Answer:
Exact distance = [tex]\sqrt{202}[/tex]
Approximate distance = 14.2127
==========================================================
Work Shown:
[tex](x_1,y_1) = (7,14) \text{ and } (x_2, y_2) = (18,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(7-18)^2 + (14-5)^2}\\\\d = \sqrt{(-11)^2 + (9)^2}\\\\d = \sqrt{121 + 81}\\\\d = \sqrt{202}\\\\d \approx 14.2127\\\\[/tex]
Note: I used the distance formula. Though you could plot the points, form a right triangle, and use the pythagorean theorem as an alternative route. The distance formula is effectively a modified version of the pythagorean theorem.
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Twelve people are participating in a community walking fund raiser. Each person has to contribute equally to walking a total distance of
28.375 miles.
What will be the distance walked by each person to the nearest thousandth of a mile?
A 2.355 miles
OB 2.365 miles
OC 2.455 miles
OD 2.465 miles
Previous
Answer:
B. 2.365
Step-by-step explanation:
Divide total distance by total people in order to get distance each person traveled.
28.375 miles / 12 = 2.36458333.......
If you round taht to nearest thousandth of a mile, the answer is: 2.365
Solve for x:
AD bisects BAC
Okay What is the value of x?
Answer:
x=75
Step-by-step explanation:
99/66=1.5
30x1.5=45
30+45 =75
A cyclist rides 24 miles at an average speed of 9 miles per hour. At what rate must the cyclist cover the next 20 miles in order to bring the overall average speed up to 12 miles per hour? The cyclist must ride at 00 miles per hour.
Answer:
20 m/hr
Step-by-step explanation:
distance / rate = time
24 miles / 9 miles/hr = 2 2/3 hr
(24 + 20 miles) / 12 miles/hr = 3 2/3 hr
3 2/3 - 2 2/3 = 1 hour to ride the next 20 miles means 20 m/hr
Solve for x and explain your steps in detail using the R-E-S-T Method
8x - 4 = 92
Answer:
12
Step-by-step explanation:
you add 92 with the 4 and get 96 then you divide the 8x with the 96 and get 12
Hope it helps <333
x = 12
Calculations ↓Our goal is to find the value of x .
To find the value of x we need to get x by itself .
The first step is to move all numbers to the right . Luckily , there's only one number here : 4.
So we add 4 on both sides :
8x=96
Now divide by 8 on both sides :
x = 12
So the value of x is 12.[tex]\footnotesize\text{hope\:helpful~}[/tex]
Help help math math math math
Answer:
(-2,1)
Step-by-step explanation:
The solution of a system of equations is wherever the two lines intersect. So, this is quite easy. We can see they intersect at (-2,1). We can tell it is (-2,1) becuase it is two units left and one units up from the origin.
That is the solution.
(-2,1)
Answer:
The answer is (-2,1). Hope this helps :)
Step-by-step explanation:
A number written in the form a + bi is called a _____ number.
A. Discriminant
B. Quadratic
C. Complex
D. Linear
Answer: A. Complex
Step-by-step explanation: hope this helps!
What is the equation of the line in slope-intercept form?
Answer:
Step-by-step explanation:
Its a linear function it goes throw the y-x Axis and is in a striaght line.
Answer:
y = [tex]\frac{5}{2}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line
m = [tex]\frac{5-0}{0-(-2)}[/tex] = [tex]\frac{5}{0+2}[/tex] = [tex]\frac{5}{2}[/tex]
the line crosses the y- axis at (0, 5 ) ⇒ c = 5
y = [tex]\frac{5}{2}[/tex] x + 5 ← equation of line
The formula d = 52t+65t can be used to find the distance, d, between two
cars after traveling t hours in opposite directions. After how many hours will
the distance between the two cars be 234 miles?
Answer: t=2
Step-by-step explanation:
add the t's and calculate
CAN SOMEBODY HELP ME PLEASE
Answer:
vertex (3, -1)y-intercept: (0, 8)x-intercepts: (2, 0), (4, 0)Step-by-step explanation:
You are being asked to read the coordinates of several points from the graph. Each set of coordinates is an (x, y) pair, where the first coordinate is the horizontal distance to the right of the y-axis, and the second coordinate is the vertical distance above the x-axis. The distances are measured according to the scales marked on the x- and y-axes.
__
VertexThe vertex is the low point of the graph. The graph is horizontally symmetrical about this point. On this graph, the vertex is (3, -1).
Y-interceptThe y-intercept is the point where the graph crosses the y-axis. On this graph, the y-intercept is (0, 8).
X-interceptsThe x-intercepts are the points where the graph crosses the x-axis. You will notice they are symmetrically located about the vertex. On this graph, the x-intercepts are (2, 0) and (4, 0).
__
Additional comment
The reminder that these are "points" is to ensure that you write both coordinates as an ordered pair. We know the x-intercepts have a y-value of zero, for example, so there is a tendency to identify them simply as x=2 and x=4. This problem statement is telling you to write them as ordered pairs.
In the figure below, triangle QRS is isosceles, with QR SR.
If mSPQ = 36° and mQRS = 32°, what is mPQR?
A.
118°
B.
138°
C.
133°
D.
128°
Answer:
D
Step-by-step explanation:
since Δ QRS is isosceles then the base angles are congruent , that is
∠ RQS = ∠ RSQ = (180 - ∠ QRS ) ÷ 2 = (180 - 32)° ÷ 2 = 148° ÷ 2 = 74°
the sum of the 3 angles in Δ SPQ = 180° , then
∠ PQS = 180° - ∠ SPQ - ∠ PSQ = 180° - 36° - 90° = 54°
Then
∠ PQR = ∠ RQS + ∠ PQS = 74° + 54° = 128°
Write the ratio as a ratio of whole numbers in lowest terms
$0.90 to $0.60
Answer:
3:2
Step-by-step explanation:
If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10.
for this problem we use 0.90 and 0.60, so our ratio is 0.90/0.60
using whole numbers can be converted now by actually dividing these data points and then multiplying to a whole number:
0.9/0.6 = 1.5
1.5 x 2 = 3
this gives 3/2 = 1.5
so we know that the ratio is 3:2 and this is the smallest whole number that it could be
Given that f(x) = 2x - 4 and g(x) = 2x + 8, determine gf(3)
[tex]\text{Given that,} ~f(x) = 2x-4~~ \text{and}~~ g(x) = 2x+8\\\\ g(f(3))\\\\=g(2\cdot 3 -4)\\\\=g(2)\\\\=2(2)+8\\\\=4+8\\\\=12[/tex]
(06.01 MC)
Classify the expression: -2x
Quadratic expression
Linear expression
Cubic expression
Exponential expression
Answer:
Linear expression
Step-by-step explanation:
The greateest exponent on a variable is 1 on x, so it is a linear expression,
Answer: Linear expression
1. Billy scored 33 points on a test worth 75 points. What is his percent score?
2. Convert 0.25 into percent
Solve the equation 64x2 − 144 = −23 by using square roots.
x = ±11/8
x = ±3/2
no real solutions
x = ±7/4
Answer:
The answers are:x = ±7/4x = ±3/2x = ±11/8
yww:)
Answer:
Option A, [tex]x =[/tex] ± [tex]11/8[/tex]
Step-by-step explanation:
Step 1: Add 144 to both sides
[tex]64x^2 - 144 = -23[/tex]
[tex]64x^2 - 144 + 144 = -23 + 144[/tex]
[tex]64x^2 = 121[/tex]
Step 2: Divide both sides by 64
[tex]\frac{64x^2}{64} = \frac{121}{64}[/tex]
[tex]x^2 = 1.890625[/tex]
Step 3: Square root both sides
[tex]\sqrt{x^2} = \sqrt{1.890625}[/tex]
[tex]x =[/tex] ± [tex]1.375[/tex]
[tex]x =[/tex] ± [tex]11/8[/tex]
Answer: Option A, [tex]x =[/tex] ± [tex]11/8[/tex]
[tex]5x^{2}+|x+1|\ \textgreater \ 0[/tex]
Can someone explain me how this is done? My book says that the answer is R (all numbers), but i get [-1; infinity) and two other roots.
50 points + brainlest if you answer correctly
Answer:
5 is the value which makes the equation true .Step-by-step explanation:
In this question we have provided an equation that is 9 ( 3x - 16 ) + 15 = 6x - 24 . And we are asked to write the steps to solve the equation with explanation and to find the value of X .
Solution : -
[tex] \longmapsto \quad \: 9(3x - 16) + 15 = 6x - 24[/tex]
Step 1 : Solving parenthesis on left side using distributive property which means multiplying 9 with 3x as well as -16 :
[tex] \longmapsto \quad \:27x - \bold{144 }+ \bold{15 }= 6x - 24[/tex]
Step 2 : Solving like terms on left side that are -144 and 15 :
[tex] \longmapsto \quad \:27x -129 = 6x - 24[/tex]
Step 3 : Adding 129 on both sides :
[tex] \longmapsto \quad \:27x - \cancel{129} - \cancel{129} = 6x \bold{ - 24 } + \bold{129}[/tex]
Now on cancelling -129 with 129 on left side and solving the terms that are -24 and 129 on right side , We get :
[tex] \longmapsto \quad \:27x = 6x + 105[/tex]
Step 4 : Subtracting with 6x on both sides :
[tex] \longmapsto \quad \: \bold{27x} - \bold{6x} = \cancel{6x} +105 - \cancel{ 6x}[/tex]
On calculating further, We get :
[tex] \longmapsto \quad \:21x = 105[/tex]
Step 5 : Now we are Dividing with 21 on both sides so that we can isolate the variable that is x :
[tex] \longmapsto \quad \: \dfrac{ \cancel{21}x}{ \cancel{21}} = \dfrac{105}{ 21} [/tex]
Now , by cancelling 21 with 21 on left side , We get :
[tex] \longmapsto \quad \:x = \cancel{\dfrac{105}{21}} [/tex]
Step 6 : Now our final step is to simplify the value of x that is 105/21 . We know that 21 × 5 is equal to 105 . So :
[tex] \longmapsto \quad \: \purple{\underline{\boxed{\frak{ x = 5 }}}}[/tex]
Henceforth , value of x is 5Verifying : -
Now we are verifying our answer by substituting value of x in the given equation . So ,
9 ( 3x - 16 ) + 15 = 6x - 249 [ 3 ( 5 ) - 16 ] + 15 = 6 ( 5 ) - 249 ( 15 - 16 ) + 15 = 30 - 249 ( -1 ) + 15 = 6-9 + 15 = 66 = 6L.H.S = R.H.SHence , Verified .Therefore, our value for x is correct that means it'll makes the equation true .
#Keep LearningA Spanish test has 30 questions. A student answers 80% correctly.
How many questions does the student answer correctly?
Enter your answer in the box.
questions
Answer:
24
Step-by-step explanation:
Lets start by working out 80% of 30
80% x 30=24
so the student answered 24 questions correctly
What are all the solutions to the equation sin 2x = 2sin x in the interval [0, 2π)?
{π}
{0, π}
{pi over 2}
{pi over 2, 3 times pi over 2}
[tex]sin(2x) = 2sin(x) \\ 2sin(x)cos(x) = 2sin(x) \\ sin(x)cos(x) = sin(x) \\ sin(x)cos(x) - sin(x) = 0 \\ \sin(x) (cosx - 1) = 0 \\ \sin(x) = 0 \\ x = \pi \: or \: x = 0 \\ cos(x) = 1 \\ x = 0 \: or \: x = \pi \\ \\ s[/tex]
[tex]s = > {0 < = > \pi}[/tex]
Can somebody help me I am a lil confused with the equation
Answer:
a) 7000 x 1.06^t
b) 11156
Step-by-step explanation:
a) This is quite a case of compound interest where you begin with a value (7000) and every year (t) it goes up by a set amount (6%). To mathematically convert this you put 7000 at the start and you convert the 6% into 1.06 since 0.06 is the amount it increases by and the 1 adds the 0.06 to the previous value. The 't' makes it so each year the value increases so 1.06^t where t is 2 would mean 1.06 x 1.06 which is basically what happens every year.
b) Since it is 8 years later (2008 - 2000), you substitute t for 8 to find the range which is 7000 x 1.06^8 = 11156.9365 which rounds down to 11156 as that's what you do when talking with whole numbers as a new fox isn't quite there yet.
Graph the line Y minus 5X equals -2
Answer:
Step 1. Rewrite in the form of y=mx+b
Step 2. Find and plot 2 points (x and y-intercepts)
Step 3. Connect dots
y=mx+b
y - 5x = -2
y = 5x - 2
Find 2 points
y-intecept = (0, -2)
x-intercept = ?
0 = 5x - 2
2 = 5x
x = 2/5
x-intercept = (2/5, 0)
BRAINLIEST please if this helped!Function or Not a Function
Step-by-step explanation:
problem 10 is function
but problem 9 is not
Alex eats 2 pieces of candy. Marisol eats 3 times as many pieces of candy as Alex. Which equation can be used to determine the amount of candy that Marisol eats? Let a represent Alex and m represent Marisol.
m=3a
m=3a+2
m=2a
m=2a+3
Answer:
m = 3a
Step-by-step explanation:
The number of pieces of candy eaten by Alex is not important.
The only thing that matters is that Marisol eats 3 times as many pieces of candy.
If a is the number eaten by Andy, then 3 times a equals the number of pieces of candy eaten by Marisol, or m=3a
Which expression is equivalent to -18a^-2b^5/-12a^-4b^-6
a. 2a^2b^11/3
b. 2a^2b^30/3
c. 3a^2b^11/2
d. 3a^2b^30/2
Answer:
c. 3a^2b^11/2
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)/(a^c) = a^(b-c)
__
[tex]\dfrac{-18a^{-2}b^5}{-12a^{-4}b^{-6}}=\dfrac{-18}{-12}a^{-2-(-4)}b^{5-(-6)}=\boxed{\dfrac{3a^2b^{11}}{2}}[/tex]
The pentagonal prism below has a base area of 38 units? and a height of 7.4 units.
Find its volume.
270.4
278.4
281.2
294.2
281.2 units³
volume of Prism: Base Area x Height
Here given:
Base Area: 38 units²
Height: 7.4 units
Solve for volume:
38 x 7.4
281.2 units³
Volume:-
Area of base×Height38(7.4)2812/10281.2units²What number is represented by point P? State your answer in scientific notation
and in standard form.
Answer:
5.7×10^-30.0057Step-by-step explanation:
Point P is marked in the expanded view on the 7th mark of the 10 marks between 5×10^-3 and 6×10^-3. That means it is representing ...
(5 +7/10)×10^-3 = 5.7×10^-3 . . . . scientific notation
__
The -3 exponent of 10 means the multiplier of the value is 1 in the 3rd place to the right of the decimal point: 0.001. So, the standard form of the number is ...
5.7×0.001 = 0.0057 . . . . . standard form
Triangle ABC and DEF are similar which proportion is true
The length of DE in centimetres is 12 .
The following proportion can be established as follow:
AB / DE = BC / EF = AC / DF
Therefore,
let's find DE as follows;
AB / DE = BC / EF
4 / DE = 3 / 9
cross multiply
9 × 4 = 3DE
divide both sides by 3
DE = 36 / 3
DE = 12 cm
learn more: https://brainly.com/question/22808925?referrer=searchResults
Please help I’ll give Brainiest
Answer:
3,00043,000412,00014,992____________
3748 x 4 = (3000+700+40+8) x 4
(3000 x 4) + (700 x 4) + (40 x 4) + (8 x 4)
12000 + 2800 + 160 + 32
= 14992
Step-by-step explanation with answer:
3748x4 = (3000+700+40+8) x 4
= 3000x4 + 700x4 + 40x4 +8x4
=12000+2800+160+32
=14992
Workers took a 10% pay cut to help their company stay open during economic hard
times. What is the reduced annual salary of a worker who originally earned $35,000?
Answer:
$31,500
Step-by-step explanation:
10% = 0.1
100% = 1
1 - 0.1 = 0.9
35,000 x 0.9 = 31,500
Kevin and randy muise have a jar containing 52 coins. all of which are either quarters or nickels. the total value of coins is $6.40. how many of each coin do they have?
Answer:
19 quarters33 nickelsStep-by-step explanation:
For mixture problems, it is convenient to let the variable represent the quantity of the high-value contributor.
Here, we can let x represent the number of quarters. Then the number of nickels is (52-x), and the total value of the coins is ...
0.25x +0.05(52 -x) = 6.40
0.20x +2.60 = 6.40 . . . . . . . . simplify
0.20x = 3.80 . . . . . . . . . . . subtract 2.60
x = 3.80/0.20 = 19 . . . . divide by the coefficient of x
The number of quarters is 19. The number of nickels is 52-19 = 33.