[tex]The two equations given arey = x …. (1)x2 + y2 = 1 …. (2)Substitute equation (1) in (2)x2 + x2 = 12x2 = 1x2 = ½x = √1/2x = ±0.707As the square can be positive or negative we get x1 = 0.707 and x2 = -0.707From equation (1) we know that y = xy1= x1= 0.707y2= x2 = -0.707Therefore, the line y = x intersects the unit circle x2 + y2 = 1 at (0.707, 0.707) and (-0.707, -0.707).[/tex]
What is intersect?A junction is a place where two lines come together or cross. In the illustration above, "point K is the intersection of line segments PQ and AB" is what we would state. The phrase "the line segment PQ crosses AB at position K" is another option.
Keep in mind that two line segments do not always need to intersect. In the illustration above, move point B higher until the intersection of the two line segments disappears. However, keep in mind that lines (as opposed to line segments) continue indefinitely in both directions, thus unless they are absolutely parallel, they will always cross someplace.
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multiple choice question. with explanation needed.
Answer: 4
Step-by-step explanation:
a store normally sells windows at $100 each. This week the store is offering one free window for each purchase of 4. Dave needs 7 windows and Doug needs 8. How much money will they save if they purchase together rather than separately?
They will save $100 if they purchase together rather than separately.
If this week, the store is offering one free window for each purchase of 4, then the price of 5 windows will be just equal to the price of 4.
1 window = $100
5 windows = 4 x $100 = $400
If
Dave needs 7 windows
Doug needs 8 windows
total they need together = 7+8 = 15 windows.
Buying at the offer of $400/5 windows,
they should buy 3 sets of 5 windows.
3 x 5 = 15
cost when bought together : 3 x $400
cost when bought together : $1200
If they bought separately,
Dave : 7 = 5 + 2
cost = $400 + 2($100)
cost = $600
Doug : 8 = 5 + 3
cost = $400 + 3($100)
cost = $700
cost when bought separately : $600 + $700
cost when bought separately : $1300
compare the two total costs and to determine how much they will save.
$1300 - $1200 = $100
They will save $100 if they purchase together rather than separately.
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Does the following expression have a value greater than 2? - 3+ (+4) +2
Yes, the resulting value of the expression is 3 which is greater than 2.
Expression:
Expression is defined as a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
An expression contains the following:
Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.
Coefficient: A coefficient is a number that is multiplied by a variable in an expression.
Given,
Expression = -3 + (+4) + 2
Here we need to check the resulting value of the expression is greater than 2 or not.
For that, first we have to simplify the given expression,
Then,
=> -3 + ( 4 + 2)
=> -3 + 6
=> 3
Now, we have know that 3 is greater than 2.
So, the expression is greater than 2.
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the data to the right represent the top speed (in kilometers per hour) of all the players (except goaltenders) in a certain soccer league. find (a) the number of classes, (b) the class limits for the second class, and (c) the class width.
which of the following statements is not correct? fewer students in the sample listed volleyball as their favorite sport than football. more students in the sample listed lacrosse as their favorite sport than basketball. more students in the sample listed basketball as their favorite sport than volleyball. the highest percentage of teenagers in the sample listed soccer as their favorite sport.
The highest percentage of teenagers in the sample listed soccer as their favorite sport. this option is correct .
What does a statistical pie chart mean?
A pie chart, often known as a circle chart, is a visual representation of the various values of a specific variable or a means to summarize a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments. A certain category is represented by each segment.Pie charts are circular charts with segments that each indicate a value and are used in data handling. Pie charts have portions (or "slices") that depict varying sizes of values. For instance, an entire class is represented by the circle in this pie chart.In this question pie chart is showing data of games .
So. by observing the chart we can say that ,
the highest percentage of teenagers in the sample listed soccer as their favorite sport.
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A projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall. the path of the projectile is modeled using the equation h(t) = â€""16t2 48t 190.approximately when will the projectile hit the ground?1.5 seconds3.2 seconds5.3 seconds6.2 seconds
The time for the projectile to hit the ground from the given position is 1.5 s, which is obtained using the concept of time period and velocity of a projectile.
What is a projectile?
