Answer:
Total weight of the nuts bought by Dan = 5.4 kg
Explanation:
Number of packets of nuts bought by Dan = 24
Weight of each packet of nuts = 225g
Total weight of the nuts bought by Dan = Number of packets of nuts bought by Dan * Weight of each packet of nuts
Total weight of the nuts bought by Dan = 24 * 225 = 5400 g = 5400/1000 kg = 5.4 kg
Total weight of the nuts bought by Dan = 5.4 kg
Antonio's father bought tickets for the planetairium.He bought 6 tickets each ticket cost 16 what is the total cost of the 6 tickets?
Answer:
$96
Step-by-step explanation:
Multiply The Number Of Tickets By Amount Of People Going
16 * 6
1. To solve x/ 0.4 = 10 You would:
a. add 0.4
b. subtract 0.4
c. multiply 0.4
d. divide 0.4
(c) multiply by 0.4
given [tex]\frac{x}{0.4}[/tex] = 10
multiply both sides by 0.4 to eliminate the fraction
x = 0.4 × 10 = 4
and [tex]\frac{4}{0.4}[/tex] = 10
A farmer will build a rectangular pen for some goats. A wall will form one side of the pen. The farmer has 36 m of fencing to form the other three sides.
The farmer plans to build the pen so that it has its maximum possible area.
What will be the dimensions of the farmer’s goat pen?
Enter your answers in the boxes.
___ m by ___ m
The pen should be built with dimensions of 9 meters by 6 meters, with the wall forming one of the 9-meter sides.
To find the dimensions of the pen that will give the maximum area, we can use the fact that for a given perimeter, a square has the maximum area. Since one side of the pen is formed by a wall, we have 36 meters of fencing for the other three sides. Let's denote the length of the pen as [tex]\( l \)[/tex] and the width. The perimeter of the three sides that need fencing is given by:
[tex]\[ P = l + 2w \][/tex]
We know that the total length of the fencing available for these three sides is 36 meters, so:
[tex]\[ l + 2w = 36 \][/tex]
To maximize the area, we want [tex]\( l \)[/tex] to be as close to [tex]\( w \)[/tex] as possible, which means we want to divide the 36 meters of fencing equally among the three sides. If we let \( w = w \), then the equation becomes:
[tex]\[ l + 2l = 36 \][/tex]
[tex]\[ 3l = 36 \][/tex]
[tex]\[ l = \frac{36}{3} \][/tex]
[tex]\[ l = 12 \][/tex]
However, this would mean that there is no fencing left for the width, as all 36 meters would be used for the length. To avoid this, we need to distribute the fencing so that two of the sides (the widths) are equal and the remaining side (the length) is the third side. To find the maximum area, we set [tex]\( l = 2w \)[/tex], which gives us:
[tex]\[ 2w + 2w = 36 \][/tex]
[tex]\[ 4w = 36 \][/tex]
[tex]\[ w = \frac{36}{4} \][/tex]
[tex]\[ w = 9 \][/tex]
Now, we can find the length [tex]\( l \):[/tex]
[tex]\[ l = 2w \][/tex]
[tex]\[ l = 2 \times 9 \][/tex]
[tex]\[ l = 18 \][/tex]
However, since we initially assumed[tex]\( l = 2w \)[/tex] to find the width, we need to adjust the length to account for the actual fencing used. We have two widths and one length, so the correct equation is:
[tex]\[ l + 2w = 36 \][/tex]
[tex]\[ 18 + 2 \times 9 = 36 \][/tex]
[tex]\[ 18 + 18 = 36 \][/tex]
[tex]\[ 36 = 36 \][/tex]
Therefore, the dimensions of the pen are 9 meters by 6 meters, with the wall forming the side of 18 meters.
The final answer is that the pen should be built with dimensions of 9 meters by 6 meters, with the wall forming one of the 9-meter sides.
Yuri has 2/7 of a bag of carrots. If he eats half the carrots, what fraction of the bag of carrots will she have left ?
Yuri will have 1/7 of a bag of carrots left. This is because half of 2 is 1.
Match the reasons with the statements in the proof.
Given: m1 = m3
m2 = m3
Prove: / | | m
1. m∠1 = m∠3 and m∠2 = m∠3 Substitution
2. m∠1 = m∠2 Definition of alternate interior angles
3. ∠1 and ∠2 are alternate interior angles If alternate interior angles are equal,
4. l||m then the lines are parallel.
