Answers
[tex]x^2 = 169[/tex]
What we must do for this case is to clear the value of x.
To do this, remember that when clearing you have two solutions.
A solution is positive.
A solution is negative.
We have then:
[tex]x = +/- \sqrt{169} x = +/- 13 [/tex]
Therefore, the solutions are:
[tex]x1 = 13 x2 = -13[/tex]
Answer:
the solutions to the equation are:
[tex]x1 = 13 x2 = -13[/tex]
Related Questions
PLEASE HELP! WILL MARK BRAINLIEST!
Answers
5x + 20 - 5 = 3x -18 + 1
combines like terms
5x + 15 = 3x - 17
subtraction properties of equality
2x + 15 = -17
subtraction properties of equality
2x = -32
coefficients: 2 and -32
answer
first one -32 and 2
Credit card A offers an APR of 25.68% compounded monthly, while credit card B offers an APR of 25.32%, compounded daily. All else being equal, which card offers a better deal for the consumer?
Answers
Answer:
Credit card B, because its effective interest rate is about 0.13% less than that of credit card A.
The deal of Credit card A is du to higher interest rate.
What is compound interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Given
APR of credit card A = 25.68% compounded monthly
APR of credit card B = 25.32% compounded daily
other details are same
let principle be 100
time = 1 year
Amount for Credit card A = P[tex](1 + \frac{r}{n})^{n t}[/tex]
where r = rate, t = time, n = time frequency
A = 100[tex](1 + \frac{0.2568}{12})^{12*1 }[/tex]
A = 128.92
amount for credit card B
A = 100[tex](1 + \frac{0.2532}{360})^{360*1 }[/tex]
A = 128.78
Hence amount for both the APR is approx. same so Credit card A is better deal with more interest rate.
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guys i am so confused right now??
Answers
it is right
Circle Area= πr^2
Circle Area= (3.14)(7)^2
CA= (3.14)(49)
C Area = 153.94
This is a half circle so divide by 2:
153.94 ÷ 2= 76.97
Parallelogram Area= base x height
PA= 7 x 6
P Area= 42
Add the two areas together:
76.97 + 42= 118.9
ANSWER: D) 118.9 cm^2
Hope this helps! :)
Which identity needs to be used to prove tan (pi/2-x)=cot x?
Answers
To prove the identity tan (pi/2-x) = cot x, we can use the identity tan(pi/2-x) = 1/tan x and simplify the expression.
To prove tan (pi/2-x) = cot x, we can use the identity tan(pi/2-x) = 1/tan x. First, rewrite tan(pi/2-x) as 1/tan x. Then, simplify 1/tan x to cot x using the definition of cot x = 1/tan x. Therefore, we have proven that tan (pi/2-x) = cot x.
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To prove tan(π/2 - x) = cot x, we use the co-function identity for tangent and cotangent, showing the relation of these functions in complementary angles. This identity confirms that tan(π/2 - x) equals cot x.
To prove the identity tan (π/2 - x) = cot x, we can use a fundamental trigonometric identity. Here's how:
Recall the co-function identity: tan (π/2 - x) = cot x. This identity is derived from the relationship between tangent and cotangent in complementary angles.
Using the identity tan (π/2 - x) = cot x, we know that the tangent of an angle's complement is equal to the cotangent of the angle.
By definition, tan θ (tangent) is the ratio of the opposite side to the adjacent side in a right triangle. For the complementary angle, the roles of the opposite and adjacent sides switch, which aligns with the definition of cot x (cotangent), i.e., the adjacent side over the opposite side.
This proves that tan (π/2 - x) = cot x.
What is the solution for the system of equations?
Use the substitution method to solve.
2x+y=20−5y=−6x+12
Enter your answer in the boxes.
( , )
Answers
So, y = 6 and x = 7
Answer:
2x+y=20 and -5y=6x+12 are your equations.
You can turn 2x+y=20 into y=-2x+20
Substitute this value of y into the other equation.
-5(-2x+20)=-6x+12
10x-100=-6x+12
16x=112
x=7
Substitute this value of x into the other equation.
2(7)+y=20
y=6
Your answer is x=7 and y=6.
PLEASE HELP ASAP! BRAINLIEST FOR RIGHT/BEST ANSWER!
