[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-\frac{3}{4}})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{\frac{5}{4}}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{5}{4}}-\stackrel{y1}{\left( -\frac{3}{4} \right)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{4}}} \implies \cfrac{~~ \frac{5 }{4 }+\frac{3}{4} ~~}{-2} \\\\\\ \cfrac{~~ \frac{ 5+3}{ 4} ~~}{-2}\implies \cfrac{~~ \frac{8 }{4 } ~~}{-2}\implies \cfrac{2}{-2}\implies -1\qquad \impliedby m[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\left(-\frac{3}{4} \right)}=\stackrel{m}{-1}(x-\stackrel{x_1}{4})\implies {\large \begin{array}{llll} y+\cfrac{3}{4}=-(x-4) \end{array}}[/tex]
Christa purchases a rare vase for £940. She wants to sell it for a higher price so that she makes a profit of 15%. How much should she try to sell the vase for?
The amount she should try to sell the rare vase to make profit of 15% would be = £1,081.
What is profit amount?Profit amount is defined as the amount of money received by an individual that is an extra amount gained when compared with the cost price of the item.
The cost price of the rare vase = £940
The percentage profit seeked for = 15% of cost price.
That is;
15/100 × 940
= 14,100/100
= £141
The profit Christa seeks= £141 additionally.
Therefore, she should attempt to sell it at a price of 940 + 141 = £1,081.
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How would I go about doing this?
⇒The shape in the picture is a pentagon because it has five sides.
⇒ The sum of the interior angles of a pentagon is 540°
meaning:
[tex]4x+(3x+3)+(5x-2)+103+100=540\\[/tex]
⇒As a results you can see above we have an equation that can enable us to solve for x.
⇒Solving for x we have
[tex]4x+3x+5x+3-2+103+100=540\\[/tex]
⇒Now let us simplify like terms since we have grouped them already.
[tex]12x+204=540\\12x=540-204\\12x=336\\\frac{12x}{12} =\frac{336}{12} \\x=28[/tex]
∴ x=28°
Note I have written the equation above, as the first step.
f(x) = 2x x = -3,5
The Value of f(x) for x = -3 is
Answer:
y = 2x we need to solve when x= -3. Using elimination, we can solve this system of equations like this:
y = 2x
x = -3
*2 *2
simplify
y = 2x
-6 = 2x
subtract
y+6=0
-6 -6
y=-6
So, when x=-3, y=-6
6x + 3y < 9
Solve for Y please
Answer: y < 3 - 2x
Step-by-step explanation:
6x + 3y < 9
3y < 9 - 6x (after subtracting both sides by 6x)
y < 3 - 2x (after dividing both sides by 3)
Which statement best represent the equation of the lone shown on the grid and it’s relationship?
The equation of the line is y = 2 and is parallel to the x-axis.
The equation of the line is [tex]y = 2[/tex] and is parallel to the x-axis.
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
As per the given graph, the equation of line which is parallel to the x-axis is [tex]y=2[/tex].
Draw the graph
Hence, the equation of line which is parallel to the x-axis is [tex]y=2[/tex].
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a recipe for cookies says 2/3 of a cup of sugar will be enough to feed 3/4 of my class. how much sugar will i need to make enough cookies to feed my whole class?
Sugar will i need to make enough cookies to feed my whole class is 11 cups.
Given:
A recipe for cookies says 2/3 of a cup of sugar will be enough to feed 3/4 of my class.
2/3 cup of sugar = 3/4 of my class
Multiply by 12 on both sides
2*12/3 = 3*12/4
24/3 = 36/4
8 cups of sugar = 9 of my class.
if 3/4 = 9 whole class = 12.a
Add plus 3 on both sides
8 + 3 = 9 + 3
11 cups of sugar = 12 of my class.
Therefore Sugar will i need to make enough cookies to feed my whole class is 11 cups.
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Solve b² +5b + 4 = 0 using completing the squares method
Answer:
b² +5b + 4 = 0
b² + 5b -41= 5.702
3
Step-by-step explanation:
1.1 Factoring b2+5b-4
The first term is, b2 its coefficient is 1 .
The middle term is, +5b its coefficient is 5 .
The last term, "the constant", is -4
Step-1 : Multiply the coefficient of the first term by the constant 1 • -4 = -4
Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is 5 .
-4 + 1 = -3 -2 + 2 = 0 -1 + 4 = 3
A regular pentagon has side lengths of 14. 1 centimeters and an apothem with length 12 centimeters. What is the approximate area of the regular pentagon?.
The approximate area of the regular pentagon is 342cm²
Using the Pythagorean theorem, we can calculate the apothem of the pentagon.
We have then:
a = √(12² - (14.1/2)²)
a = 9.7
Then, the area of the pentagon is given by:
Area = 5 (1/2) x l x a
Where,
L: side of the pentagon
a: apotema
Substituting values:
area = 5(1/2) x 14.1 x 9.7
area = 341.925 cm²
Rounding the nearest whole we have: 342 cm²
Hence, the approximate area of the regular pentagon is 342cm²
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Ruben bought 6 new books for his collection. This increased his collection by 12% How many books did he have before this purchase? Please explain
Answer:
Ruben had 50 booksStep-by-step explanation:
Let the initial number of books be x.
Set equation:
x + 6 = x + 12%x + 6 = x + 0.12x0.12x = 6x = 6/0.12x = 50Answer:
50 books
Step-by-step explanation:
Forming the equation,
→ x + ((x/100) × 12) = x + 6
Now the value of x will be,
→ x + ((x/100) × 12) = x + 6
→ x - x + (12x/100) = 6
→ 0.12x = 6
→ x = 6/0.12
→ [ x = 50 books ]
Hence, answer is 50 books.
Solve the compound inequality. Graph the solution set and write it in interval notation
x< 1 and and x > -5
help asap! only the solution set
The interval notation of the compound inequality (x < 1) and [x > (-5)] is
[(-5) < x < 1], and the graph of it's solution set is a straight line lying on the x-axis from 1 to (-5).
As per the question statement, we are provided with a compound inequality (x < 1) and [x > (-5)],
And we are required to determine the interval notation of the above mentioned compound inequality, and graph it's solution set.
Now, the interval notation of a compound inequality is simply the combination of the separate inequalities, that is, the interval notation of the compound inequality (x < 1) and [x > (-5)] is [(-5) < x < 1].
And since "x" is less than 1, but greater than (-5), the values in the solution set of [(-5) < x < 1] are (0, -1, -2, -3, -4), and the graph of these values is a straight line lying on the x-axis from 1 to (-5).
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A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Range ($)
0 - 10,000
10,001 - 50,000
50,001 - 100,000
Progressive
Tax Rate
3%
5%
5.5%
Calculate the state income tax owed on a $60,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
Enter
The state income tax owed on a $60,000 per year salary.
is tax = $2850.
What is Percentage ??A percentage is a figure or a ratio that is expressed as a fraction of 100. The percentage sign, "%," is used to denote it. The percentage is denoted by the abbreviations "pct" or "pc." In other words, the percentage is measured in terms of 100 and is defined as the proportion of one quantity that is made up of another.
The % has no boundaries. It implies that they are dimensionless numbers. When we state a number is 60% of something, we are implying that it is 60% of everything. Even fractional versions, like 0.56% or 0.87%, can be used to express it. Students' exam scores in any subject are calculated as a percentage. For instance, Pooja received a 78% on his exam.
Tax slab is as follows:-
0 - 10,000 = 3%
10,001 - 50,000 = 5%
50,001 - 100,000 = 5.5%
So total salary = $60000
Till $10000 tax deduction will be 3%
So, $10000 * 0.03 = $300
Then from $10,001 - $50,000 tax deduction will be 5%
Hence, the tax deduction will be $40000 * 0.05 = $2000
And from $50,001 - $100,000 tax deduction will be 5.5%
Only $10000 will be available for tax deduction
so, $10000 * 0.055 = 550
Hence total tax deduction will be $2850.
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consider an interval from 0 to 1 with ten uniformly distributed points in it. what is the distribution of the difference between the 6th and the 5th smallest point?
Answer: It has to be between 0.1 to 0.3
Step-by-step explanation:
y=sin^4(3x).find dy/dx
Keeping it short.
Differentiate each term with respect to [tex]x[/tex], then solve for [tex]y'.[/tex]
[tex]\frac{dy}{dx} =12\sin^3(3x)\text{cos}(3x)[/tex]
Thanks.
What does Pascal's triangle represent?.
In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of every binomial formula, such as (x + y)ⁿ.
Explain the term Pascal's triangle?Although it is much older, it bears the name of the French scholar Blaise Pascal from the 17th century. In the eleventh century, the Chinese mathematician Jia Xian created a triangular form for the coefficients.
For instance, the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21), which was first discovered by the mediaeval Italian mathematician Leonardo Pisano ("Fibonacci") in his Liber abaci (1202; "Book of the Abacus"), is produced by drawing parallel "shallow diagonals" and adding the numbers on each line together. Another intriguing characteristic of the triangle is that it will form a fractal understood as the Sierpiski gasket, named for Polish mathematician Wacaw Sierpiski, who lived in the 20th century, if all the positions comprising odd numbers are shaded in black and every positions enclosing even numbers are shaded in white.To know more about the Pascal's triangle, here
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Let the graph of g be a vertical stretch by a factor of 2 and a
reflection in the x-axis, followed by a translation 3 units down of
the graph of f(x) = x². Write a rule for function g and identify the
vertex.
Vertex is slang for a corner or a place where two lines converge.The four corners of a square, for instance, are each referred to as a vertex.
Write a rule for function g and identify the vertex ?
The graph of g is a vertical stretch by a factor of 2 followed by a translation of 3 units down of the graph of f(x) = (x-1)²then the function g(x) = 2(x+4)²
f(x) =x²-2x+1 The graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of .f(x) =x²-2x+1
Rewrite the given function f(x).
f(x) = (x-1)²
Now, the graph is stretched vertically by a factor of 2.
= 2(-x-1)²
reflect the graph about the y-axis.
2(x+1)²
move to the left by 3 units.
= 2(x+3+1)²
=2(x+4)²
The function g(x) =2(x+4)²
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The length of a rectangle in longer than it’s width. If the perimeter of the rectangle is 70 in, find the length and width.
When the perimeter of the rectangle is 70 in, the length and width are 19 and 16 inches.
How to calculate the length?It should be noted that the perimeter of a rectangle will be calculated as:
= 2(Length + Width)
In this case, the length of a rectangle is 3in longer than it’s width and the perimeter of the rectangle is 70 in.
Therefore, width = w
length = w + 3
The perimeter will be:
2(w + w + 3) = 70
2(2w + 3) = 70
4w + 6 = 70
Collect like terms
4w = 70 - 6
4w = 64
Divide
w = 64 / 4
w = 16
Width = 16 inches
Length = w + 3 = 16 + 3 = 19 inches.
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Complete question
The length of a rectangle is 3in longer than it’s width. If the perimeter of the rectangle is 70 in, find the length and width.
You enter a bid. Your cost on the product you make is $112 per unit. If you bid at $138 per unit, what percent is the price you bid over your cost? (round to the nearest percent).
The price bid will be increased by 23% over the cost, according to the question.
What do you mean by percentage?
A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.
According to data in the given question,
We have given data:
Cost on the product you make is $112 per unit.
Bid amount $138 per unit,
Cost over the bid= $138-$112 = $26
Now, we need to determine the Percentage increase,
Percentage increase[tex]= \frac{26}{112}*100 \\[/tex]
= 23%
Therefore, the price bid will be increased by 23% over the cost.
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If g(x) = 1-3/4x, find each value
G(10)
-5•g(4)-1
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The complete table of values is:
x -2 -1 0 1 2
y 1/9 1/3 1 3 9
How to complete the table of values?From the question, we have the following equation:
f(x) = 3ˣ
From the table of values, we have the following x values
x = -2, -1, 0, 1 and 2
Substitute x = -2, -1, 0, 1 and 2 in the equation f(x) = 3ˣ
When x = -2
f(-2) = 3⁻² = 1/9
When x = -1
f(-1) = 3⁻¹ = 1/3
When x = 0
f(-1) = 3⁰ = 1
When x = 1
f(1) = 3¹ = 3
When x = 2
f(2) = 3² = 9
Hence, the complete table of values is:
x -2 -1 0 1 2
y 1/9 1/3 1 3 9
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Suppose you are interested in learning about how much time seventh grade students at your school spend outdoors on a typical school day.
Select all the samples that are a part of the population you are interested in
Answer: how do you do the question what the
Step-by-step explanation:
If $10,000 is borrowed with an interest of 5. 0% compounded annually, what is the total amount of money needed to pay it back in 5 years? round your answer to the nearest cent and do not include the dollar sign. Do not round at any other point in the solving process; only round your answer.
The amount of money that is needed to pay after 5 years is 12762.9 .
In the question ,
it is given that ,
the amount borrowed(P) = $10000
the rate at which the amount is borrowed (r) = 5% = 0.05
the time for which the amount is borrowed (t) = 5 years
the number of times the interest is charge (n) = 1 .
The final amount for the compound interest is calculated using the formula .
Amount = [tex]P\times(1+\frac{r}{n})^{nt}[/tex]
Substituting the value of P , r , n and t , in the formula ,
we get
Amount = 10000 (1 + 0.05)⁵
= 10000*(1.05)⁵
= (10000)*(1.2762815625)
= 12,762.815625
≈ 12762.9
Therefore , The amount of money that is needed to pay after 5 years is 12762.9 .
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The density of copper is 9.86 g/cm3.
Work out the mass of the solid copper cuboid in kg.
10 cm
3 cm
5 cm
The mass of the solid copper is 1479 g.
According to the question,
We have the following information:
The density of copper is 9.86 g/[tex]cm^{3}[/tex].
Measurements of the solid copper cuboid = 10 cm, 3 cm and 5 cm
We know that the following formula is used to find the volume of cuboid:
Volume = length*breadth*height
Volume = 10*3*5
Volume = 150 [tex]cm^{3}[/tex]
Now, we know that the following formula is used to find the density of an object:
Density = mass/volume
9.86 = mass/150
Using the cross multiplication method:
Mass = 150*9.86
Mass = 1479 g
Hence, the mass of the solid copper is 1479 g.
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Given the properties, write a quadratic function for:
f(3+sqrt(2))=f(3-sqrt(2))=0
if f(1)=-8
Quadratic function for the given properties is [tex]y=-4x^{2} +24x-28[/tex].
The roots are [tex]3+\sqrt{2}[/tex] and [tex]3-\sqrt{2}[/tex]; that means the axis of symmetry is x=3; which means the vertex has x coordinate 3. Then the vertex form of the equation is
[tex]y = a(x-3)^{2}+k[/tex]
Then since y is 0 when x is [tex]3+\sqrt{2}[/tex],
[tex]0=a(\sqrt{2} )^{2} +k[/tex]
[tex]0=2a+k[/tex] (1)
And when x = 1, y = -8,
[tex]-8 = a(-2)^{2}+k[/tex]
[tex]-8=4a+k[/tex] (2)
Then from equations (1) and (2)
[tex]-8=2a[/tex]
[tex]a = -4[/tex]
And then from either equation (1) or (2), k = 8.
So the equation is
[tex]y = -4(x-3)^{2}+8[/tex]
[tex]y=-4(x^{2} -6x+9)+8[/tex]
[tex]y=-4x^{2} +24x-28[/tex]
Solving this equation using the quadratic formula verifies that the roots are [tex]3+\sqrt{2}[/tex] and [tex]3-\sqrt{2}[/tex]; evaluating the expression for x=1 verifies that the y value is -8.
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The sequence of 11,21,31
Answer:
1,11,21,31,41,51,61,71,81,91,101..
Step-by-step explanation:
The coordinates of the vertices of quadrilateral ABCD are A (8, -3), B(-2, 1), C (-4,-4), and D(6, -8).
Jorge states that quadrilateral ABCD is a parallelogram. Prove or Disprove Jorge's statement.
Yes, quadrilateral ABCD is a parallelogram.
What are the properties of parallelogram?
A parallelogram is a particular sort of polygon. It is a quadrilateral in which the opposite side pairs are parallel to one another.
Properties:
1. Opposite sides are congruent.
2. Opposite angels are congruent.
3. Consecutive angles are supplementary.
4. If one angle is right, then all angles are right.
5. The diagonals of a parallelogram bisect each other.
6. Each diagonal of a parallelogram separates it into two congruent
It is given that the coordinates of the vertices of quadrilateral ABCD are A (8, -3), B(-2, 1), C (-4,-4), and D(6, -8).
According to distance formula,
If A(a,b) and B(x,y) are two coordinates then
AB = [tex]\sqrt{(x-a)^{2}+(y-b)^{2}}[/tex]
Now, using this distance formula in quadrilateral ABCD
AB = [tex]\sqrt{(-2-8)^{2}+(1+3)^{2}}= \sqrt{(-10)^{2}+(4)^{2}}=\sqrt{100+16}=\sqrt{116}[/tex]
CD = [tex]\sqrt{(6+4)^{2}+(-8+4)^{2}}=\sqrt{10^2+(-4)^2}=\sqrt{100+16}=\sqrt{116}[/tex]
Now, If we have two coordinates A(a,b) and B(x,y) then
Slope of AB = [tex]\frac{y-b}{x-a}[/tex]
Using this formula , finding slope of AB and CD of quadrilateral ABCD we get ,
Slope of AB = [tex]\frac{1+3}{-2-8}=\frac{4}{-10}=\frac{2}{-5}[/tex]
Slope of CD = [tex]\frac{-8+4}{6+4}=\frac{-4}{10}=\frac{-2}{5}[/tex]
As slope of both AB and CD is equal therefore, we can say that AB and CD are parallel.
As AB = CD and AB is parallel to Cd Therefore, ABCD is a parallelogram as opposite sides of parallelogram are equal and parallel.
Hence, quadrilateral ABCD is a parallelogram.
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2) In a packet of 50 skittles, 12 are red, 8
are yellow, 10 are green, 14% are
orange and the rest are blue.
What percentage of the skittles are
blue?
Answer: 26%
Step-by-step explanation: 50 x 0.14 = 7. 12 + 8 + 10 + 7 = 37, 37÷50=0.26 so 26%
The percentage of blue skittles is 26%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Total number of skittles = 50
Red skittles = 12
Yellow skittles = 8
Green skittles = 10
Orange skittles = 14%
This means,
= 14/100 x 50
= 7
Blue skittles.
= 50 - (12 + 8 + 10 + 7)
= 50 - 37
= 13
The percentage of blue skittles.
= 13/50 x 100
= 1300/50
= 26%
Thus,
26% of blue skittles.
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In the next door school café, Petri café, they sell apples and pears. One
day they discover that as many apples as pears are rotten, ⅔ of all apples
are rotten and that ¾ of all pears are rotten.
What proportion of the total number of apples and pears were rotten?
Simplify your answer
A total of 81 apples and 72 spears are there in total.
What are ratios and proportion?Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A statement expressing the equality of two ratios A:B and C:D is called a proportion. We can express proportion as -
A : B ∷ C : D
AND
A x D = B x C
Product of extremes equal to product of means.
Given is in a Petri café they discovered that as many apples as pears are rotten, ⅔ of all apples are rotten and that ¾ of all pears are rotten.
Assume that there are [x] apples and [y] pears in total.
Then, rotten apples = 2x/3
rotten paears = 3y/4
Since, they are equal, we get -
2x/3 = 3y/4
2x (4) = 3y (3)
8x = 9y
The whole number coordinates satisfying the equation are - (81, 72). Refer to the graph attached.
Therefore, a total of 81 apples and 72 spears are there in total.
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Provide an explanation please
Answer: 84m
Step-by-step explanation:
If one of the perimeters are 2m longer than the other that means on side can be expressed as x and the other expressed as x+2
So the equation for the area is [tex]x^{2} \\[/tex]+2x
Becasue the shaded area has an gap of in it we need to find the area of the gap to find the total area of the square
0.5x3x4=6
114+6
So the total area is 120
So we can use the area equation from before to figure out x
120=[tex]x^{2} \\[/tex]+2x
0=[tex]x^{2} \\[/tex]+2x-120
0=(x-10)(x+12)
Since its a measurement x must equal 10
Now we know that one side is 20m and the other is 22m
So the perimetre must be 84
The equation of line p is y=3/7x+9. Line q is parallel to line p. What is the slope of line q
The slope of line q is 3/7
The equation of line p is y=3/7x+9
The standard form of equation of a line is
y = mx + c
where m represents the slope of the line
Upon comparing the standard form with the given equation
y = 3/7 x + 9
we get that the slope of this line is 3/7
and the y intercept c is 9
When two lines are parallel to each other, then the slope of both the lines are same.
the slope of line q is same as the slope of line p as line q is parallel to line p
the slope of line q is 3/7
Therefore, the slope of line q is 3/7
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The graph of the exponential function y = (3/4)^x is given by the following option:
Option A.
How to obtain the graph of the exponential function?The general format of an exponential function is defined as follows:
[tex]y = ab^x[/tex]
The meaning of the parameters a and b are given as follows:
a is the initial value of the function, which is the value of the function when it crosses the y-axis.b is the rate of change of the function, determining if the function increases or decreases, and how fast it decreases of increases.In this problem, the function is given by:
y = (3/4)^x.
Hence the values of the parameters are:
a = 1, b = 3/4.
The parameter a = 1 means that the function crosses the y-axis at y = 1, hence options B and C are removed.
From the table given in the problem, at x = -2 the function is very close to 2, while it decreases to a value close to 0.5 at x = 2, hence option A is the correct option for the graph of the exponential function.
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