The triangle that is produced is a right-angled triangle, as can be seen in the diagram. ∴ Area of a right-angled triangle [tex]=\frac{1}{2} \times$ base $\times[/tex]height
What is triangle?In geometry, a triangle is a three-sided polygon with three edges and three vertices. The most important feature of triangles is that their internal angles sum to 180 degrees.Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. A triangle with the vertices A, B, and C is referred to as Triangle ABC. Any three points in Euclidean geometry that are not collinear determine a singular triangle and a singular plane simultaneously.The triangle that is produced is a right-angled triangle, as can be seen in the diagram.
∴ Area of a right-angled triangle [tex]=\frac{1}{2} \times$ base $\times[/tex]height
Additionally, the right-angled triangle's area ($) (0,0),
[tex](\mathrm{x}, 0),(0, \mathrm{y})=$ $\frac{1}{2}|x y|$ sq.units[/tex]
⇒ Area of the right-angled triangle formed by the points
(0,0),(4,0),(0,3) = [tex]$\frac{1}{2}|4 \times 3|$[/tex] sq.units
[tex]$=\frac{1}{2} \times(12)[/tex]
= 6 sq.units
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3. Using the item below, calculate how much you would pay for the jeans
with the extra 60% off code and sales tax of 10.25% (Chicago) included.
Show your work.
High Rise Kick Fit Jeans with Washwell
***** 67
$29.99
Extra 60% Off With Code SALE
ise of the
Answer:
We start by calculating the discount amount for the extra 60% off with code SALE:
$29.99 * 60% = $17.99
Then we calculate the new price of the jeans after applying the discount:
$29.99 - $17.99 = $12
Next, we calculate the sales tax of 10.25% for the discounted price:
$12 * 10.25% = $1.23
Finally, we add the sales tax to the discounted price to find the final price:
$12 + $1.23 = $13.23
So the total cost of the jeans, with the extra 60% off code and sales tax of 10.25% included, would be $13.23.
Find f of 8 for the following equation
The d f of 8 for the following equation is- 7698
f₍ₓ₎ = ᵃˣ²+ᵇˣ²+c
f₍₀₎ = a*0²+b*0+c = 2
= 0+0+c=2
c=2
f₍₃₎ = a(3)²+b*3+c = 128
= 9a + 3b +2 = 128
= 9a+3b = 128-2
9a+3b = 126 equation (i)
f₍₅₎ = a (5)² + b*5 + c = 2048 = 25a + 5b + 2 = 2048
25a+ 5b = 2046 equation ( ii)
equation (ii) is multiplied by 3 and equation (i) multiplied by 5 we get,
25a+ 5b = 2046
9a+3b = 126
Subtracting equation (ii) from equation (i)
75a + 15b = 6138
45a + 15b = 630
30a = 5508
a = 5508/30
a = 184
now , putting the value of a in equation (i)
9*184+3b+2 = 128
1656+3b +2 = 128
3b = 128-1658
b = -510
f₍ₓ₎ = 184 x² - 510x + 2
= 184*64 - 510*8 +2
= 11776 - 4080+2
= 7698 ans.
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Calculate the percentage error to the nearest 1 cm, if the footpath around a building is 400 m long
Answer:
4000cm
Step-by-step explanation:
1m is equal to 100cm
so 400m is equal to 400 x 10 which is 4000
so 1cm dividided by 400m ks 400m
You put $500 in an account. The
account earns $55 simple interest in 5
years. What is the balance of the account?
HURRY HELP
The total amount present in the account is $555 in 5 years with a rate of 2.2%.
What is Simple Interest ?Simple interest is a way to figure out how much interest will be paid on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the following year's principal to compute interest, the principal amount under simple interest remains constant.
Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the initial principle amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of several forms of interest that banks charge.
It is given The initial Principal is $500
The interest earned is $55
The total amount present in the account is $(500 + 55) = $555 in 5 years
The rate of interest is r(say)
principal * rate * time = interest
⇒500* r * 5 = 55
⇒ r = 0.022 = 2.2 %
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its for a grade i need 3 questions done
A table of equivalent ratios for the number of toss and amount of dollars is as follows:
Toss Dollars
25 4
50 8
75 12
What is a proportional relationship?In order to have a proportional relationship and equivalent ratios, the variables x for toss and y for dollars must have the same constant of proportionality.
Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 12/75
Constant of proportionality (k) = 0.16.
When hours y = 8, the amount of dollars x is given by:
x = y/k
x = 8/0.16
x = 50.
When the amount of dollars x = 25, the number of toss y is given by:
y = kx
y = 0.16(25)
y = 4.
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Order equivalent equations of 2(−3) = 4 2 x - 3 = 4 x to solve for x .
The missing 3 steps for the given equivalent equation are as follows:
1st step: 2x - 6 = 4x
2nd step: -6 = 2x
3rd step: -3 = x
What are equivalent equations?Algebraic equations with equivalent solutions or roots are called equivalent equations.
An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation.
An equation is equivalent if both sides are multiplied or divided by the same non-zero value.
So, we have the equation:
2(x-3) = 4x
Now, solve further as follows:
2(x-3) = 4x
1st step: 2x - 6 = 4x
2nd step: -6 = 2x
3rd step: -3 = x
Therefore, the missing 3 steps for the given equivalent equation are as follows:
1st step: 2x - 6 = 4x
2nd step: -6 = 2x
3rd step: -3 = x
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What is the decimal equivalent of 714.45/9 ?
Answer:
Step-by-step explanation:
decimal equivalent of 714.45/9
divide it by 9 taking to 79.383333
Six pupils obtained the following marks in mathematics contest 23, 24, 39, 40, 26, 37 find the probability that a pupil selected at random obtained more than 27 marks
Answer:
In order to find the probability that a pupil selected at random obtained more than 27 marks, we need to know the total number of pupils and the number of pupils who scored more than 27 marks.
Let's call the total number of pupils "n" and the number of pupils who scored more than 27 marks "x".
From the given data, we know that n = 6 and the pupils who scored more than 27 marks are 39, 40, 37.
x = 3
Now we can use the formula for probability:
Probability = (x/n)
Probability = (3/6)
Probability = 0.5
So the probability that a pupil selected at random obtained more than 27 marks is 0.5 or 50%.
Step-by-step explanation:
Michelle is also a contestant. On day 21, she is informed by the wellness team that she has lost 17% of her body weight. Michelle weighed 145 lb. at the start of the competition. How much does she weigh now?
Answer:
Michelle weighs 120.15 lb. now.
You can calculate it by
145lb x (1-.17) = 145lb x .83 = 120.15lb
abcd is a parallelogram with sides ad=6 cm and ab=12 cm. point e dc and the extensions of be and ad intersect at point f. if the mid segment of the trapezoid abed is 10 cm long, find df and the ratio between the areas of def and abf
E and F are the midpoints of AB and CD, respectively, making ABCD a parallelogram. Any line that crosses AD, EF, and BC at G, P, and H is designated as GH. So, GP = PH.
What is meant by parallelogram?A quadrilateral with opposite sides that are parallel and equal is known as a parallelogram. The interior opposite angles of it are equal. Additionally, the angles on the same side of the transversal are complementary to one another or add up to 180 degrees. A quadrilateral is referred to as a parallelogram in geometry. The opposite sides of a parallelogram are parallel and of equal length. Rhombus, rectangle, and square are a few instances of parallelograms.Parallelograms come in 4 different varieties, including 3 unique varieties. The four varieties are rhombuses, parallelograms, squares, and rectangles.E and F are midpoints, resulting in AB and CD, respectively.
[tex]$\therefore \mathrm{AE}=\mathrm{BE}=\frac{1}{2} \mathrm{AB} \text { and } \mathrm{CF}=\mathrm{DF}=\frac{1}{2} \mathrm{CD}[/tex]
But, [tex]$\mathrm{AB}=\mathrm{CD}$[/tex]
[tex]$\therefore \frac{1}{2} \mathrm{AB}=\frac{1}{2} \mathrm{CD} \Rightarrow \mathrm{BE}=\mathrm{CF}[/tex]
Also, [tex]BE \| CF $\quad[\because \mathrm{AB} \| \mathrm{CD}]$[/tex]
therefore BEFC is a parallelogram.
[tex]$\Rightarrow \mathrm{BC} \| \mathrm{EF}$[/tex] and [tex]$\mathrm{BE}=\mathrm{PH}$[/tex]
Now, BC \| EF
[tex]$\Rightarrow \mathrm{AD} \| \mathrm{EF} \quad\left[\because \mathrm{BC} \| \mathrm{AD}\right.$[/tex] as ABCD is a [tex]$\left.\|^{\mathrm{gm}}\right]$[/tex]
[tex]$\Rightarrow \mathrm{AEF} \mathrm{D}$[/tex]is a parallelogram
[tex]$$\Rightarrow \mathrm{AE}=\mathrm{GP}$$[/tex]
But, [tex]\mathrm{E}$ is the mid-point of $\mathrm{AB}$[/tex]
[tex]\therefore \mathrm{AE}=\mathrm{BE}[/tex]
[tex]\Rightarrow \mathrm{GP}=\mathrm{PH} \quad$ [Using (i) and (ii)[/tex]
The complete question is:
ABCD is a parallelogram, E and F are the mid-points of AB and CD respectively. GH is any line intersecting AD, EF and BC at G,P and H respectively. Prove that GP = PH.
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Krutika was thinking of a number. Krutika subtracts 9.9 from the number and gets an answer of 31.6. Form an equation with x from the information.
Answer:
x - 9.9 = 31.6
Suppose that 18 inches of wire cost 72 cents At the same rate, how much (in cents) will 13 inches of wire cost?
So right now in the the given question we use the proportional method
In this case the proportion used is inverse
What is Inverse Proportion ?In direct proportion, if one quantity is increased or decreased then the other quantity increases or decreases, respectively. But in indirect or inverse proportion, if one quantity increases then other quantity decreases and vice-versa.
Eg: As the variable y decreases the variable x will also decrease
When we apply the given values into a fraction we get
[tex]\frac{18}{72} = \frac{13}{x}[/tex]
Cross Multiplying we get,
[tex]18x = 72X13[/tex]
[tex]18x = 936[/tex]
[tex]x = \frac{936}{18}[/tex]
[tex]x = 52[/tex]
Hence, 13 inches of wire costs 52 cents
Find the equation of the line, in slope-intercept form, which has a slope of 2/3 and contains the point (3, -4).
Answer:
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
To find the equation of the line with a slope of 2/3 and passing through the point (3, -4), we can plug in the point and the slope into the equation:
y = 2/3 * x + b
-4 = 2/3 * 3 + b
-4 = 2 + b
b = -6
So the equation of the line is:
y = 2/3 x - 6
Help with stem & leaf
The 15th percentile can be found to be 66.5
How to find the 15 th percentile ?The value that a specific percentage falls under is known as the percentile. The most typical definition of a percentile is a number below which a predetermined proportion of scores fall.
To find the 15 th percentile, the formula is:
= ( Percentile / 100 ) x Number of values in set
The 15th percentile is therefore:
= 15 / 100 x 117
= 17.55
= 18 th position
The value in the 18th position which is the 15th percentile is 66.5
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Find the slope of the line described in the table.
m = 0
m = 1
m = 2
m = 3
m = 4
The slope of the line described in the table is m=3.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The points from the table are (2, 6) and (3, 9)
Slope=9-6/3-2
=3/1
=3
Hence, the slope of the line described in the table is m=3.
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(4x-10) x (3x²)
Find the area of the rectangle
If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be [tex]$x=-\frac{2}{3}, x=-\frac{5}{2}$$[/tex].
How to find the area of rectangle?The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.
A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.
Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.
Area of rectangle = length × breadth
= (3x +2) × (4x +10)
simplifying the above equation, we get
= (3x) × (4x +10) + 2(4x +10)
= 12x² + 30x +8x +20
12x² + 38x + 20 = 0
simplifying the above equation, we get
By using quadratic equation, then
[tex]$x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$[/tex]
simplifying the above equation, we get
[tex]$$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$[/tex]
Separate the solutions, we get
[tex]$$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$[/tex]
The solutions to the quadratic equation are:
[tex]$x=-\frac{2}{3}, x=-\frac{5}{2}$$[/tex]
The complete question is:
Find the area of rectangle with length (3x+2) units and width (4x+10)units.
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Assuming large between subject variability, which of the following tests is usually the most sensitive (N held constant)? 1. they are all equal in sensitivity 2. t test for independent groups 3. t test for correlated groups 4. sign test
The t-test for independent groups is usually the most sensitive test when there is large between-subject variability and the sample size (N) is held constant.
The t-test for independent groups allows for the comparison of two independent groups, and can detect differences in the means between the two groups that may not be detected by other tests. The t-test for correlated groups is less sensitive than the t-test for independent groups, as it assumes that the two groups are related or correlated. The sign test is a non-parametric test and is less sensitive than the t-test for independent groups as it does not take into account the variability between the two groups.
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need help on this question asap!
Answer:
≈ +1
Step-by-step explanation:
Firstly, the r value, or the correlation coefficient, would be positive because the correlation is positive. The set of points are moving from bottom to top.
It would be close if not exactly to 1 because the closer the set of points are all clustered closely around or on one singe line, the closer it is to 1. In this case, all points seem to be on one single line, suggesting that it has a perfect correlation of 1.
Tiana needs to wrap 2 gifts with no overlap. The boxes are shaped as right rectangular prisms. The length of each box is 22.2 in, the width is 4.8 in, and the height is 14 in. How much wrapping paper does Tiana need to buy? Round to the nearest hundredth. Leave out units
Answer:
971.92 square inches of wrapping paper.
Step-by-step explanation:
Please find the attachment for detail
Which equation represents the graph of function j?
The required equation that represents the graph is j(x) = (-x + 4)¹/². Option D is correct.
What is a parabola?A parabola is a cross-section cut out of the cone and represented by an equation x = y².
here,
The given graph is of the left parabola,
-x = y²
When we translate the above expression 4 units right we get the graph,
So
-x + 4 = y²
put y = j(x)
-x + 4 = j(x)²
j(x) = [-x + 4]¹/²
Thus, the required equation that represents the graph is j(x) = (-x + 4)¹/². Option D is correct.
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Could someone please help me?
Answer:
B
Step-by-step explanation:
[tex](x-1)(x+1) = x^2 -1\\(x+5)(x-5) = x^2 -25[/tex]
Pizza sales increase by 8% this year then decrease by 4% the following year then your sales are up by what %?
The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Pizza sales increase by 8% this year then decrease by 4%. Then we have
P = [1 - (1 + 0.08) x (1 - 0.04)] x 100
P = [1 - 1.08 x 0.96] x 100
P = [1 - 1.0368] x 100
P = [1 - (1 + 0.0368)] x 100
P = 0.0368 x 100
P = 3.68%
The percentage that your sales are up will be 3.68%.
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Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.9
years with a standard deviation of 0.8
years.
Step 2 of 2 : If a sampling distribution is created using samples of the ages at which 68
children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.
The standard deviation of the sampling distribution of sample means will be 0.097.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
Assume that an investigation of primary school understudies reports that the mean age at which youngsters start perusing is 5.9 years with a standard deviation of 0.8 years.
The standard deviation of the sampling distribution of sample means is given as,
⇒ 0.8 / √68
⇒ 0.8 / 8.246
⇒ 0.097
The standard deviation of the sampling distribution of sample means will be 0.097.
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Which statement is true about this function for all values of
x
<
4
?
A nonlinear graph intercepts x-axis at points (2.8, 0) and (5.5, 0) with vertex point at (4, minus 2)
The function is decreasing, is true about this function for all values of x < 4.
What does the term "graph" mean?To develop a graph is to make a diagram that depicts the relationship between two or more objects. Make a sequence of bars on graph paper as an example of a graph.
A nonlinear graph can have more than one x-intercept, but it cannot have exactly two x-intercepts for all values of x. The vertex of a nonlinear graph is a special point that occurs when the graph changes from increasing to decreasing or vice versa, but it is not necessarily an x-intercept.
Therefore, the statement that the function intercepts the x-axis at points (2.8, 0) and (5.5, 0) with vertex point at (4, -2) is not true and decreasing for all values of x.
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Complete question:
Which statement is true about this function for all values of x < 4
The function is positive.
The function is decreasing.
The function is increasing.
The function is negative.
what is the length x of a side of the small inner square? express your answer in terms of some or all of the variables a , b , and c .
The length x of a side of the small inner square in terms of some of the variables a , b is expressed as x = (b - a).
We have, length x which is side of inner square in above figure. We have to determine the value of x in terms of " a and b." See the figure carefully and draw the important results. As we see,
there is a big square with side length c.One inner square with side length x There is two pairs of similar right angled triangles. The side length of yellow triangle is equals to the a.The side length of blue triangle is equals to the b.Also, see in above figure, the side length of blue triangle is equals to the sum of side length of yellow triangle and side length inner square. In expression form , b = x + a . But we want to determine the value of x, so x = b - a.
Hence, required length is ( b - a).
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Complete question:
what is the length x of a side of the small inner square? express your answer in terms of some or all of the variables a , b , and c.
The above figure complete the question.
Which equation could generate the curve in the graph below?
Answer:
below
Step-by-step explanation:
When y = 0 the negative x value of the vertex needs to be a negative number ....the second equation will do this...the first will not
f(x) = 2x + 7 and g(x) = 3x − 2, find f(g((6))
Answer:
To find f(g(6)), we need to first find g(6) by plugging 6 into the function g(x) and solving for the output:
g(6) = 3x - 2 = 3 * 6 - 2 = 16
Next, we plug the result of g(6), which is 16, into the function f(x) and solve for the final output:
f(g(6)) = f(16) = 2x + 7 = 2 * 16 + 7 = 31
So f(g(6)) = 31.
help will mark brainlist
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
we have here 3 triangle sides.
the painter can only paint the sides, not the base area.
the painting area is therefore the sum of the 3 sides :
3× 50×40/2 = 3× 50×20 = 3000 ft²
75% of the area = 3000 × 0.75 = 2250 ft²
100 ft² in 18 minutes
it takes
2250/100
times of the time it takes to paint 100 ft² (18 minutes).
so,
18 × 2250/100 = 405 minutes
it takes the painter 405 minutes to paint 75% of the pyramid.
The usher at a wedding asked each of the 80 guests whether they werea friend of the bride or of the groom. The results are: 59 for Bride, 50 for Groom, 30 for both. Given that the randomly chosen guest is the friend of groom, what is the probability that the guest is the friend of bride, P (bride | groom)
The probability that can be determined by the randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.
Given information is that, at a wedding, each guest asked the 80 guests if they were a friend of the bride or of the groom.
Probability is measured by the ratio of the number of favorable outcomes to the total number of outcomes of an event.
The total Number of Guests which forms the Sample Space, n(S)=80
Let the event for a friend of the bride=A
Let the event be for a friend of the groom=B
n(A) =59
n(B)=50
Friends of both bride and groom,
So,
n(A∪B)=n(A)+n(B)-n(A∩B)
n(A∪B)=59+50-30
n(A∪B)=79
The number of people or Guests who are the friends of the bride OR of the groom = 79
Thus,
P(A∪B)=n(A∩B)/n(S)
= 79/80
P(A∪B)= 0.9875
Therefore, the probability that a randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.
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Please help me with this question.
The equation of the parabola with given vertex and focus is (y-11)² = 36(x-7).
What is an equation of a parabola?A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.
The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.
Given that, Vertex (7, 11), focus (16, 11).
Let us find an equation of the parabola for vertex (h, k)=(7, 11) and focus (16, 11).
It can be observed that both focus and vertex lie on y = 11, thus the axis of symmetry is a horizontal line.
a = 16-7 = 9 as y coordinates are the same.
Since the focus lies to the left of vertex, a = 9
Use the equation (y-11)² = 4×9(x-7)
(y-11)² = 36(x-7)
Therefore, the equation of the parabola with given vertex and focus is (y-11)² = 36(x-7).
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The standard equation of the parabolas with vertex (7, 11) and focus (16, 11) are:
(y - 11)² = 36(x - 7)
What is a parabola?A parabola is an equation of a curve, such that any point on the curve is equidistant from a fixed point called the focus and a fixed line called the directrix of the parabola.
We have,
(y - k)² = 4p (x - h) open right
(y - k)² = -4p (x - h) open left
Where focus = (h - p, k) or (h + p, k) and vertex = (h, k)
Now,
Equation of parabola (y - k)² = -4p (x - h) that open left.
(h, k) = (7, 11)
h = 7 and k = 11
(h - p, k) = ( 16, 11)
h - p = 16
7 - p = 16
7 - 16 = p
p = -9
So,
(y - 11)² = 36(x - 7)
Equation of parabola (y - k)² = 4p (x - h) that open right.
(h, k) = (7, 11)
h = 7 and k = 11
(h + p, k) = (16, 11)
h + p = 16
7 + p = 16
p = 16 - 7
p = 9
So,
(y - 11)² = 36 (x - 7)
Thus,
The standard equation of the parabolas is:
(y - 11)² = 36(x - 7)
(y - 11)² = 36 (x - 7)
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