Answer:
principal = $400
Step-by-step explanation:
amount(a)=principal(p) + interest(y).........(1)
Interest(y)=principal(p) x rate(r) x time(t)....(2)
In (1), p= a - y...........(3)
putting (3) in (2),
y = (a - y) x r% x t
y = (432 - y) x 8% x 1
y = 3456%-8y%
y + 0.08y = 3456%
1.08y = 34.56
y = 32
but a - y = p
432 - 32 = p
p = 400
principal = $400
p varies jointly as q and the square of r, and p = 200 when q = 2 and r = 3. Find p when q = 5 and r= 2.
Step-by-step explanation:
If a variables varies jointly, we can just divide it by the other variables in relation to it.
For example, since p variables jointly as q and square of r, then
[tex] \frac{p}{q {r}^{2} } = k[/tex]
where k is a constant
First, let find k. Substitute p= 200
q= 2, and r=3.
[tex] \frac{200}{2(3) {}^{2} } = k[/tex]
[tex] \frac{200}{18} = k[/tex]
[tex] \frac{100}{9} = k[/tex]
Now, since we know our constant, let find p.
[tex] \frac{p}{q {r}^{2} } = \frac{100}{9} [/tex]
Q is 5, and r is 2.
[tex] \frac{p}{5( {2}^{2}) } = \frac{100}{9} [/tex]
[tex] \frac{p}{20} = \frac{100}{9} [/tex]
[tex]p = \frac{2000}{9} [/tex]
7. Miguel draws a square on a coordinate plane. One vertex is located at (5, 4). The
length of each side is 3 units. Circle the letter by all the ordered pairs that could be
another vertex.
A. (5, 1)
B. (5, 7)
C. (7, 8)
D. (2, 6)
E. (2, 1)
Answer:
A, B and E
Step-by-step explanation:
Answer: A,B and E i did the test
Step-by-step explanation:
In the diagram Below
Answer:
∠UTC = 55°∠UCD = 70°∠BCT = 55°Step-by-step explanation:
In this figure of overlapping parallelograms, each angle is related to the others by several different theorems involving triangles, parallelograms, and parallel lines. That is, there are several different ways one can arrive at the answers to this question.
__
UTC∠UTC ≅ ∠UDC = 180° -∠EDU . . . opposite angles of parallelogram; linear pair
∠UTC = 180° -125° = 55°
__
UCD∠UCD ≅ ∠TBC = 180° -∠TBA . . . . corresponding angles; linear pair
∠UCD = 180° -110° = 70°
__
BCT∠BCT ≅ ∠UTC = 55° . . . . alternate interior angles
can someone please help mee
Answer:
x = -2y
y-intercept: ( 0, 0 ) and slope: [tex] \frac{1}{2} [/tex]
You’re planning to place an order from an online boutique. Leggings are $12 each and shipping is a flat rate of $5. Write an expression that represents the total cost of your order (not including tax) based on the number of leggings (l) you buy.
Answer:
For the cost of each legging to be $12, and the shipping of $5, the expression is a straight line C = 12x + 5 where x is the number of leggings.
Step-by-step explanation:
It is given that each legging costs $12. This means that for x number of leggings, the cost will be $12x. Now there is an additional cost of shipping that is $5. So, total cost will be a linear equation and can be written as
C = 12x + 5
This equation represents a straight line like y = mx + c. Here y = C, m = 12 and c = 5.
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evaluate the following expression when x=-4 and y=4
x³-x /4y[tex]\frac{x}{y}[/tex]
Answer: - 60
Step-by-step explanation:
[tex]\frac{(-4)^3 - (-4)}{4(4)^-4/4} \\\\= -60[/tex]
Given the quadrilateral below is a rhombus, solve for the length of the side of the rhombus.
Answer:
7.21
Step-by-step explanation:
There is a formula to find the area of a side of a rhombus given 2 diagonals.
It is: [tex]\frac{\sqrt{p^{2}+q^{2} } }{2}[/tex]
64 + 144 = 208
[tex]\sqrt{208}[/tex] = 14.42
14.42 / 2 =
7.21
There are 12 ducks and 11 geese in a certain park. Find the ratio of geese to ducks.
Answer:
11:12
Step-by-step explanation:
You first have to put the number of geese to ducks in a ratio form and since 11 and 12 have no common factors one cannot reduce the ratio
cotpheta•sin2pheta=
1+cos2pheta
1+cospheta
1+sin2pheta
Answer:
Step-by-step explanation:
Did you mean.
[tex] = \cot( \theta) . \sin(2 \theta) [/tex]
[tex] = \frac{ \cos( \theta) }{ \sin( \theta) } .(2 \sin( \theta) \cos( \theta) )[/tex]
[tex] = \frac{2 \sin( \theta) \cos {}^{2} ( \theta) }{ \sin( \theta) } [/tex]
[tex] = 2 \cos {}^{2} ( \theta) [/tex]
[tex] = 2.(1 - \sin {}^{2} ( \theta) )[/tex]
[tex] = 2 - 2 \sin {}^{2} ( \theta) [/tex]
No option Solution.
NEED HELP ON THIS ASAP!!!!!!
Answer: Choice B (If you need to do questions like this in the future i recommend using the desmos graphing calculator online, inputting the equations and comparing them)
express 80 as a product of its prime factors, write the prime numbers in accending order
Answer:
80 as a product of prime numbers can be expressed as 2×2×2×2×5
Jamar is attempting to factor the expression 15x^2-16x-15. In his first step, he rewrites the expression as 15x^2-25x+9x-15. Which of the following statements in true about Jamar’s work?
A. Jamar's first step is correct. He should continue to factor the expression.
B. The two middle coefficients add to the correct number, but do not multiply to the correct number.
C. The two middle coefficients multiply to the correct number, but do not add to the correct number.
D. The two middle coefficients do not add or multiply to the correct number.
Jamar's first step is correct. He should continue to factor the expression. Then the correct option is A.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
Jamar is attempting to factor the expression 15x² – 16x – 15.
In his first step, he rewrites the expression as 15x² – 25x + 9x – 15.
Jamar's first step is correct. He should continue to factor the expression.
Then the correct option is A.
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Mark's Digital Place has a compact digital camera at a price of $425, a 8 inch tablet for $540 and a
game console for $610. If you want to get an additional three years warranty, then you need to pay
15% extra on the original price and $50.
Daphne wants to buy a digital camera and a tablet to start a photography course. When she went into
the store, she found that the store id offering a discount of 5% on the camera and 80 on the tablet.
Daphne also want the additional three years warranty. How müch money does Daphne need to pay to
buy both the items with a three years additional warranty on each item?
Answer:
jjxfzhfxjgjhzjjjtxjxjxktxjtxjtxtxh
1. Decide if the following is a properly formed syllogism. If you are going to wrap Holly’s gift, you need wrapping paper. If you need wrapping paper, you have to go to the store. Therefore, if you go to the store, then you’re going to wrap Holly’s gift.
A) This is a syllogism.
B) This is not a syllogism.
This is not a syllogism. Hence option B is correct.
What is a syllogism?A logical structure for a formal argument that includes a major, minor, and conclusion.
This syllogism cannot be concluded without a given statement.
You'll need wrapping paper if you're going to wrap Holly's present. To get wrapping paper, you must visit a store.
Therefore, you will wrap Holly's present if you visit the store. This isn't a syllogism
Hence option B is correct.
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Answer:
This is not a syllogism
Step-by-step explanation:
I took the quiz. :)
Suppose that F(x) = x² and G(x) = 3x^2 + 8. Which statement best compares the graph of G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) stretched vertically and
shifted 8 units to the left.
B. The graph of G(x) is the graph of F(x) compressed vertically and
shifted 8 units to the left.
C. The graph of G(x) is the graph of F(x) compressed vertically and
shifted 8 units up.
D. The graph of G(x) is the graph of F(x) stretched vertically and
shifted 8 units up.
Answer:
The graph of G(x) is the graph of F(x) stretched vertically and shifted 8 units up.
x(3y - 2)
Multiply this problem
Answer:
3xy-2x
Step-by-step explanation:
Distribute x to both 3y and -2: 3y*x-2*x.
In which funtion is x=2 mapped to 32?
The function g(x)=4(x+3)² - 68 is mapped to 32.
What is equation?An equation is a mathematical expression in terms of one or more unknown variable.
Given are the following functions:
f(x)= - 3x² - 4
g(x)= 4(x+3)²-68
f(x)= 3x
f(x)= 2x-62
To get the mapped function, we substitute the value of x in all function,
a) f(x)=-3x²- 4
Put x=2,
f(2)= -3 (2)² - 4
f(2)= -16
It is not mapped.
b) g(x)=4(x+3)² - 68
Put x=2,
g(2) = 4(2+3)² - 68
g(x) =32
It is mapped to 32.
c) f(x)=3x
Put x=2,
f(2) = 3 x 2 =6
It is not mapped.
d) f(x)=2x - 62
Put x=2,
f(2) =2x2 -62
f(2) = -58
It is not mapped.
Therefore, the function g(x)=4(x+3)² - 68 is mapped to 32.
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Reece and Sarah share some money in the ratio 9 : 16.
Reece says that Sarah gets more than 60% of this money. Show that Reece is correct.
Answer:
64% > 60%
Step-by-step explanation:
Total Units = 9 + 16 = 25 units.
Sarah Receives 16 units out of 25.
Percentage = 16/25 * 100
= 64%
Therefore Sarah received more than 60% of this money and therefore Reece is correct.
12. How many grams is of of 800 g?
[tex] \frac{3}{8} [/tex]
of 800 g ?
Answer:
800
Step-by-step explanation:it's cuz g represents
The additive inverse of an element of x of a set is the number, which when added to x gives the answer 0. In the set {-3, -2, -1, 0, 1, 2, 3}, what is the additive inverse of -2?
Answer:
2
Step-by-step explanation:
the additive inverse of - 2 is 2 , since
- 2 + 2 = 0
Students are selling T-shirts for a school fundraiser. The table shows the amount they raise from the T-shirt sales.
Shirts Sold 1 2 3 4
Amount Raised (dollars) 4 8 12 16
Complete each statement.
The amount raised ? proportional to the number of shirts sold.
is
is not
Answer:..
Step-by-step explanation: what is is not?
Answer:
1. is
2. amount raised, number of shirts sold
3. dependent, independent
4. 4
5. 4x
Step-by-step explanation:
The circumference of a circle is 237 cm.
What is the area, in square centimeters?
Express your answer in terms of T.
Answer:
Circumference of a circle = 2 pie r
237 = 2 * pie * r
237 / 2 * Pie
118.5/ pie = r
118.5 = Pie*r
Area of circle = Pie *r²
= Pie r * r
= 118.5 * 118.5/ Pie
= 118.5 * 118.5 / pie
= 14042.25/ pie
taking value of pie = 3.14
= 4472.05 sq. cm
A group of 328 people consists of men ,women, and children. There are five times as many men than children and twice as many women then children. How many women are there
Step-by-step explanation:
Ultimately we know:
Men = * 5
Women = * 2
Children =
We can already make the estimation that the amount of children will be below 50. So by trial and error you will get to your answer by substituting with 41.
Children - 41
Women - 41 x 2 = 82
Men - 41 x 5 = 205
205 + 41 + 82 = 328
So your answer is 41
Can anyone help me with this
Fnd the value of x.
x = ?
Answer:
X=62 degrees
Step-by-step explanation:
The solution is in the image
Answer:
62°
Step-by-step explanation:
We know that the sum of the interior angles in a triangle is added up to 180°.
Therefore,
68.5° + 49.5° + x = 180°
118° + x° = 180°
x = 180° - 118°
x = 62°
if cos^4+cos^2=1 prove that cot^4a-cot^2a=1
Step-by-step explanation:
We can solve this kind of trigonometric problem
easily by the followings method :
Given :
cos^4a + cos^2a = 1
or, cos4^a = 1 - cos^2a
Therefore; cos^4a = sin^2a
Again,
To prove: cot^4a - cot^2a = 1
L.H.S = Cot^4a - cot^2a
= Cos^4a÷ sin^4a - Cos^2a ÷ sin^2a
= Sin^2a ÷ Sin^4a - cos^2a ÷ Sin^2a
= 1 ÷ Sin^2a - cos^2a ÷ Sin^2a
= 1 - cos^2a ÷ Sin^2a
= Sin^2a ÷ Sin^2a
= 1 = R.H.S proved.
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Please help! Which of the following would result in an integer?
Answer:
B
Step-by-step explanation:
Cube root of 27 is 3, which is in integer
A dial combination lock has dials numbered 0 to 5. The lock is set to an even number. How many different numbers could it be?
I need some help on this one, anyone know?
The number of combinations will be 6 for even numbers.
What is the combination?The arrangement of the different things or numbers in a number of ways is called the combination.
Given that:-
A dial combination lock has dials numbered 0 to 5. The lock is set to an even number. How many different numbers could it be?The total sample numbers are from 0 to 5 which are 0,1,2,3,4,5.
The even numbers are 0,2,4.
The combinations will be given by:-
C = 3!
C = 3 x 2 x1
C = 6
Therefore the number of combinations will be 6 for even numbers.
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PLEASE HELP. FUNCTIONS AND RELATIONS. PROVIDE ANSWER OPTION A,B,C OR D? THANKS!!
Step-by-step explanation:
please mark me as brainlest
A quilt is designed using a square pattern. Each square contains two rectangles. Each rectangle contains a shaded rhombus.
Each rectangle contains a shaded rhombus. The left angle is 50 degrees and the top angle is (2 x + 20) degrees.
What is the value of x?
50
55
125
145
According to the computations, this rhombus's value of x is equal to 55°.
How can we calculate x's value?The total of all the angles in a rhombus should be 360 ° because the opposing angles in a rhombus are always identical.
We may infer the preceding information from the rhombus's picture:
Neighboring angles= 2x+ 20 & 50°
Opposite angles=2x+ 20 & 50°
Combining the angles results in:
2x+20+50+2x+20+50=360
⇒4x+140= 360
⇒4x=360-140
⇒4x=220
⇒x=220/4
⇒x=55°
Hence, it is concluded that the value of x is (b) 55°.
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How do u solve 3/8+1/8-2/7+1/4
Answer:
13/28
Step-by-step explanation:
using pemdas we can determine that the equation is directly solves from left to right
so
first
we have
3/8 + 1/8
which is 4/8
you can simplify this to 1/2
then you have 1/2 - 2/7
you must make them have the same numerator
you can multiple 1/2 by 7/7 and 2/7 by 2/2
7/14 - 4/14 = 3/14
now you must add 3/14 and 1/4
but you to make them have the same numerator
so you multiply 3/14 by 2/2 and 1/4 by 7/7
6/28 + 7/28 = 13/28
that is your final answer
