kn + mp = q
Solve for p
Subtract kn from both sides of the equation:
kn-kn+mp = q - kn
mp= q-kn
Divide both sides by m
mp/m = (q-kn)/m
p= (q-kn)/m
Paul bought a student discount card for the bus. The card allows him to buy daily bus passes for $1.60. After one month, Paul bought 24 passes and spent a total of $42.80.How much did he spend on the student discount card?Paul spent $______ on the student discount card
The total amount Paul spent that month is the value of the discount card plus the value of the passes he bought.
He bought 24 passes each costing $1.6, therefore:
[tex]\text{passes}=24\cdot1.6=\text{ \$}38.4[/tex]The value of the passes added to the value of the card must be equal to the total spent.
[tex]\begin{gathered} \text{total}=\text{card}+\text{passes} \\ 42.8=\text{card}+38.4 \\ \text{card}=42.8-38.4 \\ \text{card}=4.4 \end{gathered}[/tex]Paul spent $ 4.4 on the student discount card.
sam is cutting 5 sq.ft of grass with scissors. He caan cut 3/4 sq ft an hour. how long will it take him to cut it all
Let X be the time taken to cut all the 5 sq ft
3/4 sq ft = 1hour
5 sq ft = X
cross-multiply
3/4 X = 5
Multiply both-side of the equation by 4/3
X= 5 x 4/3
X = 20/3
X=6.667 hours
X= 6 hours 40 minutes
It will take Sam 6hours40 minute to cut it all
a triangle has side lengths of 6 8 and 10 . Is it a right triangle? explain
For a triangle to be right angled triangle, it muist satisfy the pythagoras theorem,
[tex]\begin{gathered} H^2=P^2+B^2 \\ 10^2=6^2+8^2 \\ 100=36+64 \\ 100=100 \\ \text{left hand side = right hand side} \end{gathered}[/tex]Hence, It is a right angle.
Determine which set or sets to which the number belongs.119Use the table below as a labeling reference.NwNatural NumbersWhole NumbersIntegers1Rational NumbersIrrational NumbersReal NumbersZROQROZ,Q,ROIRO Q. ZWRNO None of the other answers are correct
The number 11/9 belongs to the Real Numbers and to Rational Numbers.
It can't be expressed as a without decimal places, with this we can rule out Natural, Whole and Integers numbers
The number exists in the real line, thus is a Real Number
And finally, it can be expressed as a ratio (it's fraction, is a ratio by definition) thus is a Rational Number.
Thus the two sets the number belongs are Real and Rational Numbers, R and Q (first option)
which of the following shows a line of symmetry correctly for the figure?
The answer is the figure below
x = 19 is a solution for the equation 14 + x = 36 true or false
We replace the value of x with the value 19 and, if the result is an identity, then x=19 is a solution:
[tex]\begin{gathered} 14+x=36 \\ 14+19=36 \\ 33\ne36 \end{gathered}[/tex]As the result is not an identiy, x=19 is not a solution to the expression.
Answer: False.
I need help Evaluate each of the following expressions. Remember to plug in the values first! SHOW ALL WORK!
the expression is:
[tex]\frac{8c}{d}[/tex]Now if we replace c=8 and d=2 the expression will be:
[tex]\frac{8\cdot8}{2}=\frac{64}{2}=32[/tex]In KLM the measure of
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
∠ M = 90
∠ K = 78
KL = 35 ft
MK = ?
Step 02:
cos α = adjacent / hypotenuse
α = 78
adjacent = MK
hypotenuse = KL = 35
cos 78 = MK / 35
35 * cos 78 = MK
7.277 = MK
The answer is:
MK = 7.3 ft
The measure of the perimeter of a triangle is30x + 40. It is known that two of the sides of thetriangle have measures of 12x + 6 and 10x + 20.Find the length of the third side.
The perimeter of a triangle is equal to the sum of all the sides of the triangle.
A triangle has 3 sides so:
Perimeter = side 1 + side 2+ side 3
We have the values of the perimeter and two sides:
perimeter = 30x + 40
Side 1= 12x + 6
Side 2= 10x + 20
S3= ?
So, replacing with the values given:
30x+40= (12x+6)+(10x+20)+ S3
Solving for S3 ( side 3)
30x+40= 12x+6+10x+20+S3
30x+40=12x+10x+6+20+S3
30x+40= 22x+26+S3
30x+40-22x-26=S3
30x-22x+40-26=S3
8x+14 =S3
Lenght of the third side = 8x+14
Hello, I'm having trouble with this equation.What is the solution to this math problem?
Solving this equation for m, we have:
[tex]\begin{gathered} 5m+1=-10m-19 \\ 5m+10m=-19-1 \\ 15m=-20 \\ m=-\frac{20}{15} \end{gathered}[/tex]So the correct option is the fourth one.
1 12 cm Find the area of the figure, (15 Points) 4.5 cm 2 cm 5 cm
area large rectangle:
[tex]A=\text{length}\times width=12\times4.5=54[/tex]area small rectangle:
[tex]A=5\times2=10[/tex]area figure = area large rectangle + area small rectangle
[tex]A=54+10=64[/tex]asnwer: 64 sq cm
Avenue B makes a 70 degree angle with Center Street what are the measures of the angles at South Street makes with Avenue B
1.- They are also perpendicular.
2.- It is also 70° .
identify all obtuse angles in the drawing belovO ZACEO ZBCD and ZBCAO ZBCE and ZECFO ZECD and ZACE
In order to solve this exercise, it is important to remember that an Obtuse angle is an angle that is larger than a Right angle (an angle that measures 90 degrees) and it is less than a Straight angle (an angle that measures 180 degrees).
You can see in the picture that there are two perpendicular lines that intersect. Since they are perpendicular, the intersection forms 4 Right angles.
Notice then that these angles measure 90 degrees:
[tex]\begin{gathered} \angle BCD \\ \angle ACD \\ \angle ACF \\ \angle BCF \end{gathered}[/tex]Notice these angles measure 180 degrees:
[tex]\begin{gathered} \angle AB \\ \angle DF \end{gathered}[/tex]Therefore, based on the definition of Obtuse angles, you can identify that these are:
[tex]\begin{gathered} \angle BCE \\ \angle ECF \end{gathered}[/tex]The answer is: Second option.
solve the equation for x. -x/8=7
Use the properties of equalities to solve the given equation:
[tex]-\frac{x}{8}=7[/tex]Multiply both sides by -8:
[tex]\begin{gathered} -\frac{x}{8}\times-8=7\times-8 \\ \Rightarrow x=-56 \end{gathered}[/tex]Therefore:
[tex]x=-56[/tex]What is the answer to number 4 and how do i solve it
Part 1: Evaluate D(0): Value of D(x) when x=0
[tex]D(0)=5204[/tex]Part 2: Ealuate D(5): Value of D(x) when x=5
[tex]D(5)=-7412[/tex]Part 3: Determine D(0)-D(5)
[tex]\begin{gathered} D(0)-D(5)=5204-(-7412)=5204+7412 \\ \\ D(0)-D(5)=12616 \end{gathered}[/tex]Use the information given to enter an equation in standard form.(2,-4) and (-1,5) are on the line.
Express the equation of a line having two points (x1,y1) and (x2,y2).
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]The points are (2,-4) and (-1,5) implies,
[tex]\begin{gathered} y+4=\frac{5+4}{-1-2}(x-2) \\ y+4=-3(x-2) \\ y+4=-3x+6 \\ y=-3x+2 \end{gathered}[/tex]Convert it into standard form ax+by=c implies,
[tex]3x+y=2[/tex]Therefore, the answer is 3x+y=2.
Let me know if you need a better picture it’s bad quality but readable
Given data:
The given table.
The expression for given table can be written as,
[tex]t(p)=a+bp[/tex]Substitute the given ( 1,6) in the above expression.
[tex]\begin{gathered} 6=a+b(1) \\ b=6-a \end{gathered}[/tex]Substitute (5, 20.4) in the expression.
[tex]20.4=a+5b[/tex]Substitute (6-a) in above expression.
[tex]\begin{gathered} 20.4=a+5(6-a)) \\ -9.6=-4a \\ a=2.4 \end{gathered}[/tex]The value of b is,
[tex]\begin{gathered} b=6-2.4 \\ =3.6 \end{gathered}[/tex]The expression is t(p)=3.6p+2.4.
Thus, the third option is correct.
Annual sales for a company are $375,000 and they increase at a rate of 7% each year. Find the company’s sales after 6 years.
Notice that 7%=7/100=0.07
After the first year, the annual sales are
[tex]375000+0.07(375000)=375000(1+0.07)[/tex]After the second year,
[tex]\begin{gathered} (375000+0.07(375000))+0.07(375000+0.07(375000))=(1+0.07)(375000+0.07(375000)) \\ =(1+0.07)^2375000 \end{gathered}[/tex]Therefore, in general, after n years, the annual sales are
[tex]f(n)=375000(1+0.07)^n[/tex]Set n=6; then,
[tex]\begin{gathered} f(6)=375000(1.07)^6=562773.881943375 \\ \Rightarrow f(6)\approx562773.88 \end{gathered}[/tex]The answer is approximately $562773.88, the exact answer is $562773.881943375
One card is randomly selected from a deck of cards. Find the odds: against getting a red queen.
Given:
One card is randomly selected from a deck of cards.
Required:
Find the odds: against getting a red queen.
Explanation:
The total number of cards in the deck = 52
14. Thirty-five percent of an University's 3000 students have a scholarship. How many students do not have a scholarship? A.800 B.1050 C.1400 D.1950
Nayelly, this is the solution:
• Number of students at the University = 3,000
,•
,• Number of students that have a scholarship = 3,000 * 0.35
,•
,• Number of students that have a scholarship = 1,050
,•
The correct answer is B. 1,050.
Hello it’s showing that I got part of the answer correctNot sure where I went wrong
The A matrix is:
[tex]\begin{bmatrix}{5} & {3} & {} \\ {-6} & {-3} & {} \\ {} & {} & {}\end{bmatrix}[/tex]We can write the system of equations in matrix form like this:
[tex]\begin{bmatrix}{5} & {3} & {} \\ {-6} & {-3} & {} \\ {} & {} & {}\end{bmatrix}\cdot\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{8} & {} & {} \\ {-6} & {} & {} \\ {} & {} & {}\end{bmatrix}[/tex]And we can express that as this:
[tex]A\cdot X=B[/tex]Then the solution is:
[tex]X=A^{-1}\cdot B[/tex]Then, we need to find the inverse of the function to find the solution, start by calculating the determinant:
[tex]\begin{gathered} \text{ Determinant:} \\ d(A)=(5)\cdot(-3)-(-6)\cdot(3)=-15+18 \\ d(A)=3 \end{gathered}[/tex]The inverse function is:
[tex]\begin{gathered} A^{-1}=\frac{1}{\det(A)}\begin{bmatrix}{-3} & {-3} & {} \\ {6} & {5} & {} \\ {} & {} & {}\end{bmatrix}=\frac{1}{3}\begin{bmatrix}{-3} & {-3} & {} \\ {6} & {5} & {} \\ {} & {} & {}\end{bmatrix} \\ A^{-1}=\begin{bmatrix}{-3/3} & {-3/3} & {} \\ {6/3} & {5/3} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-1} & {-1} & {} \\ {2} & {5/3} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex]Thus, the solution is:
[tex]\begin{gathered} \begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-1} & {-1} & {} \\ {2} & {5/3} & {} \\ {} & {} & {}\end{bmatrix}\cdot\begin{bmatrix}{8} & {} & {} \\ {-6} & {} & {} \\ {} & {} & {}\end{bmatrix} \\ \end{gathered}[/tex]Now, solve the multiplication:
[tex]\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-1\cdot8+(-1)(-6)} & {} & {} \\ {2(8)+5/3\cdot(-6)} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-2} & {} & {} \\ {6} & {} & {} \\ {} & {} & {}\end{bmatrix}[/tex]For the stem and leaf plot below find the range of the Data set
For the stem and leaf plot shown;
[tex]\begin{gathered} \text{The smallest value is } \\ 1|0=10 \\ \text{The largest value is } \\ 4|4=44 \\ \text{The range of a data set is given as;} \\ Largest\text{ value-smallest value} \\ \text{Range}=44-10 \\ Range=34 \end{gathered}[/tex]ANSWER:
The correct answer is the second option;
RANGE
Select all the true statements.Through any three collinear points, there is exactly one plane.A segment is part of a line between two points on the line called the endpoints.If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.The midpoint of a segment is equidistant from the endpoints.If two angles are supplementary to the same angle, then the angles must be obtuse.If two angles form a linear pair, then the angles are complementary.
From the given statements, let's determine the true statements.
• Through any three collinear points, there is exactly one plane.
Collinear points are three or more points that are on same straight line. Collinear points can exist on different planes.
Therefore, this statement is FALSE.
• A segment is part of a line between two points on the line called the endpoints.
A segment can be said to be a part of a line with two endpoints.
This statement is TRUE.
• If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.
Using the Parallel Postulate, we can say this statement is TRUE.
• The midpoint of a segment is equidistant from the endpoints.
The midpoint of a line segement is the middle point of the line joining the two endpoints.
Since the midpoint is at the middle, this statement is TRUE.
• If two angles are supplementary to the same angle, then the angles must be obtuse.
Supplementary angles are angles that sum up to 180 degrees.
An obtuse angle is an angle that is greater than 90 but less than 180 degrees.
If two angles are supplementary to the same angle, the angles must be congruent and they may either be obtuse or acute angles.
Therefore, this statement is FALSE.
• If two angles form a linear pair, then the angles are complementary.
Complementary angles are angles that sum up to 90 degrees.
If two angles form a linear pair, then the angles are supplementary(sum up to 180 degrees) not complementary.
Therefore, this statement is FALSE.
Therefore, the true statements are:
• A segment is part of a line between two points on the line called the endpoints.
,• If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.
,• The midpoint of a segment is equidistant from the endpoints.
ANSWER:
• A segment is part of a line between two points on the line called the endpoints.
• If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.
• The midpoint of a segment is equidistant from the endpoints.
The data set lists the number of tickets purchased for a school dance each day for 9 days. {13, 6, 13, 8, 2, 19, 11, 16, 17}If 32 is added to the data set, which statement will be TRUE?
D
1) The median is by nature more consistent and resistant to changes when some value is added to the data set. Let's visualize how that happens:
2) Mean
[tex]\begin{gathered} \left\{13,6,13,8,2,19,11,16,17\right\} \\ \bar{x}=\frac{13+6+13+8+2+19+11+16+17}{9}=11.67 \\ 2)\operatorname{\{}13,\:6,\:13,\:8,\:2,\:19,\:11,\:16,\:17,32\operatorname{\}} \\ \bar{x}=\frac{\sum_{i=1}^na_i=137}{10}=13.7 \end{gathered}[/tex]As we can see, the addition of 32 to the data set changes the mean.
3) Now, let's check the Median. Rewriting that into the ascending order:
[tex]\begin{gathered} 2,\:6,\:8,\:11,\:13,\:13,\:16,\:17,\:19 \\ Median:13 \end{gathered}[/tex]Note that 13 divides the distribution into two halves.
Now, let's add 32 to that dataset and check it:
[tex]\begin{gathered} 2,\:6,\:8,\:11,\:13,\:13,\:16,\:17,\:19,\:32 \\ Md=\frac{13+13}{2}=13 \end{gathered}[/tex]Thus, we can tell that the answer is:
Suppose there is a tree debris drop-off in temperature for every thousand feet and airplane climbs into the sky if the temperature on the ground with at sea level is 53° what would be the temperature when the plane reaches an altitude of 30000 ft
Since we have that every thousand feet the temperature drops by 3°, and the starting altitude (Sea level) is at 0 meters but with a temperature of 53°, we solve as follows:
*First we determine the decrease in temperature if, and since it behaves linearly we will have that at 30000ft the total drop in temperature is of:
[tex]d=\frac{30000\cdot(-3)}{1000}\Rightarrow d=-90[/tex]So, when the place climbs 30 000 ft there is a drop of 90°. Now, we subtract 90° from 53° and we will get the temperature when the plane reaches 30000ft, that is:
[tex]53-90=-37[/tex]So, the temperature when the plane climbs 30000ft is of -37°.
Find the 9th and 10th term for the sequence an = 3n + 4
Answer:
9th term = 31
10th term = 34
Explanation:
The formula for the nth term of the sequence is
an = 3n + 4
where n is the number of terms
1) For 9th term,
if n = 9,
a9 = 3 * 9 + 4
a9 = 31
1) For 10th term,
if n = 10,
a10 = 3 * 10 + 4
a10 = 34
If f(x) = 8x + 1 and g(x) = 8(x - 2) + 1, how does the graph of g compare to the graph of f?
OA. the graph of g is the graph of f shifted up 2 units
OB. the graph of g is the graph of f shifted left 2 units
OC. the graph of g is the graph of f shifted down 2 units
D. the graph of g is the graph of f shifted right 2 units
The graph of g is the graph of f shifted to the left by 2 units
How to compare the graph of g with the graph of f?
A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given: f(x) = 8x + 1 and g(x) = 8(x - 2) + 1
To solve this problem, we need to understand the direction of movement. In the cartesian plane or graph, the x-axis is either a movement to the left(negative) or right(positive).
Since f(x) = 8x + 1, looking at g(x) = 8(x - 2) + 1, you will notice that 2 is subtracted from the value x. This is a movement in the negative x-axis (left shift) and the shift is by 2 units.
Therefore, the graph of g is the graph of f shifted left 2 units. So option OA is the answer
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Find the volume of the right cone below in term of
Solution:
Given:
The volume of a cone is given by;
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ where; \\ h=21 \\ r=8 \\ \\ Hence, \\ V=\frac{1}{3}\times\pi\times8^2\times21 \\ V=448\pi\text{ cubic units} \end{gathered}[/tex]Therefore, the volume of the cone is;
[tex]V=448\pi\text{ }units^3[/tex]If an item that originally cost $19 is decreased to $16, what is the percentage of decrease in the item?
Round your answer to 3 decimal places.
15.789% is the percentage decrease of the item with an originally cost of $19 and decreasing to $16
What is the percentage decrease of the item?Percentage decrease is simply the amount of decrease from the original value to the new value in terms of 100 parts of the original value.
The formula for percentage decrease is expressed as;
D = ((x₁ - x₂) / x₁)100%
Given the data in the question;
original value x₁ = $19New value x₂ = $16Percentage decrease D = ?To determine the percentage decrease, plug the given values into the percentage decrease formula above.
D = ((x₁ - x₂) / x₁)100%
D = (( 19 - 16 ) / 19 )100%
D = (( 3 ) / 19 )100%
D = ( 0.1578947 )100%
D = 15.789%
Therefore, the percentage decrease of the item is 15.789%.
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Select all that apply. Daryl is a tourguide. His tour group walks 2 miles in anafternoon. The graph describes themotion of Daryl's tour group.Which statements below are correct?In part A, the tour group walks 2 miles.In part B, the tour group does not walk forward.In part C, the tour group walks for 2 hours.
Answer:
The statements that are correct are Statements B and C.
Explanation:
Here is the description for each part of the graph.
Part A - The group walked for 2 hours and covered 1 mile only.
Part B - The group did not move for 1 hour.
Part C - The group continued their walk for 2 hours more and covered 1 more mile.