Answer:
use vertex form of parabola:
y=a%28x-h%29%5E2%2Bk....if vertex (0,7), we have
y=a%28x-0%29%5E2%2B7
y=ax%5E2%2B7......use point (3,2) to find a
2=a%2A3%5E2%2B7
2=9a%2B7
2-7=9a
-5=9a
a=-5%2F9
so, your equation is: y=-%285%2F9%29x%5E2%2B7
Step-by-step explanation:
2^2x = 2^3 ,what is the value of x?
Answer:
[tex]x = \frac{3}{2} [/tex]
Step-by-step explanation:
[tex] {2}^{2x} = {2}^{3 } \\ 2x = 3 \\ x = \frac{3}{2} [/tex]
please help!!! will mark brainliest. only 2 questions, and worth 50 pts.
Answer:
1) 13,434
2) During 2038 (by 2039)
Step-by-step explanation:
We can model this problem using an exponential equation.
General form of an exponential equation: [tex]y=ab^x[/tex]
where:
a is the initial value b is the base (or growth factor) in decimal formx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
As the population increases by 3% each year, each year it will be 103% of the previous year. Therefore, the growth factor in decimal form is 1.03
Given:
a = 8,888b = 1.03 x = time (in years)y = populationSubstituting the given values into the equation:
[tex]y=8888(1.03)^x[/tex]
To find the population in 2025:
2025 - 2011 = 14
Therefore, set x = 14 and solve for y:
[tex]\begin{aligned}\implies y &=8888(1.03)^{14}\\& =13433.89747\\& = 13,434\end{aligned}[/tex]
To find the year in which the population will reach 20000, set y = 20000 and solve for x:
[tex]\implies 8888(1.03)^x=20000[/tex]
[tex]\implies (1.03)^x=\dfrac{20000}{8888}[/tex]
[tex]\implies \ln (1.03)^x=\ln \left(\dfrac{20000}{8888}\right)[/tex]
[tex]\implies x\ln (1.03)=\ln \left(\dfrac{20000}{8888}\right)[/tex]
[tex]\implies x=\dfrac{\ln \left(\frac{20000}{8888}\right)}{\ln (1.03)}[/tex]
[tex]\implies x=27.43785809[/tex]
2011 + 27.437... = 2038.437...
Therefore, the population will reach 20,000 some time during 2038.
. Find (x² + 7x + 14) ÷ (x + 4) by using long division
[tex]\dfrac{x^2 +7x +14 }{x+4} = x+3+ \dfrac{2}{x+4}[/tex]
what is the second step to solving this equation 9x -23 = 49 A subtract 23 from both sides. B multiply both sides by nine. C divide both sides by nine. D Add 23 to both sides.
Answer:
C- divided both sides by 9
Step-by-step explanation:
[tex]9x - 23 = 49[/tex]
[tex] 9x = 72[/tex]
[tex]x = 8[/tex]
A line passes the points (0, 11) and (12,-13). Can you write the equation of a line passing through
the point (4, 3) so that the system of equations represented by the two lines has no solution? If so,
give the equation. Otherwise, coxplain why not,
7)
72, 43, 15, 66, 32, 72, 52, 19, 28, 81
Mean :
Median
Mode
Range
If the measure of angle B=35 degrees, a=43, and c=19 then find the measure of angle A
Answer: 123.3364311 degrees approximately
Round that value however your teacher instructs.
==========================================================
Explanation:
Use the law of cosines to find side b
[tex]b^2 = a^2 + c^2 - 2*a*c*\cos(B)\\\\b^2 = 43^2 + 19^2 - 2*43*19*\cos(35)\\\\b^2 \approx 871.5055596\\\\b \approx \sqrt{871.5055596}\\\\b \approx 29.521273\\\\[/tex]
Now use the law of sines to find angle A.
[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\\\\frac{\sin(A)}{43} \approx \frac{\sin(35)}{29.521273}\\\\\sin(A)\approx 43*\frac{\sin(35)}{29.521273}\\\\\sin(A) \approx 0.8354581\\\\A \approx \sin^{-1}(0.8354581) \text{ or } A \approx 180-\sin^{-1}(0.8354581)\\\\A \approx 56.6635689^{\circ} \text{ or } A \approx 123.3364311^{\circ}\\\\[/tex]
Due to the side angle side (SAS) congruence theorem, we know that only one triangle is possible (notice angle B is between sides 'a' and c). This means only one of those values for angle A is possible.
The question is: Which one?
Well if you were to use the converse of the pythagorean theorem, then you'll find that the triangle is obtuse.
For any obtuse triangle, the longest side is always opposite the obtuse angle (aka the angle over 90 degrees). The side a = 43 is the longest side of this particular triangle.
This means angle A must be obtuse and the only possibility is that angle A = 123.3364311 degrees approximately.
Which equation best fits the graph below?
Find all x-intercepts of the function. Express your answer as a list of x-values.
f(x) = x3 – 4x2 – 16x + 64
Answer:
all x intercepts [-4, 0] [4, 0]
Step-by-step explanation:
x-intercept, i.e. y=0
f(x) = x^3 - 4x^2 - 16x + 64 = 0
(x^3 + 4^3) - 4x^2 - 16x = 0 [FYI, x^3 + y^3 = (x + y)(x^2 - xy + y^2)]
(x + 4)(x^2 - 4x + 16) - 4x^2 - 16x = 0
(x + 4)(x^2 - 4x + 16) - 4x(x + 4) = 0
(x + 4)(x^2 - 4x + 16 - 4x) = 0
(x + 4)(x^2 - 8x + 16) = 0
(x + 4)(x - 4)^2 = 0
x = -4 or 4
all x intercepts [-4, 0] [4, 0]
Step-by-step explanation:
one thing immediately catches the eye : the factors of the terms in the function follow the powers of 4 :
4⁰, 4¹, 4², 4³
and they are going against the powers of x :
x³ has the factor 4⁰
x² has the factor 4¹
x has the factor 4²
x⁰ has the factor 4³
with that we see that one 0 solution (an x- intercept) is x = 4.
f(4) = 4³ - 4×4² - 4²×4 + 4³ = 4³ - 4³ - 4³ + 4³ = 0
so, the functional expression is
(x-4)(x² + ...)
the other 2 zero solutions are covered by the quadratic term.
to get the quadratic term we divide f(x) by (x-4).
x³ - 4x² - 16x + 64 ÷ x - 4 = x² - 16
- x³ - 4x²
-----------------------------
0 0 - 16x + 64
- - 16x + 64
----------------------‐--------
0 0
so,
f(x) = (x - 4)(x² - 16)
and as we know
(a² - b²) = (a + b)(a - b)
we get
f(x) = (x - 4)(x + 4)(x - 4) = (x - 4)²(x + 4)
so, x = 4 counts as 2 zero solutions, it is a point, where the curve makes a turn and only touches the x-axis, but does not fully intercept it (in the sense to continue on the other side of the x-axis).
and x = -4 is the third zero solution.
so, the x-intercepts are at x = -4, +4
Please help me with my assignment
Write the product using exponents
The product of the expression [tex]\frac{2}{3} *\frac{2}{3}*\frac{2}{3}*\frac{2}{3}[/tex] is [tex](\frac{2}{3})^{4}[/tex] or [tex]\frac{16}{81}[/tex].
What are exponents and powers?Power can be defined as an expression that represents repeated multiplication of the same number whereas exponent is the quantity that represents the power to which the number is raised.
Given expression is : [tex]\frac{2}{3} *\frac{2}{3}*\frac{2}{3}*\frac{2}{3}[/tex]
=[tex]\frac{2^{4}}{3^{4}}[/tex]
= [tex](\frac{2}{3})^{4}[/tex] [[tex]\frac{a^{4}}{b^{4}} = (\frac{a}{b} )^{4}[/tex]]
=[tex]\frac{16}{81}[/tex]
Hence, [tex]\frac{2}{3} *\frac{2}{3}*\frac{2}{3}*\frac{2}{3}[/tex] = [tex](\frac{2}{3})^{4}[/tex]
Learn more about exponents and powers here:
https://brainly.com/question/15722035
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Giving Brainiest ~~ :)
Answer:
28 meters cubed
Step-by-step explanation:
V = 1/3 BH
V = 1/3 (4)(21)
V = 28
Hope this helped :))
have a great day :D <3
20 POINTS PLS HELP ME Find the surface area of each pyramid. Round to the nearest tenth if necessary.
Answer:
633.94 squared inches
Step-by-step explanation:
15.75 x 15.75 = 248.0625
12.25 x 15.75 x 1/2 = 96.46875
since there are 4 triangles and they are equivalent...
96.46875 x 4 = 385.875
Surface area is...
385.875 + 248.0625 = 633.9375
changing my answer hh
Find the marked price when a radio is sold at Rs 3000 after 40% discount .
Rs. 5000
Step-by-step explanation:
To Find MP = ?
GivenSP = rs 3000
Discount = 40%
Solution=> MP-MP×40/100=3000
Taking LCM=> 100MP-40MP/100= 3000
=> 60MP/100 = 3000
MP = 3000 × 100 / 60
MP = 500 × 10
MP = Rs. 5000
What is the title of the graph? blank
What kind of graph is shown? blank
Whose family has the most number of kilograms of rice donated? blank
Whose family has the least number of kilograms of rice donated? blank
What is the total number of kilograms of rice donated? blank
540 kg Vertical graph Dioneda family Number of kilogram of rice donated for Typhoon Roly's Victim Cariaga Family
The title of this graph shown in the image attached below is "Number of Kg. of rice donated for Typhoon Roly's victim."
The title of the graph.Generally, the title of a graph is typically placed at the top. Based on the information provided in the graph (see attachment), the title of this graph is "Number of Kg. of rice donated for Typhoon Roly's victim."
What kind of graph is shown?In this scenario, the kind of graph shown is referred to as a bar graph.
A family with the most number of kilograms of rice donated is the "Carlage family" because their data has the tallest rectangular bar, which corresponds with 150 kg.
A family with the least number of kilograms of rice donated is the "Dioneda family" because their data has the shortest rectangular bar, which is equal to 75 kg.
The total number of kilograms of rice donated is given by:
Total number = 150 + 100 + 175 + 120 + 100
Total number = 645 kg.
Read more on bar graph here: https://brainly.com/question/24741444
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On a certain hot summers day 339 people used the public swimming pool. The daily prices are $1.75 for children and $2.50 for adults. The receipts for admissions totaled $750.50. How many children and how many adults swam at the public pool that day?
Answer:
the number of children = 156
the number of adults = 183
Step-by-step explanation:
let x be the number of children
y be the number of adults
We have to solve this system:
[tex]\begin{cases}x+y=339&\\ 1.75x + 2.50y = 730.50&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}y=339-x&\\ 1.75x + 2.50(339-x) = 730.50&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}y=339-x&\\ -0.75x + 847.5 = 730.50&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}y=339-x&\\ -0.75x =-117&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}y=339-156=183&\\ x =156&\end{cases}[/tex]
Find the equation of the line that goes through the points (0, 6) and (12, 2).
y = -3x + 6
y = -1/3 x + 2
y = -1/3 x + 6
y = 12x + 2
Use the information provided to answer Part A and Part B. A store owner paid \$ 15$15 for a book. She marked up the price of the book by 40\%40% to determine its selling price. Part A What is the selling price, in dollars, of the book? Enter your answer in the box. Part B A customer buys a different book that has an original selling price of \$ 38$38. The book is discounted 25\%25%. The customer must pay a 6\%6% sales tax on the discounted price of the book. What is the total amount, in dollars, the customer pays for the discounted book? Enter your answer in the box.
Answer City's breaking down on a camel's back
PLEASE HELP MEEEE i'll give brainliest if it's answered w work thank u lololol im failing this class
Answer:
3. 261 ft³
Step-by-step explanation:
Volume of the figure = ½(volume of cylinder) + volume of triangular prism)
✔️Volume of cylinder = πr²h
r = 3 ft
h = 10 ft
Volume of cylinder = π*3²*10 = 282.74 ft³
✔️Volume of right triangular prism = ½*b*h*l
b = 3*2 = 6 ft
h = 4 ft
l = 10 ft
Volume of triangular prism = ½*6*4*10 = 120 ft³
✔️Plug in the values into the equation:
Volume of the figure = ½(282.74) + 120 = 261.37 ≈ 261 ft³
Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is a spade given that the second card is a club
Answer:
Recheck your question
Step-by-step explanation:
I think your question should be what is the probability that the second card is a spade given that the first one was a club
19. The average yearly income for 28 married couples living
in city C is $58,219. The standard deviation of the sample is
$56. Find the 95% confidence interval of the true mean.
20. The number of unhealthy days based on the AQI
Answer:
[tex]\{58198.2573,58239.7427\}[/tex]
Step-by-step explanation:
We assume that the following conditions are true before constructing the confidence interval:
Assumption #1: Random Sampling.
Assumption #2: Independence.
Assumption #3: Large Sample.
Assumption #4: The 10% Condition (sample size is no bigger than 10% of population
Assumption #5: The Success / Failure Condition.
Assumption #6: Homogeneity of Variances.
A 95% confidence level correlates to a critical value of [tex]z^*=1.96[/tex], hence:
[tex]\displaystyle CI=\bar{x}\pm z^*\biggr(\frac{s}{\sqrt{n}}\biggr)\\\\CI=58219\pm 1.96\biggr(\frac{56}{\sqrt{28}}\biggr)\\\\CI=58219\pm20.7427\\\\CI=\{58198.2573,58239.7427\}[/tex]
Therefore, we are 95% confident that the true mean of the average yearly income for a married couple living in city C is between $58,198.2573 and $58,239.7427
HELPPPPPPP PLEASEEEE
Answer: 4 = 80, 1 = 100, 5 = 80, 3 = 80
Step-by-step explanation:
Answer:
80°
Step-by-step explanation:
Vertically Opposing Angles are equal when they are cut by a transversal.
Here ∠4 and 80° are vertically opposite anglesHence, ∠4 = 80°The subtraction of rational numbers is _________
Answer:
The Answer would be associative and commutative
Step-by-step explanation:
don't really have a explanation just remember this from a question of a quiz I took
Find the equation of a line that passes through the points (1,-3) and (3,-1).
Leave your answer in the form
y=mx+c
please help me with this assignment ; )
Answer:
The answer is A
Step-by-step explanation:
Because it's square all of the sides will be equal so 18*18=324. Hope this helps.
Need Explanation For This Asap! <3
528 cm2
538 cm2
558 cm2
Answer:
528 cm²
Step-by-step explanation:
The surface area of this prism comprises:
2 congruent triangles (the bases of the prism)2 congruent rectangles (rectangle 1 and 2) - since the triangle has 2 sides of equal length1 rectangle (rectangle 3)Area of a triangle = 1/2 × base × height
= 1/2 × 16 × 6
= 48 cm²
Area of rectangle 1 / 2 = width × length
= 10 × 12
= 120 cm²
Area of rectangle 3 = width × length
= 16 × 12
= 192 cm²
Total Surface Area = 2 triangles + 2 rectangles + rectangle 3
= (2 × 48) + (2 × 120) + 192
= 96 + 240 + 192
= 528 cm²
Area of two triangles
2×1/2BHBH16(6)96cm²Area of base rectangle
12(16)192cm²Area of rest two rectangles
2LB2(10)(12)120(2)240cm²Total area
240+192+96528cm²pls help
6 in
5 in
Volume=
Step-by-step explanation:
Volume of cylinder = π.r^2.h
h = 5 inch, r = 6 inch, π = 3.14
==> Volume = (3.14)×(6×6)×(5)
==> Volume = 565.2 inch^3
Hence the volume of cylinder is 565.2 cubic inches.
There are 12 animals in the field Some are goats and some are ducks. There are 36 legs in all.
How many of each animal are in the field?
Answer:
6 goats and 6 ducks
Step-by-step explanation:
Give an example of a binomial of degree 27
Answer:
x27 + y.
Step-by-step explanation:
Binomial means having 2 terms so binomial of degree 27 is x^27 + y type.
For example,
x^27+y+2
If there are 2 degree terms of x, degree of the one having highest degree is taken.
For example,
In x^27+x^10
As highest degree is 27, this is a binomial of degree 27.
6/6 = 8/8 because they both equal 1. Oleg adds one part to each. Will the results be equal?
Use the drop-down menus to complete an explanation.
Rewrite the fractions as decimals:
7/6 = 1.167
9/8 = 1.125
7/6 is greater then 9/8
the parts in 7/6 are greater than the parts in 9/8
so 7/6 is farther from 1 than 9/8 is