Find the directrix of the parabola y = (1/8)(x – 5)2 - 3.
Answer:
y= -5
Step-by-step explanation:
rewrite as standard form [tex]4.2(y-(3-))=(x-2)^{2}[/tex]
(h.k) = (2, -3), P=2
y= -3 -P
y= -3 -2
y= -5
A first grader measures 1 meter high how much bigger is a first grader compared to the height of a book
To solve this problem, we would be needing the actual height or size of the book which is not given in the problem. However for the sake of calculation let us assume that the average height of a book is 8.5 inches.
Then the next step we have to do is to convert the height of the first grader from units of meter to units of inches. We know that:
1 meter = 39.37 inches
Therefore the height of the first grader is 39.37 inches.
Taking the ratio with the bigger number in the numerator (height of the 1st grader / height of the book):
ratio = 39.37 inches / 8.5 inches
ratio = 4.63
Therefore this means that the first grader is about 4.63 times taller than the book.
a machine fills 150 bottles of water every 8 minutes. How many minutes will it take this machine to fill 675 bottles?
John received $0.76 change from a purchase in the drugstore. if he received eight coins, and five of the coins are the same denomination, how many quarters did he receive?
5 nickels , 2 quarters, and 1 pennies = 8 coins.
he received 2 quarters
If $10,000 is invested in an account at the rate of 6.25% compounded monthly, then the amount after 15 years is approximately
The amount after 15 years is approximately $26,971.67.
Explanation:To calculate the amount after 15 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amountP = the principal amount (initial investment)r = annual interest rate (in decimal form)n = number of times interest is compounded per yeart = number of yearsIn this case, P = $10,000, r = 0.0625 (6.25% as a decimal), n = 12 (monthly compounding), and t = 15. Substituting these values into the formula:
A = $10,000(1 + 0.0625/12)^(12*15) = $26,971.67 (approximately).
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How do i graph the line y=2/3x+ 490 using the slope intercept method?
Graph of the line [tex]y = \frac{2}{3} x+490[/tex] is drawn with slope [tex]m = \frac{2}{3}[/tex] and y-intercept 490 and x-intercept = -735.
What is slope?
"Slope of the line is defined as the ratio of difference in the increment in y coordinates to the difference in increment in x-coordinates."
Formula used
standard equation of line
y = mx + c
m = slope of the line
c = y- intercept
According to the question,
Given equation of line,
[tex]y = \frac{2}{3} x+490[/tex]
Compare it with standard equation of line y = mx + c we get,
Slope [tex]m = \frac{2}{3}[/tex]
y-intercept = 490
Calculate x-intercept by putting y=0
x-intercept = -735
Now plot it on the graph as shown and join the points with slope [tex]m = \frac{2}{3}[/tex]
Hence, graph of the line [tex]y = \frac{2}{3} x+490[/tex] is drawn with slope [tex]m = \frac{2}{3}[/tex] and y-intercept 490 and x-intercept = -735.
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Given the function g(x) = 4(3)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.
A) Find the average rate of change of each section. (4 points)
Line PQ has endpoints at P (-2,3) and Q (4,1). The center of dilation is (-1,4) and the scale factor is 2. What are the coordinates of the endpoints of P'Q'?
Write the equation of a hyperbola with vertices (0, -4) and (0, 4) and foci (0, -5) and (0, 5).
HELP PLEASE THANKS (;
The photo printed has length of 6 imams width of 4. A smaller picture is printed the ratio of the new picture to the size of the first picture is 1.5 to 2. What's the length and width of the new picture?
The new picture will have a length of 4.5 inches and a width of 3 inches.
There is asking about the size of a scaled-down photo in comparison to the original photo that has a length of 6 inches and a width of 4 inches. Given the ratio of the new picture to the size of the first picture is 1.5 to 2, we need to calculate the new dimensions.
The scale factor from the original to the new photo is 1.5 / 2, which simplifies to 0.75. Thus, we multiply the original dimensions by 0.75 to find the dimensions of the new picture:
Length of new picture = 6 inches * 0.75 = 4.5 inches
Width of new picture = 4 inches * 0.75 = 3 inches
There are exactly four positive integers $n$ such that \[\frac{(n + 1)^2}{n + 23}\] is an integer. Compute the largest such $n$.
To find the largest positive integer $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer, we need to find the largest perfect square that is less than or equal to $n + 23$. The largest such $n$ is $41$.
Explanation:To find the largest positive integer $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer, we can start by considering the numerator. The expression $(n + 1)^2$ is a perfect square, so it will always be divisible by $n + 23$ if $n + 23$ is also a perfect square. Therefore, we need to find the largest perfect square that is less than or equal to $n + 23$.
