a. The expanded and simplified form is: -4a + 16
b. The expanded and simplified form is: 3a^2 + 6a
c. The expanded and simplified form is: 6x - 10
d. The expanded and simplified form is: x^2 - x - 6
e. The expanded and simplified form is: x^2 + 8x + 16
Sure, let's expand and simplify each expression step by step:
a. -4(a - 4)
Step 1: Apply the distributive property (multiply -4 by each term inside the parentheses).
-4(a) + -4(-4)
Step 2: Simplify the terms.
-4a + 16
So, the expanded and simplified form is: -4a + 16
b. 3a(a + 2)
Step 1: Apply the distributive property (multiply 3a by each term inside the parentheses).
3a * a + 3a * 2
Step 2: Simplify the terms.
3a^2 + 6a
So, the expanded and simplified form is: 3a^2 + 6a
c. 4x - 2(5 - x)
Step 1: Apply the distributive property (multiply -2 by each term inside the parentheses).
4x - 2 * 5 + 2 * x
Step 2: Simplify the terms.
4x - 10 + 2x
Step 3: Combine like terms.
6x - 10
So, the expanded and simplified form is: 6x - 10
d. (x - 3)(x + 2)
Step 1: Apply the distributive property (multiply x by each term inside the second parentheses and then multiply -3 by each term inside the second parentheses).
x * x + x * 2 - 3 * x - 3 * 2
Step 2: Simplify the terms.
x^2 + 2x - 3x - 6
Step 3: Combine like terms.
x^2 - x - 6
So, the expanded and simplified form is: x^2 - x - 6
e. (x + 4)^2
Step 1: Apply the square of a binomial formula: (a + b)^2 = a^2 + 2ab + b^2
(x)^2 + 2(x)(4) + (4)^2
Step 2: Simplify the terms.
x^2 + 8x + 16
So, the expanded and simplified form is: x^2 + 8x + 16
To know more about simplify:
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Find the volume of a cone with radius 10 feet and height of 4 feet.
Answer:
[tex]\frac{400}{3} \pi[/tex]
Step-by-step explanation:
Formula for Cone: π[tex]r^{2}\frac{h}{3}[/tex]
Since we have all the components, we can find the volume of the cone.
R = 10
H = 4
π[tex]10^{2}\frac{4}{3}[/tex]
10×10 = 100
100π[tex]}\frac{4}{3}[/tex]
[tex]}\frac{4}{3}[/tex]×100
4 100 400
--- × ----- = ------
3 1 3
Answer: [tex]\frac{400}{3} \pi[/tex]
Hope this helped.
Find the volume of a cone with radius 10 feet and height of 4 feet.
Solution :Given Data :
Radius = 10 feet
Height = 4 feet
Formulae :
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: \blue{ \underline{ \overline{ \green{ \boxed{ \frak{{ \sf V}olume_{(Cone)} = \pi {r}^{2} \frac{h}{3}}}}}}}[/tex]
Putting the values we get
[tex] \frak{ Volume_{(Cone)} = 3.14 × (10)² × \frac{4}{3} }[/tex]
[tex] \frak{Volume_{(Cone)} = 3.14 × 100 × \frac{4}{3} }[/tex]
[tex] \frak{Volume_{(Cone)} = 314 \times \frac{4}{3} }[/tex]
[tex] \frak{Volume_{(Cone)} = 418.67 \: ft³ }[/tex]
Henceforth, the volume is 418.67 ft³
3. The upward velocity of the water in a particular fountain is given in feet per second by
v = -32t + 44, where t is the number of seconds after the water leaves the fountain. While
going upward the water slows down until, at the top, the water has a velocity of zero. How long
does it take each water particle to reach its maximum height?
ll,,Step-by-step explanation:
Which angle is coterminal to a 175 degree angle?
Answer:
Step-by-step explanation:
-185
lus
Find the probability that a randomly
selected point within the circle falls
in the white area.
r = 4 cm
4 √2cm
[? ]%
Answer:
1-[tex]\frac{2 }{\pi }[/tex] = 1- .64 = .36 = 36%
[tex](4\sqrt{2}) ^{2} = 32\\[/tex]
[tex]\pi 4^{2}[/tex]= 16[tex]\pi[/tex]
[tex]\frac{32}{16\pi }[/tex]= [tex]\frac{2 }{\pi }[/tex]
Step-by-step explanation:
calculate the calculate the area of a circle whose diameter is 9 cm and pie is 22/7
Answer: 63.64 cm² (rounded to the hundredth place)
Step-by-step explanation:
Concept:
Here, we need to understand how to find the area of a circle.
The general formula is: A = πr²
π = 3.14 (or any constants that equals to this value)
r = radius = (1/2) diameter
Solve:
π = 22/7
r = d/2 = 9 / 4 = 4.5
A = πr²
A = (22/7) (4.5)²
A = (22/7) (4.5)²
A = 63.64 cm² (rounded to the hundredthe place)
Hope this helps!! :)
Please let me know if you have any question
Answer:
63.64 cm²
Step-by-step explanation:
r = d/2 = 9 / 4 = 4.5
A = πr²
A = (22/7) (4.5)²
A = (22/7) (4.5)²
A = 63.64 cm² (rounded to the hundredth place)
find the missing side of the triangle.
Answer:
2[tex]\sqrt{10\\}[/tex]
Step-by-step explanation:
Because this is a right triangle, we have:
[tex]x^{2} + 3^{2} = 7^{2} (Pytago)\\x^{2} + 9= 49\\x^{2} =40\\x=\sqrt{40} \\x=2\sqrt{10}[/tex]
Finding an irrational number between which given pair of numbers supports the idea that irrational numbers are dense in real numbers? 3.14 and pi 3.33 and 1/3 e squared and square root of 5 square root of 64 over 2 and square root of 16
Answer:
So, we need to find irrational numbers between the given pairs.
Remember that the sum between an irrational number and an rational number is irrational.
For example, for the first case, we want a irrational number between:
3.14 and pi:
pi = 3.14159265.... is irrational
pi - 0.0001 = 3.14159265... - 0.0001 = 3.14149265...
So this number:
3.14149265...
is an irrational number larger than 3.14 and smaller than pi.
Second cacse:
3.33 and 1/3
(here the range would be actually:
1/3 = 0.33 and 3.33
So we want an irrational number larger tan 0.33 and smaller than 3.33
here we can just use pi = 3.141592...
third case:
e^2 and √5
Firs let's write these numbers so we can see how they look.
e^2 =7.389...
√5 = 2.236
So we want a number larger than 2.236... and smaller than 7.389...
Again, here we can use pi = 3.141592...
2.236... < 3.141592... < 7.389...
final case:
√(64/2) and √16
we have:
√(64/2) = 5.65
√16 = 4
So we want an irrational number larger than 4 and smaller than 5.65
Again, let's use our beloved number pi.
we have that:
pi + 1 is an irrational number:
pi + 1 = 3.14159265... + 1.0 = 4.14159265....
This number, 4.14159265..., is irrational, is larger than 4 and is smaller than 5.65, so we found the irrational number between the given pair of numbers.
Answer:
3.33 and 1/3
Step-by-step explanation:
Calculate the correlation coefficient, r, for the data below. Row chart ( (x )(y ) ) row chart ( ( -10 )( 2 ) ) row chart ( ( -8 )( -3 ) ) row chart ( ( -1 )( -15 ) ) row chart ( ( -4 )( -10 ) ) row chart ( ( -6 )( -6 ) ) row chart ( ( -7 )( -5 ) ) row chart ( ( -5 )( -8 ) ) row chart ( ( -3 )( -13 ) ) row chart ( ( -2 )( -14 ) ) row chart ( ( -9 )( -1 ) )
Answer:
The correlation coefficient is approximately -0.9949
Step-by-step explanation:
The given data is presented as follows;
[tex]\begin{array}{lcl}x&&y\\-10&&2\\-8&&-3\\-1&&-15\\-4&&-10\\-6&&-6\\-7&&-5\\-5&&-8\\-3&&-13\\-2&&-14\\-9&&-1\end{array}[/tex]
The correlation coefficient, r is given as follows;
[tex]r = \dfrac{\sum(x_i - \overline x) \cdot (y_i - \overline y)}{\sqrt{\sum (x_i- \overline x)^2\times \sum (y_i- \overline y)^2 } }[/tex]
From MS Excel, we have;
∑([tex]x_i - \overline x[/tex])·([tex]y_i - \overline y[/tex]) = -155.5
∑([tex]x_i - \overline x[/tex])² = 82.5
∑([tex]y_i - \overline y[/tex])² = 296.1
Therefore, r = -155.5/(√(82.5 × 296.1)) ≈ -0.9949
The correlation coefficient, r ≈ -0.9949
I NEED HELP WITH THIS QUESTION ASAP ITS REALLY REALLY URGENT!!!!
—
Two kids, Albert and Bhara, are 20.0 m apart. Albert sees a soccer ball 25.0 m away. If the angle between the line formed by Albert and Bhara and the line from Albert to the soccer ball is 25 degrees, how far is Bhara from the soccer ball? Correctly round your answer to the nearest tenth of a meter.
Step-by-step explanation:
I can give you a formula SOH-Sinø=Opposite\Hypotenuse
CAH-Cos=Adjacent\Hypotenuse
TOA-Tan=Opposite\Adjacent
Name the quadrant or axis where the point (4.-6) is located.
Answer:
Step-by-step explanation:
(4, -6) is in quadrant IV , (quadrant 4)
For a party Justin buys a pizza and cuts it into 24pieces.Marc eats 1/6 of portion of the pizza and claudine eats 1/4 of what remains after both of them have eaten, Sylvia eats 1/3 of the result.Justin gets to eat what is left over what fraction of the pizza did Justin not eat
Answer:
Justin did not eat 7/12 of the pizza
Step-by-step explanation:
Marc eats 1/6 × 24 = 4, 24 - 4 = 20 left over
Claudine eats 1/4 × 20= 5, 20 - 5 = 15 left over
Sylvia eats 1/3 × 15 = 5, 15 - 5 = 10 left over
Justin eats 10.
24 - 10 = 14
Justin did not eat 14/24 = 7/12
please help i've been stuck on this for a while
Answer:
SSS Postulate
Step-by-step explanation:
The first says 2 sides are the same
The second says 2 sides are the same
The last says 2 sides are the same
Side side side
SSS Postulate
Solve for x:
( x - 6 ) ^ 2 = 7
Answer: x= 6 +/- root of 7
Step-by-step explanation:
1. Expand the left hand side: e.g, 3^2 = 3×3 =9
(x-6)(x-6) = 7
2. Multiply the brackets first by "separating" one of them, and take 7 to the left hand side:
x(x-6) - 6(x-6) =7
x^2 - 6x -6x +36-7=0
Simplify by adding like terms
x^2 -12x +29=0
3.Now your equation is in the form ax^2+bx + c =0, it means you can use the quadratic formula which is x= [-b +/- root of (b^2 - 4ac)]÷ 2a
Then SUBSTITUTE where:
a=1
b= -12
c=29
Therefore, x should be 6+ root of 7 OR 6- root of 7
Answer:
uhhhh okay thank you for removing my answer
Step-by-step explanation:
Write the ratio: 3 1/6 to 17/6
as a fraction in lowest terms.
Answer: [tex]\frac{19}{6} : \frac{17}{6}[/tex]
Step-by-step explanation:
Let us first represent the ratio.
3[tex]\frac{1}{6} : \frac{17}{6}[/tex]
Now we need to convert 3[tex]\frac{1}{6}[/tex] into a improper fraction.
[tex]\frac{19}{6} : \frac{17}{6}[/tex]
Now it is in its simplest form.
The final answer is [tex]\frac{19}{6} : \frac{17}{6}[/tex]
You are responsible for hiring a company to take care of snow removal in the winter time. Company A charges an annual winter fee of $1050 plus $150 for each snow removal job that they complete. Company B charges no annual winter fee, but $200 for each snow removal job that they complete. a) Determine an equation to represent the cost structure of each snow removal company [KNOW-4 marks] b) Solve the linear system of equations that you created in part a) [KNOW-4 marks] c) How can you decide which company would be hired based on your solution in part b) - provide a detailed explanation for full marks. [COMM-3 marks]
Answer:
1050 + (150)times the amount of jobs they do for you during that winter, for A. 0 + (200)times the amount of jokes they do for you during that winter, for B.
Step-by-step explanation:
Boom I would choose B because it would be cheaper, since we do most of the snow removal ourselves.
Help anyone can help me do this question,I will mark brainlest.
Answer:
[tex]344 {cm}^{2} [/tex]
Step-by-step explanation:
[tex]area \: of \: the \: square \\ = 40cm \times 40cm \\ = 1600 {cm}^{3} \\ [/tex]
[tex]area \: of \: the \: circle \\ = \pi {r}^{2} \\ = 3.14 \times {(20)}^{2} \\ = 3.14 \times 400 \\ = 1256 {cm}^{2} \\ [/tex]
[tex]area \: of \: shaded \: region \\ = 1600 {cm}^{2} - 1256 {cm}^{2} \\ = 344 {cm}^{2} \\ [/tex]
A chocolate factory made 369.84 pounds of milk chocolate in 2 days. How much milk chocolate, on average, did the factory make per day?
Answer: 184.92 lbs
Step-by-step explanation:
If the total amount they made in 2 days was 369.84, the avg per day would just be half of that
369.84/2=184.92 lbs
Answer:
The factory made 184.92 pounds of milk chocolate per day.
Step-by-step explanation:
369.84 ÷ 2 = 184.92
Have a great day :)
Write the quadratic equation whose roots are −2 and −5, and whose leading coefficient is 4.