Given
Answer:
Given: [tex]m\angle 1 = m\angle 3[/tex] and [tex]m\angle 2 = m\angle 3[/tex]
To prove that:
[tex]l || m[/tex]
1. [tex]m\angle 1 = m\angle 3[/tex] [Given]
[tex]m\angle 2 = m\angle 3[/tex]
Substitution property of equality says that:
If x = y, then x can be substituted in y, or y can be substituted in x.
2 [tex]m\angle 1 = m\angle 2[/tex] [ By Substitution Property]
Alternate interior angles states that when two lines are crossed by transversal , a pair of angles on the inner sides of each of these two lines on the opposite sides of the transversal line.
3. [tex]\angle 1[/tex] and [tex]\angle 2[/tex] are alternate interior angles [By definition Alternate interior angle].
Alternating interior angles theorem states that if two parallel lines are intersected by third lines, then the angles in the inner sides of the parallel lines on the opposite sides of the transversal are equal.
4. [tex]l || m[/tex] ; then the lines are parallel [By Alternate interior angles theorem]
Correct match is as follows:
1. [tex]m\angle 1 = m\angle 3[/tex] [Given]
[tex]m\angle 2 = m\angle 3[/tex]
2. [tex]m\angle 1 = m\angle 2[/tex] [Substitution]
3. [tex]\angle 1[/tex] and [tex]\angle 2[/tex] are alternate interior angle [By definition of alternate interior angles ]
4. [tex]l || m[/tex] the lines are parallel [If alternate interior angles are equal]
The question involves a geometrical proof where measurements of angles are given and a conclusion regarding parallel lines need to be derived. The steps of proof are matched with relevant geometric concepts. The matching involves principles like substitution, definition of alternate interior angles, and a theorem about alternate interior angles and parallel lines.
Explanation:In the context of the given problem, the matching would be as follows:
m∠1 = m∠3 and m∠2 = m∠3 would be matched with Substitution. This is because the measure of angle 1 is set to equal the measure of angle 3, and similarly, the measure of angle 2 is set to equal the measure of angle 3. This is a direct application of the substitution postulate in geometry. m∠1 = m∠2 would be matched with Definition of alternate interior angles. We know that alternate interior angles are equal in measure when two lines are cut by a transversal. So, when m∠1 = m∠2, these angles are defined as alternate interior angles.∠1 and ∠2 are alternate interior angles would be matched with If alternate interior angles are equal, then the lines are parallel. This phrase essentially summarizes the transversal line theorem, which states that if the pairs of alternate interior angles are equal, then the two lines that are cut by the transversal are parallel.l∥m would be matched with Given. This is provided as a part of the problem statement.Learn more about Geometry here:https://brainly.com/question/31408211
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A container holds 62 cups of water how much is this in a gallon
A container holds 62 cups of water how much is this in a gallon
Answer: We are given that a container contains 62 cups of water.
We are required to find how much water is contained in the container in terms of gallons.
We know that:
[tex]1[/tex] gallon [tex]=16[/tex] cups
[tex]\therefore 62[/tex] cups [tex]=\frac{62}{16}[/tex] gallons
[tex]=3.875[/tex] gallons
Therefore, a container contains 3.875 gallons of water.
Final answer:
To convert cups to gallons, divide the number of cups by 16 (since 1 gallon = 16 cups). For 62 cups, the conversion is 62 cups ÷ 16 cups/gallon = 3.875 gallons.
Explanation:
To convert cups to gallons, we must first know the conversion factors between these units. Using the provided reference information, we know that 1 gallon is equal to 16 cups since there are 4 quarts in a gallon and each quart is equivalent to 4 cups. Therefore, to convert from cups to gallons, we would divide the number of cups by 16.
Converting 62 cups to gallons:
Divide the total number of cups by the number of cups in a gallon: 62 cups ÷ 16 cups/gallon = 3.875 gallons.So, the container holds 3.875 gallons of water.
Determine the number of real solutions each quadratic equation has.
y = 12x2 - 9x + 4 _____real solution(s)
10x + y = -x2 + 2 _____real solution(s)
4y - 7 = 5x2 - x + 2 + 3y ______ real solution(s)
y = (-x + 4)2 ______real solution(s)
Answer:
1) a=12 , b=-9 , c=4
2) a=-1 , b=-10 , c=2
3) a=5 , b=-1 , c=9
4) a=1 , b=-8 , c=16
Step-by-step explanation:
(1) y = 12x² - 9x + 4 no real solutions.
(2) 10x + y = -x² + 2, two real solutions.
(3) 4y - 7 = 5x² - x + 2 + 3y, no real solution.
(4) y = (-x + 4)², one real solution.
How to calculate the solutions of the quadratic equations?The number of real solutions for each quadratic equation is determined using discriminant.
The discriminant, denoted as Δ, is used to determine the nature of the roots of a quadratic equation of the form ax² + bx + c = 0.
Δ = b² - 4ac
From the given equations;
y = 12x² - 9x + 4
a = 12, b = -9, c = 4
Δ = (-9)² - 4(12)(4)
Δ = 81 - 192
Δ = -111
Since the discriminant Δ is negative (-111), this quadratic equation has no real solutions.
10x + y = -x² + 2
y = -x² - 10x + 2
a = -1, b = -10, c = 2
Δ = (-10)² - 4(-1)(2)
Δ = 100 + 8
Δ = 108
Since the Δ is positive and greater than zero, the equation has two real solutions.
4y - 7 = 5x² - x + 2 + 3y
4y - 3y = 5x² - x + 2 + 7
y = 5x² - x + 9
a = 5, b = -1, c = 9
Δ = (-1)² - 4(5)(9)
Δ = 1 - 20(9)
Δ = 1 - 180 = -179
No real solution.
y = (-x + 4)²
when y = 0
0 = -x + 4 or
0 = -x + 4
x = 4
The equation has one real solution.
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Of the 125 people in a company , three-fifths have a smartphone . How many children do not have a smartphone
HAVE smart phones + do NOT have smart phones = 125
Have smart phones
[tex]\frac{3}{5} *125 = \frac{3(125)}{5} = 3(25) = 75[/tex]
HAVE + NOT = 125
75 + NOT = 125
-75 -75
NOT = 50
Answer: 50 people do not have a smart phone
Which steps transform the graph of y = x2 to y = –2(x – 2)2 + 2? (1 point)
A. translate 2 units to the left, translate down 2 units, stretch by the factor 2
B. translate 2 units to the right, translate up 2 units, stretch by the factor 2
C. reflect across the x-axis, translate 2 units to the left, translate down 2 units, stretch by the factor 2
D. reflect across the x-axis, translate 2 units to the right, translate up 2 units, stretch by the factor 2
y = x^2 to Green
y = –2(x – 2)^2 + 2 Blue
The correct answer is D.
Answer:
The correct option is D.
Step-by-step explanation:
The parent function is
[tex]y=x^2[/tex]
The transformed function is
[tex]y=-2(x-2)^2+2[/tex] .... (1)
The translation is defined as
[tex]f(x)=k(x+a)^2+b[/tex] .... (2)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
From (1) and (2) it is clear that
[tex]a=-2,b=2,k=-2[/tex]
It means,
a=-2<0 the graph shifts 2 units right.
b=2>0 the graph shifts 2 units up.
k=-2, the graph reflect across the x-axis and stretch by the factor 2.
The graph reflect across the x-axis, translate 2 units to the right, translate up 2 units, stretch by the factor 2. Therefore the correct option is D.
What is the best estimate of the square root of 96 to the nearest tenth
I believe the answer is 9.8
Hope this helps :)
Which package has the lowest ratio of cost to number of lessons? $90 for 10 lessons $160 for 20 lessons $80 for 10 lessons $120 for 20 lessons
$90/10 = 9
$160/20 = 8
$80/10 = 10
$120/20 = 6
The package that has the lowest ratio cost to number of lessons is $120 for 20 lessons.
Hope this Helps!!
The package with the lowest ratio of cost to number of lessons is the $120 for 20 lessons option, calculating to a cost of $6 per lesson, which is the most cost-effective option.
To find this, we calculate the cost per lesson for each package by dividing the total cost by the number of lessons.
For $90 for 10 lessons: $90 / 10 = $9 per lessonFor $160 for 20 lessons: $160 / 20 = $8 per lessonFor $80 for 10 lessons: $80 / 10 = $8 per lessonFor $120 for 20 lessons: $120 / 20 = $6 per lessonTherefore, the package with the lowest ratio of cost to number of lessons is $120 for 20 lessons, with a cost of $6 per lesson.
A car travelled at 16km an hour . How long did it travel in 2 1/2 hours
I would travel 40hours. 16 times two is 32 plus 8 is 40.
Factor the expression completely over the complex numbers.
x^4−625
Factor the expression completely over the complex numbers.
x^4+10x^2+25
[tex]x^4-625=(x^2-25)(x^2+25)=(x-5)(x+5)(x-5i)(x+5i)\\\\x^4+10x^2+25=(x^2+5)^2=((x-\sqrt5i)(x+\sqrt5i))^2=(x-\sqrt5i)^2(x+\sqrt5i)^2[/tex]
Answer:
1) [tex]x^4-625=(x+5i)(x-5i)(x+5)(x-5)[/tex]
2) [tex]x^4+10x^2+25=(x+\sqrt{5}i)^2(x-\sqrt5 i)^2[/tex]
Step-by-step explanation:
1) Given : Expression [tex]x^4-625[/tex]
To find : Factor the expression completely over the complex numbers ?
Solution :
We can re-write the expression as,
[tex]x^4-625=(x^2)^2-(25)^2[/tex]
Applying identity, [tex]a^2-b^2 = (a+b)(a-b)[/tex]
[tex]x^4-625=(x^2+25)(x^2-25)[/tex]
[tex]x^4-625=(x^2+25)(x^2-5^2)[/tex]
Again apply same identity,
[tex]x^4-625=(x^2+25)(x+5)(x-5) [/tex]
The factor of [tex]x^2+25=(x+5i)(x-5i)[/tex]
Factor form is [tex]x^4-625=(x+5i)(x-5i)(x+5)(x-5)[/tex]
2) Given : Expression [tex]x^4+10x^2+25[/tex]
To find : Factor the expression completely over the complex numbers ?
Solution :
Expression [tex]x^4+10x^2+25[/tex]
Let [tex]x^2=y[/tex]
[tex]y^2+10y+25[/tex]
To factor we equate it to zero.
[tex]y^2+10y+25=0[/tex]
Apply middle term split,
[tex]y^2+5y+5y+25=0[/tex]
[tex]y(y+5)+5(y+5)=0[/tex]
[tex](y+5)(y+5)=0[/tex]
Substitute back,
[tex](x^2+5)(x^2+5)=0[/tex]
[tex](x^2+5)^2=0[/tex]
[tex]x^2+5=0[/tex]
[tex]x^2=-5[/tex]
Taking root both side,
[tex]x=\sqrt{-5}[/tex]
[tex]x=\pm \sqrt{5}i[/tex]
So, The factors are [tex](x+\sqrt{5}i)(x-\sqrt5 i)[/tex]
Factor form is [tex]x^4+10x^2+25=(x+\sqrt{5}i)^2(x-\sqrt5 i)^2[/tex]
Can someone explain # 6 and #8
I have a quiz tomorrow and I need to understand this carp so please EXPLAIN it
Thanks
URGENT MATH HELP NEEDED PLEASE!!! WILL MARK BRAINLIEST!!!!
1. A bag contains the letters of the word “PROBABILITY”.
A. If a single tile is chosen at random, what is the probability the letter “B” is chosen? (Show your work).
B. If a single tile is chosen at random, what is the probability a vowel OR a “T”? (show your work).
C. If two tiles are chosen (with replacement) what is the probability of choosing an “O” and a “B”? (Show your work).
probability has 11 letters
2/11 chances that you could get a B
5/9 for a T or vowel
3/11 for an O or B
you just look at the letters and the number of them
Carol has only 20p and 10p coins in her purse she has three times as many 20p coins and 10p coins if Carol has ?4.20 altogether, how many 20p coins does she have
Suppose that Carol has x 10p coins in her purse. Since she has three times as many 20p coins as 10p coins, then she has 3x 20p coins in her purse.
x coins of 10p value $0.10x and 3x coins of 20p value $0.60x.
In total this amount of money is $(0.10x+0.60x)=$0.70x that is exactly $4.20. Thus, you get the equation
0.70x=4.20.
Solve it:
[tex]x=\dfrac{4.20}{0.70}=6.[/tex]
Carol has 6 coins of 10p and 3·6=18 coins of 20p.
Answer:
I'm not sure how euros work but I'm almost certain there are 18 20p coins
Step-by-step explanation:
Graph the function
x+y=6
-Can someone help and tell me how would i graph this?
This is how you would graph your function.
During 4 days, the price of the stock of PEV Corporation went up 1/4 of a point, down 1/3 of a point, down 3/4 of a point, and up 7/10 of a point. What was the net charge?
The price of the stock of PEV Corporation varies as shown. we have to determine the net charge. Net change is just how much it changed overall, so we will look for all the ups minus all the downs.
Here, "went up" goes with a + sign, and "went down" goes with a - sign.
So, Net charge = [tex]\frac{1}{4} - \frac{1}{3}-\frac{3}{4} + \frac{7}{10}[/tex]
= [tex]\frac{1}{4}-\frac{3}{4}- \frac{1}{3} + \frac{7}{10}[/tex]
= [tex]-\frac{2}{4}- \frac{1}{3} + \frac{7}{10}[/tex]
= [tex]-\frac{1}{2}- \frac{1}{3} + \frac{7}{10}[/tex]
LCM of 2,3 and 10 is 30
= [tex]\frac{-15-10+21}{30}[/tex]
= [tex]\frac{-4}{30}[/tex]
= [tex]\frac{-2}{15}[/tex]
So, the net charge is [tex]\frac{-2}{15}[/tex]
Hello everyone! Can you answer today's question?
Joy ate 1/4 of a pizza. If she divides the rest of the pizza into pieces equal to 1/8 for her family, how many pieces will her family get?
( Marking brainiest today! )
$.87 per day is equal to how many dollars per year
5 times 2/4 in simplest form 10 POINTS!!!
Your answer is 5/2.
Steps:
Convert element to fraction
Multiply fractions
Cancel the common factor (1)
--
Hope this helped!
If you have $10 and bananas cost 80 cents per pound and apples are $1.40 per pound will you have enough money
Samuel has 20$ in his savings account before he makes a deposit of $160. After 2 weeks, he withdraws $160. How did samuels savings account balance change?
There was no change in Samuel's savings account balance. He made a deposit of $160 but after two weeks, he withdrew the same sum. He still had $20 in his account as a result.
Explanation:This math query relates to fundamental financial operations. Samuel has $20 in his savings account at the start of the story. His total now stands at $180 after his subsequent $160 deposit. He withdraws $160, though, after two weeks. He now has $20 in his account after that. Finally, there was no change in Samuel's savings account balance. His account was $20 from beginning to end.
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Solve 3kx + 24 = 9kx for x.
24 = 6kx
4 = kx
4/k = x
Let's solve for x.
3kx+24=9kx
Step 1: Add -9kx to both sides.
3kx+24+−9kx=9kx+−9kx
−6kx+24=0
Step 2: Add -24 to both sides.
−6kx+24+−24=0+−24
−6kx=−24
Step 3: Divide both sides by -6x.
[tex]\frac{-6kx}{-6x}[/tex] = [tex]\frac{-24}{-6k}[/tex]
[tex]x=\frac{4}{k}[/tex]
Answer is: 4/k
1. Simplify by collecting like terms. Show your work when more than one step is required.
A and B for #1 are done I just need C
c. ?
2. Evaluate each expression for the given value of the variable. Show your work.
I need both A and B
a. ?
b. ?
3. The freshman class will be selling carnations as a class project. What is the class's income after it pays the florist a flat fee of $200 and sells c carnations for $2 each? Write an algebraic expression that models the situation.
I need this one as well
Hello,
Please, see the attached files.
Thanks.
A cube shaped packing box can hold 729 cubic inches of packing material. Solve 729= s ^3 to find the length of one side of the box
729 = s^3
9^3 = s^3
s = 9 in.
Jason spent half of his allowance going to the movies. he washed the family car and earned 8 dollars. What is his weekly allowance if he ended up with 11 dollars.
$6 dollars because 11-8 = 3, 3x2 =6
He starts with $6.00
It says he spends 1/2 of his allowance on the movies. 6/2=3
He has $3. Then it says He gained $8.00 for washing the "family" car.
$6.00+$8.00
=$11
Answer=$6.00
HELP I'M TIMED! Reflect triangle ABC over the y-axis. What is the relationship between the segments created if you connect the points to the line of reflection. I WILL GIVE YOU BRAINLIEST!
This is your answer thanks!
Answer:
they are perpendicular to each other
Step-by-step explanation:
Based on the quadratic model, what was the approximate number of workers that were hired during the seventh year?
To determine the approximate number of workers hired during the seventh year based on the quadratic model, we need more information about the model and the values of a, b, and c.
Explanation:To approximate the number of workers hired during the seventh year based on the quadratic model, we need more information about the model. Quadratic models are typically of the form y = ax^2 + bx + c, where x represents the time and y represents the number of workers hired. Without knowing the values of a, b, and c, we cannot determine the exact number of workers hired in the seventh year. However, if we have the values of a, b, and c, we can substitute x = 7 into the equation to find the approximate number of workers hired during the seventh year.
What’s the answer?? (SOMEONE PLEASE HELP ME)
x = 6 or x = - 1
rearrange the equation into standard form and factorise
subtract ( - 2x - 4 ) from both sides
x² - 5x - 6 = 0 ← in standard form
the factors of - 6 which sum to - 5 are - 6 and + 1
(x - 6)(x + 1) = 0
equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 1 = 0 ⇒ x = - 1