The solution to the given system of equation is (3, 3, 3)
Solving system of equationsGiven the following system of equation expressed as:
2x-y+5z=16
X-6у +2z=-9
3x+4y- z=32
Multiply equation 2 by 2 to have:
2x-y+5z=16
2X-12у +4z=-18
Subtract
10y+z = 34 .........4
Similarly
3X-18у +6z=-27
3x+4y- z=32
Subtract
-22y+7z = -59 ........... 5
Equate 4 and 5
10y+z = 34 .........4 * 7
-22y+7z = -59 ........... 5 * 1
_______________________
70y+7z = 238
-22y+7z = -59
Subtract
92y = 297
y = 3
Recall that
10y+z = 34
10(3) + z = 34
z = 3
Since x - 6y +2z = -9
x-6(3)+2(3) = -9
x - 18 + 6 = -9
x = 3
Hence the solution to the given system of equation is (3, 3, 3)
Learn more on system of equation here: https://brainly.com/question/25976025
#SPJ1
Part D
Now use GeoGebra to measure the lengths of segments AB and BC and calculate the area of rectangle ABCD. Do you get the same result that you obtained in part C? Take a screenshot with the lengths of the sides labeled and the area displayed, and paste it below.
Answer:
id ont givea
efijhaoieuvbhzoiubhoewivbawzoufhbealivjhbr
Step-by-step explanation:
idsifui piuh vSeth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:
In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.
The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.
Which of these could be a step to prove that BC2 = AB2 + AC2?Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:
In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.
The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.
Which of these could be a step to prove that BC2 = AB2 + AC2?Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:
In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.
The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.
Which of these could be a step to prove that BC2 = AB2 + AC2?Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:
In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.
The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.
Which of these could be a step to prove that BC2 = AB2 + AC2?
What is 2x2 + 1000 x 1000
Answer: 2x2 + 1000 x 1000 = 1000004
Step-by-step explanation: you add on 5 0's to the one and 2x2 = 4 so add on the 4 also
Answer:
1000004
Step-by-step explanation:
First we do can separate it into the parentheses: (2*2) + (1000*1000)
= 4 + 1000000
= 1000004
Find the surface area of the regular pyramid.
A square pyramid. The length of the base is 1 inch. The height of each triangular face is 2 inches.
Answer:
Love helping people so here's the answer :)
Step-by-step explanation:
A square pyramid has 5 faces: 1 square base and 4 triangular faces. The surface area of the pyramid is the sum of the areas of all its faces.
The area of the square base is 1 * 1 = 1 square inch.
The area of each triangular face is (1/2) * base * height = (1/2) * 1 * 2 = 1 square inch.
Since there are 4 triangular faces, the total area of the triangular faces is 4 * 1 = 4 square inches.
Therefore, the surface area of the pyramid is 1 + 4 = 5 square inches.
Your parents are considering renting you an apartment instead of paying room and board at your college. The month-
to-month contract is $539.00/month and the annual contract is $467.00/month. If you break the annual contract,
there is a 2-month penalty.
3. How much do your parents save if you stay a whole year by entering into an annual contract
rather than a month-to-month contract?
4. If you enter into an annual contract but decide to leave after 5 months, how much do your parents lose by not doing the month-to-month contract?
Answer:
Step-by-step explanation:
3: ANSWER = 864
4; ANSWER = I DONT KNOW TNH YOU JUST HAVE TO MULTIPLY AMD THEN SUBRACT BOTH
g working. In a class of 75 students, 45 students study French and 25 students study Ara only. If 10 students study both Arabic and French, (I)illustrate the information on a Venn
; (ii)how many students study (a) only French (b) only one subject;(c) neither Arabic nor French.
Answer:
(i) Attached below. You can copy what I drew
(ii) (a) 35, (b) 60, (c) 5
Step-by-step explanation:
We're told that 25 students study Arabic only and 10 students' study both French and Arabic. Thus, this leaves 40 other students, as 75 - (10 + 25) = 40.We know that 45 students study French and this includes those who study French only and those who study both French and Arabic. Thus, we can subtract the number of students who study both languages from the number of students who study French (generally) to find the number of students who study French only: 45 - 10 = 35.(a) Thus, 35 students study French only.
