Answer: -20xy + 3y² + 3x²
Step-by-step explanation:
(xy + 2y² + 3y² - x²) - (12xy - 10y² - 18x² + 9xy + 12y² + 14x²)
(xy + 5y² - x²) - (21xy + 2y² - 4x²)
xy + 5y² - x² - 21xy - 2y² + 4x²
-20xy + 3y² + 3x²
Three uniform shirts sell for $34.50. How much will 5 uniform shirts cost?
Answer:
57.5
Step-by-step explanation:
Recognize our numbers
3,5,34.50
Three uniform shirts sell for 34.50
34.50/3
=11.5
How much will five cost?
5x11.5
=57.5
Hope this helps!
Answer:
55.25
Step-by-step explanation:
1. First we need to work out the price of ONE shirt. To do that we divide the total price of 3 shirts by 3.
34.50 / 3 = 11.05
2. Now we know that the price of one shirt is $11.05p we can multiply that by 5 to get the price of 5 shirts.
11.05 * 5 = 55.25
= $55.25p
Miguel can drive 4 times as fast as Raul can ride his bicycle. If it takes Raul 3 hours longer than Miguel to travel 68 miles, how fast (in mph) can Raul ride his bicycle? Round your answer to two decimal places, if needed.
Answer:
17 mphStep-by-step explanation:
Miguel's speed = m, Raul's speed = rGivenm = 4rDistance = 68 milesTime difference = 3 hoursSolutiontime = distance/speedSubstitute values and solve for r the equation of the time difference:
68/m + 3 = 68/r68/4r + 3 = 68/r17/r + 3 = 68/r17 + 3r = 683r = 68 - 173r = 51r = 17Raul's speed is 17 mph
Answer:
[tex] \huge \boxed{ \boxed{ \red{ \tt17 \: mph}}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:equationequation word problemsPEMDASgiven:Miguel can drive 4 times as fast as Raul can ride his bicycle. If it takes Raul 3 hours longer than Miguel to travel 68 miles, how fast (in mph) can Raul ride his bicycletips and formulas:t=d/sto findhow fast can Raul ride his bicyclelet's solve:let's the speed of Raul be x
likewise
Miguel can drive 4 times as fast as Raul can ride his bicycle
therefore
4x
according to the question
[tex] \sf \frac{68}{4x}+3=\frac{68}{x}[/tex]
[tex] \implies \sf \frac{68 + 12x}{4x} = \frac{68}{x} [/tex]
[tex] \sf factor \: out \: 4 \: and \: reduce \: it : \\ \sf \implies \frac{4(17 + 3x)}{4x} = \frac{68}{x} \\ \\ \implies\sf \frac{17 + 3x}{x} = \frac{68}{x}[/tex]
[tex] \sf multipy \: both \: sides \: by \: x : \\ \sf \implies (\frac{17 +3 x}{x} )x = (\frac{68}{x} )x \\ \implies \sf 17 + 3x = 68[/tex]
[tex] \sf cancel \: 17 \: from \: both \: sides : \\ \implies \sf 17 - 17 + 3x = 68 - 17 \\ \implies \sf 3x = 51[/tex]
[tex] \sf divide \: both \: side s \: by \: 3 : \\ \sf \implies \frac{3x}{3} = \frac{51}{3} \\ \therefore x = 17[/tex]
3) Cory is standing on a cliff that is 48 feet above the ground. He throws a rock in to the air. The height, h, of the rock
after t seconds is given by h(t) = -2t+4t +48.
a) What is the initial height?
b) How many seconds does it take to reach the maximum height?
c) What is the rock's maximum height?
d) How many seconds does it take to for the rock to land on the ground?
Answer:
a) The initial height of the rock is of 48 feet.
b) It takes 1 seconds for the rock to reach maximum height.
c) The rock's maximum height is 50 feet.
d) It takes 6 seconds for the rock to land on the ground.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
The height of the ball after t seconds, in feet, is given by:
[tex]h(t) = -2t^2 + 4t + 48[/tex]
Which is a quadratic equation with [tex]a = -2, b = 4, c = 48[/tex]
a) What is the initial height?
This is [tex]h(0) = 48[/tex]. So the initial height of the rock is of 48 feet.
b) How many seconds does it take to reach the maximum height?
