Answer:
Step-by-step explanation:
Because we have 3 unknowns, we need to come up with 3 equations. If the total number of animals is 440 and that number is made up of a combination of goats (g), ducks (d), and chickens (c) the first equation is
g + d + c = 440
The next equation is found in the fact that the number of ducks is one-quarter the number of chickens:
[tex]d=\frac{1}{4}c[/tex] and solving for c gives us that
c = 4d
The last equation says that of the total number of animals, 440, half the goats and half the ducks got away, leaving only 320 animals behind. The last equation, the tricky one, is:
[tex]440-\frac{1}{2}g-\frac{1}{2}d=320[/tex] and simplifying that:
[tex]-\frac{1}{2}g-\frac{1}{2}d=-120[/tex] and because nobody hates fractions more than I do, I'm going to get rid of them by multiplying everything by 2 to get:
-g - d = -240
We've got these equations now, but what I'm going to do is to sub in what c equals (c = 4d) for c in the first equation:
g + d + 4d = 440 and
g + 5d = 440 and pair that with the one right above:
-g - 1d = -240 and use elimination to solve. The g's cancel each other out, leaving us with 4d = 200 and d = 50. So there were 50 ducks originally. Now we will sub that in to solve for c:
c = 4d so
c = 4(50) and
c = 200. Now we will sub both those values into the very first equation we put together to solve for g:
g + 200 + 50 = 440 and
g + 250 = 440 so
g = 190.
Add them all together just to be sure we have the 440 that we were told we had in the beginning (and we do, so we're all done!)
a man bought second hand bicycle for rs 1120 and spend rs160 to repair it. he sold it for rs1344, find his profit or loss percent
Answer:
5 %Solution,
Total Cost price (CP) = Rs 1120 + Rs 160
= Rs 1280
Selling Price (SP) = Rs 1344
Here,
SP > CP , so he made profit.
Amount of profit = SP - CP
= Rs 1344 - Rs 1280
= Rs 64
Now, finding the profit percent,
Profit %=[tex] \frac{profit \: }{cp} \times 100 \: percent[/tex]
[tex] \frac{64}{1280} \times 100 \: percent[/tex]
[tex]5 \: percent[/tex]
Profit percent = 5%
Hope this helps...
Good luck on your assignment...
1) Which of the following is a surd ? a) 64 b) 6 root 64 c) 4 root 64 d) 3 root 64
Answer:
[tex]\text{c) }\sqrt[4]{64}=2\sqrt[4]{4}[/tex]
Step-by-step explanation:
[tex]\text{a) }64\qquad\text{an integer; not a surd}\\\\\text{b) }\sqrt[6]{64}=2\qquad\text{an integer; not a surd}\\\\\text{c) }\sqrt[4]{64}=2\sqrt[4]{4}\qquad\textbf{a surd}\\\\\text{d) }\sqrt[3]{64}=4\qquad\text{an integer; not a surd}[/tex]
help me quickly please!!! what is the area of the composite figure if line AB is congruent to line BC which is congruent to line CD which is congruent to line DA which is congruent to DN?
(2pi+28)mm^2
(2pi+32)mm^2
(2pi+40)mm^2
(2pi+48)mm^2
======================================================
Work Shown:
Segments AB, BC, CD, DA, and DN are all the same length (4 units)
The semicircle has area of
A = (1/2)*pi*(radius)^2
A = 0.5*pi*2^2
A = 2pi
The square has area of
B = (side length)^2
B = 4^2
B = 16
The trapezoid has area of
C = (height)*(base1+base2)/2
C = (DN)*(CD+MK)/2
C = (4)*(4+8)/2
C = 24
Add up the results of A, B and C to get the total area
A+B+C = 2pi+16+24 = 2pi+40
The total area is 2pi+40 square mm
The area of the figure will be 2π + 40 mm². Then the correct option is C.
What is the area?The area of a two - dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.
