Answer:
the height would be around 19.2 cm
Step-by-step explanation:
hyp length = 63
base = 60
length = sqrt(63^2 - 60^2) = sqrt(369)
Which of the following represents a quadratic function?
a. y = 3x - 2
b. y=6+5x + x²
c. x³10x = 21
d. y= 2² +4
Answer:
○ [tex]y = 6 + 5x + x^2[/tex]
Explanation:
What is a quadratic equation?A quadratic equation is an algebraic equation where the highest power of [tex]x[/tex] is 2. The general form of a quadratic equation is as follows:
[tex]\boxed{ax^2 + bx + c = 0}[/tex],
where a, b, and c represent known constants, and [tex]x[/tex] is the unknown.
In this question, if you take a look at the second option, you will see that it is possible to rearrange the equation to make it look the general form:
[tex]y = 6 + 5x + x^2[/tex]
⇒ [tex]y = x^2 + 5x + 6[/tex]
Therefore, this equation is quadratic.
The other three options are not quadratic equations because none of them have an [tex]x^2[/tex] term in them.
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
[tex]\leadsto[/tex] A quadratic equation is an algebraic equation of the second degree. The formula is:
▪ [tex]\longrightarrow \sf{y = ax^2 + bx + c}[/tex]
This can also be written as:
▪ [tex]\longrightarrow \sf{y = c + bx+ax^2}[/tex]
Comparing the equation above with each of the options, the equation that represents a quadratic function is:
[tex]\longrightarrow \sf{y=6+5 + x^2}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex] \large\bm{b. \: y=6+5x + x^2}[/tex]
A balloon has a circumference of 28 in use the circumference to approximate the surface area of the ballon to the nearest square inch
The surface area of the balloon is 249 in².
What is the surface area of the balloon ?A balloon has the shape of a sphere. The distance round the sphere is equal to the circumference of the sphere.
Circumference of the sphere = 2πr
Where:
r = radius π = pi = 22 / 7Radius - circumference / 2π
28 / ( 2 x 22/7) = 4.45 inches
Surface area of a sphere = 4πr²
4 x 22/7 x 4.45² = 249 in²
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Name plane K using three noncollinear points.
Answer:
plane HNA, HMB, ANG ...
Step-by-step explanation:
Any combination of three points on plane K will work unless all three are on the same line.
Find the nth term of the arithmetic sequence -1, 2, 5,.. ..
Answer:
8
Step-by-step explanation:
i think it's 8 but I'm not sure i will check it for you
Find the measure of Angle BAC.
Applying the inscribed angle theorem, the measure of angle BAC is: 110°.
What is the Inscribed Angle Theorem?According to the inscribed angle theorem, the measure of angle BAC is half the measure of the intercepted arc, x + 50°.
x - 30 + x + 50 = 360
2x + 20 = 360
2x = 360 - 20
2x = 340
x = 170
m∠BAC = 1/2(x + 50)
Plug in the value of x
m∠BAC = 1/2(170 + 50)
m∠BAC = 110°
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A 13km stretch of road needs repairs. Workers can repair 3 1/2 km of road per week.
How many weeks will it take to repair this stretch of road?
The computation shows that the number of weeks that it take to repair this stretch of road will be 4 weeks.
How to compute the number of weeks?From the information given, we are told that a thirteen kilometers stretch of road needs repairs and that the workers can repair three and half kilometers of road per week.
The question is simply for us to calculate the number or weeks that it will take to be able to repair the stretch of road.
Therefore, based on the information given, it should be noted that to get the number of weeks that will be used to repair the road, we simply have to divide the total distance or the road by the distance that is repaired every week.
Therefore, the number of weeks that it will take to be able to repair this stretch of road will be:
= 13/3.5
= 3.7
= 4 weeks approximately
Therefore, based on the information given, the number of weeks that's required is 4 weeks.
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Jolene set up a retirement account. She arranged to have $350 taken out of each of her monthly checks; the account will earn 2.1 % interest compounded monthly. She just turned 33 and her ordinary annuity comes to term when she turns 60. Find the value of her retirement account at that time
Answer:
$152,419.36
Step-by-step explanation:
The future value of an ordinary annuity is given by the formula ...
