Answer:
21, 9
Step-by-step explanation:
If girls are x, then boys are x + 12
x + x + 12 = 30
2x + 12 = 30
2x = 18
x = 9
There are 9 girls and 21 boys
help
What should be added to –7mn+2m2+3n2
to obtain 5m2+2mn-9n2
The polynomial to be added to –7mn + 2m² + 3n² to obtain 5m² + 2mn - 9n² is: 3m² - 11n² + 9mn.
Addition of PolynomialsLike terms should be combined together when adding polynomials.
Let x represent the polynomial expression that would be added to –7mn + 2m² + 3n² to obtain 5m² + 2mn - 9n².
Therefore:
–7mn + 2m² + 3n² + x = 5m² + 2mn - 9n².
x = 5m² + 2mn - 9n² - (-7mn + 2m² + 3n²)
x = 5m² + 2mn - 9n² + 7mn - 2m² - 3n²
Combine like terms together.
x = 3m² - 11n² + 9mn
Therefore, the polynomial to be added to –7mn + 2m² + 3n² to obtain 5m² + 2mn - 9n² is: 3m² - 11n² + 9mn.
Learn more about polynomial on:
https://brainly.com/question/24662212
If the focus is (2, 5) and the directrix is y=3, find the equation of the parabola.
Answer:
(x-2)^{2}=4(y-4)
Answer:
y = 1/4 (x - 2)^2 + 4
Step-by-step explanation:
The equation of a parabola is
y = a(x - h)^2 + k
This is for a parabola that opens in the y direction (up or down) If you make a sketch of the focus and directrix you'll be able to see what direction it opens. See image. The parabola kind of curls around the focus and opens away from the directrix. Also, this sketch can help you find the vertex which we need, which is actually a point on the curve and which is exactly half way between the focus and directrix.
The vertex is (h, k) for this problem it is (2, 4). h is 2 and k is 4. You will fill in the 2 and 4 in the parabola formula. Then the last thing you need is the a infront of the paranthesis on the right side of the equation.
Use the formula
a = 1/4p (the p is in the denominator).
p is the distance from the vertex to the focus, so for this question, it is 1. see image.
a = 1/4(1)
a = 1/4
Fill it in the parabola formula.
y = a (x - h)^2 + k
y = 1/4 (x - 2)^2 + 4
Explain your answer fully
WILL GIVE BRAINLIEST IF CORRECTT
Matt and Adam each improved their yards by planting hostas and shrubs. They bought their
supplies from the same store. Matt spent $192 on 10 hostas and 8 shrubs. Adam spent $96 on 2
hostas and 8 shrubs. What is the cost of one hosta and the cost of one shrub
What is the measure of AngleP to the nearest whole degree? 35° 52° 57° 72°.
You can use the law of cosine to find the measure of angle P.
The measure of angle P is given by
Option C : 57°
What is law of cosine?Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
[tex]c^2 = a^2 + b^2 - 2ab\cos(\theta)}[/tex]
(c is opposite side to angle A)
Using the law of sines to find the measure of angle P in the given contextRefer to the attached figure below.
Using the cosine law, we get
|PQ| = a = 17 units, |QR| =length of opposite side to P = c = 15 units, |PQ| = b = 14 units.
Thus, let angle QPR be of θ degrees, then
[tex]cos(\theta) =\dfrac{a^2 + b^2 - c^2}{2ab} = 0.546\\\\\theta = arccos(0.546) = 56.9^\circ, -56.9^\circ[/tex]
triangle's angles are measured positive, thus, measure of angle P came out as 56.9 degrees or approx 57°
Thus,
The measure of angle P is given by
Option C : 57°
Learn more about law of cosine here:
https://brainly.com/question/17289163
Answer:
The answer is 57
Step-by-step explanation:
1. Find the area of the parallelogram. (1 point)
67 ft
60 ft
52ft
A 3,302 ft 2
B 3,484 ft 2
C 3,752 ft 2
D 4,020 ft 2
What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)? A. X2 y2 − 4x 2y 1 = 0 B. X2 y2 4x − 2y 1 = 0 C. X2 y2 4x − 2y 9 = 0 D. X2 − y2 2x y 1 = 0.
well, we know it's centered at (-2 , 1) and it passes through (-4 , 1), if it passes through there, that means that the distance from the center to (-4 , 1) must be its radius.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-4 - (-2)]^2 + [1 - 1]^2}\implies d=\sqrt{(-4+2)^2+0^2}\implies d=2[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-2}{ h},\stackrel{1}{ k})\qquad \qquad radius=\stackrel{2}{ r} \\\\\\\ [x-(-2)]^2+[y-1]^2=2^2\implies (x+2)^2+(y-1)^2=4[/tex]
What is the range of the function {(0, 15), (4, 6), (6, 4), (8, 0)}?
The range of a function is the set of output values of the function
The range of the function is: {15, 6, 4, 0}
How to determine the rangeThe function is defined as:
(x,y) = {(0, 15), (4, 6), (6, 4), (8, 0)}
The range is the y-values.
So, we have:
y = {15, 6, 4, 0}
Hence, the range of the function is: {15, 6, 4, 0}
Read more about range at:
https://brainly.com/question/1770447
8 + 8a - 2a - 4
Pls help
Answer:
that would 6a+4
Step-by-step explanation:
8a - 2a , 8 - 4
Answer:
6a + 4
Step-by-step explanation:
8 + 8a - 2a - 4
Combine Like Terms
(8a - 2a) + (8 - 4)
6a + 4
Orlando's class needs 1,000 tree leaves for a project.
They collected 497 leaves last week and 409 leaves this week.
What is the best estimate for the number of leaves they have collected so far?
Answer:
The total is 906 but. The estimated would be 900. Or 910.
1
• Write an expression that is equivalent to
4X+1+
3
4
2 1
- -2.
3 29
1
3
2
1
х
2
=
4x +1+1x
xt
?
4
3
If Jonny buys 6 shirts and every shirt is 20% off but the normal price is $20.00. how much will Jonny pay in total?
Answer:
Okay I will do this in two orders cause I do not understand if the shirt cost 20 dollars each or all together
Step-by-step explanation:
1. if each shirt cost 20 bucks 2x6=12 add the 0 = $120
20% off 120 = $96
2. if in all the shirt cost 20 bucks
20% off 20 = $16 bucks
Hope This Helped!
The population of a city has been increasing by 2% annually. The sign shown is from the year 2000.
Write an exponential growth function that represents the population t years after 2000.
What will the population be in 2020? Round your answer to the nearest thousand. The population will be about:
We have that the exponential growth function and population be in 2020 is mathematically given as
y=325000e^{0.002t}y=469925From the question we are told
The population of a city has been increasing by 2% annually. The sign shown is from the year 2000.Write an exponential growth function that represents the population t years after 2000.What will the population be in 2020? Round your answer to the nearest thousand. The population will be about:Populationa)
Generally the equation for the standard form of exponential function is mathematically given as
y=325000e^{0.002t}
b)
With T =20
Hence
y=325000e^{0.002(20)}
y=469925For more on Population visit
https://brainly.com/question/905400?referrer=searchResults
What is the difference between 35-(-8)
Answer:
43
Step-by-step explanation:
add 8 because --=+
Answer:
43
Step-by-step explanation:
35-(-8) is basically doing 35+8. The 2 negatives make a positive.
Here are the first four terms of an arithmetic sequence. 3,10,17,24. Is 150 a term in this sequence?
Answer:
1046
Step-by-step explanation:
formula for arithmetic sequence is:
aₙ = a₁ + (n-1)d
a₁ = first value in sequence
n = term value
d = common difference
a(150) = 3 + (150-1)7
= 3+1043
= 1046
150 is a term in this sequence, its 22nd of the sequence
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n-1)d, ...
Its nth term is
T_n = a + (n-1)d
(for all positive integer values of n)
And thus, the common difference is
T_{n+1} - T_n
for all positive integer values of n
Given;
The arithmetic sequence; 3,10,17,24
D= 10-3=7, a=3
150=3+(n-1)7
150=3+7n-7
150=7n-4
150+4=7n
7n=154
n=154/7
n=22
Therefore, 150 is 22nd term of the sequence.
Learn more about arithmetic sequence here:
https://brainly.com/question/3702506
#SPJ2
Diego has a skateboard, scooter, bike, and go-cart. He wants to know which vehicle is the fastest. A friend
records how far Diego travels on each vehicle in 5 seconds. For each vehicle, Diego travels as fast as he can
along a straight level path.
100 inches equal 254 centimeters. What is the distance each vehicle traveled in centimeters?
Answer:
To solve, I need more data...
