Let S be Sydney's age.
Macy = S + Liyo, Alle = (1/2)S - 1.
Given, S + (S + Liyo) + ((1/2)S - 1) = 31.
Substituting Liyo = S and solving gives Sydney = 10, Macy = 15.
So, Macy is 15 years old.
To solve this problem, let's assign variables to represent each sister's age. Let S be Sydney's age. Given that Macy is Liyo years older than Sydney, Macy's age would be S + Liyo. Since Allie is one year less than half the age of Sydney, Allie's age can be represented as (1/2)S - 1.
The sum of their ages is given as 31, so we can set up the equation: S + (S + Liyo) + ((1/2)S - 1) = 31. Substituting Liyo with S, we can solve for Sydney's age (S). Once we find Sydney's age, we can then find Macy's age by adding Liyo to Sydney's age.
By solving the equation, we find that Sydney is 10 years old. Thus, Macy is 15 years old (10 + Liyo). Therefore, Macy is 15 years old.
Complete Question:
Macy, Sydney, and Alle are sisters. Macy is liyo years older than Sydney and Allie is one war less than half the age of Sydney. If the sum of their ages is 31, how old is Magy?
2+2 is 4
4+4 is 8
What is 8+8
Answer:
The answer is 16
Step-by-step explanation:
Roxanne has $3,000 that she plans to invest into an account that earns 7% simple interest.Assuming she makes no additional deposits or withdrawals, how much interest will Roxanne earn after 15 years? *
Answer:
$3150
Step-by-step explanation:
I = P • R • T
Intrest Equals Principal Amout times Rate of Intrest times Amount of Time
P is our Principal amount of $3,000
R is our Rate of 7%
T is the time span of years
Now if we plug in the values and solve the equation we get $3150 dollars in intrest.
Final answer:
Roxanne will earn $3,150 in interest after 15 years.
Explanation:
To calculate the interest Roxanne will earn, we can use the formula:
Interest = Principal x Rate x Time
Where Principal is the initial amount invested, Rate is the interest rate, and Time is the number of years.
Plugging in the given values, we get:
Interest = $3,000 x 0.07 x 15
Interest = $3,150
Therefore, Roxanne will earn $3,150 in interest after 15 years. This implies that Roxanne will accumulate $3,150 in interest after 15 years, illustrating the straightforward application of the interest formula to quantify the financial growth derived from the initial investment over the specified period.
The HCF of 2 numbers is 75 and their LCM is 1500. If one of the numbers is 300, find the other.
The other number is 375.
Step-by-step explanation:
The given information are,
The HCF of two numbers is 75.The LCM of the two numbers is 1500.The one number out of the two numbers is 300.
Let, the another number be assumed as 'x'.
The first number = 300 and the second number = x.
To find the number x :
The HCF × LCM = product of two Numbers is a logic to used to find the unknown number.
We know the values of HCF = 75 , LCM = 1500 and one number = 300 and the second number is x.
Therefore, substituting those values in the above formula, we get
⇒ 75 × 1500 = 300 × x
⇒ 1125 / 3 = x
⇒ 375 = x
Therefore, the second number is 375.
volume of a cone with a diameter of 3.5 and a height of 8.4.
Answer: volume is 26.9
Step-by-step explanation:
Volume of a cone is calculated by V=πr^2h/3
Where π is a constant, with value of 3.14
h is height, given as 8.4
r is radius, radius = diameter ÷ 2
Since Diameter is given as 3.5, radius = 3.5/2 = 1.75
Slot the values into the formula
V= 3.14 x 1.75^2 × 8.4/3
= 3.14 x 3.06 x 2.8
=26.9
I hope this helps.
Answer:
0.416
Step-by-step explanation:
Find the least common multiple of the following polynomials: 5y2 -80 and y + 4.
