Answer:
3x = 3
Step-by-step explanation:
x + y = 4 × 2
= 2x + 2y = 8
2x + 2y = 8 + x - 2y = -5
3x = 3
Eight years ago, the daughters age was thrice the son's age. Now the daughter's age is 4 years more than the son's age. Find their present ages.
Answer:
Let s be the son’s current age and d be the daughter’s current age. The system of equations is:
s - 10 = 2(d - 10)
s = 3 + d
Since s is already set to an equation, we can use the substitution method for s in the other equation:
s = 3 + d
s - 10 = 2(d - 10)
3 + d - 10 = 2(d - 10)
Simplify and solve for d:
3 + d - 10 = 2(d - 10)
-7 + d = 2d - 20
-7 = d - 20
13 = d
The daughter is 13 years old. To solve for the son’s age, we will plug in the solution for d into one of the equations. The second one is simpler so we will use that:
s = 3 + d
s = 3 + 13
s = 16
The son is 16 years old. Let us use the other equation to check our solutions:
s - 10 = 2(d - 10)
16 - 10 = 2(13 - 10)
6 = 2(3)
6 = 6
It checks out. The son is 16 years old, and the daughter is 13 years old.
The present age of the daughter and son are 14 and 10 years respectively.
Let the age of the daughter be x
Let the age of the son be y
If the daughter's age is 4 years more than the son's age now, then,
x = y + 4 ............. 1
If Eight years ago, the daughters' age was thrice the son's age, then;
Daughter = x - 8
Son = y - 8
Hence, x - 8 =3(y - 8).................. 2
Substitute equation 1 into 2 to have:
x - 8 =3(y - 8).
y + 4 - 8 = 3(y - 8)
y - 4 = 3y - 24
y - 3y = -20
-2y = -20
y = 10
Recall that x = y + 4
x = 10 + 4
x = 14
Hence the present age of the daughter and son are 14 and 10 years respectively.
LEarn more here: https://brainly.com/question/16510024
Find the missing side lengths
Answer:
x = 4; y = 2
Step-by-step explanation:
x = 2[tex]\sqrt{3}[/tex] ÷ sin60
= 2[tex]\sqrt{3}[/tex] ÷ [tex]\frac{(\sqrt{3} )}{2}[/tex]
= 4
y = 2[tex]\sqrt{3}[/tex] ÷ tan60
= 2 [tex]\sqrt{3}[/tex] ÷ [tex]\sqrt{3}[/tex]
= 2
I wasn't sure about my answer so used the Gauthmath app
Solve the equation. Type the value of the variable in the answer box below. (Note: repeating decimals should be entered into the answer box as improper fractions.)
88=10+30−4
Answer: y = 9⅓
Step-by-step explanation:
The equation given here is
88 = 10y + 30 - 4y
The first thing to do is to collect terms
88 - 30 = 10y - 4y.
58 = 6y
Divide both side by 6
6y = 58
6y/6 = 58/6
y = 9 ⅓
Therefore, the value of y is 9⅓.
If x=3 ,y=4 than what is the value?
Find the distance between (-8,-2) and (6,-1)
Step-by-step explanation:
hope it helps you........
Answer:
[tex]\sqrt{14^2 + 1^2} = \sqrt{197} = 14.03566885[/tex]
Step-by-step explanation:
CINDY BOUGHT A 12.3 POUND TURKEY AND AN 11.7 POUND HAM FOR HOLIDAY DINNER AND PAID $34.68. Her friend Samantha bought a 10.7 pound turkey and 9.5 pound ham for $29.05. What is the cost per pound of turkey and the cot per pound of ham
Answer:
Cost of Turkey per pound is $ 1.25 and Ham is $ 1.65.
Step-by-step explanation:
Cindy:
cost of 12.3 pound Turkey and 11.7 pound Ham = $ 34.68
Samantha:
cost of 10.7 pound Turkey and 9.5 pound Ham = $ 29.05
Let the cost of one pound of Turkey is T and one pound of Ham is H.
So,
12.3 T + 11.7 H = 34.68 ..... (1)
10.7 T + 9.5 H = 29.05 ......(2)
Solve both these equations, we get
T = $ 1.25 and H = $ 1.65
Which system of linear inequalities is graphed?
Answer:
The first one.
Step-by-step explanation:
Graph lines as if the inequalities were equal signs.
X = -3 is a vertical line at x = -3, because it's less than we shade to the left. All numbers less than -3 are to the left. The line is dashed because there is no equal to. Only less than. The line is not included in the solution set.
y = -x - 1 is a line with a y-intercept of -1 and a slope of -1. All values that are less that y are below the line. Because it's less than or equal to the line is solid.
Answer:
A
Step-by-step explanation:
The vertical line is dotted at -3 and shaded to the left
x < -3
This gives us two choices left
A and C
The other line has a y intercept at -1 and is solid and shaded to the left
It is of the form
y ≤ mx+1
We know the slope is negative since is goes down from left to right
The only Choice is A
I'm not sure how to answer this!!
Answer:
I think it's a
Step-by-step explanation:
hsjshbwibs hshhsvsu hshsbsbus
Your cellphone plan is by the minute . Each minute of use costs $0.10 . Create a relation that represents the amount spent ,A, per minute ,m, of call time . Then, use the relation to find the amount spent if you talk 65 minutes. Show your work.
Answer:
Talking 65 minutes, $ 6.50 must be paid.
Step-by-step explanation:
Since your cell phone plan is by the minute, and each minute of use cost $ 0.10, to create a relation that represents the amount spent, A, per minute, m, of call time, and then use the relation to find the amount spent if you talk 65 minutes, the following calculations must be performed:
0.10 x M = A
0.10 x 65 = A
6.50 = A
Find the value of x that will make L||M.
6x + 8
4x + 2
X =[?]
Answer:
6x+8+4x+2=180
so!! 10x+10=180
10x=170
x=17
Answer:
[tex]x=17[/tex]
Step-by-step explanation:
The two angles labelled [tex]6x+8[/tex] and [tex]4x+2[/tex] are co-interior angles. When two parallel lines are cut by a traversal, co-interior angles are supplementary, meaning they add up to 180 degrees. Therefore, if line L is parallel to line M, [tex]6x+8[/tex] and [tex]4x+2[/tex] must be supplementary:
[tex]6x+8+4x+2=180[/tex]
Combine like terms:
[tex]10x+10=180[/tex]
Subtract 10 from both sides:
[tex]10x=170[/tex]
Divide both sides by 10:
[tex]x=\frac{170}{10}=\boxed{17}[/tex]
Good Afternoon. I hope you’re well:) I need to understand how to go about solving this without a calculator, please. Thank you so much and have a blessed day!
Answer:
Step-by-step explanation:
Being able to do this requires that you understand what is being asked and that you understand domain. This is a piecewise function, made up of 4 different parts, and each part has a domain different from every other part. Now look at the solutions. We are given coordinates, x and y. So this is how this problem is done.
In a. the coordinate is (-1, 1), right? x = -1 here, so the equation that we "pick" (I'll explain that in a sec) has to have a domain where -1 will fall. The first part of this piecewise has a domain of less than or equal to -11. Is -1 less than or equal to -11? No, it is not. -1 is greater than -11, so the equation we "pick" to use will not be this one. Look at the next piece of the function and note its domain. This domain is that x is greater than -11 and less than 5. Does -1 fit in that domain? Is -1 included in that spread of numbers? Yes it is, so that is the equation we will use. By use I mean that we will plug in -1 for x and see if y = 1 (that number comes from the coordinate (-1, 1) where y = 1). The equation is y = x + 2 and plugging in -1 for x:
y = -1 + 2 so
y = 1 and this point is on the piecewise. Let's do one more example so you can see how it looks when it DOESN'T work out, ok?
Look at b. The coordinate is (-2, -10). x = -2, so the same domain, same equation: x + 2. We plug in -2 for x to find y:
y = -2 + 2 so
y = 0. 0 does not equal -10, so this point is not on that graph.
The key here is picking the equation whose domain includes your x value and evaluating the equation at that value of x to find y.
Doanh nghiệp bán trả góp 1 bất động sản có giá thanh toán là 32.000trđ . Thu điều cả vốn lẫn lãi trong 10 năm với lãi suất trả chậm là 10% / năm . Xác định số vốn phải thu ở năm thứ 6 ?
Answer:
Step-by-step explanation:
I only need the answer
Answer:
1
Step-by-step explanation:
The given equation of the function is y = -a·(x - h)² + 1
The positive constants of the equation = a, and h
The points the function crosses the x-axis = 2, and 4
Where the function crosses the x-axis, y = 0, and x = 2, and 4, therefore, when x = 2, we have;
y = 0 = -a·(2 - h)² + 1
When x = 4, we have;
0 = -a·(4 - h)² + 1
-a·(2 - h)² + 1 = -a·(4 - h)² + 1
-a·(2 - h)² = -a·(4 - h)²
(2 - h)² = (4 - h)²
±(2 - h) = +#±(4 - h)
When
(2 - h) is negative, and (4 - h) is positive, but the same magnitude, we have';
-(2 - h) = +(4 - h)
2·h = 4 + 2 = 6
h = 3
0 = -a·(4 - h)² + 1 = -a·(4 - 3)² + 1 = -a + 1
Therefore, a = 1
Solve using the Pythagorean identity
Answer:
Solution given
Cos[tex]\displaystyle \theta_{1}=\frac{3}{5}[/tex]
consider Pythagorean theorem
[tex]\bold{Sin²\theta+Cos²\theta=1}[/tex]
Subtracting [tex]Cos²\theta[/tex]both side
[tex]\displaystyle Sin²\theta=1-Cos²\theta[/tex]
doing square root on both side we get
[tex]Sin\theta=\sqrt{1-Cos²\theta}[/tex]
Similarly
[tex]Sin\theta_{1}=\sqrt{1-Cos²\theta_{1}}[/tex]
Substituting value of [tex]Cos\theta_{1}[/tex]
we get
[tex]Sin\theta_{1}=\sqrt{1-(\frac{3}{5})²}[/tex]
Solving numerical[tex]Sin\theta_{1}=\sqrt{1-(\frac{9}{25})}[/tex]
[tex]Sin\theta_{1}=\sqrt{\frac{16}{225}}[/tex]
[tex]Sin\theta_{1}=\frac{\sqrt{2*2*2*2}}{\sqrt{5*5}}[/tex]
[tex]Sin\theta_{1}=\frac{4}{5}[/tex]
Since
In IVquadrant sin angle is negative
[tex]\bold{Sin\theta_{1}=-\frac{4}{5}}[/tex]
Answer:
[tex]\sin(\theta_1)=-\frac{4}{5}[/tex]
Step-by-step explanation:
We'll use the Pythagorean Identity [tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex] to solve this problem.
Subtract [tex]\cos^2(\theta)[/tex] from both sides to isolate [tex]\sin^2(\theta)[/tex]:
[tex]\sin^2(\theta)=1-\cos^2(\theta)[/tex]
Substitute [tex]\cos(\theta)=\frac{3}{5}[/tex] as given in the problem:
[tex]\sin^2(\theta_1)=1-(\frac{3}{5}^2)[/tex]
Simplify:
[tex]\sin^2\theta_1=1-\frac{9}{25}[/tex]
Combine like terms:
[tex]\sin^2\theta_1=\frac{16}{25}[/tex]
For [tex]a^2=b[/tex], we have two solutions [tex]a=\pm \sqrt{b}[/tex]:
[tex]\sin\theta_1=\pm \sqrt{\frac{16}{25}},\\\begin{cases}\sin \theta_1=\frac{4}{5},\\\sin \theta_1=\boxed{-\frac{4}{5}}\end{cases}[/tex]
Since the sine of all angles in quadrant four return a negative output, [tex]\frac{4}{5}[/tex] is extraneous and our answer is [tex]\boxed{\sin(\theta_1)=-\frac{4}{5}}[/tex]
Please help me! I cant figure this out
AB is the same as A multiplied by B. In order to get this value, we need to figure out the value of A and B.
We have two equations here:
a + 5b = 2b + 13
a = 3b - 5
The second equation already has A isolated. So, we can take that equation and plug in the value for A. Doing so will allow us to solve for B.
(3b - 5) + 5b = 2b + 13
8b - 5 = 2b + 13
6b - 5 = 13
6b = 18
b = 3
Now that we know B, we can use our equation that isolated A.
a = 3(3) - 5
a = 9 - 5
a = 4
Therefore, a = 4 and b = 3, and ab = 12.
Hope this helps!
Can you help me find the value of x and y for both
Answer:
For the First Question:
x = 61
y = 61
For the Second Question:
x = 12
y = 7
Step-by-step explanation:
Second question:
96 = 11y + 19
11y = 77
y = 7
96 = 8x
x = 12
Scarlett made a profit of $250.00 with her mobile car wash company
Not enough information to solve..... Please make your question more clear
What is the factored form of x3 + 216?
Answer:
[tex](x+6) (x^2-6x+36)[/tex]
Step-by-step explanation:
Use the identity [tex]a^3+b^3[/tex] × [tex](a^2-ab+b^2)[/tex] and the fact that [tex]216=6^3[/tex]
we have that,
[tex]x^3+6^3=(x+6)(x^2-6x+36)[/tex]
Answer:
[tex] B. (x + 6)(x^2 - 6x + 36) [/tex]
Step-by-step explanation:
x^3 + 216
x^3 is the cube of x.
216 is the cube of 6.
This is the same as x^3 + 6^3 and follows the pattern
[tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)[/tex]
[tex] x^3 + 216 = (x + 6)(x^2 - 6x + 36) [/tex]
Can someone help me with this math homework please!
Answer:
Step-by-step explanation:
Instructions: Point R is the centroid. Find DU if DR = 14.
sec²x + cosec²x ≡sec²xcosec²x
proving qn pls i nd it by tdy
Step-by-step explanation:
sec²x + cosec²x = sec²x.cosec²x
1/cos²x + 1/sin²x = 1/cos²x.1/sin²x
or, (sin²x+cos²x)/sin²x.cos²x = 1/(sin²x.cos²x)
or, 1/(sin²x.cos²x) = 1/(sin²x.cos²x)
Hence,
sec²x + cosec²x = sec²x.cosec²x proved!!
If Tanya cleans a 1500 square foot building for a total of $107.00, what is the amount Tanya gets paid per square foot?
Answer:
Tanya will get approximately $0.07 per square foot.
This can be solved by creating a ratio between the amount she is paid and the amount of square feet she cleans.
(1500)/(107)=(1)/(x) = 0.0713
Answer:
0.0713
Step-by-step explanation:
Tanya will get approximately $0.07 per square foot.
This can be solved by creating a ratio between the amount she is paid and the amount of square feet she cleans.
(1500)/(107)=(1)/(x) = 0.0713
Can someone help me with this math homework please!
Answer:
(-3,-6) and (-3,2)
Step-by-step explanation:
A line with an undefined slope is vertical. In this case it must have x coordinates equal to -3
Find XZ given the mid-segment?
Answer:
16
having a hunch ig
what’s the answer to this problem ? 3+i/2-i * 4+i/2+i
Answer:
= -2i + 3
Step-by-step explanation:
3+i/2-i * 4+i/2+i
Group like terms
= i/2 + i/2 - 4i + i + 3
Combine the fractions i/2 + i/2: i
= i - 4i + i + 3
Add similar elements: i - 4i + i = -2i
= -2i + 3
Find the distance between the points (-2, -10) and (-9,-5) on a coordinate plane.
Answer:
√74
Step-by-step explanation:
1 Which one of the following expression represents the sum of the expressions (5x - 13xy + 14y) and (12xy - 6x - 12y)?
Answer:
(12xy-6x -12y)
12xy-18xy
6xy
Answer:
- xy - x + 2y
Step-by-step explanation:
5x - 13xy + 14y + 12xy - 6x - 12y ← collect like terms
= (- 13xy + 12xy) + (5x - 6x) + (14y - 12y)
= - xy - x + 2y
Please help explanation if possible
Answer:
y = + 1/2x -3
Step-by-step explanation:
x - 2y = 6
slope intercept form: y = mx + b
In order to put the given equation in slope intercept form we will need to isolate ( we can do this by solving algebraically ) y as seen in the equation shown above.
x - 2y = 6
Solve for y
Subtract x from both sides
x - x - 2y = 6 - x
-2y = 6 - x
Divide both sides by -2
-2y/-2 = (6 - x)/-2
y = -3 + 1/2x
* Swap -3 and 1/2x *
The equation in slope intercept form would be y = 1/2x - 3
Answer:
y = + x/2 +( - 3)
Step-by-step explanation:
make y the subject of the formula by placing x on the opposite side of y, which is right in this case, then divide every by negative two, then you'll get the answer that I've written.
The graph shows the function f(x) = 2x
What is the value of x when fx) = 8?
Answer:
4 = x
Step-by-step explanation:
f(x) =2x
Let f(x) = 8
8 =2x
Divide each side by 2
8/2 = 2x/2
4 = x
Answer:
4
Step-by-step explanation:
f(x) = 2x
When f(x) = 8, x = 8/2 = 4.
Hope this helped,
~cloud
SOMEONE HELP ME PLEASE
Answer:
(36+22+19)=77
then add red and yellow
=(36+22)
=58
then the probability will be
58/77
HOPE IT HELP YOU.......
