[tex]72:36 = \dfrac{72}{36} = \dfrac{36 \times 2}{36} = 2:1[/tex]
Question 16
What is the shortest distance between the line y = 2x+4 and the point at (0.0)? Round to the nearest tenth.
O A) 1.8
O B) 2.0
O C) 3.2
O D) 4.0
The shortest distance between the line y = 2x+4 and the point at (0.0) is 1.8 units option (A) is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that:
The equation of the line is:
y = 2x + 4
Or
2x - y + 4 = 0
The point is (0, 0)
As we know, the formula for the shortest distance between the line and a point:
D = |ax + bx + c|/√(a²+b²)
Plug x = 0 and y = 0
a = 2, b = -1, and c = 4
D = |2(0) + -1(0) + 4|/√(2²+(-1)²)
D = 4/√5
D = 1,78 ≈ 1.8 units
Thus, the shortest distance between the line y = 2x+4 and the point at (0.0) is 1.8 units option (A) is correct.
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A middle school principal is signing the diplomas of the school's graduating eighth graders.
She previously signed 37 diplomas. Now, she is signing more diplomas at a rate of 0.5 per
second. If the principal signs diplomas for 60 seconds, what will the total number of signed
diplomas be?
Answer: 67 diplomas
Step-by-step explanation:
0.5 diplomas per second = 1 diploma per 2 seconds
60/2 = 30
30+37 = 67
Correct me if I am incorrect
An equation that shows how the total number of diplomas signed depends on the number of seconds the principal spends signing them is y = 37 + 0.5x.
What is an equation?
An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, let x be number of seconds the principal spends signing them. The principal already signed 37 diplomas. Th equation to illustrate this is 37 + 0.5x.
According to the Rational Root Theorem, the following are potential roots of f(x) = 2x2 2x â€" 24. â€"4, â€"3, 2, 3, 4 Which are actual roots of f(x)?.
Rational root theorems are used to determine the potential roots of a polynomial function
The actual roots are 3 and -4The potential roots are [tex]\pm0.5, \pm1, \pm 1.5, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]The function is given as:
[tex]f(x) = 2x^2 + 2x - 24[/tex]
Expand
[tex]f(x) = 2x^2 + 8x - 6x - 24[/tex]
Expand
[tex]f(x) = 2x(x + 4) - 6(x + 4)[/tex]
Factor out x + 4
[tex]f(x) = (2x -6)(x + 4)[/tex]
Set to 0
[tex](2x -6)(x + 4) = 0[/tex]
Split
[tex](2x -6) = 0\ or\ (x + 4) = 0[/tex]
Make x the subject in both cases
[tex]2x = 6\ or\ x= -4[/tex]
Solve for x
[tex]x = 3\ or\ x= -4[/tex]
So, the actual roots are 3 and -4
Recall that, the function is:
[tex]f(x) = 2x^2 + 2x - 24[/tex]
For a function,
[tex]f(x) = px^n + ax^{n-1} +.......+q[/tex]
According to rational root theorem, the roots of f(x) are:
[tex]Roots = \pm \frac{Factors\ of\ q}{Factors\ of\ p}[/tex]
The roots of 24 are:
[tex]24 = \pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]
The roots of 2 are:
[tex]2 = \pm1, \pm2[/tex]
So, the possible roots are:
[tex]Roots = \frac{\pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24}{\pm 1, \pm 2}[/tex]
This gives:
[tex]Roots = \pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24,\pm0.5, \pm1, \pm 1.5, \pm 2, \pm 3, \pm 4, \pm6\pm 12[/tex]
Remove repetitions
[tex]Roots = \pm0.5, \pm1, \pm 1.5, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]
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3 and -4 dudes and dudettes
edg2022
A polygon with area 10 square units is dilated by a scale factor of k. Find the area of the image for each value of k.
a k=4
square units
b. k=1.5
square units
ck=1
square units
Answer:
a = 160 square units
Step-by-step explanation:
The areas of the image are 160, 22.5 and 10 square units
The area of the polygon is given as:
A =10 square unit
The area of the image of the polygon is calculated as:
[tex]A_k = A * k^2[/tex]
When k = 4, we have:
[tex]A_4 = 10 * 4^2[/tex]
[tex]A_4 = 160[/tex]
When k = 1.5, we have:
[tex]A_{1.5} = 10 * 1.5^2[/tex]
[tex]A_{1.5} = 22.5[/tex]
When k = 1, we have:
[tex]A_{1} = 10 * 1^2[/tex]
[tex]A_{1} =10[/tex]
Hence, the areas of the image are 160, 22.5 and 10 square units
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Which function has the same domain as y= 2 sqrtx
Answer: the first option.
Step-by-step explanation:
Answer:
[tex]f(x) = \sqrt{x } - 2 \ \\ f(x) = 5 \sqrt{x} [/tex]
is 6:1 equivalent to 12:3
Answer: No, absolutely not,
Step-by-step explanation: 6x2 = 12, so you have to multiply by 2 on each side. 1x2=2, so the equivilent ratio is 12:2!
Answer: Nope
Step-by-step explanation: No, because you can see they multiply 1 x 3 to get to 3, but if you multiply 6 x 3, it equals 18, not 12. (6 x 2 = 12) but they have to have the same denominator and numerator to be equivalent. Therefore, no, they are not equivalent.
Please solve this .
The graph shows the linear function. I hope this helps.
If y ♾x and y = 2 when x = 8, then y = 3 when x =
Answer:
12
Step-by-step explanation:
The Constant (K) is equal to 8/2 aka 0.25 making the formula now y = 0.25 × x
We have y as 3 so
3 = 0.25 × x we take the 0.25 to the other side by dividing on both sides.. this makes it cancel out on the right.
x is now equal to 3/0.25 which is 12. X = 12
Answer:
Is the answer 9 for the last x
Step-by-step explanation:
hope this helps
7+2x/3=5 please give me an answer as soon as you can
Answer:
x = -3
Step-by-step explanation:
7 + 2x/3 = 5
3 . 7 + 2x
-------------- = 5
3
21 + 2x
----------- = 5
3
Solve the equation 6(2x+4)^2=(2x+4)+2 a x=-5/3 or -9/4
Answer:
x=5/3
Step-by-step explanation:
Answer:
-5/3 or -9/4 is the answer
Step-by-step explanation:
Just completed it
The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation h = 15 cosine (StartFraction pi Over 20 EndFraction t). How long does it take for the waterwheel to complete one turn? 5 seconds 10 seconds 20 seconds 40 seconds.
Solving the trigonometric equation, it is found that it takes 40 seconds to complete one turn.
The height is modeled by:
[tex]h(t) = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]
The initial height is [tex]h(0) = 15[/tex], hence, one turn is completed when h(t) = 15.
[tex]h(t) = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]
[tex]15 = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]
[tex]\cos{\left(\frac{\pi}{20}t\right)} = \frac{15}{15}[/tex]
[tex]\cos{\left(\frac{\pi}{20}t\right)} = 1[/tex]
The length of one turn is of [tex]2\pi[/tex], and [tex]\cos{(2\pi)} = 1[/tex], hence, the solution is found according to:
[tex]\frac{\pi}{20}t = 2\pi[/tex]
[tex]t = \frac{40\pi}{\pi}[/tex]
[tex]t = 40[/tex]
It takes 40 seconds to complete one turn.
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Answer:
D. 40 seconds!! Props to guy above.
Which equation could have been used to create this table?
y = 3x
y = x + 3
y = x + 2
y = 4x
Answer:
y = 3x
Step-by-step explanation:
please explain why. Thanks
Is (x-2) is a factor of x³-3x²-x +7 –
Yes No ☑Explanation :-We are given –
Polynomial function, P(x) = x³-3x²-x +7In order to check if x - 2 is a factor of x³-3x²-x +7 or not, we must show that P(2) = 0.Let's find value of x![tex]\qquad[/tex] [tex]\twoheadrightarrow\bf P(x) = x³-3x²-x +7[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf Q(x) =x - 2 [/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf If \:Q(x) = 0[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf x - 2 = 0[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf x = 2[/tex]
Now Put x = 2 into the polynomial –
[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\bf P(2) = 2³-3(2)²-2+7}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf P(2) = 8 - 3 \times 4 +5[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf P(2) = 8 -12 +5[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf P(2) = 13-12[/tex]
[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\bf P(2) =1 }[/tex]
Since the value of the polynomial function st x = 2 is not Zero (0). Henceforth, ( x - 2) is a factor of x³-3x²-x +7.________________________________________
Plz help I really need help, I’m gonna give brainlist
Answer:
angle 4 is 47 degrees....
What are the solutions to the quadratic equation 2x2 + 10x - 48 = 0?
O A. x= -8 and x = 3
O B. x = -4 and x = 6
O C. x= -6 and x = 8
O D. x= -8 and x = 2
EUR
Answer:
A
Step-by-step explanation:
The solutions to the given quadratic equation are x=-8 and x=3. Therefore, option A is the correct answer.
What is the solution of a quadratic equation?The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The given quadratic equation is 2x²+10x-48=0.
Here, x²+5x-24=0
x²+8x-3x-24=0
x(x+8)-3(x+8)=0
(x+8)(x-3)=0
(x+8)=0 and (x-3)=0
x=-8 and x=3
Therefore, option A is the correct answer.
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Can someone please help me with this and tell me the points?
Answer:
Graph: Refer to attached image
Solution: (-5,-3)
Step-by-step explanation:
First graph to two equations.
Refer to the image attached to see what the equations would look like when graphed.
Wherever they intersect is the solution.
They intersect at (-5,-3) therefore (-5,-3) is the solution to the system of equations
B is the midpoint of AC Find AB, BC and AC.
Step-by-step explanation:
Since B is the midpoint of AC. So,
AB = BC
12x - 12 = 4x + 28
12x - 4x = 28 + 12
8x = 40
x = 40/8
x = 5
Now,
AB = BC = 4(5) + 28
= 20 + 28
= 48 cm
Now
AC = AB + BC
AC = 48 + 48
AC = 96 cm
An account that yields 6% simple interest annually has $2,000. How much will be in the account after 3 years if no other deposits or withdrawals are made?
Answer:
$2,382.03
Step-by-step explanation:
Interest = Principal x Rate x Time
What is 1/3 of 9/5 please help.
Your yard is a mess, and you decide to hire a landscaper. The garden pros charges 50$ consultation fee plus 30$ per hour for the actual work. What is the total cost if your yard takes 5 hour’s to fix up
Answer:
$200
Step-by-step explanation:
$50 consutation + $150 5 hour fee.
=$200
Harry and Matthew, have 56 toys to build. harry builds three fourths of the toys, while matthew builds one seventh of the toys. How many toys are there left to build?
Answer:
i don't know
Step-by-step explanation:
How to slove this equation in simple form -9(8v-2v)+10b - (100v+6)
Answer:
- 154v + 10b - 6
Step-by-step explanation:
-54v + 10b - 100v - 6
-154v + 10b - 6
A rectangular sticker has an area of 50 square centimeters. Its perimeter is 30 centimeters. What are the dimensions of the sticker?
___centimeters by ____ centimeters
Length + width = 1/2 the perimeter:30/2 = 15
Area = length x width
List the factors of 50: 1, 2, 5, 10, 25, 50.
Find the two factors that when added together equal 15:
Dimensions are 5 cm by 10 cm.
See attachments for answer and math work.
Solve for x
2x+5=33
Answer: x=14
hopes this helps
Answer: your anwser is 19
Step-by-step explanation:
Add 55 to both sides.
2x=33+5
2x=33+5
2 Simplify 33+533+5 to 3838.
2x=38
2x=38
3 Divide both sides by 22.
x=\frac{38}{2}
x=
2
38
4 Simplify
2
38
to 1919.
x=19
x=19
please mark brainliest
Term insurance has no value as an investment and is the most expensive type of life insurance.
True
Or false
Answer:
False
Step-by-step explanation:
It is true that term insurance has no value as an investment. However, it is the least expensive type of life insurance. The compound statement is false, because one of the elements of the statement is false.
Answer:
false
Step-by-step explanation:
hehehehehehhhehehe help
Answer:
Y=2
Step-by-step explanation:
If x=3 we can see that every two lines is 1 number up then the last
same for y access. Y=-2
Answer:
-2
Step-by-step explanation:
if a necklace was on discount 10% and the original price was $20 what was the amount of discount?
Answer:
10$
Step-by-step explanation:
dollars hope it helps
Answer:
its 10$
Step-by-step explanation:
which ordered pair is a solution to The equation y=-7-3x
Answer:
can you add the options that would help
Step-by-step explanation:
vvvv
what number is 100`000 more than seven hundred two thousand eight three
Answer:
802,083
Step-by-step explanation:
Help on these two please
Answer:
21
Step-by-step explanation:
CANT SEE THEM