To multiply the expression 6z^2 by the trinomial (7z^2+3z-2), distribute 6z^2 across each term in the trinomial to obtain 42z^4 + 18z^3 - 12z^2.
Explanation:The student has asked to multiply the expression 6z2 by the trinomial (7z2+3z-2). To solve this problem, we'll apply the distributive property, which entails multiplying the term outside the parenthesis by each term inside the parenthesis.
Multiply the term 6z2 by 7z2, which gives 42z4.Multiply 6z2 by 3z, yielding 18z3.Finally, multiply 6z2 by -2 to get -12z2.Combine all the products to get the final expanded expression: 42z4 + 18z3 - 12z2.
The product of [tex]\(6z^2\)[/tex] and [tex]\(7z^2 + 3z - 2\)[/tex] is [tex]\(42z^4 + 18z^3 - 12z^2\)[/tex].
To multiply [tex]\(6z^2\)[/tex] by the trinomial [tex]\(7z^2 + 3z - 2\)[/tex], you need to distribute [tex]\(6z^2\)[/tex] to each term inside the parentheses. Here's how you can do it stepwise:
1. Multiply [tex]\(6z^2\)[/tex] by the first term of the trinomial [tex](\(7z^2\))[/tex]:
[tex]\[ 6z^2 \cdot 7z^2 = 42z^4 \][/tex]
2. Multiply [tex]\(6z^2\)[/tex] by the second term of the trinomial [tex](\(3z\)):[/tex]
[tex]\[ 6z^2 \cdot 3z = 18z^3 \][/tex]
3. Multiply [tex]\(6z^2\)[/tex] by the third term of the trinomial [tex](\(-2\))[/tex]:
[tex]\[ 6z^2 \cdot (-2) = -12z^2 \][/tex]
Now, combine these results:
[tex]\[ 6z^2(7z^2 + 3z - 2) = 42z^4 + 18z^3 - 12z^2 \][/tex]
So, the product of [tex]\(6z^2\)[/tex] and [tex]\(7z^2 + 3z - 2\)[/tex] is [tex]\(42z^4 + 18z^3 - 12z^2\)[/tex].
What is the domain of g(x)?
The graph of f(x) = 6(0.25) and its reflection across the y-
axis, g(x), are shown.
COND
all real numbers
all real numbers less than 0
all real numbers greater than 0
all real numbers greater than or equal to 0
g(x)
A
+
1 +
f(x)
5
4 3
2
1
1 2
3
4
5 x
Answer:
y=(x+6)
2
−6
Step-by-step explanation:
Find the median for the frequency table above
Answer:3
Step-by-step explanation:
the median is always the middle number
hope this helps.
Amelia runs a catering business. Based on her records, her
weekly profit can be approximated by P = 2x2 - 44x – 150,
where x is the number of meals she caters and P is her profit.
When P is negative, Amelia has lost money.
1) What is the least number of meals Amelia needs to cater
in order to begin making a profit?
2) If she caters no meals one week, how much money does
she lose?
3) What is her profit for catering 50 meals?
Answer: (1) The least number of meals is 26 (2) She loses 150 if she caters no meal in one week. (3) Her profit would be 2,650 if she caters for 50 meals in one week
Step-by-step explanation: The weekly profit is given as a quadratic equation which is;
P = 2x² -44x - 150
We begin by solving for the value of x.
When 2x² -44x - 150 = 0
Divide all through by 2
x² - 22x - 150 = 0
By factorization,
(x - 25) (x + 3) = 0
(x -25) = 0 OR (x + 3) = 0
When x - 25 = 0
x = 25
When x + 3 = 0
x = -3
What this implies is that when Amelia caters for 25 meals in a week, her profit is calculated as follows
P = 2x² - 44x -150
P = 2(25)² - 44(25) - 150
P = 2(625) - 1100 - 150
P = 1250 - 1100 - 150
P = 0
(1) Therefore she must cater for at least 26 meals before she can begin to make any profit.
(2) She loses 150 if she caters no meal in one week.
