Final answer:
To solve the equation for a, subtract z from both sides, factor out a, and then divide by (m - b), resulting in a = -z / (m - b), assuming m and b are not equal.
Explanation:
To solve the equation z + ma = ba for a, we need to isolate a on one side of the equation. We can rewrite the equation, moving all terms involving a to one side and all other terms to the opposite side. This process is called collecting like terms.
Here are the steps to isolate a:
Subtract z from both sides of the equation to get ma = ba - z.
Since both terms on the right hand side involve a, factor a out: a ( m - b ) = -z.
Finally, divide both sides of the equation by (m - b) to solve for a: a = -z / (m - b), assuming that m ≠ b.
This algebraic manipulation gives us the value of a in terms of z, m, and b.
Solve by factoring write the steps.
x2−7x+10=0
Please help show me all the steps and the answers
Factor completely. a2+3a−28 Enter your answer in the box.
Solution :
To factor completely
[tex] a^{2} + 3a-28 [/tex]
To factor it completely , first take the product of first and third term, and then break the second term in two parts in such a way that its sum equals the second term and the product equals the product of first and third term.
Product of first and third term is [tex] (a^{2})(-28) = -28 a^{2} [/tex]
Second term is 3a, Re-write 3a as sum of 7a and -4a.
Lets check it Product of 7a and -4a is [tex] -28 a^{2} [/tex] wich is eaqual to product of first and third term and sum of 7a and -4a is 3a which is the second term.
Now factorise, we get
[tex] a^{2}+3a-28\\\\ = a^{2} +7a-4a-28\\\\=a(a+7)-4(a+7)\\\\=(a+7)(a-4) [/tex]
Hence, [tex] (a+7)(a-4) [/tex] is the factor of [tex] a^{2}+3a-28 [/tex].
In a game played with a standard deck of cards, each face card has a value of 10 points, each ace has a value of 1 point, and each number card has a value equal to its number. two cards are drawn at random. it at least one card is an ace, what is the probability that the sum of the cards is 7 or less?
Which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 8mn5 – 2m6 + 5m2n4 – m3n3 + n6 – 4m6 + 9m2n4 – mn5 – 4m3n3 n6 + 7mn5 + 14m2n4 – 5m3n3 – 6m6 –2m6 – 5m3n3 + 14m2n4 + 7mn5 + n6 14m2n4 + 7mn5 – 6m6 – 5m3n3 + n6 n6 – 6m6 + 7mn5 + 14m2n4 – 5m3n3
The correct combining of like term is
f(m, n) = [tex]n^{6}[/tex] + 7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ -6[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]
What is polynomial equation?A polynomial equation is the equation in which the unknown variable is one and the highest power of the unknown variable is n.
Given:
8m[tex]n^{5}[/tex] - 2[tex]m^{6}[/tex] +5m²[tex]n^{4}[/tex] - m³n³ + [tex]n^{6}[/tex] - 4[tex]m^{6}[/tex] + 9m²[tex]n^{4}[/tex] - m[tex]n^{5}[/tex] - 4m³n³
Now, Combining the like terms
(8m[tex]n^{5}[/tex] - m[tex]n^{5}[/tex]) + 5m²[tex]n^{4}[/tex] + 9m²[tex]n^{4}[/tex] - m³n³ - 4m³n³ + [tex]n^{6}[/tex] - 4[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]
=7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ - 6 [tex]m^{6}[/tex] + [tex]n^{6}[/tex]
now, arranging according to their powers
[tex]n^{6}[/tex] + 7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ -6[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]
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calculate the length of the circumference of a circle with diameter of 9cm
16. For quadrilateral ABCD, determine the most precise name for it. A (-2, 3), B (9, 3), C (5, 6) and D (2, 6). Show your work and explain.
Answer:
Trapzoid
Step-by-step explanation:
Given: A (-2, 3), B (9, 3), C (5, 6) and D (2, 6)
We will find the slope of each line.
Formula:
[tex]\text{Slope, m}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\text{Slope of AB, m}_1=\dfrac{3-3}{9+2}=0[/tex]
[tex]\text{Slope of BC, m}_2=\dfrac{6-3}{5-9}=-\dfrac{3}{4}[/tex]
[tex]\text{Slope of CD, m}_3=\dfrac{6-6}{2-5}=0[/tex]
[tex]\text{Slope of AD, m}_4=\dfrac{6-3}{2+2}=\dfrac{3}{4}[/tex]
Slope of AB = Slope of CD = 0
[tex]m_1=m_3=0[/tex]
Thus, AB is parallel to CD
Slope of BC ≠ Slope of AD
[tex]m_2\neq m_4[/tex]
Thus, BC is not parallel to AD
The quadrilateral ABCD has two sides are parallel and two are not parallel.
Hence, The quadrilateral is trapzoid
What is the equation, in slope-intercept form, of the line that is perpendicular to the line Y-4=-2/3(X-6) and passes through the point (-2,-2)
Answer:
d
Step-by-step explanation:
if the xy-plane, the graph of y=x^2 and the circle with center (0,1) and radious 3 have how many points of intersection?
A. none
b. one
c, two
d. three
e. more than three
The answer could be A or c but idk which one is the right one please help
Leah has a piece of cloth that is 3 ft 8 in long. She decides to cut 2/11 of the cloth off. How long is the cloth now?
Chris is building a large deck for the community center. The deck is shaped as a rectangle. The width of the deck is 29 ft. The perimeter of the deck is to be at least 134 ft. (please answer both questions)
1) Write an inequality that represents all possible values for the length of the deck.
2) Solve algebraically to find all possible values for the length of the deck.
K - 263.48 = 381.09 solve this equation
1.One of the lamp posts at a bank has a motion detector on it, and the equation (x+15)2+(y−12)2=25 describes the boundary within which motion can be sensed.
What is the greatest distance, in feet, a person could be from the lamp and be detected?
5 ft
10 ft
50 ft
125 ft
Answer:
5ft
Step-by-step explanation:
The required greatest distance, in feet, a person could be from the lamp and be detected is 5 ft. Option A is correct.
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
Here,
Given equation
(x+15)²+(y−12)²=25
The above equation is the equation of the circle, so the longest distance that person could be from the lamp and be detected is the radius of the circle,
Which is given as,
r² = 25
r = √25
r = 5
Thus, the required greatest distance, in feet, a person could be from the lamp and be detected is 5 ft. Option A is correct.
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The population density of ground crickets at oldmill farm is about 15 per square meter. assuming that the crickets are randomly distributed, about how many crickets would you expect to find in a rectangular section of land that is 6 meters × 2 meters?
Cassandra lives in Oklahoma and makes $60,000 a year. If the median annual income in Oklahoma is $64,105 and the median annual income in the United States as a whole is $50,233, is Cassandra likely to qualify for Chapter 7 bankruptcy?
Answer:
Cassandra is likely to qualify for Chapter 7 bankruptcy.
Step-by-step explanation:
Given scenario is : Cassandra lives in Oklahoma and makes $60,000 a year. The median annual income in Oklahoma is $64,105.
A person qualifies for chapter 7 bankruptcy, if his annual median income is below the median income of his state. So, here the annual median income of Cassandra is below the median income of her state, Oklahoma.
So, she will qualify for chapter 7 bankruptcy.
Write the equation of the line, in standard form, that passes through the origin and is parallel to x + y = 6. Include your work in your final answer.
I understand the answer is x + y = 0
I want to understand how that is determined. Using point slope form and all that.,
helppppppppppppppppppppp
Answer:
1/4
Step-by-step explanation:
If a circle has an diameter of 14, what would the area be?
Use 3.14 for π
How to tell whether a slope is positive negative zero or undefined?
On Monday Mrs. Wise bought 3 lbs of apples at $4 per lb. On Tuesday, apples were on sale for 20% off so she bought another 5 lbs. What was the price of apples on Tuesday? NEED ANSWER ASAP!
It is given that on Tuesday, apples were on sale for 20% off. Now, we know that on Monday Mrs. Wise bought 3 lbs of apples at $4 per lb. This means that if we have a 20% off on Tuesday then this must be with respect to the price on Monday which is $4. Thus the price of Tuesday can be calculated as:
[tex] 4-\frac{20}{100}\times 4=4-0.8=3.2 [/tex]
Thus, the per pound price of apples on Tuesday was $3.2
Which diagram could be used to prove △ABC ~ △DEC using similarity transformations?
(from top to bottom, first pictures top option is A for example)
A.
B.
C.
D.
To prove similarity, the triangles must have three angles or any three components must be equal. According to the statement, option A seems to be proof the triangles are similar to each other.
There are two images given in the question.
Let us segregate the images into image 1 and image 2.
Take image 1.
In image 1, three different triangles are given,
One angle is equal in all the triangles, which is represented as a single arc.Another angle is represented as a double arc is equal.If two angles are equal in triangles then the third angle is automatic get equal.According to the above bullet points, image 1 qualifies all the requirements for the similarity of the triangles.
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according to the tree diagram below what is the probability that someone buys a book that is paperback and fiction
see the attached figure to better understand the problem
we know that
[tex]0.65\ (65\%)[/tex] of the buyers buy paperback and [tex]0.45\ (45\%)[/tex] of them buy fiction.
Hence
The probability that they buy both fiction and paperback is equal to
[tex]0.65*0.45=0.2925[/tex]
the answer is
[tex]0.2925[/tex]
Please help me on that question for my Algebra. I don't understand it.
Also, how would you rate my pfp?
What is the equation of the line described below written in slope-intercept form? the line passing through point (0, 0) and parallel to the line whose equation is 3x + 2y - 6 = 0
Answer:
The slope intercept form of the required line is [tex]y=\frac{-3}{2}x[/tex].
Step-by-step explanation:
If a line is defined as
[tex]Ax+By+C=0[/tex] ... (1)
Then the slope of the line is
[tex]m=\frac{-A}{B}[/tex]
The given equation is
[tex]3x+2y-6=0[/tex] .... (2)
From (1) and (2), we get
[tex]A=3, B=2, C=-6[/tex]
The slope of the line is
[tex]m=\frac{-3}{2}[/tex]
The slope of parallel line is same. So, the slope of required line is -3/2.
The slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
The slope of required line is -3/2 and y-intercept is at (0,0).
[tex]y=\frac{-3}{2}x+0[/tex]
[tex]y=\frac{-3}{2}x[/tex]
Therefore the slope intercept form of the required line is [tex]y=\frac{-3}{2}x[/tex].
What is the value of this expression when z = 36?
10 - /z
4
6
-8
-26
The provided expression with 'z = 36' is incomplete and lacks an operation or additional numbers, making it impossible to calculate its value. The student is advised to provide the full expression for proper assistance.
Explanation:The student asked: What is the value of this expression when z = 36?
Unfortunately, there is a typographical error in the expression provided. It seems to be missing an operation or additional numbers. Given the format '/z', it seems like it should have been a mathematical operation involving the variable 'z'. However, without an operator such as '+' (plus), '-' (minus), '*' (multiply), or '/' (divide), we cannot determine what the expression is supposed to be or calculate its value given z = 36.
If this is an expression from a specific textbook or sheet, I recommend double-checking the source material for the correct expression. If it's a part of a larger problem or context, please provide the full details so that an accurate computation can be made.
Please help me out :)
Find the perimeter of the rectangle.
If the rectangle has vertices M(−2,4), N(1,5), O(3,−1), and P(0,−2), what is the perimeter of the rectangle?
Round each side length to the nearest tenth, if necessary.
Find the probability that when a couple has four four children, at least one of them is a girl girl. (assume that boys and girls are equally likely.)
Simplify the expression below. (xy)^8
A regular n-gon has an interior angle and an exterior angle with equal measures. What is the value of n?