Answer:
35.3
Step-by-step explanation:
Actually, there are none but 35.3. Here you have already defined x as 35.3. 35.3 satisfies the given equation.
The solution to the given equation x = 35.3 is simply x equals 35.3. There are no further calculations required for this straightforward linear equation.
Explanation:The equation given, x = 35.3, is a simple linear equation where the variable x is already isolated on one side of the equation. The solution to this equation is straightforward: x equals 35.3. There is no need for further calculation or iterative numerical methods, as this is not a quadratic equation nor does it require techniques such as least squares to find a solution. The equation simply states that x is equal to the real number 35.3.
However, if you are given a quadratic equation or more complex equations, there can be different methods to solve for x. For example, the quadratic formula, iterative methods, or writing computer programs for finding least squares solutions in systems of equations with multiple variables.
Write 3 different ways you can express multiplication using the problem 8 times a number
Answer:
1) 8x5
2) 8x10
3)8x20
Round 20.155 to the nearest tenth
Answer:
20.2
The thousandth position doesn't affect the rounding of the numbers. Since the hundredth position contains a 5, you will round up, meaning the tenth position will change from a 1 to a 2.
Answer:
20.2
AMG Mark as brainlist!
HELP ASAP!!!! Please tell me the steps and answer on how to do it.
Answer:
71.4
Step-by-step explanation:
For this, we will use Heron's Formula, or
[tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex],
with p as the perimeter divided by 2, and a, b, and c are the side lengths.
Plugging our values in, (11.6+20+13)/2 = 22.3 = p, and
[tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex] = [tex]\sqrt{5103.8679} =71.4[/tex] rounded to the nearest tenth
help me on my home work
what is 2*2*2*2*0=
Answer:
0
Step-by-step explanation:
Anything multiplied by 0 gives you an answer of 0, therefore 2*2*2*2*0=0
Answer:
0
Step-by-step explanation:
In most cases, zero times anything is zero.
Here we have 2*2*2*2 = 2^4 = 16. Thus,
2*2*2*2*0 = 16(0) = 0
HELP ME! Z-135=41,show your work
Answer:
[tex]\huge \boxed{z=176}\checkmark[/tex]
Step-by-step explanation:
Add by 135 from both sides of equation.
[tex]\displaystyle z-135+135=41+135[/tex]
Simplify, to find the answer.
[tex]\displaystyle41+135=176[/tex]
[tex]\huge \boxed{z=176}[/tex], which is our answer.
Hope this helps!
Answer: Z=176
Step-by-step explanation: All you need to do is isolate z. Add 135 to each side.
135+41=176=Z
Which sequence is modeled by the graph below? (1 point) coordinate plane showing the points 1, 5; 2, 0.5; and 3, 0.05 an = 5(−10)n − 1 an = 0.5(10)n − 1 an = one tenth (5)n − 1 an = 5( one tenth )n − 1
Answer:
[tex]\large\boxed{a_n=5\left(\dfrac{1}{10}\right)^{n-1}}[/tex]
Step-by-step explanation:
Check:
[tex]n=1\\\\a_1=5\left(\dfrac{1}{10}\right)^{1-1}=5\left(\dfrac{1}{10}\right)^0=5(1)=5\qquad\bold{CORRECT}\ (1,\ 5)\\\\n=2\\\\a_2=5\left(\dfrac{1}{10}\right)^{2-1}=5\left(\dfrac{1}{10}\right)^1=5\left(\dfrac{1}{10}\right)=\dfrac{5}{10}=0.5\qquad\bold{CORRECT}\ (2,\ 0.5)\\\\n=3\\\\a_3=5\left(\dfrac{1}{10}\right)^{3-1}=5\left(\dfrac{1}{10}\right)^2=5\left(\dfrac{1}{100}\right)=\dfrac{5}{100}=0.05\qquad\bold{CORRECT}\ (3,\ 0.05)[/tex]
[tex]a_{n}[/tex] [tex]= 5 (\frac {1}{10} )^{n-1}[/tex]
Mathematical sequences are the set of numbers that makes a pattern or can be simple and complicated, finite and infinite. Explore sequences, terms in a sequence, and the different kinds of mathematical sequences, including the famous Fibonacci sequence.
