Answer:
-3
Step-by-step explanation:
Parallel lines share the same slope. Therefore, the slope of cd is -3.
determine the equation of the circle graphed below
Answer:
The equation would be (x – 3)^2 + (y – 4)^2 = √26^2 or 26.
Step-by-step explanation:
Firstly, we need to find the radius of the circle. In this case, through the Pythagorean theorem, we can find it to be √(9-4)^2 + (4-3)^2 = √25 + 1 = √26.
Therefore, the equation of the circle would be (x – h)^2+ (y – k)^2 = r^2, where h and k are the x and y-coordinates of the center of the circle respectively, and r is the radius. Hence, the equation of this circle would be (x – 3)^2 + (y – 4)^2 = √26^2 or 26.
Hope this helped!
Answer:
(x - 3)² + (y - 4)² = 26Step-by-step explanation:
Equation in standard form:
(x - h)² + (y - k)² = r²,where (h, k) is the center and r- radius
On the graph we have (h, k) = (3, 4)
Find the r² using the distance formula:
r² = ( 4 - 3)² + (9 - 4)² = 1² + 5² = 26The equation is:
(x - 3)² + (y - 4)² = 26Here are some cards with angles written on them.
45° ||165°
5°
90° 102°
102°|| 31°
53°
Moira picks one of the cards at random.
What is the probability that the angle on the card is greater than 100°?
Answer:
below
Step-by-step explanation:
three cards angles are greater than 100°
total cards = 8
probability = 3/8
Find the value of each variable. Round your answers to the nearest tenth. (Soh Coh Toa)
Answer:
k = 8.4, j = 13.1
Step-by-step explanation:
Solve for k:
[tex]tan(40)=\frac{k}{10}\\10(tan(40))=k\\8.4=k[/tex]
Solve for j:
[tex]8.4^2+10^2=j^2\\70.56+100=j^2\\170.56=j^2\\13.1=j[/tex]
Answer:
k = 10 tan (40) = 8.39 (to 2 decimals)
J = 10 / cos(40) = 13.05 (to 2 decimals)
Step-by-step explanation:
It is SOH CAH TOA, or
Sin = Opposite / Hypotenuse
Cos = Adjacent / Hypotenuse
Tan = Opposite / Adjacent
Using SOH CAH TOA,
tan(40) = k/10, so k = 10 tan (40) = 8.39 (to 2 decimals)
cos(40) = 10 / j, so J = 10 / cos(40) = 13.05 (to 2 decimals)
Does the equation x² - 4x + y2 = -3 intersect the x-axis?
a. yes, because the center is on the x-axis.
b. no, because the center is at (2,0) and the radius is 1
c. no, because the circle is entirely in the first quadrant.
d. yes, because the center is at (-2,0) and the radius is 3.
Answer: a. yes, because the center is on the x-axis.
========================================================
Explanation:
The x intercepts always occur when y = 0.
Replace y with 0 and solve for x
x^2-4x+y^2 = -3
x^2-4x+0^2 = -3
x^2-4x+0 = -3
x^2-4x = -3
x^2-4x+3 = 0
(x-3)(x-1) = 0
x-3 = 0 or x-1 = 0
x = 3 or x = 1
This shows that the x intercepts are located at (3,0) and (1,0). Refer to the diagram below. The diagram shows that the roots are at points A and B. The center is the midpoint of A and B. The center is also on the x axis.
-----------------
Here's another approach:
The general template of a circle is (x-h)^2 + (y-k)^2 = r^2
Let's complete the square of the original given equation to get it into that template form above.
x^2 - 4x + y^2 = -3
(x^2-4x) + y^2 = -3
(x^2-4x+4) + y^2 = -3+4 ... add 4 to both sides
(x-2)^2 + y^2 = 1
(x-2)^2 + (y-0)^2 = 1^2
The equation is now in the template form mentioned earlier. The center is at (h,k) = (2,0) which is on the x axis.
5(1 + 4m) – 2m = -13
Answer and Step-by-step explanation:
Solve for m.
First, distribute the 5.
5 + 20m - 2m = -13
Combine like terms.
5 + 18m = -13
Subtract 5 from both sides of the equation.
18m = -18
Divide by 18 to both sides of the equation.
m = -1 <- This is the answer.
#teamtrees #PAW (Plant And Water)
[tex]\longrightarrow{\green{ \: m = - 1 }}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]5 \: (1 + 4m) - 2m = - 13[/tex]
➼ [tex] \: 5 + 20m - 2m \: = \: - 13[/tex]
➼ [tex] \: 18m = - 13 - 5[/tex]
➼ [tex] \: 18m = - 18[/tex]
➼ [tex] \: m = \frac{ - 18}{18} [/tex]
➼ [tex] \: m = - 1[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
[tex]5 \: (1 + 4 \times - 1) - 2 \times - 1 = - 13[/tex]
➼ [tex] \: 5 \: (1 - 4) + 2 = - 13[/tex]
➼ [tex] \: 5 \times ( - 3) + 2 = - 13[/tex]
➼ [tex] \: - 15 + 2 = - 13[/tex]
➼ [tex] \: - 13 = - 13[/tex]
➼ [tex] \: L.H.S.=R. H. S[/tex]
Hence verified.
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
PLEASE HELP ATTACHED BELOW
MATH HELP PLEASE HELP
Answer:
75 cm
Step-by-step explanation:
150÷2 = 75
Good luck with your exam :)
Answer:
75
Step-by-step explanation:
Essentially this question for the radius as it ask for the distance from the middle of the pit to the outside of the pit.
We are given the diameter (150) which is a straight line through the middle from one end to the other
To find the radius given the diameter you simply divide by 2
So answer = 150/2 = 75
please help me!!!!!!
Answer:
B
Step-by-step explanation:
Answer:
5tan25°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan25° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{CA}{5}[/tex] ( multiply both sides by 5 )
5tan25° = CA
A bag contains 3 red marbles, 4 blue marbles and 7 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 100oth, that both marbles drawn will be red?
Answer: 0.214
Step-by-step explanation:
There are a total of 14 marbles in the bag, with only 3 being red. 3/14 converts to 0.214
A Group of students is tracking a friend, John, who is riding a Ferris wheel. They know that John reaches the Maximum height of 11 m at 10 seconds and then reaches the minimum height of 1 m at 55 seconds.
What is the period of the function and what does it represent in this situation?
The period represents how long it takes go from one max to the next max (ie peak to peak). It also represents going from min to min.
======================================================
Explanation:
It reaches the max at 10 seconds, and then it reaches the min at 55 seconds. This is a timespan of 55-10 = 45 seconds. This is exactly half the period. It doubles to 2*45 = 90 seconds. This is the time period between any two points in time when you're at the max height (from one max to the next adjacent max).
So you're at the max height at 10 seconds, then min at 55 seconds, then the max again at 100 seconds. Note how 100-10 = 90.
The period of any trig function is basically telling us when the function or cycle repeats itself. Once we reach the peak again, the ride repeats itself from before.
-----------
Notes:
90 seconds = 1 minute, 30 seconds = 1.5 minutesThe actual heights listed (11 m and 1 m for the max and min respectively) do not play a role in determining the period. So the heights can be anything we want, and the period will stay at 90 seconds.What is the value of x?
Answer:
5x
Step-by-step explanation:x
Drag each tile to the correct box.
Match each term in the credit card statement to its description
the amount owed by the consumer
before the current billing cycle
the amount available for the
consumer to spend
the amount the consumer currently
owes
available credit
previous balance
new balance
Answer:
Available credit :- the amount the consumer currently owes.
Previous balance :- the amount owed by the consumer before the current billing cycle
new balance :- the amount available for the consumer to spend.
Hope this answer is right!!
Answer:
AVAILABLE CREDIT- the amount the consumer currently owes.
PREVIOUS BALANCE- the amount owed by the consumer before the current billing cycle
NEW BALANCE-the amount available for the consumer to spend.
Step-by-step explanation: PLATO
Roger just ran 5 laps. He is at 20% of his goal.
How many more laps until he is finished reaching
his goal?
25 laps The Principal never visited the arts section.
4 laps The Principal never visited the bathroom
15 laps The Principal never visited the History section
20 laps The Principal never visited the office or arts
section.
Answer: 20 laps
Step-by-step explanation:
Given
Roger just ran 5 laps and completes 20% of his goal
Suppose his goal is x laps
So, 20% of x must be equal to 5
[tex]\Rightarrow 20\%\times x=5\\\Rightarrow 0.2x=5\\\\\Rightarrow x=\dfrac{5}{0.2}\\\\\Rightarrow x=\dfrac{50}{2}\\\\\Rightarrow x=25\ \text{laps}[/tex]
So, he needs 20 more laps to complete his goal.
Find Sin/Cos/Tan and Csc/Sec/Cot of A.
Answer:
Sin A = 5/13,
Cos A = 12/13,
tan A = 5/12
CSC A = 13/5
Sec A = 13/12
Cot A = 12/5
8) what is the side ratio
9) what is the perimeter RST
PLEASE ITS AN EMERGENCY
Answer:
c
24
Step-by-step explanation:
A scale drawing is a reduced form in terms of dimensions of an original image / building / object
the scale drawing is usually reduced at a constant dimension
scale of the drawing = original dimensions / dimensions of the scale drawing
/LM/ is similar to /SR/
scale = 9 / 6 = 1.5 = 3/2
length of /ST/ = 12 / 1.5 = 8
Length of /TR/ = 15 / 1.5 = 10
Perimeter = sum of sides
8 + 10 + 6 = 24
Given that cot A = 16/63 and that angle A is in Quadrant I, find the exact value of cscA in simplest radical form using a rational denominator.
Answer:
Below in bold.
Step-by-step explanation:
cot = adjacent side / opposite side = 16/63
So the hypotenuse = √(16^2 + 63^2)
= √4225
= 65.
So csc A = hypotenuse /opposite side
= 65/63
Please give real answers with explaination. I will follow + I will give brainliest. No Docs/No Files/No Links only answer with explaination.
Answer:
True.
Step-by-step explanation:
This is true with any quadrilateral.
So, in a quadrilateral ABCD,
The pairs of opposite sides is parallel and equal.
For instance:
A = 1, 1
B = 2, 2
C = 3, 3
D = 4, 4
The midpoint of AB is (1+2)/2, (1+2)/2
The midpoint of CD is (3+4)/2, (3+4)/2
And so on and so forth, therefore the midpoints of the two opposite sides bisect the area of the rectangle.
Consider the equation below.
2(n + 4) = 8–6(n-4)
Solve the equation for n.
A
-3
B
D
16
Answer:
N=3
Explanation:
Look at image below
will mark brainliest!!!!]
Find the distance between the points (-5, -10) and (2, 4).
Answer:
15.65 units
Step-by-step explanation:
Given data
x1=-5
y1=-10
x2=2
y2=4
The expression for the distance between two points is
d=√((x_2-x_1)²+(y_2-y_1)²)
substitute
d=√((2-(-5))²+(4-(-10))²)
d=√(2+5)²+(4+10)²
d=√7²+14²
d=√49+196
d=√245
d=15.65 units
Hence the distance between the points is 15.65 units
A piece of wood is 21 m long. How much piece of wood 07m 'long wood can be cut from it?
Equation = 21/7=?
Revision: 7 x ? = 21
7+7+7 = 21
7 x 3 = 21
21/7 = 3
Answer = 3
helppppppppppppp. a and b partttt
Answer:
a) 220.17 cm
b) 2127.12 cm²
Step-by-step explanation:
perimeter = circumference
it is the sum of the inner and the outer arc and the 2 side lines of 25.
we know a full circle has 360 degrees. but we only look at a segment of a circle of 150 out of the total of 360 degrees.
the circumference of a circle is
C = 2×pi×r
the 150 degree part is then
C = 2×pi×r×150/360 = 2×pi×r×15/36 = pi×r×15/18 =
= pi×r×5/6
the radius of the inner circle is 20.
=>
Ci = pi×20×5/6 = pi×50/3
the radius of the outer circle is 20 + 25 = 45
Co = pi×45×5/6 = pi×75/2
so, the total perimeter/ circumference is
C = Ci + Co + 25 + 25 = pi×50/3 + pi×75/2 + 50
= pi×100/6 + pi×225/6 + 50 = pi×325/6 + 50 =
= 220.17 cm
the area of the shaded shape is the area of the large circle segment minus the area of the small circle segment.
the area of a circle is
A = pi×r²
the 150 degree part is then
A = pi×r²×150/360 = pi×r²×5/12
so, for the inner circle that is
Ai = pi×20²×5/12 = pi×400×5/12 = pi×100×5/3 = pi×500/3
for the outer circle that is
Ao = pi×45²×5/12 = pi×2025×5/12 = pi×10125/12 =
= pi×3375/4
so, the total area of the shaded shape is
A = Ao - Ai = pi×3375/4 - pi×500/3 = pi×(10125-2000)/12 =
= pi×8125/12 = 2127.12 cm²
A first number is 4 less than a second number. Four times the first number is 6 more than twice the second. Find the numbers
Answer:
first number = 7
second number = 11
Step-by-step explanation:
A first number is 4 less than a second number
f = s - 4
Four times the first number is 6 more than twice the second
4f = 2s + 6
-----------------------------
Substitute for f = s - 4
4(s - 4) = 2s + 6
distribute
4s - 16 = 2s + 6
subtract 2s from both sides
2s - 16 = 6
add 16 to both sides
2s = 22
Divide both sides by 2
s = 11
Substitute for s = 11 in
f = s - 4
f = 11 - 4
f = 7
Factor the following expression.
x4 + x2 – 20
Answer:
2(2x+x-10)
Step-by-step explanation:
The common factor of this expression is 2 so when you factor out a 2 you have to divide everything in the expression by 2.
Answer: (−2)(+2)(/2+5)
Help me pls i'm struggling need help fast!
DUE IN 25 MINUTES OMG- PLS HELP IF YOU CAN
Convert factored form to standard form then identify y-intercept
(2x + 1) (x - 3)
Answer:
2 x ^2 − 5 x − 3
Step-by-step explanation:
Answer is the problem in standard form then the y-intercept would be -3
Factorize x²+7x+10. Show working please
Answer:
(x + 2)(x + 5)
Step-by-step explanation:
Given
x² + 7x + 10
Consider the factors of the constant term (+ 10) which sum to give the coefficient of the x- term (+ 7)
The factors are + 2 and + 5 , since
5 × 2 = + 10 and 2 + 5 = + 7 , then
x² + 7x + 10 = (x + 2)(x + 5) ← in factored form
Determine the equation of a line in slope, y-intercept form, that has a slope of -2/5 and passes through the point (-5,7)
Answer:
y = -2/5x + 5
Step-by-step explanation:
y = -2/5x + b
7 = -2/5(-5) + b
7 = 2 + b
5 = b
The sum of 9 and y is less than or equal to 16.
Answer:
[tex]9+y[/tex] ≤ [tex]16[/tex]
Step-by-step explanation:
The sum of [tex]9[/tex] and [tex]y[/tex] which is [tex]9+y[/tex] is less than or equal to 16, which is ≤ [tex]16[/tex]
Hope this is helpful.
Please help what’s the answer ??!
Answer:
50-(5+18)
=50-23
=27
3x=27
x=9
Answer:
x = 9
Add 5 and 18, and you will get 23. Then add 9 and 23 three times.
5 + 18 = 23
23 + 9 + 9 + 9 = 50
Patty measured the elementary school and made a scale drawing. The scale she used was 7 centimeters = 1 meter
What is the drawing's scale factor?
Simplify your answer and write it as a ratio, using a colon.
Write the scale of the drawing as a fraction. Put the shorter length in the numerator.
[tex] \frac{7 \: cm}{1 \: cm} \\ [/tex]
First convert the denominator to the same units as the numerator. Write an equivalent fraction with centimeters in the denominator. Since 1 meter is equal to 100 centimeters, multiply the denominator by 100 to get centimeters in the denominator.
[tex] \frac{7 \: cm}{100 \: cm} = \: \frac{7}{100} \\ [/tex]
Write the scale factor as a ratio, using a colon
7/100 → 7:100
The scale factor is 7:100.
[tex] \\ [/tex]
#CarryOnLearning!