Answer:
m² + 8m + 7 = (m + 1) (m + 7)
m² – 6m + 8 = (m – 2) (m – 4)
Step-by-step explanation:
If a trinomial ax² + bx + c is "factorable", you can use the AC method.
1. Multiply a and c.
2. Find factors of ac that add up to b.
3. Divide the factors by a and reduce.
4. The numerators are the constants, the denominators are the coefficients.
For example:
m² + 8m + 7
a = 1, b = 8, c = 7
1. ac = 1×7 = 7
2. Factors of 7 that add up to 8 are 1 and 7.
3. Divide by 1: 1/1 and 7/1
4. The factors are (m + 1) and (m + 7).
Therefore, m² + 8m + 7 = (m + 1) (m + 7).
Let's try one with a negative coefficient:
m² – 6m + 8
a = 1, b = -6, c = 8
1. ac = 1×8 = 8
2. Factors of 8 that add up to -6 are -2 and -4.
3. Divide by 1: -2/1 and -4/1
4. The factors are (m – 2) and (m – 4)
Therefore, m² – 6m + 8 = (m – 2) (m – 4).
You can check your answers by distributing.
HOBBIES Tawa wants to increase her rock collection by a power of three this year and
then increase it again by a power of two next year. If she has 2 rocks now, how many
rocks will she have after the second year?
Answer:
64
Step-by-step explanation:
Multiply 2 by itself three times, which gives you 8. Multiply 8 by itself twice, which gives you 64.
Tawa will multiply her initial 2 rocks by 3 in the first year, giving her 6 rocks.
In the second year, she multiplies the 6 rocks by 2, which results in a total of 12 rocks after two years.
Explanation:To solve how many rocks Tawa will have after two years, we follow two steps of exponential growth.
Initially, she has 2 rocks.
After the first year, her collection will increase by a power of three, which means we will multiply 2 by 3 to find the new total:
2 rocks × 3 = 6 rocks.
After the second year, the number of rocks is going to increase by a power of two.
We then take the new total from the first year and multiply it by 2:
6 rocks × 2 = 12 rocks.
So after increasing her collection by a power of three in the first year, and then by a power of two in the second year, Tawa will have a total of 12 rocks
Select the correct answer.
Which of the following correctly matches the banking term with the appropriate definition?
A. A deposit is the total amount of money you have in the bank.
B. A withdrawal is an amount of money you take out of the bank.
C.
Your balance is the money you put into the bank.
D.
All of the above
Reset
Next
Answer:
B. A withdrawal is an amount of money you take out of the bank.
Which of the following is written as a rational function?
A. P(x)=7x+1
B. G(x)=-4x
C. F(x)=x-5//3x (correct answer
D. Q(x)=x^2+6x-3
Answer:C
Step-by-step explanation:
The required rational function is F(x) = x-5/3x. Option C is correct.
From the options correct rational function is to be determined.
A rational number is defined as the number written in the form of the f ratio.
Here,
The property of rational function is it contains function on both numerator and denominator.
By looking to the property, only function F(x) = x-5/3x seems to rational functions.
Thus, the required rational bis F(x) = x-5/3x.
Learn more about rational numbers here
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6x − y + z = −3
4x − 3z = −13
2y + 5z = 15
Find the solutions?
Answer:
The solution of the equation are x = - 1 , y = 0 and z = 3
Step-by-step explanation:
Given three linear equation as :
6 x - y + z = - 3 ......A
4 x - 3 z = - 13 ......B
2 y + 5 z = 15 ......C
Solving eq A and C
I.e 2× (6 x - y + z ) = -3 ×2
or, 12 x - 2 y + 2 z = - 6
So, ( 12 x - 2 y + 2 z ) + ( 2 y + 5 z) = - 6 + 15
Or, 12 x + 7 z = 9 ......D
Solving eq B and D
I.e 3 × ( 4 x - 3 z ) = - 13 × 3
or, 12 x - 9 z = - 39
So, ( 12 x + 7 z ) - ( 12 x - 9 z ) = 9 + 39
or, 16 z = 48
∴ z = [tex]\frac{48}{16}[/tex]
i.e z = 3
put the value of z in eq D
So, 12 x + 7×3 = 9
Or, 12 x = 9 - 21
or, 12 x = - 12
∴ x = - [tex]\frac{12}{12}[/tex]
I.e x = - 1
Now, Put The value of z in eq C
or, 2 y + 5 z = 15
or, 2 y + 5 × 3 = 15
Or, 2 y = 15 - 15
or, 2 y = 0
∴ y = 0
Hence The solution of the equation are x = - 1 , y = 0 and z = 3 Answer
11,12,15 please I am confuuuuused
Answer:
11.x>50
12.y is greater than or equal to 8
15. z<8
Step-by-step explanation:
Determine the value of y in proportion 6 y - 10 / 5 + 7 y equals 1/2
Answer:
The value of y is [tex]\frac{5}{26}[/tex] .
Step-by-step explanation:
Given expression as :
6 y - [tex]\frac{10}{5}[/tex] + 7 y = [tex]\frac{1}{2}[/tex]
or, 6 y - 2 + 7 y = [tex]\frac{1}{2}[/tex]
Or, 13 y = [tex]\frac{1}{2}[/tex] + 2
Or, 13 y = [tex]\frac{5}{2}[/tex]
So, y = [tex]\frac{5}{2\times 13}[/tex]
Or, y = [tex]\frac{5}{26}[/tex]
Hence the value of y is [tex]\frac{5}{26}[/tex] . Answer
Select the correct answer.
What is the product of 3
-
2
0
0
Answer:
I think it's supposed to be 200-3=? from what it looks like... the answer would be 197 if that is the case.
Step-by-step explanation:
Answer:
3-200= -197
Step-by-step explanation:
you can use a calculator, but you can also subtract 200 by 3 which equals 197. then add a negative sign to the left of the number :
-197. A soccer club has 15 players for every team, with the exception of two teams that have 16 players each. Is the number of players proportional to the number of teams?
Answer: No
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
It doesn't tell you how many teams there but if there are two teams that have extra player it is obviously not proportional.
The expression 4x^2-px-7 leaves a remainder of -2 when divided by (x-3) find the value of p
The expression 4x^2-px-7 leaves a remainder of -2 when divided by (x-3). Then the value of p is 10.33
Solution:Given the expression is [tex]4x^2 - px - 7[/tex] leaves a remainder of -2 when divided by (x-3)
To find: value of p
x - 3 = 0
x = 3
Let [tex]g(x) = 4x^2 - px - 7[/tex]
Hence we can say,
g(3) = -2
Substitute x = 3 in g(x) we get,
[tex]g(3) = 4(3)^2 - p(3) - 7\\\\-2 = 4(3)^2 - p(3) - 7[/tex]
On solving we get,
-2 = 4(9) - 3p - 7
-2 = 36 - 3p - 7
3p = 36 - 7 + 2
3p = 31
[tex]p = \frac{31}{3} = 10.33[/tex]
Thus the value of p is 10.33
Mr. Rivona bought 5 pounds of
bananas for $0.45 per pound
How much did she spend in all
Answer:
2.25
Step-by-step explanation:
5*.45=2.25
Denita has 4 coins. If Denita flips all the coins at once, how many outcomes are in the sample space?
Answer:
16
Step-by-step explanation:
describe the location of the point having the following coordinates
Answer:
Step-by-step explanation:
What are the coordinates????
2.The diagonals of a rhombus are in the ratio 5:12. If its perimeter is 104 CM, findthe lengths of the sides and the diagonals.
Answer:
Lenghts of the sides: [tex]26\ cm[/tex]
Lenghts of the diagonals: [tex]48\ cm[/tex] and [tex]20\ cm[/tex]
Step-by-step explanation:
Look at the rhombus ABCD shown attached, where AC and BD de diagonals of the rhombus.
The sides of a rhombus have equal lenght. Then, since the perimeter of this one is 104 centimeters, you can find the lenght of each side as following:
[tex]AB=BC=CD=DA=\frac{104\ cm}{4}= 26\ cm[/tex]
You know that the diagonals are in the ratio [tex]5:12[/tex]
Then, let the diagonal AC be:
[tex]AC=12x[/tex]
This means that AE is:
[tex]AE=\frac{12x}{2}=6x[/tex]
And let the diagonal BD be:
[tex]BD=5x[/tex]
So BE is:
[tex]BE=\frac{5x}{2}=2.5x[/tex]
Since the diagonals of a rhombus are perpendicular to each other, four right triangles are formed, so you can use the Pythagorean Theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse and "b" and "c" are the legs.
In this case, you can choose the triangle ABE. Then:
[tex]a=AB=26\\b=AE=6x\\c=BE=2.5x[/tex]
Substituting values and solving for "x", you get:
[tex]26^2=(6x)^2+(2.5x)^2\\\\676=36x^2+6.25x^2\\\\\sqrt{\frac{676}{42.25}}=x\\\\x=4[/tex]
Therefore, the lenghts of the diagonals are:
[tex]AC=12(4)\ cm=48\ cm[/tex]
[tex]BD=5(4)\ cm=20\ cm[/tex]
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< BACK TO HOMEPAGE - NORTHWEST CLASSEN NS ALGEBRA I S1 CR 2019-2020
What is the value of
What is the value of g( – 3) when g(x) = 2x – 22
when
Enter your answer in the box.
g(-3) =
Answer: [tex]g(-3)=-28[/tex]
Step-by-step explanation:
For this exercise it is important to remember the multiplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(-)(+)=-[/tex]
You have the following function g(x) provided in the exercise:
[tex]g(x) = 2x - 22[/tex]
The problem asks to find the value of [tex]g(-3)[/tex]. In order to find it, you need to substitute [tex]x=-3[/tex] into the function g(x):
[tex]g(-3) = 2(-3) - 22[/tex]
The final step is to evaluate.
Applying this procedure, you get that the value of [tex]g(-3)[/tex] is:
[tex]g(-3) = -6 - 22\\\\g(-3)=-28[/tex]
** sum of 3 elevens and 4 fives
Eighty minus the product of 10 and 4
Write the expressions in numerical form. Then, compare the expressions using >, < =
The difference between 60 - 50
3x10
5 fifteens
50 + 20
The sum of 1 eleven and 3 elevens
35 x 15
42 + 35
The product of 9 and 8
Answer:
hope this helped i was kinda confused by the question
Step-by-step explanation:
3 x 11 = 33
4 x 5 = 20
33 + 20 = 53
10 x 4 = 40
80 - 40 = 40
53 > 40
60 - 50 = 10
3 x 10 = 30
5 x 15 = 75
50 = 20 = 70
11 + 33 = 44
35 x 15 = 525
42 + 35 = 77
9 x 8 = 72
How do we use graphic technology
Answer:
f light is imagined as a flow of particles, the particles are called photons with each photon carrying a discrete packet of energy.
David bought a 20 ounce bottle of soda. How many quarts of soda are in the bottle?
A
5/32 quarts
B
5/8 quarts
C
1 1/4 quarts
D
2 1/2 quarts
Answer:
The answer is B. 5/8 quarts
Step-by-step explanation:
1 ounce is equal to .03125 quarts so to find the amount of quarts, you multiply 20 times .03125 to get .625 or 5/8.
Final answer:
There are 5/8 quarts of soda in a 20 ounce bottle, which is found by dividing 20 by the conversion factor of 32 ounces per quart.
Explanation:
The student has asked how many quarts of soda are in a 20 ounce bottle. To convert ounces to quarts, we use the conversion factor that there are 32 ounces in a quart. To find the number of quarts in 20 ounces, we divide 20 by 32.
20 oz ÷ 32 oz/qt = 0.625 qt
This can also be written as 5/8 quarts, which is option B. Therefore, there are 5/8 quarts of soda in a 20 ounce bottle.
In Exercises 26-28, write an equation. Then solve.
26. DRY ICE The temperature of dry ice is - 109.3°F. This is 184.9°F less than
the outside temperature. What is the outside temperature?
Answer:
The temperature outside is 75.6°F
Step-by-step explanation:
We are given the following in the question:
The temperature of dry ice = - 109.3°F
Let x be the temperature outside in Fahrenheit.
It is given that the temperature of dry ice is 184.9°F less than the outside temperature.
Thus, we can write the equation:
[tex]x - 184.9 = -109.3[/tex]
Solving, the above equation, we get:
[tex]x - 184.9 = -109.3\\x = -109.3 + 184.9\\x = 75.6[/tex]
Thus, the temperature outside is 75.6°F
-30=4-8x solve for x
Answer: x=4.25
Step-by-step explanation:
-30=4-8x
subtract 4 from both sides
-8x=-34
divide by -8 on both sides
x=4.25
The area of a rectangular room is given by the trinomial 3x^2-13x-30 what are the possible dimensions of the frame? Use factoring.
Answer:
(3x + 5) and (x - 6).
Step-by-step explanation:
3x^2-13x-30
Use the 'ac' method:
a * c = 3*-30 = -90.
We need two numbers whose product is -90 and whose sum is -13. They are -18 and + 5, so we have
3x^2 - 18x + 5x - 30 Factor by grouping:
= 3x(x - 6) + 5(x - 6)
= (3x + 5)(x - 6).
Answer:
A (3x + 5) and (x - 6
Step-by-step explanation:
A student memorized the statement the product of any rational number and an irrational number is irrational label this statement as true or false and explain your reasoning
A student memorized the statement the product of any rational number and an irrational number is irrational holds true for non-zero rational number
Solution:
A rational number is a number that can be written as a fraction.
When a rational number fraction is divided to form a decimal value,
it becomes a terminating or repeating decimal.
An Irrational Number is a real number that cannot be written as a simple fraction. It cannot be expressed as a fraction with integer values in the numerator and denominator.
When an irrational number is expressed in decimal form, it goes on forever without repeating.
"The product of a rational number and an irrational number is SOMETIMES irrational."
If you multiply any irrational number by the rational number zero, the result will be zero, which is rational.
Any other situation, however, of a product of rational and irrational will be irrational.
A better statement would be:
"The product of a non-zero rational number and an irrational number is irrational."
Let us understand this with a example
[tex]\text { non - zero rational number } \times \text { irrational number }=\text { irrational number }[/tex]
Consider [tex]\frac{1}{2} \rightarrow rational number[/tex]
[tex]\frac{\sqrt{3}}{4} \rightarrow irrational number[/tex]
Now multiply both,
[tex]\frac{1}{2} \times \frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{4}=0.433012701[/tex]
We got 0.433012701 which is a irrational number because in decimal form, it goes on forever without repeating.
Thus we can frame two statements:
"The product of a rational number and an irrational number is SOMETIMES irrational." "The product of a non-zero rational number and an irrational number is irrational."Answer:
True.Step-by-step explanation:
"The product of any rational number and an irrational number is irrational"
To know if the statement is true or false, we can test an example. Lets use the rational number [tex]\frac{3}{2}[/tex] and the irrational number [tex]\pi[/tex]. Id we calculate the product of these two we would have:
[tex]\frac{3}{2}\pi= 4.71238898038469...[/tex]
As you can observe, the product is an irrational number, because it's infinite and not periodic, it doesn't have any pattern.
Therefore, the statement is true.
Need help with this math problem
Answer:
X=13
Step-by-step explanation:
15x-15= 180
15x-15+15=180+15
15x/15=195/15
X=13
Now just plug X in to every equation
(Q) 4(13)-22= 30
(P) 10(13)-4= 126
(R) 1(13)+11=24
Factor the expression X2+4X +4
Answer:
2(3+2x)
Step-by-step explanation:
Answer:
(X + 2)^2
Step-by-step explanation:
Factor using the perfect square rule
Hope this helps.
PLEASE, consider brainliest. I only have one left and then my rank will go up.
What information can be used to compare linear
relationships? Explain why.
Answer:
Step-by-step explanation:
The slope and the y intercept (you can tell there linear if the slope is the same and the y-intercepts are different).
Answer:
Information from dependent and independent variables.
Step-by-step explanation:
Information from dependent and independent variables and how they are related to each other. A relationship is linear only is every ordered pair is related by the same number, which is represented by the slope.
Simplify this expression.
m13 × m6 =
Answer: 78m^2
Step-by-step explanation:
multiply coefficients and variables
m13 x m6 = 78m^2
Answer:
78m
Step-by-step explanation:
Since the variables are alike, you would just multiply them as you would do a normal multiplication problem! I used to have so much trouble with this omg. Anyway, 13x6=78 so the answer would be 78m
the ratio to staff to guests at the gala was 3 to 5 . there was a total of576 oeople in the ball room .how many guests were at the gala
Select all of the ratios that are equivalent to 4 to 7
Answer:
4/7= 12/21- mutiply the fraction by 3
(4)(3)/(7/(3)= 12/21
4/7= 16/28 - mutiply by 4
4/7= 20/35- mutiply by 5
Equivalent ratios are those that when reduced yield the same value. Any ratios that when reduced become 4/7 are equivalent to the ratio 4 to 7. An example is 8 to 14.
Explanation:In mathematics, two ratios are equivalent if the fractions they represent are equal. For your question, you are asked to find all ratios that are equivalent to the ratio 4 to 7. Essentially, you need to find ratios where when reduced will become 4/7 or we can upscale the values while maintaining proportions. For instance, if we multiply both numbers in the ratio 4 to 7 by 2, we get the ratio 8 to 14. These two ratios are equivalent because 4/7 = 8/14.
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1=(6/-15)(-5)+b
What is the answer
Answer:
b=-1
Step-by-step explanation:
1=(6/-15)(-5)+b
-6/15=-2/5
(-2/5)(-5)=10/5=2
2+b=1
b=1-2=-1
The circumference of a circle is 44 inches. What is the area? (Use 22 for pie.)
I need the answer pls
Answer:
A
Step-by-step explanation:
To rite the equation of the function, take two points from the table. Let them be (1,21) and (3,15).
The slope of the function is
[tex]\dfrac{21-15}{1-3}=\dfrac{6}{-2}=-3[/tex]
Thus, the equation of the function in slope-intercept form is
[tex]f(n)=-3n+b[/tex]
Find b by substituting coordinates of the first point into the function expression:
[tex]21=-3\cdot 1+b\\ \\b=21+3\\ \\b=24[/tex]
Therefore,
[tex]f(n)=-3n+24[/tex]