Answer:
12 years old
Step-by-step explanation:
Set up the following equation:
x + 2 = 2(x - 5) (distribute the 2)
x + 2 = 2x - 10 (subtract 2 from both sides)
x = 2x - 12 (subtract 2x from both sides)
-x = -12 (multiply both sides by negative 1)
x = 12
Brainliest, please :)
Answer: 12
Step-by-step explanation:
Let's algebraically represent this situation. Say his current age is x. We can rephrase the sentence to say that in two years, his age is the same as twice his age 5 years ago.
The phrase "in two years" means when his age is 2 more than his current age, or x + 2.
The phrase "same as" represents equality. The expressions on both sides have the same value.
The phrase "twice his age 5 years ago" is his age minus 5, multiplied by 2. We can write this as 2*(x-5).
Now that we have "translated" the equation from words to numbers, let's put it all in one equation and solve:
[tex]x+2=2(x-5)[/tex]
[tex]x+2=2x-10[/tex] [Distributive Property]
[tex]x+2-2x-2=2x-10-2x-2[/tex] [Adding -2x-2 to both sides]
[tex]-x=-12[/tex] [Combining like terms and simplifying]
[tex]x=12[/tex] [Multiplying both sides by -1 to remove the negative]
Hence, Billy's age is 12.
Simplify the trigonometric expression (sin^2(x/2)) (1 + cos(x)) using Half-Angle Identities.
Answer:
B
Step-by-step explanation:
1-cos2x=2sin²(x/2)
[tex]sin^2(\frac{x}{2} )=\frac{(1-cos(2x))}{2}\\(sin^2(\frac{x}{2} ))(1+cos(x))= \frac{(1-cos(2x))(1+cos(x))}{2}[/tex]
During a recent poll with a travel agency, 24 customers were surveyed to determine the most popular cities in the US to visit.
The Venn diagram shows this information for the three most popular cities: New York, Los Angeles, and Orlando.
a. Which customers chose Orlando but not New York or Los Angeles?
b. How many customers chose New York and Los Angeles, but not Orlando ?
c. Which customers liked Orlando and New York only?
Based on the Venn diagram with results from the travel agency and the popular cities to visit, the following are true:
5 people.1 person.2 people.What cities were the most popular in the U.S.?The Venn diagram shows that the number of people who chose Orlando alone are 5 people namely: John, Michael, Angel, Andrew, and Sally.
Only one customer in the person of Jordan preferred New York and Los Angeles.
2 people liked Orlando and New York only and they were Luke and Robert.
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Determine the interval(s) on which the given function is decreasing?
Answer:
[tex](-\infty, -1) \cup (0, \infty)[/tex]
Step-by-step explanation:
The function is decreasing if, as x increases, the value of the function (y) gets smaller. This means as you read the graph from left-to-right, the function is decreasing if the graph is falling.
From -infinity to -1, the graph is falling, then the graph rises (f is increasing) until x =0, then the graph falls again from x = 0 to infinity.
what is f(x) in the expression?
[tex]f(x) = 7x {}^{2} - 3x {}^{4} [/tex]
Select the correct answer. What is the domain of y = tan (x)?
At 90 degrees, the tangent of x is undefinable.
What does determining the domain mean?The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain. Keep in mind that a fraction's denominator (bottom) cannot be zero when determining the domain. The integer that comes after a square root symbol in this section needs to be positive.The domain of y = tan (x):
y = tan(x)
Except for 90, all sets of positive real numbers fall within the domain of y = tan(x).
At 90 degrees, the tangent of x is undefinable.
Due to the exclusion of 90, all sets of positive real numbers are included in the domain of y = tan(x).
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Pakistan scored 270 runs and fell short of India's score by 10%. How much did
India score?
Answer:
India score 290 more than pakistan
Step-by-step explanation:
India score 20 more
PLEASE HELP!
A game board with 17 spaces. Start, green, green, star, quesiton mark, question mark, star, question mark, green, cat town, green, green, star, question mark, green, green, star, green, end.
You are playing a board game and your playing piece begins the game at START. You roll a single number cube numbered 1 to 6 to find out how many spaces you can move.
What is the theoretical probability of landing on a question mark space on your first roll.
A 1/6
B 1/4
C 1/3
D 1/2
Answer:
C 1/3
Step-by-step explanation:
out of the 6 possible moves you have the possibility of landing on question mark twice. 2/6 -> 1/3
The x-intercept of a line is 2 and the y-intercept is 4. Explain how to use this information to write the equation of the line.
Answer:
y = -2x + 4
Step-by-step explanation:
The x-intercept would be the point (2,0) and the y intercept would have the point (0,4). Once we know two points we can write the equation in the line intercept for of y = mx + b.
We need to find the slope and the y intercept. The slope is the steepness of the line and it is the change in y over the change in x.
The ordered pairs are written in the form of (x, y). From our two points, we will subtract the y's to find the top number of our fraction.
0 - 4 = -4 that is the numerator (top number) of our slope. We do the same with the two x numbers that we have been given.
2 - 0 = 2 This is our numerator (or bottom number of our slope)
Our slope is -4 /2 to simplify, we divide the top and bottom number by 2 to get -2 / or just -2
Now that we have the slope we need to find the y-intercept. We can use either of our original two points and our slope to determine the y-intercept. It does not matter if you use the point (2,0) or (0,4). I will use (2,0) and the slope of -2
y = mx + b
0 = -2(2) + b
0 = -4 + b add 4 to both sides of the equation
4 = b
Now that we have the slope and the y-intercept, we can write the equation
y = mx + b
y = -2x + 4
The table below shows some inputs and outputs of the invertible function f with domain all real numbers.
The values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4
How to evaluate the function?As a general rule;
f⁻¹(f(x)) = x
This means that:
f⁻¹(f(6.022)) = 6.022
Also, we have:
f⁻¹(10) + f(-6)
From the table of values, we have:
f⁻¹(10) = -6 and f(-6) =10
So, we have:
f⁻¹(10) + f(-6) = -6 + 10
Evaluate
f⁻¹(10) + f(-6) = 4
Hence, the values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4
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A recipe for a cake instructs you to bake it at 220° C for 45 minutes. How many degrees Fahrenheit is this?
This is an exercise on Thermometric scales.
We have as data:
T = 220 °CT = °F ??We apply the following formula:
[tex]\large\displaystyle\text{$\begin{gathered}\sf ^{\circ}F=\frac{9}{5}\ ^{\circ}C+32 \end{gathered}$}[/tex]
We substitute data in the formula:
[tex]\large\displaystyle\text{$\begin{gathered}\sf ^{\circ}F=\frac{9}{5}\times220+32 \end{gathered}$}[/tex]
First multiply 9 x 220, then the result of this division is divided by 5.
[tex]\large\displaystyle\text{$\begin{gathered}\sf =396+32 \ \ \to \ \ [Add] \end{gathered}$}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf =428 \ ^{\circ}F \end{gathered}$}}[/tex]
Therefore the cake recipe that should be baked at 220 °C for 45 minutes, on the Fahrenteir scale is 428 °F. Which indicates that it will be very hot.
select all the statements that are true
Answer:
C & D
Step-by-step explanation:
A. 4 is greater than 0, so use the third equation to find f(x). 4*4 - 1 = 15, so A is wrong.
B. -2 is less than 0, so use the first equation to find f(x). -(-2) + 1 = 3, so B is also wrong.
C. -1 is less than 0, so use the first equation to find f(x). -(-1) + 1 = 2, so C is correct.
D. 1 is greater than 0, so use the third equation to find f(x). 1*1 - 1 = 0, so D is also correct.
If f(x) = 3x + 10x and g(x) = 2x - 4, find (f+ g)(x).
Answer:
25x-4
Step-by-step explanation:
3x+10x
+ 2x. -4
=5x+10x-4
=15x-4
If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f + g)(x) = 0?
hi
f(x) = x² -2x
g(x) = 6x+4
(f+g) (x) = x²-2x +6x+4 = x²+4x +4 = (x+2)² = (x+2) (x+2)
(f+g) (x) = 0 means = (x+2) (x+2) = 0
so x+2 = 0
x = -2
(f+g) (x) = 0 for x = -2
How much money is borrowed if the interest rate is 9.25% simple interest and the loan is made for 3.5 years and has 904.88 interest
The amount borrowed is 2795
What is Principal?Principal is the amount loaned or invested in a bank or a financial institution that gives a certain interest on a specific rate over a period of time.
Analysis:
P = principal = unknown
R = rate = 9.25%
T = time = 3.5 years
I = interest = 904.88
simple interest(I) = PRT/100
P = 100I/RT
P = 100 x 904.88/3.5 x 9.25 = 2795
In conclusion, the amount borrowed is 2795.
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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 46 ounces and a standard deviation of 11 ounces.
Use the Empirical Rule and a sketch of the normal distribution in order to answer these questions.
a) 68% of the widget weights lie between________and_______
b) What percentage of the widget weights lie between 24 and 57 ounces?
c) What percentage of the widget weights lie below 79
Using the Empirical Rule, it is found that:
a) 68% of the widget weights lie between 35 and 57.
b) The percentage is 81.5%.
c) The percentage is 99.85%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.For this problem, we have that:
In item a, 68% of the widgets are within 1 standard deviation of the mean, hence between 35 and 57.In item b, between 2 standard deviations below the mean(95% of 50% due to the symmetry of the normal distribution) and 1 above(68% of 50%), hence the percentage is: P 34% + 47.5% = 81.5%.For item 3, below 3 standard deviations above the mean, hence removes only the top 0.15%, hence 99.85%.More can be learned about the Empirical Rule at https://brainly.com/question/4079902
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Compute the monthly payments for each add-on interest loan. The amount of the loan is $1150. The annual interest rate is 6%. The term of the loan is 4 years
The monthly payments for each add-on interest loan is $29.7.
What is interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
According to the question,
Principal (P) = $1150
Rate of Interest(R) = 6%
Time (T) = 4 years
The interest is calculated as follows:
SI = (P × R × T)/100
SI = (1150 × 6 × 4)/100
SI=$ 276
Amount (A) = P + SI
A = $(1150 +276)
A = $1426
Monthly payment with interest = A/(4×12)
= $ 1426/48
= $29.7
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Find the arc length of the partial circle.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
The arc length of the partial circle is 7.5π
Calculating arc lengthFrom the question, we are to determine the arc length of the partial circle
The length of an arc can be calculated by using the formula
[tex]l = \frac{\theta}{360^\circ} \times 2\pi r[/tex]
Where [tex]l[/tex] is the length of the arc
[tex]\theta[/tex] is the angle subtended
and r is the radius
From the diagram,
θ = 270°
r = 5
Putting the values into the equation, we get
[tex]l = \frac{270 ^\circ}{360^\circ} \times 2\pi \times 5[/tex]
[tex]l = \frac{3}{4} \times 2\pi \times 5[/tex]
[tex]l = \frac{30\pi}{4}[/tex]
[tex]l = \frac{15}{2}\pi[/tex] OR 7.5π
Hence, the arc length of the partial circle is 7.5π
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i need the answer to this.
The simplifications of all the given ratios are as detailed below.
How to simplify ratios?The simplification of each of the given ratios are;
1) 56 : 49
The highest common multiple is 7 and so we divide by 7 to get;
56 : 49 = 8:7
2) 36:48
The highest common multiple is 12 and so we divide by 12 to get;
36 : 48 = 3:4
3) 48:42
The highest common multiple is 6 and so we divide by 6 to get;
48 : 42 = 8:7
4) 24:36
The highest common multiple is 12 and so we divide by 12 to get;
24 : 36 = 2:3
5) 20:30
The highest common multiple is 10 and so we divide by 12 to get;
20 : 30 = 2:3
6) 24:32
The highest common multiple is 8 and so we divide by 8 to get;
24 : 32 = 3:4
7) 18:27
The highest common multiple is 9 and so we divide by 9 to get;
18 : 27 = 2:3
8) 16:14
The highest common multiple is 2 and so we divide by 2 to get;
16 : 14 = 8:7
9) 9:12
The highest common multiple is 3 and so we divide by 3 to get;
9 : 12 = 3:4
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1. The mean urine sodium concentrationof18caseswas120mmol/L with standard deviation of 15 mmo/L. assume the urine sodium is normally distributed, what is the 95%confidence interval within which the mean of the total population of such cases is expected lie
Using the t-distribution, the 95% confidence interval within which the mean of the total population of such cases is expected lie is:
(112.5, 127.5).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 18 - 1 = 17 df, is t = 2.1098.
The parameters for this problem are:
[tex]\overline{x} = 120, s = 15, n = 18[/tex].
Hence the bounds of the interval are:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 120 - 2.1098\frac{15}{\sqrt{18}} = 112.5[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 120 + 2.1098\frac{15}{\sqrt{18}} = 127.5[/tex]
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The temperature was 56 degrees this morning, but dropped one degree per hour through the rest of the day. The equation is y=-x+56. You may usey=56-x . They are the same equation. Use x-values: 0, 5, and 10.
At x=0
y=56-0y=56°CAt x=5
y=56-5y=51°CAt x=10
y=56-10y=46°CCompute the monthly payments for each add-on interest loan. The amount of the loan is $1150. The annual interest rate is 6%. The term of the loan is 4 years.
The monthly payments for each add-on interest loan will be $29.71.
Given Information and Formula Used
Principal Amount, P = $1150
Rate of Interest, R = 6%
Duration of loan in years, T = 4
The formula for simple interest is given as,
I = (P × R × T)/100
Calculating the Add-On Interest For Each Month
Interest, I = (P × R × T)/100
Substituting the values of P, R, and T in the above formula, we get,
I = $ (1150 × 6 × 4)/100
I = $ 27600/100
I = $276
Calculating the Total Monthly Payment With Interest
Amount of add-on interest loan, A = P + I
A = $1150 + $276
A = $1,426
Monthly payment with interest = A/(4×12)
= $ 1426/48
= $29.71
Hence, the monthly payments for each add-on interest loan would be $29.71.
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Find the missing coordinate.
x=t+2
y = 1 + 3/t
(-1,[?])
Answer:
0
Step-by-step explanation:
Since the x coordinate is -1, 2+t = -1, and thus t = -3.
So, y = 1+(3/(-3)) = 0.
What numbers are the arrows pointing to?
a)
b)
c)
60
∞
2.5
70
3.5
Using proportions, the numbers that the arrows are pointing to are:
a) 62.
b) 8.8.
c) 2.8.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In item a, the arrow is 2/10 of the way from 60 to 70, hence the number is:
60 + 0.2(70 - 60) = 60 + 2 = 62.
In item b, the arrow is 8/10 of the way from 8 to 9, hence the number is:
8 + 0.8(9 - 8) = 8.8.
In item c, the arrow is 3/10 of the way from 2.5 to 3.5, hence the number is:
2.5 + 0.3(3.5 - 2.5) = 2.8.
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What is 13 2/3 subtracted from 49 1/3
Answer:
35 2/3
Step-by-step explanation:
49 1/3 - 13 2/3
First convert both into improper fractions, which is
148/3 - 41/3
Then subtract!
107/3
Next simplify the fraction.
35 2/3
find the slope of this line
Answer:
0
Step-by-step explanation:
On a graph, any line that is horizontal has a slope of zero. Try any points and and plug them into the slope formula equation
(Y2-Y1/X2-X1).
The answer will always be zero.
Evaluate 8xy+16y/5x
if x = 4 and y=-5.
A-42
B-7
C-23
D-12
Answer:
D
Step-by-step explanation:
substitute x = 4 , y = - 5 into the expression
[tex]\frac{8(4)(-5)+16(-5)}{5(4)}[/tex]
= [tex]\frac{-160-80}{20}[/tex]
= [tex]\frac{-240}{20}[/tex]
= - 12
Which of the following inequalities has no solutions?
Ox>3 and x < 2
Ox>3 and x < -2
Ox>3 and x < 2
Ox>3 and x > - 2
Answer:
A) x > 3 and x < 2 has no solutions
Step-by-step explanation:
Given inequalities below and we are looking for a pair with no solution.
Let's verify:
A) x > 3 and x < 2,
It has no solutions since the two inequalities have no common interval.B) x > - 3 and x < - 2,
Its solution is -3 < x < - 2, the interval between two given endpoints.C) x > - 3 and x < 2,
Similar to option B, the interval is between two endpoints:- 3 < x < 2D) x > - 3 and x > - 2,
Its solution is x > - 2, the two inequalities cover almost same interval.The arrival times of geese to a gaggle were recorded (in seconds) and given in the stemplot below.
Stem&Leaf
What is the 12th fastest time a goose took to join the gaggle? Make sure to use labels and avoid the use of abbreviations.
The 12th fastest time a goose took to join the gaggle is 49 seconds.
What is the 12th fastest time a goose took to join the gaggle?
A Stem and Leaf Plot is a type of graph where the data is divided into a stem (the first digit or digits) and a leaf (usually the last digit).
The data in the stem plot arranged from the first fastest time it takes a goose to join the gaggle is: 13, 14, 15, 19, 19, 21, 27, 27, 28, 32, 45, 49, 49, 62, 62.
The 12th fastest time is 49
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Which is the graph of the function f(x) = 1/2x2 + 2x - 6?
Answer:i would need to see the graph but here is what i think you are talking about and it shows how to it popular- problems /Algebra/ 262080
Step-by-step explanation:
Answer: man i wish i knew
Step-by-step explanation:
find x and y
can someone pls solve
First, we need to understand that these two triangles are
similar.
we know this because their lines (the arrows) prove they are the same direction. A similar triangle does
NOT mean they are proportional,
they are just similar by ratio.
Lets call the triangle on the left ABC and the triangle on the right A'B'C'.
I will attach an image of the labels.
Because they are similar triangles, angle A is the same as angle A'. Angle B is the same as angle B', angle C is the same as angle C'.
Based on that information, we know xº is = 65º. We know that the interior angles add up to 180º. So for triangle A'B'C', we can do 180º-40º-65º which is 70º. This means angle C' is 70º.
Now the important part is getting yº. A line is 180º. That means that 180º-70º=yº which is 110º.
If you do not understand anything, please let me know and I will try to teach you.