Answer:
12 - (¼*x)
Step-by-step explanation:
If something is "decreased by" in mathematics we are looking at a minus sign (-).
For instance 5 decreased by 2 is 5 - 2
Grace and her dad are planning to attend the state fair. An adult ticket is $15.00. The price of an adult ticket is one half the price of a student ticket plus $8.00. Write an equation to determine how much Grace will pay for a student ticket.
one halfx + 8 = 15
one halfx − 8 = 15
one halfx + 15 = 8
one halfx − 15 = 8
Answer:
Option 1 is the correct equation.
Step-by-step explanation:
x = price of the student ticket.
One half price of x + $8 = adult ticket price ($15)
Answer:
The correct answer is A
Because taking the student ticket to be x
one half of x + 8 =15
1. Your school's Key Club decided to sell fruit baskets to raise
money for a local charity. The club sold a total of 80 fruit
baskets. There were three different types of fruit baskets.
Small fruit baskets sold for $15.75 each, medium fruit baskets
sold for $25 each, and large fruit baskets sold for $32.50
each. The Key Club took in a total of 52086.25. and they sold
twice as many large baskets as small baskets.
a. Formulate a system of three linear equations in three
variables to represent this problem situation. Be sure to
define your variables.
b. Solve the system of three linear equations using
technology with matrices. Write your answer in terms of
the problem situation.
c. Describe the solution in terms of the problem situation.
2. Is it always easier to solve a system of linear equations using
matrices? Explain your reasoning.
Let the small , medium and large baskets be denoted by s,m & l
Formulating the equations
s+m+l= 80--------- equation1
$15.75s+ $25 m + $32.5l = $2086.25------equation2
2s=l---------equation 3
Using the technology s=15, m=35 and l= 30
15+35+30= 80--------- equation1
$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2
2(15)=(30)---------equation 3
Yes because multiple variables can be easily calculated through matrices using technology
In Matrix form
[tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex] [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex] = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]
Let A= [tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex]
Z= [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex]
B = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]
Z= A⁻¹ B
A⁻¹= A mod/ det A
det A= -1
Using the technology s=15, m=35 and l= 30
15 small baskets,
35 medium baskets
30 large baskets were sold.
Part C:
15+35+30= 80--------- equation1
$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2
236.25+ 875+ 975=$2086.25
$2086.25=$2086.25
2(15)=(30)---------equation 3
Answer 2:
Yes because multiple variables can be easily calculated using technology.
N.B There is a typing error in question its $2086.25 not 52086.25
HELP ASAP!!!
The line (y-1)=(2/3)(x+1) contains point (a,-3).
What is the value of a? Show
your work.
Answer:
-7
Step-by-step explanation:
The line (y-1)=(2/3)(x+1) contains point (a,-3)
=> (-3-1) = (⅔)(a+1)
-4 = (⅔)(a+1(
(a+1)= -4 ÷ ⅔
a + 1 = -4 × 3/2
a+ 1 = -6
a = -6-1
a = -7
The value of 'a' will be;
⇒ a = - 7.
What is substitution method?To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The equation of line is,
⇒ (y - 1) = (2/3) (x + 1)
And, The point on the line = (a, - 3)
Now,
Since, The point on the line = (a, - 3)
Hence, It satisfy the equation of line.
Substitute x = a and y = - 3, we get;
⇒ (y - 1) = (2/3) (x + 1)
⇒ (- 3 - 1) = (2/3) (a + 1)
⇒ - 4 × 3 = 2a + 2
⇒ - 12 - 2 = 2a
⇒ 2a = - 14
⇒ a = - 7
Thus, The value of a = - 7
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Use the graphical representation and algebraic reasoning to identify the key features of the graph of the function
g(x) = -f(x) + 10.
Select all the correct answers.
horizontal asymptote of y = 0
range of {y 0 < y < 00}
range of {y-oo < y < 10}
no x-intercept
y-intercept at (0,9)
horizontal asymptote of y = 10
x-intercept at (1,0)
increasing y-values
Answer:
4 answers to this question
Step-by-step explanation:
4 Answers: (#s 3, 5, 6, 7)
y-intercept at (0,9)
horizontal asymptote of y=10
x-intercept at (1,0)
range of {y|-∞<y<10}
PLEASE HELP!!!!!! Im being timed
Answer:
9,6 hope this helps
Can someone help me
Answer:
first statement
Step-by-step explanation:
64 < 77 < 81 , then
[tex]\sqrt{64}[/tex] < [tex]\sqrt{77}[/tex] < [tex]\sqrt{81}[/tex] , that is
8 < [tex]\sqrt{77}[/tex] < 9
Thus [tex]\sqrt{77[/tex] is to the left of 9 on the number line
Answer:
OPTION A IS CORRECT.
BRAINLIST PLEASE!!!
true or false? in a two-column proof, the left column states your reasiong
John's family drinks
7/9 of milk a day.
How many liters do they drink in 4 days?
[tex]\frac{28}{9}[/tex] liters do they drink in 4 days.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
According to the question
John's family drinks 7/9 of milk a day.
Liters do they drink in 4 days: X
Using unitary method
X = [tex]\frac{7}{9} \times4[/tex]
X = [tex]\frac{28}{9}[/tex]
[tex]\frac{28}{9}[/tex] liters do they drink in 4 days.
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Pls help fast, with steps
Answer:
answer is D
Step-by-step explanation:
PAR = 25
RPA= 25
PRA= 130
PRQ = 180- 130 = 50
PRQ =PQR = 50
X= 180 +(50 +50) =80
(1/2)^x=2^-x could anyone tell me why
Answer:
Anything to a negative power is always the reciprocal. An example might be 2⁻² can be written as 1/4
Step-by-step explanation:
The letters a and b represent nonzero constants solve
ax-b=12.5 for x
Answer:
x=(12.5+b)/a
Step-by-step explanation:
ax-b=12.5
ax=12.5+b
x=(12.5+b)/a
The solution for the equation ax - b = 12.5 for x is:
x = (12.5 + b) / a
We have,
To solve the equation ax - b = 12.5 for x, follow these steps:
- Add b to both sides of the equation:
ax - b + b = 12.5 + b
This simplifies to:
ax = 12.5 + b
- Divide both sides of the equation by "a":
(ax) / a = (12.5 + b) / a
Simplify:
x = (12.5 + b) / a
Thus,
The solution for the equation ax - b = 12.5 for x is:
x = (12.5 + b) / a
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Martha has a French cookie recipe that calls for baking the cookies for 14 to 18 minutes at 180∘C. Her oven measures temperature in Fahrenheit only. At what temperature in degrees Fahrenheit should she set her oven to make the cookies per the recipe?
Answer:
180° Celsius is equal to approximately 356° Fahrenheit
Step-by-step explanation:
I hope this helps.
The value of 180 degree Celcius in Fahrenheit is 356.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Martha has a French cookie recipe that calls for baking the cookies for 14 to 18 minutes at 180∘C.
The temperature in Fahrenheit will be calculated as,
F = 1.8C + 32
F = ( 1.8 x 180 ) +32
F = 356
Therefore, the value of 180 degree Celcius in Fahrenheit is 356.
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Rachel’s free-throw average for basketball is 60%. How many times do you think she will make a free-throw in her next 50 tries?
Answer:
Rachel will make 30 free-throws!
Step-by-step explanation:
Hello!
I came up with this solution with some easy mental math! If you weren't aware, 60% of 50 is a whole number! Meaning that 60% of 50 is 30. You could even double 50 to make it 100, everyone knows that dealing with percentages with the number 100 make them a whole lot easier!
Back to what I was saying, if you used 100, you would also have to take 60% of 100, which is 60. And then have to divide 60 by 2 because you doubled the 50! Giving you 30 free-throws, which is the correct answer!