Answers
Assume a team plays 6 games. If the team is equally likely to win as to lose each game, what is the probability that they win a string of at least 4 games in a row? I found my sample size to be 2^6=64 and I've tried listing out all the sequences, what I found was. W W W W W W ; W W W W W L ; W W W W L L ; L W W W W L ; L W W W W W ; L L W W W W,
Answers
Answer:
I THINK A
Step-by-step explanation:
A square has an area of 256 square meters. How long is each side?
Answers
256 = (side)^2
sqrt{256} = sqrt{(side)^2}
16 = side
Each side is 16 meters.
The square root of 265 will be the amount of meters long each side of the square is . . .
Square root of 256 = 16 <-----
Each side of the square is 16 meters long.
Hope this helps you.
Have a great day!
hat is the volume of this prism?
Rectangular prism composed of unit cubes. Prism is 6 units by 9 units by 7 units.
-----units3
Answers
At summer camp, 150 kids had the opportunity to choose their activities. 1/3 of those kids selected archery for their morning activity. Of that group,1/5 also chose to study drama in the afternoons. How many kids chose both archery in the morning and drama in the afternoons? kids chose archery for their morning activity. Of those kids who chose archery in the mornings, also chose drama in the afternoons.
Answers
Answer:
50&10...
Step-by-step explanation:
Experimental vs. Theoretical Probability:
John is about to roll a six-sided, fair number cube 60 times. He wants to predict how many times the cube will land on an even number. He makes a prediction of 20 times. Is it a good prediction? What would your prediction be based on theoretical probability?
Answers
To start the numbers 1 through 6 are on a number cube.
Half of them are even, 2, 4, and 6.
So it makes sense that when you roll the cube 60 times, you should have 30 even numbers. The theoretical probability is 30.
A predication of 20 is 10 less than the expected value of 30.
10 out of 30 is 33%.
The predication is off by 33%, I would argue that it is not a very good prediction.
I hope this helps, Good luck!
MrEquation
Answer:
Guy above is correct
Step-by-step explanation:
What is the area of a sector with a central angle of 2pi/9 radians and a diameter of 20.6mm? Use 3.14 for Ali and round your answer to the nearest hundredth.
Answers
A=πr²
A is the area of the circle.
π=3.14
r is the radius of the circle.
- To calculate the area of the sector indicated in the problem, you must apply the following formula:
As=(θ/2π)πr²
As is the area of the sector.
θ is the central angle (θ=2π/9)
π=3.14
r is the radius.
- First, you must find the radius:
r=Diameter/2
r=20.6 mm/2
r=10.3 mm
- Now, you can substitute the values into the formula As=(θ/2π)πr². Then, you have:
As=(θ/2π)πr²
As=(2π/9/2π)(π)(10.3)²
As=(π/9π)(π)(10.3)²
As=(3.14/9x3.14)(3.14)(10.3)²
- Finally, the area of the sector is:
As= 37.01 mm²
The area of the sector rounded to the nearest hundredth is [tex]$37.02 \, \text{mm}^2$[/tex].
To find the area of a sector, we use the formula:
[tex]\[ \text{Area of sector} = \frac{\text{Central angle}}{2\pi} \times \pi r^2 \][/tex]
Given that the central angle is [tex]\( \frac{2\pi}{9} \)[/tex] radians and the diameter (which is twice the radius) is [tex]$20.6 \, \text{mm}$[/tex], the radius is [tex]\( \frac{20.6 \, \text{mm}}{2} = 10.3 \, \text{mm} \)[/tex].
Now, substituting these values into the formula:
[tex]\[ \text{Area of sector} = \frac{\frac{2\pi}{9}}{2\pi} \times \pi (10.3)^2 \][/tex]
[tex]\[ = \frac{1}{9} \times \pi \times 10.3^2 \][/tex]
[tex]\[ = \frac{1}{9} \times 3.14 \times 106.09 \][/tex]
[tex]\[ = \frac{1}{9} \times 333.2086 \][/tex]
[tex]\[ \approx 37.02 \, \text{mm}^2 \][/tex]
Rounded to the nearest hundredth, the area of the sector is approximately [tex]$37.02 \, \text{mm}^2$[/tex].