The figure is made by semicircle, square, and trapezium. Then the area is given as,
A = Area of a semicircle + Area of square + Area of trapezium
A = (π / 2) x r² + (AB)² + 1/2 x (CD + MK) x DN
A = (π / 2) x 2² + (2 x 2)² + 1/2 x (4 + 8) x 4
A = 2π + 16 + 24
A = 2π + 40 mm²
The area of the figure will be 2π + 40 mm². Then the correct option is C.
More about the area link is given below.
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In the figure, triangle ABC is similar to triangle APQ. Therefore, the value of x is , and the value of y is
Answer:
the same
Step-by-step explanation:
Answer:
Step-by-step explanation:
x = 70 degrees.
All triangles have 180 degrees.
So ABC has 180 degrees.
70 + 50 + ACB = 180 Combine like terms
120 + ACB = 180 Subtract 120 from both sides
ACB = 180 - 120
ACB = 60
y = ACB
y = 60 degrees
A bag contains orange, purple, and blue marbles. If a marble is selected at random from the bag, the probability it is orange is 0.2, the probability it is purple is 0.3, and the probability it is blue is 0.5. Which colour marble is most likely to be selected? Explain.
Answer:
blue marble
Step-by-step explanation:
Probability is how likely something is to happen. Between the three colors, blue has the greatest probability, meaning it will most likely be selected.
0.5 > 0.2
0.5 > 0.3
A rectangle has the sides: 7cm and 3cm. A square has the same perimeter as the rectangle. What is the side length if the square
Answer:
5
Step-by-step explanation:
Perimeter of the rectangle: 3+7+3+7=20
Square perimeter is same as rectangle, so square perimeter is also 20.
Side length is 20/4, which is 5
Find the y-intercept of the parabola y = x2 – 8.
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Submit
Answer:
-8.
Step-by-step explanation:
You can get the y-intercept when you find the y-value when x = 0.
y = x^2 - 8
y = 0^2 - 8
y = 0 - 8
y = -8
So, the y-intercept is -8.
Hope this helps!
Answer:
y = -8, if x2 mean 2 times x.
y = -7, if x2 mean X^2
Step-by-step explanation:
Y-intercept mean x = 0.
Plug x = 0, into the parabola, you get the answer.
f(x) = 3x + 2
What is f(5)?
Answer:
17
Step-by-step explanation:
3(5) + 2 = 15 + 2
= 17
Therefore x= 17
Answer:
[tex]\huge\boxed{f(5)=17}[/tex]
Step-by-step explanation:
[tex]f(x)=3x+2\\\\f(5)=?\\\\\text{substitute}\ x=5\ \text{to}\ f(x):\\\\f(5)=3(5)+2=15+2=17[/tex]
Is Triangle ABC cong Triangle DEF? If so name the postulate that applies
Answer:
D. Congruent - SAS
Step-by-step explanation:
Two sides and the included angle of a triangle are congruent to the corresponding parts of another triangle.
The triangles are congruent by SAS.
Pleaaaaase help!!!!
Answer:
see below
Step-by-step explanation:
sqrt(20)
sqrt(4*5)
We know that sqrt(ab) = sqrt(a) sqrt(b)
sqrt(4) sqrt(5)
2 sqrt(5)
Answer:
We can factor down 20 with it's greatest prime GCF, which is 5. We get a 4. When we factor that down the same way, we get 2. If we repeat that process, we get 5, 2, and 2, which turns into [tex]2\sqrt{5}[/tex].
Simplify: ( ++)2 + ( −+)2 + ( +−)2
Answer:
[tex]-2[/tex]
Step-by-step explanation:
[tex]( ++)2 + ( -+)2 + ( +-)2[/tex]
[tex]++ = +[/tex]
[tex]-+ = -[/tex]
[tex]+- = -[/tex]
[tex]( +)2 + ( -)2 + ( -)2[/tex]
[tex]2-2-2[/tex]
[tex]=-2[/tex]
Simplify the following expression: (1 point) 2x − 2y + 5z − 2x − y + 3z
Answer: -3y + 8z
Step-by-step explanation:
2x -2x = 0
-2y + - y= -3y
5z + 3z= 8z
-3y + 8z
The expression 2x − 2y + 5z − 2x − y + 3z is simplified as − 3y + 8z.
What is simplification?Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The expression is given below.
⇒ 2x − 2y + 5z − 2x − y + 3z
Simplify the expression, then we have
⇒ 2x − 2y + 5z − 2x − y + 3z
⇒ 2x − 2x − 2y − y + 5z + 3z
⇒ 0 − 3y + 8z
⇒ − 3y + 8z
The expression 2x − 2y + 5z − 2x − y + 3z is simplified as − 3y + 8z.
More about the simplification link is given below.
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What is the slope of the line through (-2,-6)and (2,2)
Answer:
Y2-y1/x2-x1
=2-(-6)/2-(-2)
=8/4
=2
Step-by-step explanation:
Given two points of a line to find the slope we use the formula; y2-y1/x2-x1 Hence the answer above.
How can we interpret the independent or conditional probability of two events?
Hello!
A conditional probability can always be computed using the formula in the definition. Sometimes it can be computed by discarding part of the sample space. Two events A and B are independent if the probability P(A∩B) of their intersection A ∩ B is equal to the product P(A)·P(B) of their individual probabilities.
Hope this helps.
How to solve the equation 4×3−15÷3×2+1
Answer:
3
Step-by-step explanation:
We use Order of Operations BPEMDAS.
Step 1: Multiply
12 - 15/3(2) + 1
Step 2: Divide
12 - 5(2) + 1
Step 3: Multiply
12 - 10 + 1
Step 4: Subtract
2 + 1
Step 5: Add
3
Answer: 3
Step-by-step explanation:
PEMDAS
P: No parenthesis
E: No exponents
M and D: 4x3 = 12(12-15÷3×2+1), 15÷3 = 5(12-5×2+1), 5*2 = 10(12-10+1)
A and S: 12-10 = 2(2+1), 2+1=3(3)
The probability that Stu buys a sandwich is 0.5.
The probability that Stu gets the bus is 0.7.
Assuming the events are independent, what is the probability that Stu buys a sandwich and gets the bus?
Answer:
probability that Stu buys a sandwich and gets the bus = 0.35
Step-by-step explanation:
Probability of success of two independent events is the product of the respective probabilities, i.e. the multiplication rule.
P(Sandwich) = P(S) = 0.5
P(Bus) = P(B) = 0.7
Assuming the events are independent,
probability that Stu buys a sandwich and gets the bus
= P(SB) = P(S)*P(B) = 0.5*0.7 = 0.35
Answer: 0.35
Step-by-step explanation:
First there is a 50% chance, or a 0.5 chance that Stu gets a sandwich. Then, ignoring the other .5, there is a .7 chance that he makes the bus. Thus, 1/2 of .7 is 0.35.
Hope it helps <3
In a geometric series, the first term is 108 and the common ratio is \frac{2}{3}. Find the sum of the first 8 terms.
Answer:
311.36
Step-by-step explanation:
For a geometric series sum of first n terms is [tex]a(1-r^n)/(1-r)[/tex]
if r is less than 1.
where a is the first term and r is the common ratio.