This is the value of t at the vertex. So
[tex]t_{v} = -\frac{b}{2a} = -\frac{4}{2(-2)} = 1[/tex]
It takes 1 seconds for the rock to reach maximum height.
c) What is the rock's maximum height?
This is the height of the ball after 1 second. So
[tex]h(1) = -2(1)^2 + 4(1) + 48 = 50[/tex]
The rock's maximum height is 50 feet.
d) How many seconds does it take to for the rock to land on the ground?
This is t for which [tex]h(t) = 0[/tex], so we solve the quadratic equation.
[tex]\bigtriangleup = (4)^2-4(-2)(48) = 400[/tex]
[tex]t_{1} = \frac{-4 + \sqrt{400}}{2*(-2)} = -4[/tex]
[tex]t_{2} = \frac{-4 - \sqrt{400}}{2*(-2)} = 6[/tex]
Time is a positive measures, so it takes 6 seconds for the rock to land on the ground.
A store owner purchased 70 soccer balls for $24.50 each. The store owne sold 40 of the soccer balls for $39.75 each. The remainder of the soccer balls were sold for $29.50 each. How much profit did the store owner earn?
Answer:
The stores profit was $757
Step-by-step explanation:
70 x 24.50=1715
they spent 1715 on 70 soccer balls.
They sold 40 of the soccer balls for 39.75 each.
so 40 x 39.75=1590
Then the the remainder of the soccer balls would be 30 since they only started with 70
so they sold 30 soccer balls for 29.50 each.
30 x 29.50= 882
So add 882+1590=2472
then take that number and subtract it from 1715
2472-1715=757 So in profit they made $757 dollars.
2/3 feet into inches
Answer:
The answer 8 inches
Hope this helps :)
Answer:
8 inches
Step-by-step explanation:
1 foot is 12 feet. 2/3 of 12 is 8.
3. His teacher praised him.
5.65 x 10 to the 5th power + 4.87 * 10 to the 3rd power
Answer:
569870
Hope this helps you. Do mark me as brainly
Answer:
the answer is very big..... it is 575,876,495
The equation of a circle is given below.
(x +12)2 + (y - 9)2 = 35
What is its center?
What is its radius?
If necessary, round your answer to two decimal places.
Answer:
center = (-12, 9)
radius = 5.92 (rounded)
Step-by-step explanation:
A little help? the question is attached
Answer:
26 units
Step-by-step explanation:
6+6+7+7 = 26 units
Please help please and thank you
Answer:
Step-by-step explanation:
2x + 3x + 8 - 3x - 2 = 2x + 6
The first and third expressions.
Answer:
1 and 3
Step-by-step explanation:
This should be correct
Will give brainliest to whoever is first!
When John was six years old he hammered a nail into his favourite tree to mark his height. Ten years later at age sixteen, John returned to see how much higher the nail was. If the tree grew by five centimetres each year, how much higher would the nail be?
Answer:The nail would be at the same height since trees grow at their tops.
Step-by-step explanation:
Answer:
speed of growth of tree = 5cm/year
Years after John Came = 10 years
5cm × 10= 50cm
The nail is 50cm higher
Step-by-step explanation:
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▕┈╰▏╰╯╰━━━━
5 ft 5 ft 4.5 ft 5 ft h 5 ft Find the area of the rhombus. [?] ft2
Answer:
56 ft square (Approx)
Step-by-step explanation:
Area of Rhombus= (1/2) * D1* D2 {D1 = 4.5; D2 = 5*5= 25}
= 1/2 * 4.5 * 25
= 56.25
= 56 ft square (Approx)
Answer:
22.5ft²
Step-by-step explanation:
4.5ft x 5ft = 22.5ft²
What is the mode of the data set (30,28,30,45,40,37,35)? Level 1-2
DOK 1
28
30
45
37
Type the integer that makes the following addition sentence true:
= 6
39 +
-33
Hope this helps. :)))))
The ratio of cats to dogs is 8:9. If
there are 27 dogs, how many cats
are there
(Help)
Answer:
24 yw :)
Step-by-step explanation:
what do you know to be true about the values of a and b
Answer:
a
Step-by-step explanation:
all angles in a triangle is equal to 180 so
60+50=110 so p =70
80+30=110 so q =70
p=q
Answer:
p=q
Step-by-step explanation:
What is the value of (x^3 − 7x^2 − 18x + 42) when x = 3?