A recovering heart attack patient is told to get on a regular walking program. The patient is told to walk a distance of 5 km the first week, 8 km the second week, 11 km the third week and so on for a period of 10 weeks. At that point the patient is to maintain the distance walked during the 10th week. How far will the patient walk during the 10th week? a. Is the sequence arithmetic or geometric? Explain your answer.
Answers
The sequence in this scenario is arithmetic, with the patient increasing their distance walked by 3 km each week. Using the formula for the nth term of an arithmetic sequence, the patient will walk a distance of 32 km during the 10th week.
Explanation:The sequence in this case is arithmetic. This can be determined by observing that the difference between the distances walked each week is consistent. In this case, the difference is 3 km, as the patient increases their distance by 3 km each week.
To find out how far the patient will walk during the 10th week, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d
Where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.
Given that the first term is 5 km, the common difference is 3 km, and we want to find the 10th term, we can substitute the values into the formula:
a10 = 5 + (10-1)3
a10 = 5 + 9 * 3
a10 = 5 + 27
a10 = 32
Therefore, the patient will walk a distance of 32 km during the 10th week.
Consider the functions f(x) = (4/5)^x and g(x) = (4/5)^x + 6. What are the ranges of the two functions?
f(x): {y| y > _____}
g(x): {y| y > _____}
(Fill in the blank with the correct answer)
Answers
The number 0 goes in the first blank for f(x)
The number 6 goes in the second blank for g(x)
----------------------------------------------------------------------------------
Explanation:
As x gets larger and larger, the expression (4/5)^x will get smaller and smaller. What's going on is that we are repeatedly multiplying (4/5) with itself over and over if we assume x is some whole number. For example, if x = 100, then we'll have 100 copies of (4/5) multiplied out. Each time we multiply by (4/5), the result gets smaller.
The results will approach 0 but not actually get there. So this is why f(x) has the horizontal asymptote y = 0. The function values f(x) will essentially be the set of positive y values, in other words, y > 0. This covers the range for f(x). To get the range of g(x), we add 6 to the range of f(x). This is because everything on g(x) is a vertical shift upward of 6 units.
The range of f(x) = (4/5)^x is {y| y > 0}, and the range of g(x) = (4/5)^x + 6 is {y| y > 6}.
Explanation:The range of a function refers to the set of all possible output values of the function. To determine the range of f(x) = (4/5)^x, we need to consider that any positive real number raised to any power will yield a positive result. Therefore, the range of f(x) is {y | y > 0}.
For g(x) = (4/5)^x + 6, we can see that adding a constant term of 6 to the function will shift the entire graph upwards by 6 units. Consequently, the range of g(x) is {y | y > 6}.
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simplify the expression. write the answer using scientific notation 4(6.2x10^11)
Answers
[tex]4*(6.2*10^{11})[/tex]
What we must do for this case, is to rewrite the expression.
For this, we can use the associative property of multiplication.
We have then that we can rewrite the expression as:
[tex]4*(6.2*10^{11}) = (4*6.2)*10^{11}[/tex]
Finally, by rewriting we have:
[tex](24.8*10^{11})[/tex]
Answer:
the answer using scientific notation is:
[tex](24.8*10^{11})[/tex]
Question 1. Evaluate 4 times a number q plus 25 when q=2
A. 27
B.31
C.33
D.42
Question 2. If p=8, evaluate 4 )2 / 9.3
A.2
B.3
C.6
D. 8
Question 3. If q=2, evaluate (24 + 18 .q) - (5q + 7)
A. 38
B. 79
C. 31
D. 21,
Answers
You and your friend each drive 50.0 km. you travel at 90.0 km/h. your friend travels at 95 km/h. how long will your friend be waiting for you at the end of the trip?
Answers
(90km/hr)/50km=1.8
1.9-1.8=0.1
so he will be waiting for .1 hrs
Answer:
He will reach 0.02 hours before me.
Step-by-step explanation:
A we know that,
Speed = Distance ÷ Time
Here we have given that Distance = 50 km
My Speed is 90 km/h
So time taken to complete my trip = Distance ÷ Speed
⇒ My Time = 50 ÷ 90 = 0.55 hours
Also, Speed of my friend is 95 km/h
So time taken to him to complete his trip = Distance ÷ Speed
His Time = 50 ÷ 95 = 0.53 hours
Thus he will reached before me as his speed is fast
He will reach 0.55 - 0.53 = 0.02 hours before me.