Thus, we've sorted 70 students so far as 35 + 10 + 25 = 70.To find the number of students who studied neither Arabic nor French, we can subtract 70 from the total number of students in the class: 75 - 70 = 5.(c) Thus, 5 students' study neither Arabic nor French
We can check our work by making sure that:the number of students who study French only + the number of students who study both French and Arabic + the number of students who study Arabic only + the number of students who study neither Arabic nor French equals 75:
35 + 10 + 25 + 5 = 75
45 + 30 = 75
75 = 75
Thus, our numbers are correct.
(b) Also, the number of students who study only subject is 60, as 35 (number of students studying French only) + 25 (number of students studying Arabic only) = 60
I attached a picture of a diagram that you can use and I'll explain what everything means:The box represents the set, which is represented by the letter S in the top-left corner of the pictureF represent the number of students who studied French only, which is why I wrote 35 in this circleThe 10 represents the number of students who study both Arabic and French and likes between the F circle and the A circle A represents the number of students who studied Arabic only, which is why I wrote 25 in this circleThe 5 outside the circles but inside the box represents the number of students who study neither Arabic nor French50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
A. Because it would simplify this equation.
John wishes to choose a combination of two types of cereals for breakfast - Cereal A and Cereal B. A small box (one serving) of Cereal A costs $0.50 and contains 10 units of vitamins, 5 units of minerals, and 15 calories. A small box (one serving) of Cereal B costs $0.40 and contains 5 units of vitamins, 10 units of minerals, and 15 calories. John wants to buy enough boxes to have at least 500 units of vitamins, 600 units of minerals, and 1200 calories. How many boxes of each cereal should he buy to minimize his cost?
Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:
10x + 5y ≥ 500 (minimum 500 units of vitamins)
5x + 10y ≥ 600 (minimum 600 units of minerals)
15x + 15y ≥ 1200 (minimum 1200 calories)
We want to minimize the cost, which is given by:
0.5x + 0.4y
This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:
10x + 5y = 500
5x + 10y = 600
15x + 15y = 1200
Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.
Next, we can calculate the value of the cost function at each corner point of the feasible region:
Corner point A: (20, 40) -> Cost = 20
Corner point B: (40, 25) -> Cost = 25
Corner point C: (60, 0) -> Cost = 30
Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.
PLEASE HELP ME ITS DUE TODAY!!!
4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.
5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.
How to verify that RSTU is a trapezoid?In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;
RU ║ ST
Slope of side RU = Slope of side ST
Slope of RU = (y₂ - y₁)/(x₂ - x₁)
Slope of RU = (1 + 3)/(5 + 3)
Slope of RU = 4/8
Slope of RU = 0.5.
Slope of RS = (y₂ - y₁)/(x₂ - x₁)
Slope of RS = (-9 + 3)/(-4 + 3)
Slope of RS = -6/-1
Slope of RS = 6.
Slope of ST = (y₂ - y₁)/(x₂ - x₁)
Slope of ST = (-2 - 1)/(10 - 5)
Slope of ST = -3/5
Slope of ST = -0.6.
Slope of UT = (y₂ - y₁)/(x₂ - x₁)
Slope of UT = (-2 + 9)/(10 + 4)
Slope of UT = 7/14
Slope of UT = 0.5.
Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.
Question 5.
In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance RT = √[(-2 + 3)² + (10 + 3)²]
Distance RT = √170 units.
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance US = √[(5 + 4)² + (1 + 9)²]
Distance US = √181 units.
Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.
Read more on isosceles triangle here: brainly.com/question/19238666
#SPJ1
Test Prep What fraction is represented by the point on the number line?
The fraction represented by the point between 1 and 2 on the number line is 5/3.
If the point is between 1 and 2 on the number line, we can determine the fraction it represents by considering the distance between the point and the two adjacent integers.
The point A lies between the numbers 1 and 2, which indicates that the whole number part of the fraction is 1.
Also note that the segment between 1 and 2 is divided into 3 equal parts. A lies on the 2nd part, which implies that the fractional part is 2/3.
2
Thus, the point A corresponds to the mixed fraction 1 -
3
2 5
1 - = (1*3)+2 / 3 = -
3 3
So, the fraction represented by the point between 1 and 2 on the number line is 5/3.
for similar questions on fraction.
https://brainly.com/question/78672
#SPJ8
1. The vertices of APQR are P(1, 3), Q(5, 4) and
R(5, 15). Find the length of the perpendicular
from Q to PR.
The distance of the perpendicular from Q to line PR is D = 2.2135 units
Given data ,
Let the triangle be represented as ΔPQR
Now , the coordinates are P(1, 3), Q(5, 4) and R(5, 15)
And , the equation of line of PR is given by
Slope m = ( 15 - 3 ) / ( 5 - 1 )
m = 3
y - 3 = 3 ( x - 1 )
Adding 3 on both sides , we get
y = 3x
y - 3x = 0
And , the point is Q(5, 4)
Now , distance of a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )
D = | ( 1 ) ( 5 ) + ( -3 ) ( 4 ) + 0 | / √ ( 1 )² + ( 3 )²
D = | 5 - 12 | / √10
D = 7/√10
D = 2.2135 units
Hence , the distance is 2.2135 units
To learn more about distance of point to line click :
https://brainly.com/question/21096072
#SPJ1
A bird sanctuary has 14 bags of bird seed. Each bird feeder holds 16 of a bag.
How many bird feeders can be filled with the bird seed?
k bro i gochu
the answer is 84 man,
do good on ur hw
also can i get a pizza
PLEASEEEE HURRYY
On Giana's map of Texas, there is a close up view of the Dallas/Fort Worth area. The map scale is 1 inch = 3.5 miles. From Garland to Mansfield is 52.5 miles. How far apart are these two cities on the map?
Answer:
The distance between Garland and Mansfield on the map is 15 inches.
Step-by-step explanation:
On Giana's map of Texas, the scale is 1 inch = 3.5 miles. To determine the distance between Garland and Mansfield on the map, we can use the scale to find the corresponding measurement. Given that the actual distance between these two cities is 52.5 miles, we can set up a proportion:
1 inch / 3.5 miles = x inches / 52.5 miles
Cross-multiplying, we have:
3.5 miles * x inches = 1 inch * 52.5 miles
3.5x = 52.5
Dividing both sides by 3.5, we find:
x = 15
Therefore, the distance between Garland and Mansfield on the map is 15 inches.
For more questions on distance
https://brainly.com/question/28342342
#SPJ11
The owner of a computer store estimates profits using
the equation P = 4x² - 15x - 20 where P is the profit, in
dollars, and x is the number of
computers sold.
What is the estimated profit when 60 computers are
sold?
$26,400
$15,320
O $14,400
$13,520
$13,480
Answer:
(e) $13,480
Step-by-step explanation:
You want the estimated profit from selling 60 computers, if the profit from selling x computers is P = 4x² -15x -20.
ProfitPut 60 where x is in the profit equation and do the arithmetic.
The result is an estimated profit of $13,480.
__
Additional comment
To simplify evaluation, the polynomial can be written in "Horner form:"
P = (4x -15)x -20
Evaluating it this way takes fewer math operations and generally involves smaller numbers.
<95141404393>
Jayda is older than her 12-year-old sister. Write an inequality for j, Jayda's age.
The inequality states that Jayda's age (j) is greater than 12 i.e., j > 12.
Let j represent Jayda's age.
Since Jayda is older than her 12-year-old sister, we can write the inequality:
j > 12
Thus, the inequality states that Jayda's age (j) is greater than 12.
Learn more about Inequality here:
https://brainly.com/question/20383699
#SPJ1
The inverse of a conditional statement is "If a number is negative, then it has a negative cube root.”
What is the contrapositive of the original conditional statement?
If a number is negative, then it does not have a negative cube root.
If a number does not have a negative cube root, then the number is not negative.
If a number has a negative cube root, then the number is negative.
If a number is not negative, then it does not have a negative cube root.
The contrapositive of the original conditional statement is B. If a number does not have a negative cube root, then the number is not negative.
How to find the contrapositive ?In logic, the contrapositive of a conditional statement is a logically equivalent statement that switches the positions of the hypothesis and the conclusion, while also negating both.
The contrapositive maintains the logical validity of the original statement. If the original statement is true, then the contrapositive is also true, and vice versa. "If a number is negative, then it has a negative cube root." The contrapositive of this statement would be: "If a number does not have a negative cube root, then the number is not negative."
Find out more on contrapositive at https://brainly.com/question/1542283
#SPJ1
Each day, Nicole earns a fixed wage plus extra money for every hour of overtime she works. The graph shows her total pay (in dollars) versus the amount of
overtime (in hours) that she works.