Check:
n=1
[tex]a_{1} = 5 (\frac {1}{10} )^{1-1} = 5 (\frac {1}{10} )^{0} = 5 (1)=5[/tex] True (1,5)
n=2
[tex]a_{2} = 5 (\frac {1}{10} )^{2-1} = 5 (\frac {1}{10} )^{1} = 5 \frac{1}{10} = 0.5[/tex] True (2, 0.5)
n=3
[tex]a_{3} = 5 (\frac {1}{10} )^{3-1} = 5 (\frac {1}{10} )^{2} = 5 \frac{1}{100} = 0.05\\[/tex] True (3, 0.05)
sequence chart is a series of the events and actions set in the order in which they take place. this is considered to be a fantastic way to represent the necessary steps taken to reach to the outcome.
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Chase and Alonzo stand next to each other and throw baseballs in the air.
The path of Chase's ball is described by the equation y = - 4x2 + 5x + 7. The
path of Alonzo's ball is shown by the graph.
Answer:
Alonzo baseball
Your question is incomplete and lacks a graph. Please check below for the full content.
Chase and Alonzo stand next to each other and throw baseballs in the air. The path of Chase's ball is described by the equation y = - 4x²+ 5x+ 7. The path of Alonzo's ball is shown by the graph. In each function, x is the horizontal distance the ball travels in meters, and y represents its height. Whose baseball reaches a greater height?
A. Both baseballs reach the same height.
B. Chase's baseball
C. Alonzo's baseball
The misssing graph is shown below.
The correct option is option C: Alonzo's baseball
What is a quadratic equation?The equation whose highest degree of the variable used in the equation is 2 and has 2 roots, is called quadratic equation.
Here the quadratic equation of the path of Chase's ball is given by y = - 4x²+ 5x+ 7
To compare the height of both paths followed by the ball
we have to first calculate the height of the path of Chase's ball.
the path of Chase's ball is f(x)=-4x²+ 5x+ 7
The function will have the highest value when f'(x) will be 0.
f'(x)=-8x+5
f'(x)=0
⇒-8x+5=0
⇒-8x=-5
⇒x=5/8
at x=5/8, function value is
f(x)=-4x²+ 5x+ 7
=-4(5/8)²+ 5(5/8)+ 7
=-4(25/64)+(25/8)+7
=(-25/16)+25/8+7
=8.5625
There maximum value of f(x) is 8.5625.
The maximum height reached by Chase's ball will be 8.5625m.
From the graph of the path of Alonzo's ball, it is clear that
The maximum height reached by Alonzo's ball will be 9m.
As 8.5625m < 9m
Alonzo's baseball will reach greater height.
Learn more about Quadratic equation
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what is
x+y+z=8
3x+y-z=4
4x-y+2z+6
[1, 4, 3]
Solve for the first variable in one of the equations, then substitute the result into the other equation.
**For more information on how to solve a system of equations in three variables, paste and copy this link:
https://youtu.be/zcC7wsn3b2g
Subscribe to my channel [USERNAME: MATHEMATICS WIZARD].
I am joyous to assist you anytime.
***By the way, in the final line, that "+" next to the 6 should be replaced with an "=".
Using the discriminant, how many real solutions does the following quadratic
equation have?
x^2 - 8x + 16 = 0
A. Three real solutions
B. No real solutions
C. Two real solutions
D. One real solution
Answer:
D one real solution
Step-by-step explanation:
x^2 - 8x + 16 = 0
This is in the form
ax^2 +bx + c = 0
so we can use the discriminant to determine the number of solutions
b^2 -4ac
(-8)^2 -4(1)(16)
64 - 64
0
Since the discriminant is zero, there is one real solution.
If f(x)=2x^2+3x−4, and g(x)=−8x−4, what does f(x)+g(x) equal?
f(x)=2x^2+5x+8
f(x)=2x^2−5x−8
f(x)=2x^2+11x−8
f(x)=2x^2+5x
[tex]\( f(x) + g(x) \) equals \( 2x^2 - 5x - 8 \).[/tex] (option b)
To find [tex]\( f(x) + g(x) \)[/tex], we need to add the functions f(x) and g(x):
[tex]\[ f(x) + g(x) = (2x^2 + 3x - 4) + (-8x - 4) \][/tex]
[tex]\[ = 2x^2 + 3x - 4 - 8x - 4 \][/tex]
[tex]\[ = 2x^2 + (3x - 8x) + (-4 - 4) \][/tex]
[tex]\[ = 2x^2 - 5x - 8 \][/tex]
Therefore, the correct answer is:
[tex]\[ f(x) = 2x^2 - 5x - 8 \][/tex]
Complete question: If f(x)=2x²+3x−4, and g(x)=−8x−4, what does f(x)+g(x) equal?
a-f(x)=2x²+5x+8
b-f(x)=2x²−5x−8
c-f(x)=2x²+11x−8
d-f(x)=2x²+5x
Please answer this correctly
Answer:
Step-by-step explanation:
the answer is 4/5
Because there are 5 section and the blueberry takes up 4 of the sections it is 4/5
Answer:
4/5
Step-by-step explanation:
So he divided something into 5 sections.
He fills one section with graph jelly and 4 sections with blueberry jelly.
Since there are 5 sections and 4 are filled with blueberry, then 4/5 is the fraction of the table he filled will blueberry.
What is the equivalent expression 3m + (m + 5)
Answer:
[tex]\large\boxed{3m+(m+5)=4m+5}[/tex]
Step-by-step explanation:
[tex]3m+(m+5)=3m+m+5\qquad\text{combine like terms}\\\\=(3m+m)+5=4m+5[/tex]
A, B, C, and D have the coordinates (-8, 1), (-2,4),(-3,-1) and (-6,5), respectively. Which sentence about the points is true?
A. A, B, C, and D lie on the same line
B. AB and CD are perpendicular lines.
c. Ag and are parallel lines.
D. AB and CD are intersecting lines but are not perpendicular.
E. AC and B are parallel lines.
Answer:
B. [tex]^\leftrightarrow_{AB}[/tex] and [tex]^\leftrightarrow_{CD}[/tex] are perpendicular lines.
Step-by-step explanation:
We can quickly plot the points in the cartesian plane as shown in the attachment.
A visual representation will help us see that A,B,C, and D do not lie on the same line.
The slope of AB is [tex]\frac{4-1}{-2--8} =\frac{3}{6}=\frac{1}{2}[/tex]
The slope of CD is [tex]\frac{5--1}{-6--3} =\frac{6}{-3}=-2[/tex]
The two slopes are negative reciprocals of each other.
It is true that line AB and line CD are perpendicular.
These two lines cannot be perpendicular and parallel at the same time.
It is also not possible that, the two lines are perpendicular but will not intersect
Therefore the correct choice is B
Answer:
B
Step-by-step explanation:
plato/edmentum
Which equation is equivalent to 2^4x = 8^x-3?
2^4x = 2^2x-3
2^4x = 2^2x-6
2^4x = 2^3x-3
2^4x = 2^3x-9
Answer:
[tex]\large\boxed{2^{4x}=2^{3x-9}}[/tex]
Step-by-step explanation:
[tex]8=2^3\to 8^{x-3}=(2^3)^{x-3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{3(x-3)}\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=2^{(3)(x)+(3)(-3)}=2^{3x-9}[/tex]
If you want a solution of this equation:
[tex]2^{4x}=8^{x-3}\\\\2^{4x}=2^{3x-9}\iff4x=x-3\qquad\text{subtract}\ x\ \text{from both sides}\\\\3x=-3\qquad\text{divide both sides by 3}\\\\x=-1[/tex]
Answer: the correct option is
(D) [tex]2^{4x}=2^{3x-9}.[/tex]
Step-by-step explanation: We are given to select the correct equation that is equivalent to the following equation :
[tex]2^{4x}=8^{x-3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Equivalent equations means two equations that can be obtained from one another using some properties of formula.
We will be using the following formula :
[tex](a^b)^c=a^{b\times c}.[/tex]
From equation (i), we have
[tex]2^{4x}=8^{x-3}\\\\\Rightarrow 2^{4x}=(2^3)^{x-3}\\\\\Rightarrow 2^{4x}=2^{3\times(x-3)}\\\\\Rightarrow 2^{4x}=2^{3x-9}.[/tex]
Thus, the required equivalent equation is [tex]2^{4x}=2^{3x-9}.[/tex]
Option (D) is CORRECT.
The main cable of a suspension bridge forms a
parabola, described by the equation
y = a(x - h)2 + k.
0
27
52.5 105
127
157.6
12
210
27
y = height in feet of the cable above the roadway
x = horizontal distance in feet from the left bridge
support
a = a constant
(h, k) = vertex of the parbola
What is the vertex of the parbola?
DONE
Answer:
The vertex of the parabola is (105 , 7)
Step-by-step explanation:
* Lets explain how to solve the problem
- The equation of the parabola is y = a(x - h)² + k, where (h , k) are
the coordinates of the vertex point of the parabola
- The points (0 , 27) , (52.5 , 12) , (105 , 7) , (157.6 , 12) , (210 , 27) are
the points lie on the parabola
- We have three unknown a , h , k to find them we will substitute the x
and y in the equation by the coordinates of some point on the
parabola
- Lets start with point (0 , 27)
∵ x = 0 and y = 27
∴ 27 = a(0 - h)² + k
∴ 27 = ah² + k ⇒ (1)
- Lets use point (210 , 27)
∵ x = 210 and y = 27
∴ 27 = a(210 - h)² + k ⇒ (2)
- Equations (1) and (2) have the same L.H.S, so we can equate them
∴ ah² + k = a(210 - h)² + k ⇒ subtract k from both sides
∴ ah² = a(210 - h)² ⇒ divide both sides by a
∴ h² = (210 - h)² ⇒ take √ for both sides
∴ h = ± (210 - h)
∵ h = 210 - h ⇒ add h to both sides
∴ 2h = 210 ⇒ divide both sides by 2
∴ h = 105
∵ h = - (210 - h)
∴ h = -210 + h ⇒ no value of h from this equation so we will ignore it
∴ The value of h is 105
- Lets substitute this value of h in the equation
∴ y = a(x - 105)² + k
- Lets use the point (105 , 7)
∵ x = 105 and y = 7
∴ 7 = a(105 - 105)² + k
∴ 7 = a(0) + k
∴ k = 7
- The coordinates of the vertex point are (h , k)
∵ h = 105 and k = 7
∴ The vertex of the parabola is (105 , 7)
Answer:
105, 7 and then for the next one y= 0.0018(x – 105)2 + 7
Step-by-step explanation:
When sales representatives for a pharmaceutical company drive to out-of-town meetings that require an overnight stay, they receive $125for lodging plus $0.80 per mile driven. How many miles did Joe drive if his company reimbursed him $301 for an overnight trip?
Answer:
220 miles
Step-by-step explanation:
Joe got $301 for an overnight trip.
As the employees get $125 for lodging. The lodging expense will be subtracted from the total amount to get the amount for the miles he drove.
So,
Expense by company for miles driver = 301 - 125 = $176
So, Joe received $176 for miles driven
Now,
amount for one mile = $0.80
Miles driven in $176 = 176/0.80 = 220 miles
Joe drove 220 miles ..
Joe drove 220 miles for his company to be reimbursed $301 for an overnight trip, after considering the fixed lodging cost and the per mile reimbursement rate.
The student wishes to know how many miles Joe drove if his company reimbursed him $301 for an overnight trip wherein he receives $125 for lodging plus $0.80 per mile driven. To solve this problem, we start by subtracting the fixed lodging cost from the total reimbursement to find the total amount reimbursed for mileage. Let's denote the number of miles driven by Joe as m.
Total reimbursement for mileage = Total reimbursement - Lodging cost
$301 - $125 = $176
Now, since Joe gets reimbursed $0.80 per mile, we can calculate the number of miles driven as follows:
$176 / $0.80 per mile = 220 miles
Therefore, Joe drove 220 miles for his company to be reimbursed $301 for an overnight trip.
At a certain distance fro a pole, the angle of elevation to the top of the pole is 28 degrees. IF the pole is 6.3 feet tall, what is the distance fro the pole?
