Answer:
Step-by-step explanation:
(2x-1)²=x²+4²
4x²-4x+1=x²+16
3x²-4x-15=0
a=3 b=-4 c= -15
D=b²-4ac
=16-4*3*(-15)=196
x1=-b+√D/2a=4+14/6=3
x2=-b-√D/2a=4-14/6=-10/6=-5/3
Answer:
x = 3
Step-by-step explanation:
Using Pythagoras' theorem on the right triangle, then
(2x - 1)² = 4² + x² ← expand parenthesis on the left side and simplify
4x² - 4x + 1 = 16 + x² ( subtract 16 + x² from both sides )
3x² - 4x - 15 = 0 ← in standard form
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 3 × - 15 = - 45 and sum = - 4
The factors are - 9 and + 5
Use these factors to split the x- term
3x² - 9x + 5x - 15 = 0 ( factor the first/second and third/fourth terms )
3x(x - 3) + 5(x - 3) ← factor out (x - 3)
(x - 3)(3x + 5) = 0
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
3x + 5 = 0 ⇒ 3x = - 5 ⇒ x = - [tex]\frac{5}{3}[/tex]
However, x must be greater than zero
Hence x = 3 cm
A jar contains balls numbered 1 to 10. Two balls are drawn with replacement. What is the probability that both balls are numbered 2 or less?
Answer:
Step-by-step explanation:
The number of ways that you can draw 2 balls without restriction is 10 * 10 = 100
Two balls will give you 2 or less (meaning 1) or 2*2 = 4
Four ways are possible
2 and 2
2 and 1
1 and 2
1 and 1
4/100 = 1/25 is the probability of making this happen.
What is 6x^2-12x+y+13=0 in vertex form of parabolas
Answer:
[tex]y=-6(x-1)^{2}-7[/tex]
Step-by-step explanation:
we have
[tex]6x^{2} -12x+y+13=0[/tex]
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]y+13=-6x^{2} +12x[/tex]
Factor the leading coefficient
[tex]y+13=-6(x^{2} -2x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]y+13-6=-6(x^{2} -2x+1)[/tex]
[tex]y+7=-6(x^{2} -2x+1)[/tex]
Rewrite as perfect squares
[tex]y+7=-6(x-1)^{2}[/tex]
[tex]y=-6(x-1)^{2}-7[/tex] -----> equation of the parabola in vertex form
The vertex is (1,-7) is a maximum, the parabola open downward
To convert 6x^2 - 12x + y + 13 = 0 to vertex form, follow the steps to complete the square and rewrite the equation as (x - 1)^2 = -y/6 - 7/6.
Explanation:The equation 6x^2-12x+y+13=0 is in the general form of a quadratic equation. To convert it into the vertex form, we need to complete the square.
First, let's group the x terms together: 6x^2 - 12x = -(y + 13).
Next, let's complete the square: 6(x^2 - 2x) = -(y + 13).
Now, we can add (2/2)^2 = 1 to both sides to complete the square: 6(x^2 - 2x + 1) = -(y + 13) + 6.
Simplifying further, we get 6(x - 1)^2 = -y - 7.
Finally, we can write the equation in vertex form by dividing both sides by 6: (x - 1)^2 = -y/6 - 7/6.
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6/10+39/100 find the sum
The answer is-
Exact form: 99/100
Decimal form: 0.99
Find the area thanks
16 x 14 = 224
[tex]answer = {224cm}^{2} [/tex]
Find the area of the triangle that has a base of 5in -‘d a height of 3 3/4
Answer:
its either c or b
Step-by-step explanation:
formula: 1/2*b*h or 1/2*5*3+3/4
the answer i got was 33/4
Which ordered pair is a solution of the equation? 7x-2y=-5
answer X= 5 over 7 and 2 over 7y step by step explaination add 2y on both sides u cancelled -2y and positive 2y u bring down 7X u get 7X=-5+3 then u divide and u get that answer yw have a nice day mark me brainliest
Answer:
2y=-x7
Love mORgan
Help plz !! Need this to graduate
One of the roots of the equation 10x2−33x+c=0 is 5.3. Find the other root and the coefficient c.
Answer:
1. The other root is [tex]-2[/tex]
2. c=-106
Step-by-step explanation:
The given equation is [tex]10x^2-33x+c=0[/tex].
If [tex]5.3[/tex] is a solution to the given quadratic equation, then [tex]x=5.3[/tex] must satisfy this equation.
[tex]10(5.3)^2-33(5.3)+c=0[/tex]
[tex]280.9-174.9+c=0[/tex]
[tex]106+c=0[/tex]
[tex]c=0-106=-106[/tex]
We now substitute [tex]c=-106[/tex] into the given equation to obtain;
[tex]10x^2-33x-106=0[/tex].
Comparing to the general equation;
[tex]ax^2+bx+c=0[/tex], we have a=10, b=-33 and c=-106.
Recall the quadratic formula;
[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
We now use the quadratic formula to obtain;
[tex]x=\frac{--33\pm \sqrt{(-33)^2-4(10)(-106)} }{2(10)}[/tex]
This implies that;
[tex]x=\frac{33\pm \sqrt{5329} }{20}[/tex]
[tex]x=\frac{33\pm73}{20}[/tex]
[tex]x=\frac{33-73}{20}[/tex] or [tex]x=\frac{33+73}{20}[/tex]
[tex]x=\frac{-40}{20}[/tex] or [tex]x=\frac{106}{20}[/tex]
[tex]x=-2[/tex] or [tex]x=5.3[/tex]
Hence the other root is [tex]-2[/tex]
. Find the area of a trapezoid with b1 = 13.8 cm, b2 = 16.8 cm, and h = 4 cm.
61.2 cm2
33.6 cm2
122.4 cm2
27.6 cm2
Answer:
61.2 cm²
Step-by-step explanation:
The area (A) of a trapezoid is calculated using the formula
A = [tex]\frac{1}{2}[/tex] h ([tex]b_{1}[/tex] + [tex]b_{2}[/tex] )
Substitute in given values
A = [tex]\frac{1}{2}[/tex] × 4 × (13.8 + 16.8 ) = 2 × 30.6 = 61.2 cm²
The answer is 61.2cm² .
[tex]((13.8 + 16.8) \times 4) \div 2[/tex]
This equation helps you get the answer.
Please !!! Someone help me
answer is the last one D
pls mark brainliest
The answer is D good luck
Point P is the image of P -2,-2 under a translation by 1 unit to the left and 3 units down.
Answer:
(- 3, - 5)
Step-by-step explanation:
A translation of 1 unit left, subtract 1 from x- coordinate
A translation of 3 units down, subtract 3 from y- coordinate
The translation rule is
(x, y) → (x - 1, y - 3), hence
(-2, - 2) → (- 2 - 1, - 2 - 3) → (- 3, - 5)
As part of your training schedule you plan to jog once a week around the reservoir shown below on the map.
One lap along the perimeter of the reservoir is 25 cm. What is the actual length of a lap?
The actual length of a lap cannot be determined without the scale of the map. The 25 cm measurement seems to be from the map, so without knowing the real-world equivalent of the map's measurements, we can't find the actual distance.
Explanation:The length of a lap around the reservoir cannot be directly determined from the information given. The measurement provided (25 cm) appears to be a distance measured on a map or plan of the area, and not in real life. In order to convert that measurement into a real-world distance, we need the scale of the map. A map's scale is typically represented as a ratio that indicates the relationship between a certain distance on the map and the real-world distance it represents.
For example, if the map's scale was 1 cm : 1 km, then a measurement of 25 cm on the map would represent a real-world distance of 25 km. However, without the scale, we cannot accurately determine the actual length of a lap around the reservoir. This concept is extremely important in geography and cartography as well as in mathematical problems dealing with maps and scales.
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What is the range of the graph
Answer:
Range: all real numbers greater than or equal to 2
Step-by-step explanation:
The range is the possible numbers that the output can take
Y can be any number greater than or equal to 2
Range: all real numbers greater than or equal to 2
The numbers of hours that 12 students say they typically spend on homework in a week are 2, 0, 10, 8,10, 8, 8, 8, 10, 10, 8, and 8. What is the mean number of hours? What are the outliers in the data set?
Answer:
The mean is 7.5 and the outliers are 0 and 2
Step-by-step explanation:
To find the mean, add all of the numbers together and divide by the amount of numbers.
2 + 0 + 10 + 8 + 10 + 8 + 8 + 8 + 10 + 10 + 8 + 8 = 90
90/12 = 7.5
To see the outliers, look for the numbers far away from the mean.
suppose that 17 inches of wire cost $0.85 at the same rate how many inches of wire can be bought for $0.55
Answer:
11 inches
Step-by-step explanation:
17/0.85 * 0.55
20 * 0.55
11.
Find the missing number: 8.4(1.5 + 2.3) = 12.6 +
Answer:
19.32
Step-by-step explanation:
One way to find the missing number is to get the value of the left side of the equation first.
8.4(1.5 + 2.3) = 31.92
Now we need to take that value and subtract it to the value on the right side of the equation.
31.92 - 12.6 = 19.32
So we have:
8.4(1.5 + 2.3) = 12.6 + 19.32
31.92 = 31.92
Answer:
The required number is 19.32
Step-by-step explanation:
Consider the provided expression.
Let the missing number is x.
[tex]8.4(1.5 + 2.3) = 12.6 +x[/tex]
Add the numbers as shown.
[tex]8.4(3.8) = 12.6 +x[/tex]
Open the parentheses.
[tex]31.92= 12.6 +x[/tex]
Subtract 12.6 from both the sides.
[tex]31.92-12.6= 12.6-12.6 +x[/tex]
[tex]x=19.32[/tex]
Hence, the required number is 19.32
what is 3(x-4)-7=(2x-3)
Solve for x by simplifying both sides of the equation, then isolating the variable.
So the answer to your question is :
x = 16.
Hope this helps,
Davinia.
Answer:
x = 16
Step-by-step explanation:
distribute parenthesis on both sides and simplify
3x - 12 - 7 = 2x - 3
3x - 19 = 2x - 3 ( subtract 2x from both sides )
x - 19 = - 3 ( add 19 to both sides )
x = 16
What is the value of x in the equation −6 + x = −1
Answer:
x=5
Step-by-step explanation:
-6+5=-1
start at -6 then go right units until u get -1 you got right 5 units
The value of x in the given equation is:
x=5
Step-by-step explanation:We are given a algebraic expression in terms of the variable x by:
[tex]-6+x=-1[/tex]
Now, we are asked to find the value of x from the equation.
i.e. we have to solve for x.
i.e. by some appropriate algebraic operation we need to solve for x.
so we will add 6 on both the sides of the equation to get:
[tex]-6+x+6=-1+6\\\\i.e.\\\\-6+6+x=5\\\\i.e.\\\\0+x=5\\\\i.e.\\\\x=5[/tex]
Hence, the value of x is: 5
Graph the solution for the following system of inequalities. Click on the graph until the correct solution is displayed. x + y > 3 x + y < -4
Answer:
The graph for the following system of inequalities is attached below.
Step-by-step explanation:
The given system of inequalities is
[tex]x+y>3[/tex] .... (1)
[tex]x+y<-4[/tex] .... (2)
From inequality (1) and (2) it is clear that (x+y) is greater than 3 adn 3 is not less than -4. So, the given system of inequality has no feasible reason or solution.
The related equation of first inequality is
[tex]x+y=3[/tex]
Put x=0 to find the y-intercept.
[tex]0+y=3\Rightarrow y=3[/tex]
The y-intercept is 3.
Put y=0 to find the x-intercept.
[tex]x+0=3\Rightarrow x=3[/tex]
The x-intercept is 3.
The related equation of second inequality is
[tex]x+y=-4[/tex]
Put x=0 to find the y-intercept.
[tex]0+y=-4\Rightarrow y=-4[/tex]
The y-intercept is -4.
Put y=0 to find the x-intercept.
[tex]x+0=-4\Rightarrow x=-4[/tex]
The x-intercept is -4.
The related lines are dotted line because the sign of inequalities are > and <.
Check each inequality be (0,0).
[tex]0+0>3[/tex]
[tex]0>3[/tex]
This statement is false. So the shaded region of first inequality is opposite sides of the origin.
[tex]0+0<-4[/tex]
[tex]0<-4[/tex]
This statement is false. So the shaded region of first inequality is opposite sides of the origin.
The graph for the following system of inequalities is attached below.
Answer:
This is the correct graph on Odyssey :)
The conditional relative frequency table below was generated by column using frequency table data comparing the number of calories in a meal to whether the meal was prepared at home or at a restaurant.
A nutritionist attempts to determine an association between where food is prepared and the number of calories the food contains. Which is most likely true?
A. An association cannot be determine because the value 0.55 is similar to the value 0.45
B. There is an association because the value 0.15 is not similar to the value 0.55
C. There is an association because the sum of each column is 1.0.
D. An association cannot ve determined because the sum of the rows going across is not 1.0.
Answer:
B. There is an association because the value 0.15 is not similar to the value 0.55
Step-by-step explanation:
Based on the above picture, for the nutritionist to determine whether there is an association between where food is prepared and the number of calories the food contains, there must be an association between two categorical variables.
The conditions that satisfy whether there exists an association between conditional relative frequencies are:
1. When there is a bigger difference in the conditional relative frequencies, the stronger the association between the variables.
2. When the conditional relative frequencies are nearly equal for all categories, there may be no association between the variables.
For the given conditional relative frequency, we can see that there exists a significant difference between the columns of the table in the picture because 0.15 is significantly different from 0.55 and 0.85 is significantly different from 0.45
We can conclude that there is an association because the value 0.15 is not similar to the value 0.55
Answer:There is an association because the value 0.15 is not similar to the value 0.55.
Step-by-step explanation:
Which of the following rules is true for all values in the input-output table below?
A x + 1 = y
B x + 2 = y
C 2x = y
D 3x − 2 = y
Answer:
The answer is b
thank you
What is the area of this triangle? please help me.
Answer:
6
Step-by-step explanation:
Area of a triangle: bh/2
4*3/2=6
Answer:
6 units²
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here b = DE = 3 units and
h is the distance from the vertex F to DE = 4 units, hence
A = [tex]\frac{1}{2}[/tex] × 3 × 4 = 6 units²
There are bytes in a gigabyte. There are bytes in a megabyte. How many times greater is the storage capacity of a 1-gigabyte flash drive than a 1-megabyte flash drive?
Answer: third option.
Step-by-step explanation:
You know that:
- There are 10⁹ bytes in a gigabyte.
- There are 10⁶ bytes in a megabyte.
Then, to know how many times greater the storage capacity of a 1-gigabyte flash drive is than a 1-megabyte flash drive, you must divide 10⁹ bytes by 10⁶ bytes.
Remember the quotient of powers property:
[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]
Then:
[tex]=\frac{10^9}{10^6}=10^3=1,000[/tex] times greater
Answer:
1,000
Step-by-step explanation:
Choose the correct answer. Distance between 2 airports = 1,450 miles. Average speed of airplane = 350 mph. Travel time by bus after arrival at airport = 20 minutes. Total travel time = _____ hours.
Please do not round
Final answer:
Using the given information, the total travel time by airplane and bus is calculated as 4.47616 hours, which includes flying time and additional travel time by bus.
Explanation:
To calculate the total travel time by airplane including the additional travel time by bus, we must first find out the time taken by the airplane to cover the distance between the two airports. This can be done by dividing the distance by the airplane's average speed. Afterward, we add the bus travel time to get the total travel time.
The time taken by the airplane to cover 1,450 miles at an average speed of 350 mph is calculated by dividing distance by speed: 1,450 miles ÷ 350 mph = 4.142857 hours. Note that we do not round this number to maintain accuracy.
Next, we convert the bus travel time of 20 minutes into hours: 20 minutes ÷ 60 minutes per hour = 0.3333 hours.
Now, we add both the airplane and bus travel times together: 4.142857 hours + 0.3333 hours = 4.47616 hours total travel time.
1.simplifyyyyyyyyyyyy
Answer:
Choice A
Step-by-step explanation:
We apply the law of exponents;
[tex](a^{b})^{c}=a^{bc}[/tex]
[tex]\sqrt{0.08^{12}}=(0.08^{12})^{\frac{1}{2}}[/tex]
applying the law of exponents we simply multiply 12 and 1/2 to get;
[tex]0.08^{6}[/tex]
Javier’s Bakery sells donuts in packages of 3 and cookies in packages of 5 today the backers sold the same number of donuts and cookies . What is the smallest number of donuts that the bakery could have sold?please help me
The answer is A.) 5 because it’s the smaller number
Steps to convert fractions into decimals 4/25
Divide 4 by 25 either by hand or by calculator. Hope this helped.
Answer: [tex]\frac{4}{25}[/tex]=0.16
Step-by-step explanation:
How convert 4/25 into a decimal is :
4÷25 Then using Long Division for 4 divided by 25 and rounding to a Max of 3 Decimal Places gives us.Which will give you your answer as 0.16 in decimal form.:)* Hopefully this helps:)!! Mark me the brainliest:)!!!
What is the axis of symmetry for f(x) = 2x2 + 4x + 2?
Choices
x = −3
x = −1
x = 1
x = 3
Answer:
-1
Step-by-step explanation:
to find the axis of symmetry, the formula is X= -b/ 2a
a is the 2 from 2x2
and b is 4 from 4x
then plug them to the formula
-b= -4 because of the negative in -b
and 2a is 2(2)
-4/4 is -1
so x= -1
hope im right
hope it helps
Claire made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If Claire doesn’t touch the money in her account, she can find the amount she’ll have the next year by multiplying her current amount by 1.03. A) how much money will Claire have in her account after 1 year? After 2 years? B) how much money will Claire have in her account after 5 years? Explain your reasoning. C) Write an expression for the amount of money Claire would have after 30 years if she never withdraws money from that account.
We can make and use the equation: A = 160( 1.03 )^y: A = amount, 160 = amount put in, 1 + .03 = 1.03 = interest, and y as the number of years, as the money is compounded every year. (This is the compound interest equation, but I put in the numbers)
A) 160 * 1.03 = $164.80, 160 * 1.03² = $169.744 ≈ $169.74
B) 160 * 1.03⁵ = 185.48385 ≈ $185.48
The expression is the same as saying (((((160 * 1.03)1.03)1.03)1.03)1.03). This is like multiplying 160 * 1.03, which gives the amount for the first year. Then, that amount is multiplied by 1.03, which is the amount for the second year. This isi repeated until 5 years.
C) 160(1.03)³⁰
Claire will have $164.80 after 1 year and $169.74 after 2 years in her savings account due to the 3% interest rate. After 5 years, she will have $185.86. The expression for the amount after 30 years is $160 × (1.03)³⁰.
Explanation:When Claire deposited $160 into her savings account at a 3% interest rate per year, she initiated a process of compound interest. This means each year, the amount of money in her account will increase by 3% of the amount from the previous year. The way to find out how much money she will have after a certain number of years is to multiply the initial amount by 1.03 raised to the power of the number of years.
Interest After 1 Year
After 1 year: $160 × 1.03 = $164.80
Interest After 2 Years
After 2 years: $160 × (1.03)² = $169.74
Interest After 5 Years
After 5 years: $160 × (1.03)⁵ = $185.86. This is calculated using the formula for compound interest: $160 × 1.03 raised to the fifth power.
Interest After 30 Years
To write an expression for the amount of money she will have in 30 years: $160 × (1.03)³⁰. This follows the general formula for compound interest, which is the initial amount times one plus the interest rate raised to the number of years.
What is the difference between an approximate and an exact number?
Answer:
An approximate number is a close number that is only off by x number of places (Like a rounded number). An exact number is exactly correct. For example:
3 - 1.5 is approximately 2, but is exactly 1.5.
Mark Brainliest if this helps!
Final answer:
An exact number is one that is known with complete precision, such as the number of books on a shelf. An approximate number, or inexact number, includes uncertainty and comes with an error range, often due to measuring limitations such as estimating a length with a ruler. The level of rounding applies to approximate values determines their reliability, and significant figures are influenced by inexact numbers.
Explanation:
The difference between an exact number and an approximate number lies in their level of precision and the source of the number. Exact numbers are count numbers that are known with complete precision. An example of an exact number is the number of students in a classroom, which might be exactly 25. On the other hand, inexact numbers, also known as measured numbers, come with an error range due to the limitations of measuring instruments or methods. For instance, when using a ruler, you might measure a length as approximately 12.7 cm, but the true length might be slightly less or more.
It's important to note that the more rounding that is applied to a number, the less reliable it becomes. Approximations are common in various fields, including physics, where scientists and engineers make educated guesses, or 'guesstimates', based on available data and formulae with limited accuracy. These approximations are essential for problem-solving and can help in making quantitative decisions and realistic predictions.
Conversion factors in measurements are considered to be exact numbers because they are defined as such by the measurement systems. In calculations involving both exact and inexact numbers, the precision of the inexact numbers dictates the number of significant figures in the result.