Choose the correct box of the best buy available. a can of tomatoes for 53¢ one can of tomatoes with a 20% discount when the regular price is 70¢ per can
Answers
option 1: a can of tomatoes for 53 cents.
option 2: a can of tomatoes for 70 cents with a 20% discount.
First we have to determine the price of the 2nd option.
10 % of 70 cents is 7 cents
20 % of 70 cents is 14 cents.
So, we have 14 cents of discount, which makes the new price (70-14=) 56 cents.
Now our two options are either 53 or 56 cents.
Therefore option 1 is the best buy available.
The solution is: a can of tomatoes for 53 cents, is the best buy available.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
Here, we have,
So, we have two options:
option 1: a can of tomatoes for 53 cents.
option 2: a can of tomatoes for 70 cents with a 20% discount.
First we have to determine the price of the 2nd option.
10 % of 70 cents is 7 cents
20 % of 70 cents is 14 cents.
So, we have 14 cents of discount, which makes the new price (70-14=) 56 cents.
Now our two options are either 53 or 56 cents.
Therefore option 1 is the best buy available.
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helpppppppppppppppppppppppppppp
Answers
The last option
Explanation:
The range is defined as all the possible values of y.
For the first function:
2^x can give a value less than 2
For example:
2^-1 = 1/2 ..........> This choice is not correct
For the second choice:
2(5^x) can also give a value less than 2
For example:
2 * (5^-1) = 2/5 ...............> This choice is wrong
For the third choice:
5^(x+2) ca also give a value less than 2
For example:
5(-3+2) = 5^-1 = 1/5 ..........> This choice is wrong
For the last option:
5^x + 2
This one will always give a value greater than 2 no matter what the value of exponent is. .......> This is the correct choice
Hope this helps :)
What is the length of a leg of the pre-image, triangle RST? 4 units 8 units 16 units 20 units
Answers
Answer:
C) 16 units
Step-by-step explanation:
The length of a leg of the pre-image is 16 units
What is Dilation?The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger. The initial figure is referred to as the pre-image, and the new figure that results from dilatation is known as the image. Dilation comes in two varieties:
Increase in an object's size is referred to as expansion.Contraction is the reduction of an object's size.Given:
Δ RST was dilated by a scale factor of 1/2
and, Δ R'S'T' is an isosceles triangle with measurement 8 units.
As, Pre-image = measure of pre-image x scale factor
So, the measure of pre-image = 8 ÷ 1/2
= 8 x 2/1
= 16 units.
Hence, the length of a leg of the pre-image is 16 units
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Angle K in △MKL is a right angle.
What is the value of tan M ?
15/17
8/17
8/15
15/8
Answers
answer
15/8
Solution :
Given that, In triangle MKL, angle K is a right angle.
To find the value of tan M,
As we know by trigonometric ratio, that In a right angled triangle
[tex] tan (\theta)= \frac{opposite }{Adjacent} [/tex]
Here Opposite means opposite side of the angle and adjacent means side adjacent to the angle.
So, [tex] tan M= \frac{KL}{KM} = \frac{15}{8} [/tex]
Hence, Value of [tex] tan M = \frac{15}{8} [/tex] .
Option D is the correct solution.
Which figure shows the correct dimensions of a 14 scale drawing of the given figure?
Answers
we know that
the given figure is 20x48
the correct dimensions of a 1/4 scale drawing of the given figure is
(1/4)*20--------> 5
and
(1/4)*48--------> 12
therefore
the correct dimensions are 5x12
the answer is the option B) 5x12
Jason draws an angle and then places the compass on the vertex and draws arc that intersects both rays. He then places the compass on each intersecting mark on each ray and draws arcs that intersect inside the angle. Which construction is he creating?
A. copying an angle
B. angle bisector
C. perpendicular bisector
D. perpendicular line through vertex of angle
Answers
Subtract 1.05 from a certain number. Multiply the difference by 0.8, add 2.84 to the product then divide the sum by 0.01 and get 700. What is the number?