URGENT PLS
Answer:
Step-by-step explanation:
quadratic equation is 4(x+2)(x+5)=0
4(x²+5x+2x+10)=0
4x²+28x+40=0
Answer:
f(x) = 4(x+2)(x+5)
Step-by-step explanation:
The quadratic function is
f(x) = a(x-b1)(x-b2) where a is a coefficient and b1 and b2 are the zeros
f(x) = a(x --2)(x--5)
f(x) = a(x+2)(x+5)
The leading coefficient is a and we know a =4
f(x) = 4(x+2)(x+5)
An iceberg weighs 450,000 pounds if it loss 0.2% of its weight in a day, what is its new weight at the end of the day
Answer:
449 100
Step-by-step explanation:
0.2% × 450000÷ 100=900
450000-900= 449 100
Answer:
Step-by-step explanation:
The answer is 449100 pounds .
Triangle LMN is dilated by a factor of 1.25 to create triangle PQR what is the length of PQ A 20 cm B 18.75 cm C 17 cm di 12 cm
Answer:
See explanation
Step-by-step explanation:
Given
[tex]\triangle LMN \to \triangle PQR[/tex]
[tex]k = 1.25[/tex]
Required
The length of PQ
[tex]\triangle LMN \to \triangle PQR[/tex] means that the side lengths of LMN are multiplied by 1.25 to get the side lengths of PQR
And it implies that the following sides are corresponding
[tex]LM \to PQ[/tex]
[tex]MN \to QR[/tex]
[tex]LN \to PR[/tex]
So, we have:
[tex]PQ = k * LM[/tex]
[tex]PQ = 1.25* LM[/tex]
The question is incomplete.
Assume LM = 16, then:
[tex]PQ = 1.25* 16[/tex]
[tex]PQ = 20[/tex]
Please i really need it rn pls
The 3rd option is correct
How would you describe the difference between the graphs of f(x)=2/3 x^3 and g(x)=2/3(-x)^3
There were some people no a boat 26 people got off the boat at the first dock 22 people got off the boat now there ate 74 people on the boat how many people were on the boat?
Answer:
Step-by-step explanation:
Let the initial number of people on the boat be x:
x - 26 - 22 = 74
x -48 = 74
x = 74 + 48
x = 122
Answered by G a u t h m a t h
Pat’s Pizza Shack offers customers two choices of crust, three choices of sauce, and four choices of toppings shown below. If a 1-topping pizza is selected at random, what is the probability that it will be deep dish crust, with traditional sauce and green peppers?
Answer:
1/24 (fraction form)
hope this helps
In this figure, a line through points X and Y will _____
Answer:
D.
Step-by-step explanation:
The line will be a straight line and will go through AB in the center. Therefore, it will be the perpendicular bisector.
Find the measure of KM. PLEASE PLEASE PLEASE HELP ASAP!!!!!!!!!!!!!!!
A. 7
B. 17
C. 12
D. 14
Answer:
C
Step-by-step explanation:
Given 2 secants from an external point to the circle, then
The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant , that is
ML × KM = MN × MR, substitute values
7 × KM = 6(6 + 8)
7 KM = 6 × 14 = 84 ( divide both sides by 7 )
KM = 12 → C
Answer:
C.) 12
Step-by-step explanation:
I got it correct on founders edtell
Can anyone do this dont mind the 15x because i done it wrong
Connor rolled a die 6 times. A 2 occurred three times. Why isn't the theoretical probability 3/6 instead of 1/6?
2 occurred 3times
[tex]\\ \sf\longmapsto S=6\times 3=18[/tex]
[tex]\\ \sf\longmapsto |S|=18[/tex]
Now
[tex]\\ \sf\longmapsto E=No\:of\:times\: 2\:occured[/tex]
[tex]\\ \sf\longmapsto |E|=3[/tex]
we know
[tex]\boxed{\sf P(E)=\dfrac{|E|}{|S|}}[/tex]
[tex]\\ \sf\longmapsto P(E)=\dfrac{3}{18}[/tex]
[tex]\\ \sf\longmapsto P(E)=\dfrac{1}{6}[/tex]
EXPLAIN:
Answer the following questions using 125 words or more:
Write about the similarity of the original comic to the enlargement. How similar are they and how can you tell? What would cause differences in the two pictures? If you drew another comic using a grid, is there anything you would do differently?
What would happen if you reduced the comic's size rather than enlarged it? Would the process be the same? What would you do differently?
Answer:
Step-by-step explanation:
The enlargement of a comic will be very similar to the original. Everything is larger but in the same proportion. The difference is if the original is enlarged so much that the individual pixel in the original comic becomes visible; causing the enlargement to be "pixelated."
If a comic is drawn using a grid, that may reduce pixelation because you can line up things with the grid.
If the comic's size is reduced, then again it will look similar but everything is smaller and in the same proportion. There will not be any pixelation effect.
bral
Explain how to use a graph of the function f(x) to
find (3).