FV = P((1 +r/12)^(12t) -1)/(r/12)
where P is the monthly payment, r is the annual interest rate, and t is the number of years.
Annuity valueFor P = 350, r = 0.021, and t = 27 (years to retirement age), the value is ...
FV = 350((1 +0.021/12)^324 -1)/(0.021/12) ≈ $152,419.36
The value of Jolene's retirement account when she turns 60 will be $152,419.36.
For the function given below, find a formula for the Riemann sum obtained by dividing the interval (0, 3) into n equal subintervals and us right-hand endpoint for each Then take a limit of this sum as c_{k}; n -> ∞ to calculate the area under the curve over [0, 3] . f(x) = 2x ^ 2 Write a formula for a Riemann sum for the function f(x) = 2x ^ 2 over the interval [0, 3]
Splitting up [0, 3] into [tex]n[/tex] equally-spaced subintervals of length [tex]\Delta x=\frac{3-0}n = \frac3n[/tex] gives the partition
[tex]\left[0, \dfrac3n\right] \cup \left[\dfrac3n, \dfrac6n\right] \cup \left[\dfrac6n, \dfrac9n\right] \cup \cdots \cup \left[\dfrac{3(n-1)}n, 3\right][/tex]
where the right endpoint of the [tex]i[/tex]-th subinterval is given by the sequence
[tex]r_i = \dfrac{3i}n[/tex]
for [tex]i\in\{1,2,3,\ldots,n\}[/tex].
Then the definite integral is given by the infinite Riemann sum
[tex]\displaystyle \int_0^3 2x^2 \, dx = \lim_{n\to\infty} \sum_{i=1}^n 2{r_i}^2 \Delta x \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac6n \sum_{i=1}^n \left(\frac{3i}n\right)^2 \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac{54}{n^3} \sum_{i=1}^n i^2 \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac{54}{n^3}\cdot\frac{n(n+1)(2n+1)}6 = \boxed{18}[/tex]
PLEASE HELP I WILL BE SO THANKFUL
Hydrogen gas has a density of 0.090/gL, and at normal pressure and 0.214°C one mole of it takes up 22.4L. How would you calculate the moles in 370.g of hydrogen gas?
Set the math up. But don't do any of it. Just leave your answer as a math expression.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The number of moles of hydrogen is 185 moles.
What is the number of moles?We know that the mole refers to the number of elementary entities that make up a substance. According to Avogadro, one mole of a substance contains 6.02 * 10^23 elementary entities which includes atoms, molecules and ions.
Now, we know the number of moles is obtained as the ratio of the mass to the molar mass of the substance.
Thus;
Mass of hydrogen = 370.g
Molar mass of hydrogen = 2 g/mol
Number of moles of hydrogen = 370.g/2 g/mol = 185 moles
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Find the value of x.
answer choices
A. 70
B. 65
C. 30
D. 40
The value of x is 70°. The correct option is A. 70
Circle GeometryFrom the question, we are to determine the value of the measure of arc x
From one of the circle theorems, we have that
The angle subtended by an arc at the center is twice the angle subtended by it at any point on the circumference.
First, we will determine the value of the third angle in the triangle formed.
Let the angle be y
y + 15° + 20° = 180°
∴ y = 180° - 15° - 20°
y = 145°
Now, the angle supplementary to this is the angle the arc subtends at the circumference.
Thus,
The angle at the circumference = 180° - 145°
The angle at the circumference = 35°
From the above theorem, we can conclude that the angle subtended by the arc at the center of the circle is 2 × 35° = 70°
∴ The measure of the arc is 70°
This is the value of x
Hence, the value of x is 70°. The correct option is A. 70
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Find the slope of a line parallel to the line that crosses ( 3 , − 2 ) and the y -intercept is ( 0 , − 3 ) . I finally figured out how to write my equations in slope intercept form and NOW this pops up, can someone please explain it to me
Answer:
y = 1/3x - 3
Step-by-step explanation:
We can find the equation of the line, by finding the slope and combine with our y-intercept (-3).
We need to use the slope formula to find the slope.