Answers
The number is 6.25
Explanation:
Assume that the number we are looking for is x
First, we will set up the equations as follows:
1- Subtract 1.05 from the number (assume the result is y):
x - 1.05 = y
2- Multiply the difference by 0.8 (assume the product is z):
0.8(y) = z
3- add 2.84 to the product (assume the result is w):
z + 2.84 = w
4- divide the sum by 0.01, the quotient is 700:
w / 0.01 = 700
Now, we will work backwards as follows:
4) w / 0.01 = 700
w = 0.01 * 700
w = 7
3) z + 2.84 = w
z + 2.84 = 7
z = 7 - 2.84
z = 4.16
2) 0.8y = z
0.8y = 4.16
y = 4.16 / 0.8
y = 5.2
1) x - 1.05 = y
x - 1.05 = 5.2
x = 5.2 + 1.05
x = 6.25
Hope this helps :)
Here's the solution for this,
{(x-1.05).08}+2.84 = 700
.01
0.8x-0.84+2.84 = 700
.01
0.8x + 2 = 700
.01
0.8x + 2 =700 x 0.01
0.8x = 7 - 2
0.8x = 5
0.8 .08
The answer would be 6.25
Jake runs either 15 kilometers or 8,500 meters each day.He alternates short and long runs. how many meters farther will he run on his two long run days than on his two short run days?Describe how you found your answer
Answers
1. The answer must be expressed in meters, so, you have to convert 15 kilometers to meters:
1 kilometer------1,000 meters
15 kilometers---x=
x=15x1000/1
x=15,000 meters
2. Then, you have:
On his two long run days=(15,000 meters)(2)=30,000 meters
On his two short run days=(8,500 meters)(2)=17,000 meters
3. Finally, you obtain:
30,000 meters-17,000 meters=13,000 meters
How many meters farther will he run on his two long run days than on his two short run days?
The answer is: 13,000 meters
[tex](15km)( \frac{1000m}{1km} )=15000km[/tex]
We now now that the ditance he covers in his long run days is [tex]15000m[/tex], and in his short run is [tex]8.5km[/tex].
Lets find out the distance he will cover on his two long run days:
[tex]2(15000m)=30000m[/tex]
Likewise, lets find the distance he will cover in his short run days:
[tex]2(8500m)=17000m[/tex]
Now, we just need to find the difference between the tow distances:
[tex]30000m-17000m=13000m[/tex]
We can conclude that we will run 13,000 meters further in his long runs than in his short runs.
What is 3/tan(30°) in radical form? (meant to be a fraction)
Answers
Four polynomials are shown below: A. 4 − 7x5 + x2 B. 5x3 + 5 − 3x4 C. 3x + 2x4 − x2 + 6 D. 3x3 − 5 + 2x5 + x Which of the above polynomials is a 4th degree trinomial? Polynomial A Polynomial B Polynomial C Polynomial D
Answers
5x^3+5-3x^4
Is 4th degree trinomial
Answer:
Polynomial B
Step-by-step explanation:
We are given 4 different polynomial. We need to choose 4th degree polynomial from given.
Degree is maximum power of x of polynomial.
Option A: [tex]4-7x^5+x^2[/tex]
Degree = 5, False
Number of term = 3 (Trinomial)
Option B: [tex]5x^3+5-3x^4[/tex]
Degree = 4
Number of term = 3 (Trinomial)
True
Option C: [tex]3x+2x^4+x^2+6[/tex]
Degree = 4
Number of term = 4 (Not Trinomial)
False
Option D: [tex]3x^3-5+2x^5[/tex]
Degree = 5
Number of term = 3 (Trinomial)
False
Hence, Polynomial B is correct whose degree 4 and number of term 3.
Karen paid $43.70 for a book. The price of the book was $40. what was the sale tax rate
Answers
Answer:
9.25%
Step-by-step explanation:
We have the price book of $40 but karen pais $43.70 then the $3.70 extra that she paid it's the value of taxes. Then to know the tax rate we have to do the next procediment:
[tex]$40\longrightarrow 100\%[\text]
[tex]$3.70\longrightarrow x\%[/tex]
Where x is the tax rate, then:
[tex]x=\dfrac{\$3.70\cdot 100\%}{\$40}[/tex]
[tex]x=\dfrac{370\%}{40}=9.25\%[/tex]
Find an equivalent function for the following:
f(x) = 3(2)4x
Answers
To find an equivalent function for this function, we can just simplify it.
f(x) = (6)4x
f(x) = 24x
is an equivalent function.
Hope this helps!
can someone help me please? i'm not sure if 4 is right and i don't understand how to do 3