Answer:
(x-1) x-12
Step-by-step explanation:
Step 1 : Multiply first term of the first bracket to the first term of the other bracket
Step 2 : Then multiply the first term of the first bracket to the last term of the second bracket.
Step 3 : Now come to the second term of first bracket, multiply second term with first term of second bracket.
Step 4 : Finally multiply last term of first bracket with the last term of the second bracket.
Step 5 : Adding all the answers got from the steps, we get the final answer.
Final answer:
The FOIL method is an algebraic technique for multiplying two binomials, represented as (First, Outer, Inner, Last). For the expression (X+3)(x-4), we apply this method to get x^2 - x - 12 after combining like terms.
Explanation:
The FOIL method is a technique used in algebra to multiply two binomials. The acronym FOIL stands for First, Outer, Inner, Last and refers to the order in which you multiply the terms in the binomials. Applying the FOIL method to the expression (X+3)(x-4), we multiply the First terms (x × x), the Outer terms (x × -4), the Inner terms (3 × x), and the Last terms (3 × -4), then sum them all.
Step-by-step, this looks like:
First: x × x = x^2
Outer: x × (-4) = -4x
Inner: 3 × x = 3x
Last: 3 × (-4) = -12
Now, combine these results to get the final expression:
x^2 - 4x + 3x - 12
Combining like terms, we have:
x^2 - x - 12
helpppppppppppppppppppppppppppppppppppppp
Answer:
For every 15 students scoring in the 60's there were 9 students scoring in the 70's.
Step-by-step explanation:
Your first step would be to rewrite the numbers into an easier to understand form like fractions, 45/3 and 27/3. Then you divide both numbers by 3, so you get comparable numbers. 45/3= 15, 27/3=9.
Name the angle in 2 different ways and name the 2 rays from the diagram below please show work
Answer:
3) TB and NT
4) ∠KLM and ∠MLK
Step-by-step explanation:
3) those two rays intersect to form the angle shown in the diagram
4) an angle can always be named from left to right or right to left as long as the middle letter is always the vertex of the angle
Jian’s family sells honey from beehives. They collected 3,311 ounces of honey from the beehives this season. They will use the honey to completely fill 4-ounce jars or 6-ounce jars. Jian’s family will sell 4-ounce jars for $5 each or 6-ounce jars for $8 each. Jian says if they use only 4-ounce jars, they could make $4,140 because 3,311 / 4 =827 R3. That rounds up to 828, and 828 multiplied by $5 is $4,140. Part A-Explain the error that Jian made when finding the amount of money his family could make if they use only 4-ounce jars. Enter your explanation in the space provided. Part B- Explain how to determine the money Jian’s family could make if they use only 6-ounce jars. Include the total amount of money and the total number of 6-ounce jars in your explanation. Enter your answers and your explanation in the space provided.
Answer:
A. Jian rounded the number of 4-ounce jars to 828 which is wrong. There are only 827 jars that can be completely filled.
B. Total number of 6-ounce jars = 551
Total money earned from 6-ounce jars = $4408
Step-by-step explanation:
A. Jian's family's collection = 3311 ounces
Number of 4-ounce jars = [tex]\frac{3311}{4}[/tex]
= 827.75
Jian rounded it to 828 which is wrong. There are 827 jars that can be completely filled.
Cost per 4-ounce jar = $5.
Total cost = 827 × 5 = 4135
B. Now, number of 6-ounce jars = [tex]\frac{3311}{6}[/tex]
= 551.83
≅ 551 jars
Cost per 6-ounce jar = $8
Total cost = 551 × 8 = 4408
Which expression will give the new price of a $15 item marked up by 28%
A. 28+0.15 X 28
B. 28-0.15 X 28
C. 15+0.28 X 15
D. 15-0.28 X 15
Answer:
the answer is
C
if i am wrong let me know
Step-by-step explanation:
Find the illegal values of b in the fraction
Answer:
[tex]b=4\text { or }b=-2[/tex]
Step-by-step explanation:
We have been given a rational expression: [tex]\frac{2b^2+3b-10}{b^2-2b-8}[/tex] and we are asked to find the illegal values of b.
Illegal values of b will be those values, which will make our denominator 0.
To solve for illegal or excluded values of b, let us set our denominator equal to 0.
[tex]b^2-2b-8=0[/tex]
We will factor out our equation by splitting the middle term.
[tex]b^2-4b+2b-8=0[/tex]
[tex]b(b-4)+2(b-4)=0[/tex]
[tex](b-4)(b+2)=0[/tex]
[tex]b-4=0\text { or }b+2=0[/tex]
[tex]b=4\text { or }b=-2[/tex]
Therefore, [tex]b=4\text { or }b=-2[/tex] are illegal values of b in the given fraction.
use the diagram to answer the questions
1. which ray is a bisector of ABC
A. BC
B. BD
C. BA
D. BF
2. what is GH
A. 5
B. 10
C. 15
D. 25
3. what is the value of y
A. 2
B. 4
C. 16
D. 20
Answer:
1. B. BD
2. C. 15
3. A. 2
Step-by-step explanation:
1. From the figure,
∠DAB = ∠DAC
Therefore, BD is the bisector of ∠ABC.
2. From the figure, IG = GH
3x = 5x - 10
10 = 5x - 3x
2x = 10
x = 5
So, GH = 5x - 10
= 5(5) - 10
= 25 - 10
= 15
Therefore, GH = 15.
3. From the figure,
∠DAB = ∠DAC
10y = 8y + 4
10y - 8y = 4
2y = 4
y = 2
What is the geometric mean of 5 and 4
Answer:
[tex]2\sqrt{5}[/tex]
Step-by-step explanation:
Geometric mean of two numbers of the square root of their product:
[tex]\sqrt{20}=\sqrt{4\cdot5}=2\sqrt{5}[/tex]
The geometric mean of 5 and 4 is [tex]2\sqrt{5}[/tex].
What is the geometric mean of two numbers?The Geometric mean of the two numbers formula is defined as the square root of the product of 2 numbers.
The following formula is used to calculate the geometric mean;
[tex]\rm Geometric \ mean = \sqrt{a \times b}[/tex]
Where a is the first term and b is the second term.
Therefore,
The geometric mean of 5 and 4 is;
[tex]\rm Geometric \ mean = \sqrt{a \times b}\\\\a=5 \ and \ b=4\\\\\rm Geometric \ mean = \sqrt{5 \times 4}\\\\\rm Geometric \ mean = \sqrt{20}\\\\\rm Geometric \ mean = 2\sqrt{5}[/tex]
Hence, the geometric mean of 5 and 4 is [tex]2\sqrt{5}[/tex].
To know more about the Geometric mean click the link given below.
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rounding decimals 4.3
Answer:
Step-by-step explanation:
If you round 4.3 to the nearest whole number, you will get 4.The reason is because a number less than 5 is closer to 4 but a number greater than five or is five will be rounded to five.
Please mark brainliest!!!!!!!
simplify yhe expression 2(10) + 2( x--4).
3x+6y=-9 and X+2y=-3
[tex]\left\{\begin{array}{ccc}3x+6y=-9&\text{divide both sides by (-3)}\\x+2y=-3\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-x-2y=3\\x+2y=-3\end{array}\right}\qquad\text{add both sides of the equations}\\. \qquad\qquad0=0\qquad TRUE\\\\Answer:\ \boxed{\text{Infinitely many solutions}}\\\\\left\{\begin{array}{ccc}x\in\mathbb{R}\\y=-\dfrac{1}{2}x-\dfrac{3}{2}\end{array}\right[/tex]
Write the equation in slope intercept form: Passes through = (2,3) (0,9)
Answer:
Y=-3x+9
Step-by-step explanation:
Slope is found using
9-3 over 0-2
This gets 6/-2
This gets -3
-3 is the slope
9 is the y-intercept
use the coordinates of the labeled points to find a point-slope equation of the line. (3,-4)
Answer:
slope=-3
y=-3x+5
Step-by-step explanation:
use two given points (3,-4)(0,5)
5- -4= 9
0-3=-3
9/-3=-3
Answer: [tex]y+4=-3(x-3)[/tex]
Step-by-step explanation:
The point-slope equation of a straight line is:
[tex]y-y_{1}=m(x-x_{1} )[/tex]
where m is the slope and [tex](x_{1}, y_{1} )[/tex] are the coordinates of a point in the line.
So, to find the equation, the firs step is to find the slope. We can see in the graphic that the line intercepts the y axis at the point (0, 5), so we're going to use that and the other given point to find the slope:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}} =\frac{-4-5}{3-0} =\frac{-9}{3}=-3[/tex]
Then, you simply substitute the slope and the coordinates of the point and you get the point-slope equation:
[tex]y-(-4)=-3(x-3)\\y+4=-3(x-3)[/tex]
How to write a linear function with the values f(3)=-4 f(5)=-4
To write a linear function with the given values f(3) = -4 and f(5) = -4, we can use the point-slope form of a linear equation. The linear function is y = -4.
Explanation:To write a linear function with the given values f(3) = -4 and f(5) = -4, we can use the point-slope form of a linear equation. The formula for point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. We can choose any point (x1, y1) from the given values. Let's choose (3, -4) as a point on the line. Now we can substitute the values into the formula to find the linear function:
y - (-4) = m(x - 3)
y + 4 = m(x - 3)
To find the slope, we can use another point on the line, such as (5, -4). Substituting the values into the formula, we get:
-4 + 4 = m(5 - 3)
0 = 2m
Solving for m, we get m = 0.
Now we can substitute the slope and one of the points back into the formula to find the linear function:
y + 4 = 0(x - 3)
y + 4 = 0
y = -4
So, the linear function with the given values is y = -4.
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Given values f(3) = -4 and f(5) = -4 suggest a horizontal line as the y-coordinate remains constant at -4 regardless of x values. Hence, the linear function is f(x) = -4.
Explanation:The student wants to know how to write a linear function with the values f(3)=-4 and f(5)=-4. The first thing we need to understand here is that a linear function is represented by the equation y = mx + b, where y is the output, m is the slope, x is the input, and b is the y-intercept. In this problem, since f(3) = -4 and f(5) = -4, it indicates that the y coordinate remains the same (-4), thus forming a horizontal line despite the changes in the x coordinates. This means the function has a slope (m) of 0. So, the linear function that satisfies these conditions is f(x) = -4.
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Error Analysis Mario has 7 cups of milk. A one-batch recipe for pancakes calls for two thirds cup of milk. To see how many batches he could make, Mario finds 7 divided by two thirds . He said that because 7 divided by two thirds equalsone seventh times three halves , he could make three fourteenths of a batch . What was his error? How many batches could he make?
A.
He multiplied the dividend by the divisor.
B.
He multiplied the reciprocal of the dividend by the divisor.
C.
He multiplied the dividend by the reciprocal of the divisor.
D.
He multiplied the reciprocal of the dividend by the reciprocal of the divisor.
[tex]\bf 7\div \cfrac{2}{3}\implies 7\cdot \cfrac{3}{2}\implies \cfrac{7\cdot 3}{2}\implies \cfrac{21}{2}\implies 10\frac{1}{2}~~\checkmark \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{so, what happened to Mario?}}{7\div \cfrac{2}{3}\implies \cfrac{7}{1}\div \cfrac{2}{3}}\implies \stackrel{\boxed{?}}{\cfrac{1}{7}}\cdot \cfrac{3}{2}\implies \cfrac{3}{14}~~\bigotimes[/tex]
he ended up multiplying the 7 by the 2 for some reason.
and an explanation could be he used the reciprocal of both numbers mistakenly.
Answer:
c
Step-by-step explanation:
At the popular restaurant Fire Wok,
55% of guests order the signature dish.
What fraction of guests order the signature dish?
Answer:
11/20
Step-by-step explanation:
Answer: [tex]\dfrac{11}{20}[/tex] represents the fraction of guests order the signature dish.
Step-by-step explanation:
Since we have given that
Percentage of guest who order the signature dish = 55%
Total percentage = 100
We need to find the fraction of guests order the signature dish.
So, Fraction of guests order the signature dish is given by
[tex]\dfrac{\text{Percentage of guest order the signature dish}}{\text{Total percentage}}\\\\=\dfrac{55}{100}\\\\=\dfrac{11}{20}[/tex]
Hence, [tex]\dfrac{11}{20}[/tex] represents the fraction of guests order the signature dish.
Dianna earns $8.50 an hour working as a lifeguard write an equation to find Dianna’s money earned?
How do I do this please dumb this down
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept fprm is
y = mx + b ( m is the slope and b the y-intercept )
y = [tex]\frac{5}{4}[/tex] x - 4 is in this form
with m = [tex]\frac{5}{4}[/tex] and b = - 4
Plot the point (0, - 4)
using the slope add 5 to the y-coordinate and 4 to the x-coordinate
(0, - 4 ) → (0 + 4, - 4 + 5) → (4, 1) ← point on the line
Plot the points (0, - 4) and (4, 1) and draw a straight line through them to obtain a sketch of the graph
HELP FAST 100 POINTS: The manager of a basketball arena randomly selected 150 fans and asked if they were pleased with the new selection of food offered in the arena. In this sample, 120 fans said that they were pleased.
How many of the 8000 fans at the game could be expected to be pleased?
7880
6400
7970
7850
Answer:
6400 fans will be pleased.
Step-by-step explanation:
Out of 150 fans, 120 were pleased. Assuming the same ratio, out of 8000 fans, 8000x120/150 = 6400 will be pleased.
Answer:
6400
Step-by-step explanation:
We need to find the fraction of fans that are pleased
120 out of 150 are please
120/150 = 12/15 =4/5
We multiply this fraction by the fans at the game
4/5 * 8000 = 6400
6400 fans should be pleased
Find the value of the permutation.
8P1 ?
Answer:
8P1 = 8
Step-by-step explanation:
Permutation
The number of elements can be selected from a set of elements.
Let r be the number of elements want to select and n be the set of elements.
It can be written as nPr
nPr = n!/(n - r)!
To find 8P1
n= 8 and r = 1
8P1 = 8!/(8-1)! = 8!/7! = (8 x 7!)/7! = 8
Therefore 8P1 = 8
Huma, Hubna and Seema received a total of ₨2,016 as monthly allowance from their mother such that Seema gets 12 of what Huma gets and Hubna gets 123 times Seema’s share. How much money do the three sisters get individually?
i need correct answer no signs used
Answer:
Huma's share =Rs x = Rs. 1.35392881
Seema's share =Rs. 12x = Rs (12 * 1.35392881) = Rs. 16.2471457
Hubna's share =Rs. 123*12x = Rs. (123*16.2471457) = Rs. 1998.39892
Step-by-step explanation:
Given :
Huma , Hubna and Seema received a total of ₨2,016 as monthly allowance from their mother.
Seema gets 12 of what Huma gets
Hubna gets 123 times Seema’s share
To find : How much money do the three sisters get individually?
Solution :
Let Huma's share be Rs. x.
Since we are given that Seema gets 12 of Huma's share
⇒ Seema's share = Rs 12x.
Since we are given that Hubna gets 123 times Seema’s share
⇒Hubna's share = Rs. (123 * 12x) = Rs. 1476x.
We are given that they received together Rs. 2016 in total .
⇒[tex]x+12x+1476x= 2016[/tex]
⇒[tex]1489x= 2016[/tex]
⇒[tex]x = \frac{2016}{1489}[/tex]
⇒[tex]x = 1.35392881[/tex]
Thus Huma's share =Rs x = Rs. 1.35392881
Thus Seema's share =Rs. 12x = Rs (12 * 1.35392881) = Rs. 16.2471457
Thus Hubna's share =Rs. 123*12x = Rs. (123*16.2471457) = Rs. 1998.39892
Gabe Amodeo, a nuclear physicist, needs 60 liters of a 60% acid solution. He currently has a 50% solution and a 70% solution. How many liters of each does he need to make the needed 60 liters of 60% acid solution? Gabe needs 30 liters for a 50% solution .
He also needs a ___ for a 70% solution . whats __?
Answer:
Gabe needs 20 liters of the 40% solution.
He also needs 40 liters of the 70% solution.
Step-by-step explanation:
Equation:
acid + acid = acid
0.40x + 0.70(60-x) = 0.60*60
40x + 70*60 - 70x = 60*60
-30x = -10*60
x = 20 liters
Gabe needs 20 liters of the 40% solution.
He also needs 40 liters of the 70% solution.
Use the substitution method to solve the system of equation.choose the correct ordered pair.
2y+4x=18
2y-3x=4
[tex]\left\{\begin{array}{ccc}2y+4x=18\\2y-3x=4&\text{add 3x to both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}2y+4x=18&(**)\\2y=3x+4&(*)\end{array}\right\\\\\text{Substitute}\ (*)\ \text{to}\ (**):\\\\3x+4+4x=18\qquad\text{subtract 4 from both sides}\\7x=14\qquad\text{divide both sides by 7}\\\boxed{x=2}\\\\\text{Put the value of x to the first equation:}\\\\2y+4(2)=18\\2y+8=18\qquad\text{subtract 8 from both sides}\\2y=10\qquad\text{divide both sides by 2}\\\boxed{y=5}\\\\Answer:\ \boxed{x=2\ and\ y=5}[/tex]
Please explain your answer.
Answer:
x=4.4
Step-by-step explanation:
To get from A to B, the scale factor is 2.5, since 4*2.5 = 10
So, to get from B to A, you divide by 2.5.
11/2.5 = 4.4
you are a plumber installing a pipe the ratio of the outside diameter to the inside diameter is 1.5 to 1. you use a pipe with a 0.5 inch inside diameter what is the smallest diameter that you will need to drill to allow the pipes to pass through the wall
The smallest diameter needed to drill through the wall is 0.75 inches, which is calculated by multiplying the inside diameter of the pipe (0.5 inches) by the ratio of the outside diameter to the inside diameter (1.5). Always measure and plan ahead to avoid mistakes.
Explanation:The subject matter of this question is mathematics, specifically ratios. To find the smallest diameter you would need to drill into the wall, you would need to multiply the inside diameter of your pipe (0.5 inches) by the ratio of the outside diameter to the inside diameter (1.5). So, 0.5 inches * 1.5 = 0.75 inches.
This means, to allow the pipes to pass through the wall, you will need to drill a hole at least 0.75 inches in diameter. This is assuming the wall is thin enough that the entire length of the pipe that needs to pass through the wall is less than the thickness of the wall.
Remember, it's always better to pre-measure and plan ahead to avoid unnecessary work and potentially costly mistakes.
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August hosted two dinner parties for his friends. Twenty guests attended the first party, and twenty-six guests attended the second party. What is the percentage increase of the number of guests from the first party to the second party?
Answer: 30%
Step-by-step explanation:
The first step is to find the increase in numbers
26-20= 6
Now you find the percent. This means you're looking for the percent 6 is equal to when compared to 20. The easiest way is to divide the increase by the original number
6/20= 0.3
To convert that to percent, multiply it by 100
0.3 * 100= 30%
There was a 30% increase.
Final answer:
To calculate the percentage increase of guests from August's first party to the second, subtract the initial number from the final number, divide by the initial number, and multiply by 100. The calculation shows a 30% increase in guests from 20 to 26.
Explanation:
The question asks to calculate the percentage increase in the number of guests from the first dinner party to the second dinner party hosted by August. To find the percentage increase, you subtract the original number of guests from the new number of guests, divide by the original number, and then multiply by 100 to get the percentage.
We start with the initial number of guests at the first party, which is 20, and the final number of guests at the second party, which is 26. Using the formula:
Percentage Increase = ((Final Number - Initial Number) / Initial Number) × 100
Percentage Increase = ((26 - 20) / 20) × 100
Percentage Increase = (6 / 20) × 100
Percentage Increase = 0.3 × 100
Percentage Increase = 30%
Therefore, the percentage increase of the number of guests from the first party to the second party is 30%.
The length of a rectangle is 8 cm longer than its width . Its perimeter is more than 28cm . If W represents the width of the rectangle what expression represents the length in terms of the width
Answer:
W + 8
Step-by-step explanation:
Given:
The length of the rectangle is 8 cm longer than its width.
Let's take "W" be the width.
Length = W + 8
The expression "w + 8" represents the length of the rectangle.
Thank you.
Answer:
L=W+8
Step-by-step explanation:
This means that whatever number of centimeters the width is, you will always add 8 centimeters in order to reach the size of the length. In order to calculate the perimeter of the rectangle you have to add all its four sides and the final formula would be as follows:
W+W+L+L=P, where W is Width and L, is Length (W+8).
In other words, you can calculate as shown below:
W+W+(W+8)+(w+8)=P
Identify the slope of the line shown in the graph below: slope = -1
Slope = 0
Slope = undefined
Slope = 1
It's a vertical line. The slope of vertical line is undefined.
The equation of a vertical line is x = a (a - any real number).
Answer: Slope = undefinedEquation of line: x = -1Answer:
Slope = undefined
Step-by-step explanation:
A vertical STRAIGHT line that represents a slope is undefined.
the sum of two numbers is 76. The difference is 24. Find the two numbers doing the elimination method
Answer:
50 and 26
Step-by-step explanation:
Make an equation! That makes it much simpler and has helped me a lot.
x+x-24=76
Combine like terms
2x+24=76
Add 24 on both sides
2x=52
Divide both sides by 2
x=26
72-26=50
To check that their difference is correct, subtract 26 from 50
50-26=24
Hope this helps!
Need help with Mathematics. I can't copy and paste so I screenshot it
Answer: 1.44
Step-by-step explanation:
1.2×1.2
1.2
1.2
__
24
120
__
144
Add two decimal places: 1.44
Answer:
1.44
Step-by-step explanation:
1.2^2 = 1.2 * 1.2
1.2 * 1.2 = 1.44
Your just finding the squad route of it. It can also be done the same way when your ^3 or even ^4 since its all timing the same number. Hope this helps out!
What is the LCD of 4/7 and 1/2 ? get this right you will be marked brainlest dont put random anwsers!
Answer:
14
Step-by-step explanation:
The LCD is the LCM of the denominators, 7 and 2. Since these numbers have no common factors, their LCM is simply their product:
... 7·2 = 14