Answer:
k = 6
Step-by-step explanation:
Step 1: Find slope m
m = (4 - 8)/(-10 - 6)
m = -4/-16
m = 1/4
y = 1/4x + b
Step 2: Find b
4 = 1/4(-10) + b
4 = -5/2 + b
b = 13/2
Step 3: Rewrite equation
y = 1/4x + 13/2
Step 4: Find k
y = 1/4(-2) + 13/2
y = -1/2 + 13/2
y = 12/2
y = 6
Answer: 6
Step-by-step explanation:
As you move left to right on the x-coordinate, your y value is increasing. If you notice, the x values are increasing by eight at a time. So, if you take the value in between 4 and 8, you get your answer, which is 6.
The domain for f(x) and g(x) is the set of all real numbers.
Let f(x) = 3x + 5 and g(x) = x2.
Find f(x) · g(x).
A. 3x3 + 3x2 + 5
B. 3x3 + 5x2
C. 3x2 + 5
D. x2 – 3x – 5
Answer:
3x3 +5x2
Step-by-step explanation:
f(x).g(x)
(3x+5)(x2)
(3x×x2)(5×x2)
3x3+5x2
what is the solution to the inequality below x<5
Answer:
The correct answer is B
Answer:
0 < x < 25
Step-by-step explanation:
What is 14v14 divided by 72 in simplest form?
Answer:
About 2.72
Step-by-step explanation:
From reading the comments, I suppose you meant v actually means x so:
14 × 14 = 196
196 ÷ 72 ≈ 2.72
Hope this helped! :)
Answer:
Hello!
I'm not sure what the " v " means but I think you meant to put x instead of v
____________________
14 x 14 = 196
196 ÷ 72 = [tex]\frac{49}{18}[/tex]
Step-by-step explanation: Reduce the expression, if possible, by cancelling the common factors.
Hope I got this right.
Find the product h · k(x) if h(x) = 2(3x – 5) and k(x) = –2x + 1?
Answer:
The answer is option C.
Step-by-step explanation:
h(x) = 2(3x – 5) = 6x - 10
k(x) = –2x + 1
h • k (x) = (6x - 10) ( - 2x + 1)
= - 12x² + 6x + 20x - 10
The final answer is
= - 12x² + 26x - 10
Hope this helps you
Answer:
C) h · k(x) = –12x2 + 26x – 10
Step-by-step explanation:
BRAINLIEST FOR CORRECT ANSWERRR
The function f(x) = −x^2 + 28x − 192 models the hourly profit, in dollars, a shop makes for selling sodas, where x is the number of sodas sold. Determine the vertex, and explain what it means in the context of the problem.
(12, 16); The vertex represents the maximum profit.
(12, 16); The vertex represents the minimum profit.
(14, 4); The vertex represents the maximum profit.
(14, 4); The vertex represents the minimum profit.
Answer:
Part A:
The vertex : x = - b / 2 a = - 28 : ( - 2 ) = 14
y = f ( 14 ) = - 14² + 28 · 14 - 192 = 196 + 392 - 192 = 4
The vertex is ( 14, 4 ). It means that the maximum hourly profit is $4, and that the shop should sell 14 sodas to reach the maximum.
Part B :
We will solve the quadratic equation:
x 1/2 = ( - 28 +/- sqrt ( 784 - 768 ) ) / ( - 2 )
x 1 = 12, x 2 = 16.
It means that if the shop must sell more than 12 and less then 16 sodas if they want to make a profit ( 13, 14, or 15 ). If they sell 12, or 16 they will brake even.
I think
The vertex of the given function is option(C) (14,4) The vertex represents the maximum profit
What is a Quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two
What is Vertex of Quadratic function?The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry
Given,
[tex]f(x) =-x^{2} +28x-192[/tex]
Vertex
x= [tex]-\frac{b}{2a}[/tex]
x= [tex]-\frac{28}{2(-1)} =14[/tex]
y= [tex]-14^{2}+28(14)-192 =4[/tex]
Vertex (14,4)
It means that the maximum hourly profit is $4, and that the shop should sell 14 sodas to reach the maximum.
Hence, the vertex of the given function is option(C) (14,4) The vertex represents the maximum profit
Learn more about Quadratic function and Vertex of quadratic function here
https://brainly.com/question/16245526
#SPJ2
Which of the following are solutions to the quadratic equation? Check all that
apply.
2x2 + 7x- 14 = x2 + 4
Answer:
[tex]\boxed{\sf \ \ \ x=-9 \ \ or \ \ x=2 \ \ \ }[/tex]
Step-by-step explanation:
hello,
[tex]2x^2+7x-14=x^2+4\\<=> 2x^2+7x-14-x^2-4=0\\<=> x^2+7x-18=0\\<=>x^2-2x+9x-18=0\\<=> x(x-2)+9(x-2)=0\\<=> (x+9)(x-2)=0\\<=> x+9 = 0 \ \text{or} \ x-2=0\\<=> x = -9 \ \text{or} \ x=2[/tex]
hope this helps
A 1 km long train is travelling at 30km/h. If the train enters a tunnel that is 1 km long, how much time will it take for the train to clear the tunnel?
Answer: 240 seconds OR 4 minutes
Step-by-step explanation:
Length of the train = 1 km
Length of the tunnel = 1 km
Therefore, length of the train + length of the tunnel = (1 + 1) km = 2 km
= 2000 m
Speed of the train = 30 km/hr = 8.333 metres per second
Therefore, time taken by the train to cross the tunnel = 2000 m/ 8.333 m/sec.
= 240 seconds = 4 minutes
solve the following system of linear equations using the elimination method
Answer:
x=-1, y=2, z=3
Step-by-step explanation:
First at all, you can divide these equations into two group. It is easier to you.
4x-2y+3z=1
3x+y+2z=5
x+3y-4z=-7
3x+y+2z=5
Then, you can simplify these group of equation that you divided.
So, we have to simplify these step by step.
First, we can simplify the first group of equation.
4x-2y+3z=1
3x+y+2z=5
We have to find which variable you want to eliminate. I choose y.
You can multiply the second equation of first group by 2 and eliminate them.
4x-2y+3z=1
6x+2y+4z=10
As the variable of y is same and we can eliminate y by addition.
4x-2y+3z=1
6x+2y+4z=10
become
10x+0+7z=11
10x+7z=11
10x+7z=11 as the third equation.
Next, simplify the second group of equation.
x+3y-4z=-7
3x+y+2z=5
Same way as the previous one. We need to find which variable that you want to eliminate. I choose y.
We need to balance for the first equation x+3y-4z=-7 at least one variable.
We need to multiply this equation by -3 below to get the same value of y to eliminate the above equation.
3x+y+2z=5 (multiply by -3)
-9x-3y-6z=-15
x+3y-4z= -7
-9x-3y-6z= -15
Here we go! Now these group has same value and variable to eliminate.
We can eliminate these equations by addition method.
x+3y-4z= -7
-9x-3y-6z= -15
-8x+0+10z= -22
-8x+10z= -22
Furthermore, we have to combine these equations that we have simplified from the previous groups.
10x+7z=11
-8x+10z= -22
10x+7z=11 and -8x+10z= -22 as a new group.
Finally, it is time to solve these equations!!
10x+7z=11
-8x+10z= -22
First equation of the above group, we can multiply by 10. Like this:
100x+70z=110
Second equation of the above group, we can multiply by 7. Like this:
-56x+70z=-154
So, we can see there are same value from these equation which are +70z and -70z.
Now, we can eliminate this variable by sum these equations.
100x+70z=110
-56x+70z=-154
44x= -44
x= -1
When we get x= -1 , we can use this value to any equation that you want. You can get the same answer as well.
When x= -1,
substitute into 100x+70z=110
100(-1)+70z=110
-100+70z=110
70z=110+100
70z=210
z=3
When z=3 and x= -1, we can substitute into x+3y-4z= -7
-1+3y-4(3)= -7
-1+3y-12= -7
3y=6
y=2
So, the answer is x= -1 , y=2 , z=3
I hope you will understand my solution and explanation. Bye!!
easy question please help fast, i just want to check my answer!
Answer:
false
Step-by-step explanation:
its false I think
The tens digit of a two-digit number is twice the units digits. If the digits are reversed, the new number is 18 less than the original number. Find the number.
Answer:
x=42
Step-by-step explanation:
The tens digit of a two-digit number is twice the units digits. put it in an equation:
10(2x)+x = 10x+2x+18
21x=12x+18
21x-12x=18
x=18/9=2
substitute x:
10(2x)+x = 10x+2x+18
10(2*2)+2=10(2)+2(2)+18
42=24+18
If f(x) = x2 + 3x - 4, find f(4).
Answer:
f(4) = 24
Step-by-step explanation:
Plug in 4 for x in the equation:
f(x) = x² + 3x - 4
f(4) = (4)² + 3(4) - 4
Remember to follow PEMDAS. PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
and is the order of operation.
First, solve the power:
(4)² = 4 * 4 = 16
Next, multiply 3 with 4:
3 * 4 = 12
Next, combine the terms:
f(4) = 16 + 12 - 4
f(4) = (16 + 12) - 4
f(4) = 28 - 4
f(4) = 24
f(4) = 24 is your answer.
~
Answer:
24
Step-by-step explanation:
Plug x as 4.
(4)² + 3(4) - 4
16 + 12 - 4
= 24
Which part of the graph is the distance from home constant? PLEAS HELP ME VERY EASY
Find lateral surface area in square units, of the following 3-
dimensional figure.
Enter just a number for your answer.
-
14 ft
7 ft
9 ft
Answer:
Lateral surface area of cuboid = 448 ft²
Step-by-step explanation:
Given:
Height of cuboid(h) = 14 ft
Length of cuboid(l) = 9 ft
width of cuboid(b) = 7 ft
Find:
Lateral surface area of cuboid
Computation:
Lateral surface area of cuboid = 2 h(l + b)
Lateral surface area of cuboid = 2(14)(9 + 7)
Lateral surface area of cuboid = 28(16)
Lateral surface area of cuboid = 448 ft²
If 6x - y = 21 and -x + 6y = 14, what is the value of x - y?
Answer:
the value of x_y is 1.
hope u get it.....
can some body help me plz
Answer:
Length of each side of the square = 8 cm
Step-by-step explanation:
In the figure attached, diagrams of a right triangle and a square have been given.
"Area of the square is twice the area of the triangle."
Let one side of the square = x cm
Therefore, area of the square = x²
Area of the given triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(16)(4)[/tex]
= 32 cm²
Therefore, x² = 2 × 32
x² = 64
x = 8 cm
Therefore, length of each side of the square will be 8 cm.
can someone help me answer this please
Answer: 19 degrees
Step-by-step explanation:
<FOE is the central angle of an arc of 52 degrees and is thus 52 degrees. Then by supplementary angles <COD is 71 degrees and angle BOA is thus also 71 degrees. Then by supplementary angles <BOC is 19 degrees and arc BC is thus also 19 degrees.
Hope it helps <3
Answer:
19 degrees
Step-by-step explanation:
Complex numbers are used in electronics to describe the current in an electric circuit. Ohm's law relates the current in a circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the circuit, R, in ohms, by the formula Solve the problem using this formula. Find E, the voltage of a circuit, if I = (16 + i) amperes and R = (2 + 4i) ohms.
Answer:
E = (28 + 66i) Volts
Step-by-step explanation:
Note that: i = √-1 ; i² = -1
Ohm's law: E = IR
E = (16+ i) (2 + 4i)
Expand the equation.
E = 16x2 + 16x4i + ix2 + ix4i
E = 32 + 64i + 2i + 4i²
E = 32 + 64i + 2i + 4(-1)
E = 32 + 64i + 2i - 4
Collect like terms:
E = 32 -4 + 64i + 2i
E = (28 + 66i) Volts
#1 Billy stacked nine pieces of wood on top of one another. If each piece was 3/4 of a foot tall, how tall was the wood pile? Round your answer to the nearest hundredth of a foot.
#2 look at the photo
please help me as soon as you can it would be greatly appreciated I’m in a hurry.
Answer:
a. 6.75 ft
b. Exponent on w is w^4
Step-by-step explanation:
a. The best thing here is to work with decimals
each piece was 3/4 foot tall which means each piece is 0.75 ft tall
Now since he staked 9, the height of the wood pile would be 9 * 0.75 = 6.75 ft
b. Firstly let’s evaluate the denominator
That becomes; 2v^-3w^8 * v^4w = 2v^(-3+4)w^(8+1) = 2vw^9
So let’s now divide this by the numerator
Since we are concerned with only the exponent on w, we place w^13 over w^9 = w^(13-9) = w^4
NEED HELP ASAP PLEASE WILL MARK BRANLIEST What would the equation of a hyperbola with directrices at x=±2 and foci at (6,0) (-6,0) be?
Answer:
The equation of the hyperbola can be presented as follows;
[tex]\dfrac{\left x \right ^{2}}{12} - \dfrac{\left y \right ^{2}}{24} = 1[/tex]
Step-by-step explanation:
We have the equation of an hyperbola given as follows;
[tex]\dfrac{\left (x - h \right )^{2}}{a^{2}} - \dfrac{\left (y - k \right )^{2}}{b^{2}} = 1[/tex]
The foal length = a² + b² = c²
c = focal length
The directrix = a²/c
The focal point are (h + c, k) and (h - c, k)
Therefore, by comparison with the given focal points, (6, 0) and (-6, 0), we have;
k = 0 and h + c = 6, h - c = -6
Therefore;
6 - c - c = -6
-2·c = -12
c = 6
h = 0
a²/c = 2
a² = 2 × 6 = 12
a = 2·√3
12 + b² = 6²
b² = 6² - 12 = 24
b² = 24
b = 2·√6
The equation of the hyper bola can then be written as follows;
[tex]\dfrac{\left (x - 0 \right )^{2}}{12} - \dfrac{\left (y - 0 \right )^{2}}{24} = 1[/tex]
Which gives
[tex]\dfrac{\left x \right ^{2}}{12} - \dfrac{\left y \right ^{2}}{24} = 1[/tex]
x² - y² = 12
y² = x² - 12.
ok gamers i just need an answer for this right here
Name the property of a definition illustrated by each of the following.
6(x-7)=6x-42
Answer:
I think this is the distributive property.
Step-by-step explanation:
help i will make u brainllest
Answer:
4 sqrt(7)
Step-by-step explanation:
We can use the leg rule
hyp leg
------- = -------------------
leg part
9+7 z
------- = -------------------
z 7
Using cross products
(9+7) *7 = z^2
16*7 = z^2
112 = z^2
Taking the square root of each side
sqrt( 16*7) = sqrt(z^2)
4 sqrt(7) = z
NEED HELP ASAP *picture included* what percent of the area underneath this normal curve is shaded?
Answer:
68.26
Step-by-step explanation:
The symbol σ represents standard deviation. 1 standard deviation (in both directions) under a normal distribution= 68.26
Answer:
68%.
Step-by-step explanation:
The 68-95-99.7 rule (also know as the Empirical Rule) states that 68% of the data lies within 1 standard deviation of the mean. 95% of the data lies within 2 standard deviations of the mean. 99.7% of the data lies within 3 standard deviations of the mean.
According to the diagram, the area shaded shows data within 1 standard deviation of the mean (one standard deviation to the left, and one to the right). That means that 68% of the data is within the shaded area.
Hope this helps!
Helllppppp
Which rule describes the composition of
transformations that maps AABC to AA'B'C"?
Answer:
reflection and rotation
Step-by-step explanation:
what is the area of shape below NEED HELP NOWWW
Answer:
15 units[tex] {}^{2} [/tex]Step-by-step explanation:
Given figure : Trapezium
Upper base of trapezium ( b1 ) = 7
Lower base ( b2 ) = 3
Height ( h ) = 3
Now, finding the area of trapezium:
[tex] \frac{1}{2} (b1 + b2)h[/tex]
Plugging the values
[tex] \frac{1}{2} \times (7 + 3) \times 3[/tex]
Calculate the sum
[tex] \frac{1}{2} \times 10 \times 3[/tex]
Reduce the numbers with G.C.F 2
[tex]5 \times 3[/tex]
Calculate the product
[tex] = 15 \: {units}^{2} [/tex]
Hope this helps..
Best regards!
help pls, Find PG if JG=18.
The length of PG using the centroid property is 6 unit.
The centroid divides each median into segments in a 2:1 ratio.
This means that the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side.
Given:
JG = 18
As, the centroid divides each median into segments in a 2:1 ratio then
PG:PJ = 1:2
So, the length of PG
= 1/3 * (18)
= 18/3
= 6 unit
Thus, the length of PG is 6 unit.
Learn more about Centroid of Triangle here:
https://brainly.com/question/4421837
#SPJ4
Here’s a graph of a linear function. Write the equation that describes that function. Express it in slope
Answer:
y = (1/3)x +4
Step-by-step explanation:
The line intercepts the y-axis at y=4. It has a "rise" of 1 unit for each "run" of 3 units, so its slope is rise/run = 1/3.
The slope-intercept form of the equation of a line is ...
y = mx + b . . . . . where m is the slope and b is the y-intercept.
When we put the proper numbers in the equation, we have ...
y = (1/3)x + 4
what is the formula for this equation?
hen spends 3 days baking 224 cookies. on the second day, he bakes twice as many as he did on the first day. on the third day, he baked half as many as he did on the first day. How many cookies did he bake o the 2nd day
Answer:
x + 2x + 1/2x = 224
Step-by-step explanation:
x + 2x + 1/2x = 224
3.5x = 224
x= 64
64×2=128
Hen baked 128 cookies on the second day
Check all that apply. If csc0=13/5, then:
I hope this helps you
Answer: B) sin θ = 5/13 and D) tan θ = 5/12
Step-by-step explanation:
[tex]\csc\theta=\dfrac{r}{y}=\dfrac{13}{5}[/tex]
Use Pythagorean Theorem: x² + y² = r² to calculate x = 12
[tex]\sin \theta=\dfrac{y}{r}=\dfrac{5}{13}\qquad \qquad \qquad \csc \theta=\dfrac{r}{y}=\dfrac{13}{5}\\\\\\\\\cos \theta=\dfrac{x}{r}=\dfrac{12}{13}\qquad \qquad \qquad \sec \theta=\dfrac{r}{x}=\dfrac{13}{12}\\\\\\\\\tan \theta=\dfrac{y}{x}=\dfrac{5}{12}\qquad \qquad \qquad \cot \theta=\dfrac{x}{y}=\dfrac{12}{5}[/tex]
ASAP!! Linear Relations Help
Answer:
Below
Step-by-step explanation:
a) To make a perpendicular line with the given linear equation, use the reciprocal of the slope, which is -(1/3) in this case.
So the equation for the first one is y = -(1/3)x
To find what x equals when going through the point (x, 4), plug in 4 for y and solve
y = -(1/3)x
4 = -(1/3)x
4/-(1/3) = -(1/3)x/-(1/3)
-12 = x
So, when y = 4, x = -12
b) Do the same thing for a, use the reciprocal for the slope for the perpendicular line, -4.
This makes the second equation y = -4x
Then plug 4 in for y again, instead using -4 as the slope
y = -4x
4 = -4x
4/-4 = -4x/-4
-1 = x
This shows that when y = 4, x = -1
Helppp!!!! please!!!
Answer:
option d is correct answer.
hope it helps..
D. 8.8 cm^3
Step-by-step explanation:
The formula for the volume of a cone is...
[tex]V=\frac{1}{3}\pi r^2h[/tex]
We can plug everything we know into the formula and convert pi to 3.14 since the answer choices aren't in pi.
[tex]V=\frac{1}{3}*( 3.14*1.45*1.45*4 )[/tex]
I prefer to do the 1/3 last, but it is entirely up to you!
Now solve...
[tex]V=\frac{1}{3}*26.4074[/tex]
Divide by 3.
V =
8.8 cm^3