Answer:
[tex]5 {y}^{2} - 80[/tex]
Step-by-step explanation:
The given polynomials are:
[tex]5 {y}^{2} - 80[/tex]
and
[tex]y + 4[/tex]
Let us factor the first polynomial to get:
[tex]5 {y}^{2} - 80 = 5( {y}^{2} - 16)[/tex]
We need to rewrite as difference of two squares:
[tex]5 {y}^{2} - 80 = 5( {y}^{2} - {4}^{2} )[/tex]
We can now factor to get:
[tex]5 {y}^{2} - 80 = 5( {y} - 4)(y + 4)[/tex]
So the least common multiple of
[tex]5( {y} + 4)(y - 4) \: and \: (y + 4) \: is \: 5( {y} + 4)(y - 4) = 5 {y}^{2} - 16[/tex]
l
Which expression is equivalent to (3x2-7
(2x - 11)-(x2+4)
(522-6)-(2x2-1)
(10x2-4)-(7x+3)
(15x2 +8)= (18x2 +1)
The equivalent value of the expression is A = ( 10x² - 4 ) - ( 7x² + 3 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 3x² - 7 be equation (1)
On simplifying , we get
Let the second expression be represented as B
where B = ( 10x² - 4 ) - ( 7x² + 3 )
On simplifying , we get
B = 10x² - 4 - 7x² - 3
B = ( 10x² - 7x² ) - ( 4 + 3 )
B = 3x² - 7
Therefore , the value of B = A
Hence , the expression is B = ( 10x² - 4 ) - ( 7x² + 3 )
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x^3-10x=100
Use a trial and improvement method to find this solution.
Give your answer to 1 decimal place.
Show working
The value of x is approximately 5.4 when x^3 -10x = 100
How to solve the equation?The equation is given as:
x^3 -10x = 100
Using trial by error, we keep testing for the value of x that is true for x^3 -10x = 100
After several attempts, we have:
x = 5.4 (approximately)
Substitute 5.4 for x in x^3 -10x = 100
5.4^3 -10 * 5.4 = 100
Evaluate
103.5 = 100
Approximate
100 = 100
This means that x is approximately 5.4 when x^3 -10x = 100
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A solution to the equation x^3 −10x=100 using the trial and improvement method is approximately x=5.3 (rounded to 1 decimal place).
let's use the trial and improvement method to find a solution for the equation
x^3 −10x=100.
Start with a reasonable guess for x. In this case, it's often helpful to start with small integers.
Substitute the guess into the equation and see if it satisfies the equation.
Let's try
5^3 −10×5=125−50=75
The result is not equal to 100. Since the result is less than 100, we need to increase our guess.
Let's try
6^3 −10×6=216−60=156
The result is still not equal to 100. Since the result is now greater than 100, we need to decrease our guess.
Let's try
5.5^3 −10×5.5=166.375−55=111.375
This result is still greater than 100, so we need to try a smaller value.
5.2^3 −10×5.2=140.608−52=88.608
Now, this result is closer to 100. We can continue to refine our guess.
Let's try
5.3^3 −10×5.3=150.097−53=97.097
This result is getting closer to 100. We can keep refining our guess, but for the sake of brevity, let's stop here.
So, a solution to the equation x^3 −10x=100 using the trial and improvement method is approximately x=5.3 (rounded to 1 decimal place).
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What is the surface area of the cylinder with height 3yd and radius 4yd?Round your answer to the nearest thousandth.
Answer:
175.93cm²
Step-by-step explanation:
Answer: 175.929 yd^2
Step-by-step explanation:
How do I do this table !!!
Answer:
Step-by-step explanation:
just mutiply 120 by 1,2,3,4,5,6,7,8
the angle of elevation from point c to the top of the cliff is 34°. if point c is 1,000 ft from the base of the cliff, how high is the cliff.
Answer:
675 ft (3 s.f.)
Step-by-step explanation:
Please see attached picture for full solution.
The bill for dinner was $73.57 you left $11.43 for the tip what percentage of the original bill was the tip ? Round to the nearest whole percent
Answer:
16%
Step-by-step explanation:
Percentage of the tip is the tip divided by the original bill and the result multiplied by 100%
That’s
$11.43/$73.57 x 100%
0.1554 x 100%
15.54
16%
The tip was 16% of the original bill
The tip was about 16% of the total bill. This was calculated by dividing the tip amount by the total bill, multiplying by 100 to get a percentage, and then rounding to the nearest whole percent.