Step-by-step explanation:
Answer: For the go kart it's 4800
Step-by-step explanation:
Tanner has a round tablecloth with a diameter of 10 feet. What is the tablecloth’s radius?
Answer:
the radius is 5
Step-by-step explanation:
radius is half the diameter
Answer:The radius of the tablecloth is 5
Step-by-step explanation: because to find the radius when u know the diameter u divide the diameter with is 10 by 2
Which set of numbers are equivalent?
es )
A)
10
50%, 0.5,
20
B)
65
65%, 0.65,
1000
C)
7
70%, 0.7,
100
D)
95
95%, 0.95,
1000
Answer:
uhhhhhh
Step-by-step explanation: uh
List the terms in the trinomial below: 3 + 7a - 2x
Answer:
Terms=3, 7a, 2x
Step-by-step explanation:
A furnace was originally priced at $907.07 but went on sale for 33% off. If Omar bought the furnace and paid 9% sales tax, how much did he pay in total?
Answer:
662.433221
Step-by-step explanation:
907.07 × 1.09 × 0.67
Answer:
662.44
Step-by-step explanation:
it says it is the correct answer on ixl
What is the y-intercept of y = -32?
A) (-3,-3)
B) (-3,0)
C) (0,-3)
D) (0,0)
make x the subject of the formula
a=bx+c
Answer:
(a-c)/b = x
Step-by-step explanation:
a = bx + c
subtract 'c' from each side to get:
(a-c) = bx
divide each side by 'b' to get:
(a-c)/b = x
it took mama thuli 1,45 hrs to bake her delicious cake.how many minutes did she spend baking?
please help ASAP What is the surface area of the square pyramid represented by the net?
Answer:
144
Step-by-step explanation:
all of the triangles add up to 108m^2 and the middle adds up to 36m^2 so add them together and you get the surface area.
Answer:
144 m²
Step-by-step explanation:
From the diagram, we can see that the shape is made up of a square and 4 triangles. (We know it's a square as its width and length are equal).
First, find the area of the square.
Area of a square = width x length = 6 x 6 = 36 m²
All the triangles are the same, so we need to find the area of one of the triangles and multiply it by 4.
Area of a triangle = 1/2 x base x height = 1/2 x 6 x 9 = 27 m²
So the total area of all 4 triangles = 4 x 27 = 108 m²
Therefore the total surface area = 36 + 108 = 144 m²
David spent 25% of his money at the department store. If he had $27.36 left, how much money did he start with
Answer:
$36.48Step-by-step explanation:
David spent 25% of his money and left with:
100 - 25 = 75%This is same as $27.36
Find initial amount, the 100%:
27.36/75*100 = 36.48
No work needed answer fast
Answer:
i believe 13
your welcome
Which of the following is the length of the
altitude a of the equilateral triangle below?
Answer:
A) [tex]\sqrt{3}[/tex]
Step-by-step explanation:
in a 30-60-90 triangle the sides, respectively, are in the ratio of 1 : [tex]\sqrt{3}[/tex] : 2
Let f(x) = 3x² + 1 and g(x) = x +4.
Find (f +g)(x)
and (f -g)(x).
Answer:
(f + g)(x) = 3x² + x + 5
(f - g)(x) = 3x² - x - 3
Step-by-step explanation:
(f + g)(x) → f(x) + g(x) → 3x² + 1 + x + 4
Combine like terms and you get: 3x² + x + 5
(f - g)(x) → f(x) - g(x) → 3x² + 1 - (x + 4)
Remember to distribute the neg. everything in the parentheses. Combine like terms and you get: 3x² - x - 3
find the equation of the tangent to the circle x²+y²-2x-y-15=0
Answer:
x−2y+5=0
Step-by-step explanation:
x2+y2−2x+4y=15
differentiating both sides with respect to x
2x+2yy′−2+4y′=0
2x−2+(2y+4)y′=0
y′=2−2x2y+4
y′(−1,2)=2+24+4=12
slope of tangent at (- 1, 2)=12
Equation of the tangent is
y−2=12(x+1)
x−2y+5=0
PLSSS HURRY A student translated the phrase below into an algebraic expression, and then evaluated if for y = 24. Is the student's work correct?
The difference of a number and 6; evaluate when y = 24:
The expression is y
6
. For y = 24, y
6
= 24
6
= 4.
No, the student wrote a division expression instead of a subtraction expression.
No, the student simplified the fraction incorrectly.
No, the student made an error when substituting.
Yes, the student’s work is correct.
