So the length of the shorter diagonal is 3 inches. The length of the longer diagonal is 7 inches.
What is the rhombus about?Let d1 and d2 be the lengths of the longer and shorter diagonals, respectively. We know that d1 = d2 + 4, and that the area of the rhombus is given by A = (d1*d2)/2 = 10.5.
Substituting d1 = d2 + 4 into the area equation, we get:
(d2+4)*d2/2 = 10.5
Multiplying both sides by 2 and simplifying, we get:
d2²+ 4d2 - 21 = 0
Using the quadratic formula, we can solve for d2:
d2 = (-4 ± [tex]\sqrt{4^2-4(-21)}[/tex]/2
d2 = (-4 ± [tex]\sqrt{100}[/tex] /2
d2 = (-4 ± 10)/2
d2 = -7 or 3
Since the length of a diagonal cannot be negative, we reject the negative solution and conclude that d2 = 3. Therefore, d1 = d2 + 4 = 7, and the length of the longer diagonal is 7 inches.
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30 60 90 triangle. Hypotenuse 40. Find legs X and y
Answer:
X = 20 and Y = √3*20, or about 34.64
Step-by-step explanation:
In a 30-60-90 triangle, the hypotenuse is double the length of the shorter leg. To find the length of the shorter leg with the hypotenuse, just divide the length of the hypotenuse by 2. 40/2=20
In a 30-60-90 triangle, the longer leg is equal to the square root of 3 times the length of the shorter leg. √3(20)=34.6410161514, which can be rounded to 34.64
just a quick addition to the great reply above by "krr2007"
Check the picture below.
The diameter of a circle is 13 in. Find its area to the nearest whole number.
Answer:
area=22/7×13=40.85=41 is the nearest whole number
There are 12 people at a Restaurant and the menu has 13 items.
How many different ways can they order?
The answer is 106993205379072 different ways that the 12 people can order from the 13 items on the menu.
There are a total of 12 people at a Restaurant and each person can order one of the 13 items on the menu. Therefore, the total number of different ways that they can order is 1312 = 106993205379072.
This is because for each of the 12 people, there are 13 choices for what they can order. So for the first person, there are 13 choices, for the second person there are 13 choices, and so on. Multiplying all of these choices together gives us the total number of different ways that they can order:
13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 = 106993205379072
So the answer is 106993205379072 different ways that the 12 people can order from the 13 items on the menu.
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Sally ate 400 fries in 20 minutes. Find her fry eating in fries per minute
Answer:
20 fries per minute.
Step-by-step explanation:
You are trying to find the amount of fries per minute, assuming that Sally eats the same amount each minute. It is given that there are 20 minutes and 400 fries in all. Divide the total amount of fries with the total amount of minutes:
(400 total fries)/(20 minutes) = (20 fries/minute)
20 fries per minute is your answer.
~
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The price of petrol is increased from R12,58 per liter to R13,28 per liter. Determine the percentage increase in the price
Javier is saving money at a constant rate to buy a new car. After saving for 2
months, Javier has $920
. After saving for 4
months, Javier has $1,030
.
Construct a function that models the relationship between the amount of money Javier has saved and the number of months he has saved for. Show or explain how you constructed the function.
Respond in the space provided.
Answer:
look in the comments and have a good
Step-by-step explanation:
look
3 + 10x+ 4x as an algebradic expression
Answer: 10x² + 3x + 4
Step-by-step explanation: I hate math.
can somebody help me i need help
The number that Sean counts, considering the sequence of numbers for this problem, is given as follows:
27.
How to obtain the sequence of numbers?Two features are needed to obtain the sequence of numbers:
The initial number.The common difference.Sam's counts by 2 from 15, hence the parameters are given as follows:
Initial number of 15.Common difference of 2.Hence the sequence is given as follows:
15, 17, 19, 21, 23, 25, 27, 29, 31, 33 and 35.
Meaning that the number 27 is counted. We can see above that the sequence is composed only by odd numbers, which eliminates the numbers 16 and 22. As 13 is a number that is less than 15, it is also eliminated.
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What is metallurgy? (4 points)
a
the study of how to domesticate animals
b
the science that studies how metals work
c
a Hindu sacred ritual for cleansing the body
d
the belief that natural objects have supernatural beings in them
Answer:
Metallurgy is the science that studies how metals work. It involves the extraction of metals from ores, their purification, and their conversion into useful alloys. Metallurgists also study the physical and chemical properties of metals, as well as their behavior under different conditions such as temperature and pressure.
Step-by-step explanation:
Hello,
the answer is "studies of how metals work."
Reason:
the answer is the science that studies how metals work.
If you need anymore help feel free to ask me!
Hope this helps!
~Matthew1756654
M6U3L15: Representing ratios using tables
Set of practical problems
Complete the table to show the amounts of yellow and red paint needed for different numbers of batches of the same shade of orange paint.
Yellow paint (quarts)
Red paint (quarts)
5
6
Explain how you know that these amounts of yellow paint and red paint will give the same shade of orange as the mixture in the first row of the table.
A car is traveling at a constant speed, as shown by the double number line.
How far does the car travel in 14 hours? Explain or demonstrate your reasoning.
The olive trees in an orchard produce 3000 pounds of olives per year. It takes 20 pounds of olives to produce 3 liters of olive oil. How many liters of olive oil can this orchard produce in a year? If you get stuck, consider using the board.
Olives (pounds)
Olive oil (litres)
20
3
100
3000
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1)The completed table is
Yellow paint (quarts) | Red paint (quarts)
5 | 3
6 | 3.6
2) The car travels 98 miles in 14 hours.
3) The orchard can produce 450 liters of olive oil in a year.
What is a ratio?
A ratio is a quantitative comparison between two or more quantities, indicating how many times one quantity contains another. It is expressed as the quotient of the two quantities or in the form of a fraction. Ratios can be represented in various ways, including as decimals, percentages, or fractions.
Complete the table to show the amounts of yellow and red paint needed for different numbers of batches of the same shade of orange paint.
Yellow paint (quarts) | Red paint (quarts)
5 | 3
6 | 3.6
To get the same shade of orange paint, we need to mix yellow and red paint in a certain ratio. This ratio will determine the hue, saturation, and brightness of the final color. In this case, we can see that the ratio of yellow to red paint is 5:3 in the first row of the table, and 6:3.6 (which simplifies to 5:3) in the second row. This means that we need the same amount of yellow and red paint for each batch of orange paint, in a 5:3 ratio.
A car is traveling at a constant speed, as shown by the double number line.
The distance traveled by the car is directly proportional to the amount of time it travels. This means that the ratio of distance to time is constant. From the given double number line, we can see that the car travels 21 miles in 3 hours. Therefore, the ratio of distance to time is 21:3 or 7:1. To find how far the car travels in 14 hours, we can set up a proportion:
distance/time = 7/1
distance/14 = 7/1
distance = 7 x 14
distance = 98 miles
Therefore, the car travels 98 miles in 14 hours.
The olive trees in an orchard produce 3000 pounds of olives per year. It takes 20 pounds of olives to produce 3 liters of olive oil.
To find how many liters of olive oil the orchard can produce in a year, we need to divide the total weight of olives by the amount of olives needed to produce one liter of oil, and then multiply by the conversion factor:
Liters of oil = (Pounds of olives / Pounds per liter) x Conversion factor
Liters of oil = (3000 / 20) x 3
Liters of oil = 150 x 3
Liters of oil = 450
Therefore, the orchard can produce 450 liters of olive oil in a year.
Hence,
1)The completed table is
Yellow paint (quarts) | Red paint (quarts)
5 | 3
6 | 3.6
2) The car travels 98 miles in 14 hours.
3) The orchard can produce 450 liters of olive oil in a year.
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Arrange in order from least to greatest (Radicals)
a. 4√3
b. 3√5
c. 5√2
d. 2√10
e. 2√13
f. 3√6
Therefore, the order from least to greatest is:d<f<a<b<c<e
d. 2√2 x √5 ≈ 5.66, f. 3√2 x √3 ≈ 6.00, a. 4√3 = 4 x √(3) ≈ 6.93, b. 3√5 ≈ 6.71, c. 5√2 ≈ 7.07, e. 2√13 ≈ 7.21
Arranging radicals( surds) in order from least to greatest,To arrange these radicals in order from least to greatest, we need to simplify them and compare the values. We can start by simplifying the radicals using prime factorization.
a. 4√3 = 4 x √(3) = 4 x√(3)
b. 3√5 = 3 x √(5)
c. 5√2 = 5 x√(2)
d. 2√10 = 2 x √(25) = 2 x √(2) x √(5) = 2√2 x√5
e. 2√13 = 2 x √(13)
f. 3√6 = 3 x √(23) = 3 x √(2) x √(3) = 3√2 x √3
Now, we can compare the values of the radicals by comparing their coefficients and the values inside the radical:
a. 4√3 = 4 x √(3) ≈ 6.93
b. 3√5 ≈ 6.71
c. 5√2 ≈ 7.07
d. 2√2 x√5 ≈ 5.66
e. 2√13 ≈ 7.21
f. 3√2 x √3 ≈ 6.00
Therefore, the order from least to greatest is:
d. 2√2 x √5 ≈ 5.66
f. 3√2 x √3 ≈ 6.00
a. 4√3 = 4 x √(3) ≈ 6.93
b. 3√5 ≈ 6.71
c. 5√2 ≈ 7.07
e. 2√13 ≈ 7.21
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Help me please I’m confused I can’t figure this out
The required function is g(x) = f(x)-7
What are functions?A function is a relation from a set of inputs to a set of possible outputs, where each input is related to exactly one output.
Given is a graph of two functions, the functions are in a way related, we need to find the relation between the two,
f(x) = x²+5
g(x) = x²-2
We can write,
g(x) = x²+5-7
g(x) = f(x)-2
We can clearly see a vertical shift of 7 units down, of f(x),
Therefore, when we subtract 7 from the function f(x) we will get g(x) [graph attached]
Hence, the required function is g(x) = f(x)-7
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what’s the value of k that transforms f into g
Answer:
Below
Step-by-step explanation:
'k' shifts the graph of f(x) UP by ' k' units k = 6 ( look how far the y-axis intercepts are shifted UP= 6 units from -2 to + 4)
Find the exact value of the following, using the point on the unit circle and the terminal side of each angle. State the point you used to find each trigonometric function value.
Show all work for all there.
Cos 17π/6
sin 20π/3
tan 15π/4
The exact values of the trigonometric functions are
To find the exact value of the trigonometric functions, we will use the reference angle and the quadrant in which the terminal side of each angle is located.
For cos 17π/6, the reference angle is π/6 and the terminal side is in the fourth quadrant. The point on the unit circle in this quadrant with a reference angle of π/6 is (√3/2, -1/2). Therefore, the exact value of cos 17π/6 is √3/2.
For sin 20π/3, the reference angle is π/3 and the terminal side is in the first quadrant. The point on the unit circle in this quadrant with a reference angle of π/3 is (1/2, √3/2). Therefore, the exact value of sin 20π/3 is √3/2.
For tan 15π/4, the reference angle is π/4 and the terminal side is in the third quadrant. The point on the unit circle in this quadrant with a reference angle of π/4 is (-√2/2, -√2/2). Therefore, the exact value of tan 15π/4 is 1.
In summary, the exact values of the trigonometric functions are:
cos 17π/6 = √3/2
sin 20π/3 = √3/2
tan 15π/4 = 1
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PLEAAAASEEEE HELPP!!!!!!!!!!! I WILL GIVE BRAINLIEST!!!!!!!!!!
The line's y-intercept is equal to -3.
An inequality to express the possible distances Jim and Lee can travel in the taxi is 1.75x + 3.00 < 45.
What is y-intercept?In Mathematics, the y-intercept is sometimes referred to as an initial value or vertical intercept and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
Based on the information provided about the line on the graph, we have the following:
y-intercept of function P = (0, -3).
Next, we would determine the possible distances Jim and Lee can travel in the taxi:
1.75x + 3.00 < 45.