Total pay
(dollars)
I Don't Know
737
Mostly cloudy
Overtime (hours)
Subm
(a) What is Nicole's total pay with 0 hours of overtime?
(b) Choose the statement that best describes how the amount
of overtime and total pay are related. Then fill in the blank.
Search
As the amount of overtime increases, the total pay
decreases.
At what rate is the total pay decreasing?
$ per hour
As the amount of overtime increases, the total pay
increases.
At what rate is the total pay increasing?
$ per hour
here is a rhombus.A strait line joining the midpoints of two of its sides are work out the size of angle a
The size of angle can be expressed as 130 degrees
How can the side of the angle be worked out?Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees.
Considering the given figure, if we look at the right top triangle we can deduced that it is an isosceles, then the supplementary angle of angle α can be calculated as
(180 - 80)/2
= 50 degrees.
Hence, α = 180 - 50
= 130 degrees.
Learn more about angle at:
https://brainly.com/question/25716982
#SPJ1
7. $60.00 in 5 hours
a. 12 hours for one dollar
b. 5/60
c. $12 per hour
d. $1.20 per hour
The calculated value of the unit rate of the situation is (c) $12 per hour
Calculating the unit rate of the situationFrom the question, we have the following parameters that can be used in our computation:
$60.00 in 5 hours
This means that
Time = 5 hours
Total costs = $60.00
using the above as a guide, we have the following:
Unit rate = Total costs / time
substitute the known values in the above equation, so, we have the following representation
Unit rate = 60.00/5
Evaluate
Unit rate = 12
Hence, the unit rate of the situation is (c) $12 per hour
Read more about unit rate at
https://brainly.com/question/4895463
#SPJ1
John received $200 dollars for his birthday. He went to Greenbriar Mail and purchased a pair of tennis shoes for $75.00. Then he went to the Cookie Store and bought $10.00 worth of cookies. Going to the car, John looked down and found $20.00 on the ground. How much money does John has now?
Help pleaseeeeeeeeee
16800 cubic inches of concrete is needed to make the stairs
How many cubic inches of concrete is needed to make the stairs?Rectangular prism is a three dimensional shape which consist of six faces. The two faces are at the top and bottom and the other faces are lateral faces.
The given stairs can be divided into 3 rectangular prisms as shown in the image attached.
Volume of a concrete needed = Volume of A + Volume of B + Volume of C
Volume of a rectangular prism = l × w × h
where l is the length, w is the width and h is the height
For A:
l = 40, w = 10 in and h = 7 + 7 + 7 = 21 in
For B:
l = 40, w = 10 in and h = 7 + 7 = 14 in
For C:
l = 40, w = 10 in and h = 7 in
Volume of a concrete needed = (40 * 10 * 21) * (40 * 10 * 14) + (40 * 10 * 7)
Volume of a concrete needed = 8400 + 5600 + 2800
Volume of a concrete needed = 16800 in³
Learn more about Rectangular Prisms on:
brainly.com/question/21308574
#SPJ1
PLS ANSWER WILL GIVE BRAINLIEST IF CORRECT (NO LINKS)
Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler's formula.
Answer:
The third option
Step-by-step explanation:
WINGSUIT A wingsuit flyer jumps off a tall cliff. He falls freely for a few seconds before deploying the wingsuit and -4.9x² +420, where y is = slowing his descent. His height during the freefall can be modeled by the function y the height above the ground in meters and x is the time in seconds. After deploying the wingsuit, the flyer's height is given by the function y = −3x + 200. deploy the wingsuit?
The total height of the flyer at any time after deploying the wingsuit would be;
y = -3x + 200 + (-4.9t² + 420),
Now, Based on the given information, we can use the two functions to determine the height of the wingsuit flyer at a particular time.
During the freefall, the height of the flyer can be calculated using the function
y = -4.9x² + 420.
Let's say the flyer falls freely for t seconds before deploying the wingsuit.
Therefore, the height at the moment of deploying the wingsuit would be,
y = -4.9t² + 420.
After deploying the wingsuit, the height of the flyer is given by the function
y = -3x + 200.
We can combine these two functions to get the total height of the flyer at any given time after deploying the wingsuit.
