Answer:
[tex]x=\dfrac{1}{2} \pi + 2\pi n[/tex]
[tex]x=\dfrac{3}{2}\pi +2 \pi n[/tex]
[tex]x=\dfrac{1}{6}\pi+2 \pi n[/tex]
[tex]x=\dfrac{5}{6}\pi+2 \pi n[/tex]
Step-by-step explanation:
Given trigonometric equation:
[tex]\sin x \cos x &= \dfrac{1}{2} \cos x[/tex]
Rearrange the equation so that it equals zero:
[tex]\begin{aligned}\sin x \cos x &= \dfrac{1}{2} \cos x\\2 \sin x \cos x &= \cos x\\2 \sin x \cos x - \cos x &=0\\ \cos x (2 \sin x - 1)&=0\end{aligned}[/tex]
Apply the zero-product property.
Case 1
[tex]\begin{aligned}\cos x &=0\\x&=\cos^{-1}(0)\\x&=\dfrac{1}{2} \pi +2\pi n, \; \dfrac{3}{2}\pi +2 \pi n\end{aligned}[/tex]
Case 2
[tex]\begin{aligned}2\sin x - 1& = 0\\2 \sin x & = 1\\\sin x & = \dfrac{1}{2}\\x&=\sin^{-1}\left(\dfrac{1}{2}\right)\\x & = \dfrac{1}{6} \pi+2 \pi n, \; \dfrac{5}{6} \pi +2 \pi n\end{aligned}[/tex]
A point has a positive x-coordinate and a positive y-coordinate. which quardrant is in it
Answer: 1
Step-by-step explanation: look at the image attached to show which quadrant is what.
when the x coord is +, it's on the right half of the graph, so by this, quadrants 1 and 4 are possible answers.
when the y coord is +, it's on the top half of the graph, this makes quadrants 1 and 2 possible answers.
look for the consistency, in this case since 1 is the only possible answer between both, the answer is 1
A group of scientists discovered a small creature at the bottom of the ocean that they called a "piknit". when this interesting creature dies, it explodes itself into a number of baby piknits called gogles. the scientists randomly selected 20 piknits from the sea-floor and measured their respective weights in grams. after the piknits died they counted the number of gogles that each piknit produced. they wanted to know if the weight of the piknits can be used to predict the number of gogles.
What are the appropriate null and alternative hypotheses?
Null Hypothesis - H0: There is no linear relationship between the weight of pinknits and the number of gogles.
Alternative Hypothesis - Ha: There is a linear relationship between the weight of pinknits and the number of gogles.
To explain the concept behind this question we first need to know about the principle of correlation.
Correlation - It is a measure of comparison of two quantities by which we compute that which two quantities are linearly equal means that if we change one quantity the other will also change at a constant rate.
This principle simply makes a relationship without causing any effect on the quantities.
Now according to the question, we can see that,
Scientists have selected = 20 pinknitsThe scientists also measured their weights in gramsScientists also wanted to know if a number of gogles could be predicted using the weight of pinknits.Therefore, from the data that scientists predicted, we can conclude that,
Null Hypothesis - H0: There is no linear relationship between the weight of pinknits and the number of gogles.
Alternative Hypothesis - Ha: There is a linear relationship between the weight of pinknits and the number of gogles.
Option 4 is correct.
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A group of scientists discovered a small creature at the bottom of the ocean that they called a "piknit". When this interesting creature dies, it explodes itself into a number of baby piknits called gogles. The scientists randomly selected 20 piknits from the sea-floor and measured their respective weights in grams. After the piknits died they counted the number of gogles that each piknit produced. They wanted to know if the weight of the piknits can be used to predict the number of gogles.
What are the appropriate null and alternative hypotheses?
Group of answer choices
H0: There is no linear relationship between the weight of piknits and the number of gogles
Ha: There is a negative linear relationship between the weight of piknits and the number of gogles
H0: Weight of piknits is a useful predictor for the number of gogles
Ha: Weight of piknits is not a useful predictor for the number of gogles H0: There is a linear relationship between the weight of piknits and the number of gogles
Ha: There is no linear relationship between the weight of piknits and the number of gogles
H0: There is no linear relationship between the weight of piknits and the number of gogles
Ha: There is a linear relationship between the weight of piknits and the number of gogles
Find the average rate of change
Answer:
[tex]\frac{3}{5\pi}[/tex]
Step-by-step explanation:
[tex]\frac{f(5\pi/6)-f(0)}{5\pi/6}=\frac{3}{5\pi}[/tex]
How much work is done on a car if you push with 100 Newtons of force but it does not move?
Answer:
0 Joules (No work)
Step-by-step explanation:
The amount of work done on an object is equal to the force applied to the object times the distance over which the force is applied. In this case, the force applied to the car is 100 newtons, but the car does not move, so the distance over which the force is applied is 0 meters.
Therefore, the amount of work done on the car is 100 newtons * 0 meters = 0 joules. This means that no energy has been transferred to or from the car as a result of the force applied to it.
Given the equation 14.25y = 99.75, determine the value of y.
114.00
85.50
7.00
1421.44
The value of y in the equation 14.25y = 99.75 is C. 7.00.
How for determine the value of y?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, the equation is given as:
14.25y = 99.75
Divide through by 14.25
y = 99.75 / 14.25
y = 7
The value of y is 7.
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help pls i don’t understand this cause my teacher can’t teach
Answer:
3/5
Step-by-step explanation:
AB = AC · cos A
18 = 30 · cos A
cos A = 18/30
cos A = 3/5
Multiple choice math
The solution of the three variable system will be (- 8, 4, - 4).
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The system of equation are,
⇒ - 5x + y - 4z = 60
⇒ 2x + 4y + 3z = - 12
⇒ 6x - 3y - 2z = - 52
Now,
Since, The system of equation are,
⇒ - 5x + y - 4z = 60
⇒ 2x + 4y + 3z = - 12
⇒ 6x - 3y - 2z = - 52
From option c;
⇒ (x, y, z) = (- 8, 4, - 4)
So, Put x = - 8, y = 4 and z = - 4
We get;
⇒ - 5x + y - 4z = 60
⇒ - 5 × - 8 + 4 - 4 × - 4 = 60
⇒ 40 + 4 + 16 = 60
⇒ 60 = 60
And, ⇒ 2x + 4y + 3z = - 12
⇒ 2 × - 8 + 4 × 4 + 3 × - 4 = - 12
⇒ - 16 + 16 - 12 = - 12
⇒ - 12 = - 12
⇒ 6x - 3y - 2z = - 52
⇒ 6 × - 8 - 3 × 4 - 2 × -4 = - 52
⇒ - 48 - 12 + 8 = - 52
⇒ - 52 = - 52
Thus, The solution of the three variable system = (- 8, 4, - 4).
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find the exact length of the curve.x = 1/3 √y (y - 3), 16 ≤ y ≤ 25
The length of the curve x = 1/3 √y (y − 3) is 64/3.
What is arc length?The distance between two point along a segment of a curve is known as the arc length.
The equation of the curve is given by:
x = 1/3 √y (y − 3), 16 ≤ y ≤ 25
Length of the curve y = f(x) between point x =a to x = b is given by:
[tex]\int\limits^b_a {\sqrt{1+[f'(x)]^2} } \, dx[/tex]
√1 + [f′(x)]2 dx.
x = 1/3 √y (y − 3)
x = 1/3 * [tex]y^\frac{3}{2}[/tex] - [tex]y^\frac{1}{2}[/tex]
Let's find the first derivative of x.
dx/dy = 1/3. 3/2. [tex]y^\frac{1}{2}[/tex]- 1/2 . [tex]y^\frac{1}{2}[/tex]
dx/ dy = 1/2 ( [tex]y^\frac{1}{2}[/tex] - [tex]y^\frac{-1}{2}[/tex])
(dx/dy)^2= 1/4 ( [tex]y^\frac{1}{2}[/tex] - [tex]y^\frac{-1}{2}[/tex])^2
= 1/4(y + [tex]y^-^1[/tex]-2)
1 + {f′(x)}2 = 1 + 1/4(y +[tex]y^-^1[/tex]-2)
= 1/4 y + 1/4[tex]y^-^1[/tex]+ 1/2
1 + {f′(x)}2= 1/4 (y + [tex]y^-^1[/tex] + 2)
√[1 + {f′(x)}2] = 1/2 ( [tex]y^\frac{1}{2}[/tex] + [tex]y^\frac{-1}{2}[/tex])
Length of curve is given by:
25
∫ [tex]\frac{\sqrt{y} }{2} +\frac{1}{2\sqrt{y} }[/tex] dy
16
= [tex]\left \{ {{y=25} \atop {x=16}} \right.[/tex] [[tex]y^\frac{3}{2}[/tex]/3 + √y]
= [(25)3/2 /3 + √25] - [(16)3/2 /3 + √16]
= [125/3 + 5] - [64/3 + 4]
= 140/3 - 76/3
= (140 - 76)/3
= 64/3
So the length of the curve is 64/3
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in the equation 0.5x - 8 + 1.5 , the decimal coefficient is ____??
