Answer:
c.7 and d.5
Step-by-step explanation:
Given the following equation :
[tex]x^{2}-6x+40=6x+5[/tex]
This equation is equivalent to the following equation :
[tex]x^{2}-6x+40=6x+5[/tex]
[tex]x^{2}-6x+40-6x-5=0[/tex]
[tex]x^{2}-12x+35=0[/tex]
Given an equation [tex]ax^{2}+bx+c=0[/tex] we can find the solutions using the quadratic equation (x1 and x2 are the solutions) :
[tex]x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
Using this equations :
[tex]x^{2}-12x+35=0[/tex]
[tex]a=1\\b=-12\\c=35[/tex] ⇒
[tex]x1=\frac{-(-12)+\sqrt{(-12)^{2}-4.(1).(35)}}{2.(1)}=7[/tex]
[tex]x2=\frac{-(-12)-\sqrt{(-12)^{2}-4.(1).(35)}}{2.(1)}=5[/tex]
Given the two solutions x1 and x2 we can write the equation :
[tex]ax^{2}+bx+c=0[/tex] ⇒ [tex]a.(x-x1).(x-x2)=0[/tex] ⇒
[tex]x^{2}-12x+35=0[/tex] is equivalent to
[tex](x-7).(x-5)=0[/tex]
The solutions for this equation are 7 and 5.
Therefore, c.7 and d.5 are the solutions for this exercise.
A sculpture is shaped like a sphere with 4 cones attached to it. Several dimensions of the sculpture, in feet, are shown in the diagram below. The total height of the sculpture from top to bottom is 12 feet. What is the volume of the sculpture, to the nearest cubic foot?
volume of the center sphere = 4/3*PI*r^3
r = 3 ( given in the picture)
so 4/3 * 3.14 *3^3 = 113.04 cubic feet
volume of 1 cone: pi *r^2 *h/3
r = 3 and h=3 ( given in the picture)
so 3.14 * 3^2 * 3/3 = 28.26 cubic feet
there are 4 cones so 28.26* 4 = 113.04 cubic feet
113.04 + 113.04 = 226.08 cubic feet
rounded to nearest cubic foot = 226 cubic feet
Write the number 7362 to the nearest thousand
nx-r=p
We need to solve for x.
Calculate the theoretical probability that sum of 2 rolls equals 7
Which statements are true? Choose all answers that are correct. A. All quadrilaterals can be classified as either parallelograms or trapezoids. B. All rhombuses are parallelograms. C. Some trapezoids are parallelograms. D. Some parallelograms are squares.
Answer:
A, B and C
Step-by-step explanation:
A snail travels 3/8 feet in 1/2 hour. How many feet did the snail travel in one hour.
Kelly wants to know the actual value of a house that she wants to buy. What should she do?
for plato the answer is, c. get a real-estate appraisal
posting this for future users!
write the equation 10x+5y=5 in the slope intercept form. Then graph the line
The equation 10x+5y=5 can be rewritten in slope-intercept form as y = -2x + 1. This equation's slope is -2 and the y-intercept is 1. The line intercepts the y-axis at (0,1) and for every 1 unit increase in x, y decreases by 2 units.
Explanation:To write the equation 10x+5y=5 in slope-intercept form, you need to solve for y. The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.
First, divide the entire equation by 5 to simplify it:
(10x+5y)/5 = 5/5 becomes 2x + y = 1.
Then, solve the equation for y:
y = -2x + 1
The slope (m) of the equation is -2 and the y-intercept (b) is 1. Therefore, the line intercepts the y-axis at the point (0,1) and for every 1 unit increase in x, y decreases by 2 units due to the negative slope.
To graph this line, first plot the y-intercept at the point (0,1). Next, from this point, move right 1 unit (increase in x) and down 2 units (decrease in y) to get the point (1,-1). Draw a straight line through these points to represent the equation y = -2x + 1.
