Answer:
The system has one solution,
Both lines have the same y-intercept,
The solution is the intersection of the 2 lines.
Step-by-step explanation:
Write the name of the definition, postulate, property or theorem that justifies the statement about the diagram.
The following are the statement justifications and explanatory reasons ;
(a) AD + DB = AB; Is justified by segment addition postulate
Reason
Segment addition postulate states that let A and B represent two points,
Then a third D can be on the line joining A and B, if and only if the
relationship between the points is according to the equation, AD + DB = AB
only
(b) m∠1 + m∠2 = m∠CDB; Is justified by angle addition postulate
Reason
Angle addition postulate states that given that a point B lies between an angle m∠AOC, then we have;
m∠AOC = m∠AOB + m∠BOC
(c) ∠2 ≅ ∠6; Is justified by vertically opposite angles theorem
Reason
Vertical angles formed by the crossing of two lines are always equal
(d) If D is the midpoint of [tex]\overline{AB}[/tex], then AD = [tex]\dfrac{1}{2}[/tex]×AB; Definition of midpoint
Reason
The midpoint of a line is the point that is of equal distance from both ends of the of the line. It is the point halfway between the endpoints
(e) If [tex]\underset{DF}{\rightarrow}[/tex] bisects ∠CDB then ∠1 ≅ ∠2; Definition of angle bisector
Reason
An angle bisector is a ray or line that divides an angle into two angles that are congruent
(f) m∠ADF + m∠FDB = 180°; Linear pair postulate
Reason
The linear pair postulate states that where we have two angles that form a linear pear (their addition forms a straight line), then the two angles are supplementary (their sum is 180°)
(g) ∠ADF and ∠4 are supplements, then m∠ADF + m∠4 = 180°; Definition of supplementary angle
Reason
Supplementary angle are defined as angles that when added together, have a sum of 180°
(h) If ∠4 is complementary to ∠5, and ∠6 is complementary to ∠5, then ∠4 ≅ ∠6; Transitive property
Reason
Transitive property states that given three real numbers, a, b, and c, if a = b and c = b, then a = c
Learn more about angle properties postulates, and theorems here;
https://brainly.com/question/14437065
Rationalize the denominator and simplify:
a) (√3 - √2)/( √3+√2)
b) (5+2√3)/(7+4√3)
c) (1+√2)/(3 - 2√2)
Answer:
A) (√3-√2)/(√3+√2)
Step-by-step explanation:
i think so
Help anyone can help me do this question,I will mark brainlest.
Answer:
[tex]344 {cm}^{2} [/tex]
Step-by-step explanation:
[tex]area \: of \: the \: square \\ = 40cm \times 40cm \\ = 1600 {cm}^{3} \\ [/tex]
[tex]area \: of \: the \: circle \\ = \pi {r}^{2} \\ = 3.14 \times {(20)}^{2} \\ = 3.14 \times 400 \\ = 1256 {cm}^{2} \\ [/tex]
[tex]area \: of \: shaded \: region \\ = 1600 {cm}^{2} - 1256 {cm}^{2} \\ = 344 {cm}^{2} \\ [/tex]
The question is
"Mia has a large bag of sweets, If i share the sweets equally among 1,2,3,4,5 or 6 people, there will always be 1 sweet left over"
with step by step pls :(
Answer:
61
or
421
Step-by-step explanation:
Find the L.C.M. of 2,3,4,5,6 and add 1.
2| 2-3-4-5-6
-------------------
2| 1-3-2-5-3
---------------------
3| 1-3-1-5-3
----------------------
5| 1-1-1-5-1
----------------------
| 1-1-1-1-1-1
L.C.M.=2×2×3×5=60
reqd. number=60+1=61
if i distribute between 2,3,4,5,6 people then reqd number is 61
if Mia is also among those people or she gets also share
then the people are2,3,4,5,6 or 7
L.C.M. of 2,3,4,5,6,7=60×7=420
so reqd number is 420+1=421
A school bought 45 band uniforms and 18 musical instruments. If the
uniforms cost $89 each, what was the total cost of the uniforms?
Answer:
45 times 89
Step-by-step explanation:
The instuments are irrelevant and are only there to distract you.
Answer:
45 times 89 equals 4005
Step-by-step explanation:
The sum of a rational number and an irrational number is irrational.
Always true,sometimes true, never true
=========================================================
Explanation:
We can prove this by contradiction.
Let's say
A = some rational numberB = some irrational numberC = some other rational numberand
A+B = C
We'll show that a contradiction happens based on this.
If A is rational, then A = p/q where p,q are two integers. The q cannot be zero.
If C is rational, then C = r/s for some other integers. We can't have s be zero.
Note the following
A+B = C
B = C - A
B = r/s - p/q
B = qr/qs - ps/qs
B = (qr - ps)/qs
B = (some integer)/(some other integer)
This shows B is rational. But this is where the contradiction happens: We stated earlier that B was irrational. A number cannot be both rational and irrational at the same time. The very definition "irrational" literally means "not rational".
In short, I've shown that if A+B = C such that A,C are rational, then B must be rational as well.
The template is
rational + rational = rational
Therefore, we've shown that if A is rational and B is irrational, then C cannot possibly be rational. C is irrational.
Another template is
rational + irrational = irrational
PLEASE SOMEONE HELP ME ANSWER THIS !!!!
Write the equations of the linear and exponential functions that pass through the points (0, 15) and (1, 5)
Linear Equation, y = mx+b
Exponential Equation, y = a(b)^x
PLEASE ANSWER IT I HAVE AN IMAGE ATTACHED IF NEEDED !!!!
Step-by-step explanation:
Part A: Linear Equation.
One of the points is (0,15). This means 0,15 is the y intercept so b=15.We can find the slope
[tex] \frac{5 - 15}{1 - 0 } = \frac{ - 10}{1} = - 10[/tex]
So our equation is
[tex]y = - 10x + 15[/tex]
Part B: Exponential Equation
We know that
[tex]15 = a \times b {}^{0} [/tex]
B to the zero power is 1 so
[tex]15 = a[/tex]
This means a =15. Now let find b.
[tex]5 = 15 \times b {}^{1} [/tex]
[tex] \frac{1}{3} = b[/tex]
So the equation is
[tex]y = 15( \frac{1}{3} ) {}^{x} [/tex]
The water level in a plastic pool changed
by −8 gallons each hour due to a small
hole in the bottom. After 6 hours, the pool
contained 132 gallons. How much water
was in the pool originally?
Answer: 180 gallons
Step-by-step explanation:
If you take 8 times 6 you get 48, now take 132 plus 48 and you get 180.(hope this helped):)
how do i convert y = 6x into y = mx + b form?
Answer:
it already is in that form
y = 6x
technically Y = 6x + 0 could be the answer...
but in math we tend to not rite "obvious" information
to reduce clutter and confusion
+1[tex]x^{1}[/tex] is technically correct but we drop the + sign for positive numbers
and also drop the exponent if it is a 1 ... similarly
+1[tex]x^{1}[/tex] + 0 + 0 + 0 would also be silly and we don't write the zeros
+1[tex]x^{1}[/tex] + 0 + 0 + 0 = x
Step-by-step explanation:
Between which two numbers does 46 lie?
A.
between 8 and 9
B.
between 6 and 7
C.
between 5 and 6
D.
between 7 and 8
Answer:
So the sqrt(46) is between 6 and 7
Step-by-step explanation:
sqrt(46)
5*5 = 25
6*6=36
7*7=49
So the sqrt(46) is between 6 and 7
Can someone help me with this question pls
Answer:
D
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = - 94 and d = a₂ - a₁ = - 112 - (- 94) = - 112 + 94 = - 18 , then
S₁₀ = [tex]\frac{10}{2}[/tex] [ (2 × - 94) + (9 × - 18) ]
= 5(- 188 - 162)
= 5 × - 350
= - 1750
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Could you please please help me with these questions this is my last attempt and it's due today
Answer:
70.20%
Step-by-step explanation:
Since you seem to be in a rush, let's go for a concise answer.
Let's add 146 and 344 to get 490, and do 344 / 490. This gives us the decimal proportion of ice cream cones that was sold. 344 / 490 = 0.70204.
Excellent. To get the percentage, let's multiply 0.70204 by 100 to get 70.204%. Rounding this to the nearest hundredth gives us 70.20%.
Hope this helps!
Note: This question seems to be badly worded, your 42.44% is correct if it's percentage of ice cream bowls in ice cream cones. I'm assuming that it's the percentage of all ice cream. :)
Whats different for the functions
In a math class of 28 students, 14 boys and 14 are girls. On a unit test, 5 boys and 9 girls made an A grade. A student is chosen at random from the class. What is the probability of choosing a girl or an A student?
A. 0.82
B. 0.68
C. 0.14
D. 0.50
Answer:
The probability of choosing a girl is 1/2.
The probability of choosing an A student who is a BOY is 5/28.
1/2 = 14/28, and 14/28 + 5/28 = 19/28. This can be simplified to 0.68
Thus, the answer is B. 0.68
Let me know if this helps!
The required probability of choosing a girl or an A student is 0.82. Option A is correct.
Given that,
In a math class of 28 students, 14 boys and 14 are girls. On a unit test, 5 boys and 9 girls made an A grade.
A student is chosen at random from the class. What is the probability of choosing a girl or an A student is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Total sample space = 28
Number of girls = 14
Number of boys = 14
Number of girls A grade student = 9
probability of a girl = 14/28 = 0.5
probability of A grader girl = 9 / 28 = 0.32
Now the probability of choosing a girl or an A grader girl student,
= 0.32 + 0.5
= 0.82
Thus, the required probability of choosing a girl or an A student is 0.82. Option A is correct.
Learn more about probability here:
brainly.com/question/14290572
#SPJ5
Jerry sold 320 tickets for the school play. He sold x adults tickets for $8 each and y child tickets for $5 each. He sold $1900 worth of tickets. Write a system of equations to model the situation.
What is the equation?
Answer:
x + y = 320
8x + 5y = 1900
Step-by-step explanation:
The equation x + y = 320 represents how 320 tickets were sold in total, from combining the adult and child tickets sold.
Since adult tickets are $8 each, the money from adult ticket sales can be represented by 8x.
The money from child ticket sales can be represented by 5y.
The equation 8x + 5y = 1900 represents how $1900 worth of tickets were sold.
So, the system of equations for the situation is:
x + y = 320
8x + 5y = 1900
Answer:
y = 220
x = 100
Step-by-step explanation:
x + y = 320
8x + 5y = 1900
x = 320 - y
8(320 - y) + 5y = 1900
2560 - 8y + 5y = 1900
2560 -3y = 1900
-2560 -2560
-------------------------
-3y = -660
----- -------
-3 -3
y = 220
x + 220 = 320
-220 -220
----------------------
x = 100
5. PLEASE HELP ME
Write the equation in standard form. Then factor the left side of the equation.
2x2 + 7x = 15
A. (2x – 3)(x + 5) = 0
B. (2x + 3)(x + 5) = 0
C. (2x + 5)(x – 3) = 0
D. (2x – 5)(x + 3) = 0
Answer:
7x=11
Step-by-step explanation:
do it
would you Rather geometry
Walk on a line or A line segment
why?
Translate this phrase into an algebraic expression.
the quotient of 14 and a number
Answer:
Step-by-step explanation:
Let the number be x
14 ÷ x = [tex]\frac{14}{x}[/tex]
Answer:
14 / x
Step-by-step explanation:
quotient = /
14 = 14
a number = the variable, let's call it x
Brainliest please!
What is the solution set of 7x 2 + 3x = 0?
{0, 3/7}
{0, -3/7}
{0, -4/7}
Answer:
the answer is b when we have two positives it makes a negitive therefore its b
Step-by-step explanation:
Simplify (Asap️ )
please answer this if you know
(full steps required )
(please no spam answers)
see the attachment hope this helps you
find the missing side of the triangle.
Answer:
x = 17
Step-by-step explanation:
x ^2 = 8^2+ 15^2
√x^2 =√64+225
x=17
Answer:
17cm.
Step-by-step explaination:
The given triangle is a right angled triangle.
Using Pythagorean Theorem,
a² + b² = c²
Putting the given values in the equation;
(15)² + (8)² = c²
225 + 64 = c²
289 = c²
17² = c² (square root of 289 = 17)
17 = c
c = 17
Therefore, the missing side of the triangle is equal to 17 cm.
find the values of x and y.
Answer:
x=15.75 y=59
Step-by-step explanation:
In total there is 360 degrees. We know y is 59 so we will replace it with that.
59+59=118. 360-118=242. 242/2=121. 29+29=58. So we can subtract that to equal 63. Now 63=4x. We can divide so 2x=31.5. x=15.75.
Therefore, 15.75=x and 59=y
I hope this helped ^^.
Which number best represents the slope of the graphed line?
A. -5
B. -1/5
C. 1/5
D. 5
Answer:
A. -5
Step-by-step explanation:
First of all this is a line that shows a negative slope.
Secondly, the formula for slope is rise/ run.
5 is your rise and 1 is your run, therefore: -5/1
And this can be reduced to : -5
Factorize:
6 + 13mn + 7m² n²
explanation
Answer:
1(6+13mn+7m^2n^2)
Step-by-step explanation:
The coefficients and variables in this equation have a common factor of 1, therefore the equation will go back to it's original state if you use 1 as the common factor.
I hope this helps and sorry if am wrong
Please help me to solve this two questions
Answer:
c.8,625grams of flour
4a. X=12
Y=30
Z=60
Step-by-step explanation:
For c. , You have to convert the mixed numbers to fractions.
2¾ cups of flour= 2×4=8
8+3=11
Answer: 11/4 (11 over 4)
You multiply the 2 (whole number) by the 4 (bottom number) and then you get *8*
You then take the 8 (which was your answer) and add 3. This will give you 11
You take the 4 and use it as your denominator (bottom number) for the 11. So no need to find a denominator, because you just use the 4
For the fruit cake, she uses *1½* cups of flour more than carrot cake
Calculation:
1½ converted to an improper fraction= 1×2=2
2+1=3
Answer: 3/2 (3 over 2)
"Customer orders *3* carrot cakes and *4* fruit cakes
How many cups of flour are required to bake for the cakes ordered by the customer?"
11/4÷3= 8,25grams
3/2÷4= 0,375grams
8,25+0,375=8,625grams in total
*Feel free to correct me as I might be wrong!*
PLS HELP ME ON TTHIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION WHILE YOU ANSWER THE QUESTION!!
Which of the following is not a step in creating a box plot?
A. Order the data
B. Find the values for the five-number summary
C. Create a number line
D. Add all of the numbers in the data set and divide by the number of data items in the set
9514 1404 393
Answer:
D (compute the mean)
Step-by-step explanation:
A box plot is a visual representation of the 5-number summary of a set of data. It is plotted against a number line.
The 5-number summary of the data set is most easily determined from an ordered set of the data, so ordering the data is usually the first step. Since the 5-number summary is plotted against a number line, the next steps are finding the 5-number summary, and creating a suitable number line.
__
The business of adding the data and dividing by the number of data items is a description of computing the mean of the data. That value is not part of the 5-number summary, and is not needed in the creation of the box plot.
Solve the inequality 8 + n > 4.
Answer:
n>-4
Step-by-step explanation:
8+n>4
n>4-8
n>-4
Answer:
-4
Step-by-step explanation
Subtract 8 from 4 to get -4.
N = -4
God Bless.
What is x in the diagram below?
Answer:
3rd option, 2√10
Step-by-step explanation:
x²=4×10
or, x=√(4×10)
or, x=2√10
Answer: C, 2√10
Step-by-step explanation:
what is 2,034,627 rounded to the nearest ten thousand
Answer:
rounded to the nearest ten thousand
2,034,627
2,030,000