Answer:
-150
Step-by-step explanation:
x^2 - 7x^2 - 18x +42
3^2 - 7(3)^2 - 18(3) + 42
9 - 63 - 54 + 42
-54 -54 + 42
-108 + 42
-150
how many hours in 1weak
Answer:
168 hours
Step-by-step explanation:
What is the reference angle of 50°?
what is the slope of the line?
Answer:
In technical terms, the slope of the line is the change in y over the change in x. But I just like to think of it as rise over run. To find the slope of the line, pick two points on the line.
Step-by-step explanation:
5у2 2is a power + бу - 4
Answer:
Its 5000
Step-by-step explanation 4883-3455=5000
*
6. Write the mixed number as an improper fraction. 11/8
Answer:
1 [tex]3/8[/tex]
Step-by-step explanation:
Solve the equation for x. 2x + 22 = 4(x+3)
Answer:
x = 5
Step-by-step explanation:
We have the algebraic expression and are asked to solve for x.
To solve, we need to isolate x.
2x + 22 = 4(x + 3)
Distribute :
2x + 22 = (4(x) + 4(3))
2x + 22 = 4x + 12
Subtract 12 from both sides :
2x + 10 = 4x
4x = 2x + 10
Subtract 2x from both sides :
2x = 10
Divide 2 from both sides to get x alone :
x = 5
Answer:
x = 5
Step-by-step explanation:
We have the algebraic expression and are asked to solve for x.
To solve, we need to isolate x.
2x + 22 = 4(x + 3)
Distribute :
2x + 22 = (4(x) + 4(3))
2x + 22 = 4x + 12
Subtract 12 from both sides :
2x + 10 = 4x
4x = 2x + 10
Subtract 2x from both sides :
2x = 10
Divide 2 from both sides to get x alone :
x = 5
Is 1/4 more than 7/3
Answer:
No
Step-by-step explanation:
In which expression should the exponents be multiplied
Answer:
when the bases are different and the powers are same
Step-by-step explanation:
(a)²★(a)³=(a)²+³........
Please I need help!!
Answer:
These expressions are both correct because they are equivalent to each other.
5(4) + 7(4) = 20 + 28 = 48
(12 x 8)/2 = 96/2 = 48
Let me know if this helps!
Evaluate the expression
15 + 6 x 7 - 12 divided by 2
Answer:
22.5
Step-by-step explanation:
It is very important to use bidmas (the order of mathematical functions - standing for brackets, indices, division, multiplication, addition, subtraction) in this question. 15 + 6 x 7 - 12 divided by 2 can also be written as (15 + 6 × 7 - 12) ÷ 2. First, you should complete the multiplication to make (15 + 42 - 12) ÷ 2. Then, complete the addition which makes (57 - 12) ÷ 2. Afterwards, do the subtraction which makes it 45 ÷ 2. This is 22.5. I hope this helps!
What is 4 - 2 and 1/4 I really need to know please
Solve for k.
B=1/2kq
Answer:
k= 2b/q
Step-by-step explanation:
see pic for explanation
In the diagram below, ZGRS - ZART, GR = 36, SR = 45, AR = 15, and RT = 18. G 36 А 15 R S T 45 18 Which triangle similarity statement is correct? A AGRS ~AART by AA B AGRS ~AART by SAS C AGRS - AART by SSS D) AGRS is not similar to A ART.
Answer: the answer is D
The triangle GRS is not similar to the triangle ART because the ratio of the corresponding sides is not in the same proportion option (D) is correct.
What is the similarity law for triangles?It is defined as the law to prove that the two triangles have the same shape but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same propertions and the corresponding angles are congruent.
We have two triangles:
ΔGRS and ΔART in which:
GR = 36 units, SR = 45 units, AR = 15 units, and RT = 18 units
To check the similarity take the ratio of the corresponding sides.
[tex]\frac{36}{15} =\frac{45}{18}[/tex] (after simplification)
[tex]\frac{12}{5} \neq \frac{15}{6}[/tex]
As we can see the ratio of the corresponding sides is not in the same proportion.
Thus, the triangle GRS is not similar to the triangle ART because the ratio of the corresponding sides is not in the same proportion option (D) is correct.
Learn more about the similarity of triangles here:
https://brainly.com/question/8045819
