Answer:
Sister = 15 years old
Brother = 12 years old
Step-by-step explanation:
Right now, if the brother is B years old and the sister is S years old, B = (4/5)S because the ratio from brother to sister is 4:5, so if one unit is X, B = 4X and S = 5X
Three years ago, the brother was B-3 years old and the sister was S-3 years old. Keeping one unit as X, we have
B = 3X
S = 4X
B-3 = (3/4)(S-3)
Therefore, we have a system of equations
B = (4/5)S
B-3 = (3/4)(S-3)
Substitute (4/5)S for B into the second equation to only have one variable
(4/5)S - 3 = (3/4)(S-3)
(4/5)S - 3 = (3/4)S - 9/4
add 3 to both sides and subtract (3/4)S from both sides to isolate the variable and its coefficient
(1/20)S = 3/4
multiply both sides by 20 to isolate the S
S = 15
B = (4/5)S = 12
Is the following statement true or false? If false, replace the bold word to make the statement
true.
A rhombus is an equiangular quadrilateral
Answer:
replace rhombus with square, or rectangle
Step-by-step explanation:
Find the solution(s) for x in the equation below.
x2 – 25 = 0
Answer:
x=5,-5
Step-by-step explanation:
what is the probability of flipping 3 coins on the same side that is getting either all heads or all tails? write the exact decimal answer withput rounding
Which situation results in a zero balance?
A Jenny uses her credit card to buy a $1,400 refrigerator and then makes a payment of
$1,400 to her credit card company.
B Pedro deposits $2,346 into a new checking account and then writes a check for $346.
C Eliza spends $150 on supplies for her business and then spends $150 in rent.
D Juanita earns $75 from her job and receives $75 from her sister.
Answer:
A
Step-by-step explanation:
0 - 1400 = -1400 + 1400 = 0
Please help what is the answer its a math question find the lcd!!!
Step-by-step explanation:
sorry I don't now but when I now I will tell you ok but mybe it 12×12×12
Last week antione had a begging balance of $90 in his account he wrote 3 checks for $10 each from his checking account , withdrew another $20 and finally made a deposit of $100. Write an expression that shows his final account balance at the end of the week
Answer:
$140
Step-by-step explanation:
90-(3x10)-20+100= 140
He started with $90: (90)
Then he wrote 3 checks of $10 each: -(3x10)
Then he withdrew $20: -20
Finally, he made a deposit of $100: +100
Thus, our equation would be: 90-(3x10)-20+100=
(You might want to simplify this expression; giving you 140)
PLZ HELP!! I will give points!
Answer:
a is -2,1 b is -3,3 c is -1,3
Step-by-step explanation:
Erin tried to multiply 70 x 30 by decomposing 70 and 30 into multiples of 10. Her work is below.
A-Step 1
B-Step2
C-Step3
D-Step4
E-Erin did not make a mistakes.
Write the equation of the line that passes through the given points.
(0,−5) and (9,−1)
Answer:
y=4/9x-5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-(-5))/(9-0)
m=(-1+5)/9
m=4/9
y-y1=m(x-x1)
y-(-5)=4/9(x-0)
y+5=4/9(x)
y+5=4/9x
y=4/9x-5
Find the center of the circle that you can circumscribe about DABC.
. A(2, 8), B (0,8), and C (2,2)
The center of the circle that circumscribe about DABC is [tex](h,k) = (1, 5)[/tex].
A circle can be modelled after a expression of the form:
[tex]A\cdot x + B\cdot y + C =-x^{2}-y^{2}[/tex] (1)
We can determine all coefficients by knowing three distinct points on plane.
If we know that [tex](x_{1}, y_{1}) = (2, 8)[/tex], [tex](x_{2}, y_{2}) = (0, 8)[/tex] and [tex](x_{3}, y_{3}) = (2, 2)[/tex], then the solution of the system of linear equations is:
[tex]2\cdot A + 8\cdot B + C = -68[/tex] (2)
[tex]8\cdot B + C = -64[/tex] (3)
[tex]2\cdot A + 2\cdot B + C = -8[/tex] (4)
[tex]A = -2, B = -10, C = 16[/tex]
Now we proceed to complete squares and factor each resulting perfect square trinomial in order to determine the coordinates of the center of the circle:
[tex]x^{2}+y^{2}-2\cdot x -10\cdot y +16 = 0[/tex]
[tex](x^{2}-2\cdot x +1)-1+(y^{2}-10\cdot y +25)-25 +16 = 0[/tex]
[tex](x-1)^{2}+(y-5)^{2}= 10[/tex]
The center of the circle that circumscribe about DABC is [tex](h,k) = (1, 5)[/tex].
To learn more on circles, we kindly invite to check this verified question: https://brainly.com/question/11833983
Find the area of the figures
4 cm
T
4 cm
12 cm
8 cm
The area is
square centimeters
Answer:
120 [cm²].
Step-by-step explanation:
1) the required area is A=Area(ABCEFD)=Area(ABCD)+Area(CEFD);
2) Area of ABCD: Area(ABCD)=AB*BC=12*8=96 [cm²];
3) Area of CEFD: Area(CEFD)=0.5(CD+EF)*HD=0.5*(8+4)*4=24 [cm²];
4) finally, the required area is: A=96+24=120 [cm²].
all the details are provided in the attachment.
Find an equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): -5, -3,1.
Assume the leading coefficient is 1.
Answer:
f(x) = x^3 + 7x^2 + 7x -15
Step-by-step explanation:
f(x) = (x+5)(x+3)(x-1)
f(x) = (x^2 + 3x + 5x + 15)(x-1)
f(x) = (x^2 + 8x + 15)(x-1)
f(x) = x^3 + 8x^2 + 15x -x^2 -8x -15
simplify
f(x) = x^3 + 7x^2 + 7x -15
Answer:
[tex]f(x) = (x + 5)\, (x + 3)\, (x - 1)[/tex].
Step-by-step explanation:
By the factor theorem, if a constant [tex]a[/tex] is zero of the polynomial [tex]f(x)[/tex], [tex](x - a)[/tex] would be a factor of this polynomial. (Notice how [tex]x = a[/tex] would indeed set the value of [tex](x - a)\![/tex] to [tex]0[/tex].)
For instance, since [tex](-5)[/tex] is a zero of the polynomial [tex]f(x)[/tex], [tex](x - (-5))[/tex] would be a factor of [tex]f(x)\![/tex]. Simplify this expression to get [tex](x + 5)[/tex].
Likewise, the zero [tex](-3)[/tex] would correspond to the factor [tex](x + 3)[/tex], while the zero [tex]1[/tex] would correspond to the factor [tex](x - 1)[/tex].
All three of these factors above are linear, and the degree of the variable [tex]x[/tex] in each factor is [tex]1[/tex]. Multiplying three such linear factors would give a polynomial of degree [tex]3[/tex].
Given the three factors, the expression of [tex]f(x)[/tex] in factored form would be:
[tex]f(x) = m\, (x + 5)\, (x + 3)\, (x - 1)[/tex] for some constant [tex]m[/tex].
When this expression is expanded, the constant [tex]m[/tex] would be the coefficient of the [tex]x^{3}[/tex] term (the leading term.) In other words, [tex]m\![/tex] is the leading coefficient of [tex]f(x)[/tex]. This question has required this coefficient to be [tex]1[/tex]. Thus, [tex]m = 1[/tex]. The expression of [tex]f(x)\![/tex] in factored form would be:
[tex]f(x) = (x + 5)\, (x + 3)\, (x - 1)[/tex].
HELP ASAP 10 POINTS
Which coordinates are the best estimate of the solution to the system of equations?
Hint: Which coordinate is closest to where the lines meet?
Question 4 options:
(6,0)
(0,5)
(1,4)
(1,5)
Answer:
(1,4)
Step-by-step explanation:
It was either (1,3) or (1,4) but there was no (1,3) so (1,4).
Hopes This Helps :)
Mark the sums of the integers as either positive or negative.
-8+(-9)
7+(-3)
5+(-12)
-12+15
The option A and C are negative. also, option B and D are positive.
What are integers numbers?Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )
Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.
WE need to write the sums of the integers as either positive or negative.
-8+(-9) = -17
This gives the negative answer.
7+(-3) = 4
This gives the positive answer.
5+(-12) = -7
This gives the negative answer.
-12+15 = 3
This gives the positive answer.
Learn more about numbers here;
https://brainly.com/question/3151755
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write in point slope form an equation of the line that passes through point (6,5) with slope 3
Answer:
y - 5 = 3(x - 6)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
Here m = 3 and (6, 5 ) a point on the line , then
y - 5 = 3(x - 6) ← equation of line
10. Given m and b, write the equation of the line:
m=-4; b=2
Answer:
y= -4x + 2
Step-by-step explanation:
Y= mx + b is used to find the equation of the line
m=-4 a d b= 2
So, you put them into the equation.
if 6 notebooks cost $15 how much would 1 notebook cost?
Answer:
well altogether it is 15 then it would be 3 dollars each
Step-by-step explanation:
:)
How many problems of each point value are on the test? 10 problems worth 5 points and 25 problems worth 2 points 14 problems worth 5 points and 15 problems worth 2 points 16 problems worth 5 points and 13 problems worth 2 points 15 problems worth 5 points and 13 problems worth 2 points.