Thus, we have (-3 - (-2)) / 0 - 3 = -1/-3 = 1/3
So our equation is y = -1/3x - 3
Can u guys please give me the correct answer
Answer:
∠ 3 = 65°
Step-by-step explanation:
∠ 2 and 115° are a linear pair and sum to 180° , that is
∠ 2 + 115° = 180° ( subtract 115° from both sides )
∠ 2 = 65°
∠ 2 and ∠ 3 are corresponding angles and and are congruent , then
∠ 3 = 65°
sirs is making lemonade to sell at her lemonade stand. she made a batch of 8 pitchers of lemonade using 24 lemons, 12 cups of sugar, and 20 liters of water. she decides to make a second batch of 6 pitchers of lemonade. how many liters of water should she use to make the second batch of lemonade?
Answer:15
Step-by-step explanation: 20 divided by 8=2.5 x 6=15
Find the dy/dx using implicit differentiation
x³-3x²y+2xy² = 12
The dy/dx of equation [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex] is [tex](6xy-3x^{2} -2y^{2} )/(4xy-3x^{2})[/tex].
Given an equation [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex].
We are required to find dy/dx of the equation.
Equation is like a relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c.
Differentiation is basically finding the change in variables.
It may be linear equation, quadratic equation,cubic equation or many more depending on the power of the variable present in the equation.
Equation:[tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex]
Differentiating with respect to x.
3[tex]x^{2}[/tex]-3([tex]x^{2}[/tex]*dy/dx+y*2x)+2(x*2y*dy/dx+[tex]y^{2}[/tex])=0
3[tex]x^{2} -3x^{2} dy/dx-6xy+4xy dy/dx+2y^{2}[/tex]=0
Taking dy/dx at one side and take the other part to other end.
[tex]-3x^{2} dy/dx+4xy dy/dx[/tex]=[tex]6xy-3x^{2} -2y^{2}[/tex]
dy/dx=[tex](6xy-3x^{2} -2y^{2})/(4xy-3x^{2} )[/tex]
Hence the dy/dx of equation [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex] is [tex](6xy-3x^{2} -2y^{2} )/(4xy-3x^{2})[/tex].
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Please help!
(02.01 HC)
Quadrilateral ABCD is located at A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2). The quadrilateral is then transformed using the rule (x + 7, y − 1) to form the image A'B'C'D'. What are the new coordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments. (10 points)
Using translation concepts, it is found that:
The new coordinates of A' are: (5,0).The new coordinates of B' are: (5,2).The new coordinates of C' are: (9,2).The new coordinates of D' are: (9,0).Since there are only two values for the x-coordinates and two values for the y-coordinates, if the corresponding vertices were connected with line segments, a rectangle would be formed.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The rule applied for each vertex of the rectangle is given as follows:
(x,y) -> (x + 7, y - 2).
The new coordinates of A' are given as follows:
(-2 + 7, 2 - 2) = (5,0).
The new coordinates of B' are given as follows:
(-2 + 7, 4 - 2) = (5,2).
The new coordinates of C' are given as follows:
(2 + 7, 4 - 2) = (9,2).
The new coordinates of D' are given as follows:
(2 + 7, 2 - 2) = (9,0).
Since there are only two values for the x-coordinates and two values for the y-coordinates, if the corresponding vertices were connected with line segments, a rectangle would be formed.
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1/2-1/6
Jzjzhhzhzhzhhz
Answer:
ummm the answer is very simple
The answer is 0/6
Step-by-step explanation:
[tex] \frac{1}{2 \times 3} - \frac{1}{6} [/tex]
[tex] \frac{1}{6} - \frac{1}{6} [/tex]
[tex]1 - 1 = \frac{0}{6} [/tex]
Can someone help me with this problem from Khan Academy?
Given that the graph shows P as a function of n, we have:
a. The more hot dogs that is sold, his profit increases.
b. Jimmy sells the hot dog for $1 each.
c. Jimmy needs to sell 16 hot dogs to recover the $8 he invested.
d. He would make a profit of $7.
e. The number of hot dogs he needs to sell is: 20.
What is a Linear Function?A linear function is expressed as, y = mx + b, where y is a function of x, m is the unit rate, and b is the starting value or initial value of the function.
We are given that profit, P, is a function of the number of hot dogs sold, n.
a. The graph of the function slopes upwards, so this means that the more hot dogs that is sold, his profit increases.
b. Cost of 1 hot dog = Unit rate = change in y / change in x = 2 units/2 units
Cost of 1 hot dog = Unit rate = 1
Thus, Jimmy sells the hot dog for $1 each.
c. If you trace profit (P) on the graph when it is $8, the corresponding number of hot dogs, n, would be 16.