Let's consider some examples. If $n + 23 = 25$, then $n = 2$. If $n + 23 = 36$, then $n = 13$. If $n + 23 = 49$, then $n = 26$. If $n + 23 = 64$, then $n = 41$. Therefore, the largest value of $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer is $41$.
There are no positive integers $n$ that satisfy the given condition, and we cannot compute the largest such $n$.
To find the largest positive integer $n$ such that $\frac{(n + 1)^2}{n + 23}$ is an integer, we need to consider the factors of the numerator and denominator.
Let's expand the numerator, $(n + 1)^2$, using the binomial expansion formula:
$(n + 1)^2 = n^2 + 2n + 1$
Now, we divide this expression by $n + 23$ and express the result as an integer:
$\frac{n^2 + 2n + 1}{n + 23}$
We can use polynomial long division to divide $n^2 + 2n + 1$ by $n + 23$:
- (n - 21)
__________
n + 23 | n^2 + 2n + 1
- (n^2 + 23n)
_____________
-21n + 1
- (-21n - 483)
_____________
484
We obtain a remainder of 484. In order for the fraction to be an integer, the remainder must be 0. However, in this case, the remainder is not 0, which means that $\frac{(n + 1)^2}{n + 23}$ is not an integer for any positive integer $n$.
Therefore, there are no positive integers $n$ that satisfy the given condition, and we cannot compute the largest such $n$.
Complete question :-
There are exactly four positive integers $n$ such that \[\frac{(n + 1)^2}{n + 23}\] is an integer. Compute the largest such $n$.
What can you say about the nature of any other zeros of the quadratic equation ax^2+bx+c=0 , which has one complex zero? Explain your answer.
Katie earned $54.30 in interest from two accounts. One account Paid 4.1% apr and the other paid 3.2% apr. if she had a total of $1500 in the two accounts, How much was in each account?
How many pints of blood does a person have for every 14 pounds of body weight?
Answer:
[tex]1[/tex] units.
Step-by-step explanation:
Here body weight is 14 pounds =[tex]\frac{14}{2.205}[/tex] kg =[tex]6.35[/tex] kg (∵ 1 kg ≈ 2.205 ponds ).
Normally, 75 ml of blood needs, if the body weight is 1 kg. Therefore total amount of blood for the body weight 14 pounds [tex](6.35 kg) = 6.35*75 ml=476.25 ml[/tex] [tex]=.47625 l[/tex] and we know that 1 litter of blood =2.11338 point of blood.
Hence total amount of blood = [tex]0.47625*2.11338[/tex] points =[tex]1.006497[/tex] units≈ [tex]1[/tex] units.
He ratio of the lengths of the corresponding sides of two rectangles is 8:3. the area of the larger rectangle is 320 ft2. what is the area of the smaller rectangle? 120 ft2 30 ft2 90 ft2 45 ft2
80 POINTS!
Create a factorable polynomial with a GCF of 2y. Rewrite that polynomial in two other equivalent forms. Explain how each form was created. (give the polynomial with the GCF of 2 AND give two more forms and explain how you got it.
which equation of a circle represents the graph?
The equation of circle will be;
⇒ x² + y² = 25
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The circle is shown in figure.
Centre of circle = (0, 0)
Radius of circle = 5
Now,
We know that;
The standard form of circle with radius 'r' and center (h, k) is,
⇒ (x - h)² + (y - k)² = r²
Hence, The equation of circle with radius '5' and center (0, 0) is,
⇒ (x - 0)² + (y - 0)² = 5²
⇒ x² + y² = 25
Thus, The equation of circle will be;
⇒ x² + y² = 25
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(08.02)How many solutions are there for the system of equations shown on the graph?
No solution
One solution
Two solutions
Infinitely many solutions
Answer:
The system of equations has no solution
Step-by-step explanation:
We have to find the number of solutions of system of equations shown in the graph.
Since, the number of solutions of system of equations is that point of thew graph on which the graph of two equations meet.
Since, we can see from the graph the two lines are parallel
Hence, they can never meet.
Hence, the system of equations has no solution.
Hence, first option is correct.
a segment is divided into two parts having lengths in the ratio of 5:3. if the difference between the lengths of the parts is 6 " find the length of the longest part
The length of the longest part is 15 units.
The length of the longest part in a segment divided into parts in the ratio of 5:3 with a difference of 6 units is 15 units.
The length of the longest part is 15 units.
Let the lengths of the two parts be 5x and 3x.Since the difference between them is 6, we can set up the equation 5x - 3x = 6.Solving for x gives x = 3, so the longest part is 5x = 5 * 3 = 15 units.Please help me I'm so confused and it's due at 7:30
At what angle do the angle bisectors of two same side interior angles intersect in construction with two parallel lines and a transversal?
