1) In geometry, the coordinate is used as to write the equations of lines as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
2) By showing that the opposite sides of the quadrilateral are congruent.
3) To prove the figure is a rhombus you must verify that all sides are the same length.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
1) Let two points on the line are (x₁ , y₁) and (x₂, y₂).
Then, The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
2) We know that;
Opposite angles in a quadrilateral are congruent, and Parallel lines have congruent corresponding angles.
Hence, In coordinate geometry, By showing that the opposite sides of the quadrilateral are congruent.
3) In coordinate geometry, To prove that it is a rhombus, remember that the definition of a rhombus is a quadrilateral with four congruent sides. Therefore, to prove it is a rhombus you must verify that all sides are the same length.
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Find p and q , if X1 = 23, n1 = 43, X2 = 29, and n2 = 52.
The values:
[tex]\bar p[/tex] = 0.547.
And [tex]\bar q[/tex] = 0.453.
What is the mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Given:
The values,
X₁ = 23,
X₂ = 29,
n₁ = 43,
And n₂ = 52.
Now, using the formula for mean,
[tex]\bar p[/tex] = (X₁ + X₂) / (n₁ + n₂)
=(23 + 29) / (52 + 43)
= 0.547.
And [tex]\bar q[/tex] = 1 - [tex]\bar p[/tex] = 1 - 0.547 = 0.453.
Therefore, all the required values are given above.
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. Ronaldinho Trading Co. is required by its bank to maintain a current ratio of at least 1.75, and its current ratio now is 2.1. The firm plans to acquire additional inventory to meet an unexpected surge in the demand for its products and will pay for the inventory with short-term debt. How much inventory can the firm purchase without violating its debt agreement if their total current assets equal $3.5 million?
The inventory can the firm purchase without violating its debt agreement is $777,777
What is liquidity ratio?Liquidity ratios are a class of financial metrics used to determine a debtor's ability to pay off current debt obligations without raising external capital.
Given that, Ronaldinho Trading Co. is required by its bank to maintain a current ratio of at least 1.75, and its current ratio now is 2.1.
Let X represent the additional borrowing against the firm’s line of credit (which also equals the addition to current assets).
We can solve for that level of X that forces the firm’s current ratio to be at 1.75
$3,500,000 / Current liabilities = 2.1
Current liabilities = $1,666,667
1.75 = ($3,500,000 + X) / ($1,666,667 + X) (1.75 * $1,666,667) + 1.75X
= $3,500,000 + X 0.75X = $3,500,000 – $2,916,667 X
= $777,777
Hence, the inventory can the firm purchase without violating its debt agreement is $777,777
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Find the measure of the three missing angles in the parallelogram below.
The measure of the three missing angles in the parallelogram are,
⇒ ∠x = 122
⇒ ∠ y = 122°
⇒ ∠z = 58°
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The parallelogram shown in figure.
We know that;
By Opposite Angles Theorem,
In parallelogram, The two opposite angles of a parallelogram are equal to each other.
Hence, We get;
⇒ ∠y = 58°
⇒ ∠x = ∠z
And, The sum of all angles in a parallelogram is 360°.
Hence, We get;
⇒ ∠x + ∠y + ∠z + 58° = 360
⇒ ∠x + ∠x +58+58 = 360
⇒ 2∠x + 116 = 360
⇒ 2∠x = 360 - 116
⇒ 2 ∠x = 244
⇒ ∠x = 122
And, ∠ z = 122°
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Question
A child's toy is in the shape of a square pyramid. The pyramid stands 20 inches tall and each side of the base measures 24 inches.
Half of the surface area of the pyramid is black and the remainder is yellow.
What is the surface area of the toy that is yellow?
Enter your answer, rounded to the nearest tenth, in the box.
in²
Answer:
The answer is 768.0 square inches.
Step-by-step explanation:
The surface area of a square pyramid can be calculated by adding the area of its four triangular faces to the area of its base, which is a square.
First, we'll find the area of the base:
24 inches x 24 inches = 576 square inches
Next, we'll find the area of each triangular face:
1/2 * 24 inches * 20 inches = 240 square inches
So, the total surface area of the pyramid is:
576 square inches + 4 * 240 square inches = 1,536 square inches
Finally, we'll find the surface area that is yellow:
1,536 square inches / 2 = 768 square inches
Rounding to the nearest tenth, we have:
768 square inches = 768.0 square inches
So, the surface area of the toy that is yellow is 768.0 square inches.
I would greatly appreciate Brainliest.
Have a nice day.
Through: (1,-3), slope= -7
Answer:
y = -7x + 4
Step-by-step explanation:
[tex]y=mx+b\\-3=-7(1)+b\\-3=-7+b\\4=b\\\\y=-7x+4[/tex]
Find g (7) if g (x) = - 10x - 7
Given:-
[tex] \rm{g ( x ) = -10x - 7 eqⁿ}[/tex][tex] \rm \bold{x = 7}[/tex][tex] \: [/tex]
now , put the value of x = 7 in da eqⁿ
[tex] \: [/tex]
[tex] \rm{g ( 7 ) = -10(7)-7}[/tex][tex] \: [/tex]
[tex] \rm{g ( 7 ) = -70-7}[/tex][tex] \: [/tex]
[tex] \underline{ \boxed{ \rm{ \red{ \bold{g ( 7 ) = -77}}}}}[/tex][tex] \: \: [/tex]
hope it helps!:)
The solution to the system of equations below is (x, y). What is the value of x?
3x + y = 13
2x - 4y = 18
Answer: x=5
Step-by-step explanation:
3x + y = 13 ------- (1)
2x - 4y =18 ------- (2)
2x = 4y + 18 ------- (3)
(3) x 3
6x = 12y + 54 ------- (4)
(1) x 2
6x + 2y = 26 --------- (5)
sub (4) into (5)
12y + 54 + 2y =26
14y + 54 = 26
14y = -28
y = -2 --------- (6)
sub (6) into (1)
3x - 2 = 13
3x = 15
x = 5
Consider the following assertion.
~(~p V q) => p V q
(a) Find a statement that is one step forward from the given.
(b) Find a statement that is one step backward from the goal. (Use the addition rule—in reverse—to find a statement from which the goal will follow.)
(c) Give a proof sequence for the assertion.
(d) Is your proof reversible? Why or why not?
Answer:(a)
One step forward from the given statement could be to simplify it to just "p V q".
(b)
One step backward from the goal statement "p V q" could be to add the assumption that "(~p V q) => p V q" to get "(~p V q) => (p V q)".
(c)
Proof sequence:
Given: (~p V q) => p V q
To prove: p V q
Assume ~p V q is true (as the antecedent of the implication)
Since ~p V q is true, either ~p is true or q is true.
If ~p is true, then p is false, but the disjunction p V q is true.
If q is true, then the disjunction p V q is true.
In either case, p V q is true.
Therefore, p V q is true under the assumption that ~p V q is true.
Since the assumption was arbitrary, we conclude that p V q is true regardless of the truth value of ~p V q.
(d)
The proof is not reversible because the contrapositive of the statement "p V q => (~p V q)" is not logically equivalent to the original statement "~p V q => p V q".
Step-by-step explanation:
(a)
One step forward from the given statement could be to simplify it to just "p V q".
(b)
One step backward from the goal statement "p V q" could be to add the assumption that "(~p V q) => p V q" to get "(~p V q) => (p V q)".
(c)
Proof sequence:
Given: (~p V q) => p V q
To prove: p V q
Assume ~p V q is true (as the antecedent of the implication)
Since ~p V q is true, either ~p is true or q is true.
If ~p is true, then p is false, but the disjunction p V q is true.
If q is true, then the disjunction p V q is true.
In either case, p V q is true.
Therefore, p V q is true under the assumption that ~p V q is true.
Since the assumption was arbitrary, we conclude that p V q is true regardless of the truth value of ~p V q.
(d)
The proof is not reversible because the contrapositive of the statement "p V q => (~p V q)" is not logically equivalent to the original statement "~p V q => p V q".
Ruby has a collection of square blocks and triangular blocks, which are lined up as shown below. She wants to have all the squares on the left and all the triangles on the right. Ruby can switch the position of any two adjacent blocks. What is the minimum number of switches that Ruby needs to make?
The minimum number of switches that Ruby needs to make would be = 39,916,800
What is permutation?Permutation is defined as the arrangement of different values of a data set into a definite order.
