The possible coordinates of the point A is (-3, -5) and (-3, 7)
How the coordinates of point A can be calculated?The given parameters are:
Point B = (5, 1)Distance between the two points, D = 10 unitsx-coordinate of point A = −3 i.e. A = (-3, y)The distance between any two points is calculated as
D = √[(x₁ - x₂)² + (y₁ - y₂)²]
Substitute the known values in the above equation
So, we have
10 = √[(-3 - 5)² + (y - 1)²]
Evaluate
100 = 64 + (y - 1)²
Evaluate the like terms
(y - 1)² = 36
Take the square roots
y - 1 = ±6
This gives
y = 1 ± 6
So, we have
y = -5 and 7
Hence, the value of point A are (-3, -5) and (-3, 7)
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Rafi's Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon, the cafe sold 69 single-shot espressos and 6 double-shot espressos. What percentage of the espressos sold were single-shot?
The percentage of the espresso sold were single shot were 92%
what is percentage?
A fraction whose denominator is 100 is known as percentage.
We are given that the number of single shot espressos sold were 69 and number of double shot espressos sold were 6
Hence the total number of espressos sold were 69+6=75
The percentage of single shot espressos sold were [tex]\frac{69}{75}[/tex]
On simplifying we get the value as 0.92
To find the percentage we multiply this by 100 we get 92%
Hence the percentage that single shot espressos were sold is 92%
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A nursery owner buys 9 panes of glass to fix some damage to her greenhouse. The 9 panes cost $.23.85 Unfortunately, she breaks 2 more panes while repairing the damage. What is the cost of another 2 panes of glass?
After doing some mathematical operations, we know that the cost of 2 panes is $5.3.
What exactly are mathematical operations?An operation, in mathematics, is a mathematical function that transforms zero or more input values into a precisely defined output value.The arity of the operation is influenced by the number of operands.The rules that specify the order in which we should carry out the operations required to solve an expression are referred to as the order of operations.PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).So, the cost of 2 panes:
The cost of 9 panes is $23.85.
Then, the cost of 1 pane will be:
23.85/9 = $2.65Now, the cost of 2 panes will be:
$2.65 × 2 = $5.3Therefore, after doing some mathematical operations, we know that the cost of 2 panes is $5.3.
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In a recent year, 23% of all college students were enrolled part-time. if 6.4 million college students were enrolled part-time that year, what was the total number of college students?
Calculate the breadth of a rectangle with length 140mm and area 98cm2
The breadth of the rectangle is 7cm or 70 mm.
It is given in the question that:-
Area of the rectangle = 98 square cm
Length of the rectangle = 140 mm
We have to find the breadth of the rectangle.
We know that,
1 cm = 10 mm
Hence,
140 mm = 14 cm
Also,
Area of a rectangle = (Length of the rectangle)* (Breadth of the rectangle)
Hence, we can write
98 = 14*(Breadth of the rectangle)
Breadth of the rectangle = 98/14 = 7 cm
Hence, the breadth of the rectangle is 7 cm or 70 mm.
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Pls help I’ll give BRAINLIEST!! :)
After doing some mathematical operations, we know that (A) Almond barks cost $0.25 more per ounce than peanut brittle.
What do we mean when we say mathematical operations?Any mathematical operation that converts zero or more discrete input values into discrete output values is known as a discrete operation.The number of operands affects how complicated the operation is.Functions that convert numerical inputs into numerical outputs are the four mathematical operations (i.e., another number).These are addition, subtraction, multiplication, and division.So, the cost of the candy per piece costs more:
Peanut brittle: weight 20 ounces and costs $20.Almond Bark: weight 16 ounces and costs $20.It is clear that Almond Bark costs more than Peanut brittle.
Now, the cost of 1 ounce:
Peanut brittle: 2/2 = $1Almond Bark: 5/4 = $1.25Difference: $1.25 - $1 = $0.25
Therefore, after doing some mathematical operations, we know that (A) Almond barks cost $0.25 more per ounce than peanut brittle.
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what is the slope of the line on the graph?.
A nursing student is budgeting for college. he spent $325.00 on books for the first semester, $460.00 on books for the second semester, and $395.00 for the third semester. how much should he budget for books for the fourth semester? round to the nearest whole dollar.
The budget for books for the fourth semester should be $430.
A nursing student is budgeting for college. He spent $325.00 on books for the first semester, $460.00 on books for the second semester, and $395.00 for the third semester.
Amount spent on books for the first semester = $325.00
Amount spent on books for the second semester = $460.00
Amount spent on books for the third semester = $395.00
Difference in amount spent in second semester and first semester = 460.00 - 325.00 = 35
Difference in amount spent in third semester and second semester = 395.00 - 460.00 = 35
The amount spent by a nursing student is increasing by $35 each semester. So,
money needed for books for the fourth semester = 395 + 35 = $430
Thus, $430 should be the budget for books for the fourth semester.
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Find the first four terms of the following
(1 + x)¹²
The first four terms are 1, 4096, 531441 and 16777216.
Define expansion.Expansion is a scale-increasing affine transformation, sometimes known as enlargement or dilatation. It is also frequently referred to as an enlargement and is the polar opposite of a geometric contraction. When a mathematical object is scaled by a scale factor that is bigger in absolute value than one, an expansion happens. The image grows larger than the actual mathematical entity when an expansion takes place. When scaling happens near a point, the transformation is known as a dilation, and the "point" is referred to as the center of the dilation. either the process of expanding or the condition of expanding. An expanded object, surface, or component. the amount by which anything extends; its degree, extent, or size. a growth, expansion, or development in a company's operations.
Given Data
(1+x)¹²
Putting x = 0
Expanding,
(1+0)¹²
1
Putting x = 1
(1+1)¹²
2¹²
Solving,
4096
Putting x = 2
(1+2)¹²
3¹²
531441
Putting x = 3
(1+3)¹²
4¹²
16777216
The first four terms are 1, 4096, 531441 and 16777216.
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A company rents storage sheds shaped like rectangular prisms. Each shed is 12 feet long, 8 feet wide, and 10 feet tall. The rental cost is $3 per cubic foot. How much does it cost to rent one shed?
Answer:
$2880
Step-by-step explanation:
Volume of rectangular prism:First find the volume of the prism.
l = 12 ft
w = 8 ft
h =10 ft
[tex]\sf \boxed {\bf Volume \ of \ rectangular \ prism = l*w*h}[/tex]
= 12 *8 * 10
= 960 cubic feet
To find the rental cost, multiply the volume of the prism by the rental cost per cubic foot.
Rental cost = 960 * 3
= $ 2880
Jenna explained that △P1P2Q and △P3P4S are similar triangles. Which best completes Jenna’s explanation?
The possible options that can correctly be used to complete Jenna's statement on the similarity of the triangles includes any of the following;
[tex] \displaystyle{\angle P_1P_2Q \cong \angle P_3P_4S \: and \: \angle P_1QP_2 \cong \angle P_3SP_4 }[/tex][tex] \displaystyle{ \frac{P_1P_2}{P_3P_4} = \frac{P_1Q}{P_3S} \: and \: \angle P_1P_2Q \cong \angle P_3P_4S} [/tex][tex] \displaystyle{ \frac{P_1}{P_3} = \frac{P_2}{P_4} = \frac{Q}{S} }[/tex]What are similar triangles?Similar triangles are triangles that have proportional sides and in which the measure of all the interior angles in one triangle is the same as the measure of the interior angles in the other triangle
Similar triangles are triangles that have
The required conditions that indicates that two triangles similar includes;
Two angles in one triangle are congruent to two angles in the other triangle.The ratio of two sides in one triangle is equal to the ratio of the corresponding two sides on the other triangle, and the inscribed or included angle of the specified two sides in both triangles are also equal The three sides of one triangle have equal proportion to the corresponding three sides of the other triangle.Therefore,
[tex] \triangle P_1P_2Q \sim \triangle \: P_3P_4S[/tex]
When any of the above three conditions are satisfied.
The possible correct options are therefore;
[tex] \angle P_1P_2Q \cong \angle P_3P_4S [/tex] and [tex] \angle P_1QP_2 \cong \angle P_3SP_4 [/tex][tex] \displaystyle{ \frac{P_1P_2}{P_3P_4} = \frac{P_1Q}{P_3S} }[/tex] and [tex] \angle P_1P_2Q \cong \angle P_3P_4S [/tex][tex] \displaystyle{ \frac{P_1}{P_3} = \frac{P_2}{P_4} = \frac{Q}{S} }[/tex]Learn more about similar triangles in geometry here;
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Pls help 20 points thx
Let's find 2/3 - 1/4
First write the subtraction with a common denominator.
Then subtract.
Answer:
[tex]\frac{2}{3} -\frac{1}{4}= \frac{8}{12} -\frac{3}{12} =\frac{5}{12}[/tex]
Step-by-step explanation:
We have to find a common denominator between the two fractions and that would be 12.
Then we multiply the fractions respectively to change both denominators to twelve and substitute them into the equation.
Answer: 11/12
Step-by-step explanation:
first, you find the common multiple of the denominators which is 12
Then you multiple by the number that got the denominator to 12 by the numerator as well
2/3= 8/12
1/4= 3/12
then you subtract the numerators
5/12
Which of the following represents the coordinates of the y-intercept for a function? ( 1 , 2 ) , ( 0 , 3 ) , ( 4 , 8 ) , ( 7 , 0 )
The ordered pair that represents the coordinates of the y-intercept for a function is: (0, 3).
How to Determine the Y-intercept of a Function?If we graph a function, especially a linear function, the line of the function will normally intercept the y-axis. At this point, the x-coordinate is usually zero while the y-coordinate of the point is what we refer to as the y-intercept of the function.
Therefore, the coordinates of the y-intercept for a given function would be expressed as (0, b), where b is the y-coordinate of the point where the line intercepts the y-axis.
An ordered pair of (0, 3), means that the line intercepts the y-axis at y = 3, when x = 0.
Therefore, given the above ordered pairs, the coordinates that represents that of the y-intercept of a function is: (0, 3).
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a line is drawn perpendicular to y=(1/2)x+6 and passes through the points (b,1) and (-3,2). what is the value of b
Answer:
[tex]{ \tt{y = \frac{1}{2} x + 6}} \\ [/tex]
- If two lines areperpendicular, their gradients have a relation below;
[tex]{ \tt{m_{1} \times m _{2} = - 1 }} \\ [/tex]
- Therefore, gradient for points (b, 1) and (-3, 2);
[tex]{ \tt{ \frac{1}{2} \times m _{2} = - 1}} \\ \\ { \tt{m = - 2}}[/tex]
- Therefore:
[tex]{ \tt{ - 2 = \frac{2 - 1}{ - 3 - b} }} \\ \\ { \tt{ - 2( - 3 - b) = 1}} \\ \\ { \tt{6 + 2b = 1}} \\ { \tt{2b = - 5}} \\ { \tt{b = - \frac{5}{2} }}[/tex]
Can anyone help me with this?
For the given question the correct order of construction is as follows -
The order is as follows:
Place the compass at A. Draw an arc that intersects both rays of angle A.Lable the points of intersections B and C.Place the compass point at C. Open the compass to the distance between B and C.Use a straightedge to draw a ray with endpoint X.Place the compass point at X and draw an arc intersecting the ray. Mark that point as Y at the intersection.Place the compass at Y and draw an arc. Label the point Z where the two acrs intersect. Use a straightedge to draw XY.What is intersection?
Any two or more lines that cross one another on a plane are said to be intersecting lines. Where the intersecting lines share a common point is known as the point of intersection, and it can be located on all intersecting lines. The junction of lines P and Q at point O is depicted.