This can be calculated as follows;
When x = 0,
P = 2x² - 44x - 150
P = 2(0)² - 44(0) - 150
P = 0 - 0 -150
P = -150
(3) When she caters 50 meals her profit becomes 2,650
P = 2x² - 44x - 150
P = 2(50)² - 44(50) - 150
P = 2(2500) - 2200 - 150
P = 5000 - 2200 - 150
P = 2650
1) The least number of meals Amelia needs to cater in order to begin making a profit is 25.
2) Amelia loses $150 if she caters no meals in a week.
3) For catering 50 meals, Amelia's profit is $2650.
Explanation:1) To find the least number of meals Amelia needs to cater in order to begin making a profit, we need to determine when her profit, P, becomes positive. In other words, we need to solve the quadratic equation 2x^2 - 44x - 150 = 0 for x. This equation can be factored as (2x + 6)(x - 25) = 0. Therefore, x = -3 or x = 25. Since the number of meals cannot be negative, the least number of meals Amelia needs to cater in order to begin making a profit is 25.
2) If Amelia caters no meals one week, the profit, P, is given by P = 2(0)^2 - 44(0) - 150. Simplifying this equation, we get P = -150. Therefore, Amelia loses $150 if she caters no meals in a week.
3) To find Amelia's profit for catering 50 meals, we substitute x = 50 into the profit equation P = 2x^2 - 44x - 150. Plugging in x = 50, we get P = 2(50)^2 - 44(50) - 150 = 5000 - 2200 - 150 = $2650.
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What should you do to get the two terms with variables on the left side of the equation?
Answer:
Either divide or multiply
Answer: you would subtract 3/4 from both sides of the equation
Step-by-step explanation:
Please help!
I don't understand..
Answer:
58 should be the answer
Step-by-step explanation:
<CBD is 90 and <BDC is 32 as well since its the same as angle <BDA and 180 in every triangle so 180-90-32=58.
Determine the vertex of the function f(x) =
-4(x-3)^2+ 6.
(6,-3)
(6,3)
(3,6)
O (-3, 6)
Answer:
C
Step-by-step explanation:
find missing angle..x=??
Answer:
X=147°
Step-by-step explanation:
Angle on a straight line is 180
And x,33 is given on a straight line
It will be solved as
X+33=180
Substrate 33 from both sides
X=147°
Therefore x=147°
a rectangles perimeter and area have the same numerical value. the width of the rectangle is 3 units . what is the length of the rectangle in units?
Answer:
6
Step-by-step explanation:
Answer:
The length is 6
Step-by-step explanation:
P= L+ L + W+ W
P = L + L + 3 x 3
P = L + L + 6
We check A and enter below.
P = 12-6 + 18-6 = 18
A = L x W = 18
A = L x 3 = 18
A = 6 x 3 =18
Hurry. A catapult launches a pumpkin with an upward velocity of 150 ft./s.
The height of the pumpkin, h, in feet after t seconds is given by the
function h = -16t2 + 150t + 20. How long does it take the
pumpkin to reach its maximum height? What is the pumpkin's
maximum height? Round to the nearest hundredth, if necessary.
Answer:
Time taken to reach maximum height=4.69 seconds
Maximum Height=371.56feet
Step-by-step explanation:
Given the height function of the pumpkin:
[Tex]h = -16t^2 + 150t + 20[/tex]
The pumpkin reaches it's maximum height at its axis of symmetry.
Therefore, we determine its equation of symmetry.
The equation of symmetry:
[Tex]t=-\frac{b}{2a}[/tex]
a=-16, b=150.
Therefore:
[Tex]t=-\frac{150}{2*-16}=4.6875[/tex]
The pumpkin reaches maximum height after 4.6875 seconds.
At t=4.6875
[Tex]h = -16(4.6875)^2 + 150(4.6875)+ 20\\=371.5625\approx 371.56 \:feet[/tex]
The pumpkin's maximum height is 371.56 feet.
Which type of individual retirement account should you choose if you want your contributions to be tax deductible?
NUMBER 10 PLS SOLVE
Answer:
D
Step-by-step explanation:
Answer:
Option C: Multiply 15 ft by 12 in/1 ft and 2.54 cm/1 in
Step-by-step explanation:
to convert feet to centimeter, we first convert to inches and from iches to centimeter
1 feet = 12 inches and 1 inches = 2.54 cm
∴ 15 feet = 180 inches and 180 inches = 457.2
This means to convert from feet to centimeter
Multiply 15 ft by 12 in/1 ft and 2.54 cm/1 in
Select all the families that -3.7 belongs to.
Natural
Whole
Integer
Rational
Irrational
Does it seem fair to you that a hit could be a home run at one stadium but not at others?Explain.
Answer:
No. If standards differ at different sports stadiums, that makes the game unfair for one team or the other. A win at one stadium could be a loss at another. To make the game fair, all facilities should be equal.
Step-by-step explanation:
The unique dimensions and characteristics of each baseball stadium, known as park factors, can impact whether a hit becomes a home run. Although it might seem unfair, it's the same for all teams and is part of the game's complexity. Not only the player's skill but also their knowledge of the park's attributes can influence the outcome of the game.
Explanation:The different sizes and features of baseball stadiums, known as park factors, can impact game dynamics, including whether a hit results in a home run. This is part of the sport's complexity and challenge, as players must adapt their strategies for different venues. It might seem unfair, but it's the same for all teams as they each host and visit various stadiums throughout the season.
In some parks, for example, the distance from home plate to the outfield wall is less, which could make it easier for a hit to become a home run. In contrast, larger parks or those at higher altitudes, where the air is thinner and ball travels further, might be tougher to score a home run.
All these make baseball a fascinating sport, where not only the player's skill but also nuanced aspects like knowledge of the park play an essential role in the outcome of the game. Thus, by definition, a home run is still a successful hit, but where that hit ends up can depend on numerous variables, including the park's attributes.
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A box shaped like a right rectangular prism
measures 5 centimeters by 3 centimeters by
2 centimeters. What is the length of the interior
diagonal of the prism to the nearest hundredth?
Answer:
[tex]\sqrt{38}[/tex]
Step-by-step explanation:
Given that:
The 3 demensions of the right rectangular prism measures 5 centimeters by 3 centimeters by 2 centimeters.
Because we do not know which one is the height, the length and the width of the box, so we assume them (it does not affect the length of the interior
diagonal )
the height : 5 centimetersthe length : 3 centimeters the width : 2 centimetersTo find the length of the interior diagonal of the prism, we use the following formula:
d = [tex]\sqrt{l^{2} +w^{2} +h^{2} }[/tex] = [tex]\sqrt{5^{2} +3^{2} + 2^{2} } = \sqrt{38}[/tex]
Hope it will find you well.
Answer
38 or about 6.16
Ava has a bag with 3 red, 2 blue, and 11 green beads.
She selects a bead at random. What is the probability that Ava does not select a green bead?
Answer:
5/16 or 31.25%
Step-by-step explanation:
There are 16 beads altogether 11 are green and the rest aren't so there for is 5 out of 16 chance green won't be selected
Answer:
5/16
Step-by-step explanation:
Factor completely. 1+12x+36x^2 what is the answer
Step-by-step explanation:
Factor using the perfect square rule.
( 1 + 6 x ) 2
Answer:
(1+6x)^2
Step-by-step explanation:
A fair 6 numbered die is rolled. What is the probability that the number rolled is greater that 3
Answer:
½
Step-by-step explanation:
Greater than 3: 4,5,6
3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
there is 6 numbers and 3 numbers greater than 3. so put that in fraction form 3/6 then simplify to 1/2
what does 2(5*-3) =
Answer:
[tex]-30[/tex]
Step-by-step explanation:
Step 1: Multiply inside the parenthesis
[tex]2(5 * -3)[/tex]
[tex]2(-15)[/tex]
Step 2: Multiply
[tex]2(-15)[/tex]
[tex]2 * -15[/tex]
[tex]-30[/tex]
Answer: [tex]-30[/tex]
Marty and Juan took turns driving a cargo truck. The ratio of the miles Marty drove to the miles Juan drove is 6 to 7. Juan drove 150 more miles than Marty. How many miles did Marty and Juan drive in all?
