Answers
Answer:
By definition, angles A and 1 are corresponding angles and angles B and 1 are consecutive angles. By the corresponding angles postulate, angles A and 1 are congruent, and by the consecutive angles theorem, angles B and 1 are supplementary. By the definition of supplementary angles, measures of angle B and 1 add up to 180 degrees (m<B + m<1 = 180). By definition of congruent angles, angles A and 1 have same measurement (m<A = m<1). By substitution property of equality, measures of angles A and B add up to 180 degrees (m<A + m<B = 180). By definition of supplementary angles, angles A and B are supplementary.
Related Questions
Isabelle is mixing red paint with blue paint to make purple paint. She adds 3/10 of a fluid ounce of red to 11/15 of a fluid ounce of blue to make 1 1/30fluid ounces of purple. How many fluid ounces of red paint will she need to make 3 fluid ounces of purple paint?
Answers
Answer:
27/31
Step-by-step explanation:
FIrst, construct a ratio. Isabelle needs 3/10 red to make 31/30 purple. So, we can divide red by purple to form a fraction to determine how much red paint for 1 fluid oz of purple. (3/10)/(31/30)=(9/30)/(31/30)=9/31. For every 1 oz of purple, we need 9/31 oz of red. Because we found how much red paint for 1 oz purple paint, we simply multiply by 3 to find how much red paint for 3 fluid oz of purple paint. (9/31)*3=27/31
The sum of two numbers is 56. The first number is 2 times greater than the second number. What is the second number?
Answers
Answer:
y = 56/3
Step-by-step explanation:
We need to write equations to solve
Let the two numbers be x and y
The sum is 56
x+y = 56
The first number is 2 times greater than the second number.
x = 2*y
Substitute this into the first equation
x+y = 56
2y+y=56
3y = 56
y = 56/3
Step-by-step explanation:
Let the numbers be x and y
The sum of the two numbers is 56 :
Step 1:
X + Y = 56.......... (1)
Also, the first number is 2 times greater than the second number:
Step 2:
2X + Y = 0........... (2)
By substitution method, make Y the subject from (2)
Step 3:
Y = -2X .......... (3)
Put (3) into (1)
Step 4
X - 2X = 56
-X = 56
[tex] \frac{ - x}{ - 1} = \frac{56}{ - 1} [/tex]
X = -56
Put X=56 into (3)
Step 5
[tex]y = - 2( - 56)[/tex]
[tex]y = 112[/tex]
The second number is now 112.
Create an equivalent system of equations using the sum of the system and the first equation. x 4y = 8 4x y = 2 x 4y = 8 5x y = 2 x 4y = 8 5x 5y = 2 x 4y = 8 4x 5y = 10 x 4y = 8 5x 5y = 10
Answers
An equivalent system of equations using the sum of the system and the first equation is:
[tex]x+4y=8\\5x+5y=10[/tex]
What are equations?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal.[tex]3x+5=14[/tex], for example, is an equation in which [tex]3x+5[/tex] and [tex]14[/tex] are two expressions separated by a '=' sign.Given:
[tex]x+4y=8\\4x+y=2[/tex]
Add the above equations to get:
[tex]x+4y+4x+y=8+2\\x+4y+4x+y=10\\5x+5y=10[/tex]
Therefore, an equivalent system of equations using the sum of the system and the first equation is:
[tex]x+4y=8\\5x+5y=10[/tex]
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The correct question is given below:
Create an equivalent system of equations using the sum of the system and the first equation.
x + 4y = 8
4x + y = 2
x + 4y = 8
5x + y = 2
x + 4y = 8
5x + 5y = 2
x + 4y = 8
4x + 5y = 10
x + 4y = 8
5x + 5y = 10
You conduct a quasi-experiment to assess the impact of raising the speed limit from 55 to 65 miles per hour. You find that there are more accidents in the 6-month period following the speed limit change than in the 6-month period before the speed limit change. Although it is tempting to say that raising the speed limit caused higher accident rates, you must be careful because
Answers
It's tempting to say that increasing the speed limit has led to higher accident rates, but you have to be careful because other variables (e.g. cheaper gas or time of year the change was introduced) can also affect accident rates. The option C is correct.
Given the impact of the speed limit increase from 55 to 65 mph, there are more crashes in the 6 months after the speed limit change than in the 6 months before the speed limit change. speed.
The dependent variable is the variable that is attempted and expected in a survey and is "dependent" on the free aspect. In a survey, the scientist tries to find the conceivable influence on the reliable variable, which can be approximated by changing the free thing. The free aspect is the variable that the experimenter adjusts or controls, and should directly affect the dependent variable. Therefore, increasing the speed limit from 55 to 65 mph resulted in higher accident rates, you have to be careful with other variables.
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ABCD is a rhombus. If AB = 2x + 12 , AC = 7x - 3, ∠=12°, and ∠ = (4y - 1)°.m ∠BAC = __ .
Answers
Answer: try 35
Step-by-step explanation:
HELP FAST PLEASE!!! Find the sample space of the situation using a table or tree diagram on
paper, and then type your sample space below.
tossing a coin (Heads or Tails) AND spinning the spinner (1-5)
Answers
Answer:
Sample space:
{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}
Step-by-step explanation:
Tossing a coin has two possible outcomes, heads (H) and tails (T).
Spinning the spinner has 5 possible outcomes, 1, 2, 3, 4, 5.
Table:
First spin H H H H H T T T T T
Second spin 1 2 3 4 5 1 2 3 4 5
Sample space:
{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}
Select the correct answer. what is this series written in sigma notation? 2.5 2.5(1.2) 2.5(1.2)2 ⋯ 2.5(1.2)87 a. ∑ k = 1 87 2.5 ( 1.2 ) k b. ∑ k = 1 87 2.5 ( 1.2 ) k − 1 c. ∑ k = 1 88 2.5 ( 1.2 ) k d.
Answers
∑ k = 1 88 2.5 ( 1.2 ) k is this series written in sigma notation.
What is the series written in sigma notation?
A series can be represented in a compact form, called summation or sigma notation. The Greek capital letter, ∑ , is used to represent the sum. The series 4+8+12+16+20+24 can be expressed as 6∑n=14n . The expression is read as the sum of 4n as n goes from 1 to 6 .Given:
2.5 + 2.5(1.2) + 2.5(1.2)2 + ⋯ + 2.5(1.2)87
If we look at the power it is always one less the term i.e., for first term the value of k=0.
So, the series in the form of summation can be written as
∑ k = 1 88 2.5 ( 1.2 ) k
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neeed help please pleasee
Answers
Answer:
Y = 2+- square root of 6
Step-by-step explanation:
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Lets solve ~
Let's calculate its discriminant ~
[tex]\qquad \sf \dashrightarrow \: {y}^{2} -4y - 2=0[/tex]
a = 1b = -4c = -2[tex]\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]
[tex]\qquad \sf \dashrightarrow \: d = (-4) {}^{2} - (4 \times 1\times - 2)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 16 - ( - 8)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 24[/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt {d }= 2 \sqrt{6} [/tex]
So, by quadratic formula :
[tex]\qquad \sf \dashrightarrow \: y= \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \: y = \dfrac{ - {(-4)}^{} \pm 2\sqrt{6} }{2 ×1} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:y=\pm \cfrac{2(2\pm\sqrt{6} }{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:y= { 2+\sqrt{6}}{} \: \: and \: \: t = {2-\sqrt{6}}{} [/tex]
A base- three-digit number is selected at random. What is the probability that the base- representation and the base- representation of are both three-digit numerals
Answers
The probability that the base-9 representation and the base-11 representation of are both three-digit numerals is 0.6753
How to determine the probability?To calculate the probability that the base-9 representation and the base-11 representation of are both three-digit numerals, we need the following parameters:
The smallest 3-digit base 11 number in base 10The largest 3-digit in base 9 in base 10 with 3 digits The count of base 10 3-digit numbersThe smallest 3-digit base-11 number is 100
When converted to base 10, the equivalent number is 121
The largest 3-digit base-9 number is 888
When converted to base 10, the equivalent number is 728
So, the total number of possibilities is:
Possibilities = 728 - 121 + 1
Possibilities = 608
The count of base 10 3-digit numbers is
Count = 999 - 100 + 1
Count = 900
The required probability is:
P = 608/900
Evaluate
P = 0.6753
Hence, the probability that the base-9 representation and the base-11 representation of are both three-digit numerals is 0.6753
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Complete question
A base-10 three-digit number is selected at random. What is the probability that the base-9 representation and the base-11 representation of are both three-digit numerals
If f(x + 1) = x + 2 then f(x - 1) is
Answers
Answer: [tex]\Large\boxed{f(x-1)=x}[/tex]
Step-by-step explanation:
Given function
f(x + 1) = x + 2
Isolate [ x + 1 ] on the right-hand side
f(x + 1) = x + 1 + 1
f(x + 1) = (x + 1) + 1
Substitute [ x + 1 ] with x
f(x) = x + 1
Substitute [ x ] with [ x - 1 ]
f(x - 1) = (x - 1) + 1
[tex]\Large\boxed{f(x-1)=x}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
You have $25 and want to buy some ice
cream sandwiches that cost $1.25 each.
How many can you buy?
Answers
For the same sample data and null hypothesis, how does the p-value for a two-tailed test of μ compare to that for a one-tailed test?.
Answers
A one-tailed test's p-value is half that of a two-tailed test.
What is the difference between the p-value for a two-tailed test and a one-tailed test?Whether it is positive or negative, when you find your test statistic, you also find a tail probability to the right or left of that test statistic. What is the likelihood that, if the null hypothesis is correct, you will obtain a value that is more extreme (far out in the tail) than the observed test statistic? If the test is two-tailed, the phrase "probability...more extreme" applies to both tails, beyond the positive and negative values of your test statistic. Your calculations will fall either on the right or left, but if the test is two-tailed, it will also apply to both tails.
What is null hypothesis ?Two possibilities sharing similarities is the null hypothesis. That the observed discrepancy is solely the result of chance is the null hypothesis. Calculating the probability that the null hypothesis is correct using statistical testing is achievable.
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Each gallon of porch and deck paint covers 200 square feet. how many gallons are needed to cover 1241 square feet?
Answers
7 gallons are needed to cover 1241 square feet.
In this question,
Each gallon of porch and deck paint covers 200 square feet.
To find out how many gallons of paint needs, we have to divide the total area of deck by the amount of deck that one gallon covers.
We use the unitary method to find out how many gallons of paint needs.
Using unitary method,
1241 / 200 = 6.205
However, we cannot buy a fraction of a gallon of paint.
So, the amount of gallons of paint needed is approximately equal to 7 gallons.
Therefore, 7 gallons are needed to cover 1241 square feet.
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Minnie bought 6 postcards during 3 days of vacation. After 8 days of vacation, how many total postcards will Minnie have bought?
A. 12
Answers
Answer:
16
Step-by-step explanation:
6/3 = 2 postcards per day
2x8 = 16 postcards
6/3 = 2 postcards a day
[tex]2x+5\ \textless \ \frac{x+1}{4}[/tex]
Answers
Given :-
2x + 5 < x + 1 / 4Solution :-
>> 2x + 5 < x + 1 / 4
>> 4 (2x + 5) < x + 1
>> 4 × (2x + 5) < x + 1
>> 8x + 20 < x + 1
>> 8x - x < 1 - 20
>> 7x < 1 - 20
>> 7x < -19
>> x = -19 / 7
[tex]\boldsymbol{\sf{2x+5 < \dfrac{x+1}{4} }}[/tex]
Multiply the two sides of the equation by 4. Since 4 is > 0, the direction of inequality remains the same.
[tex]\boldsymbol{\sf{8x+20 < x+1 }}[/tex]
Resta x en los dos lados.
[tex]\boldsymbol{\sf{8x+20-x < 1 }}[/tex]
Combine 8x and −x to get 7x.
[tex]\boldsymbol{\sf{7x+20 < 1 }}[/tex]
Subtract 20 on both sides.
[tex]\boldsymbol{\sf{7x < 1-20 \ \ \longmapsto \ \ [To \ subtract] }}[/tex]
[tex]\boldsymbol{\sf{7x < -19 }}[/tex]
Divide the two sides by 7. Since 7 is >0, the direction of inequality remains the same.
[tex]\boldsymbol{\sf{x < -\dfrac{19}{7} } }[/tex]
As the end result, it is not simplified or divided, then
[tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ x < -\frac{19}{7} }}}}[/tex]
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https://brainly.com/question/23265395What is the annual interest paid on an account that has a $1000 balance if the rate is [tex]7\frac{1}{2}[/tex]%?
Answers
The annual interest paid on the account is $75
How to determine the annual interest
The formula for determining annual interest is given as;
Interest = PRT/100
where;
P is the principal amount = $1000R is the rate = 7. 5%T is the time = 1 year, since it's an annual paymentSubstitute the values
Annual Interest = 1000 × 7. 5 × 1/ 100
Annual interest = 7500/ 100
Annual interest = $75
Thus, the annual interest paid on the account is $75
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Which function in vertex form is equivalent to f(x) = 4 + x² - 2x?
O f(x) = (x - 1)² + 3
O f(x) = (x-1)² + 5
O f(x) = (x + 1)² + 3
O f(x) = (x + 1)² +5
Answers
Answer:
f(x)=(x-1)^2+3
Step-by-step explanation:
Both equations vertexes equal (1, 3) while the rest do not match.
f(x) = (x - 1)² + 3 function in vertex form is equivalent to f(x) = 4 + x² - 2x.
We can use the technique of completing the square to rewrite the given function f(x) in vertex form.
f(x) = 4 + x² - 2x
f(x) = (x² - 2x) + 4
Adding and subtracting (1) inside the parentheses
f(x) = (x² - 2x + 1) + 4 - 1
f(x) = (x - 1)² + 3
So, the equivalent function in vertex form is f(x) = (x - 1)² + 3.
Therefore, the correct option is f(x) = (x - 1)² + 3.
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Study island surface area
Answers
Answer:
C. 206 unit^2.
Step-by-step explanation:
Area = 2*11*5 + 2*11*3 + 2*3*5
= 110 + 66 + 30
= 206.
Factor the greatest common factor: −5k2 20k − 30. −1(5k2 − 20k 30) −5(k2 − 4k 6) −5k(k2 − 4k 6) −5(k2 4k − 6)
Answers
The greatest common factor−5k2 20k − 30 is [tex]-5(k^{2} -4k-6).[/tex]
What is meant by the greatest common factor?The most common factor in mathematics is the highest number that may divide evenly into two other numbers.The largest factor that splits both numbers is the greatest common factor. List the prime factors of each integer before calculating the greatest common factor. One 2 and one 3 are shared by those aged 18 and 24. We multiply them to obtain the GCF. Therefore the GCF for 18 and 24 is 2 * 3 = 6.The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a collection of whole numbers.To find the greatest common factor:
−5k2 20k − 30.
Factor the expression: [tex]5(-k^{2} +4k-6)[/tex]
Factor the expression: [tex]5(-k^{2} -4k+6)[/tex]
Multiply the monomials: [tex]5(k^{2} +4k+6)[/tex]
The greatest common factor: [tex]-5(k^{2} -4k-6).[/tex]
The greatest common factor−5k2 20k − 30 is [tex]-5(k^{2} -4k-6).[/tex]
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The complete question is:
Factor the greatest common factor: [tex]-5k^2+ 20k - 30.[/tex]
a) [tex]-1(5k^2- 20k+ 30)[/tex]
b) [tex]-5(k^2 -4k+ 6)[/tex]
c)[tex]-5k(k^2 - 4k +6)[/tex]
d) [tex]-5(k^2 +4k - 6)[/tex]
The greatest common factor of −5k² + 20k − 30 exists -5( k² - 4k + 6 ).
Therefore, the correct answer is option a) -5 ( k² - 4k + 6 ).
What is greatest common factor (GCF)?The greatest common factor (GCF) of a set of numbers exists the biggest factor that all the numbers share.
Given : −5k² + 20k − 30.
Taking common -5 from each term, we get
−5k² + 20k − 30 = -5 ( k² - 4k + 6 ).
The greatest common factor of −5k² + 20k − 30 exists -5( k² - 4k + 6 ).
Therefore, the correct answer is option a) -5 ( k² - 4k + 6 ).
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Here is the histogram of a data distribution. What is the shape of this distribution?
Answers
Considering it's histogram, the shape of the distribution is given by:
D. Bimodal.
What is an histogram?An histogram of a data-set is a graph that shows the number of times each element of x was observed.
In this problem, elements 1 and 10 were each observed 5 times, meaning that there are two modes in the data-set, hence the data-set is bimodal and option D is correct.
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Tanya is training a turtle for a turtle race. For every 1/3 of an hour that the turtle is crawling, he can travel 2/23 of a mile. At what unit rate is the turtle crawling?
Answers
Answer: 6/23 mph
Step-by-step explanation: We change the 1/3 of an hour to 1 hour by multiplying 1/3 and 2/23 by 3. 1/3 times 3 is 1(hour) and 2/23 x 3 is 6/23(miles). So the unit rate the turtle is traveling at is 6/23 mph.
Which point is a solution to the system of inequalities graphed here? y ≤ 2x 2 y ≥ -5x 4
Answers
The point that is a solution to the system of inequalities is (5, 0)
How to determine the points on the solution?The system of inequalities is given as:
y ≤ 2x + 2
y ≥ -5x + 4
Next, we test the given options.
From the list of options, we have
(x, y) = (5, 0)
Substitute (x, y) = (5, 0) in y ≤ 2x + 2 and y ≥ -5x + 4
y ≤ 2x + 2
0 ≤ 2 * 5 + 2
0 ≤ 12 -- this is true
y ≥ -5x + 4
0 ≥ -5 * 5 + 4
0 ≥ -21 -- this is true
Since both results are true, then it means that the point that is a solution to the system of inequalities is (5, 0)
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Complete question
Which point is a solution to the system of inequalities graphed here? y ≤ 2x + 2
y ≥ -5x + 4
A. (1,6)
B. (-6,0)
C. (0,5)
D. (5,0)
5. In a recent year, the population of Springfield, Illinois was one hundred
sixteen thousand, four hundred eighty-two. Write this number in standard
form. Show your work in the space below. Remember to check your solution
Answers
Answer: 16482
Step-by-step explanation:
Let's divide the number into three parts:
sixteen thousand | four hundred |eighty-two
A thousand is 1000, so sixteen thousand should be 16000.
A hundred is 100, so four hundred should be 400.
Eighty-two is just 82.
Let's add all of these:
[tex]16000+400+82=16482[/tex]
Solve for n
-19=-8+n
Answers
Answer:
8-18=n
-10=n
therefore
n=-10
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{n = -11}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{-19 = -8 + n}[/tex]
Find: [tex]\textsf{Solve for n}[/tex]
Solution: In order to solve for n we need to add 8 to both sides which would cancel -8 on the right side and isolate n giving us the value of n.
Add 8 to both sides
[tex]\textsf{-19 + 8 = -8 + 8 + n}[/tex][tex]\textsf{-19 + 8 = n}[/tex][tex]\textsf{-11 = n}[/tex]Therefore, the final answer would be that n is equal to -11.
Identify the equation for the line tangent to the circle x^2 + y^2 = 100 at the point (−6, 8).
Answers
The equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex] at the point (-6,8) is -6x+8y=100.
Given the equation of circle [tex]x^{2} +y^{2} =100[/tex]
and point at which the tangent meets the circle is (-6,8).
A tangent to a circle is basically a line at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of circle to the point P.
Linear equation looks like y=mx+c.
Tangent to a circle of equation [tex]x^{2} +y^{2} =a^{2}[/tex] at (z,t) is:
xz+ty=[tex]a^{2}[/tex].
We have to just put the values in the formula above to get the equation of tangent to the circle [tex]x^{2} +y^{2} =100[/tex] at (-6,8).
It will be as under:
x(-6)+y(8)=100
-6x+8y=100
Hence the equation of tangent to the circle at the point (-6,8) is -6x+8y=100.
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Which issue is least likely arise in machine learning (ml) and artificial intelligence (ai)?
Answers
The issue of too many proficient business-savvy programmers is least likely to arise in machine learning(ml) and artificial intelligence(ai).
What is machine learning?
The process by which computers learn to recognize patterns, or the capacity to continuously learn from and make predictions based on data, then make adjustments without being specifically programmed to do so, is known as machine learning (ML), a subcategory of artificial intelligence.
The operation of machine learning is quite complicated and varies according to the task at hand and the algorithm employed to do it. However, at its foundation, a machine learning model is a computer that analyzes data to spot patterns before using those realizations to better fulfill the work that has been given to it. Machine learning can automate any task that depends on a set of data points or rules, even the more difficult ones.
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On the unit circle, where 0 undefined?
Answers
Type the correct answer in each box. use numerals instead of words. the surface area of a cylinder is approximately 640.56 square meters. the radius of the cylinder is 5 meters less than the height of the cylinder. to the nearest whole meter, what are the radius and height of the cylinder? the radius is approximately meters, and the height is approximately meters.
Answers
The radius of cylinder = 6 meter
The height of cylinder = 11 meter
According to the question,
Surface area of the cylinder = 640.56 m²
Let the height of the cylinder = x meters
Let the radius of the cylinder = (x-5)meters
Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)
640.56 = 2 (3.14) (x-5) (x)
640.56/(6.28) = x² - 5x
x² - 5x =102
x² - 5x - 102 =0
using quadratic equation, [-b±√(b² - 4ac)]/2a.
b = -5; a=1; c=102
x =[-(-5) ±√(-5)² - 4(1)(102)]/2
= [5 ± √433]/2
x = 11 and -7
since x=-7 neglect negative value, we get x=11.
The height of the cylinder is 11 meters
The radius of the cylinder is (11 - 5) = 6 meters.
Hence, The radius of cylinder = 6 meter.
The height of cylinder = 11 meter.
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Answer:
Step-by-step explanation:
The radius of cylinder = 6 meter
The height of cylinder = 11 meter
According to the question,
Surface area of the cylinder = 640.56 m²
Let the height of the cylinder = x meters
Let the radius of the cylinder = (x-5)meters
Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)
640.56 = 2 (3.14) (x-5) (x)
640.56/(6.28) = x² - 5x
x² - 5x =102
x² - 5x - 102 =0
using quadratic equation, [-b±√(b² - 4ac)]/2a.
b = -5; a=1; c=102
x =[-(-5) ±√(-5)² - 4(1)(102)]/2
= [5 ± √433]/2
x = 11 and -7
since x=-7 neglect negative value, we get x=11.
The height of the cylinder is 11 meters
The radius of the cylinder is (11 - 5) = 6 meters.
Hence, The radius of cylinder = 6 meter.
The height of cylinder = 11 meter.
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let h(x)=-1/3x+2. Find -4h(9)
Answers
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \: - 4 \: h(9) = 4[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:h(x) = - \cfrac{1}{3} x + 2[/tex]
we need to find -4 h(9) :
[tex]\qquad❖ \: \sf \: - 4 \: h(9)[/tex]
[tex]\qquad❖ \: \sf \: - 4 \bigg(- \dfrac{1}{3} \times 9 + 2 \bigg)[/tex]
[tex]\qquad❖ \: \sf \: - 4( - 3 + 2)[/tex]
[tex]\qquad❖ \: \sf \: - 4( - 1)[/tex]
[tex]\qquad❖ \: \sf \:4[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \: - 4 \: h(9) = 4[/tex]
If function g has the factors (x − 7) and (x 6), what are the zeros of function g? a. -7 and 6 b. -6 and 7 c. 6 and 7 d. -7 and -6
Answers
The correct option B.
The value of the zeros of function g is -6 and 7
What is Quadratic equation?Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.
According to the given information:The factors are (x − 7) and (x + 6)
On simplifying the we get:
x²+ 6x -7x -42 = 0
x² - x - 42 = 0
The factorizing these equation we get.
So the zeros are -6 and 7 , so option b is correct.
[tex]x_{1,2}=\frac{-(-1) \pm \sqrt{(-1)^{2}-4 \cdot 1 \cdot(-42)}}{2 \cdot 1}[/tex]
[tex]$$x_{1,2}=\frac{-(-1) \pm 13}{2 \cdot 1}\\[/tex]
[tex]x_1,_2[/tex] = ((1) ± 13)/2.1
[tex]x_1[/tex] = (1+13)/2.1
[tex]x_2[/tex] = (1 - 13)/2.1
[tex]X_1\\[/tex] = 7 , [tex]X_2[/tex] = -6
The Zeros of the function are: (7 , -6)
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