Answer:
The distance from the pole is 11.8 ft
Step-by-step explanation:
Let
x------> the distance from the pole
we know that
The tangent of angle of 28 degrees is equal to divide the opposite side to angle of 28 degrees ( the height of the pole) by the adjacent side to angle of 28 degrees ( the horizontal distance from the pole)
so
tan(28°)=6.3/x
Solve for x
x=6.3/tan(28°)=11.8 ft
Final answer:
The distance from the pole is found by using the tangent function with the given angle of elevation (28 degrees) and the pole's height (6.3 feet), resulting in a distance of approximately 12.04 feet.
Explanation:
To calculate the distance from the pole given the angle of elevation and the height of the pole, you can use trigonometric functions. The angle of elevation is 28 degrees and the height of the pole is 6.3 feet. You can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side to the adjacent side.
Let d represent the distance from the pole. The tangent of the angle of elevation (28 degrees) equals the opposite side (6.3 feet) over the adjacent side (distance d).
tan(28°) = 6.3 / d
To find d, rearrange the equation: d = 6.3 / tan(28°). Using a calculator for tan(28°), you obtain d ≈ 12.04 feet.
Therefore, the distance from the pole is approximately 12.04 feet.
What is the value of b in the equation below: 5^6/5^2=a^b
Step-by-step explanation:
for x^a/x^b = x^(a-b)...eqn 1
thus for 5^6/5^2 = a^b,
if a = 5, following eqn 1...
then b = 6-2 = 4
Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.
_____<√32<_____
Answer:
5 < √32 < 6.
Step-by-step explanation:
√25 = 5 and √36 = 6 so
5 < √32 < 6.
I’ve tried it many times but I can’t seem to get it can someone please help please please help I really do need help
A) -4
B) -1/4
C)4
D)1/4
Answer:
-1/4
Step-by-step explanation:
You can find the slope from a graph several ways.
Here are two ways of doing it.
Method 1. Slope formula
Find two points, then apply the slope formula, m = (y2 - y1)/(x2 - x1)
We read two easy to read points of the graph: (0, -2) and (4, -3)
m = (y2 - y1)(/(x2 - x1) = [-3 - (-2)]/(4 - 0) = (-3 + 2)/4 = -1/4
Method 2. Rise/Run
Slope = m = rise/run
Pick two points. Start at one point and go to the other point by going vertically (rise) and horizontally). The vertical distance is the rise, and the horizontal distance is the run. Up is positive, and down is negative. Right is positive, and left is negative.
Pick points (0, -2) and (4, -3).
Start at (0, -2). To go to (4, -3), move 1 unit down. That is a rise of -1. Now go horizontally 4 inits to the right. That is a run of 4.
slope = rise/run = -1/4
which equation have no real solution?
a.x^2+4x+16=0
b.4x^2+4x-24=0
c.5x^2+3x-1=0
d.2x^2-4x+4=0
To find out which equation has no real solutions, we need to calculate the discriminant for each of these given equations.
For calculating the discriminant, we need to first compare these equations with the general formula which is ax²+bx+c.
So, let's get started.
1) x² + 4x + 16 = 0
a=1, b=4, c=16
D = b²-4ac
= (4)² - 4(1)(16)
= 16-64
= -48
√D = √-48
2) 4x² + 4x - 24 = 0
a=4, b=4, c=-24
D = b²-4ac
= (4)² - 4(4)(-24)
= 16 - 16(-24)
= 16 + 384
= 400
√D = √400 = +20 or -20
3) 5x² + 3x - 1 = 0
a=5, b=3, c=-1
D = b²-4ac
= (3)² - 4(5)(-1)
= 9 + 20
= 29
√D = √29
4) 2x² - 4x + 4 = 0
a=2, b=-4, c=4
D = b²-4ac
= (-4)² - 4(2)(4)
= 16 - 32
= -16
√D = √-16
Now from all these above calculations, we can see that discriminant was negative in first equation and in last equation.
If D<0 then roots does not exist, as the square root can not contain a negative value or the equation does not have any real solutions.
Roots in such case can be calculated but those roots are known as imaginary roots, which is a higher concept.