1.75x < 45 - 3
1.75x < 42
x < 42/1.75
x < 24.
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Six times the quantity negative two x plus three y
Answer: 12x+18y
Step-by-step explanation:
First analyze the statement "two x plus three y." This means you are multiplying 2 x's, multiplying 3 y's, and adding the addends. So its 2x+3y. Then apply the statement "six times the quantity." This means you are taking the quantity found (2x+3y) and multiply by 6. So its 6(2x+3y). Finally apply distributive property theorem: a(b+c)=ab+ac. So its 6(2x+3y) = 12x+18y.
Shaquille baked 4 times as many chocolate chip cookies as vanilla cupcakes. He baked 48 chocolate chip cookies. Write an equation that can be used to find the number of vanilla cupcakes, x, that Shaquille baked.
Shaquille baked 12 vanilla cupcakes and the equation to depict the number of vanilla cookies is 48 = 4x.
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution technique. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve. Learn about the graphical approach and the algebraic method before beginning to solve the linear equations using the substitution method.
Let us suppose the number of vanilla cupcakes = x.
The chocolate chip cookies are:
48 = 4x
x = 12
Hence, Shaquille baked 12 vanilla cupcakes and the equation to depict the number of vanilla cookies is 48 = 4x.
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Giving Brainlist
Please show the steps :)
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Let
f(x)=−2x+4 and g(x)=−6x -7. Find f(x)−g(x).
Identify the number of solutions of the polynomial equation. Then find all the solutions. 4x^(5)-8x^(4) +6x^(3)=0
The number of solutions of the polynomial equation, 4x^(5)-8x^(4) +6x^(3)=0 is 5 and the solutions are x=0, x=3/2, and x=1.
The polynomial equation at hand is of degree 5, which means that the highest power of the variable present in any term is 5.
Therefore, we can infer that the equation can be written in the form of ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0, where a, b, c, d, e, and f are constants and x is the variable. To solve this equation, we can try factoring it:
4x^(5)-8x^(4) +6x^(3)=0
2x^(3)(2x^(2)-4x+3)=0
2x^(3)(2x-3)(x-1)=0
The solutions are x=0, x=3/2, and x=1.
Therefore, the number of solutions of the polynomial equation is 5 and the solutions are x=0, x=3/2, and x=1.
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SSD Provided Links O RATIONAL EXPRESSIONS Simplifying a ratio of factored polynomials: Linear factors Simplify. (18(3x-4))/(6(x-8)(3x-4)) You may leave the numerator and denominator of your answer in
The simplified ratio of factored polynomials is 18/(6(x-8)).
What is polynomial?A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial is x^2 + 5x + 6.
The question is asking to simplify the ratio of factored polynomials (18(3x-4))/(6(x-8)(3x-4)). To simplify this ratio, we can divide the numerator and denominator by the common factors.
The numerator and denominator both have the factor of 3x-4, so we can divide both the numerator and denominator by this common factor.
The numerator then becomes 18/(6(x-8)) and the denominator becomes 1.
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A drilling crew dug to a height of -323 feet during their first day of drilling. On the second day, the crew dug down 1933 feet more than on the first day. Describe the height of the bottom of the hole after the second day.
The height of the bottom of the hole after the second day is 2579 feet.
What is Addition?Mathematicians employ the action of addition to combine numbers. The sum of the given numbers is the outcome of addition, or the total of the given numbers.
As per the given data:
Drilling on first day = 323 feet.
Drilling on second day = drilling on first day + 1933 feet
Drilling on second day = 323 feet + 1933 feet
= 2256 feet
Total drilling = Drilling on first day + Drilling on second day
= 323 feet + 2256 feet
= 2579 feet
Hence, the height of the bottom of the hole after the second day is 2579 feet.
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6. General questions 1. volume of pyramid b) progress , ideas • some people remembered a formula for volume of pyramid V = 1/3 lwh MAIN PROBLEM: where dues this come from? Why 1/3 ? • one strategy: dissect cube (orrectangule box) (assume for now l=w=h= 1) what is volume of negative space, compared to pyramid ? • second strategy glut multiple priemies together • third strategy: Slice pyramid horizontally Problems: • Keep thinking about strategy one and the • For strategy 3, fiad fald volume for four blocks that I drew above. (That is an overestimat) • Also we smiler stratey to set can underestimate That give range? • Try ti make more
These three strategies can help you understand why the volume of a pyramid is 1/3 lwh.
The formula for the volume of a pyramid is V = 1/3 lwh and the reason why the value is 1/3 is because of the three different strategies that can be used to calculate it.
The first strategy is to dissect a cube (a 3-dimensional rectangle) into the pyramid and the remaining negative space (assuming l=w=h=1). Comparing the volume of the pyramid to the negative space will show that the pyramid takes up 1/3 of the cube.
The second strategy is to stack multiple pyramids together. This will show that the sum of their volumes is equal to one third the total volume of the base they are stacked on.
The third strategy is to slice the pyramid horizontally, and calculate the volume of the four blocks. This will overestimate the volume of the pyramid, but by subtracting this volume from the total volume of the base, you can get a lower limit for the volume of the pyramid.
These three strategies can help you understand why the volume of a pyramid is 1/3 lwh.
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35% of the campers went on a hike after dinner. If 35 campers went on the hike, what is the total number of campers at the camp
The total number of campers at the camp is calculted to be 100 campers.
To find the total number of campers at the camp, we need to use the given information about the percentage of campers that went on the hike and the number of campers that went on the hike.
35% = 35 campers / Total number of campers
Cross-multiplying and simplifying gives us:
35% * Total number of campers = 35 campers
Dividing both sides by 35% gives us:
Total number of campers = 35 campers / 35%
Converting 35% to a decimal gives us:
Total number of campers = 35 campers / 0.35
Solving for the total number of campers gives us:
Total number of campers = 100 campers
So the total number of campers at the camp that went on for hike is 100 campers.
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What types of angles are shown by the window-glass shapes? Or, what kind of angles could there be?
In the given window there are both acute and obtuse angles are shown.
What is Coordinate system?a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space
We have to find the types of angles are shown by the window-glass shapes
An angle is formed when two straight lines or rays meet at a common endpoint.
As we observe the angles are less than 180 degrees.
Angles between 0 and 90 degrees are called acute angles.
Angles between 90 and 180 degrees are known as obtuse angles.
Hence, In the given window there are both acute and obtuse angles are shown.
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Which points would you find on the graph for |x|+3>7?
7
-5
-4
-2
For the inequality |x| + 3 > 7, the points which are on its graph is -5 and 7.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
To solve the inequality |x| + 3 > 7, we need to isolate the absolute value by subtracting 3 from both sides, and then split it into two cases -
|x| > 4 and -(|x|) > 4 (by multiplying both sides by -1)
Simplifying the second inequality, we get -
|x| < -4
But this is impossible, because the absolute value of any number is always non-negative.
Therefore, the second inequality has no solutions.
For the first inequality, we have -
|x| > 4
This means that x is either less than -4 or greater than 4.
Therefore, the points on the graph that satisfy the inequality are -
-5 and any value less than -4
Any value greater than 4
So the points on the graph that satisfy the inequality are -
-5 and any value less than -4 or greater than 4.
Therefore, the correct options are -
-5 and 7.
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An 80.0-kg fisherman jumps from a dock into a 100.0-kg rowboat which is not moving. If the velocity of the fisherman is 4.00 m/s when he jumps into the boat, what is the final velocity of the fisherman and the boat?
If the velocity of the fisherman is 4.00 m/s when he jumps into the boat, then the final velocity of the fisherman and the boat is 1.78 m/s.
What is momentum?Momentum is a vector quantity, which means that it has both magnitude and direction.
According to question:We can solve this problem using the law of conservation of momentum, which states that the total momentum of a system is conserved if there are no external forces acting on it.
The system's starting momentum is determined by:
p1 = m1v1
where p1 is the initial momentum of the fisherman, m1 is his mass, and v1 is his initial velocity. Since the boat is initially at rest, its momentum is zero. As a result, the system's overall initial momentum is:
p1tot = p1 + p2 = m1v1
where p2 is the initial momentum of the boat and is equal to zero.
When the fisherman jumps into the boat, the system becomes a closed system with no external forces acting on it. As a result, the system's overall momentum must be conserved.
p1tot = p2tot
where p2tot is the final momentum of the system. The system's final momentum is determined by:
p2tot = (m1 + m2)vf
where m2 is the mass of the boat, and vf is the final velocity of the boat and the fisherman.
We can rearrange these equations to solve for the final velocity vf:
p1tot = p2tot
m1v1 = (m1 + m2)vf
vf = (m1v1)/(m1 + m2)
Substituting the given values, we get:
vf = (80.0 kg)(4.00 m/s)/(80.0 kg + 100.0 kg)
vf = 1.78 m/s
Therefore, the final velocity of the fisherman and the boat is 1.78 m/s.
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Use the unpaid balance method to find the finance charge on the credit card account. Last month's balance, the payment, the annual interest rate, and any other transactions are given below. Last month's balance, $530
Payment, $350
Interest rate, 19.6%
Bought dog. $190
Bought pet supplies, $55
Paid veterinarian b, $100
The finance charge is 5
(Round to the nearest cent as needed)
The finance charge for the credit card account for this billing cycle is $96.08.
How do we calculate the finance charge?The finance charge is the cost of consumer credit. It includes any charge payable directly or indirectly by the consumer and imposed directly or indirectly by the creditor as a result of or as a condition of credit extension.
Step 1: To calculate the average daily balance
Daily balance for days 1-29:
= $530 (the balance from last month)
Daily balance for day 30:
= $530 - $350 payment + $190 dog + $55 pet supplies - $100 vet bill
= $275
The average daily balance for the billing cycle is:
= (29 x $530 + 1 x $275) / 30
= $16,400 / 30
= $546.67
Step 2:
The portion of the balance subject to interest is the average daily balance minus the payment. The portion subject to interest is:
= $546.67 - $350
= $196.67
Step 3: Calculate the interest charged for the billing cycle
Monthly interest rate = 19.6% ÷ 12 = 0.01633
The Interest charged for the cycle is:
= Portion subject to interest x Monthly interest rate x Number of days in the billing cycle
= $196.67 x 0.01633 x 30
= $96.08
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Write the subtraction sentence that is shown on the number line (Do not reduce the fractions)
We get 3/4 when we subtract 4.4/4 from 7.5/4.
How does subtract example work?
In mathematics, subtraction involves removing anything from a grouping or a number of objects. Whatever is left inside the group gets smaller as you subtract. The following subtraction issue, five minus three equals, is an illustration. 2
Does it say subtract or subtraction?
Short version: "Subtract" and "subtraction" (without the "s") are the proper forms. The fact that many languages have a term with a similar meaning that does contain an "s"—for example, solitaire in French and substrate in Spanish—probably explains how frequently English language learners make the error.
In light of the stated query
There is a number line with two numbers on it.
The one just after 4/4 and another one is after 7/4
Hence, the final answer is 7.5/4 -4.5/4 = 3/4
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Find the gradients of lines A and B.
26/63 Marks
B
6
4
3
21
1
-3-2-10 1 2 3 4 5 6
2
A
do No
70%
X
Answer:
Gradient of A: [tex]2[/tex]
Gradient of B : [tex]- 1[/tex]
Step-by-step explanation:
Gradient of a line is the slope of the line
Slope = rise/run
rise = difference in y values between any two points on the line
run = difference in x values between the corresponding points
Line A
Take points (0, 1) and (3,7)
rise = 7 - 1 = 6
run = 3 - 0 = 3
slope = gradient = 6/3 = 2
Gradient of a line which goes diagonally up from left to right is positive
Line B
Take points (0,5) and (5, 0)
rise = 0 - 5 = - 5
run = 5 - 0 = 5
slope = gradient = -5/5 = - 1
Gradient of a line which goes diagonally down from left to right is negative
A baseball diamond is a square with side length about 27 m.
The player throws the ball from second base to home plate.
How far did the player throw the ball? Round your answer to
the nearest whole number.
Answer:
half
Step-by-step explanation: