Answer:
cost price = £ 600
discount = 5%
selling price =
5/100 * 600.
5 * 6
30 £
price = 600 - 30
= 570
Examine the system of equations.
y=2x-3
y=-3
Which statement about the system of linear equations
is true?
O The lines have different slopes.
O There is no solution to the system.
O The lines have the same slope, but different y-
intercepts.
O The solution is (-3, -9).
For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The correct option is A.
What is the System of equations?Inconsistent System
For a system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.
If the two of the given system of equations are plotted on the graph, then it can be observed that the two lines have different slopes. Therefore, the correct option is A.
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During its descent, the pair of sunglasses passed by a climber in the canyon 6 seconds after stefano dropped them. To the nearest meter, what is difference in elevation between stefano and the climber?.
Answer:
20 can be the answer of it
Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?
Answer:
13x = 39
x=3
y=10
75 POINTS PLEASE RESPOND ASAP
Have you ever been swimming in a pool, and your eyes were red when you get out? This means the chemicals in the pool were not adjusted correctly! More specifically, the measurement of the pool's pH was not quite right.
pH is a measurement of hydronium ions and can be modeled by the function f(x) = −log10x. The variable x represents the amount of hydronium ions, and f(x) gives the pH level.
Different liquids have ideal pH values that are different. Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, and a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.
Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.
Use your graph to find the ideal pH level if the amount of hydronium ions is raised to 0.50.
The pool company developed new chemicals that transform the pH scale. Using the pH function f(x) = −log10x as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Be sure to label each transformation on the graph.
f(x) + 1
f(x + 1)
ANSWER :
The pH level of a swimming pool indicates the level of acidity or alkalinity
of the swimming pool.
Correct Responses;
First Part: Please find attached the required graph of the pH function created with MS Excel.
The pH value is 0 when x = 1
The pH value is 1 when x = 0.1
The pH level if the hydronium ions is raised to 0.50 is approximately 0.301029996.
Second Part: The transformation that results in a y-intercept is f(x + 1), because f(0 + 1) exists and is equal to 0.
STEPS
Method by which the above responses are obtained
First part
The given pH function is f(x) = -㏒₁₀x
Where;
x = The amount of hydronium ions
A substance with a pH < 7 is acidic
A substance with a pH > 7 is alkaline
A neutral solution has pH = 7
Water is a neutral solution
The graph of the pH function created with MS Excel is attached
The table of values of the graph is as follows;
From the graph, we have;
When the pH value is 0, the hydronium ion concentration is 1
The pH value is 1 when x = 1 × 10⁻¹ = 0.1
The pH level if the hydronium ions, x = 0.5 is given from the graph as follows;
pH = f(0.5) = -㏒₁₀(0.5) ≈ 0.301029996
The pH value when the hydronium ions is 0.5 is pH ≈ 0.301029996
Second Part
Using f(x) = -㏒₁₀x as the parent function, the graph of f(x) + 1, and f(x + 1) are plotted
From the graph, we have;
The graph of f(x) + 1 = -㏒₁₀x + 1
The graph of f(x + 1) = The graph of -㏒₁₀(x + 1)
At the y-intercept, x = 0, therefore;
f(x) + 1 = f(0) + 1 = -㏒₁₀0 + 1 = Undefined
f(x + 1) = f(0 + 1) = -㏒₁₀(0 + 1) = 0
Therefore;
The transformation that results in a y-intercept is f(x + 1) because f(0 + 1) is 0, which is defined.
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Which values of a and b make the following equation true?
(5x7y²)(-4x²y5)--20xy
a=11, b = 7
a = 11, b = 10
a=28, b = 7
a=28, b= 10
Answer:
A. is correct answer
Step-by-step explanation:
full explanation
A financial planner has three portfolios: A, B, and C. Because investors have different tolerances for risks, 35% of people are likely to invest in portfolio A, 25% are likely to invest in B, and 40% are likely to invest in C. Each portfolio has both stocks and bonds, and investors are equally likely to choose either.
This is a tree diagram that represents the probability of investors choosing the different financial products.
What is the probability of an investor choosing both stocks AND bonds from portfolio B?
The probability of an investor choosing both stocks AND bonds from portfolio B is 0.25 or 25%.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
A financial planner has three portfolios: A, B, and C.
Each portfolio has stocks and Bond
P(stock) = 0.5
P(bond) = 0.5
Customers are equally likely to choose stocks.
P(stock and bond from B) = P(stock, B) + P(bond, B)
= 0.25×0.5 + 0.25×0.5
= 0.25 or
= 25%
Thus, the probability of an investor choosing both stocks AND bonds from portfolio B is 0.25 or 25%.
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how much is 20 Pepsi if one Pepsi is sold at the rate of 20 naira
Answer:
Let x= cost of 20 pepsi
so 1 Pepsi = 20 naira
20 = x
x= 20*20
x= 400 naira
Therefore the cost of 20 pepsi is 400 naira
In your research study measuring the relationship between time spent playing video games and course grades, you find that grades increase at about the same rate as time spent playing video games decreases. What do you conclude
Research study measuring relationship suggests that video games may have a detrimental effect on an individual's grades.
This study analyzes the correlation between video game usage and academic performance. Scholastic Aptitude Test (SAT) and grade-point average (GPA) scores were used to gauge academic performance. The amount of time a student spends playing video games has a negative correlation with students' GPA and SAT scores. As video game usage increases, GPA and SAT scores decrease.
A chi-squared analysis found a p value for video game usage and GPA was greater than a 95% confidence level (0.005 < p < 0.01). This finding suggests that dependence exists. SAT score and video game usage also returned a p value that was significant (0.01 < p < 0.05). Chi-squared results were not significant when comparing time spent studying and an individual's SAT score. This research suggests that video games may have a detrimental effect on an individual's GPA and possibly on SAT scores. Although these results show statistical dependence, proving cause and effect remains difficult, since SAT scores represent a single test on a given day. The effects of video games maybe be cumulative; however, drawing a conclusion is difficult because SAT scores represent a measure of general knowledge. GPA versus video games is more reliable because both involve a continuous measurement of engaged activity and performance. The connection remains difficult because of the complex nature of student life and academic performance. Also, video game usage may simply be a function of specific personality types and characteristics.
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√4x-3-1=√x+1
What is the value of x
I'm kinda lost in this problem. Can you teach me how to solve these
53) Vertical angles are congruent, so [tex]m\angle IDA=121^{\circ}[/tex]
54) [tex]\angle YDA[/tex] and [tex]\angle YDF[/tex] are supplementary, so [tex]m\angle YDA=180^{\circ}-121^{\circ}=59^{\circ}[/tex]
55) Because vertical angles are congruent, [tex]m\angle FDI=59^{\circ}[/tex]. Now, because DR bisects [tex]\angle FDI[/tex], this means [tex]m\angle RDI=\frac{59}{2}=29.5^{\circ}[/tex]
56) This is a geometric sequence where the next term is obtained by multiplying the previous term by -2, so the next two numbers are 16, -32
can someone please help mee
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:Domain : \fbox{-3}\leqslant x \leqslant \fbox{-1}[/tex]
[tex]\qquad \tt \rightarrow \:Range :\:\:\fbox{-4}\leqslant x \leqslant \fbox{-3}[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Domain = All possible values of x for which f(x) is defined
[ generally the extension of function in x - direction ]
Range = All possible values of f(x)
[ generally the extension of function in y - direction ]
[tex] \large\textsf{For the given graph : } [/tex]
[tex]\qquad \tt \rightarrow \: domain : \fbox{-3}\leqslant x \leqslant \fbox{-1}[/tex]
[tex]\qquad \tt \rightarrow \: range : \:\:\fbox{-4}\leqslant x \leqslant \fbox{-3}[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Find the HCF of
x^4 y^2 and x^3 y^3
Here's your answer down here↓:
Step-by-step explanation:
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
(x^4 - y^4) = (x^2 - y^2)(x^2 + y^2) = (x - y)(x + y)(x^2 + y^2)
Ok. So the factor (x-y) appears once in the top line and once in the second line. So we are going to take it the least amount of times.
So, the factor (x + y) appears in the top line zero times and in the second line one time so we will take it where it appears the least which is zero times so we are still at (x - y)
And it Same goes for the factors of (x^2 + y^2) and (x^2 + xy + y^2)
Determine the measure of angle BFE 1 ) 69 degrees 2 ) 112 degrees 3 ) 11 degrees 4 ) 224 degrees
Answer:
option 2
Step-by-step explanation:
the chord- chord angle BFE is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is
∠ BFE = [tex]\frac{1}{2}[/tex] ( BE + DC) = [tex]\frac{1}{2}[/tex] (72 + 152)° = [tex]\frac{1}{2}[/tex] × 224° = 112°
In the diagram below, triangle lmn is congruent to cba. What is the length of segment ln?
Answer:
this is step by step explenation
see more...
Are the equations 5x=3-x and 5x=-x+3 equivalent?
Answer:
yes
Step-by-step explanation:
The commutative property of addition applies to let you swap the order of the summands.
__
Here is how the commutative property can be applied.
5x = 3 -x . . . . . given
5x = (3) +(-x) . . . . shown as a sum
5x = (-x) +(3) . . . . order swapped using commutative property of addition
5x = -x +3 . . . . . . equivalent equation
Figure 1 is similar to figure 2. What is TS?
1 unit
4 units
8 units
2 units
Answer:
8 units
Step-by-step explanation:
ratios
(x-3) /( x+1) = (x-2)/(x+3) cross multiply
x^2 -x -2 = x^2 - 9
-x - 2 + 9 = 0
x = 7
so TS = x + 1 = 8 units
find the least nu,ber which is exactly divisible by 12 16 and 24
Answer:
The smallest number all three numbers can be divided by is 4.
Step-by-step explanation:
12/4=3
16/4=4
24/4=6
Hope this helps!
If not, I am sorry.
There is a bag filled with 6 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting at least 1 blue?
Answer:
1/11
Step-by-step explanation:
probability =total number of items ÷ 1
=11÷1
=1/11
which expression is equivalent to 354x + 332, If x=0?
Answer:
10x + 332
when, x=0
Step-by-step explanation:
Please give me brainlist.
Which equation would have real zero(s) corresponding to the x-intercept(s) of the graph below?
Answer:
the first one listed (y = -[tex]2^{x}[/tex] + 4)
Step-by-step explanation:
a 0 at an x-intercept means that when plugging in that number, you get a 0 as a y-value.
So, the easiest method to use is to plug x=2 into each equation listed, because we can see that (2,0) is a point on this graph
if y= -[tex]2^x\\[/tex] + 4
y = -2² + 4
y = -4 + 4
y = 0
This means that this graph has corresponding real zero(s) to the function y= [tex]-2^x[/tex] + 4
(I chose which graph to test by looking to see which option seemed right)
ab (2a²b² - 4b) = what is the answer
Answer:
2ab(a2b−2)
Step-by-step explanation:
Find the area of a regular octagon with an apothem of 2 cm.
The area of a regular octagon with an apothem of 2 cm is 3cm ^2.
The area of a regular octagon with an apothem of 2 cm.
Given the apothem length,
What is the area of the regular polygon?the area of a regular polygon becomes,
[tex]A=\frac{1}{2}\times P\times A[/tex]
P= the perimeter of the regular polygon
A is the apothem of the regular polygon
Here, we get
p=2=2cm, a=3cm.
So, plugging in the given values, we get
[tex]A=\frac{1}{2} \times 2cm\times 3cm[/tex]
A=1cm⋅3cm
A=3cm^2
Therefore the area of a regular octagon with an apothem of 2 cm is 3cm ^2.
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find the value of x
Answer:
1 = 120
2 = 120
Step-by-step explanation:
Sam pays #512 .75k less than the amount rob pays for his meal .ridwan pays three times the amount rob pays for his meal. if the total amount paid by them is #47,645.25k. How much does same paid for his meal
The amount paid by sam will be 11526.75k for the meal.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
Sam pays 512 .75k less than the amount rob pays for his meal .ridwan pays three times the amount rob pays for his meal. if the total amount paid by them is 47,645.25k.
We will form an expression from the data given above in the question.
Amount paid by Sam = ( r - 512.75 )
Amount paid by rob = r
( r - 512.75 ) + 3r = 47645.25
( r + 3r ) = 47645.25 + 512.75
4r = 48158
r = 12039.5
The amount paid by sam will be calculated as:-
S = r - 512.75
S = 12039.5 - 512.75
S = 11526.75
Therefore the amount paid by sam will be 11526.75k for the meal.
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To support a shelf, the diameter of a bolt can measure anywhere from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm. Which graph represents the possible measures of the diameter of the bolt?
Please i need it for now PLSSSS
The measure of the other side of a quadrilateral is [tex]3\sqrt{13}[/tex] cm.
In the given quadrilateral one side is unknown we need to find the unknown side.
By dividing the given quadrilateral into a rectangle and a triangle we can find the other side.
What is Pythagoras theorem?The Pythagoras theorem states that if a triangle is right-angled, then the square of the hypotenuse is equal to the sum of the squares of the other two sides. That is, [tex]c^{2}=a^{2}+b^{2}[/tex].
Now, [tex]x^{2} =9^{2}+6^{2}=81+36=17[/tex]
⇒[tex]x=\sqrt{13 \times 9} =3\sqrt{13}[/tex]
Therefore, the measure of the other side of a quadrilateral is [tex]3\sqrt{13}[/tex] cm.
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Work out the angle of elevation from the
rabbit to the top of the tree.
18 m
9√3m
Not drawn accurately
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:Angle \:\: of \:\: elevation= 30° [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Let the angle of elevation be " x "
[tex]\qquad \tt \rightarrow \: \cos(x) = \dfrac{9 \sqrt{3} }{18} [/tex]
[tex]\qquad \tt \rightarrow \: \cos(x) = \dfrac{ \sqrt{3} }{2} [/tex]
[tex]\qquad \tt \rightarrow \: x = \cos {}^{ - 1} \bigg( \cfrac{ \sqrt{3} }{2} \bigg ) [/tex]
[tex]\qquad \tt \rightarrow \: x = 30 \degree \: \: or \: \: \cfrac{ \pi}{6} \: \: rad[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
The angle is 60 degree.
Step-by-step explanation:
First of all, we will find the height if the tree by using Pythagorean theorm.
Let, height of tree be x.
18^2=(9(3^1/2))^2+x^2
324=243+x^2
x^2=324-243
x^2=81
x=9
Now, let the angle be y.
tan y= x/base
tan y=9/9×(3^1/2)
tan y=1.73
y=cot 1.73
y= 60
What is the area of a sector with measure of arc equal to 90° and radius equal to 1 foot?
Answer:
0.7855 square feet
Step-by-step explanation:
90/360×3.142×1 squared
=0.7855
This circle is centered at the origin, and the length of its radius is 8. What is
the equation of the circle?
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x² + y² = 64[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Standard equation of circle is :
[tex]\qquad \tt \rightarrow \: (x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]
[tex] \textsf{h = x - coordinate of centre of circle} [/tex][tex] \textsf{k = y - coordinate of centre of circle} [/tex][tex] \textsf{r = radius= 8} [/tex]Since the circle is centered at origin, h = k = 0
[tex]\qquad \tt \rightarrow \: (x - 0) {}^{2} + (y - 0) {}^{2} = {8}^{2} [/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + {y}^{2} = 64 [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Kit and Kat are building a kite for the big kite festival. Kit has already
cut his sticks for the diagonals. He wants to position P so that he will
have maximum kite area. He asks Kat for advice. What should Kat
tell him?
Kat should tell Kim that It's too late to change the area of this kite because the length of the diagonals of a kite determines its area.
How to calculate the area of a kite?In Mathematics, the area of a kite is equal to one-half the product of the length of its diagonals. Mathematically, the area of a kite can be calculated by using this formula:
A = ½ × d₁ × d₂
Where:
A is the area of a kite.d₁ and d₂ are the length of the diagonals of a kite.Since Kit has already cut his sticks for the diagonals, Kat should tell him that it's too late to change the area of this kite because the length of the diagonals of a kite determines its area.
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