Explanation:To find out what percentage the tip was of the original bill, you would divide the amount of the tip by the total bill before the tip, and then multiply that number by 100 to get a percentage. Here's how you would calculate it in this case:
First, divide $11.43 (the amount of the tip) by $73.57 (the original bill). This will give you the decimal 0.1554285.Multiply this decimal by 100 to convert it to a percentage. This will give you 15.54285. Round this number to the nearest whole percent. The rounded percentage in this case is approximately 16%.So, the tip was about 16% of the total bill.
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How to get the answer for this?
Answer:
NF = 16 units
Step-by-step explanation:
The in-center of a triangle is a point inside the triangle and equidistant from the three sides of the triangleIt is the center of the circle which touch the three sides of the triangle (each side of a triangle is tangent to the circle and the segments drawn from it to the points of tangent are radii of the circle)∵ N is the in-center of ΔABC
∴ N is equidistant from the sides AB, BC and CA
- That means the perpendicular segments from N to AB, BC
and AC are equal
∴ ND = NE = NF
∵ ND = 6x - 2
∵ NE = 3x + 7
- Equate them to find x
∴ 6x - 2 = 3x + 7
- Subtract 3x from both sides
∴ 3x - 2 = 7
- Add 2 to both sides
∴ 3x = 9
- Divide both sides by 3
∴ x = 3
- Substitute the value of x in ND to find its length
∵ ND = 6(3) - 2 = 18 - 2
∴ ND = 16 units
∵ ND = NE = NF
∴ NF = 16 units
HELP PLSSSSSSSSSSSSSSSSSSSSSQ
[tex]m\angle B= 41^{\circ},[/tex] [tex]m\angle F= 70^{\circ},[/tex] [tex]m\angle H = 61^{\circ},[/tex] [tex]m\angle K= 56^{\circ}.[/tex]
Step-by-step explanation:
Step 1:
The total of the angles in any triangle is 180°.
So to determine the third angle of the given triangles, we subtract the sum of the other two sides from, 180°.
The third angle = 180° - (the first angle + the second angle).
Step 2:
For triangle ABC,
[tex]m\angle B=180^{\circ}-(\angle A+\angle C)[/tex],
[tex]m\angle B=180^{\circ}-(83^{\circ} + 56^{\circ}) = 180^{\circ} - 139^{\circ} = 41^{\circ}.[/tex]
So [tex]m\angle B= 41^{\circ}.[/tex]
For triangle DEF,
[tex]m\angle F=180^{\circ}-(\angle D+\angle E)[/tex],
[tex]m\angle F=180^{\circ}-(61^{\circ} + 49^{\circ}) = 180^{\circ} - 110^{\circ} = 70^{\circ}.[/tex]
So [tex]m\angle F= 70^{\circ}.[/tex]
Step 3:
For triangle GHI,
[tex]m\angle H=180^{\circ}-(\angle G+\angle I)[/tex],
[tex]m\angle H=180^{\circ}-(49^{\circ} + 70^{\circ}) = 180^{\circ} - 119^{\circ} = 61^{\circ}.[/tex]
So [tex]m\angle H = 61^{\circ}.[/tex]
For triangle JKL,
[tex]m\angle K=180^{\circ}-(\angle J+\angle L)[/tex],
[tex]m\angle K=180^{\circ}-(83^{\circ} + 41^{\circ}) = 180^{\circ} - 124^{\circ} = 56^{\circ}.[/tex]
So [tex]m\angle K= 56^{\circ}.[/tex]
find P(A or B),if the events are disjointed
P(A)=9/25
P(B)=9/25
A 4/25
B 18/25
C 0
D 9/25
Answer: I dont know
Step-by-step explanation:
He is almost dead and wants the pp
Solve the equation 3^(2x) -4*3^(x+1) + 27 = 0. use rules of exponents to change 3^(x+1)
Answer:
[tex]\huge\boxed{x=1\ \vee\ x=2}[/tex]
Step-by-step explanation:
[tex]3^{2x}-4\cdot3^{x+1}+27=0\\\\\text{use}\ (a^n)^m=a^{nm}\ \text{and}\ a^n\cdot a^m=a^{n+m}\\\\\left(3^x\right)^2-4\cdot3^x\cdot3^1+27=0\\\\\left(3^x\right)^2-12\cdot3^x+27=0\\\\\text{substitute}\ 3^x=t>0\\\\t^2-12t+27=0\\\\t^2-3t-9t+27=0\\\\t(t-3)-9(t-3)=0\\\\(t-3)(t-9)+0\iff t-3=0\ \vee\ t-9=0\\\\t-3=0\qquad\text{add 3 to both sides}\\\boxed{t=3}\\\\t-9=0\qquad\text{add 9 to both sides}\\\boxed{t=9}[/tex]
[tex]\text{We return to substitution:}\\\\3^x=t\\\\3^x=3\ \vee\ 3^x=9\\\\3^x=3^1\ \vee\ 3^x=3^2\\\\\boxed{x=1}\ \vee\ \boxed{x=2}[/tex]
Final answer:
To solve the given equation involving exponents, convert 3^(x+1) and solve as a quadratic equation.
Explanation:
The equation is: 3^(2x) - 4*3^(x+1) + 27 = 0. To solve this, we can use the rules of exponents to change 3^(x+1) into 3*3^x.
Step-by-step solution:
Substitute 3^(x+1) with 3*3^x in the equation.
Now, you have a quadratic equation in terms of 3^x, solve it to find the value of 3^x.
Once you find the value of 3^x, proceed to find the value of x.
Which statements are true about the components of a circle? Check all that apply.
The radius is half the length of the diameter.
The circumferences is triple the radius.
The circumference is the perimeter of a circle.
To find the circumference, multiply it by the diameter.
The diameter is triple the length of the radius.
The radius of a circle is half the length of the diameter, and the circumference is the perimeter of the circle. However, the circumference is not triple the radius, and the diameter is not triple the length of the radius.
Explanation:In the context of Mathematics, particularly geometry, the following statements are indeed true about the components of a circle:
The radius is half the length of the diameter. This is because the radius of a circle is defined as the distance from the center of the circle to its edge, while the diameter is the distance across the circle passing through the center. The circumference is the perimeter of the circle. This perimeter is also called the circumference in the context of circles, as it is the length around the edge of the circle.However, the statements that the circumference is triple the radius, to find the circumference multiply it by the diameter, and the diameter is triple the length of the radius, are incorrect. The circumference of a circle is calculated as 2πr (two times the radius times Pi), and the diameter is twice the length of the radius, not triple.
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Find the value of each variable. If you answer is not an integer, express it in simplest rauitar
Also find the perimeter of the triangle.
4,6, 12, 5, 8 mean, median,mode
Answer:
mean: 7
median: 6
mode: no mode
Step-by-step explanation:
To find the mean, add all numbers together and subtract by how many numbers there are:
4 + 6 + 12 + 5 + 8 = 35
35/5 = 7
To find the median, you put the numbers in order from smallest to largest and find the very center number:
4, 5, 6, 8, 12
The very center number is 6
To find the mode, you choose the number that appears most often. Since every number in this set only appears once, there is no mode.
Answer:
median=6, mean=5, mode=none
Step-by-step explanation:
median= number in the middle, mean= add up all numbers then divide by how many numbers there are, mode= most common number
The roots of a quadratic equation depend on the values of the coefficients.
True
False
Answer:
True
Step-by-step explanation:
The nature of roots of a quadratic equation are determined by
[tex] {b}^{2} - 4ac[/tex]
where a, b, and c are the coefficients of the quadratic equation
[tex]a {x}^{2} + bx + c = 0[/tex]
Therefore it is true that, the roots of a quadratic equation depend on the values of the coefficients.
Factor the following polynomial: "4x2−16"
Answer:
Step-by-step explanation:
does it have to be right?