So Final answer is,
Equation 1 => x² + 4x + 16 = 0
and
Equation 4 => 2x² - 4x + 4 = 0
has no real solutions.
Which ratio is equivalent to 8:6
Answer:
4:3
Step-by-step explanation:
You divide 8 and 6 by 2 to simplify it
Two cars are 270 miles apart and travel toward each other on the same road. They meet in 3 hours. One car travels 2 mph faster than the other. What's the average speed of each car?
A. 42 mph and 44 mph
B.44 mph and 46 mph
C.41 mph and 43mph
D.43mph and 45mph
Answer:
B.44 mph and 46 mph
Step-by-step explanation:
This question is on relative speed
when cars move towards each other, you add their individual speeds to get their relative speed
Lets have two cars , A and B
Let car A to have an average speed of x m/h towards the right hand side
Let car B to have an average speed of x+2 m/h towards the opposite direction
The distance between the cars is 270 miles
Time of meeting is 3 hours
The relative speed will be x+x+2=2x+2 miles per hour
Apply the formula for time=Distance/speed =D/S
[tex]t=\frac{D}{S} \\\\\\3=\frac{270}{2x+2} \\\\\\3(2x+2)=270\\\\\\6x+6=270\\\\\\6x=270-6\\\\\\6x=264\\\\\\x=\frac{264}{6} =44[/tex]
x=44 miles per hour
x+2=44+2=46 miles per hour
solution
44 mph and 46 mph
Final answer:
Two cars are traveling towards each other at speeds where one car is 2 mph faster than the other. They meet after 3 hours covering 270 miles. By setting an equation with the distance formula, we find that the slower car's speed is 44mph and the faster car's speed is 46mph. (Option B)
Explanation:
The question involves calculating the average speed of two cars traveling towards each other on the same road and meeting after a certain time. To solve this, we can set up an equation using the formula for speed, which is distance divided by time.
Let's denote the speed of the slower car as ‘s’ mph (miles per hour). Consequently, the faster car travels at ‘s+2’ mph. When they meet after 3 hours, both cars together will have covered a distance of 270 miles. Thus, the total distance covered by both cars can be written as:
Total distance = (speed of car A)×(time) + (speed of car B)×(time)
270 miles = s×3 hours + (s+2)×3 hours
This simplifies to:
270 = 3s + 3s+ 6
Combining like terms and simplifying, we get:
270 = 6s + 6
Subtract 6 from both sides to find:
264 = 6s
Dividing both sides by 6 yields:
s = 44 mph
Therefore, the slower car travels at 44 mph and the faster car at 44+2 = 46 mph.
The correct answer is B. 44 mph and 46 mph.
Make a table with the domain of {2,3,4,5,6} and draw a graph of the absolute value function y = 2|x-4| + 3.
Answer:
Table for y = 2|x-4| + 3 on domain {2,3,4,5,6} is given as:
x y
2 2|x-4| + 3 = 2|2-4| + 3 = 7
3 2|x-4| + 3 = 2|3-4| + 3 = 5
4 2|x-4| + 3 = 2|4-4| + 3 = 3
5 2|x-4| + 3 = 2|5-4| + 3 = 5
6 2|x-4| + 3 = 2|6-4| + 3 = 7
The graph of the absolute value function y = 2|x-4| + 3 for the given domain is attached.
Step-by-step explanation:
The absolute value parent function, written as function(x) = | x |, is defined as:
|x| = x and |-x| = x
In our case;
For x = 2
y = 2|x-4| + 3
= 2|2-4| + 3
= 2|-2| + 3
= 2*2 + 3
= 4 + 3
= 7
Similarly, for all other values of x in the given domain, value of y can be calculated.
Answer:
In the attachment.Step-by-step explanation:
[tex]|a|=\left\{\begin{array}{ccc}a&for\ a\geq0\\-a&for\ a<0\end{array}\right[/tex]
Put each value of x from the set {2, 3, 4, 5, 6}
to the equation y = 2|x - 4| + 3:
x = 2 → y = 2|2 - 4| + 3 = 2|-2| + 3 = 2(2) + 3 = 4 + 3 = 7 → (2, 7)
x = 3 → y = 2|3 - 4| + 3 = 2|-1| + 3 = 2(1) + 3 = 2 + 3 = 5 → (3, 5)
x = 4 → y = 2|4 - 4| + 3 = 2|0| + 3 = 2(0) + 3 = 0 + 3 = 3 → (4, 3)
x = 5 → y = 2|5 - 4| + 3 = 2|1| + 3 = 2(1) + 3 = 2 + 3 = 5 → (5, 5)
x = 6 → y = 2|6 - 4| + 3 = 2|2| + 3 = 2(2) + 3 = 4 + 3 = 7 → (6, 7)
Mark the points in the coordinates system.
The domain is only five numbers, therefore the graph of this function is only five points.
A group of friends go to the movies. The function h(x) represents the amount of money spent, where x is the number of friends at the movies. Does a possible solution of (6.5, $95.25) make sense for this function? Explain your answer.
This answer does not make sense because you can't buy half a movie ticket
Answer: If h(x) represents the amount of money spent and x the amount of friends, then we can write it as in a pair as (x, h(x))
Then the pair given is (6.5, $92.25)
Here you see a problem, x is 6.5, knowing that x represents the amount of friends, this is a problem because you need to have a whole number ( you can't have a 0.5 of a friend)
So the domain of h(x) is only the natural numbers, then the possible solution of (6.5, $92.25) doesn't make sense because 6.5 is not a natural number.
What is the equation of the line that passes through the point (-1, -3) and has a slope of -5?
A) y=-5x-8
B) y=-5x-16
C) y=-5x+16
D) y=-5x+8
Answer:
A) y = -5x - 8Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
We have the slope m = -5, and the point (-1, -3). Substitute:
[tex]y-(-3)=-5(x-(-1))\\\\y+3=-5(x+1)[/tex]
Convert to the slope-intercept form (y = mx + b):
[tex]y+3=-5(x+1)[/tex] use the distributive property
[tex]y+3=-5x-5[/tex] subtract 3 from both sides
[tex]y=-5x-8[/tex]
A scale model of a rectangle building lot measures 7 ft by 5ft. Id the actual house will be built using a scale factor of 12. What is the area of the actual building lot?
Answer:
5040 ft^2
Step-by-step explanation:
The area of rectangle is: 7 ft by 5 ft
The scaling is done by multiplying the dimensions with the sale factor.
so,
The area of actual house will be:
(7*12) x (5*12)
= 84 * 60
= 5040 ft^2
So the area of actual building is 5040 ft^2 ..
1. From a total yearly budget of
$360,000, the Kimball Foundation
spends $30,000 on leasing office
space. What is the ratio of dollars
spent on office space to dollars spent
on other costs?
A. 12:1
B. 11:1
C. 1:11
D. 1:12
Answer:
Option C. 1:11
Step-by-step explanation:
Let
x-----> dollars spent on office space
y ----> dollars spent on other costs
we know that
x+y=$360,000 -----> equation A
x=$30,000 ----> equation B
substitute equation B in equation A and solve for y
30,000+y=360,000
y=360,000-30,000=$330,000
Find the ratio of dollars spent on office space to dollars spent on other costs
Divide the dollars spent on office space by the dollars spent on other costs
so
x/y
substitute
30,000/330,000=1/11
(–1) + 5 – (–6) – 5 =
Answer:
5
Step-by-step explanation:
(-1) + 5 - (-6) - 5 =
v
4 - (-6) - 5 =
v
10 - 5 =
v
5
What is the value of e rounded to 4 decimal places
e = Euler's constant
e ≈ 2.718281828459045, rounded up e = 2.7183.
= 4.17356
How do you round numbers to 4 decimal places?the number after the line is lower than 5, round the number down (keep it the same). If the number is 5 and more than it round the number upwards. therefore in example 1 you need to round 4.17356 to 4 decimal places. This means you have 2 choices, either 4.17356 or 4.17357.
When we say round to 4 it means to fewer the digits to 4 to the right of the decimal point. The basic rule of remember is, if the number in the 5th place ( to round it any decimal place, consider this next digit) is > 5 then add 1 on the 4th digit and else remains the same.
Learn more about decimal place here https://brainly.com/question/17255119
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