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MATH HELP!!!!!!!!!!!!!!!!!!!!!!!!1
4(50) +3r = 365
200+3r = 365
3r =165
r = 165/3
r = 55
A jar contains 3 red, 5 green, 2 blue and 6 yellow marbles. a marble is chosen at random from the jar. after replacing it, a second marble is chosen. what is the probability of choosing a green and then a yellow marble
A 2.2 GB game is being downloaded on your laptop. When you have downloaded half a gigabyte, you notice that your computer has been downloading at the rate of .01GB per minute. (A) Write an inequality that represents at least how many minutes it will take to download the game (b) Your computed only has two hours of battery life, will it be enough to download the game?
The game which is 2.2 GB will need 170 minutes to download at a rate of 0.01 GB per minute. But the computer has only 120 minutes of battery life which is insufficient.
Explanation:The total size of the game is 2.2 GB. The part that is already downloaded is 0.5 GB, so the remaining size of the game to be downloaded is 2.2 GB - 0.5 GB = 1.7 GB. Now, since the downloading speed is 0.01 GB/minute, we extrapolate the remaining time as (1.7 GB) / (0.01 GB/min) which equals 170 minutes.
(a) So, the inequality representing at least how many minutes it will take to download the rest of the game is x ≥ 170, where x is the required time in minutes.
(b) Two hours of battery life is equivalent to 2*60 = 120 minutes. Since 170 minutes is required to download the game and the available battery life is only 120 minutes, the battery will not be enough to download the game.
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Solve for x. 23=79(6x−36)+9 Enter your answer in the box.
The value of the equation 1429/237.
Let's solve for x in the given equation:
[tex]\[23 = 79(6x - 36) + 9\][/tex]
First, distribute the 79 on the right side:
[tex]\[23 = 474x - 2844 + 9\][/tex]
Combine like terms:
[tex]\[23 = 474x - 2835\][/tex]
Now, isolate the term with x by adding 2835 to both sides:
[tex]\[474x = 2858\][/tex]
Finally, divide both sides by 474 to solve for x:
[tex]\[x = \frac{2858}{474}\][/tex]
Now, you can simplify the fraction:
[tex]\[x = \frac{1429}{237}\][/tex]
So, the solution for x is [tex]\(x = \frac{1429}{237}\).[/tex]
Final answer:
To solve the equation, distribute the 79 on the right side, combine like terms, and then isolate and solve for x to get x = 6.05.
Explanation:
To solve the equation 23=79(6x−36)+9, we first expand the right side of the equation and then isolate the term with x on one side.
First, distribute the 79:
23 = 79(6x) - 79(36) + 9,
which simplifies to:
23 = 474x - 2844 + 9.
Combine like terms:
23 = 474x - 2835.
Now, add 2835 to both sides to isolate the term with x:
2868 = 474x.
Finally, divide both sides by 474 to solve for x:
x = 2868 / 474.
After performing the division, we find that x = 6.05.
Cheryl wants to purchase a par value $500 bond from Agram Imports. Agram imports bonds have a market rate of 102.114 and offer 8.1% interest. If Cheryl’s broker charges a commission of 2.5% of the market value of each bond sold, what is the current yield on Cheryl’s bond?
A. 0.077
B. 0.078
C. 0.081
D. 0.040
Answer:
the answer is A. my friends
if √a/√b=x, which statement must be true? A. x^2=a/b B. √x=a/b C. |x|=a/b D. x=a/b
Answer:
x^2 = a/b
Step-by-step explanation:
[tex]\frac{\sqrt{a}}{\sqrt{b} } =x[/tex]
If we have square root at the top and bottom then we take single square root with fraction inside
[tex]\sqrt{\frac{a}{b}} =x[/tex]
To remove square root we take square on both sides because square and square root will get cancelled
[tex]\frac{a}{b}=x^2[/tex]
x^2 = a/b is true
The statement that must be true is:
[tex]x^2 = a/b[/tex]
How to find an equivalent expression?
To find an equivalent expression, we just need to rewrite the given expression.
Here we will use the fact that the square root is distributive with respect to the division, which means that we can rewrite:
[tex]\frac{\sqrt{a} }{\sqrt{b} } = x\\\\\sqrt{\frac{a}{b} } = x[/tex]
Now if we square both sides of that expression, we will get:
[tex]\sqrt{\frac{a}{b} }^2 = x^2\\\\\frac{a}{b} = x^2[/tex]
So we can see that the correct option is A.
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Suppose you flip a coint and roll a 10-sided die. what is the probability of flipping tails and rolling a 7?
A circle has a diameter of 12mm . what is its circumference? use 3.14 for π , and do not round your answer. be sure to include the correct unit in your answer.
With a diameter of 12mm and using π as 3.14, the circumference is calculated as 37.68mm.
The circumference of a circle can be calculated using the formula:
Circumference = π x diameter
Given: Diameter = 12mm
Using π = 3.14:
Circumference = 3.14 x 12mm = 37.68mm
Therefore, the circumference of the circle is 37.68mm.
what is the perimeter of this triangle
An experienced bricklayer can construct a small wall in 4 hours. an apprentice can complete the job in 12 hours. find how long it takes if they work together.
They take 3 hours to complete the work together.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
An experienced bricklayer can construct a small wall in 4 hours.
And, An apprentice can complete the job in 12 hours.
Now,
Since, An experienced bricklayer can construct a small wall in 4 hours.
Hence, In 1 hour it will be completed 1/4 work.
And, An apprentice can complete the job in 12 hours.
So, In 1 hour it will be completed 1/12 work.
Let number of hour to complete the work together = x
in 1 hour both together completed 1/x work.
So, we can formulate;
1/4 + 1/12 = 1/x
Solve for x;
3/12 + 1/12 = 1/x
4/12 = 1/x
1/3 = 1/x
x = 3 hours.
Thus, They take 3 hours to complete the work together.
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A parchment fragment was discovered that had about 61% as much 14c radioactivity as does plant material on earth today. estimate the age of the parchment. (round your answer to the nearest hundred years.)
The estimated age of the parchment is approximately 4,086.17 years.
To estimate the age of the parchment, we can use the concept of carbon dating.
Carbon-14 (14C) is a radioactive isotope of carbon that is commonly used for dating archaeological artifacts.
The amount of 14C in an organism remains relatively constant while the organism is alive because it continuously takes in carbon from the atmosphere and food.
However, after the organism dies, it no longer takes in new carbon, and the 14C begins to decay at a known rate.
The half-life of carbon-14 is approximately 5,730 years. This means that after 5,730 years, half of the original amount of carbon-14 in a sample would have decayed.
Let's use the information provided: the parchment fragment had about 61% as much 14C radioactivity as does plant material on Earth today.
This means that the remaining 14C in the parchment is 61% of the original amount. The remaining 14C is the amount that has not yet decayed, and the rest has decayed over time.
Now, we can set up an equation:
[tex]0.61 = (1/2)^{(t/5730)[/tex]
Where:
t = time in years since the parchment was alive.
Now, we need to solve for 't.' Taking the logarithm of both sides to isolate 't':
[tex]\log(0.61) = (t/5730) \times \log(1/2)[/tex]
Now, solving for 't':
[tex]t = (5730 \times \log(0.61)) / \log(1/2)[/tex]
Using a calculator, we find:
t ≈ 4,086.17 years
So, the estimated age of the parchment is approximately 4,086.17 years.
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Using the concept of radiocarbon dating and the fact that the parchment has 61% as much 14C radioactivity as present plant material, the calculated estimate for the parchment's age is approximately 2,200 years, rounded to the nearest hundred years.
Explanation:To estimate the age of the parchment based on the information that it had about 61% as much 14C radioactivity as does plant material on Earth today, we use the concept of radiocarbon dating. The half-life of carbon-14 (14C) is 5,730 years, which means after every 5,730 years, the amount of 14C decreases by half. Given that the parchment retains 61% of its original 14C, we can formulate the decay equation to solve for the parchment's age.
The decay equation is given by: \(N_t = N_0(1/2)^{t/T}\), where \(N_t\) is the remaining amount of 14C, \(N_0\) is the original amount of 14C, \(t\) is time, and \(T\) is the half-life of 14C. In this case, \(N_t/N_0 = 0.61\), and we know \(T = 5730\) years.
By substituting the given values into the decay equation and solving for \(t\), we find that the parchment is approximately 2,200 years old, rounded to the nearest hundred years. This estimation assumes the natural 14C to 12C ratio in the atmosphere has been constant over the time period in question.
A candle is 7 in. tall after burning for 1 h. The same candle is in. tall after burning for 4 h. How tall will the candle be after burning for 6 h?
After burning 6 hours the candle will be 4 1/2 in. tall.
High School Mathematics 5+3 pts
Two runners are saving money to attend a marathon. The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. The second runner has $50 in savings and will save $60 each month.
What is the value of the function at x=−2?
y=−2
y = 0
y = 2
y = 3
Answer:
y = 2
Step-by-step explanation:
When we have graph is given also one value from x and y is given then for finding the other value, We simply see the line where x = -2 is graphed and then we will see what is the value of y there.
Here at x = -2, y = 2 this is clearly apparent from the graph.
What units would you use to describe the volume of a box measured in inches?
cubic inches or inches³ would we use to describe the volume of a box measured in inches.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law
Volume is the measure of the 3-dimensional space occupied by matter, or enclosed by a surface, measured in cubic units.
As volume we measure by using three dimensions so the unit will be in cubics.
If we have to measure volume of box in inches then it will be cubic inches or inches³.
Hence cubic inches or inches³ units would we use to describe the volume of a box measured in inches.
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The Tigers lost 15% of the 60 games that they played this season. How many games did they win?
What is (are) the x-intercepts of the function graphed above?
Answer:
The x intercepts are -4, -1 and 5 or (-4,0), (-1,0) and (5,0).
Step-by-step explanation:
Consider the provided graph.
Here we need to find the x intercepts of the function.
The x-intercepts are where the graph crosses the x-axis.
Here, the provided graph crosses the x axis 3 times.
Thus there must be 3 x intercepts of the function.
Now label the points on which graph intersect the x axis as shown in figure 1.
Thus the labeled points are (-4,0), (-1,0) and (5,0)
Hence, the x intercepts are (-4,0), (-1,0) and (5,0) or -4, -1 and 5.
What is the perimeter of a polygon with vertices at (−1, 3) , (−1, 6) , (2, 10) , (5, 6) , and (5, 3) ?
Enter your answer in the box. Do not round any side lengths.
Answer:
FOR ALL THOSE LAZY PPL, HERE'S THE ANSWER....
22 units.
Have a nice day mates.
How many ones are there in the number ab98 in base 16?
Find the value of x so the rectangles have the same area
Using formula:
Area of rectangles = width [tex]\bold{\times}[/tex] length.Using the first image to calculate the area:
[tex]\to \bold{ x\times 12 = 12x }[/tex]
Using the second image to calculate the area:
[tex]\to \bold{16\times (x-2) = 16x -32 }[/tex]
equalling both the area:
[tex]\to \bold{12x = 16x -32}\\\\\to \bold{32 = 16x -12x}\\\\\to \bold{32 = 4x }\\\\\to \bold{4x=32 }\\\\\to \bold{x=\frac{32}{4}}\\\\\to \bold{x=8}\\\\[/tex]
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Which is the endpoint of a ray?
point R
point S
point T
point U
The endpoint of a ray in the diagram given is the point S.
A ray is often referred to as the sides of a angle.
An angle is produced when two different rays share or have a common endpoint which forms the vertex.
From the diagram given above ; an angle is formed at S.
S depicts a point where three different rays meet.
Rays SR, SU and ST
SINCE , the point where two or more rays meet leading to the formation of an angle is called an endpoint. Then , point S is an endpoint.
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Evaluate the expression 15/3x-6, when x=4.
The expression 15/3x-6 evaluates to -4.75 when x=4. The solution involves substitution followed by the order of operations: first multiplication, then division, and finally subtraction.
The student asked to evaluate the expression 15/3x-6 when x=4. To do this, we first substitute the value of x into the expression, which then becomes 15/(3*4)-6.
Now we simplify the expression step by step:
Multiply 3 by 4, which is 12.Divide 15 by 12, which gives 1.25.Subtract 6 from 1.25, which results in -4.75.So, when x equals 4, the value of the expression 15/3x-6 is -4.75.