The total number of the shapes of the blocks are = 11
Therefore, the minimum number of switches that Ruby needs to make would be the permutation of the total number = 11*10*9*8*7*6*5*4*3*2*1 = 39,916,800.
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1.2 : 3/2
so confused what's it asking for? can't seem to find anything on it could someone please explain?
Answer:
is that the question?
Step-by-step explanation:
Given: DEF
Prove: DEF is isosceles.
Both the side of triangle DEF have equal distance DF = DE. so it is isosceles triangle.
How can you demonstrate that an isosceles triangle is made up of the specified vertices?
The distance between any two of the supplied points must be the same for two pairs of the given points in order to determine whether the given points are the vertices of an isosceles triangle. We can infer that DF = DE from the DF, FE, and DE data mentioned above.
we have 3 coordinates of triangle .
D(x1,y1) = D(1 , 2)
F(X2,Y2) = F(-2 , -2)
E(X3,Y3) = E(-3 , -1)
if given triangle is isosceles triangle than distance DF = DE.
Distance between two points :-
Distance (DF) =[tex]\sqrt{((x_1 - x_2)^{2} + (y_1 - y_2)^{2})} = \sqrt{((1 + 2)^{2} + (2 +2)^{2})} = 5[/tex].
Distance (DE)= [tex]\sqrt{((x1 - x3)^{2} + (y1 - y3)^{2})}= \sqrt{((1 + 3)^{2} + (2 + 1)^{2})} = 5[/tex]
hence, both the side have equal distance DF = DE. so it is isosceles triangle.
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Each side of the base of a square pyramid measures 8 inches. The height of each lateral face of the pyramid is also 8 inches.
What is the surface area of the pyramid?
The surface area of the pyramid is 3136 square inches.
What is pyramid?A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid. The lateral face is a triangle face formed by the connection of each edge of the base to the apex.
Given:
Each side of the base of a square pyramid measures 8 inches.
The height of each lateral face of the pyramid is also 8 inches.
The perimeter of the base P is 32 inches.
The base area B = 8 x 8 = 64 square inches.
The surface area of the pyramid,
= B + 12(P x L)
= 64 + 12(32 x 8)
= 3136 square inches.
Therefore, the surface area is, 3136 square inches.
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The equations of the lines shown are y =3/2x+9 and y=3/2-6
Is AOB~COD?
Answer:
Yes
Step-by-step explanation:
The lines are parallel. Alternate angles and vertically opposite angles are equal. True by angle axiom.
at which values of x does the graph of the function f(x) have a vertical asymptote? check all that apply. F(x) = x+2/X^2+2x-24
The graph of f(x) has a vertical asymptote at x = -2 and x = 6, as the denominator of the fraction approaches zero and the numerator approaches a finite value as x approaches those values from either direction.
Answer:
The graph of the function F(x) has vertical asymptotes at x = 2 and x = 6. This is because the denominator of the function (x2 + 2x - 24) is equal to 0 when x = 2 and x = 6.
Step-by-step explanation:
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How much money will be in the account in three years if $100 was invested at 6%,
compounded quarterly?
The car salesman tells you that for every $2,000 a car costs, your monthly payment goes up by $45. If you are looking at a car that costs $30,000 how much would your monthly payment be? Just place the whole number not the dollar sign.
I will give you 100 points if you answer RIGHT NOW PLEASE :)
Answer: $675
Step-by-step explanation:
To calculate the monthly payment, we need to determine the number of $2,000 increments that the car costs. $30,000 ÷ $2,000 = 15.
So, the car costs 15 $2,000 increments.
Next, we need to multiply the number of increments by the $45 increase in payment per increment to find the monthly payment. 15 increments × $45/increment = $675.
Therefore, the monthly payment for a $30,000 car would be $675.
HELP ASAP PLEASE !!!!!!!!!!!!
Answer:
Step-by-step explanation:
so the graph shows so 4+9 = 13
f the terminal side of angle θ goes through the point (15/17,−8/17) on the unit circle, then what is cos(θ)?
The value of cos θ from the unit circle is cos θ = 0.88235
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
Given data ,
The terminal side of angle θ intersects the unit circle in the first quadrant at ( 15/17,-8/17 )
So , the equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Substituting the values of x and y in the equation , we get
x = 15/17
And , y = -8/17
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
So , the value of cos θ = ( 15/17 ) and sin θ = ( -8/17 )
On simplifying the equation , we get
cos θ = ( 15/17 )
cost θ = 0.88235
Hence , the value of cos θ = 0.88235
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I NEED HELP
Which of the following best describes the technique used to graph the equation y = 9x + 4 using the slope and y-intercept?Mark a point at 9 on the y-axis, go up 4 and left one and mark this point.
Mark a point at 9 on the y-axis, go up 4 and left one and mark this point.
Mark a point at 9 on the y-axis, go up 4 and right one and mark this point.
Mark a point at 9 on the y-axis, go up 4 and right one and mark this point.
Mark a point at 4 on the y-axis, go down 9 and right one and mark this point.
Mark a point at 4 on the y-axis, go down 9 and right one and mark this point.
Mark a point at 4 on the y-axis, go up 9 and right one and mark this point.
Answer:
The technique used to graph the equation y = 9x + 4 using the slope and y-intercept is to mark a point at 4 on the y-axis, go up 9 and right one and mark this point. This is because the slope of the equation is 9 and the y-intercept is 4, so the graph can be plotted by starting at the y-intercept and moving up 9 units and right 1 unit. Unfortunately I need to wrap this conversation up and can only talk a little more. Is there anything you'd like to discuss before we close?
Step-by-step explanation:
Rosa dives into a pool from a diving board that is 3 meters above the surface of the water. During the dive, she descends to a depth of –2.8 meters, relative to the surface of the water. Which value represents the change in Rosa’s elevation, in meters, during the dive, relative to the diving board?
Rosa's change in elevation, relative to the diving board, in meters during the dive, which is a measure of her displacement, is -5.8 meters.
What is a displacement?Displacement is the change in the position of an object, with regards to a frame of reference. Displacement is a vector quantity, that has both magnitude and direction, indicated by the sign (positive or negative), and the magnitude, which is the measured value.
The height of the diving board above the surface of the water = 3 meters
The depth to which Rosa descends relative to the water surface = -2.3 meters
Therefore, Rosa's initial elevation when on the diving board = 3 meters
Rosa elevation when at the depth to which she dives = -2.8 meters
Her change in elevation can be obtained by finding her displacement from the diving board, when she descends to the depth of -2.8 meters.
Rosa's change in elevation, Δh = Final elevation - Initial elevation
Therefore, Δh = -2.8 m - 3 m = -5.8 m
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A hose fills a hot tub at a rate of 3.76 gallons per minute. How many hours will it take to fill a 286-gallon hot tub?
Answer:
93.75min
Step-by-step explanation:
Solution:
The rate of fill up is, Rate = 3.2 Gallons / minute = 3.2 g/min
The hut tub volume is 300 Gallons
You can set up this problem as follows:
Every 3.2 gallons require 1 minute, How many minutes 300 gallons require?
3.2 g 1min
300 g ? min = (300 gallons x 1min/ 3.2 gallons)=(300/32)min
= 93.75 min
or simply the number minutes is the time required (T) the rate is (R) and the volume is (V)
such that T=V/R= (300g/3.2 g/min)= 93.75 min
There is no conversion of units in this problem, but manipulation of units
City A and City B are 312 miles apart. John leaves City B, driving towards City A at an average rate of 70 miles per hour. Pat leaves City A at the same time, driving towards City B in her antique auto, averaging 34 miles per hour. How long will it take them to meet?
Pat and John will meet in 3 hours.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
here, we have,
How to calculate the value?
It should be noted that speed = Distance / Time
The appropriate equation will be:
80t + 24t = 312
104t = 312
t = 312/104
t = 3. hours
Therefore, it will take them 3 hours to meet.
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What percent of 18 is 23? Round your answer to the nearest tenths.
The percent of 18 that equals 23 rounded to the nearest tenth is 127.8%.
What percent of 18 is 23?
Percentage is simply number or ratio expressed as a fraction of 100.
Given the data in the question;
Let x% represent the percentage of 18 that is equal to 23.
Note that x% is the same as x/100
Hence;
x/100 × 18 = 23
Solve for x
18x/100 = 23
Cross multiply
18x = 23 × 100
18x = 2300
Divide both sides by 18
18x/18 = 2300/18
x = 2300/18
x = 127.8
Therefore, the required percentage is 127.8%.
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If the terminal side of angle t goes through the point (3√10/10,√10/10) on the unit circle, then what is cos(t)?
The value of cos t from the unit circle is cos t = 0.94868
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
Given data ,
The terminal side of angle θ intersects the unit circle in the first quadrant at ( 3√10/10,√10/10 )
So , the equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Substituting the values of x and y in the equation , we get
x = 3√10 / 10
x = 3/√10
And , y = √10/10
y = 1/√10
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
So , the value of cos θ = ( 3/√10 ) and sin θ = ( 1/√10 )
On simplifying the equation , we get
cos t = ( 3/√10 )
cost t = 0.94868
Hence , the value of cos t = 0.94868
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Please help with geometry question finding perimeter of triangle
Step-by-step explanation:
perimeter means to add all sides
SO
perimeter of triangle is
QR+QP+RP
SO
= 63+70+47
=180
Answer:
perimeter= 180
Step-by-step explanation:
Add 63+70+47=180
63
70
47
+
---------
180
You use a coordinate plane to design a poster for the Florida Strawberry Festival. The vertices of the design are A(2,4),B(34,4), C(2,-44) , and D(34,-44) . The coordinates are measured in inches. Find the least number of square yards of paper you need to make the poster.
The least number of square yards of paper required to make the poster is 11 square yards.
How did we get the value?The area of a rectangle can be found by multiplying the length of its sides. To find the length and width of the rectangle, we can subtract the x and y values of the opposite vertices.
The length of the rectangle is 34 - 2 = 32 inches, and the width is -44 - 4 = -48 inches. We will have to make the width positive to find the area, so the area is 32 * 48 = 1536 square inches.
Since 1 square yard is equal to 144 square inches, we need to divide 1536 by 144 to find the number of square yards: 1536 / 144 = 10.67 square yards.
Therefore, the least number of square yards of paper required to make the poster is 11 square yards.
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One alloy containing 32% aluminum and another containing 44% aluminum how many pounds of each alloy must he use to make 54 pounds of a third alloy containing 36% aluminum
what are factors of 10^3.
Answer:
2^3 x 5^3
Step-by-step explanation:
In a recent snail race, the winning snail traveled 5.85 cm in 1 minute. How fast was the snail
traveling in centimeters per second?
Answer:
Step-by-step explanation:
since there are 60 seconds in 1 minute, we can do
5.85 = 60second
5.85/60 to show how many cm happened in 1 second.
0.0975 cm per second.
An oil exploration firm is to drill 10 wells, each in different locations. Each well has a probability of 0.1 of producing oil. It will cost the firm $60,000 to drill each well. A successful well will bring in $1 million, taking into account the cost of drilling.
1. What is the probability that the firm will lose money on the ten wells?
2. What is the probability that the firm will gain $1.5 or more from the ten wells?
The probability the firm will lose money from 10 wells is 0.99 and the probability the firm will gain 1.5 million from the ten wells is 1 minus the CDF of 4 successful wells.
What is the probability the firm will lose or gain money1.
The expected profit from each well is $1 million - $60,000 = $940,000. The expected profit from all ten wells is $940,000 * 10 = $9,400,000. The probability of losing money on all ten wells is 1 - (0.1)^10 = 0.99
2.
To calculate the probability of gaining $1.5 million or more, we can use the cumulative distribution function (CDF) of the binomial distribution, which models the number of successful wells out of ten. The CDF gives the probability of getting a certain number of successful wells or fewer. To get the probability of getting more than a certain number of successful wells, we subtract the CDF of that number from 1. To get the probability of getting 2 or more successful wells, we subtract the CDF of 1 from 1, and so on. To get the probability of getting 5 or more successful wells, we subtract the CDF of 4 from 1, and so on. To get the probability of getting $1.5 million or more, we need to find the probability of getting 5 or more successful wells, since 5 wells at $1 million each give $5 million. The CDF of 4 successful wells can be found using statistical software or by using tables or approximations. The final answer is 1 minus the CDF of 4 successful wells.
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