The total miles are 1950 miles. Marty drove 900 miles and Juan drove 1050 miles, if the ratio of the miles Marty drove to the miles Juan drove is 6 to 7 and Juan drove 150 more miles than Marty.
Step-by-step explanation:
The given is,
Ratio of the miles Marty drove to the miles Juan drove is 6 to 7
Juan drove 150 more miles than Marty
Step:1
Calculate the difference in the ratio of the miles Marty drove to the miles Juan drove,
X = 7-6 = 1
Calculate the difference in the miles of Marty drove to the miles of Juan drove,
X = 150 ( Juan drove 150 more miles than Marty)
Equate the Difference between ratio and miles,
From the above values,
X = 150 miles
Step:2
From the ratio of Marty : Juan = 6 : 7
Distance drove by Marty,
= 6X = ( 6 × 150 ) = 900
Distance drove by Marty = 900 miles
Distance drove by Juan,
= 7X = ( 7 × 150 ) = 1050
Distance drove by Juan = 1050 miles
Step:3
Check for solution,
Difference in the miles of Marty drove to the miles of Juan drove
150 = 1050 - 900
150 = 150
Result:
The total miles are is 1950 miles. Marty drove 900 miles and Juan drove 1050 miles, if the ratio of the miles Marty drove to the miles Juan drove is 6 to 7. Juan drove 150 more miles than Marty
I need help with this I've been trying to solve it for over half an hour.
Answer:
659.4 cm^2
Step-by-step explanation:
The area of the curved surface of the cone = πrL
= π*7*16
= 3.14 * 112
= 351.68 cm^2,
Surface area of the hemisphere = 2 π r^2
= 2*3.14*7^2
= 307.72 cm^2.
Total area = 351.68 + 307.72
= 659.4 cm^2.
what is missing blank
Answer:
-1
Step-by-step explanation:
the y s are decreasing by 3 while the x s are increasing by 2.
brainliest?
Answer:
-1
Step-by-step explanation:
if you look at the pattern, the x's pattern is minus 2, and the y's pattern is minus 3. to find the answer you just continue the pattern.
Hope this helps!
Can you solve for x please.
Answer:
3/4
Step-by-step explanation:
Multiply both sides by x
2x/3 = 1/2
Multiply both sides by 3
2x = 3/2
Divide both sides by 2
x = 3/4
What is the mode of the following set of numbers? 15, 20, 18, 20, 15, 20 A 20 B 18 C 5 D 19 .
Answer:
A
Step-by-step explanation:
Mode is the one that appears the most. The number that is there the most is 20 that makes it the mode.
The correct answer is A. 20.
To find the mode of a set of numbers, one must identify the number that appears most frequently in the list. In the given set of numbers: 15, 20, 18, 20, 15, 20, we can see that the number 20 appears three times, which is more frequent than any other number in the set. The number 15 appears twice, while the numbers 18 and 20 each appear once. Since 20 is the number with the highest frequency, it is the mode of the set.
Therefore, the mode of the given set of numbers is 20.
The coned shaped room has a height of 15 ft and a radius of 72. Find the volume
Answer:
81430.08
Step-by-step explanation:
Final answer:
The volume of a cone with a height of 15 ft and a radius of 72 ft is found using the formula V = (1/3)πr²h, and the calculated volume is approximately 81457.9 cubic feet.
Explanation:
The question is asking to find the volume of a cone, which has a height of 15 ft and a radius of 72 ft. The formula to calculate the volume of a cone is V = (1/3)πr²h, where 'V' represents the volume, 'r' is the radius of the base, and 'h' is the height of the cone.
To solve for the volume:
V = (1/3)π(72 ft)²(15 ft)
V = (1/3)π(5184 ft²)(15 ft)
V = (1/3)π(77760 ft³)
V = 25920π ft³
Therefore, the volume of the cone is approximately 25920π cubic feet, or when π is approximated as 3.14159, the volume is about 81457.9 cubic feet.
Line segment BA is tangent to the circle.
A circle is shown. Secant D B and tangent B A intersect at point B outside of the circle. Secant D B intersects the circle at point C. The length of A B is x, the length of B C is 55, and the length of C D is 120.
What is the length of line segment BA? Round to the nearest unit.
Answer:
Hence the length of line segment BA as 98 units
Step-by-step explanation:
Given:
BA as tangent to circle ,DB as secant which intersect at point C at circle
Length BC= 55 and CD=120
To Find:
Length of line segment AB.
Solution:
This follows the relationship between tangent and secant in circle terms as:
Consider as figure such that ,
AB as tangent , DB as secant C be point at circle
So secant total distance = DB=BC+CD =55+120=175
Using formula as ,
[tex]AB^2=BC(BC+CD)[/tex]
We have to find AB
Here BC=55 and CD=120
[tex]AB^2=55(120+55)[/tex]
[tex]AB^2=55(175)[/tex]
[tex]AB^2=9625[/tex]
[tex]AB=98.10[/tex]
So nearest unit for length will be 98
Hence the length of line segment BA as 98 units
Answer:
98 units
Step-by-step explanation:
edge
Round 18.4049629645 to 4 decimal places
A circle is shown. Secants R S and R T intersect at point R outside of the circle. Secant R S intersects the circle at point U. Secant R T intersects the circle at point V. The length of R U is 6, the length of U S is 10, and the length of R V is 8.
If secant segments SR and TR intersect at point R, find the length of VT.
Start by relating the secants and segments theorem to this diagram:
(RS)() = ()(RV)
Substitute values from the diagram into the equation:
(16)() = ()(8)
Solve for VT:
VT =
Answer:
Everything in -> [x]
(RS) [(RU)] = [(RT)] (RV)
(16) [(6)] = [(8+VT)] (8)
VT = [4]
Step-by-step explanation:
I just did the assignment, you're welcome.
Answer:
(RS) [(RU)] = [(RT)] (RV)
(16) [(6)] = [(8+VT)] (8)
VT = [4]
Step-by-step explanation:
Here mi amor
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Use the properties of exponents to solve for each
variable
4^8 •4² = 4^a
(2^4)^5 = 2^b
5^6
Step-by-step explanation:
[tex] \because \: {a}^{m} . {a}^{n} = {a}^{m + n} \\ \therefore \: {4}^{8} . {4}^{2} = {4}^{8 + 2} = {4}^{10} \\ \\ \because \: ({a}^{m})^{n} = {a}^{m \times n} \\ \therefore \:({2}^{4})^{5} = {2}^{4 \times 5} = {2}^{20} \\ \\ {5}^{6} = 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 15625[/tex]
The solution are:
a = 10b = 205^6 = 15625To solve for each variable using the properties of exponents, we can use the following steps:
Identify the base and exponent in each expression.
Use the properties of exponents to simplify the expressions.
Solve for the variable.
4^8 •4² = 4^a
Identify the base and exponent in each expression:
Base: 4
Exponent: 8 in the first expression, 2 in the second expression, and a in the third expression
Use the properties of exponents to simplify the expressions:
4^8 •4² = 4^(8+2) = 4^10
Solve for the variable:
4^a = 4^10
a = 10
(2^4)^5 = 2^b
Identify the base and exponent in each expression:
Base: 2
Exponent: 4 in the first expression, 5 in the second expression, and b in the third expression
Use the properties of exponents to simplify the expressions:
(2^4)^5 = 2^(4*5) = 2^20
Solve for the variable:
2^b = 2^20
b = 20
5^6
Identify the base and exponent:
Base: 5
Exponent: 6
Simplify the expression:
5^6 = 5*5*5*5*5*5 = 15625
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I need help on this Question.!
Answer:
see below
Step-by-step explanation:
m/n = 1/7
Using cross products
7m = n
This is a direct proportion
What is the ratio of the volume of Sphere A to the volume of Sphere B
Answer:1
Step-by-step explanation:
To find the ratio of the volume of sphere A to B
We get
A:B
V=4/3πr^3:4/3πr^3
4/3πr^3×3/4πr^3
Ratio of A to B
=1
Answer: 27
Step-by-step explanation: