The horse weighs 615 pounds.
Explanation:Let's assume the rider's weight is x.
The horse's weight is 6 times the rider's weight plus 45 pounds: 6x + 45.
The total weight of the horse and rider is 710 pounds: 6x + 45 + x = 710.
Combining like terms: 7x + 45 = 710.
Subtract 45 from both sides: 7x = 665.
Divide both sides by 7: x = 95.
So, the rider weighs 95 pounds.
Substitute x = 95 back into the equation to find the horse's weight: 6(95) + 45 = 570 + 45 =
The horse weighs 615 pounds.
To solve this problem, we will set up an equation where [tex]\( h \)[/tex] represents the horse's weight and [tex]\( r \)[/tex] represents the rider's weight. According to the problem:
1. The horse's weight is 45 pounds more than six times the rider's weight, so we can express this as:
[tex]\[ h = 6r + 45 \][/tex]
2. The total weight of the horse and the rider is 710 pounds, so we have:
[tex]\[ h + r = 710 \][/tex]
Now we have a system of equations:
[tex]\[ h = 6r + 45 \][/tex]
[tex]\[ h + r = 710 \][/tex]
We can substitute the first equation into the second to solve for \( r \):
[tex]\[ (6r + 45) + r = 710 \][/tex]
[tex]\[ 7r + 45 = 710 \][/tex]
Now, we solve for[tex]\( r \)[/tex]:
[tex]\[ 7r = 710 - 45 \][/tex]
[tex]\[ 7r = 665 \][/tex]
[tex]\[ r = \frac{665}{7} \][/tex]
[tex]\[ r = 95 \][/tex]
Now that we have the rider's weight, we can find the horse's weight:
[tex]\[ h = 6r + 45 \][/tex]
[tex]\[ h = 6 \times 95 + 45 \][/tex]
[tex]\[ h = 570 + 45 \][/tex]
[tex]\[ h = 615 \][/tex]
As a regular pentagon is dilated by a scale factor of 3 to create a new pentagon. Which statement is true?
F. The perimeter of the new pentagon is 9/4 the perimeter of the original.
G. The perimeter of the new pentagon is 9/2 the perimeter of the original.
H. The perimeter of the new pentagon is 15/2 the perimeter of the original.
J. The perimeter of the new pentagon is 3/2 the perimeter of the original.
When a shape is dilated by a scale factor, all lengths within the shape are multiplied by that factor. So, when the regular pentagon is dilated by a scale factor of 3, the perimeter of the new pentagon is 3 times the original. The correct answer is that the perimeter of the new pentagon is 9/2 the perimeter of the original.
Explanation:In the subject of Mathematics, particularly with shapes and scaling, when a shape is dilated by a scale factor, all lengths within the shape are multiplied by that factor. So, when your regular pentagon is dilated by a scale factor of 3, this means that each side of the pentagon is multiplied by 3. As the pentagon has 5 sides, the total perimeter will be multiplied by 3 as well.
Therefore, the perimeter of the new pentagon is 3 times the perimeter of the original pentagon. This eliminates options F, H, and J, and we find that the correct answer is:
G. The perimeter of the new pentagon is 9/2 the perimeter of the original.
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What is 1.47 x 10 minus 3.56 x 10
−2i⋅(−2i) i need help with this problem pleas someone
The sum of two consecutive odd integers is 32. Find the integers
When do you need to compare real-world numbers?
A yard is equal in length to three feet. The function f(x) takes a measurement in yards (as input) and returns a measurement in feet (as output). What number will the function return if the input is 15.4?
Answer:
This may be perfectly expressed in a Rule of Three as:
If 1 yard is equal to 3 feet
15.4 yards are equal to x feet
1 yard-----3feet
15.4 yards------x
Then:
[tex]x=\frac{(15.4 yards)(3 feet)}{1 yard}[/tex]
[tex]x=46.2 feet[/tex]
Therefore the answer is 46.2 feet
carol has 8 hours to spend on a mountain hike. she can walk up the trail at an average of 2 mph and can walk down at an average of 3 mph. how long should she plan to hike uphill before turning around
A circle is inscribed in a square whose side is 6. Express the area of the circle in terms of PI.
HOW CAN YOU SAY 100,203 IN WORD FORM!!!!!
Can someone please help me
(x-4)(x+4)(x-7) is greater than or equal to 0
30tens-3tens3tenths=
the population of middleton is six thousand fifty four people write this number in standard form
Answer:
The answer to that question is 6,054
How is dividing fractions related to multiplying
What Is 16/6 As a Mixed Number/
the sum of twice a number and 13 is 75
one table sale has 75 cookies. Another table has 60 cupcakes. which table allows for more rectangular arrangements when all the cookies and cupcakes are displayed?
Rectangular arrangements are made when the number of items can be arranged into rows and columns to form a rectangle. When comparing the number of these arrangements that can be made with 75 cookies and 60 cupcakes, the table with 60 cupcakes allows for more arrangements.
Explanation:The subject of this question falls under the topic of mathematics, specifically, it is related to the concept of rectangular arrangements or factoring numbers. In this scenario, we have to determine which number (75 cookies or 60 cupcakes), when all items in a table are displayed, allows for more rectangular arrangements.
A rectangular arrangement can be made when the number of items can be arranged into rows and columns to form a rectangle. For instance, 12 items can form a 3x4 or 2x6 rectangular arrangement.
Now let's figure out how many rectangular arrangements can be made for each table:
75 (cookies) = 1x75, 3x25, 5x15 are three rectangular arrangements.60 (cupcakes) = 1x60, 2x30, 3x20, 4x15, 5x12, 6x10 are six rectangular arrangements.So, the table with 60 cupcakes allows for more rectangular arrangements than the one with 75 cookies.
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you have $12 to buy five goldfish for your new fish tank. Write and solve an inequality that represents the prices you can pay per fish.
Answer:
The required inequity is: [tex]5x\leq 12[/tex]
The price of a gold fish should be less than or equal to $2.4 so that you can by 5 fish.
Step-by-step explanation:
Consider the provided information.
You have $12 to buy five goldfish for your new fish tank.
Let the cost of a goldfish is $x.
For 5 gold fish you needs to pay $5x.
Thus, the required inequity is:
[tex]5x\leq 12[/tex]
We use less than equal to sign as you can pay $12 but not more than it.
Now simplify the above inequity as shown:
Divide both the sides by 5
[tex]\frac{5x}{5}\leq \frac{12}{5}[/tex]
[tex]x\leq 2.4[/tex]
Thus, the price of a gold fish should be less than or equal to $2.4 so that you can by 5 fish.
How many times does 3/4 go into 8 1/2
Why doesn’t zero have an opposite
Final answer:
Zero does not have an opposite because it is the identity element in addition; adding zero to any number yields that number without change. Zero's opposite is itself since 0 + 0 = 0. The concept of an 'opposite' is inapplicable for zero displacement or the null vector in vector algebra due to their lack of direction and magnitude.
Explanation:
The question is asking why zero does not have an opposite. In mathematics, zero is unique because it is the only real number that is neither positive nor negative. When we talk about the opposite of a number, we typically mean a number that, when added to the original number, yields zero. For any non-zero number, its opposite is the number with the same magnitude but a different sign. However, zero is the identity element for addition, which means that when you add zero to any number, you get the same number back without any change. Therefore, zero's opposite is itself, because 0 + 0 = 0.
In the context of displacement and vectors, an opposite might refer to direction rather than a notion of being negative or positive. For instance, a displacement of -100 m represents a movement of 100 m in the direction opposite of the chosen positive direction. However, zero displacement means no movement at all, so there can't be an opposite direction.
To elaborate on the concept, when dealing with vector algebra, the equivalent of zero is the null vector, which has no magnitude or direction. Therefore, it doesn't have an opposite because there is no direction or magnitude to invert or negate. Similarly, for an object making a round trip and returning to its starting point, there's zero displacement because its starting and ending points are the same, despite any distance traveled during its journey. This is another instance where zero's unique properties make the concept of an opposite meaningless.
True or false all fraction can be written as a repeating decimal if it's false write example that proves this statement is false
The expression to find the perimeter of a rectangle is 2(length + width). What is the perimeter, in units, of a rectangle of length fraction 1 over 7 unit and width fraction 1 over 2 unit?
Answer:
perimeter of rectangle is 9/7 units.
Step-by-step explanation:
The perimeter of a rectangle is given by
Perimeter = 2(length + width)
Given that
[tex]length=\frac{1}{7}\\\\width=\frac{1}{2}[/tex]
Substituting these values in the above formula
[tex]P=2(\frac{1}{7}+\frac{1}{2})[/tex]
Add the fractions. The LCD is 14. So, multiply and divide by 14
[tex]P=\frac{2}{14}(\frac{1}{7}\times14+\frac{1}{2}\times14)\\\\P=\frac{1}{7}(2+7)\\\\P=\frac{9}{7}[/tex]
Thus, perimeter of rectangle is 9/7 units.
Item 2 Solve the equation. 6.7x=5.2x+12.3
how was it 17? and I pretty much know the rest
Express 8 inches as a fraction of 3 feet in lowest terms
3 feet = 36 inches
so the fraction is 8/36
36/4 = 9
8/4=2
so 8/36 reduces to 2/9
A statement and portions of the flowchart proof of the statement are shown.
Which reason should appear in the box labeled 1?
Ruler Postulate
Angle Addition Postulate
Linear Pair Postulate
Angle Congruence Postulate
Answer :- Angle addition postulate is the reason which should appear in the box labeled 1.
Explanation:-
Angle addition postulate states that for a given angle ∠AOC if P is interior of ∠AOC then ∠AOC=∠AOP+∠POC.
In the given figure it can be seen that
C is interior of ∠BAD then by angle addition postulate
∠BAC+∠CAD=∠BAD which in box 1.
Thus the second option is correct . "Angle Addition Postulate" is the reason which should appear in the box labeled 1.
Write and solve a proportion to answer the question. What number a is 70% of 70
The number that is 70 percent of the number 70 will be 49.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Let the number be 'x'. Then the equation is given as,
x = 70% of the 70
Simplify the equation, then the value of the number is calculated as,
x = 70% of the 70
x = 0.70 × 70
x = 49
The number is 49.
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Evaluate Each Expression: | 4/13 |
The expression | 4/13 | evaluates to 4/13 because the absolute value of a positive number is the number itself.
The student's question asks to evaluate the expression | 4/13 |, which involves the use of absolute value. The absolute value of a number is the distance of that number from 0 on the number line, regardless of the direction. Therefore, the absolute value of any positive or negative number is a positive number, and the absolute value of 0 is 0 itself.
In this case, since 4/13 is a positive number, its absolute value is the same as the number itself. So the evaluation of the expression | 4/13 | is simply 4/13.
umm.......how the heck do I solve this??? either or both just plz I need ur help guys
simplify each expression m³m⁴