Answer:
y = 20°
x = 35°
Explanation:
Equation's:
1) 2y + x + 105° = 180°
2) 3x + x + 2y = 180°
Make y subject in equation 2
3x + x + 2y = 180
4x + 2y = 180
2y = 180 - 4x
y = 90 - 2x
Insert this into equation 1
2(90 - 2x) + x + 105° = 180°
180 - 4x + x + 105 = 180
-3x = -105
x = 35°
Find value of y
y = 90 - 2x
y = 90 - 2(35)
y = 20°
Find the equation of the line which is parallel to y = 4x -2 and passes through thepoint (-2,3).
Answer:
y = 4x + 11
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 )
y = 4x - 2 ← is in slope- intercept form
with slope m = 4
• Parallel lines have equal slopes , then
y = 4x + c ← is the partial equation
to find c substitute (- 2, 3 ) into the partial equation
3 = - 8 + c ⇒ c = 3 + 8 = 11
y = 4x + 11 ← equation of line
A standard pair of six-sided dice is rolled. What is the probability of rolling a sum greater than or equal to 7? Express your answer as a fraction or a
decimal number rounded to four decimal places.
Answer:
7/12 or 0.5833
Step-by-step explanation:
So you're going to have 36 combinations, because for each number 1-6 which may be rolled for the first roll, you're going to also have 6 other possible numbers for the second roll. This gives you 6 * 6 or 36. So you could define the entire sample space, but you could also just list the sample space with all the sums less than 7 that way you don't have to list all of the sample space, since you already know how many combinations there are going to be
Let's start with the case that you roll a 1, for the first roll:
1+1 = 2
1+2 = 3
1+3=4
1+4=5
1+5=6
These are the only combinations that will be less than 7 so stop here
Now do the case where you roll a 2, for the first roll
2+1 = 3
2+2= 4
2+3 = 5
2+4 = 6
The next roll will result in a roll greater than 6. This time there were only 4 combinations which is one less than the previous. This makes sense, since you're still increasing in intervals of 1, except the starting number is increasing by 1, meaning as the first roll increases, the amount of combinations with that starting roll that are below 7, will decrease by 1. So this means that:
1: 5 combinations
2: 4 combinations
3: 3 combinations
4: 2 combinations
5: 1 combination
6: 0 combination
This means there are going to be a total of 15 combinations which are less than 7, that means there are 36-15 combinations which are greater than or equal to 7. This simplifies to 21/36 which simplifies to 7/12. This can also be expressed as: 0.5833
find x and y
helppppp !!
3x + 6 = 48 (alternate angles are equal)
- 6
3x. = 42
÷3
x = 14 degrees
180-48 - 2y + 5y-9 =180
123 + 3y = 180
-123
3y = 57
÷3
y = 19 degrees
Explanation:
To find the last angle on the top straight line, do:
180 - (the 2 given angles).
So, 180 - (3x + 16, which is 48 due to alternate angles being equal). Then, minus the 2y.
(180 - 48 - 2y) & simplify => 132 - 2y
This gives you the equation for the missing angle on our top straight line.
Thus, co-interior angles add to 180. So, we add the new equation (132 - 2y) to 5y - 9.
Simplify
=> 123 + 3y (because - 2+5 =3)
and put it equal to 180. Solve for y
Hope this helps!
Select the three equations that pass through the points (–4, –16) and (5, 2):
y + 4 = 2(x – 16)
y – 2 = 2(x – 5)
y = 2x – 8
y + 16 = 2(x + 4)
Answer:
y-2=2(x-5), y=2x-8, y+16=2(x+4)
Step-by-step explanation
Simplify the expression.
Answer:
4x
Step-by-step explanation:
[tex]\frac{500x^{4} }{(5x)^{3} }[/tex] = [tex]\frac{500x^{4} }{125x^{3} }[/tex] = [tex]4x[/tex]
Round
8724 to the nearest whole number
Round
8724 to the nearest whole number is 8720
Which number completes the system of linear
inequalities represented by the graph?
y ≥2x - 2 and x + 4y
The number that completes the System of Linear Inequalities represented by the Graph y >= 2x – 2 and x + 4y > = is -12. Hence, x + 4y [tex]\geq[/tex] -12
What is a System of Linear Inequalities?
A collection of linear inequalities in the same variables is referred to as a system of linear inequalities. Any ordered pair that fulfills all of the inequalities is the solution.
What is the calculation to prove the above assertion?Recall that:
The linear equation with slope m and intercept c is given as follows.y = mx + c
The formula for slope of line with points and can be expressed asm = (y2 - y1)/(x2 - x1)
Given that
The orange line intersects y-axis at (0,-2), therefore the y-intercept is -2.
The orange line intersect the points that are (1,0) and (0, -2).
The slope of the line can be obtained as follows:
m = (-2-0)/(0-1)
= -2/-1
= 2
The slope of the line is m = 2.
Therefore, the orange line is y [tex]\geq[/tex] 2x -2
The blue line intersects y-axis at (0,-3), therefore the y-intercept is -3.
The blue line intersect the points that are (-4, -2) and (0, -3)
The slope of the line can be obtained as follows.
m = (-3-(-2))/(0-(-4))
= (-3 + 2)/4
= - (1/4)
The slope of the line is:
m = -(1/4)
The inequalities is x + 4y [tex]\geq[/tex] b passes through the point (0, -3)
(0) + 4 (-3) = b
-12 =b
Thus, -12 in is the number that completes the system. Hence, x + 4y [tex]\geq[/tex] -12
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Simplify your answer
Answer:
0Step-by-step explanation:
If 2u-6=4, let's solve for u.
Add 6 to both sides
2u-6+6 = 4+6
Simplify
2u = 10
Divide both sides by 2
u = 5
Now, we can solve u-5
5-5 = 0
find x and y
please help ! tyyyy
Answer:
x = 41* & y = 90.
Step-by-step explanation:
Since we know that the figure is a right triangle, we can solve for y easily, as 90+y = 180
y = 90
to solve for x, we have 49+90+x, since the angle that makes up the left side is perpendicular to the triangle,
so 139+x = 180
x = 180-139
x = 41
Jillian had 2/ 9 m of a cloth. She used 1 /9 m of it for sewing a blanket. How much of the cloth does she have remaining?
Answer:
1/9m. just take 2/9- 1/9 then you'll get the material remaining good day.
Using the concept of subtraction of fractions, Jillian have 1/9m of cloth left.
What are fractions?Fractions are a way to represent numbers that are not whole numbers. They represent parts of a whole or divisions of a quantity. A fraction consists of two parts: a numerator and a denominator.
The numerator is the number on the top of the fraction and represents the number of parts being considered or counted. The denominator is the number on the bottom of the fraction and represents the total number of equal parts into which the whole is divided.
In this problem, we can easily determine the amount of cloth she have left.
Since she used 1/9 of it, we can proceed as;
2/9 - 1/9 = 1/9m
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You start your working career when you are 24 years oldEach month, you deposit $144 into a pension planYou continue making deposits into the plan un you are 68 years oldWhat is the balance, in dollars, when the plan earns 6%, compounded monthly? Round your answer to the nearest cent
Using the monthly payment formula, it is found that the balance of the plan is of $26,731.23.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
A is the monthly payment.P is the total amount.r is the interest rate.n is the number of payments.The parameters for this problem are given as follows:
A = 144, r = 0.06, n = (68 - 24) x 12 = 528.
Then:
r/12 = 0.06/12 = 0.005.
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]144 = P\frac{0.005(1 + 0.005)^{528}}{(1 + 0.005)^{528} - 1}[/tex]
[tex]P = 144\frac{(1 + 0.005)^{528} - 1}{0.005(1 + 0.005)^{528}}[/tex]
P = $26,731.23.
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How could you correctly rewrite the equation 4(5 + 3) = 2(22-6) using the distributive property ?
Write the equation for the quadratic function in the graph
Answer:
[tex] {x}^{2} - 16 = 0 \: is \: the \: equation[/tex]
Step-by-step explanation:
[tex]x = - 4 \\ or \: x = 4[/tex]
[tex](x + 4) = 0 \: or \: (x - 4) = 0 \\ (x + 4)(x - 4) = 0 \\ open \: the \: bracket[/tex]
[tex]x(x - 4) + 4(x - 4) = 0[/tex]
[tex] {x}^{2} - 4x + 4x - 16 = 0 \\ {x}^{2} - 16 = 0[/tex]
Given: Triangle ABC, mmBC=24 cm, line segment AL- < bisector
Find: AL
AL= __cm
Please answer in detail ASAP thank you so much it would help a lot <3
The value of line AL is 21. 51cm
How to determine the lengthLet's start by finding line AB using
Sin α = opposite/ hypotenuse
Sin 90 = x/ 24
1 = x/24
Then, cross multiply
We have line AB = 24cm
Now, let's find line AC
Sin angle B = line AC/24
Let's find angle B
We know that angle A + angle B + angle C = 180
But angle B = 2 Angle A
x + 2x + 90 = 180
3x + 90 = 180
3x = 180-90
x = 30°
Then Angle B = 2 × x = 2 × 30 = 60°
Sin 60 = x/ 24
0. 8660 = x/24
Cross multiply
x = 24 × 0. 8660
x = 20. 78cm
From the diagram, we have the angle of A in the given triangle to be divide into two by the bisector, angle A = 15°
To find line AL, let's use
Cos α = adjacent/ line AL
Cos 15 = 20. 78/ line AL
Line AL = 20. 78/ cos 15
Line AL = 20. 78 / 0. 9659
Line AL = 21. 51 cm
Thus, the value of line AL is 21. 51cm
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The amounts spent by 12 customers at a Burger King's restaurant were as follows:
11.01
10.50 5.70 14.67 9.50 12.54
8.90 13.56 11.23 6.80 3.00 10.55
Find the mean amount spent by these customers.
Explanation:
The first step is to add up all the values given:
11.01 + 10.50 + 5.70 + 14.67 + 9.50 + 12.54 + 8.90 + 13.56 + 11.23 + 6.80 + 3.00 + 10.55 = 117.96
Then we divide this sum over n = 12 since this is the sample size given (i.e. the number of customers)
117.96/n = 117.96/12 = 9.83
The function V(t) = 38000 (0.94)^t represents the value (in dollars) of a car "t" years after its purchase. Use this function to complete the statements below.
The value of this car is decreasing at a rate of ______
Describe how an exponential function model helped you answer this question.
*will give brainliest!
The value of this car is decreasing at a rate of 6% per year.
The function V(t) = 38000 (0.94)^t represents the value (in dollars) of a car "t" years after its purchase
Rate of change is defined as the change in value with rest to the time is called rate of change.
Here,
V(t) = 38000 (0.94)^t
Cleary, above function is an exponential function
while putting certain values in equation we have certain outcomes.
for,
V(1) = 35720; V(2) =33576.8; V(3) = 31562.192
Now, the rate of change is given by = [V(2)-V(1)/ V(1)] x 100
= [(33576.8-35720)/35720]*100
= 6%
now V(2) x 6% = V(3)
33576.8 x 6% = 31562.192 = V(3)
Thus, The required rate of decreasing care price is 6%.
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please help me asap...
Answer:
( x-7) ( x-5)
Step-by-step explanation:
x^2 -12x + 35
To factor this problem, we want to know that two numbers multiply to 35 and add to -12
-7 * -5 = 35
-7 + -5 = -12
( x-7) ( x-5)
Answer:
The answer is (x-7)( x-5)
Step-by-step explanation:
We need to find two numbers that add up to −12 and those same two numbers should have a product of 35
Here the common factors are -7 and -5 because when added they give -12 and when multiplied they give 35.
Therefore we write the answer as (x-7)(x-5)
The number of registered users logged in to the new social media app varies with time. The table shows the average number of users logged in, y, on any given weekday, x hours after 6:00 a.m.
Answer:
1,483
Step-by-step explanation:
The equation that models this set of data is y=17.2x^2-226.3x+2184.5. Since x=0 represents 6:00 a.m, x=5 represents 11:00 a.m. Substitute 5 for x in the model, and solve for y.
Based on the number of registered users who log into the social media app during weekdays and weekends, the following are true:
1,483 users are logged in after 11 am. During the week, post at 8pm.During the weekends, post at 12 pm. When should the marketing department post the update?The given model for the users in the week is:
y = 17.2x² - 226.3x + 2,184.5
x is 5 because 11 am is 5 hours after 6 am:
= 17.2(5)² - 226.3(5) + 2,184.5
= 1,483 users
The company should post when there are the most people online and on weekdays that's 14 hours after 6 am which is:
=14 + 6
= 20:00
= 8 pm
On weekends this is 6 hours after 6 am:
= 6 + 6
= 12 pm
Missing information from question:
Model for calculating weekday users y = 17.2x² - 226.3x + 2,184.5.
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When you keep brushing your wig will it be fine or will you have to buy a new one?
Answer asap
Answer:
it should be fine, but it can also depend on the quality of the wig
Step-by-step explanation:
will wig curls come out of synethic wigs??? or do they stay there forever?
Answer asap for brainlist
Answer:
No ! The only thing that will take a wave or curl out of a synthetic wig is heat.
Step-by-step explanation:
PLEASEEE HELP!!!!!!!
9 and 1/9 subtracted by 1 and 4/5
The results of the expression 9 and 1/9 subtracted by 1 and 4/5 is 7 14/45
Subtraction of Fraction9 and 1/9 subtracted by 1 and 4/5
= 9 1/9 - 1 4/5
= 82/9 - 9/5
= (410-81) / 45
= 329/45
= 7 14/45
Therefore, 9 and 1/9 subtracted by 1 and 4/5 is 7 14/45
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Find the simple interest owed for the use of the money. Assume 360 days in a year. P=16,500, r=6%, t=180 days
The formula for simple interest is the following:
[tex]S=Prt[/tex]
In this formula, [tex]S[/tex] is the amount of interest, [tex]P[/tex] is the principal (or initial) amount, [tex]r[/tex] is the interest rate, and [tex]t[/tex] is the length f time, typically in years.
First, let's make a couple of changes to how we wrote down the variables.
Change the interest rate, [tex]6\%[/tex], to the decimal value [tex]0.06[/tex].Convert the length of time to years. 180 days divided by 360 days per year equals [tex]0.5[/tex] years.Substitute in the values and solve with a calculator.
[tex]\begin{aligned}S&=16,500\cdot0.06\cdot0.5\\&=\boxed{495}\end{aligned}[/tex]
I struggle with math and am having difficulty solving this problem. Please only solve if you definitively know the answer. Thank you!
The equivalent expression of [tex]6^\frac 25[/tex] is [tex](\sqrt[5]{6})^2[/tex]
How to determine the equivalent expression?The expression is given as:
[tex]6^\frac 25[/tex]
The law of indices states that:
[tex]a^\frac mn = (\sqrt[n]{a})^m[/tex]
Using the above as a guide, we have:
[tex]6^\frac 25 = (\sqrt[5]{6})^2[/tex]
Hence, the equivalent expression of [tex]6^\frac 25[/tex] is [tex](\sqrt[5]{6})^2[/tex]
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100 POINTS! Using the following equation, find the center and radius of the circle. You must show and explain all work and calculations to receive credit. Be sure to leave your answer in exact form.
Answer:
Center: (-4, 1)
Radius: √2
Explanation:
Circle general equation is represented by (x - h)² + (y - k)² = r²
where (h, k) is the center and "r" resembles radius
To write in general equation form, start completing square:
x² + y² + 8x -2y + 15 = 0
x² + 8x + y² - 2y + 15 = 0
(x + 4)² - 4² + (y - 1)² - (-1)² + 15 = 0
(x + 4)² + (y - 1)² - 16 - 1 + 15 = 0
(x + 4)² + (y - 1)² - 2 = 0
General equation form:
(x - (-4))² + (y - 1)² = (√2)²
From here, comparing with the formula equation.
It is determined: center: (-4, 1) and radius: √2
Answer:
center = (-4, 1)
radius = √2
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusGiven equation:
[tex]x^2+y^2+8x-2y+15=0[/tex]
Subtract 15 from both sides to move the constant to the right side of the equation:
[tex]\implies x^2+y^2+8x-2y=-15[/tex]
Rearrange the left side to collect like variables:
[tex]\implies x^2+8x+y^2-2y=-15[/tex]
Add the square of half the coefficients of the variables x and y to both sides:
[tex]\implies x^2+8x+\left(\dfrac{8}{2}\right)^2+y^2-2y+\left(\dfrac{-2}{2}\right)^2=-15+\left(\dfrac{8}{2}\right)^2+\left(\dfrac{-2}{2}\right)^2[/tex]
[tex]\implies x^2+8x+16+y^2-2y+1=2[/tex]
Factor the two perfect square trinomials on the left side:
[tex]\implies (x+4)^2+(y-1)^2=2[/tex]
Compare the found equation with the general form to find the center and radius of the circle:
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which number best represents the slope of the graphed line -5,-1/5,1/5,5
The slope of the line will be – 1/5. Then the correct option is B.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
Take two point from the graph.
(0, 2) and (1, –3)
Then the slope will be
m = (2 – (–3)) / (0 – 1)
m = 5 / (–1)
m = – 1/5
Then the correct option is B.
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the polynomial of degree 3, P(x), has a root of multiplicity 2 at x=2 and a root of multiplicity 1 at x=-4. the y-intercept . is y=-11.2
find a formula for P(x)=
The formula of P(x) = -0.7 (x-2)²(x+4)
What is a root of a polynomial ?A root of a polynomial is defined as the point or value at which the overall value of the polynomial = 0
It is given that
for a polynomial of degree 3
root x=2, multiplicity 2: (x-2)²
root x= - 4, multiplicity 1: (x+4) ³ ²
P(x) = a(x-2)²(x+4)
here a is constant
y-intercept = -11.2
P(0) = -11.2
a(0-2)²(0+4) = -11.2
a * 4 * 4 = -11.2
16a = -11.2
a = -11.2/(16)
a= -11.2/16
P(x) = -(11.2/16)(x-2)²(x+4)
P(x) = -0.7 (x-2)²(x+4)
Therefore the formula of P(x) = -0.7 (x-2)²(x+4)
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What is 0.6% as a fraction in simplest form
Answer:
3/500
Step-by-step explanation:
.6% = .006 = 6/1000 = 3/500
Completely simplify the rational expression 6-(x-1)/(x+1)
Answer:
-x + 7 / x + 1
Step-by-step explanation:
6 -(x - 1)/ x + 1
Apply distributive law: -(x - 1) = -x + 1
= 6 - x + 1 / x +1
Group like terms:
= -x + 7/ x + 1
Answer: its 5x+7/x+1
Step-by-step explanation:
help please! thanks so much!
Answer: D
Step-by-step explanation:
Answer: Choice D
Open hole at -3 with shading to the left.
==========================================================
Explanation:
The inequality [tex]-3 > \text{x}[/tex] is the same as [tex]\text{x} < -3[/tex]
When swapping both sides, the inequality sign flips as well.
Since we're looking for numbers smaller than -3, this includes things like -4, -5, -6, -7, and so on. Therefore we shade to the left of -3 on the number line.
We have an open hole at -3 to indicate it's not included as part of the solution set. We would include it if there as an "or equal to" as part of the inequality sign.