Hope this helped! Let me know if you have any further questions! :)
PLZZZZ help it will mean a lot :)
3x = 18
Divide both sides by 3 and simplify
x=6
Answer:
Step-by-step explanation:
assuming that you need to find the value of x
3x = 18
-divide both sides by 3
3x/3 = 18/3
-use the facts that 3/3 =1 and 18/3 = 3*6/3 = 6
x = 6
Change the following fraction to a decimal. 8 4/5 = ?
Answer:
The answer is 8.8
Step-by-step explanation:
4/5 x 20/20 = 80/100
80/100 = .8
Step-by-step explanation:
[tex]8 + \frac{4}{5} = \frac{40 + 4}{5} \\ = \frac{44}{5} = 8.8 \\ thank \: you[/tex]
5. After paying a tax of 8 palsa per rupee a man saves Rs. 18,400 per month Then his monthly income is 2 Points) 20,000
Answer:
92% of Income is Rs 18400
Step-by-step explanation:
I = 18400/.92 = Rs 20000
Find the value of the expression when x = 4 and y = 6.
8x + 2y + 3
Answer:
47
Step-by-step explanation:
8(4) + 2(6) + 3 = 47
32 + 12 + 3 = 47
solve the following pair of simultaneous equations. you can use any 3 methods. 2x- y= 5, x+2y=5.
Answer:
2x-y= 5, x + 2y=5
Step-by-step explanation:
x = 3, y = 1
350 rounded to the nearest hundred is
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{350 rounded to the nearest hundred is...}[/tex]
[tex]\huge\text{Rounding is basically is the}\\\huge\text{approximation of the given number.}[/tex]
[tex]\huge\bullet\huge\text{ So, when you are looking at 350, you are}\\\huge\text{asking yourself is it closer to 300 or 400.}\\\huge\text{If you are looking at the number correctly}\\\huge\text{you would see it is closer to \underline{\underline{400}} when you}\\\huge\text{rounded to NEAREST HUNDRED.}[/tex]
[tex]\huge\boxed{\textsf{Therefore, your ANSWER/RESULT is: \bf 400}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
A certain forest covers an area of 4900 km². Suppose that each year this area decreases by 7%. What will the area be after 8 years?
Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
area after 8 years is 2156km²
Step-by-step explanation:
Area of forest=4900 km²
decrease in area in 1 year=4900km² × 7%
decrease in area in 1 year= 343km²
decrease area in 8 years=343km² × 8
=2744km²
Remaining area= (4900-2744)km²
=2156km²
Note:If you have any question about it please ask.
Practice
1. Hyatt Home Improvement uses H-shaped tile Design 1 Design 2
Design 3
designs on their buildings, advertisements, and
vehicles. The designs they use follow a specific
pattern. The first three designs are shown.
a. Describe the pattern in the designs.
b. Write two different expressions to represent
the number of tiles used in Design n. Use
algebraic properties to prove the two expressions are equivalent.
c. Explain how you could use technology to prove the two expressions in part (b)
are equivalent.
d. Create a table that displays the number of tiles used in each of the first 6 designs.
e. Create a graph of the data points in your table on the coordinate plane shown. Draw a smooth
curve to connect the points.
f. Do all of the points on the smooth curve make sense in terms of the problem situation? Explain
your reasoning.
g. Describe the pattern as linear, exponential, quadratic, or none of these. Explain your reasoning.
h. The owner of Hyatt Home Improvement wants to put one of their designs on an empty
rectangular sign in front of their headquarters. The empty sign is 10 feet tall and 12 feet wide. If he
Patterns are set of rules that guide the creation of a dataset. The observation from the first three designs are as follows:
The pattern is that the number of tiles increases as the design number increasesThe expressions for the number of tiles are [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex]The expression can be proved to be equivalent using graph technology The points on the curve make sense in this scenario because all values are positiveThe pattern is quadratic.The largest design number that can enter an empty 10 by 12 ft sign is design number 8The pattern
The first three design show that, as the design number increases (i.e. 1, 2, 3), the number of tiles used also increases (i.e. 7, 12, 19)
The expressions for the number of tiles
The design number and the number of tiles is represented as follows
[tex]1 \to 7[/tex]
[tex]2 \to 12[/tex]
[tex]3 \to 19[/tex]
From the designs, we observe that some tiles are at the middle, while other tiles are at the sides.