Mrs.Kennedy has 1/4 liter of oranges she want to give 3 students in her advisory
Antoine manages a number of apartment buildings that use natural gas for heating, cooking, and laundry. The scatter plot shows the correlation between the outside air temperature and Antoine’s natural gas bill. Which type of correlation does the plot illustrate? A. strong negative B. strong positive C. weak negative D. weak positive Scatter plot is attached
Answer:
A. Strong negative
General Formulas and Concepts:
Statistics
Positive Correlation - trend of data points has a best line of fit that is positive (sloping up)Negative Correlation - trend of data points has a best line of fit that is negative (sloping down)No Correlation - trend of data points does not have a best line of fitStep-by-step explanation:
According to the graph and the data set, we can see that we do indeed have a negative correlation trend. Therefore, options B and D can be eliminated.
Looking at the graph, we can see that we can definitely tell that it is a negative slope and it would be pretty steep. Therefore, the best answer choice would be A. Strong negative.
Please help asap!! Will give brainlist :)
a car dealership pays 8,350 for a car. they mark up the price by 17.4% to get the retail price. what is the retail price at this dealership
Answer:
9802.9
Step-by-step explanation:
find 17.4% of 8350 and then add that to the original price
Olivia ate four times as many nachos as Reagan. If Reagan ate r nachos, which equation can be used to find the number of nachos Olivia ate, v?
A. 4r = v
B. r + 4 = v
C. 4v = r
D. v + 4 = r
(as i noramlly say im terrible at math)
Answer:
A. 4r=v
Step-by-step explanation:
It says that she ate 4 times as many as Reagen and r represents the number that Reagen at so it would be 4r. While v represents how many Olivia ate which is 4r so 4r = v.
Answer:
A.4r = v
Step-by-step explanation:
Because is really asking for a ratio so the comparison of two objects
so if Olivia ate four times as much as Reagan then first start off by finding the variables which is R and V .R is how much Reagan ate well we know she at 4 times more than Olivia so 4R and now you gotta figure V how much Olivia ate so 4R = V
if you need any more help let me know ...
what is it ????????????????????
Answer:
B. 1/10 i think c:
Step-by-step explanation:
Answer: 0.65 I think 1/10
Step-by-step explanation: You find 25% of 1, (.25), then add 2/5
Simply the equation
1/4(-16x+8)
ill give whoever solves it ten points helppp
Answer:
-4x+2
Step-by-step explanation:
rewright factor and reduce
Find the equation of the line that passes through the points (-800, 200) and (-400, 300).
Answer:
y=1/4x+400
Step-by-step explanation:
Slope=Rise/Run=(300-200)/(-400-(-800))=100/400=1/4
Now we have the slope, making our equation:
y=1/4x+b
We need b, the y-intercept, which we can use any ordered pair to plug in:
200=1/4(-800)+b
200=-200+b
400=b
So the equation that passes through the points (-800, 200) and (-400, 300) is: y=1/4x+400
The equation of line that passes through the points P(-800, 200) and Q(-400, 300) is y = x/4 + 400.
What is the general equation of straight line?
The general equation of straight line is -
y = mx + c
Given is a line that passes through the points P(-800, 200) and
Q(-400, 300).
First we will find the slope of the line -
m = (y₂ - y₁)/(x₂ - x₁)
m = (300 - 200)/(-400 + 800)
m = 100/400
m = 1/4
Now, the line passes through the point Q(-400, 300). Therefore -
300 = (1/4) x (- 400) + c
300 = - 100 + c
c = 400
The final equation of the line will be -
y = x/4 + 400
Therefore, the equation of line that passes through the points P(-800, 200) and Q(-400, 300) is y = x/4 + 400.
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Which number could the point D represent?????????
Answer:
[tex]\leq[/tex]11
Step-by-step explanation:
Answer:
115
Step-by-step explanation:
Adam got 97, 70, 89, 99, 100, 78, 79, 89, 77, and 72 on his reading test. What is the mean of Adam's reading test?
Answer:
97+70+89+99+100+78+79+77+72=85