Answer:
We conclude that the equation of a linear function with f (5) = -1 and f(0) = -5 will be:
f(x) = 4/5x - 5Step-by-step explanation:
Given
f(5) = -1f(0) = -5f(5) = -1 means at x = 5, y = -1
Hence, the point (5, -1) lies on the line function.
f(0) = -5 means at x = 0, y = -5
Hence, the point (0, -5) lies on the line function.
Thus, the two points on the linear line function graph are:
(5, -1)(0, -5)Finding the slope between the points (5, -1) and (0, -5)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(5,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:-5\right)[/tex]
[tex]m=\frac{-5-\left(-1\right)}{0-5}[/tex]
[tex]m=\frac{4}{5}[/tex]
The slope-intercept form of the linear line function
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
We have already determined the slope which is: m = 4/5
We know the y-intercept can be determined by setting x = 0 and solving for y.
Thus, the point (0, -5) represents the y-intercept b = -5.
Now, substituting m = 4/5 and b = -5 in the slope-intercept form
[tex]y = mx+b[/tex]
y = 4/5x + (-5)
y = 4/5x - 5
Therefore, we conclude that the equation of a linear function with f (5) = -1 and f(0) = -5 will be:
f(x) = 4/5x - 5A motorboat travels 172 km in 3 hours going upstream and 372 in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Answer:
The rate of the boat is 75.17 km/h and the rate of the stream is 17.83 km/h
Step-by-step explanation:
System of Equations
Let's call:
B = speed (rate) of the boat in still water
S = speed (rate) of the stream
The boat travels 172 km in 3 hours when going upstream, that is when the speed of the stream subtracts its own speed. The speed is the distance divided by the time, thus:
[tex]\displaystyle B-S=\frac{172}{3}[/tex]
Multiplying by 3:
3B - 3S = 172 [1]
The boat travels 372 km in 4 hours downstream when the speed of the current adds to its own:
[tex]\displaystyle B+S=\frac{372}{4}=93[/tex]
B + S = 93
Solving for B:
B = 93 - S [2]
Substituting in [1]
3(93 - S) - 3S = 172
Operating:
279 - 3S - 3S = 172
279 - 6S = 172
Subtracting 279:
- 6S = 172 - 279
- 6S = -107
Multiplying by -1 and solving for S:
[tex]S = \frac{107}{6}\approx 17.83\ km/h[/tex]
From [2]:
[tex]B = 93 - \frac{107}{6}[/tex]
[tex]B=\frac{451}{6}\approx 75.17\ km/h[/tex]
Good Mornting hru?
3(7)+4(6)=
Answer:
45
Step-by-step explanation:
im good, u?
Yuto and Hila attempted to solve the same inequality. Their work is shown below.
Yuto’s Work
Hila’s Work
Negative two-thirds x + 9 greater-than 7. Negative two-thirds x + 9 minus 9 greater-than 7 minus 9. Negative two-thirds x greater-than negative 2. (Negative three-halves) (Negative two-thirds x) less-than (Negative three-halves) (Negative StartFraction 2 over 1 EndFraction). x less-than 3.
Negative two-thirds x + 9 greater-than 7. Negative two-thirds x + 9 minus 9 greater-than 7 minus 9. Negative two-thirds x greater-than 16. (Negative three-halves) (Negative two-thirds x) less-than (Negative three-halves) (StartFraction 16 over 1 EndFraction). x less-than negative 24.
Which statement is true about the work shown above?
Yuto is correct because he isolated the variable correctly and reversed the inequality symbol.
Yuto is incorrect because he should not have reversed the inequality symbol.
Hila is correct because she isolated the variable correctly and reversed the inequality symbol.
Hila is incorrect because she should not have reversed the inequality symbol.
Answer:
Yuto is correct because he isolated the variable correctly and reversed the inequality symbol.
Step-by-step explanation: hi
Answer:
The answer is A
Step-by-step explanation:
In other words, Yuto is correct because he isolated the variable correctly and reversed the inequality symbol.
In a complete paragraph, explain why it's important to think about the complexity of your speech.
Use your own words please.
Answer:
I will try it :)
Step-by-step explanation:
thanks for the points.
CAN SOMEONE PLEASE HELP ME???
Answer:
f(x)=525+4.75x
Sue makes and sells cupcakes. If she has a cost of $1,500 per year plus a cost of $1 per cupcake, how many cupcakes must she sell in order to make a profit if each cupcake sells for $3?
Answer:
751 cupcakes must be sold to make a profit
Step-by-step explanation:
From the question we are told that
Annual cost= $1,500 per year plus a cost of $1 per cupcake
Each cup cake sell at $3
Generally the profit off the top of each cupcake is $2
Therefore
[tex]\frac{1500}{2}=750[/tex]
This implies that 750 cupcakes will be sold to cover the annual cost excluding cupcake cost
Generally
751 cupcakes=$1502
Total Annual cost to make a profit
[tex]1(cost\ of\ each\ cupcake)*751+1500=\$2251[/tex]
Total Annual sale
[tex]3(sale of each cupcake)*751=\$2253[/tex]
Mathematically
[tex]2253\$-2251\$=2\$[/tex]
Therefore
751 cupcakes must be sold to make a profit
Hi I need help please
Answer:
15%
Step-by-step explanation:
Percent Error formula is the difference between the Actual and the guess value divided by the actual.
So it's 198- 172 / 172 x 100
= 15%
HELP PLEASE!!!!!!!
A restaurant sells 10 garden salads. If garden salads represent 20% of their total salad sales, how many salads did they sell?
What should be done to both sides of the equation in order to solve -5 m = -40?
Multiply by -5.
Multiply by -40.
Divide by -5.
Divide by -40.
Answer:
I know for a fact that it is Devide by nagative 5
Step-by-step explanation:
Pls help me I’ll give 100 points
Answer:
Try option B
Step-by-step explanation:
sub to Pen Paper
Hi there!
So what we have to do here is...
turn 2³ - 1 into 2·2·2-1=4·2=8-1=7.
[tex]\frac{35}{7}=5[/tex]
Final Result: 5
When paying for a restaurant order, a customer spent $18.00 ( for tip and cost) for a $15.00 meal. What percent was the tip? *
Answer:
16.67%
Step-by-step explanation:
The customer spent a total of $18 on a $15 meal. This means that, if counting tax within the $15 meal, the tip is $3.
Divide 3 with the total cost:
3/18 = ~0.1667
Change to percentage. Simply move the decimal point to the right two place values, and add a percentage sign:
0.1667 to a percent = 16.67%
16.67% is your answer.
~
Answer:
1.6 %
Step-by-step explanation:
15/18= 8.4
What is the simplest form of this expression?
-x(4x2 - 6x + 1)
Answer:
−4x3+6x2−x
Step-by-step explanation:
(−x)(4x2−6x+1)
=(−x)(4x2+−6x+1)
=(−x)(4x2)+(−x)(−6x)+(−x)(1)
=−4x3+6x2−x
The value of a baseball player's rookie card began to increase once the player retired. When he retired in his card was worth $. The value has increased by $ each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in ?
Answer:
No, x and y are not proportional
The value of card in 2006 = $38.05
Step-by-step explanation:
I got this! I hope this helps!
ASAP! please help, thanks
Answer:
d should be correct
Step-by-step explanation:
prove me wrong
Order from least to greatest.
1.603; 1.036; 1.36; 1.063
Answer:
1.036, 1.063, 1.36, 1.603
Step-by-step explanation:
Hope this helped, have a great day :)
4. Solve the inequality. 9+8 l 4a - 5 l >113
Answer:
i need this for a challenge
Step-by-step explanation:
solve for x each figure is a parallelogram
Answer:
[tex]18x + 8= (180 - 46) = 134 \\ 18x = 126 \\ \boxed{x = 7}[/tex]
7 is the right answer.Solve for X
6(x + 2) = 66
X =
Answer:
6(x+2)=66
6x+12=66 -12
6x= 54 :6
x=9
Step-by-step explanation:
prove me wrong
Determine, in general form, the equation of the line that goes through the
point (3,-6) and is perpendicular to the line shown: 5x + 3y + 9 = 0
Answer:
I got
y=3/5x -39/5
Step-by-step explanation:
Hope this helps
Can someone please help me with number 16?
Answer:
I got 105°
Step-by-step explanation:
Triangle ABC is an isosceles triangle so base angles are equal. <A = 30° (given)
180 - 30 = 150°
150/2 = 75°
the little triangle is also isosceles. the original base angles have been bisected so the base angles are 37.5.
37.5 X 2 = 75°
180-75 = 105°
D = 105°
Work out the surface area of the solid cuboid.
8m
5m
2m
Answer:
Step-by-step explanation:
T.S.A=2(LXW) + 2(LXH) + 2(WXH)
=2(8mx5m) + 2(8mx2m) + 2(5mx2m)
=(2x40m²) + (2x16m²) + (2x10m²)
=80m² + 32m² + 20m²
=132m²
I= $164.50, P = $940, t = 2.5
Find the annual interest rate
250.35 that the anwers hope this help a lot
How to find percents of numbers using multiples of 100, 10, and 1%?
I need this for my summary, please help!!
Answer:
Im not too sure what the question is
Step-by-step explanation:
but when finding the percent of any number, 10% will always move the decimal over to the left once. So 10% of 300 is 30.0 This also works for 1%, you just move the decimal over twice. So 1% of 300 is 3
Merideth made a model of a pyramid like the one shown for history class.
What is the height of the model?
I un
15 in
app
The
Great!
e Building on the Essential Question How do you solve
Answer:
12
Step-by-step explanation:
there is a right angle so you can use Pythagoras therom to get the height it's going to be (15)^2-(9)^2 all under a square root = 12 in.
In a system of two linear equations, the lines represented by each equation have the same slope. Which could be the total number of solutions to the system of equation
Answer:
Please see explanation
Step-by-step explanation:
A system of linear equations in two variables represents two lines on graph.
When both the lines have same slope, there can be two cases
Same slope with different y-interceptsWhen two lines have same slope and different y-intercepts, that means that both lines are parallel and parallel lines have no solution.
Same slope with same y-interceptsWhen the slope of both lines is same and the y-intercept is also same, this means that both the equations refer to the same line. This means that the system has infinite number of solutions.
pls help as soon and as quick as possible I really need help
Answer:
(1,7)
(0,2)
(-1,-3)
(-2,-8)
put dots on these points and put a line through all of them making on line
9. The hypotenuse of a 45°-45°-90° triangle is 5 sqrt 6. Find the length of one leg of the right triangle.
Answer:
5 ✓ 3
Step-by-step explanation:
using Pythagoras Theory
(5 ✓ 6 )2 =, 2 x square side
square leg length= 150/ 2=, 75
length =5 ✓ 3
How to calculate slope for a line that goes through
two points.
10.2: Practice
y
Find the slope of the line through these points. Try
making a table.
-3
6
(5.-3) and (-1.6)
Answer:
The slope is [tex]m=-\frac{3}{2}[/tex]
Step-by-step explanation:
The slope point equation is given by:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here:
The first point is (x1,y1)=(5,-3)
The first point is (x2,y2)=(-1,6)
Then, the slope will be:
[tex]m=\frac{6-(-3)}{-1-5}[/tex]
[tex]m=\frac{9}{-6}[/tex]
[tex]m=-\frac{3}{2}[/tex]
I hope it helps you!
Lee needs some school supplies. He will buy 3 notebooks for $1.29 each, 2 dozen
pencils at $3.45 a dozen and a box of pens for $14.85.a box. Lee estimates that he
will spend about $25 on these school supplies.
Is Lee's estimation reasonable? How much will he spend exactly?
Class A has 20 pupils and class B has 19 pupils.
Both classes site the same maths test
The mean score for class A is 33.
The mean score for class B is 62
What is the mean score (rounded to 2 DP) in the maths test across
both classes?
Answer:
47.5
Step-by-step explanation:
33+62=95
95/2=47.5