So, the total height of the flyer at any time after deploying the wingsuit would be;
y = -3x + 200 + (-4.9t² + 420),
where x is the time after deploying the wingsuit and t is the time of freefall before deploying the wingsuit.
Learn more about the addition visit:
https://brainly.com/question/25421984
#SPJ1
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
3/8 = (3 + AD)/20
8(3 + AD) = 60
24 + 8AD = 60
8AD = 36
A = 4 1/2
B is the correct answer.
can be repeated. Complete parts (a) and (b).
(a) What is the probability of randomly selecting the correct access code on the first try?
(b) What is the probability of not selecting the correct access code on the first try?
Question content area bottom
Part 1
a. The number of possible access codes. The number of different codes available is 343.
b. The probability of randomly selecting the correct access code on the first try is 0.003
How to calculate the probabilitya. To find the number of possible access codes. The number of different codes available is:
= 7* 7* 7
= 343
(b) The probability of randomly selecting the correct access code is nnothingwill be:
P = 1/343
= 0.003
Learn more about probability on
https://brainly.com/question/24756209
#SPJ1
The access code for a safe consists of three digits. Each digit can be any number from 0 through 6 , and each digit can be repeated. Complete parts (a) through (c). a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try? (a) Find the number of possible access codes. The number of different codes available is nothing . (b) What is the probability of randomly selecting the correct access code on the first try?
please help me with this math question with solutions please
2×+4=4!
Answer: x= 10
Step-by-step explanation:
2x+4=24
2x=24-4
2x=20
x=10
Answer:
Step-by-step explanation:
2x+4=4
subtract 4 from both sides
2x=0
divide by 2 on both sides
x=0
Help pls anyone I’m rlly bad at these
144.) The value of X if the two angles of the triangle are congruent would be = 4. That is option D.
145.) The equation that should be used to find the value of X would be = 13x -15 = 22x + 9. That is option H.
How to determine the value of X when two triangles are congruent?
For question 144.)
Two triangles are congruent means that the angles are equal to each other. That is;
2.3x +25 = 5.8x + 11
Bring like terms together;
5.8x-2.3x = 25-11
3.5x = 14
X = 14/3.5
= 4.
For question 145.)
When two parallel lines are being cut across by a diagonal line a relationship exists between the angles that are formed.
The two given angles are congruent;
That is;
13x -15 = 22x + 9
Therefore the expression that can be used to calculate X would be = 13x -15 = 22x + 9
Learn more about congruent angles here:
https://brainly.com/question/30449822
#SPJ1
I need help with this
Answer:
B. {1, 6, 7, 8} ∩ {6, 8, 9} = {6, 8}
Step-by-step explanation:
The intersection of two sets is a set containing the elements that are present in both sets.
{1, 6, 7, 8} ∩ {6, 8, 9} = {6, 8}
At hollywood connection, edgar plays laser tag 6 minutes for every 8 minutes he plays arcade games. If edgar plays arcade games for 48 minutes. for now many minutes will he play laser tag
Answer:
36
Step-by-step explanation:
48/8 = 6. 6*6 = 36.
Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.
What are the missing segment lengths shown in the image?
14√2
14
45
14√2
14√3
45
7√2 7√3
The legs of the big triangle are 14 units and the legs of the small triangle are 7√2 units
How to determine the lengths of the missing segmentsFrom the question, we have the following parameters that can be used in our computation:
The right triangles
The right triangles are special triangles with acute angles of 45 degrees
This means that the relationship between the legs and the hypotenuse of the triangles is
Hypotenuse = Leg√2
Leg = Hypotenuse/√2
Using the above as a guide, we have the following:
Leg = 14√2/√2
Leg = 14
i.e. the legs of the big triangle are 14 units
Leg = 14/√2
Leg = 7√2
i.e. the legs of the small triangle are 7√2 units
See attachment for the triangles
Read more about right triangles at
https://brainly.com/question/2437195
#SPJ1
Answer:
Step-by-step explanation:
A field in the shape of a right triangle is bordered on one side
by a lake, on another side by a street, and on a third side by a
tree line.
What angle does this lake make with the street?
Round only your final answer to the nearest degree.
Put just the number in the blank.
Lake
32 ft
Tree Line
18 ft
Street
Cos = 20/27 = 0.7407
so
angle that stream makes with the road = 42.2
answer
42 (Round only your final answer to the nearest degree)