[tex] \frac{8}{t} + 5 = t - \frac{3}{t} + 5 + \frac{1}{3} \\ \\ 1. \: \frac{8}{t} = - \frac{3}{t} + \frac{1}{3} \\ \\ 2. \: 24 = 3t^{2} - 9 + t \\ \\ 3. \: 24 - 3t^{2} + 9 - t = 0 \\ \\ 4. \: 33 - 3t ^{2}- t = 0 \\ \\ 5. \: t = \frac{1 + \sqrt{397} }{ - 6} \: \frac{1 - \sqrt{397} }{ - 6} \\ \\ 6. \: t = - \frac{1 + \sqrt{397} }{6} \: - \frac{1 - \sqrt{397} }{6} [/tex]
Answer:
Final answer is t=7.
Step-by-step explanation:
[tex]\frac{8}{t+5}=\frac{t-3}{t+5}+\frac{1}{3}[/tex]
[tex]=\frac{8}{t+5}\cdot3\left(t+5\right)=\frac{t-3}{t+5}\cdot3\left(t+5\right)+\frac{1}{3}\cdot3\left(t+5\right)[/tex]
[tex]8\cdot3=3\left(t-3\right)+\left(t+5\right)[/tex]
[tex]24=3t-9+t+5[/tex]
[tex]24=4t-9+5[/tex]
[tex]24=4t-4[/tex]
[tex]24+4=4t[/tex]
[tex]28=4t[/tex]
[tex]\frac{28}{4}=t[/tex]
[tex]7=t[/tex]
[tex]t=7[/tex]
Hence final answer is t=7.
How to do stem and leaf plot?
I found this, Hope this helps you.
A stem-and-leaf plot is a graphical representation of data that shows the distribution of values in a data set. It is created by writing the stem values in ascending order on the left side of the vertical line and the leaf values next to the corresponding stem value, in increasing order.
Explanation:A stem-and-leaf plot is a graphical representation of data that shows the distribution of values. It is especially useful when dealing with small to medium-sized data sets. Here are the steps to create a stem-and-leaf plot:
Write the stem values in ascending order on the left side of the vertical line.Write the leaf values next to the corresponding stem value, in increasing order.Label the plot with a title, a key, and any other necessary information.For example, if you have the following data set: 12, 15, 19, 22, 23, 28, the stem-and-leaf plot would look like this:
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Determine if the two triangles are congruent. If they are state how you know.
Answer:
3,4,5 are congruent angles
Step-by-step explanation:
Congruent Angles have the same angle (in degrees or radians). That is all. They don't have to point in the same direction. They don't have to be on similar sized lines.
Answer:
#3 is congruent by SAS; #4 is congruent by SSS; #5 is congruent by AAS; #6 is congruent by ASA
Step-by-step explanation:
For #3, there are sides marked in each so we know we have 2 congruent sides, but the angle where the triangles meet are vertical angles. So that congruency statement is SAS
For #4, there are again two sides marked in each triangle giving us 2 congruent sides, but since the two triangles share that one side, that gives us the third side for SSS
For #5, we have two angles marked congruent between the two triangles and they also share a side, so AAS is the congruency statement for that one
For #6, again 2 congruent angles and a shared side between, so ASA on that one.
You're in geometry now, yes?
Solve.
What percent of 146 is 29.2?
% of 146 is 29.2.
Answer: 146 is 500% of 29.2
Step-by-step explanation:
100%/x%=29.2/146
(100/x)*x=(29.2/146)*x - we multiply both sides of the equation by x
100=0.2*x - we divide both sides of the equation by (0.2) to get x
100/0.2=x
500=x
x=500
now we have:
146 is 500% of 29.2
For this case we propose a rule of three:
146 ----------> 100%
29.2 ---------> x
Where the variable "x" is the percentage that represents 29.2 of 146.
[tex]x = \frac {29.2 * 100} {146}\\x = \frac {2920} {146}\\x = 20[/tex]
So, 29.2 is 20% of 146
Answer:
29.2 is 20% of 146
How do u solve 2x less than or equal to 30
2x ≤ 30
You must isolate x. To do this divide 2 to both sides
2x/2 ≤ 30/2
x ≤ 15
x is less then or equal to 15
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer: x ≤ 15
Step-by-step explanation:
Because...
2x ≤ 30
[tex]\frac{2x}{2} \leq \frac{30}{2}[/tex]
so after dividing 30 by 2 you get 15.
* Therefor, the answer is x ≤ 15
* Hopefully this helps:) Mark me the brainliest:)!!!
Which angle must be complementary to angle 3?
Answer:
It is angle 4 because they make 90 degrees together. This is if there are choices for the problem.
It would be ∠4
Angle 4 is the complementary angle of 3 because the sum of these angles is 90 degrees.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have:
From the angle diagram, angle 4 makes the complete right angle.
The sum of the complementary angles is 90 degree
Angle 3 + Angle 4 = 90 degree
Thus, angle 4 is the complementary angle of 3 because the sum of these angles is 90 degrees.
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how many repeating digits are in 0.64
Final answer:
0.64 is a finite decimal with zero repeating digits as it does not have digits that continue infinitely after the decimal.
Explanation:
The number 0.64 is a decimal that has two digits after the decimal point. These digits (6 and 4) do not repeat infinitely, making them non-repeating decimal digits. Therefore, there are zero repeating digits in 0.64. A repeating decimal would have one or more digits after the decimal point that continue infinitely, often denoted by a bar over the repeating digits. Since 0.64 does not exhibit this pattern, it is a finite decimal.
Which expression is equivalent to log_5(x/4)^2?
For this case we must find an expression equivalent to:
[tex]log_ {5} (\frac {x} {4}) ^ 2[/tex]
So:
We expanded [tex]log_ {5} ((\frac {x} {4}) ^ 2)[/tex]by moving 2 out of the logarithm:
[tex]2log_ {5} (\frac {x} {4})[/tex]
By definition of logarithm properties we have to:
The logarithm of a product is equal to the sum of the logarithms of each factor:
[tex]log (xy) = log (x) + log (y)[/tex]
The logarithm of a division is equal to the difference of logarithms of the numerator and denominator.
[tex]log (\frac {x} {y}) = log (x) -log (y)[/tex]
Then, rewriting the expression:
[tex]2 (log_ {5} (x) -log_ {5} (4))[/tex]
We apply distributive property:
[tex]2log_ {5} (x) -2log_ {5} (4)[/tex]
Answer:
An equivalent expression is:
[tex]2log_ {5} (x) -2log_ {5} (4)[/tex]
Answer: the answer is c
Step-by-step explanation: 2log5x-2log54
–29 + 40Add or subtract.
Answer:
11
Step-by-step explanation:
We are given the following expression which we are to solve:
[tex] - 2 9 + 4 0 [/tex]
Since there are no brackets, multiplication or division signs so we will solve this from left to right starting from the negative sign.
Adding 40 to -29 or subtracting 29 from 40 is the same so we get:
[tex] - 2 9 + 4 0 = 1 1 [/tex]
Write and expression you can use to find the value of the cube then find the value if y=9 feet
Answer:
V = s^3
V = 729 ft^3 when the side length is 9 ft
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the length of a side
Assuming you mean the side length is 9 ft
V = 9^3
V = 9*9*9
V =729 ft^3
PLEASE HELP!!!! solve for x.
Answer: x=11.67
Step 1
Use the following equation to find x. We can use this equation because Triangle 1 (triangle within triangle ABC) and Triangle 2 (triangle ABC) are proportional and we can use the system of equations below to create and equation.
[tex]\frac{x}{9}=\frac{x+5}{12}[/tex]
Step 2
We can then use the equation below by cross multiplying the previous equation in step 1.
12x= 9x+35
Step 3
Then solve the equation to find x!
12x=9x+35
3x=35
x=11.67 (rounded to the nearest hundredth)
Triangle ABC is to be dilated through point P with a scale factor of 3. How many units away from point A along ray PA will A’ be located?
Answer:
A' will be located 10 units from point A along ray PA
Step-by-step explanation:
we know that
The scale factor is equal to 3
To obtain PA', multiply PA by the scale factor
so
PA'=PA*3
PA=5 units
substitute
PA'=(5)*3=15 units
AA'=PA'-PA=15-5=10 units
therefore
A' will be located 10 units from point A along ray PA
Answer:10 units
Step-by-step explanation:
if ST=15 and RT=40 then RS= ?
See the attached picture:
If 3 times a certain number is increased by 4 the result is 28 what is the number
Answer: The number is 8
Step-by-step explanation:
Let be "x" the certain number. Then "3 times a certain number" means that the number "x" is multiplied by 3. This is:
[tex](3)(x)=3x[/tex]
Now, "3 times a certain number is increased by 4" means that the we must add 4 to [tex]3x[/tex], in other words, this indicate an addition:
[tex]3x+4[/tex]
And finally "3 times a certain number is increased by 4 the result is 28" means that [tex]3x+4[/tex] is equal to 28. Then the expression is:
[tex]3x+4=28[/tex]
To find the number "x", subtract 4 from both sides of the equation:
[tex]3x+4-4=28-4[/tex]
[tex]3x=24[/tex]
Dividing both sides of the equation by 3, you get that the number is:
[tex]\frac{3x}{3}=\frac{24}{3}\\\\x=8[/tex]
Sadie is 3 years older than Kareem, and Kareem is twice as old as Nadra. The sum of their ages is 33. A student used the steps below to find each person’s age.Which corrects the student’s first error?
The solution is :the ages of the three are: 12, 15, 6.
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
1)
Let x - Kareem's age => Sadie's age - x + 3, Nadra - x/2
We end up with the expression;
x + x + 3 + x/2 = 33
Multiply by 2 to get rid of the fraction;
2x + 2x + 6 + x = 66
5x = 60
x = 12 - Kareem's age;
2) x + 3 = 12 + 3 = 15 - Sadie's age;
3) x / 2 = 12 / 2 = 6 - Nadra's age;
Hence, The solution is :the ages of the three are: 12, 15, 6.
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Final answer:
The student's first error in determining the ages of Sadie, Kareem, and Nadra was in the setup of the equation, incorrectly representing Nadra's age as 2x instead of ½x. Correcting this mistake involves modifying the equation to accurately reflect the relationships between their ages.
Explanation:
The first error made by the student is in the setup of the initial equation for the ages of Sadie, Kareem, and Nadra. The equation (x + 3) + x + 2x = 33 inaccurately represents Nadra's age in relation to Kareem's. Given that Kareem is twice as old as Nadra, Nadra's age should be represented as ½x (half of Kareem's age), not 2x.
Correcting the initial equation should look like this: (x + 3) + x + ½x = 33. This equation accurately represents Sadie being 3 years older than Kareem and Kareem being twice as old as Nadra. To solve this corrected equation, we first combine like terms to simplify: 2½x + 3 = 33. Then, we solve for x to determine each person's age correctly.
NEED HELP!! 15 POINTS!!
The graphs of f(x) and g(x) are shown above:
What are the solutions to the equation f(x)=g(x)?
A) x=-1, 5.4
B) x=-3,4
C) x=-1,2
D) x=-10,12
Answer:
A
Step-by-step explanation:
Given the graphs of f(x) and g(x) then the solution to f(x) = g(x) are at the points of intersection of the 2 functions.
That is at the points with x- coordinates
x = - 1 and x ≈ 5.4 → A
The solutions to the equation f(x)=g(x) is x=-1, 5.4
WHAT IS FUNCTIONS?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Given
the graphs of f(x) and g(x) then the solution to f(x) = g(x) are at the points of intersection of the 2 functions.
That is at the points with x- coordinates
x = - 1 and x ≈ 5.4
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Ytterbium decays 50% every 4.2 days. How much of an 80g sample would be left after 54.6 days? Use exponential decay formula.
A. 67 g
B. 53,211.33 g
C.41.76 g
D. 9.80 g
E. 0.12 g
Answer: Option E
[tex]0.120\ g[/tex]
Step-by-step explanation:
The exponential decay formula is:
[tex]C (t) = pe^ {-rt}[/tex]
Where p is the initial amount of Ytterbium
r is the rate of decrease
C(t) is the amount of Ytterbium in grams as a function of time
t is the time in days
In this problem:
[tex]p = 80\ g\\\\r=\frac{50\%}{100\%}\\\\r=0.5[/tex]
t is the time in units of 4.2 days
Then
[tex]C(t) = 80e^{-0.5t}[/tex]
We want to calculate the amount of Ytterbium in 54.6 days.
Then as t is the time in units of 4.2 days
[tex]t = \frac{54.6}{4.2} = 13\\\\t = 13[/tex]
Finally
[tex]C(t=13) = 80e^{-0.5*13}[/tex]
[tex]C(t) = 0.120\ g[/tex]
PLEASE HELP ME SOLVE THIS
Answer:
z = 24°
Step-by-step explanation:
The 3 angles 48, x and x form a straight angle and sum to 180°, thus
x + x + 48 = 180
2x + 48 = 180 ( subtract 48 from both sides )
2x = 132 ( divide both sides by 2 )
x = 66
The 3 angles in a triangle sum to 180°
sum the 2 known angles and subtract from 180
z = 180° - (66 + 90)° = 180° - 156° = 24°
Answer:
z=24
Step-by-step explanation:
-2x = 16–8y
x+4y= 25
Solve by substitution
Answer:
([tex]\frac{17}{2}[/tex], [tex]\frac{33}{8}[/tex]
Step-by-step explanation:
Given the 2 equations
- 2x = 16 - 8y → (1)
x + 4y = 25 → (2)
Rearrange (2) expressing x in terms of y by subtracting 4y from both sides
x = 25 - 4y → (3)
Substitute x = 25 - 4y into (1)
- 2 (25 - 4y) = 16 - 8y ← distribute left side
- 50 + 8y = 16 - 8y ( add 8y to both sides )
- 50 + 16y = 16 ( add 50 to both sides )
16y = 66 ( divide both sides by 16 )
y = [tex]\frac{66}{16}[/tex] = [tex]\frac{33}{8}[/tex]
Substitute this value into (3) for corresponding value of x
x = 25 - 4 × [tex]\frac{33}{8}[/tex] )
= [tex]\frac{50}{2}[/tex] - [tex]\frac{33}{2}[/tex] = [tex]\frac{17}{2}[/tex]
Solution is ( [tex]\frac{17}{2}[/tex], [tex]\frac{33}{8}[/tex] )
To solve the given system of equations using substitution, solve one equation for one variable and substitute that expression into the other equation. The solution to the system is x = 17 and y = 6.25.
Explanation:To solve the system of equations using substitution, we need to solve one equation for one variable and substitute that expression into the other equation. Let's solve the first equation for x:
-2x = 16 - 8y
Adding 2x to both sides, we get:
0 = 16 - 8y + 2x
Now, we solve the second equation for x:
x + 4y = 25
Substituting the expression for x into the second equation, we get:
16 - 8y + 2x + 4y = 25
Simplifying the equation:
-4y + 16 + 25 = -2x + 2(25)
Combine like terms:
41 - 4y = 50 - 2x
Now, let's isolate x:
-2x = 41 - 4y - 50
Simplifying the equation:
-2x = -4y - 9
Dividing by -2, we get:
x = 2y + 4.5
Now we have the expression for x, which we can substitute into either of the original equations to find the value of y. Let's substitute it into the first equation:
-2(2y + 4.5) = 16 - 8y
Simplifying the equation:
-4y - 9 = 16 - 8y
Adding 8y to both sides:
4y - 9 = 16
Adding 9 to both sides:
4y = 25
Dividing by 4, we get:
y = 6.25
Now that we have the value of y, we can substitute it into the expression for x:
x = 2(6.25) + 4.5
Simplifying the expression:
x = 12.5 + 4.5
Simplifying further:
x = 17
So, the solution to the system of equations is x = 17 and y = 6.25.
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Name the intersection of plane KCG and a plane that contains L and D
Answer:
444
Step-by-step explanation:
Damon wants to grow grass in a backyard that is in the shape of a rectangle. The dimensions of the yard are shown in the
diagram.
19.25 ft
14.5 ft
Which of these is equal to the area of the backyard?
@
266 square feet
277
square feet
© 279 square feet
©
285 square feet
Answer:
279 ft^2
Step-by-step explanation:
The area of a rectangle of length L and width W is A = LW.
Here, that area is (19.25 ft)(14.5 ft) = 279.125 ft^2, or approx. 279 ft^2
What is the value of x?
Answer:
x = 8
Step-by-step explanation:
Since the triangle is right use Pythagoras' identity to solve for x
The square on the hypotenuse is equal to the sum of the squares on the other two sides, thus
x² + 6² = 10²
x² + 36 = 100 ( subtract 36 from both sides )
x² = 64 ( take the square root of both sides )
x = [tex]\sqrt{64}[/tex] = 8
I got no clue how to do this.
Answer:
Step-by-step explanation:
Just to keep the computer happy by not having to figure out rounding answers that involve square roots and other problem numbers. I've chosen numbers that should work out evenly. And you should be able to draw the trapezoid.
Givens
H = 14
a = 23
b = 25
Area = 336
Formula
Area = (a + b)*h/2
Solution
Area = (23 + 25)*14/2
Area = 48 * 7
Area = 336
Note if a + b = 48 any values for a and b will work.
Which of the following is a reasonable estimate for the weight of an 18-wheeler truck?
A.
8 × 10-4 lb
B.
8 × 102 lb
C.
8 × 10-2 lb
D.
8 × 104 lb
By moving the decimal according to the number of places expressed by the exponents, we can see the real value of each answer choice.
A. .0008 lbs not a realistic weight for an 18-wheeler
B. 800 lbs closer but still not enough weight
C. .08 nope not this one either.
D. 80,000 lbs. this is probably in the range we are looking for.
If the exponent is negative, move the decimal that many spaces left. If the exponent is positive, move the decimal that many space right.
The correct answer is D.
Answer:
The reasonable estimate for the weight of an 18-wheeler is [tex]8 * 10^{4} lb[/tex]
Step-by-step explanation:
The average and legally maximum weight of an 18-wheeler is 80,000 pounds.
From option a through d, we check which of the measurement is close or equivalent to 80,000 pounds
[tex]8 * 10^{-4}[/tex]By converting this, we have
[tex]= 8 * \frac{1}{10000} lb[/tex]
[tex]= \frac{8}{10000} lb[/tex]
[tex]= 0.0008 lb[/tex]
[tex]8 * 10^{2}[/tex]By converting this, we have
[tex]= 8 * 100 lb[/tex]
[tex]= 800 lb[/tex]
[tex]8 * 10^{-2}[/tex]By converting this, we have
[tex]= 8 * \frac{1}{100} lb[/tex]
[tex]= \frac{8}{100} lb[/tex]
[tex]= 0.08 lb[/tex]
[tex]8 * 10^{4}[/tex]By converting this, we have
[tex]= 8 * {10000} lb[/tex]
[tex]= {80000} lb[/tex]
From the 4 conversions, only [tex]8 * 10^{4} lb[/tex] is equivalent to the average and legally maximum weight of an 18-wheeler, 80,000 pounds.
Hence, the reasonable estimate for the weight of an 18-wheeler is [tex]8 * 10^{4} lb[/tex]
Which of the following expressions is equivalent to -6? 10 - (-4) 4 - 10 4 - (-10) -4 - (-10)
Answer
-4-(-10)
explain
-4+10=6
the dude above me is correct
P(x)=-2x^2+16x-24 help plz
Step-by-step explanation:
hope it helps you!!!!!!!!!!
Quadrilaterals find m
Answer:
Measure B= 121
Measure C=59
Step-by-step explanation:
10x-19=7x+23
3x=42
x=14
plug in x to the problem and you'll find Measure B is 121 so to find Measure C you'll have to subtract 180 and 121 to get 59.
The value of angle B is 121 degree and Angle C is 59 degree, and Angle D has the same measure as the angle B
What is quadrilateral?It is defined as the four-sided polygon in geometry having four edges and four corners and two pairs of congruent sides. It has one pair of opposite congruent angles.
We have a quadrilateral in which angle B and angle D are given.
As we know the opposite angles in the quadrilateral are same in measure.
10x - 19 = 7x + 23
3x = 42
x = 14
Angle B = 10x - 19 = 10(14) - 19 = 121 degree
Angle C = 7x + 23 = 7(14) + 23 = 121 degree
Angle A + Angle C = 360 - 121 -121 = 118
Angle C = 118/2 = 59
Thus, the value of angle B is 121 degree and Angle C is 59 degree, and Angle D has the same measure as the angle B
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X^2+11=36
X^2-25/x+5 =0
What is the value of x for both
Answer:
x = 5Step-by-step explanation:
[tex]x^2+11=36\qquad\text{subtract 11 from both sides}\\\\x^2=25\to x=\pm\sqrt{25}\\\\x=-5\ or\ x=5\\============================\\\\\dfrac{x^2-25}{x+5}=0\qquad Domain:\ x+5\neq0\to x\neq-5\\\\\dfrac{x^2-25}{x+5}=0\to x^2-25=0\qquad\text{add 25 to both sides}\\\\x^2=25\to x=-5\notin D\ or\ x=5\in D[/tex]
A famous fast food chain opened two branches in different parts of a city. Branch A made a profit of $50,000 in the first year, and the profit increased by 4% every year. Branch B made a profit of $35,000 in the first year, and the profit increased by 5.5% every year.
Which function can the fast food chain use to determine its total profit, P(x), after x years, and how much money will the chain have made in profit after 4 years?
Oops wrong one man I’m sorry
Answer: The function would be,
[tex]P(x)=50000(1.04)^x+35000(1.055)^x[/tex]
The approximate total profit after 4 years is $ 97341.65.
Step-by-step explanation:
Given,
For branch A,
First year profit = $ 50,000,
And, the profit increased by 4% every year.
Thus, the profit of branch A after x years,
[tex]P_1=50000(1+\frac{4}{100})^x[/tex]
[tex]\implies P_1=50000(1.04)^x[/tex]
Also, for branch B,
First year profit = $ 35,000,
And, the profit increased by 5.5% every year.
Thus, the profit of branch B after x years,
[tex]P_2=35000(1+\frac{5.5}{100})^x[/tex]
[tex]\implies P_2=35000(1.055)^x[/tex]
Hence, the total profit,
[tex]P=P_1+P_2[/tex]
[tex]\implies P(x)=50000(1.04)^x+35000(1.055)^x[/tex]
Which is the required function.
After 4 years, x = 3,
Therefore, the total profit after 4 years would be,
[tex]\implies P(3)=50000(1.04)^3+35000(1.055)^3=\$ 97341.648125\approx \$ 97341.65[/tex]
What does w=11 plus negative 7
Answer:
w=4
Step-by-step explanation:
adding a negative is like subtracting so w=11-7
Answer:
w = 4
Step-by-step explanation:
w = 11 + (-7)
w = 11 - 7
w = 4
Derek purchased a 2010 model sedan for $21,000. The dealership offered him a $149/month payment plan for 60 months, at the end of which the unpaid balance will be due. If the interest rate is 6%, find the balloon payment due at the end of 60 months.
Answer:
$17,930.12
Step-by-step explanation:
A suitable financial calculator can tell you the unpaid balance is $17,930.12 after 60 monthly payments of $149.
___
It seems likely the formulas and examples in your reference material will be helpful, too.
Answer: $17,930.12
Step-by-step explanation:
confirmed