Find the volume of a cylinder with a diameter of 8 inches and a height that is three times the radius round to the nearest hundredth
volume for cylinder = pi x r^2 x h
radius = half the diameter = 8/2 =4
height = 3 times the radius = 3*4 =12
using 3.14 for pi
volume = 3.14 x 4^2 x 12 = 602.88 cubic inches
Mike forgot to replace the cap on a bottle of room freshener. The room freshener began to evaporate at the rate of 15% per day. If the original amount of room freshener in the bottle was 40 grams, which of the following graphs best represents the amount of room freshener f(x) that would remain in the bottle after x days?
graph of function f of x equals 30 multiplied by 0.88 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis
graph of function f of x equals 50 multiplied by 0.82 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis
The person under is wrong but there chart is right. 100%-15%=85%
85%=.85
F(x)= 40(.85)^x
Write that in desmos graphing and you will get the chart.
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can anyone help me calculate AC, AD, and EC?
AC = sqrt(56^2 + 33^2) = 65cm
EC = sqrt(65^2 - 16^2) = 63 cm
to find AD 33-25 = 8
8^2 + 56^2 = AD^2
64 + 3136=3200^2
square root (3200) = 56.5685 round off to 56.6cm
Prove that for any x in the reals 5 divides x if and only if 5 divides x squared
Find the area of the circle. Leave your answer in terms of pi diameter is 4.1 m
Answer:
Area of the circle will be (4.20 [tex]\pi[/tex])
Step-by-step explanation:
We have to find the area of the circle with diameter given is 4.10 m.
Since radius of a circle is represented by [tex](\frac{diameter}{2})[/tex]
Therefore, radius of the circle = [tex](\frac{4.1}{2})[/tex] = 2.05 m
Formula of the area of a circle is A = [tex]\pi r^{2}[/tex]
So area of the circle with radius 2.05 m will be
A = [tex]\pi (2.5)^{2}[/tex]
= 4.20 [tex]\pi[/tex]
Area of the circle will be (4.20 [tex]\pi[/tex])
One of the acute angles of a right triangle is 50° and its hypotenuse is 7 inches. find the lengths of its legs to the nearest tenth of an inch.
Final answer:
To determine the lengths of the legs of a right triangle with a hypotenuse of 7 inches and an acute angle of 50°, we use the trigonometric functions cosine and sine. The adjacent leg (A) is approximately 4.5 inches and the opposite leg (B) is approximately 5.4 inches, both to the nearest tenth.
Explanation:
The student asked: "What are the lengths of the legs of a right triangle if one of the acute angles is 50° and the hypotenuse is 7 inches?"
To find the lengths of the legs of a right triangle, we can use trigonometry. The cosine of an angle in a right triangle is equal to the adjacent leg divided by the hypotenuse, and the sine of an angle is equal the opposite leg divided by the hypotenuse.
Since we know the hypotenuse (7 inches) and one acute angle (50°), we can find:
the length of the opposite leg (leg B) using sine (sin(50°) = leg B / 7 inches).
By solving these equations:
leg A = cos(50°) × 7 inches
leg B = sin(50°) × 7 inches
After calculating, we find:
leg A ≈ 4.5 inches (to the nearest tenth)
leg B ≈ 5.4 inches (to the nearest tenth)
In four to five sentences, explain some of the factors that cause shifts in supply and demand and what the effects of these shifts are.
Answer:
Sample Response: Shifts in supply and demand occur when the amount of goods available increases or decreases, or when the demand for a particular good increases or decreases. Shifts in supply can happen when consumers change their spending habits, when competitors produce similar goods, or when the availability of labor or resources changes. Shifts in demand occur when the price changes or when the number of people trying to buy the good changes. It can also happen when people's tastes change.
Which graph represents the function of f(x) = 9x 2 -36/3x+6 Please help
The given function is a quadratic equation, not a linear one, and so it would be represented by a parabolic curve on a graph, not a straight line.
Explanation:The function you're asking about, f(x) = 9x² - 36/3x + 6, is a quadratic equation. Quadratic equations are represented by parabolas on the graph not a straight line. Parabolas usually have a shape like a U (or an upside down U, depending on the equation).
The equation you've given should result in a parabolic graph. The straight line equations and graphs you’re referring to, like y = 9+3x, would not represent your function. The line graph with a y-intercept of 9 and a slope of 3 is not a representation of your function.
Also, it's important to note that the equation you provided, f(x) = 9x² - 36/3x + 6, can be simplified to f(x) = 9x² - 12x + 6.
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