So, Jimmy needs to sell 16 hot dogs to recover the $8 he invested.
d. When n = 15, P, from the graph would be 7.
Thus, if Jimmy sells 15 hot dogs, he would make a profit of $7.
e. When P = 12, from the graph, the corresponding n value is 20.
Therefore for Jimmy to make $12, the number of hot dogs he needs to sell is: 20.
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Dominique has been working at an regular rate of $14. He works 54 hours per week and is paid time and a half for overtime. What is Dominique's average hourly rate?
Based on the given task content about the average hourly rate, Dominique's average hourly rate is $0.26.
Average hourly rateRegular rate of Dominique payment = $14Number of hours worked = 54 hoursAverage hourly rate = Regular rate of Dominique's payment ÷ Number of hours worked
= $14 / 54 hours
= 0.25925925925925
Approximately,
Average hourly rate = $0.26
Therefore, Dominique's average hourly rate is $0.26
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When the equation a-bx=cx
+d is solved for x, the result is
Answer:
x=a-d/c+b
Step-by-step explanation:
a-bx =cx+d
collect like terms
a-d=cx+bx
a-d=x(c+b)
x=a-d/c+b
Attached as a photo.
Applying the initial conditions, the specific solution is:
[tex]y = e^{-2x}(-3\sin{3x} + 4\cos{3x})[/tex]
What is the general solution?The general solution is given by:
[tex]y = e^{-2x}(C_1\sin{3x} + C_2\cos{3x})[/tex]
How to find the specific solution?We apply the initial conditions to find the specific solution.
First, we have that y(0) = 4, then:
[tex]4 = e^{-2(0)}(C_1\sin{3(0)} + C_2\cos{3(0)})[/tex]
Since cos(0) = 1, we have that:
[tex]C_2 = 4[/tex]
Then:
[tex]y = e^{-2x}(C_1\sin{3x} + 4\cos{3x})[/tex]
The derivative is:
[tex]y^\prime(x) = -2e^{-2x}(C_1\sin{3x} + 4\cos{3x}) + e^{-2x}(3C_1\cos{3x} - 4\sin{3x})[/tex]
Since y'(0) = -17, then:
[tex]-17 = -8 + 3C_1[/tex]
[tex]3C_1 = -9[/tex]
[tex]C_1 = -3[/tex]
Then the specific solution is:
[tex]y = e^{-2x}(-3\sin{3x} + 4\cos{3x})[/tex]
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What is the solution to the equation 4 + = 6? y = 1 y = 4 y = 500 y = 2000
Step-by-step explanation:
pls make did make sense, darling!!
Find the value of x in the triangle shown below.
x =
98°
27°
Answer: 55
Step-by-step explanation: There is one simple theorem we need to know in order to solve for this.
Triangle Angle-Sum Property: All three angles interior angles of a triangle add up to 180°.
Thus, we could label the points A, B, and C, and set up an algebraic expression.
Let A = 27, B = 98, and C = x.
A + B + C = 180°.
Substituting A, B, and C we get:
27 + 98 + x = 180°.
Adding, we get:
125 + x = 180°
Subtracting 125 by 180, we get:
x = 55°
Thus, the angle X is 55°.
We could have simply solved this by just doing 180 - 98 - 27 = 55 in the first place, but I wanted to show you how I got such results.
Give the standard form for 7000+300+40+2
Answer:
7×10³+3×10²+4×10¹+2×10 or 7.342×10³
FIND THE INDICATED PROBABILITY FOR THE FOLLOWING:
A) IF P(A OR B) = 0.6, P(B) = 0.3, AND P(A AND B) = 0.1, FIND P(A).
The value of the probability P(A) is 0.40
How to determine the probability?The given parameters about the probability are
P(A or B) = 0.6
P(B) = 0.3
P(A and B) = 0.1
To calculate the probability P(A), we use the following formula
P(A and B) = P(A) + P(B) - P(A or B)
Substitute the known values in the above equation
0.1 = 0.3 + P(A) - 0.6
Collect the like terms
P(A)= 0.1 - 0.3 + 0.6
Evaluate the expression
P(A)= 0.4
Hence, the value of the probability P(A) is 0.40
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Investments increase exponentially by
about 26% every 3 years. If you made a
$2,000 investment, how much money
would you have after 45 years?
Future Amount = $[?]
Hint: Future Amount = [(1 + r)t
-pt
↑
initial
amount
growth
rate
←time
periods
Round to the nearest dollar.
Answer:
9060$ is the final amount because 7060 is the interest
The amount of money after 45 years will be $64,060.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Investments increase exponentially by about 26% every 3 years.
If you made a $2,000 investment.
Then the equation will be
[tex]\rm A = 2000 \times \left (1.26 \right )^{\frac{t}{3}}[/tex]
Where t is the number of years.
Then the amount of money after 45 years will be
[tex]\rm A = 2000 \times \left (1.26 \right )^{\frac{45}{3}}[/tex]
Simplify the equation, then we have
A = 2000 × (1.26)¹⁵
A = 2000 × 32.03
A = $64,060
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Mira buys a gold ring for ₹ $8740$ inclusive of $15\%$ tax. The ring was sold at a discount of $5\%$ .
What is the marked price of the ring? ₹
The marked price of the ring given the cost as 8740 inclusive of 15% tax and discount of 5% is $7,283.3.
Marked priceCost of the gold ring = $8740Tax = 15%Discount = 5%Marked price = x8740 = x + (15% of x) + (5% of x)
8740 = x + (0.15x) + (0.05x)
8740 = x + 0.15x + 0.05x
8740 = 1.20x
x = 8740 / 1.20
x = 7283.33333333333
Approximately,
x = $7,283.3
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Miriam charges $5 per trip for deliveries plus $0.50 per mile, If x= the number of miles
Miriam drives for a trip and y = the total cost for a trip, which of these ordered pairs is a
solution to the equation that describes this situation? (1 Point)
(10, 10)
(2,7)
(12, 12)
(5, 6.5)
Answer:
(10,10)
Step-by-step explanation:
y = .5x + 5
If you put in 10 for x, we get 10 for y.
y = .5(10) + 5
y =5 + 5
y = 10
When x is 10, y is 10 (10,10)
m..................................find the value of x ...y and z..
Step-by-step explanation:
x =130.......................
This box plot represents the number of pages that several students in sixth grade have read in a month. Use the shape of the box plot to describe the data set. Select all that apply.
The total range of pages read is 20 .
The lowest quarter of data is more dispersed than the highest quarter of data.
One-half of the students have read between 72 and 86 pages.
The median number of pages of the sixth graders is 76.
One-fourth of the students have read weigh 72 and 76 pages.
One-fourth of the students read more than 76 pages.
One-fourth of the students have read less than 72 pages.
The true statements are:
The median number of pages of the sixth graders is 76.
One-fourth of the students have read less than 72 pages.
One-half of the students have read between 72 and 86 pages.
What are the true statements?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers.
The end of the first line represents the minimum number and the end of the second line represents the maximum number. The difference between the minimum number and the maximum number is the range.
Range = 92 - 61 = 31
On the box, the first line to the left represents the lower (first) quartile. 1/4 of the score represents the lower quartile. The next line on the box represents the median. 1/2 of the score represents the median. The third line on the box represents the upper (third) quartile. 3/4 of the scores represents the upper quartile.
First quartile = 72
Third quartile = 86
Median = 76
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find the fourth roots of i
Answer:
1∠22.5°, 1∠112.5°, 1∠202.5°, 1∠292.5°
Step-by-step explanation:
A root of a complex number can be found using Euler's identity.
ApplicationFor some z = a·e^(ix), the n-th root is ...
z = (a^(1/n))·e^(i(x/n))
Here, we have z = i, so a = 1 and z = π/2 +2kπ.
Using r∠θ notation, this is ...
i = 1∠(90° +k·360°)
and
i^(1/4) = (1^(1/4))∠((90° +k·360°)/4)
i^(1/4) = 1∠(22.5° +k·90°)
For k = 0 to 3, we have ...
for k = 0, first root = 1∠22.5°
for k = 1, second root = 1∠112.5°
for k = 2, third root = 1∠202.5°
for k = 3, fourth root = 1∠292.5°