Design 1 has 1 tile at the center and 6 tiles at either sides.
So, we have:
[tex]1 \to 1 + 6[/tex]
[tex]2 \to 4 + 8[/tex]
[tex]3 \to 9 + 10[/tex]
Expand
[tex]1 \to 1^2 + 6 \to 1^2 + 2 \times 3 \to 1^2 + 2 \times (1 + 2)[/tex]
[tex]2 \to 2^2 + 8 \to 2^2 + 2 \times 4 \to 2^2 + 2 \times (2 + 2)[/tex]
[tex]3 \to 3^2 + 10 \to 3^2 + 2 \times 5 \to 3^2 + 2 \times (3 + 2)[/tex]
Notice the pattern,
The number of tiles in design n will be:
[tex]Tiles = n^2 + 2 \times (n + 2)[/tex]
Open bracket
[tex]Tiles = n^2 + 2n + 4[/tex]
Hence, the expressions for number of tiles in design n are:
[tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex]
Technology to prove that both expressions are equivalent
To prove that [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] are equivalent using technology, the graphs of [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] can be plotted and then compared
The table and graph for the first 6 designs
The table entry for the first 6 designs is calculated as follows:
[tex]n = 1\ \ \ \ \ Tiles = 1^2 + 2 \times 1 + 4 = 7[/tex]
[tex]n = 2\ \ \ \ \ Tiles = 2^2 + 2 \times 2 + 4 = 12[/tex]
[tex]n = 3\ \ \ \ \ Tiles = 3^2 + 2 \times 3 + 4 = 19[/tex]
[tex]n = 4\ \ \ \ \ Tiles = 4^2 + 2 \times 4 + 4 = 28[/tex]
[tex]n = 5\ \ \ \ \ Tiles = 5^2 + 2 \times 5 + 4 = 39[/tex]
[tex]n = 6\ \ \ \ \ Tiles = 6^2 + 2 \times 6 + 4 = 52[/tex]
So, we have:
[tex]\begin{array}{cc}Design & {Tiles} & {1} & {7} & {2} & {12} & 3 & {19} & {4} & {28} & {5} & {39}& {6} & {52} \ \end{array}[/tex]
See attachment for the graph of the above table
All the points on the curve make sense in this scenario because all values are positive.
The pattern type
We have:
[tex]Tiles = n^2 + 2n + 4[/tex]
When an equation has a degree of 2, the equation is quadratic.
Hence, the pattern is quadratic.
The largest design that an empty sign of 10ft by 12ft can contain.
From the first three designs:
The number of tiles on a complete row and column are always the same.
Design 1 has 3 tiles in its complete row and column
Design 2 has 4 tiles in its complete row and column
Design 3 has 5 tiles in its complete row and column
The relationship between the design number (d) and the number of complete tiles (t) is:
[tex]d = t - 2[/tex]
For the 10ft by 12ft empty sign
[tex]t = 10[/tex] because [tex]10 < 12[/tex]
So, we have:
[tex]d = t - 2[/tex]
[tex]d = 10 - 2[/tex]
[tex]d = 8[/tex]
Hence, the largest design number is design 8
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PLSSS HELPPPPP- Evaluate the expression. 1 1 4 25 3 Write your answer as a fraction or as a whole or mixed number.
Answer:
Mixed number form 4 4/5 exact form 24/5
Step-by-step explanation:
hope this helps
Answer:
Step-by-step explanation:
8/15
find the length indicated.
Answer:
none
Step-by-step explanation:
just need help with math before its due tomarrow
Answer:
(6_4)(6+4)
6(6+4)-4(6+4)
36+24-24-16
36-16
Given that f(x)=2x-8, determine the average rate of change over the interval [2, 8].
Answer:
2
Step-by-step explanation:
The average rate of change over [2, 8] is the change in the y-values over the change in the x-values.
[tex]\frac{f(8) - f(2)}{8 - 2}[/tex]
[tex]f(8) = 2(8) - 8 = 16 - 8 = 8[/tex]
[tex]f(2) = 2(2) - 8 = 4 - 8 = -4[/tex]
[tex]\frac{8 - (-4)}{8-2} = \frac{8 + 4}{8-2} = \frac{12}{6} = 2[/tex]
What’s the answer???
Answer:
Step-by-step explanation:
An ant walk about 3 inches per second how many miles per day could an ant travel if it walked without a break?
Answer:
Step-by-step explanation:
45/11 miles per day or ~4.091 miles per day
Step-by-step explanation:
3 inches per second
24 hours in a day
60 minutes in 1 hour
60 seconds in 1 minute
Amount of inches per minute: 3 x 60 = 180 inches
Amount of inches per hour: 180 x 60 = 10,800 inches
Amount of inches per day 10,800 x 24 = 259,200 inches
To find the number of feet that 259,200 inches is, divide by 12.
259,200/12 = 21,600 feet per day
To find the number of miles that 21,600 feet is, divide by 5280.
21,600/5280 = 45/11 = 4.09090909091 = ~ 4.091
So, an ant could walk 45/11 miles per day or ~4.091 miles per day if it walked without taking a break.
Please help! Please don't answer if you don't know!
Answer:
[-0.25 1.25]
[ ]
[-0.75 2.75]
If not satisfied than..
You can write it in other way as show in step by step
Step-by-step explanation:
Step 1:
First of all find the determinate.
Cross multiply the number 11 ✖ -1
detA = 11 × -1= -11 ---eq1
And now cross multiply the number 3 ✖ - 5
detA = 3 × -5= -15 ---eq2
Now we use eq 1 and 2
detA = (-11)-(-15)
Minus cancels minus
So it becomes
detA = -11 + 15
= 4
Step 2:
We find adjacent of the given.
[11 -5]
adjA= [ ]
[3 -1 ]
We change the places. The number 11 goes to in place of -1. -1 goes in place of 11.
And we change the signs of -5 and 3. -5 becomes 5 and 3 becomes -3.
We get
[-1 5]
adjA = [ ]
[-3 11]
Step 3:
Now we use the following formula
1
A^-1 = -------- adjA
detA
1 [-1 5]
A^-1 = ------- [ ]
4 [-3 11]
And now multiply
1
---- with each number of adjA.
4
And than subtract..
And you will get the inverse matrix
If the answer comes same than that's the answer for inverse matrix
Thank you.
the basics of geometry
Answer:
go to MME click revise gcse maths and it would say geomatry foundtion Step-by-step explanation:
Answer:
Step-by-step explanation:
point: the basic unit of geometry
line: it extends to 2 directions without any end
line Segment: it is a line but has end points eg the length of you book
(And there are a few types of lines like parallel lines and intersecting lines you can check that on You tube)
Rays: Rays are like line segments but has only 1 end point
curves: do i have to explain its just some squiggles
Polygons: polygons are shapes that are made up of straight line Segments
polygons are named based on the number of sides it has
3 sides: TRIANGLES
4 sides: QUADRILATERALS
5 sides: PENTAGONS
6sides : HEXAGONS and there are many more...
THERE WAY TOO MUCH LIKE ANGLES, INTEROR POINT, EXTEROR POINT, CIRCLES ETC sorry i can't explain that much......
Anyone know the answers 11 through 14?Please help me.I’m tired
Answer:
11. [tex]x^{5}[/tex]
12. 5*[tex]x^{2}[/tex]
13. x+21
14. 2x-8
Step-by-step explanation:
