $2000 each your commission is 25%
x represents the number of pieces of art sold
y represents the total commission
K represents the commission per piece of art
The equations of the commissions are
Sara: y = 15xRavi: y = 500xHow to determine the equations and the graphFrom the question, we have the following parameters that can be used in our computation:
Sara's pieces of art sell for $25 and commission is 60%Ravi's pieces of art sell for $2000 and commission is 25%Also from the question, we have:
x represents the number of pieces of art soldy represents the total commissionThis means that:
Commission = Unit rate * Commission proportion * Number of pieces
Using the above as a guide, we have the following:
Sara: y = 25 * 60% * x
Ravi: y = 2000 * 25% * x
Evaluate
Sara: y = 15x
Ravi: y = 500x
See attachment for the graph of the commission equations
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