Answer:
[tex]f(x)=2x+3[/tex]
Step-by-step explanation:
So we know that:
[tex]f(1)=5 \text{ and } f(3)=9[/tex]
In other words, we have 2 coordinates: (1,5) and (3,9).
With this, we can figure out the slope. Let (1,5) be x₁ and y₁ and let (3,9) be x₂ and y₂. The slope formula is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:
[tex]m=\frac{9-5}{3-1}\\m=4/2=2[/tex]
So, the slope is 2.
Now, use the point-slope form to figure out the y-intercept. The point-slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
For consistency, let's continue to use (1,5) as x₁ and y₁. Now, we can use 2 as m. Thus:
[tex]y-(5)=2(x-1)[/tex]
Distribute:
[tex]y-5=2x-2[/tex]
Add 5 to both sides:
[tex]y=2x+3[/tex]
So:
[tex]f(x)=2x+3[/tex]
And that's our equation :)
Identify the domain intervals over which the inverse of the graphed function is also a function. Select all that apply.
Answer:
A, B and D
Step-by-step explanation:
There are two inverse linear functions graphed. One of the is decreasing up to x = 3 excluded, the other one is increasing from the point x = 3 included.
Domain range of the decreasing one is:
( - oo, 3 )Domain range of the increasing one is:
[ 3, +oo )Correct choices are: A, B and D
Note: A and B are same
Which of the following statements is true?
A) Two similar triangles must be congruent.
B) Two congruent triangles must be similar.
C) Two triangles having ye same area must be congruent.
D) Two triangles having the same perimeter must be similar.
Answer:
A or C
Step-by-step explanation:
Given the points A(-1, 2) and B(7, 14), find the coordinates of the point P on directed line segment stack A B with bar on top that partitions stack A B with bar on top in the ratio 1:3. Show your work.
Answer:
(1, 5)
Step-by-step explanation:
The desired point is the weighted average of the end point coordinates. The weights are the reverse of the relative line segment lengths.
P = (3A +1B)(3+1) = (3(-1, 2) +(7, 14))/4 = (-3+7, 6+14)/4 = (1, 5)
The point of interest is (1, 5).
Solve 2x^2+16x+34=0?????
Answer:
2([tex]x^{2}[/tex]+8x+17)
Step-by-step explanation:
Factor out 2 of the equation.
Answer:
For real numbers: no solution
For complex numbers: [tex] x = -4 \pm 4i [/tex]
Step-by-step explanation:
2x^2 + 16x + 34 = 0
Divide both sides by 2.
x^2 + 8x + 17 = 0
There are no two numbers whose product is 17 and whose sum is 8, so this polynomial is not factorable.
We can use the quadratic formula.
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
We have a = 1; b = 8; c = 17
[tex] x = \dfrac{-8 \pm \sqrt{8^2 - 4(1)(17)}}{2(1)} [/tex]
[tex] x = \dfrac{-8 \pm \sqrt{64 - 68}}{2} [/tex]
[tex] x = \dfrac{-8 \pm \sqrt{-64}}{2} [/tex]
If you have not learned imaginary or complex numbers, stop here. Since the discriminant is negative, there is no real solution.
If you have learned complex numbers, then we continue.
[tex] x = \dfrac{-8 \pm 8i}{2} [/tex]
[tex] x = -4 \pm 4i [/tex]
Josh and David collect pecans for their mother to make a pecan pie. Josh collects 3.25 pounds of pecans, and David harvest 4 3/8 pounds. How many more pounds of pecans does David collect than Josh?
Answer:
1 1/8
Step-by-step explanation:
So the first step is to convert all of them to fractions, so 3.25 become 3 1/4
Next, we do 4 3/8- 3 1/4
We convert 1/4 to 2/8
So, it's now 4 3/8- 3 2/8
The answer is 1 1/8
How many atoms are contained in 1cm of
interstellar space?
Answer:
0.1 atoms
Step-by-step explanation:
Typically, there is 0.1 atoms in each cubic centimeter of interstellar wind, and 10 ions in each cubic centimeter of solar wind (versus surface air which contains 3 x 10^19 molecules per cc). This means there is a great deal of dead space between the very tiny particles and collisions are rare.
Answer-1 billion
Step-by-step explanation:
k squared - 13k+36
[tex]18n + 20n - 378[/tex]
Answer:
k^2-13+36
38n-378
Step-by-step explanation:
k^2-13k+36
k^2-13+36
The above expression can't be simplified further because they are not like terms.
18n+20n-378
38n-378
Hope this helped ;) ❤❤❤
A telemarketer earns a base salary of $3,000 per month, plus an annual bonus of 2.5% of total sales above $250,000. Which function represents the annual salary for total sales of x dollars, where x is greater than $250,000? A) S(x) = 3,000 + 0.025(x – 250,000) B) S(x) = 3,000 + 2.5(x – 250,000) C) S(x) = 12(3,000) + 0.025(x – 250,000) D) S(x) = 12(3,000) + 2.5(x – 250,000)
Answer:
answer is c.
I got it right on edge
Function S(x) = 12(3,000) + 0.025x (x ≥ 250,000) represents the annual salary for total sales of x dollars, where x is greater than $250,000. Option C is correct.
Given that,
A telemarketer earns a base salary of $3,000 per month, plus an annual bonus of 2.5% of total sales above $250,000.
To determine which function represents the annual salary for total sales of x dollars, where x is greater than $250,000.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
According to the question,
annual salary be S
S(x) = annual base salary + annual bonus earned
S(x) = 12 * 3000 + 0.025x (where x is > $250,000)
Thus, function S(x) = 12(3,000) + 0.025x (x ≥ 250,000) represents the annual salary for total sales of x dollars, where x is greater than $250,000. Option C is correct.
Learn more about function here:
brainly.com/question/21145944
#SPJ2
1. Three people board the subway train at the first stop. Five people board the train at
the second stop. Seven people board the train at the third stop. If this pattern
continues and no one gets off the train, how many people are on the subway train when
it reaches the seventh and final stop?
Answer:
48 people.
Step-by-step explanation:
The sequence is 3 5 7 ...
The common difference is 2 so by the 7th stop 6 lots of people have boarded and the total is:
3 + 5 + 7 + 9 + 11 + 13 = 48 people.
=
Joe earned $10 in allowance this week and $2 for each extra chore he did. Let (c) represent the number of extra chores Joe did this week. Which of the following expressions best represents Joe's income for the week? a. 10 + 2c b. 10 + 2 c. 10 + c + 2 d. 10c + 2
Answer:
10 + 2c (i think)
Step-by-step explanation:
You do the $10 for his cores plus $2x The Amount of extra chores he did
3 and one half times two eleventh’s divided by two and one third times eleven equals...
Emma wants to know how much her dog weighs. She held her dog and stepped on the scale. Their combined weight is 118.6 pounds. Emma weighs 85.4 pounds, so how many pounds does her dog weigh?
Answer:
33.2
Step-by-step explanation:
If he pays $46.80 for one year. He receives one magazine each month for 12 months. Find the dollars he pays for each
magazine
Answer:
Each magazine costs 3.90
Step-by-step explanation:
Take the total cost and divide by the number of magazines
46.80/12
3.90
Answer:
3.90$ per magazine is paid
A cabinet is 6 feet high, 3 feet wide and 2 feet long. The entire outside of the cabinet is being painted, except for the bottom. What is the surface area being painted?
Answer:
66ft²Step-by-step explanation:
The cabinet is rectangular shaped. Using the formula for calculating the surface area of a reactangular bos to solve the problem.
Surface area = 2(LW+WH+LH) where;
L is the length of the cabinet
W is the width of the cabinet
H is the height of the cabinet.
If the entire outside of the cabinet is being painted, except for the bottom, then the surface area of the painted area will be expressed as;
S = LW+2WH+2LH
Given L = 2 feet, W = 3 feet and H = 6 feet
S = 2(3)+2(3*6)+2(2*6)
S = 6+2(18)+2(12)
S = 6+36+24
S = 66 feet²
Hence the surface area of the painted part is 66ft²
Emma drew 2 hearts and 37 circles. What is the ratio of circles to all shapes?
Answer:
37:39
Step-by-step explanation:
You write the amount of circles then add 37 to 2 and make a ratio table.
Answer: 37:39
Step-by-step explanation: there are 37 circles and there are 39 shapes in all (37 circles plus the two hearts)
is 8.3 greater than 83 tenths?
Answer:
NO
Step-by-step explanation:
They are equal
83 tenths divided by 10 is 8.3
Hope this helps :-)
Convert the following to standard notation.
1.5 x 10
Answer:
15
Step-by-step explanation:
1.5*10 =15
Answer:
15.
Step-by-step explanation:
1.5 x 10 is expanded notation, so you just solve it (by multiplying) to convert it into standard notation.
HELP PLZ WILL GIVE BRAINLIEST
Answer:
x = 31 °
Step-by-step explanation:
90 = 58 + x
x = 90 - 58
x = 31 °
Answer:
x° = 32°
Step-by-step explanation:
∠BAC = ∠IAK = 58° (Vertically opposite angles)
∠GCJ = ∠ACB = x° (Vertically opposite angles)
Angles of a Δ ABC = 180°
Δ ABC = 90° + 58° + x° = 180°
⇒x° = 180° - 90° - 58 °
⇒x° = 32°
I need help on how to explain my answer.
Answer:
(1,-1)
Step-by-step explanation:
(1,-1) because if you subtract 5-6 you get -1 and 2-1 you get 1.
Answer:
if F where to move down 6 points then it would be 2, -1.
then if it where to move left 1 unit the coordinants for F prime would be
(1, -1)
HCF of 15 and 60
in full form
Answer: 15
Step-by-step explanation: Easy way to do it is of you just list all the factors and find the highest common factor, 15= 1,3,5,15. 60= 1,2,3,4,5,6,10,12,15,30,60.
The common factors here are 3 and 15 the highest common factor is 15.
Now another method is to draw the division diagrams which are shown in the image below...
Answer:
Step-by-step explanation:
HCF of two or more numbers is the largest number that divides the number without leaving remainder.
Prime factorize 15 and 60
15 = 3 * 5
60 = 2 * 2 * 3 * 5
HCF = 3 * 5 = 15
12. What value of c would make x = 4 in the
equation 5 + cx = 13 ?
Look at this graph:
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer: 1/3
Step-by-step explanation:
Two points on this graph are (40, 80) and (70, 90). These points can be used to find the slope. The formula for slope is (y2-y1)/(x2-x1).Plugging our numbers into the formula: (80-90)/(40-70) = (-10)/(-30) = 1/3Write an equivalent expression for the following.
-3(ab +6ba) -(4+b)
A particle is thrown vertically upwards with velocity 20 metre per second find a the distance travelled by the particle in first 3 second and displacement of the particle in 3 seconds
Step-by-step explanation:
[tex]\huge\underline\bold\blue{ƛƝƧƜЄƦ}[/tex]
[tex]\huge\underline\bold\green{Gïvëñ}[/tex]
[tex]\small\underline\bold\red{ v=0}[/tex]
[tex]\small\underline\bold\blue{ v = u+gt}[/tex]
[tex]\small\underline\bold\blue{0=20-10t}[/tex]
[tex]\small\underline\bold\blue{t = 2 sec}[/tex]
[tex]\huge\underline\bold\yellow{distance in first 2 second }[/tex]
s = s(t=0 to 2 second) + s(2second to 3 second)
s = (ut+1\2(at)^2+ (ut+1\2at^2)
s = 20×2-1\2×10×4+1\2×10×1
s = 25
[tex]\huge\underline\bold\blue{Displacement}[/tex]
s = 20 - 5 = 15
Hope it helps
Please explain with working!!! Find the set of values of x that satisfy the inequality 9x^2-15x<6
Answer:
[tex]\displaystyle -\frac{1}{3} < x < 2[/tex]
Step-by-step explanation:
We want to solve the quadratic inequality:
[tex]9x^2-15x<6[/tex]
In order to solve a quadratic inequality, find its zeros. That is, let the inequality sign be an equal sign and solve for x. We do this because it denotes when the graph crosses the x-axis: that is, when it is positive and/or negative. This yields:
[tex]9x^2-15x=6[/tex]
Solve for x:
[tex]\displaystyle \begin{aligned} 9x^2-15x-6 &= 0\\ 3x^2 - 15 -6 &= 0 \\ (3x+1)(x-2) &= 0\end{aligned}[/tex]
By the Zero Product Property:
[tex]\displaystyle 3x + 1 = 0 \text{ or } x - 2 = 0[/tex]
Hence:
[tex]\displaystyle x = -\frac{1}{3}\text{ or } x = 2[/tex]
Now, we can test intervals. The three intervals are: all values less than -1/3, values between -1/3 and 2, and all values greater than 2.
To test the first interval, let x = -1. Substitute this into our original inequality:
[tex]\displaystyle \begin{aligned}9(-1)^2 -15(-1) \, &?\, 6 \\ 9+15 \, &? \, 6 \\ 24&> 6 \xmark \end{aligned}[/tex]
The resulting symbol is "greater than," which is not our desired symbol.
To test the interval between -1/3 and 2, we can let x = 0:
[tex]\displaystyle \begin{aligned} 9(0)^2 - 15(0) \, &? \, 6 \\ (0) - (0) \, &? \, 6 \\ 0 &< 6\, \checkmark\end{aligned}[/tex]
The resulting symbol is indeed less than. So, the interval (-1/3, 2) is a part of our solution.
Finally, to test the third interval, let x = 3. Then:
[tex]\displaystyle \begin{aligned} 9(3)^2 - 15(3) \, &? \, 6 \\ (81) - (45) \, &? \, 6 \\ 36 &> 6\end{aligned}[/tex]
Again, this is not our desired symbol.
In conclusion, our only solution is the interval:
[tex]\displaystyle \left(-\frac{1}{3}, 2\right)[/tex]
Or as an inequality:
[tex]\displaystyle -\frac{1}{3} < x < 2[/tex]
1. Triangle ABC with coordinate points A(-2,3); B(-1,0); C(5,-4) is rotated 90 degrees clockwise. What
are the new image points for triangle A'B'C'?
Answer: A'(3,2), B'(0,1) and C'(-4, -5).
Step-by-step explanation:
When we rotate (a,b) 90 degrees clockwise, the new point will be (b,-a).
i.e. rotation rule for 90 degrees clockwise : (x,y) → (y,-x)
Given: Triangle ABC with coordinate points A(-2,3); B(-1,0); C(5,-4) is rotated 90 degrees clockwise.
Then, the new image points for triangle A'B'C' will be :
A(-2,3) → A'(3,-(-2)) =A'(3,2)
B(-1,0)→ B'(0,-(-1)) = B'(0,1)
C(5,-4) → C'(-4, -5)
Hence, the new image points for triangle A'B'C' are A'(3,2), B'(0,1) and C'(-4, -5).
Evaluate f + g2 - 3g if f= 3 and g = 5.
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{13}}}}}[/tex]
Step-by-step explanation:
Given, f = 3 and g = 5
[tex] \sf{f + {g}^{2} - 3g}[/tex]
Plug the values
⇒[tex] \sf{3 + {5}^{2} - 3 \times 5}[/tex]
Evaluate the power
⇒[tex] \sf{3 + 25 - 3 \times 5}[/tex]
Multiply the numbers : 3 and 5
⇒[tex] \sf{3 + 25 - 15}[/tex]
Add the numbers : 3 and 25
⇒[tex] \sf{28 - 15}[/tex]
Subtract 15 from 28
⇒[tex] \sf{13}[/tex]
Hope I helped!
Best regards! :D
Find an equation of the line that passes through the given point and has the indicated slope m.
Answer:
y = -5.5
Step-by-step explanation:
The only lines that have a slope of 0 are horizontal lines. Horizontal lines are always in the form y = c where c is a constant. Basically, on a horizontal line, no matter what x is, y will always be the constant c. Therefore, the x coordinate of our given point does not matter and we only have to look a the y-coordinate, which is -5.5. Therefore, the equation is y = -5.5.
Using the graph provided, find f(x)=2
Answer:
so x=3
Step-by-step explanation:
f(x) = 2
We want to find the x value when y =2
Going across where y = 2
Then go down to find the x value x=3 when y = 2
f(3) =2
so x=3
90 POINTS PLEASE HELP Choose one problem below and use trigonometry to solve for the missing side x of the right triangle
Answer:
x = 13.28
Step-by-step explanation:
basic trig ratios: using tanФ = opp/adj.
tan(38) = x / 17
x = tan(38) * 17
x = 13.28
to get more idea of the subject, read below:
The cotangent (cot)
The cotangent is the reciprocal of the tangent. It is the ratio of the adjacent side to the opposite side in a right triangle.
tan(A) = opp/adj = a/b
cot(A) =adj/opp = b/c
Answer:
[tex]\Huge \boxed{x \approx 13.28}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trig functions to solve for the problem.
[tex]\sf \displaystyle tan (\theta)=\frac{opposite}{adjacent}[/tex]
[tex]\sf \displaystyle tan (38)=\frac{x}{17}[/tex]
Multiplying both sides by 17.
[tex]\sf \displaystyle 17 \cdot tan (38)=\frac{x}{17} \cdot 17[/tex]
[tex]\sf x= 13.28185565...[/tex]
The measure of x is approximately 13.28.
[tex]\rule[225]{225}{2}[/tex]