The question is an illustration of system of equations
There are 14 problems worth 5 points and 15 problems worth 2 points
The system of equations is given as:
[tex]x + y = 29[/tex]
[tex]5x + 2y = 100[/tex]
Make x the subject in [tex]x + y = 29[/tex]
[tex]x = 29 - y[/tex]
Substitute 29 - y for x in [tex]5x + 2y = 100[/tex]
[tex]5(29 - y) + 2y = 100[/tex]
Open brackets
[tex]145 - 5y + 2y = 100[/tex]
Evaluate like terms
[tex]145 - 3y = 100[/tex]
Collect like terms
[tex]- 3y = 100-145[/tex]
Evaluate like terms
[tex]- 3y = -45[/tex]
Divide both sides by -3
[tex]y = 15[/tex]
Substitute 15 for y in [tex]x = 29 - y[/tex]
[tex]x = 29 - 15[/tex]
[tex]x = 14[/tex]
This means that there are 14 problems worth 5 points and 15 problems worth 2 points
Read more about system of equations at:
https://brainly.com/question/14323743
Kim needs 10 cups of apple juice for a recipe. How many quarts does she need?
She will need 2.5 quarts.
Kim will need 2.5 quarts.
How to find the quarts she needs?
Given = 10 cups quarter
From the given data = 10/4
⇒ 2.5
The answer is 2.5 quarts.
What does 1 quart equal to in cups?
There are 4 cups in 1 quart. There are 8 cups in 2 quarts. There are 16 cups in 4 quarts.
Learn more about problem solving here: brainly.com/question/23945932
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The Zenith occurs in fall equinox. At the same day, find the altitude of the sun at noon at Phnom Penh city (11.50N).
Note: subject Earth Science.
Answer:
78.50°
Step-by-step explanation:
On either equinox, the sun is overhead at the equator. At 11.50 N, the sun will be at elevation ...
90° -11.50° = 78.50°
60% of the 7th grade students take the bus. If there were 120 students on the busses, how many 7th grade students are there?
Answer: 200 Students
Step-by-step explanation:
Your friend has $100 when he goes to the fair. He spends $10 to enter the fair and $29 on food. Rude lady at the fair cost $2 per rude. Which function can be used to determine how much money he had left over after x rides?
Answer:
y=-2x-39
Step-by-step explanation:
Answer:
100=39+2x
Step-by-step explanation:
hoped that hedlp:P
A jacket's REGULAR price is $65.00. It is on clearance for 40% off. you have to pay 5% sales tax What is the final price for the jacket. Please show how to calculate the 5% sales tax thoroughly.
Answer:
circle tttdonuts
Step-by-step explanation:
d crystal
Sarah works for 8 minutes and for every 8 minutes she gains 23 coins everytime she works and she is saving for 2,000 coins in total. How many hours will it take Sarah to get 2,000 coins?
Answer:
11.59 hours {Basically 12 hours]
Step-by-step explanation:
Sarah's coin rate is 23 coins/8 minutes, or 2.875 coins/minute
Rate * Time(X) = Coins
(2.875 coins/min)*(X) = 2000 coins
X = (2000 coins)/(2.875 coins/min)
X = 695.65 minutes
(695.65 minutes)*(1 hour/60minutes) = 11.59 hours
What is an equivalent expression to 7x - 3y + 8x ?
Pls look at the image that I uploaded
Answer:
15x - 3y
Explaination:
Adding 7x and 8x will give you 15x and the -3y doesn't need to be added up.
I hope this helps you.
d= sqrt ( 2 )^ 2 +( 12 )^ 2
Answer:
d = 146
Step-by-step explanation:
Answer:
d=146
Step-by-step explanation:
the sqrt of 2(2) is 4 which can be simplified to 2 and the 12 raised to the second power is 144 so 2+144 is 146
What is (0,1) and (4,2) in slope intercept form
Answer:
y = 0.25x+1
Step-by-step explanation:
Y= mx+b
m= 0.25
b= 1
hope this helps
Need some help :(
A)12.7
B)13.3
C)12.4
Answer:
i am just here for points
Step-by-step explanation:
(6, 10)
(a, 8)
(4,5)
(2, 2)
1. Find the slope of the line. Explain or show your reasoning
2. Write an equations for the line.
3. Find the values for a and b. Explain or show your reasoning
4. What is the y-coordinate when x = 0? Explain or show your reasoning.
Exterior Angles and Isosceles Triangles
Step-by-step explanation:
this is not an isoceles triangle.
anyway, we need to remember 2 things :
1. the sum of all angles in a triangle is always 180°.
2. the sum of all angles around a single point on a line is 360° (as this point wound be the center of an invisible circle). and as the line cuts this circle in half, the angles on one side of the line around this point is therefore 180°.
so, the internal angle Q is then
180 = 50 + 55 + Q
Q = 180 - 50 - 55 = 180 - 105 = 75°
the exterior angle x at Q is then
180 = Q + x = 75 + x
x = 180 - 75 = 105°