Evaluate the expression 4a - 3b + c when a = 2, b = 3, and c = 5.
Answers
Final Answer:
The expression 4a - 3b + c, when a = 2, b = 3, and c = 5, evaluates to 4.
Explanation:
To evaluate the expression 4a - 3b + c when a = 2, b = 3, and c = 5, we substitute these values into the expression:
Substitute the values of a, b, and c into the expression:
4(2) - 3(3) + 5
Perform the operations in order:
8 - 9 + 5
Calculate the final result:
-1 + 5 = 4
So, the expression evaluates to 4 when a = 2, b = 3, and c = 5.
Substituting values into expressions: When you have variables in an expression, you can substitute specific values for those variables to find the result. This is a fundamental concept in algebra and mathematics in general, used for solving equations and evaluating expressions.
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Answer:
4
Step-by-step explanation:
given the expression
4a - 3b + c ← substitute a = 2, b = 3, c = 5 into the expression
= 4(2) - 3(3) + 5
= 8 - 9 + 5
= - 1 + 5
= 4
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How do you write 282% as a decimal
It will take five builders 62 days to complete a particular project. At this rate, how long would the project take if there were only two builders?(SHOW WORK)
Answers
Sn = a((1-r^n) / (1-r))
The given values are:
n = 30
a = 0.5 mi
r = 1.10 (10% more each day)
S30 = 0.5 ((1-1.10^30) / (1-1.10))
S30 = 82.25 mi
After 30 days, he will have traveled 82.25 miles.
Answers
The multiples of 7 are 7,14,21,28,35,42,49 : 7 balls
The multiples of 5 are 5,10,15,20,25,30,35,40,45,50 :10 balls
In total there are 50 balls
But there is a commun ball 35
p=(7+10-1)/50=16/50=8/25=0.32
Answers
Answer:
Step-by-step explanation:
Using the formula for calculating the distance between two points as shown;
D = √(x2-x1)²²+(y2-y1)²
Given the coordinates (-2, 4) and (10,2)
x1 = -2, y1 = 4, x2 = 10 and y2 = 2
substitute into the formula;
D = √(10+2)²+(2-4)²
D = √(12²+(-2)²
D = √144+4
D = √148
D = 12.17 units
Hence the distance of Mac,s house from Nate's house is 12.17 units
Final answer:
To find the coordinates of Mac's house, we use the section formula in mathematics. By substitifying the given locations of Nate's house and the park into the formula, we conclude that Mac's house is located at approximately (2, 3.33) which is one third the distance from Nate's house to the park.
Explanation:
In this math problem, we are dealing with points in a 2D cartesian coordinate system. Nate's house is at (-2, 4) and the park is at (10, 2). Mac's house is located one third of the distance between these two points. Following the formula for the coordinates of a point dividing a line segment in a given ratio, we can find Mac's house location.
Let the coordinates of Mac's house be (x, y). We use the formula for section formula which is:
x = [(m*x2 + n*x1) / (m+n)] and y = [(m*y2 + n*y1) / (m+n)]
Here, x1, y1 (-2, 4) are the coordinates of Nate's house, x2, y2 (10, 2) are the coordinates of the park and the ratio m:n is 1:2 since it's one third of the distance from Nate's house to the park.
By substituting these values in the formula, we get x = [(1*10 + 2*-2) / (1+2)] = 2 and y = [(1*2 + 2*4) / (1+2)] = 3.33
So, the coordinates of Mac's house are approximately (2, 3.33).
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Answers
The correct result would be f(x) = 5(27)x.
= 5*3*3*x
= 45x
So an equivalent function is f(x) = 45x
f(x) = 45x
Hope this helps.
Geometry Questions? (20 PTS)
Answers
A triangle is:
either scalene, isoceles, or equilateral, and
either acute, right, or obtuse.
Question 1: The triangle is right b/c it has a right angle.
The triangle is isoceles because it has two congruent sides.
Right isoceles triangle
Question 2: The triangle is obtuse b/c it has an obtuse angle. (>90°)
The triangle is isoceles b/c it has two congruent sides.
Obtuse isoceles triangle
Question 3: All angles in a triangle add up to 180°. Let's find the 3rd angle.
180 - (80 + 60) = 180 - 140 = 40°
Congruent angles
If the angles are all different, the sides are all different and the triangle is scalene. It is also acute because all angles are <90°.
Acute scalene triangle
Question 4
An exterior angle of a triangle = the sum of its remote interior angles.
what does this mean? In this case, it means that
4x + 10 = 50 + x + 5
The reason this works: <ACD is supplementary to <ACB, so they must both add up to 180. Likewise, the angles of the triangle <ACB, <BAC, and <ABC all add up to 180. Since both = 180, we can set them equal (substitution prop)
m<ACD + m<ACB = m<ACB + m<BAC + m<ABC
subtract m<ACB from each side
m<ACD = m<BAC + m<ABC
now let's solve our equation.
4x + 10 = 50 + x + 5
4x + 10 = 55 + x
subtract x from each side
3x + 10 = 55
subtract 10 from each side
3x = 45
divide by 3
x = 15
the measure of the interior angle = (x+5)° = (15+5)° = 20°
the measure of the exterior angle = (4x+10)° = (4(15)+10)° = (60+10)° = 70°
Question 5
As we can see from the diagram...
AB = CD, AD = BC
<ABD = <BDC, <ADB = <CBD
Also obvious from the reflexive prop...
BD = BD
And because the three angles add up to 180° and we know that two of them are the same, the third must be the same as well.
<A = <C
(three points don't need specified because only one angle is possible with this vertex)
Question 6
Because the angles in a triangle add up to 180°...
m<A + m<ADB + m<ABD = 180°
We know that m<A = 60°...
60 + m<ADB + m<ABD = 180°
We know that m<DBC = 70°, and from the diagram, <ADB is cong. to <DBC.
Therefore m<ADB = 70°.
60 + 70 m<ABD = 180°
130 + m<ABD = 180°
m<ABD = 50°
Answer:
lo que el o ella dijo
Step-by-step explanation: