Answers
Related Questions
Is it possible for a line ax+by=c to lack a y-intercept? To lack an x-intercept
Answers
Complete the two-column the proof.
Given: is complementary to .
bisects .
Prove: is complementary to .
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<1 is complementary to <2 Given
BD bisects <ADC Given
m<1 + m<2 = 90 Definition of complementary angles
m<2 = m<3 Definition of bisection
m<1 + m<3 = 90 Substitution property of equality
<1 is complementary to <3 Definition of complementary angles
Molly walked four more miles than Tim. Together, they walked ten miles. How many miles did each walk? The replacement set is {1, 2, 3, 4}.
a. Define the variable, and write expressions for the number of miles each person walked.
b. Write an equation that represents the problem.
c. Solve the equation. (Be sure to try every element in the replacement set and to show all of your work.)
d. Answer the question. (Remember, answers to word problems have units.)
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A) Variable = x ( miles Tim walked )
B) Tim walked X miles, Molly walked 4+x miles ( 4 more than Tim)
Equation: x + x+4 = 10
C) x +x+4 = 10
2x+4 = 10
2x =6
x = 3
D)
Tim walked 3 miles, Molly walked 7 miles
The sum of twice a first number and five times a second number is 78. If the second number is subtracted from five times the first number the result is 33. Find the numbers.
Answers
___________________________________
Explanation:
___________________________________
Let: "x" be the "first number" ; AND:
Let: "y" be the "second number" .
___________________________________
From the question/problem, we are given:
___________________________________
2x + 5y = 78 ; → "the first equation" ; AND:
5x − y = 33 ; → "the second equation" .
____________________________________
From "the second equation" ; which is:
" 5x − y = 33" ;
→ Add "y" to EACH side of the equation;
5x − y + y = 33 + y ;
to get: 5x = 33 + y ;
Now, subtract: "33" from each side of the equation; to isolate "y" on one side of the equation ; and to solve for "y" (in term of "x");
5x − 33 = 33 + y − 33 ;
to get: " 5x − 33 = y " ; ↔ " y = 5x − 33 " .
_____________________________________________
Note: We choose "the second equation"; because "the second equation"; that is; "5x − y = 33" ; already has a "y" value with no "coefficient" ; & it is easier to solve for one of our numbers (variables); that is, "x" or "y"; in terms of the other one; & then substitute that value into "the first equation".
____________________________________________________
Now, let us take "the first equation" ; which is:
" 2x + 5y = 78 " ;
_______________________________________
We have our obtained value; " y = 5x − 33 " .
_______________________________________
We shall take our obtained value for "y" ; which is: "(5x− 33") ; and plug this value into the "y" value in the "first equation"; and solve for "x" ;
________________________________________________
Take the "first equation":
________________________________________________
→ " 2x + 5y = 78 " ; and write as:
________________________________________________
→ " 2x + 5(5x − 33) = 78 " ;
________________________________________________
Note the "distributive property of multiplication" :
________________________________________________
a(b + c) = ab + ac ; AND:
a(b − c) = ab − ac .
________________________________________________
So; using the "distributive property of multiplication:
→ +5(5x − 33) = (5*5x) − (5*33) = +25x − 165 .
___________________________________________________
So we can rewrite our equation:
→ " 2x + 5(5x − 33) = 78 " ;
by substituting the: "+ 5(5x − 33) " ; with: "+25x − 165" ; as follows:
_____________________________________________________
→ " 2x + 25x − 165 = 78 " ;
_____________________________________________________
→ Now, combine the "like terms" on the "left-hand side" of the equation:
+2x + 25x = +27x ;
Note: There are no "like terms" on the "right-hand side" of the equation.
_____________________________________________________
→ Rewrite the equation as:
_____________________________________________________
→ " 27x − 165 = 78 " ;
Now, add "165" to EACH SIDE of the equation; as follows:
→ 27x − 165 + 165 = 78 + 165 ;
→ to get: 27x = 243 ;
_____________________________________________________
Now, divide EACH SIDE of the equation by "27" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
_____________________________________________________
27x / 27 = 243 / 27 ;
→ to get: x = 9 ; which is "the first number" .
_____________________________________________________
Now; Let's go back to our "first equation" and "second equation" to solve for "y" (our "second number"):
2x + 5y = 78 ; (first equation);
5x − y = 33 ; (second equation);
______________________________
Start with our "second equation"; to solve for "y"; plug in "9" for "x" ;
→ 5(9) − y = 33 ;
45 − y = 33;
Add "y" to each side of the equation:
45 − y + y = 33 + y ; to get:
45 = 33 + y ;
↔ y + 33 = 45 ; Subtract "33" from each side of the equation; to isolate "y" on one side of the equation ; & to solve for "y" ;
→ y + 33 − 33 = 45 − 33 ;
to get: y = 12 ;
So; x = 9 ; and y = 12 . The numbers are: "9" and "12" .
____________________________________________
To check our work:
_______________________
1) Let us plug these values into the original "second equation" ; to see if the equation holds true (with "x = 9" ; and "y = 12") ;
→ 5x − y = 33 ; → 5(9) − 12 =? 33 ?? ; → 45 − 12 =? 33 ?? ; Yes!
________________________
2) Let us plug these values into the original "second equation" ; to see if the equation holds true (with "x = 9" ; and "y = 12") ;
→ 2x + 5y = 78 ; → 2(9) + 5(12) =? 78?? ; → 18 + 60 =? 78?? ; Yes!
_____________________________________
So, these answers do make sense!
______________________________________
HELP! WHAT IS 15/16 - 3/4
Answers
15/16 on a decimal is 0.9375
3/4 as a decimal is .75!
now do
0.9375-.75 which is
0.1875!
As a salesperson, you are paid $100 per week plus $3 per sale. This week you want your pay to be at least $160. Write an inequality for the number of sales you need to make, and describe the solutions. A) 100 - 3s ≤ 160; s ≤ 20 B) 100 + 3s ≥ 160; s ≥ 18 C) 100 - 3s ≤ 160; s ≤ 18 D) 100 + 3s ≥ 160; s ≥ 20
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Answer:
The answer is D. Hope it helps!
3x - 7 = 14 implies that 3x = 21
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Suppose FLX =ZAQ Which other congruency statements are correct
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XLF=QAZ
FXL=ZQA
XFL=QZA
Five times the sum of a number (x) and three is equal to the sum of that number (x) and fifteen.
I just need to know how to put this from Word-Form into Number form and solve for the
x. Please help.
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its simple
5x + 15 = x + 15...subtract x from both sides, subtract 15 from both sides
5x - x = 15 - 15
4x = 0
x = 0 <=
Prove or disprove: if p and q are prime numbers then pq - 2 is also a prime number.
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Counterexample:
[tex] p=2\\
q=3\\\\
pq-2=2\cdot3-2=4 [/tex]
4 is not a prime number. So, it's false.
the present age of sahil's mother is three time the present age of sahil . after 5 years their ages add up to 66 years . find theor present ages
Answers
Sahil = x
After 5 years:
3x + 5 + x + 5 = 66
4x + 10 = 66
You finish.
Can someone help me write an equation for this problem?
Felicity put down $800 on a used car. She took out a loan to pay off the balance of the cost of the car. Her monthly payment will be $175. After 9 months how much will she have paid for the car?
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And then just solve for y.
The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.
Which statement correctly describes the relationship between △DEF and △D′E′F′ ?
The triangles are not congruent because △D′E′F′ is a translation of △DEF , and a translation is not a rigid motion.
The triangles are congruent because △D′E′F′ is a rotation of △DEF , and a rotation is a rigid motion.
The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
The triangles are congruent because △D′E′F′ is a reflection of △DEF , and a reflection is a rigid motion.
Answers
Answer:
The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
Step-by-step explanation:
The rule we have is (x, y)→(2x, 2y). This means that each x-coordinate and each y-coordinate are multiplied by 2. This is a dilation by a factor of 2.
This will stretch the image by a factor of 2; this means the sides will be twice as long. This means they will not be congruent.
Answer: The triangles are not congruent because △D′E′F′ is a dilation of △DEF .
Step-by-step explanation:
Rigid motions form congruent figures, the common rigid motions are:
1) translation (moves figure about some distance)
2) reflection (creates mirror image)
3) rotation (rotate figure about some degrees)
Dilation : It does not create congruent images. It creates an image that is the exactly same shape as the original, but have a different size with the help of a scale factor k .
Given : The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.
Here the coordinates of the image are increased by using a scale factor 2.
So △D′E′F′ must be an enlargement of △DEF.
⇒△D′E′F′ is a dilation of △DEF
It means : The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
What is vertex on a graph
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I need the steps to this, please. It says solve for x. Each figure is a parallelogram. Show your work.
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FH is one diagonal that is split into two equal pieces by the other diagonal EG.
