The most appropriate choice for distance between numbers will be given by -
Distance between 3 and 15 is 12 units
What is distance between two numbers?
At first it is important to know about number line.
A pictorial representation of real numbers has been done along a horizontal straight line. That horizontal straight line is called number line. On a number line, all the integers has been placed at equal distance apart. In between integers, fractions, decimal numbers, rational numbers and irrational numbers can be marked. Number line can be used for addition or subtraction.
Distance between two numbers indicates how far one number is situated from other number on the number line.
Here,
Distance between 3 and 15 = 15 - 3
= 12 units
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Solve for y:
4x-8y=32
Answer: y = -4 + x/2
Step-by-step explanation:
3x3 determinant of -2, 3, 8 6, 7, 1 4, 5, 9
?????????? Image attached!
I will gladly take your help!
Answer:
-1/2; take both points which equals to -1/2
Step-by-step explanation:
Christina is doing an obstacle course in gym class. First, she runs 100 feet and jumps over a hurdle. Then, she crawls through a 20-foot tunnel. Finally, she dribbles a soccer ball 60 feet to the finish line. How many yards long is the obstacle course?
Answer:
60 yards
Step-by-step explanation:
100 feet + 20 feet + 60 feet = 180 feet
180 feet = 60 yards (there are 3 feet in 1 yard)
A line passes through the points (–3, –4) and (6, 2).
A coordinate plane.
What is the x-intercept of this line?
Answer:
x intercept is -3
Step-by-step explanation:
We need to find the equation for the line First we find the slope m = (y2-y1)/(x2-x1) = (2- -4)/(6- -3) = (2+4)/(6+3) =6/9 = 2/3 The we can write the equation y= mx+b y = 2/3x +b We can substitute in (6,2) 2 = 2/3(6) +b 2 =4+b Subtract 4 from each side 2-4 =b b =-2 y = 2/3 x-2 We want to find the x intercept, so set y =0 and solve for x 0 = 2/3x -2 Add 2 to each side 0-2 = 2/3x Multiply each side by 3/2 to isolate x -2 *3/2 = 2/3x * 3/2 -3 =x The x intercept is -3
Find a translation that has the same effect as the composition of translations below. T(5.3) (X,Y) followed by T -3,6) (X,Y) Choose the correct answer below. c A. (x,y)=(x + 2,y - 3) O B. (x,y)=(x + 2 y + 9) o C. (x,y)=(x + 8.y + 9) O D. (x,y)—(X + 8.y-3)
letter D is the answer
the average depth of the arctic ocean is 3.953x10^3 feet while the average depth of the atlantic ocean is 1.2851x10^4 feet. approximately how many times deeper is the atlantic ocean than the arctic ocean
By taking the quotient between the average depth of the oceans, we conclude that the atlantic ocean is 3.251 times deeper.
How many times deeper is the Atlantic Ocean?We know that the average depth of the arctic ocean is 3.953x10^3 feet and the average depth of the atlantic ocean is 1.2851x10^4 feet
Notice that both of these are in scientific notation.
To see how many times deeper is the atlantic ocean than the artic ocean we need to take the quotient between the average depth of the atlantic ocean and the average depth of the arctic ocean, this gives:
(1.2851x10^4)/(3.953x10^3) = (1.2851/3.953)*(10^4/10^3)
= 0.3251*(10^1) = 3.251
The atlantic ocean is 3.251 times deeper than the artic.
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) What is the surface area in square In
8 in
10 in
12 in
10 in
10 in
Answer:
Surface area is the total area of the faces of a three-dimensional shape.
A square can not have a surface area since it's two dimensional. If you meant the area of a square then the formula is:
A = a²
a = length of side
8 in = 64 in
10 = 100 in
12 = 144 in
Which of the following represents the dimensions of the room
Given:
The length of the rectangular room is 6 more than the width.
The area of the room, A = 27 square units.
Required:
We need to find the dimensions of the given rectangular room.
Explanation:
Let w be the width of the rectangle.
6 more than means add 6.
The length of the rectangle, l= w+6.
Consider the area of the rectangle formula.
[tex]A=lw[/tex]Substitute A = 27, and l=w+6 in the formula.
[tex]27=(w+6)w[/tex][tex]27=w^2+6w[/tex]Subtract 27 from both sides of the equation.
[tex]27-27=w^2+6w-27[/tex][tex]0=w^2+6w-27[/tex][tex]w^2+6w-27=0[/tex][tex]Use\text{ }6w=9w-3w.[/tex][tex]w^2+9w-3w-27=0[/tex]Take out the common multiple.
[tex]w(w+9)-3(w+9)=0[/tex][tex](w+9)(w-3)=0[/tex][tex](w+9)=0,(w-3)=0[/tex][tex]w=-9,3[/tex]The measure is always positive.
[tex]w=3\text{ units,}[/tex]Substitute w =3 in the equation l =w+6.
[tex]l=3+6=9\text{ units.}[/tex]We get l =9 units and w =3 units.
Final answer:
The dimensions of the room are 3 and 9.
Use the information provided to answer questions 2 - 5. Leah would like to earn at least $ 120 per month. She babysits for $ 5 per hour and works at an ice cream shop for $ 8 per hour. Leah cannot work more than a total of 20 hours per month. Let x represent the number of hours Leah babysits and let y represent the number of hours Leah works at the ice cream shop.
Leah would like to earn at least $120 per month. This expression means she ould like to earn $120 as a minimum and possible higher than that. In other words, she wants to earn either 120 or above that. If the number of hours she babysits is x, and the number of hours worked at the ice cream shop is y, then her earnings as per x and y woud be;
[tex]\begin{gathered} 5x+8y\ge120---(1) \\ x+y\leq20---(2) \\ Solve\text{ these on a graph and you'll have;} \end{gathered}[/tex]The red graph represents x + y =<20
The blue graph represents 5x +8y =>120
Observe that the region where the blue and red are "mixed" together represent the solution region.
Option A (4, 15)
Option B (5, 12) and
Option C (10, 9) are possible solutions
Determine the relationship between lines a, b, and c line a y=5x -3 line b X + 5y=2 line c -10y - 2x =0
Among the given lines line a y = 5x - 3, line b x + 5y = 2, and line c -10y - 2x =0, lines a and line b are intersecting, lines a and c are intersecting whereas lines b and c are parallel to each other.
Write the given lines in standard form
Line a -5x + y = -3
Line b x + 5y = 2
Line c -2x - 10y = 0
a1 = -5, b1 = 1, c1 = -3
a2 = 1, b2 = 5, c2 = 2
a3 = -2, b3 = -10, c3 = 0
a1/a2 = -5/1
b1/b2 = 1/5
c1/c2 = -3/2
As we see that
a1/a2 ≠ b1/b2
Hence, lines a and b are intersecting.
a1/a3 = -5/-2
b1/b3 = 1/-10
As we see that
a1/a3 ≠ b1/b3
Hence, lines a and c are intersecting.
a2/a3 = 1/-2
b2/b3 = 5/-10 = 1/-2
c2/c3 = 2/0
As we see that
a2/a3 = b2/b3 ≠ c2/c3
Hence, lines b and c are parallel.
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In an examination, Sarah obtained 87.5% by gaining 105 marks. How
many marks did she lose?
Answer: 14
Step-by-step explanation:
87.5% of 105 is 91.875 (91)
105-91=14
Find the two square roots of 1/16
Answer:
1/4
Step-by-step explanation:
The square root of 1/16 = 1/4
they probably
how do I simplify it to find the determinant in an easy way
The determinant of the given matrix is [tex]2a^4bc+2c^4ab+6a^3b^2c+6a^3bc^2+6c^3ab^2+6a^2b^3c+12a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4[/tex]
Determinant of the matrix:
Determinant of the matrix is defined as a scalar value which is associated with the square matrix.
Given,
Here we have the matrix show in the question.
Now, we need to find the determinant of the matrix.
To find the determinant of the matrix we have to do the following steps:
1) First we have to pick any row or column in the matrix. It does not matter which row or which column you use, the answer will be the same for any row or column.
2) After the selection you have to multiply every element in that row or column by its cofactor and add. The result is the determinant.
This process can be elaborated in the following steps:
[tex]=(b+c)^2 \times ((a+c)^2 \times (a+b)^2 - b^2 \times c^2) -a^2 \times (b^2 \times (a+b)^2 - b^2 \times c^2) +a^2 \times (b^2 \times c^2 - (a+c)^2 \times c^2)[/tex]
When we expand the equation then we get,
[tex]=(b+c)^2 \times (a^4+2a^3b+2a^3c+a^2b^2+4a^2cb+c^2a^2+2c^2ab+c^2b^2+2acb^2 -b^2c^2) -a^2 \times(b^4+2b^3a+b^2a^2 -b^2c^2) +a^2 \times(b^2c^2 -c^4-2c^3a-c^2a^2)[/tex]
Group the similar terms and arrange them in order,
[tex]=(b+c)^2 \times (a^4+2a^3b+2a^3c+a^2b^2+4a^2cb+c^2a^2+2c^2ab+2acb^2) -a^2 \times (b^4+2b^3a+b^2a^2-b^2c^2) +a^2 \times (-c^4-2c^3a+b^2c^2-c^2a^2)[/tex]
Again we have to expand it and then we get,
[tex]= a^4b^2+2a^4bc+a^4c^2+c^4a^2+2c^4ab+2a^3b^3+6a^3b^2c+6a^3bc^2+2a^3c^3+6c^3ab^2+a^2b^4+6a^2b^3c+10a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4 -b^4a^2-2b^3a^3-b^2a^4+b^2c^2a^2 -c^4a^2-2c^3a^3+b^2c^2a^2-c^2a^4[/tex]
After the simplification, the resulting determinant is
[tex]=2a^4bc+2c^4ab+6a^3b^2c+6a^3bc^2+6c^3ab^2+6a^2b^3c+12a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4[/tex]
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Mia needs to order some new supplies for the restaurant where she works. The
restaurant needs at least 690 knives. There are currently 208 knives. If each set on
sale contains 10 knives, write and solve an inequality which can be used to determine
x, the number of sets of knives Mia could buy for the restaurant to have enough
knives.
Using inequality, we know that Mia needs to buy 41 sets of knives.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Relationships between two expressions that aren't equal to one another are known as inequalities. Inequalities are represented by the symbols, >, <, ≤, ≥, and ≠ has the meaning "7 is greater than" (or "is less than 7," when read left to right).So, the number of sets of knives Mia could buy:
There are currently 248 knives in the restaurant.There are 10 knives in each set that is for sale, so there are 10s knives added to each set.If s sets are purchased, there will be a total of, T = 248 + 10s.At least 657 knives are required by the restaurant, so:
T ≥ 657The difference is:
10s + 248 ≥ 657Now, solve as follows:
10s ≥ 409s ≥ 409/10s ≥ 40.9Rounding off: 41
Therefore, using inequality, we know that Mia needs to buy 41 sets of knives.
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Determine the intercepts
Y - 3 = 5(x-2)
Answer: x-intercept(s): (7/5, 0)
Y intercept(s): (0,−7)
In this case, I need to find the value of x. Whatever x is I need to substitute it into the expressions representing sides. I am informed that this is an isosceles triangle.
Remember all angles of a triangle equal 180 degrees, and all the other geometry stuff.
Please help :)
Answer:
x = ?
Step-by-step explanation:
Since there are two congruent angles, their respective sides are also congruent (an angle's respective side is the side opposing it, the side that it does not touch). Meaning, the 3x-7 side is congruent to the 2x side.
So just set them equal to each other to find x.
3x - 7 = 2x
x = ? (You can do this. Solve for x algebraically.)
The 4x-10 doesn't really matter here since you just need to find x.
-9 (-5 - 4c) simplify the expression and show your work. please this is due tomorrow
The simplified value of the expression given as -9 (-5 - 4c) is 45 + 36c
How to simplify the expression?From the question, the expression is given as
-9 (-5 - 4c)
To simplify the expression, we start by opening the bracket
So, we have the following equation
-9 (-5 - 4c) = -9 (-5 - 4c)
Remove the brackets
So, we have
-9 (-5 - 4c) = -9 x -5 -9 x - 4c
Evaluate the products
So, we have
-9 (-5 - 4c) = 45 + 36c
Hence, the value of the expressions is -9 (-5 - 4c) = 45 + 36c
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Which one is it because i thought it was 32g+26
The equivalent expression of 4(8g + 5) + 6 is 4(5 + 8g) + 6
How to find equivalent expression?Equivalent expressions are expressions that work the same even though they look different.
In other words, two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Therefore, let's find the equivalent expression of 4(8g + 5) + 6.
Hence,
4(8g + 5) + 6
32g + 20 + 6
32g + 26
Hence, the equivalent expression is 32g + 26 or 4(5 + 8g) + 6
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My friend sandy bought 3 pair of jeans and 7 shirts for $60. my friend dan bought 2 pair of jeans and 3 shirts for $30. what are the prices for jeans and shirts?
The prices for jeans and shirts are $6 and $6
Calculations and ParametersGiven that:
3 pairs of jeans and 7 shirts for $60.
And 2 pairs of jeans and 3 shirts for $30.
Let jeans be x
Let shirts be y
3x + 7y = 60.... eq 1
2x + 3y = 30...... eq 2
Let us make x the subject formula from equation 2
2x = 30-3y
x= (30-3y)/2..... eq 3
Put the value of x into equation 1
3 * (30-3y)/2 + 7y = 60
(90- 9y)/2 + 7y = 60
45 - 4.5y + 7y = 60
2.5y =15
y = 6
Then, put the value of y into eq 3
x= (30-3(6))/2
x= 15 - 9
x= 6
Hence, we can see that the values of x and y are 6 apiece.
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Answer:
yeah it's correct , very much well
find X and Y so that the quadrilateral is a parallelogram 5 y 55 ,11x
A few properties of a parallelogram.
1) Opposite sides are always equal.
2) Opposite angles are always equal.
3) The sum of all the angles is 360.
In part 2, we are given the angles. Therefore, we can apply the 2nd property.
11x = 55
5y = z (lets say the unknown is z).
Now, 11x = 55
x = 55/11
x = 5
Now, we have to angles of 55 degrees but we don't know about y and z. Therefore, we have to apply the third property.
55 + 55 + 5y + z = 360
110 + 5y + z = 360
5y + z = 360 -110
5y + z = 250. (i)
According to property 2, 5y = z. Hence, put the value of 5y in the equation (i), we get
5y + z = 250
z + z = 250
2z = 250
z = 250/2
z = 125
From the value of z, we can find the value of y using z = 5y
125 = 5y
5y = 125
y = 125/5
y = 25
Hence, x = 5 and y = 25
Tyler thinks he knows one of the linear factors of . After finding that , he suspects that is a factor of P(x). Here is the diagram he made to check if he’s right, but he set it up incorrectly. What went wrong?
Linear factors are the factors of a polynomial
What went wrong is that: Tyler's linear factors are incorrect
The polynomial function is given as:
Rewrite as:
Further rewrite as:
Factorize the above polynomial
Factor out x - 1 from the polynomial
This means that:
The linear factors are x - 1 and x^2 - 8x + 15
From the given diagram, Tyler's linear factors are x - 1 and x^2 - 8x - 15
Hence, Tyler's linear factors are incorrect
When Elizabeth left her phone in her house this morning
The telephone company offers two billing plans for local calls. Plan 1 charges $24 per month for unlimited calls and Plan 2 charges $18 per month plus $0.05 per call.
Answer:
plan b
Step-by-step explanation:
unless your making 120 calls or more plan B is better
24-18=6
6/0.05
=120
Name the object below.
Thank you :’)
Answer:
The answer is option A.
been stuck on this for ages
A bearing is a measurement of direction that uses North as a point of reference. Your bearing is 00° if you are moving north.
The angle from north to this bearing, measured counterclockwise, is the actual bearing. Utilize the knowledge that west is 270° from the north, south is 180°, and east is 90°.
The number of degrees in the angle measured counterclockwise from the north line to the line connecting the center of the compass is the bearing of a point.
How do you determine bearing angle?
The bearing is the angle subtracted in a clockwise direction from north to west. The bearing is 270° - 17° = 253° since the angle from north to west is 270°.
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consider the following basket of goods: 15 lollipops, 10 bars of chocolate, four jars of peanut butter, and two ice-cream cakes. suppose that in 1999, each lollipop was 10 cents, each bar of chocolate was $1.50, each jar of peanut butter was $2.50, and each ice-cream cake was $7.99. in 2018, each lollipop was 80 cents, each bar of chocolate was $3.75, each jar of peanut butter was $4.25, and each ice-cream cake was 12.99. what was the value of the basket in 2018?
The value of the basket in 2018 was $92.48 if the basket contains 15 lollipops, 10 bars of chocolate, four jars of peanut butter, and two ice-cream cakes.
The value of the basket in 2018 can be calculated by using multiplication and addition.
First, we multiply the cost of each good in 2018 by the number of that good in the basket to calculate their total cost.
Lollipop: $0.80 × 15 = $12
Chocolate: $3.75 × 10 = $37.5
Peanut butter: $4.25 × 4 = $17
Ice-cream cake: $12.99 × 2 = $25.98
Now the value of the basket in 2018 can be calculated by adding these amounts of each good. Therefore;
Value of basket = $12 + $37.5 + $17 + $25.98
Value of basket = $92.48
Hence the value of the basket in 2018 is $92.48
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convert the polar representation of this complex number into its standard form
Given:
[tex]z=6(\cos300\degree+i\sin300\degree)[/tex]Required:
To
p(x) = x^3 − 3x^2 − 10x + 24 , has a known factor of (x-4).
rewrite p(x) as the product of linear factors
The product of linear factors for p(x) is given as (x-4)(x^2+x-6).
What is the factor theorem?The factor theorem states that;
p(x) is divisible by x-a if and only if p(a)=0p(x) is divisible by x+a if and only if p(-a)=0From the question, given that x-4 is a factor of
p(x) = x^3 − 3x^2 − 10x + 24,
then it is divisible by x-4 and p(4)=0.
Dividing x^3 − 3x^2 − 10x + 24 by x-4 using the long division will result to another factor x^2+x-6 with a remainder of zero.
We can then conclude that (x-4)(x^2+x-6) is the product of linear factors for p(x).
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Write the equation of the line that passes through
the given point and is parallel to the given line.
SEE EXAMPLE 1
15. (5, −4); y = ≤⁄x − 4
17. (-3, 2); y=-4
16. (2, 7); 3x - y = 5
18. (6, 4); 2x + 3y = 18
Answer:
I'll do #17 as an example of how to do the others. #15 doesn't make sense. What is "= ≤⁄x?"
Step-by-step explanation:
17. (-3, 2); y=-4
y=4 is a horizontal line, where all values of y are 4, regardless of x. A horizontal line has a slope of 0. [Y does not depend on x].
That leaves us with y =0x + b
For this line to go through point (-3,2), it would have to have a y-intercept (b) of 2 [b is the value of y when x=0]. Since y=0 regardless of x, b must be 2.
The parallel line that goes through (-3,2) is:
y = 0*x + 2, or
y = 2