Answer:
0.5
Step-by-step explanation:
A coefficient is a number that multiplies an unknown
What is the slope of the lines that passes through (0,0) and (7,6)
Answer:
Slope is (6/7)
Step-by-step explanation:
6-0= -6
7-0= -7
-6/-7= 6/7
find the centroid of the region in the first quadrant bounded by the given curves. y = x6, x = y6
The area of centroid of the region in the first quadrant bounded by the given curves. y = x6, x = y6 is 17 units.
The centroid can be found if we will integrate the result obtained by subtracting the given two functions .
∫ f(x) - g(x) dx
The limits will be a and b where a = 0 and b =1.
f(x )= x⁶
g(x) =y⁶
= ∫ x⁶ - y⁶dx
=∫ x⁶dx - ∫ y⁶dx
= 1/7 x⁷ - 1/7 x⁷
Now since limits are 0 and 1 ,
1/7 1⁷ - 1/7 0⁷
=17 units
The central point of any geometric figure is known as centroid.
Different figure have different centroid and the all have unique properties.
Integration is a branch of calculus which means to add things up to form a whole.
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points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints. t or f
The given statement is true that the points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.
A line that splits another line segment into two equal halves by intersecting it perpendicularly is known as a perpendicular bisector. A rule, compass, and pencil can be used to create a perpendicular bisector.
When two lines cross at right angles or 90 degrees, they are said to be perpendicular to one another. A line that splits a line into two equally sized parts is known as a bisector. A line segment's perpendicular bisector suggests that it meets the segment at a 90-degree angle and splits it into two equal halves.
Perpendicular bisector theorem"Perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment’s endpoints".
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I only require the explanation, not the answer.
The children in a class state how many children there are in their family.
The numbers they state are given below: 1, 2, 1, 3, 2, 1, 2, 4, 2, 2, 1, 3, 1, 2, 2, 2, 1, 1, 7, 3, 1, 2, 1, 2, 2, 1, 2, 3
So the question that I do not understand is:
Which is the most sensible average to use in the case.
The person with the most through explanation will get brainliest and will get awarded 75 points!
The most sensible average to use in this case would be the mode, which is the value that appears most frequently in the data set. In this case, the mode is 2, which appears 9 times in the data set. This means that the most common number of children in a family in the class is 2.
In this case, the most sensible average to use would be the mode, which is the number that appears most frequently in the data set. This is because the mode represents the most common number of children in the families of the children in the class, which is likely to be a more accurate representation of the typical family size in the class than the mean or median.
To find the mode, we first need to count how many times each number appears in the data set. In this case, the numbers 1, 2, 3, and 4 appear in the data set as follows:
1: 7 times
2: 11 times
3: 3 times
4: 1 time
We can see that the number 2 appears most frequently, with a count of 11. Therefore, the mode in this case is 2, and this is the most sensible average to use in this situation.
A body of ma 80kg i lifted vertically through a ditance 5. 0 metre calculate the work done
4000 N is the work done .
In math, what is a distance?
The length of the segment of the line that connects the supplied two points determines the distance between them. The length of the shortest line segment connecting a point to a line represents the distance between them.
Distance is the sum of an object's movements, regardless of direction. Regardless of an object's starting or ending point, distance can be defined as the amount of ground it has traveled.
m = 80 kg
d = 5m
g = 10 m/s²
work done = force × distance
= mgh
= 80 × 10 × 5
= 4000 N
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which two numbers when multiply gives you 15 and when added gives you -12?
Answer:
The numbers that when multiplied give 15 and when added give -12 are -3 and 5. Multiplying -3 by 5 gives -15, and adding -3 and 5 gives -8.
Explanation:
To find the numbers that when multiplied give 15 and when added give -12, we need to find two numbers that multiply to give -15 and add to give -12. One pair of numbers that satisfy these conditions is -3 and 5. When multiplied, -3 and 5 give -15, and when added, -3 and 5 give -8.
What is the quotient of three and one third ÷ three fourths?
Answer:
Read Below:
12 or 40/9
Unclear, please comment to clarify.
Step-by-step explanation:
Quotient: x, when: [tex]\frac{a}{b} = x[/tex], answer to a division problem.
This could be interpreted 2 ways:
[tex]\frac{(\frac{3}{1/3} )}{3/4}[/tex]
[tex]\frac{9}{3/4}[/tex]
12
or
3 1/3 = 10/3
[tex]\frac{10/3}{3/4}[/tex]
10/3 * 4/3
40/9
1.) Graph the system of equations on the grid below.
4x +2y=-12
3x-5y = -35
Answer:
first equation = red line
second equation = blue line
Step-by-step explanation:
First, we solve for y for both equations
4x + 2y = -12
2y = -12 - 4x
2y = -4x -12
y = -2x - 6
3x - 5y = -35
-5y = -35 - 3x
-5y = -3x - 35
y = (-3/5)x + 7
Select the equations for the lines on the graph.
Answer:
second option
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Red line
using (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (2, 8) ← 2 points on the line
m = [tex]\frac{8-0}{2-0}[/tex] = [tex]\frac{8}{2}[/tex] = 4 , then
y = 4x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (0, 0 ) then
0 = 4(0) + c
0 = 0 + c
0 = c
y = 4x + 0 , that is y = 4x ← equation of red line
Black line
using (x₁, y₁ ) = (0, 10) and (x₂, y₂ ) = (2, 8) ← 2 points on the line
m = [tex]\frac{8-10}{2-0}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1
the line crosses the y- axis at (0, 10 ) ⇒ c = 10
y = - x + 10 ← equation of black line
the residents of a city voted on whether to raise property taxes. the ratio of yes votes to no votes was 8 to 5. if there were 4955 no votes, what was the total number of votes?
A city's citizens cast ballots on whether or not to increase property taxes. There were 8 yes votes and 5 nay votes, in that order. if there were 4955 no votes,The total number of votes was 6,940.
The ratio of yes votes to no votes was 8 to 5, meaning for every 8 yes votes there were 5 no votes.
This ratio can be expressed as a fraction: 8/5.
To calculate the total number of votes, we need to know only the number of no votes, which we know is 4955.
We can then multiply this number by the fraction 8/5. This gives us a total of 6,940 votes.
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(Attached imagine) PLEASE HELP!! Simplifying complex numbers
Answer:
6i-4
Step-by-step explanation:
To simplify the expression 4i+(8-3i) - 12+√-25, you can start by combining like terms.
First, you can combine the terms 4i and -3i to get 1i. You can also combine the constants 8 and -12 to get -4.
So, the expression becomes 1i - 4 + √-25.
Next, you can simplify the square root. √-25 is the same as √(-25) which is the same as √(5*-5), which is the same as 5√(-1). √(-1) is equal to i, so 5√(-1) is equal to 5i.
Therefore, the final simplified form of the expression is 1i - 4 + 5i, which is equal to 6i - 4.
There is a line that includes the point (9,1) and has a slope of -1/6. What is its equation in point-slope form?
It's equation in point-slope from is -1/6x+5/2.
What is equation?An equation is a formula that is express the equality of two equation.
Based on the given condition the formula
M= -1/6
Substitute {m -1/6
{ X= 9
{Y = 1
(Into y= mx+b)
1=-1/6×9+b
Reduce the expression into the Lowest term
1=-1/2×3+b
Write as a single fraction
1=-3/2+b
Rearrange variables to the left side of the equation.
-b= -3/2-1
Now we have to find the denominator and write the numerators above common denominator
-b=-3-2/2
Calculate the sum or difference
-b=-5/2
b=5/2
Substitute {m=-1/6 b=5/2 into y mx+b
Y=-1/6x+5/2
Rewrite the equation of the line
Y= -1/6x+5/2 in point-slope
Y-1 = -x-9/6
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a shipment of 14 televisions sets contains 4 defective sets. a hotel purchases 8 of these televisions sets. what is the probability that the hotel receives at least one of the defective sets?
The probability that the hotel receives at least one of the defective sets is 0.571 or 57.1%.
The probability of receiving at least one of the defective sets is calculated using the formula for the binomial distribution. The formula has 3 variables: the number of trials (n) being 8, the probability of success (p) being 0.286 (4 defective sets divided by 14 total sets) and the number of successes (k) being 1. We calculate the probability by plugging the variables into the formula and summing the probabilities of all the k values from 1 to 8. This gives us a probability of 0.571 or 57.1%.
P(k≥1) = Σ P(X=k)
= P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8)
= 0.286^1.0 x 0.714^7.0 + 0.286^2.0 x 0.714^6.0 + 0.286^3.0 x 0.714^5.0 + 0.286^4.0 x 0.714^4.0 + 0.286^5.0 x 0.714^3.0 + 0.286^6.0 x 0.714^2.0 + 0.286^7.0 x 0.714^1.0 + 0.286^8.0 x 0.714^0.0
= 0.571 or 57.1%
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What is a triangle? How do you name a triangle using three vertices? Give an example.
A triangle is closed, with a 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
A triangle is a three-sided polygon that consists of three edges and three vertices.
The labels of the vertices of the triangle, which are generally used in capital letters, are used to name a triangle and we can call the triangle ABC since A, B, and C are vertices of the triangle.
Parts of a Triangle:
A triangle has 3 sides, which consist of ABC, the sides are AB, BC, and CA. The angle formed by any two sides of a triangle is the angle of the triangle, denoted by the symbol ∠.
A triangle has three angles, whose angles of triangle ABC are ∠ABC, ∠BCA, and ∠CAB. These angles are also called ∠B, ∠C, and ∠A.
The point of intersection of any two sides of a triangle is known as a vertex. A triangle has three vertices. In triangle ABC, the vertices are A, B, and C.
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Officer thomas prefers to use a 35mm single-lens camera to document crime scenes. What is one advantage of using a 35mm camera at a crime scene instead of using a digital camera?.
In 35mm single-lens camera the images produce negative that can be used as backups instead of using a digital camera.
what is single lens camera?A single-lens reflex camera (SLR) is a type of camera that typically employs a mirror and prism system (hence the word "reflex" from the reflection of the mirror) and allows the photographer to look through the lens to preview the exact scene that will be photographed.
Most SLR cameras have a mirror that swings out of the way of the light when the shutter button is depressed, allowing light to reach the light receptor and capturing the image.
The roof pentaprism found in the optical path between the reflex mirror and viewfinder of most SLR cameras enables upright and laterally accurate vision.
A camera's manual focus adjustment or an autofocus system's automated focus adjustment are both options.
The images produce negative that can be used as backups in 35mm single-lens camera instead of using a digital camera.
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Tom is shopping for school supplies at CVS. The cost of 3 markers and 2 pencils came
out to be $1.80. When Angie went shopping at the same CVS, her cost of 4 markers and
6 pencils was $2.90. Determine the cost of 1 marker and 1 pencil.
Answer:
Marker = $0.50
Pencil = $0.15
Step-by-step explanation:
The cost of 3 markers and 2 pencils can be represented as 3M + 2P = $1.80.
The cost of 4 markers and 6 pencils can be represented as 4M + 6P = $2.90.
Now that we have our two equations, we can solve for M and P. To do this, we can eliminate one of the variables by multiplying one equation by a constant and adding the two equations together.
For example, if we multiply the first equation by 4 and the second equation by -3, we get:
12M + 8P = $7.20
-12M - 18P = -$8.70
Adding these two equations together, we get:
-10P = -$1.50
Dividing both sides by -10, we get:
P = $0.15
Now that we have found the value of P, we can substitute it back into one of our original equations to find the value of M. If we substitute P = $0.15 into the first equation, we get:
3M + 2($0.15) = $1.80
3M + $0.30 = $1.80
3M = $1.50
M = $0.50
So, the cost of 1 marker is $0.50, and the cost of 1 pencil is $0.15.
Bo went to the grocery tore and bought ome bottle of oda and bottle of juice. Each bottle of juice ha 25 gram of ugar. Bo purchaed a total of 7 bottle of juice and oda which collectively contain 250 gram of ugar. Determine the number of bottle of oda and juice purchaed. Someone tell me how to write out the equation, I know the anwer I jut need the written out equation
The two simultaneous equations are 50x + 25y = 250 and x + y = 7
What are simultaneous equations?Simultaneous equations are a set of two or more equations that contain variables. The values of the variables can be calculated using either method of elimination or substitution. The values of the variables must then satisfy all the equations
How to make simultaneous equations from given information?Assuming the bottle of soda has 50 grams of sugar in each bottle (since this information is not given). Let the bottles of soda bought be x and bottles of juice bought be y. Two equations will be formed so that we can solve them simultaneously.
50x = total amount of sugar in soda bottles
25y = total amount of sugar in juice bottles
50x + 25y = 250 (total amount of sugar in all bottles)
x + y = 7 (total number of bottles)
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The sides of an rectangle are in the ratio of 3:7. If the area of the rectangle
is 3024, find the length and width of the rectangle. Enter two integers
separated by a comma, no spaces.
Answer:
Step-by-step explanation:
Step-by-step explanation:
length = 3x
breadth= 7x
area = 1029m2
area = length × breadth
(3x) × (7x)= 1029
now,
3×7=21
7×7=49
(verification 21×49=1029)
so length = 21
breadth = 49
now perimeter = 2(l+b)
=2(21+49)
=2(70)
= 140
so perimeter = 140m
e^x+1=2^x+2
How do I solve this problem? (find x)
The solution to the equation eˣ + 1 = 2ˣ + 2 is x = 1.2
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
eˣ + 1 = 2ˣ + 2
Split to system of equations
This gives
y = eˣ + 1
y = 2ˣ + 2
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the curves intersect at (1.2, 4.3)
This means that
x = 1.2 (approximated)
Hence, the solution is x = 1.2
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three hearts are dissected from individuals with unknown histories. two of the three hearts are enlarged. what is a possible reason why the two hearts may be enlarged
they belong to high-performance athletes
It may be a sign of a family history of early heart disease. If one of your close relatives, such as a parent or sibling, has experienced a heart attack, a stroke, or was previously diagnosed with heart disease before the age of 60. Thus, option B, C is correct.
What individuals with a history of heart disease?The CDC's Response to the Risk Factors in the Country. Leading causes of heart disease and stroke risk factors include high blood pressure, high levels of low-density lipoprotein (LDL) cholesterol, diabetes, smoking, exposure to second-hand smoke, obesity, a poor diet, and inactivity.
People who are aware of their situation make wiser decisions, live longer, and experience greater well-being. Even if you have heart failure, it is still possible to lead a regular life. The secret to success is realizing heart failure and taking charge of it.
Therefore, They are from well-trained professional athletes, and They are from individuals with a history of heart disease.
Learn more about hearts here:
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The question is incomplete, complete question with option given below:
Three hearts are dissected from individuals with unknown histories. Two of the three hearts are enlarged. Select all of the possible reasons the two hearts may be enlarged.
A. They are from individuals who had low blood pressure histories.
B. They are from well-trained professional athletes.
C. They are from individuals with a history of heart disease.
D. They are from individuals who had arthritis issues.
in a fruit basket there are 120 fruits some are plums costing 2$ each and others are peaches costing 3$ each total cost of plims was 30$ more than the cost of peaches how many plums and how many peahces are there
Answer:
There are 78 plums and 42 peaches.
Step-by-step explanation:
Let p = number of plums.
Let e = number of peaches.
The value of the plums is 2p.
The value of the peaches is 3e.
"total cost of plims was 30$ more than the cost of peaches"
2p = 3e + 30
"there are 120 fruits some are plums [...] others are peaches"
p + e = 120
We have a system of simultaneous equations.
2p = 3e + 30
p + e = 120
2p = 3e + 30
p = -e + 120
2p = 3e + 30
+ 3p = -3e + 360
------------------------------
5p = 390
p = 78
p + e = 120
78 + e = 120
e = 42
Answer: There are 78 plums and 42 peaches.
Check:
78 plums cost 78 × $2 = $156
42 peaches cost 42 × $3 = 126
$156 - $126 = $30
The plums do cost $30 more than the peaches.
78 + 42 = 120
The total is indeed 120.
The answer above is correct.