The two parts of FH (KH and KF) are congruent to each other, so KH = KF. They combine back to FH
By the segment addition postulate
KH + KF = FH
KH + KH = FH .... KF has been replaced with KH (works because KF = KH)
2*KH = FH
Now use substitution
2*KH = FH
2*15 = FH .... replace KH with 15 (since KH = 15)
2*15 = 4x-2 ... replace FH with 4x-2 (since FH = 4x-2)
and solve for x
2*15 = 4x-2
30 = 4x-2
30+2 = 4x-2+2 ... add 2 to both sides
32 = 4x
4x = 32
4x/4 = 32/4 ... divide both sides by 4
x = 8
----------------------------------------
----------------------------------------
Answer: x = 8
The area of a rectangle is 16 square feet, determine the length and width if the legnth is 4 times the width
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What is the slope of the line represented by the equation y = - 1/2x + 1/4
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50h + 0.20s + 40 part
a.identify a coefficient, a variable, and a constant in this expression. part
b.if corinne works for 25 hours and sells $300 in magazines, how much does she earn for the week? show your work to receive full credit. part
c.if corinne gets a raise and begins earning $9 per hour, would the coefficient, variable, or constant in the equation change? why?
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Coefficient: 50
Variable: h
Constant: s
b.
50(25) + 0.20(300) + 40
1250 + 60 + 40
1350
Corinne earns $1350
c.
The coefficient would change because a coefficient is the number in front of a variable, and the number changed, not the variable or constant.
which angle is included angle forJL and KL
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Classify each number by indicating in which set or sets it belongs 8 and 0.25
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0.25 is a rational number
The number 8 belongs to the sets of natural numbers, integers, rational numbers, and real numbers, while the number 0.25 only belongs to the sets of rational and real numbers.
Explanation:In mathematics, numbers can belong to various sets such as the natural numbers, integers, rational numbers, real numbers, etc. In this case, the number 8 belongs to all these sets because it is a whole number without fractions or decimals. Therefore, it is a natural number, integer, rational number and real number.
On the contrary, 0.25 is a decimal which belongs to the sets of rational numbers and real numbers. It does not belong to the sets of natural numbers or integers because it is not a whole number.
Learn more about Number classification here:https://brainly.com/question/32665385
What two numbers multiply to 12 and add to negative 4?
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The two numbers that multiply to 12 and add to negative 4 are -6 and 2.
To find the two numbers, we need to solve the system of equations:
1. xy = 12 (Equation 1)
2. x + y = -4 (Equation 2)
From Equation 2, we can express y in terms of x:
y = -4 - x (Equation 3)
Now, we substitute Equation 3 into Equation 1:
[tex]\( x(-4 - x) = 12 \)\\ \( -4x - x^2 = 12 \)\\ \( x^2 + 4x - 12 = 0 \)[/tex]
We can factor this quadratic equation:
[tex]\( (x + 6)(x - 2) = 0 \)[/tex]
Setting each factor equal to zero gives us two possible solutions for x:
[tex]\( x + 6 = 0 \) or \( x - 2 = 0 \)[/tex]
So, [tex]\( x = -6 \) or \( x = 2 \)[/tex].
Using Equation 3 to find the corresponding y values:
If ( x = -6 ), then ( y = -4 - (-6) = 2 ).
If ( x = 2 ), then ( y = -4 - 2 = -6 ).
Therefore, the two pairs of numbers that satisfy both conditions are (-6, 2) and (2, -6). Since the question asks for two numbers, and both pairs contain the same numbers, the answer is -6 and 2.
Bob has some 10 lb weights and some 3 lb weights. Together, all his weights add up to 50 lbs. If x represents the number of 3 lb weights and y represents the number of 10 lb weights, which equation can be used to find the number of each type of weight Bob has?
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x = number of 3-lb weights
y = number of 10-lb weights
weight of 3-lb weights = 3x
weight of 10-lb weights = 10y
total weight = 3x + 10y
equation
3x + 10y = 50
What is the answer to 7x+3y=8 solve for y
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3y=-7x+8 divide by 3
y=-7/3x+8/3
3y=8-7x
y=8/3-7x/3
hope this answers the question:)
7x - 2 = 2y 3x = 2y - 1
Solve the system of equations by substitution.
(3/4, 13/8), (1/4, -1/8), no solution, coincident
Answers
7x = 2y + 2
so
7x = 2y + 2
3x = 2y - 1
----------------subtract
4x = 3
x = 3/4
7x - 2 = 2y
7(3/4) - 2 = 2y
21/4 - 2 = 2y
21/4 - 8/4 = 2y
13/4 = 2y
so
y = 13/4 * 1/2
y = 13/8
answer
(3/4, 13/8)
Answer:
7x - 2 = 2y
7x = 2y + 2
so
7x = 2y + 2
3x = 2y - 1
----------------subtract
4x = 3
x = 3/4
7x - 2 = 2y
7(3/4) - 2 = 2y
21/4 - 2 = 2y
21/4 - 8/4 = 2y
13/4 = 2y
so
y = 13/4 * 1/2
y = 13/8
answer
(3/4, 13/8)
Step-by-step explanation:
How do you find the amount of nuetrons in an atom?
Answers
A bookcase contains 2 statistics books and 5 biology books. if 2 books are chosen at random, the chance that both are statistics books is
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number of ways to choose any 2 books out of 5 biology books =⁵C₂ = 5!(2! x 3!) =10
number of ways to choose 2 statistic books out of 2 = ²C₂ = 1
So, probability that both two books are statistics books = 1/10
The chance that both the book are of statistics is [tex]\boxed{\dfrac{1}{21}}[/tex].
Further Explanation:
Given:
The total number of statistics book is [tex]2[/tex].
The total number of biology book is [tex]5[/tex].
Concept used:
Probability is defined as the ratio of favorable outcomes to total outcomes.
[tex]\boxed{\text{Probability}=\dfrac{\text{favorable outcomes}}{\text{total outcomes}}}[/tex].
Combination is defined as the selection of all or part of object without considering the order of the object.
[tex]\boxed{^{n}C_{r}=\dfrac{n!}{r!\cdot (n-r)!}}[/tex]
Here, [tex]n[/tex] is the total number of object and [tex]r[/tex] is the number of object to be chosen.
Calculation:
The total number of book is [tex]7[/tex].
The chance of getting the statistics books is the favorable outcomes for the problem.
The selection of two statistics book from two statistics book is represented as follows:
[tex]\boxed{^{2}C_{2}}[/tex]
The total outcomes can be obtained by selection of two books from seven books which is represented as follows:
[tex]\boxed{^{7}C_{2}}[/tex]
Write the formula to obtain the chance that both the books are statistics.
[tex]\boxed{P=\dfrac{^{2}C_{2}}{^{7}C_{2}}}[/tex]
Solve the above equation to obtain the chance that both the books are of statistics.
[tex]\begin{aligned}P&=\dfrac{^{2}C_{2}}{^{7}C_{2}}\\&=\dfrac{\frac{2!}{2!\cdot (2-2)!}}{\frac{7!}{2!\cdot (7-5)!}}\\&=\dfrac{1}{\frac{7\times 6}{2}}\\&=\dfrac{1}{21}\end{aligned}[/tex]
Therefore, the probability that the two selected books are of statistics is [tex]\boxed{\dfrac{1}{21}}[/tex].
Learn more:
1. Simplification: https://brainly.com/question/1602237
2. Quadratic equation: https://brainly.com/question/1332667
Answer details:
Grade: High school.
Subject: Mathematics.
Chapter: Probability.
Keywords: Probability, statistics, favorable, outcomes, total outcomes, 0.047, \frac{1}{{21}}, chance, biology books, 2, 7, chances, randomly chosen.
Factor this expression completely.
ab + 4 + a + 4b
Answers
Rearrange.
[tex]ab+4+a+4b[/tex]
[tex]ab+a+4+4b[/tex]
Factor by grouping.
[tex]a(b+1)+4(1+b)[/tex]
[tex]a(b+1)+4(b+1)[/tex]
Find the GCF.
[tex](b+1)(a+4)[/tex]
Hope this helped.
-Benjamin
explain how you can solve 40 × 16 by breaking apart the numbers.
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which of the following statement are false? o vertical angles are congruent. o angles with measures between 0 and 90 are complementary. o straight angles are supplementary. o angles with measures between 90 and 180 are obtuse
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2. Angles with measures between 90 and 0 degrees are complementary. Assuming this means that two angles add to a sum of 90, this is true.
3. Straight angles are supplementary. Since a straight angle is only one angle, it is not supplementary, even though it is 180 degrees. This is false.
4. Angles with measures between 90 and 180 degrees are obtuse. This is true.
Which ordered pair can be removed so that resulting graph represent a function ?
Answers
The ordered pair which can be removed so that resulting graph represent a function is:
(1,3)
Step-by-step explanation:Function--
A function is a relation in which each of the element of first set is mapped to a single element of the other set.
i.e. no element is mapped to two elements i.e. there is a single image for each pre-image.
Here in the graph we have ordered pairs as:
(-5,-3) (-4,-4) (-2,2) (1,-2) (1,3) (2,1) (5,-4)
Hence, we see that element " 1 " is mapped two different elements
1 is mapped to -2 ( since, we have ordered pair (1,-2) )
and 1 is mapped to 3 ( since, we have ordered pair (1,3) )
If we remove the ordered pair (1,3) then the resulting graph will be a graph of a function.