____________________________\
given
a = 108
r = [tex]\frac{2}{3}.[/tex]
n = 8
thus , sum of n term is
[tex]a(1-r^n)/(1-r)\\=>108(1-(2/3)^8)/(1-2/3)\\=> 108 (1 - 256/6561)/1/3\\=> 108(6561-256)/ 6561/1/3\\=> 108(6305)/2187\\=>311.36[/tex]
Thus sum of first 8 terms is 311.36
Write a polynomial f(x)that satisfies the given conditions,
Polynomial of lowest degree with zeros of - 4 (multiplety 1), 3 (multiplicly 3), and with f(0)= 216,
Answer:
[tex]\boxed{\sf \ \ \ -2(x+4)(x-3)^3 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let's note k a real, we can write the polynomial as
[tex]k(x-(-4))^1(x-3)^3=k(x+4)(x-3)^3[/tex]
and we know that f(0)=216 so
[tex]216=k(0+4)(0-3)^3=k*4*(-1)^3*3^3=-27*4*k=-108k\\\\<=> k=-\dfrac{216}{108}=-2[/tex]
So the solution is
[tex]-2(x+4)(x-3)^3[/tex]
hope this helps
If the sequence 3, 3, 6, 9, 15, ... were to follow the same pattern as the Fibonacci sequence, what are the next three terms?
Answer:
24, 39, 63
Step-by-step explanation:
The next 3 terms are 9 + 15 = 24, 15 + 24 = 39, and 24 + 39 = 63.
Answer:
3: 3+3=6,3+6=9,6+9=15
Step-by-step explanation:
Then the sequence will be (... 24,39,63,...)
TEN POINTS !!!!1 . Type the correct answer in the box. Simplify this expression:
Answer:
1
Step-by-step explanation:
Add the exponents of the as inside the parenthesis.
8+6 =14
Power to a power = multiplication of exponents.
14 times 1/7 = 2
[tex]\frac{a^2}{a^2}[/tex] When you divide, subtract exponents.
2-2 = 0
Any number to the zeroth = 1
The answer is 1.
2 Points
Classify the following triangle. Check all that apply.
A. Scalene
B. Isosceles
C. Right
D. Equilateral
E. Acute
F.Ootuse
Answer:
D and F
Step-by-step explanation:
Answer:
b isosceles and e acute
Jordan lives 6 kilometers due south of his parents' house and 4 kilometers west of his grandparents' house. On his birthday, Jordan drove from his house to his parents' house. From there, he drove in a straight line to his grandparents' house and then back home. How far did Jordan drive on his birthday? If necessary, round to the nearest tenth.
Answer:
Step-by-step explanation:
The direction of movement of Jordan on his birthday forms a right angle triangle. His movement from his house to his parents due south represents the opposite side of the right angle triangle. His movement due west represents the adjacent side and the movement back home along the straight line, d represents the hypotenuse. To determine d, we would apply the Pythagorean theorem. Thus
d² = 6² + 4² = 52
d = √52 = 7.2 km
The total distance that he drove on his birthday is
6 + 4 + 7.2 = 17.2 km
Please help me thanks I’ll mark good
Answer:
A. 4^15.
Step-by-step explanation:
When a power of a number is then raised to a power, the powers multiply. So, this would be 4^(3 * 5) = 4^15. A.
Hope this helps!
Figure 6.21
From knowledge of the sum of the angles
at a point.
b By calculating the sizes of the angles of a
regular octagon using the (n - 2) × 180°
formula
Answer:
L
Step-by-step explanation:
360 hhjnjjuffdsaadtOn a coordinate plane, line P Q goes through (negative 6, 4) and (4, negative 4). Point R is at (4, 2).
Which point is on the line that passes through point R and is perpendicular to line PQ?
(–6, 10)
(–4, –8)
(0, –1)
(2, 4)
Answer:
(–4, –8) im positive
Step-by-step explanation:
plz give brainliest
The point (-4, -8) is on the line that passes throgh point R and perpendicular to line PQ option (B) is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have:
Line P Q goes through (-6, 4) and (4, -4).
Point R is at (4, 2).
To find the point on the line that passes through (4, 2) and is perpendicular to line PQ.
First, calculate the slope of the line PQ:
[tex]\rm m =\dfrac{-4-4}{4-(-6)}[/tex]
m = -8/10
m = -4/5
The slope of the perpendicular to the line PQ:
M = -(1/m)
M = 5/4
The equation of the line has a slope 5/4 and passes through point R
y - 2 = (5/4)[x - 4]
Plug x = -4
y = -8
-8 - 2 = (5/4)[-4 - 4]
-10 = (5/4)[-8]
-10 = -10 (true)
Thus, the point (-4, -8) is on the line that passes throgh point R and perpendicular to line PQ option (B) is correct.
Learn more about the straight line here:
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The height of a tree at time t is given by h(t) = 2t + 3, where h represents the height in inches and t represents the number of months. Identify the independent and the dependent variables.
Answer:
Step-by-step explanation:
You see that 't' is the 'argument' or 'input' to h: h(t). It is always safe to assume that t is the independent variable and h is the depend
Question 1) While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent. 1 European euro = 1.3687 US dollars Question 2) To fit between two windows, the width of a bookshelf must be no greater than Six and one half feet. Mrs. Aguilar purchases a bookshelf that is 77 inches wide. Which statement describes the relationship between the width of the bookshelf and the distance between the windows? Question 3) Alina is able to swim at a rate of about 2.5 miles per hour. Talia is able to swim at a rate of 1.8 meters per second. Which statement comparing the two swimmers is accurate? 1 mile 1,609 meters.
Find the measure of each angle: Complementary angles with measures (5x)° and (4x−18)°
Answer:
60° and 30°
Step-by-step explanation:
Since they are complementary, the 2 equations add up to 90°
5x + 4x - 18 = 90
9x - 18 = 90
9x = 108
x = 12
Simply plug in x to find our angles:
5(12) = 60°
4(12) - 18 = 48 - 18 = 30°
Answer:
5x = 60°, 4x - 18 = 30°
Step-by-step explanation:
Sum of complementary angles is 90°.
5x + 4x - 18 = 90
9x = 90+18
9x = 108
x = 12
5x = 5* 12= 60°
4x - 18 = 4*12 - 18 = 30°
The two cones are similar. (a) Write down the value of l. (b) When full, the larger cone contains 172 cm3 of water. How much water does the smaller cone contain when it isfull?
Answer/Step-by-step explanation:
a. Since both cones, as shown in the figure attached below, are similar, 11/8 = l/4
Cross multiply to find l
4*11 = 8*l
44 = 8l
l = 44/8
l = 5.5cm
b. Given the slant height and diameter of cone, volume of cone can be calculated using the formula ⅓πr²*√(l² - r²)
Where, r = diameter ÷ 2 = 4/2 = 2cm
l = 5.5cm
Volume of smaller cone = ⅓*3.142*2²*√(5.5² - 2²)
= ⅓*3.142*4*√30.25 - 4)
= ⅓*12.568*√26.25
= ⅓*12.568*5.124
= 64.40/3
Volume of small cone ≈ 21.5 cm³
Quadrilateral rust has a vertex (2,4). What are the coordinates of r' after a dilation of scale factor 3, centered at the origin, followed by translation (x,y) to (x+4,y)
Answer:
The coordinates of r' are x = 10 and y = 12.
Step-by-step explanation:
The vertex experiments two operations: Dilation and translation, whose definitions are presented herein:
Dilation with respect to origin
[tex](x',y') = (0,0) + 3\cdot (x,y)[/tex], [tex]\forall \,x,y \in \mathbb{R}[/tex]
Translation
[tex](x',y') =(x+4,y)[/tex], [tex]\forall\,x,y\in \mathbb{R}[/tex]
If [tex]x = 2[/tex] and [tex]y = 4[/tex], then:
1) [tex](2,4)[/tex] Given.
2) [tex](0,0) + 3\cdot (2,4)[/tex] Dilation with respect to origin.
3) [tex](6,12)[/tex] Vectorial sum and scalar multiplication.
4) [tex](6+4,12)[/tex] Translation.
5) [tex](10,12)[/tex] Vectorial sum. Result.
The coordinates of r' are x = 10 and y = 12.
Answer:
10,12 is the answer
Step-by-step explanation:
I just did it on a p e x