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Point L is a centroid of the triangle FWD. If RL = 36 cm, what is RD?
The length of RD in the triangle is 108 cm
How to determine the length of RDThe given parameters are
Shape = TriangleLength RL = 36 cmCentroid point = LAs a general rule, the centroid of a triangle divides the triangle into the following ratio
Ratio of centroid = 1 : 2
This means that
Ratio of centroid, RL : LD = 1 : 2
Substitute 36 for RL
So, we have
36 : LD = 1 : 2
Multiply the right ratio by 36
36 : LD = 36 : 72
By comparison, we have
LD = 72
The length of RD is calculated as
RD = RL + LD
This gives
RD = 36 + 72
Evaluate
RD = 108
Hence, the value of RD is 108 cm
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A phone company charges a monthly fee of $13 plus 12 cents per text message. Another company charges $20 each month plus 8 cents per text message for the same plan. How many text messages will have to be sent for the cost of a phone plan from the first company to equal the cost of a phone plan from the second company?
The number of text messages that will have to be sent for the cost of a phone plan from the first company to equal the cost of a phone plan from the second company is 175.
Number of text messagesWe have to formulate and equation and then use the formulated equation to find the number of text messages.
Let c represent charges
Let t represent test messages
c = 13 + 0.12t
c = 20 = 0.08t
Hence,
13 +0.12t = 20 +0.08t
Collect like terms
7 =0.04t
Divide both side by 0.04t
t = 7 / 0.04
t= 175
Therefore 175 is the number of text messages needed.
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Margaret go to the store to buy curtains without measuring the length of her Windows she guesses the windows are 36 in length. when she gets home she measures and finds out they are 40 inches in length. what is the percent error of her geuss
The percentage error of Margaret's guess she made while buying curtains without measurement is 11.11%
How to find the percentage error of Margaret's guessThe term percentage error is one that has to do with the difference that lies between the estimated value and the value that is the actual value and the way that it is compared to the actual value. This usually measured in terms of percentages.
percentage error is found by
= ( actual price - guessed price ) / guessed price * 100
= ( 40 inches - 36 inches ) / 36 inches * 100
= 4 inches / 36 inches * 100
= 0.1111 * 100
= 11.11 %
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2 Sue is x years old. She is over 2.
Ben is twice as old as Sue.
Ceri is 4 years older than Sue.
The total of their three ages is less than 28.
a Write this information as an inequality.
b What age could Sue be?
c What are the corresponding ages of Ben and Ceri?
a. x < 2
b. Sue's age = 4
c. Ben's age = 8 and Ceri's age = 16
How to solve Ages problems ?
- If the present age is y, then n times the present age = ny.
- If the present age is x, then age n years later/hence = x + n.
According question,
Sue = x
She is over 2, so Sue = x+2
Ben age is twice as old as Sue,
so, Ben = 2(x+2)
Ceri is 4 years older than Sue.
so, Ceri = 4(x + 2)
The eq. will form as,
(x+2) + 2(x+2) +4(x+2) < 28
=> x + 2 + 2x+ 4 + 4x + 8 < 28
=> 7x < 28 - 14
=> 7x < 14
=> x < 2
Sue age = x + 2 = 2 + 2 = 4
Ben's age = 2( x + 2) = 2(2 + 2) = 8
Ceri's age = 4(x + 2) = 4(2 + 2) = 16
Therefore, the answer of a. x < 2
b. Sue's age = 4
c. Ben's age = 8 and Ceri's age = 16
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What is the correct standard form of the equation of the parabola? Enter your answer below. Be sure to show each step of your work.
The equation of parabola is y = -6x² + 24x - 30
Define Parabola
A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile travelling under the pull of gravity will travel along a curve similar to this one.
We know the equation of parabola in vertex form,
y = a(x - h)² + k
And , we know the vertex (h, k) = (2, -5) and a = -6
put these values in given equation,
y = a (x - h)² + k
y = -6(x - 2)² + (-6)
y = -6(x² + 4 - 4x) - 6
y = -6x² - 24 + 24x - 6
y = -6x² + 24x - 30
Hence, the equation of parabola is y = -6x² + 24x - 30
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jose va a comprar una bicicleta de tiene 28% de descuento si la bicicleta cuesta 3,600 ¿cuanto fue el descuento? ¿cuál es el nuevo precio de la bicicleta?
Answer:2,592
Step-by-step explanation:
Tienes que quitar de 3,600-28% = 2,592.
Answer:
el porcentaje es 0.28 o .28 y pagara por la bici 2402
Step-by-step explanation:
primero sacamos porcentaje 100 entre 28= 0.28
luego multiplico 3600 x .28= 998.00 (se le puede quitar los 00)
despues resto 3600-998 = 2402
y listo xdd
Giorgio fills up his car which is 60 liters.
After a certain distance, 340 deciliters remained in the tank.
How many liters did it consume?
How much did you spend if 1 liter costs € 1.45? How many liters of petrol can you buy for € 58?
My book has the answer but not step by step explanation
[ 26 liters; €37,70; 40 liters ]
The most appropriate choice for unitary method will be given by-
Volume of petrol consumed = 26 liters
Cost of 60 liters petrol = € 37.70
€ 58 is the cost of 40 liters of petrol
What is unitary method?
Unitary method is the method in which the value of single unit can be calculated from the value of multiple unit and value of multiple unit is calculated from the value of single unit.
Here,
Total volume of petrol filled by Giorgio in his car = 60 liters
Volume of petrol left = 340 deciliters
= [tex]\frac{340}{10}[/tex] liters
= [tex]34[/tex] liters
Volume of petrol consumed = (60 - 34) liters
= 26 liters
Cost of 1 liter petrol = € 1.45
Cost of 60 liters petrol = € 1.45 [tex]\times[/tex] 26
= € 37.70
€ 1.45 is the cost of one liter of petrol
€ 1 is the cost of [tex]\frac{1}{1.45}[/tex] liters of petrol
€ 58 is the cost of [tex]\frac{1}{1.45} \times 58[/tex] liters of petrol
€ 58 is the cost of 40 liters of petrol
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van is opening a new pizza restaurant that will use a combination of workers and ovens to produce pizzas. van knows from experience that the total number of pizzas he can produce in an hour is given by the function q
The values of "L" for q1 are 12, 18, and 36.
The values of "L" for q2 are 25/3, 25/2, and 25.
The function "q1" is given below :
q1 = 5[(K)^(0.5)]*[(L)^(0.5)]
The value of "q1" is 30.
The values of "K" are 3, 2, and 1.
Put the values in the above equation of the function "q1" and get the respective values of "L".
The respective values of "L" are 12, 18, and 36.
The function "q2" is given below :
q2 = 6[(K)^(0.5)]*[(L)^(0.5)]
The value of "q2" is 30.
The values of "K" are 3, 2, and 1.
Put the values in the above equation of the function "q2" and get the respective values of "L".
The respective values of "L" are 25/3, 25/2, and 25.
Complete question: van is opening a new pizza restaurant that will use a combination of workers and ovens to produce pizzas. van knows from experience that the total number of pizzas he can produce in an hour is given by the function q1 = 5[(K)^(0.5)]*[(L)^(0.5)] find the value of K and L.
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jeffrey has $1.20 more than ryan. when ryan hands jeffrey $7.50, jeffrey's money becomes 7 times as much as Ryan's. How much money did they each have at the beginning?
Ryan had $1.45 and Jeffrey had $2.65 in the beginning.
Let Ryan has $x. So, amount with Jeffrey is x + 1.20.
As per the information on exchange of money, the equation relating their possession is -
x + 1.20 + 7.50 = 7x
Evaluating the equation to find the value of x
7x - x = 7.50 + 1.20
Performing subtraction on Left Hand Side and addition on Right Hand Side
6x = 8.70
x = 8.70 ÷ 6
Performing division on Right Hand Side of the equation
x = 1.45
Amount with Jeffrey = 1.45 + 1.20
Amount with Jeffrey = $2.65
So, at the beginning Ryan had $1.45 and Jeffrey had $2.65.
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An airplane covered the ff. distances in three separate trips.
Hongkong-Manila: 1116 kilometers
Singapore-Manila: 2391 kilometers
Korea-Manila: 2601 kilometers
A. What is the average distance traveled by the airplane in the three trips?
B. If the airplane travels with an average speed of 760km/h, how long will it take the airplane to travel in each flight? which trip took the longest time to travel?
The average distance that the airplane covered in three flights is = 2036 kilometers,
From Hong Kong to Manila travel time is = 1.468 hours,
From Singapore to Manila travel time is = 3.146 hours,
From Korea to Manila travel time is = 3.422 hours and the trip from Korea to Manila took longest time to travel.
The distance a plane traveled over three separate trips:
Hongkong-Manila : 1116 kilometers,
Singapore-Manila : 2391 kilometers,
Korea-Manila : 2601 kilometers.
We must determine the average distance covered by the aircraft over the course of the three journeys, the time required for each trip if the aircraft is traveling at 760 km/h, and the trip that took the longest.
The average distance flown by the aircraft across the three trips
= [tex]\frac{1116+2391+2601}{3}[/tex]
= [tex]\frac{6108}{3}[/tex]
= 2036 kilometers
We know that,
Speed = distance/time.
So,
We can write,
Time = Distance/speed
From Hong Kong to Manila travel time = 1116/760
= 1.468 hours
From Singapore to Manila travel time = 2391/760
= 3.146 hours
From Korea to Manila travel time = 2601/760
= 3.422 hours
We can observe that the trip from Korea to Manila took longest time to travel.
Therefore,
The average distance that the airplane covered in three flights is 2036 kilometers,
From Hong Kong to Manila travel time is 1.468 hours,
From Singapore to Manila travel time is 3.146 hours,
From Korea to Manila travel time is 3.422 hours and the trip from Korea to Manila took longest time to travel.
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Ben can type 153 words in 3 minutes,at this rate,how many words can he type in 10 minutes
Answer:
510 words
Step-by-step explanation:
[tex]\frac{153}{3} =51[/tex] → Ben can type 51 words in 1 minute
[tex]51*10 = 510[/tex] → Ben can type 510 words in 10 minutes.
Solve for x and y
Please help I forgot what I needed to do!
hi help please thanks
∠8 and ∠4 are the pair of alternate exterior angles.
What are alternate exterior angles?The pair of angles known as alternate exterior angles are those that are formed on the outer side of the parallel lines but on the transverse side. A triangle's exterior angle is the product of its two opposite interior angles. 180 degrees is the sum of the exterior angle and the interior angle. They form two pairs (four total angles) of alternate exterior angles because they are situated "outside" the two parallel lines but on opposite sides of the transversal.So, in the given image ∠8 and ∠4 are the pair of alternate exterior angles.
Therefore, ∠8 and ∠4 are the pair of alternate exterior angles.
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Edward is one of the six people who each are writing 180 math problems. When he solves every problem, he gets an incorrect answer for 10% of the problems that he wrote and for 5% of theproblems written by the others. For what fraction of the problems does Edward get the wrong answer? Express your answer as a common fraction.
This can be determined by adding the numbers in a set and dividing the result by the set's total number of numbers. The value of a function at a specific moment is equivalent to the value of the function when the values for the function's variables are plugged in. Value can also refer to an object's mathematical worth.
What is meant by fraction? Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. Because they let you know how much of a whole you need, have, or want, fractions are crucial.To know more about fraction refer to:
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Which recursive sequence would produce the sequence 6,15,42,...?
Answer: 123
Step-by-step explanation:
