Answer: The equations are 5t + e = 725 and 3t + e = 505
Step-by-step explanation: We shall start by assigning letters to the unknown variables, hence we shall call the treadmill t, and we shall call the elliptical machine e.
If on Saturday, she ran 5 miles on the treadmill and 1 mile on the elliptical machine and she burned 725 calories in the process, we can express this as
5t + e = 725 ------(1)
Also on Sunday, she ran 3 miles on the treadmill and 1 mile on the elliptical machine and burned 505 calories in the process, that too can be expressed as
3t + e = 505 ------(2)
We now have a pair of simultaneous equations which an be solved by the elimination method (reason being that on of the unknowns have the same coefficient, that is variable e).
Subtract equation (2) from equation (1) and you arrive at;
2t = 220
Divide both sides of the equation by 2
t = 110
Having calculated the value of t, substitute for the value of t into equation (1)
5t + e = 725
5(110) + e = 725
550 + e = 725
Subtract 550 from both sides of the equation
e = 175
The above calculations shows that the calories burned on each gym equipment are;
Treadmill = 110 per hour
Elliptical = 175 per hour
What is the approximate surface area of the sphere?
What is the area of the shape below? Hint: use the formula: A =1/2 h (b1 + b2) *
A. 54.6 yd squared
B. 172.5 yd squared
C. 112.5 yd squared
D. 120 yd squared
Answer:
B. 172.5 yd squared
Step-by-step explanation:
FIrst, we must find half of the height, which is 15/2 or 7.5.
Next we have to multiply 7.5 times (15+8) which is B.
What is the value of the rational expression when x=-2? -7 -9 9 7
The value of the rational expression [tex]\frac{2x^2+5x+9}{x^2+2x-1}[/tex] when x =-2 is -7
What is ration expression?A rational expression is an expression that can be written in the form of a ratio of two polynomial expressions. Specifically, it is a fraction in which the numerator and denominator are both polynomials.
How to find value of rational expression?To find the value of the rational expression when x=-2, we substitute -2 for x in the expression and simplify:
[tex]\frac{2x^2 + 5x + 9}{x^2 + 2x - 1}[/tex]
= [tex]\frac{(2(-2)^2 + 5(-2) + 9)}{((-2)^2 + 2(-2) - 1)}[/tex]
=[tex]\frac{8 - 10 + 9}{4 - 4 - 1}[/tex]
= [tex]\frac{7}{-1}[/tex]
= -7
Therefore, the value of the rational expression [tex]\frac{2x^2+5x+9}{x^2+2x-1}[/tex] when x =-2 is -7.
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The question is incomplete, see full details in the attached image.
The value of the expression is Option a. -7.
To find the value of the rational expression (2x² + 5x + 9) / (x² + 2x - 1) when x = -2, we need to substitute -2 into the expression.
First, let's calculate the numerator:
2(-2)² + 5(-2) + 9= 2(4) -10 + 9= 8 - 10 + 9= 7Next, we calculate the denominator:
(-2)² + 2(-2) - 1= 4 - 4 - 1= -1Now, we divide the numerator by the denominator:
= 7 / (-1)= -7So, the value of the rational expression when x = -2 is -7. Therefore, the correct answer is Option a. -7.
Complete question:
What is the value of the rational expression (2x²+5x+9)/x²+2x-1 when x=-2
a. -7
b. -9
c. 9
d. 7
If tan(θ) = cot(40°), what is θ?
Answer:
50 lol
Step-by-step explanation:
Answer:
Θ = 50°
Step-by-step explanation:
Using the cofunction identity
tan(90 - x)° = cotx°
Given
cot40°, then
tan Θ = tan(90 - 40)° = tan50°
Thus Θ = 50°
how do i find the area of a trapezoid (pictures provided)
Answer:
(10x - 5) square units.
Step-by-step explanation:
Let the lengths of equal sides be x units.
Hence, AB + AD + DC = x + x + x = 3x
Therefore, BC = 3x - 2
[tex]Area \: of \: trapezoid \\ = \frac{1}{2} (AD + BC) \times 5 \\ = \frac{1}{2} (x + 3x - 2) \times 5 \\ = \frac{1}{2} (4x - 2) \times 5 \\ = \frac{1}{2} \times 2 (2x - 1) \times 5 \\ = (2x - 1) \times 5 \\ = (10x - 5) \: {units}^{2} [/tex]
Which rules of exponents will be used to evaluate this expression? Check all that apply.
StartFraction left-brace (negative 8) Superscript 4 Baseline right-brace Superscript negative 5 Baseline Over (negative 8) Superscript 6 Baseline EndFraction
product of powers
quotient of powers
power of a power
power of a product
negative exponent
zero exponent
Answer:
quotient of powers power of a power negative exponentStep-by-step explanation:
Given
( -8⁴)⁻⁵ / ( -8⁶)Evaluating:
( -8⁴)⁻⁵ / ( -8⁶) =( -8⁴ˣ⁻⁵) / ( -8⁶) = ⇒ Power of a power (nᵃ)ᵇ = nᵃᵇ(-8⁻²⁰)/( -8⁶) =8⁻²⁰⁻⁶ = ⇒ Quotient of powers nᵃ/nᵇ = nᵃ⁻ᵇ8⁻²⁶ = 1/8²⁶ ⇒ Negative exponent n⁻ᵃ = 1 / nᵃUsed rules:
quotient of powers power of a power negative exponentAnswer:
B-quotient of powers
C-power of a power
E-negative exponent
Step-by-step explanation:
Two nickels are what fraction of a dollar?
Answer:
1/10
Step-by-step explanation:
Answer:
2/20?
Step-by-step explanation:
At Marvin's Motorcycle's a pair of gloves sell for $85. Marvin purchases them from the manufacturer for $50. What is the percent markup on the gloves?
Plz help! 10 points
A sphere has been placed inside an cylinder with the same dimensions;both have a radius of 6cm,and a height of 12cm How many cubic centimeters of space does the sphere fill not fill up. A.432pi cm B.72 pi cm C.288 pi cm D.144 pi cm
Answer:
D
Step-by-step explanation:
Final answer:
To find the cubic centimeters of space not filled by the sphere in the cylinder, subtract the volume of the sphere (288π cm³) from the volume of the cylinder (432π cm³), yielding 144π cm³. Therefore, the correct answer is D. 144π cm³.
Explanation:
To determine how many cubic centimeters of space the sphere does not fill in the cylinder, we first need to calculate the volume of the cylinder and then subtract the volume of the sphere from it.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. In this case, with a radius of 6 cm and height of 12 cm, the volume is:
[tex]V_{cylinder}[/tex] = π × (6 cm)² × 12 cm = 432π cm³.
The volume of a sphere is given by the formula V = 4/3 πr³. With a radius of 6 cm, the volume is:
[tex]V_{sphere[/tex] = 4/3 π × (6 cm)³ = 288π cm³.
The space the sphere does not fill up in the cylinder is:
Space not filled = [tex]V_{cylinder}[/tex] - [tex]V_{sphere[/tex] = 432π cm³ - 288π cm³ = 144π cm³.
Therefore, the answer is D. 144π cm³.
3 x + 9 = box If the equation has no solution, which expression can be written in the box on the other side of the equation?
Answer:
Step-by-step explanation
3x+9=?
subtract 9 from both sides
3x=-9
divide by 3
x=-3
Now plug it in to find your soultion that is not correct
3(-3)+9=
-9+9=
0
Answer:
To find the expression for the box, we need to simplify the equation. Let's break it down step by step:
3 (x + 1) + 9 = box
First, distribute the 3 to the terms inside the parentheses:
3x + 3 + 9 = box
Next, combine like terms:
3x + 12 = box
Now, we can compare the simplified equation to the given expressions:
3 (x + 4)
2 (x + 6) + x
4(x – 3) – x
3 (x + 1) + 9
We are looking for an expression that matches our simplified equation, which is 3x + 12. By comparing the expressions, we can see that 3 (x + 1) + 9 is the same as 3x + 12.
Therefore, the expression that can be written in the box is 3 (x + 1) + 9.
Please give me brainliest!
Please help me with #3.
Answer:
Total lateral surface of the pyramid = 54 [tex]cm^{2}[/tex]
which agrees with the first listed answer.
Step-by-step explanation:
Notice that the pyramid has for base an equilateral triangle of base 5 cm, and has three lateral triangles which have all the same dimensions for their base (5 cm - since they are all connected to the base of the pyramid), and their height (7.2 cm).
The actual LATERAL surface, includes only the surface of the three lateral triangles.
We use the formula for the area of a triangle: [tex]Area=\frac{base \,*\, height}{2}[/tex]
to calculate the area of each lateral triangle:
[tex]Area=\frac{5\,cm \,*\, 7.2\,cm}{2} \\Area=18 \,cm^2[/tex]
and then multiply the result by three (to account for the three lateral faces)
Therefore, the total lateral surface is:
Total lateral surface = 3 * 18 = 54 [tex]cm^{2}[/tex]
do the side lengths 4.1,8.2,and 12.2 for a triangle
Answer:
Step-by-step explanation:
Three line segments can form a triangle if the length of the longest segment is greater than the sum of the lengths of the shorter segments.
4.1 + 8.2 > 12.2
12.3 > 12.2
true
They can form a triangle.
Now if c is the length of the longest side and a and b are the lengths of the shorter sides, then:
- if , [tex]c^{2}[/tex] = [tex]a^2 + b^2[/tex] the triangle is right
- If [tex]c^2 < a^2 + b^2[/tex]
- if [tex]c^2 > a^2 + b^2[/tex] the triangle is obtuse
[tex]4.1^2 + 8.2^2 = 16.81 + 67.24 = 84.05\\12.2^2 = 148.84\\148.84 > 84.05[/tex]
The triangle is obtuse.
PLEASE ANSWER ASAP!!!
Find the volume of the figure. Round to the nearest tenth, if necessary.
a regular hexagonal prism with base area 25 in? and height 8 in.
The volume of the figure is
Answer:
The volume of the figure is since you have to do width times height so 25 times 8 which would be 200 as your answer.
Hope it helps
It costs $25 to buy 5 sandwiches from a vending machine. At this rate, what is the cost for 8 sandwiches?
Answer:
x = 40
Step-by-step explanation:
We can use a ratio to solve
$25 x
------- = --------
5 8
Using cross products
25*8 = 5x
200 = 5x
Divide each side by 5
200/5 = 5x/5
40 =x
3. Of the three expressions shown, which two
are equivalent?
3+2(9 + 2n) 7(3 + 4n) 21 + 4n
Answer:
the answer would be the first and last equation
Step-by-step explanation:
both equations equal 21+4n
Final answer:
After simplifying the expressions, it's found that 3 + 2(9 + 2n) simplifies to 21 + 4n, and the third expression is exactly 21 + 4n. These two expressions are equivalent.
Explanation:
To determine which two of the three expressions are equivalent, we need to simplify each expression and compare them.
Let's simplify each expression:
3 + 2(9 + 2n) = 3 + 18 + 4n = 21 + 4n
7(3 + 4n) = 21 + 28n
21 + 4n = 21 + 4n
Now, we can compare them:
The first expression, after simplification, becomes 21 + 4n.
The second expression is 21 + 28n, which is not equivalent to the first.
The third expression is exactly 21 + 4n, which is equivalent to the first expression.
So, the expressions 3 + 2(9 + 2n) and 21 + 4n are equivalent.
If a circle has a radius of 17 cm. What is the circumference of the circle ?
Answer:
106.81 cm or 107 cm.
Step-by-step explanation:
The formula for finding the circumference (perimeter) of a circle is 2 times pi times r or the radius of the circle, or you can find the diameter by multiplying the radius by 2, in this case 34 and multiply that by pi. The diameter is 34 so multiply that by pi and you get 106.81 cm as an approximate. Hope this helps!
The circumferences of the circle is 106.76 cm.
What is circumferences?The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its centre.
Given that, a circle has radius = 17 cm
We know that, circumference = π × diameter
diameter = 2 × radius = 17 × 2 = 34
circumference = 34 × 3.14 = 106.76 cm
Hence, the circumference of the circle is 106.76 cm
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Find the value of x, then use this value to determine the measure of each of the angles.
x =
The measurement of angle AOB = degrees.
The measurement of angle COB = degrees.
Answer:
x=15
AOB= 15
COB= 165
Step-by-step explanation:
Help me ok thank you
Answer:
-422
Step-by-step explanation:
The elevation of the Dead Sea is 422 meters below sea level, meaning that it is -422.
172.7=3.14d
Solve for d
Answer:
55
Step-by-step explanation:
Divide both sides by 3.14 to get d by itself.
172.7 / 3.14 = 55 = d
a(x−b) +bx+c=a+b solve for x helpp
88 out of 132 in fraction form
Answer:
[tex]\frac{2}{3}[/tex]
Answer:
2/3
Step-by-step explanation:
Divide both the numerator and denominator by the GCD
88 ÷ 44
132 ÷ 44
Reduced fraction:
2
3
Therefore, 88/132 simplified is 2/3
A wire is needed to support a vertical pole 18 feet high. The cable will be
anchored to a stake 10 feet from the base of the pole. How much cable is
needed?
The sum of two numbers increased by 5
Answer:
(x+y)+5
Step-by-step explanation:
To solve this, all you need is two variables to represent the 2 numbers. In this case, I used x and y. After that it says the sum of those 2 numbers increased by 5. All you need to know about that is that after x+y is done, you need to increase it by 5. So in this case,
(x+y)=5 satisfies the statement.
What is the value of x? 6 8 10 12
Answer:
Its 8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
Corri needs to get milk, eggs, bread, and cereal at the store. Since the bread is close to the cereal, Corri always picks up the cereal right after getting bread. List all of the different combinations of ways she can pick up the items she needs. Use the first letter of each item in your list (M, E, B, C)
Answer:
bread
cereal
milk
eggs
Step-by-step explanation:
Answer:mebc,embc, bcem,bcme.
Step-by-step explanation:
The radius of a circle is 1 inch. What is its circumference?
Step-by-step explanation:
use the image below to help
Solve 5 - 2x < 7. Please help me
Answer:
x > -1
Step-by-step explanation:
Answer:
[tex]x>-1[/tex]
Step-by-step explanation:
[tex]5 - 2x < 7[/tex]
[tex]5-2x-5<7-5[/tex]
[tex]-2x<2[/tex]
[tex]$\frac{2x}{2}>\frac{-2}{2}$[/tex]
[tex]x>-1[/tex]
Determine which diagram could be used to prove AABC - AEDC using similarity transformations,
The diagram which could be used to prove AABC - AEDC using similarity transformations is A.
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles; are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]
(|AB| denotes length of line segment AB, and so on for others).
We are given that;
The three figures in the picture
Now, in first figure
Angle BAC= Angle CED
(given)
Angle BCA= Angle ECD
(interior opposite angles)
So, both triangles are congruent
Therefore, by congruent triangles answer will be figure A.
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An atom of lithium has 3 protons 4 neurons and 2 electrons.
What is the overall charge on this atom
A) -3
B) -1
C) +1
D) +3
Answer:
positive 1
Step-by-step explanation:
hope it helps.
give me the brain PLZ:)
Work out the area of this circle.
Take a to be 3.142 and write down all the digits given by your calculator.
13 cm
The area of the circle is found by substitifying the radius into the formula A = πr². In this case, with a given radius of 6.5 cm and π as 3.142, the calculated area is approximately 132.732 square centimeters.
Explanation:To find the area of a circle, you use the formula A = πr², where A represents the area, π is a mathematical constant whose value is given as 3.142 in this case, and r is the radius of the circle.
Since the radius (r) is not directly mentioned in the question, we should understand that the given 13 cm refers to the diameter of the circle, hence the radius will be half, i.e., 13/2 = 6.5 cm.
Substituting these values into the formula gives: A = 3.142 * (6.5)². When you perform the calculation, the result would be about 132.732 square centimeters.
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