A projectile is defined as an object that has the force of gravity as the only force occurring on it. Acceleration in the projectile motion always acts vertically.
Calculation of the time taken by projectile to hit the ground
The given parameters:
The starting velocity of the projectile, u = 48 ft / s
Height of the projectile, h = 190 ft
Model of the projectile path, h(t) = - 16(t)2 + 48t + 190 —-- 1
When the projectile hits the ground, the final velocity, v = 0
differentiating equation 1 w.r.t t, we get,
(dh(t)) / (dt) = - 32t + 48
Putting dh(t) / dt = 0, we have,
- 32t + 48 = 0
32t = 48
t = 48 / 32
t = 1.5 s
Hence, the time taken by the projectile to hit the ground is 1.5 s.
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Several batches of stew were made yesterday. Each batch required 1 and two-thirds pounds of meat. All together, 10 and StartFraction 5 over 6 EndFraction pounds of meat was used. Janice tried to find the number of batches of stew made. Her work is shown below.
Answer:
Step-by-step explanation:
Answer:
no of batches of street made is 2345
srry i don't know
Step-by-step explanation:
5(6+5v)+5(-8-4v) pls explain how to do this
Answer:
-10 + 5v
Step-by-step explanation:
5(6 + 5v) + 5(-8 - 4v)
We distribute first
30 + 25v -40 - 20v
Then we can combine like terms: 30 plus (-40) is -10. 25v plus (-20v) = 5v.
-10 +5v
Can someone help me with these? ASAP please
a. Length of AB = 7 units
Length of CDS = 3 units
Line segment AB and line segment CD are not congruent.
b. Length of AB = 7 units
Length of CD = 7 units
Line segment AB and line segment CD are congruent.
c. Length of AB = 9 units
Length of CD = 7 units
Line segment AB and line segment CD are not congruent.
How to Find the Length of a Segment?Given two points on a coordinate plane, where the two points are on a horizontal or vertical line, the distance between the two points is the absolute difference between their coordinates.
a. Given:
A(10, -4)
B(3, -4)
C(-1, 2)
D(-1, 5)
Length of AB = |10 - 3| = |7|
Length of AB = 7 units
Length of CD = |5 - 2| = |3|
Length of CDS = 3 units
Line segment AB and line segment CD are not congruent.
b. Given:
A(-5, 6)
B(-5, -1)
C(-4, 3)
D(3, 3)
Length of AB = |6 - (-1)| = |7|
Length of AB = 7 units
Length of CD = |-4 - 3| = |-7|
Length of CD = 7 units
Line segment AB and line segment CD are congruent.
c. Given:
A(8, 3)
B(-1, 3)
C(5, 10)
D(5, 3)
Length of AB = |8 - (-1)| = |9|
Length of AB = 9 units
Length of CD = |10 - 3| = |7|
Length of CD = 7 units
Line segment AB and line segment CD are not congruent.
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question 15(multiple choice worth 1 points) (03.02 lc) abcd is a rectangle. what is the value of x? rectangle with length 56 m, width x m, and diagonal 65 m 9 meters 28 meters 33 meters 65 meters
The width of the rectangle is: 33m, by Pythagoras theorem.
What is Pythagoras Theorem?The Pythagorean Theorem describes a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.Now,
given:
Length of rectangle = 56m (say, l)Diagonal = 65m (say, d)TO find: Width of rectangle = ? (say, w)
Finding:
BY Pythagoras theorem, in the rectangle ABCD,
For l = AB, w = BC and d = AC,
=> l² + w² = d²
Ob substituting the values, we get: 56² + w² = 65²
=> w² = 65² - 56²
=> w² = 4225 - 3136
=> w² = 1089
=> w = 33m
Hence, for the given values of rectangle, the width of the rectangle is 33m by Pythagoras Theorem.
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Tanisha and some friends are going to the movies. At the theater, they sell a bag of
popcorn for $5.50 and a drink for $4. How much would it cost if they bought 4 bags
of popcorn and 6 drinks? How much would it cost if they bought p bags of popcorn
and d drinks?
Al caer la tarde, la temperatura en seattle era de 7 C. A medianoche ‘ la temperatura había caído 15C cual era la temperatura a media noche
Answer:
hh jkj
Step-by-step explanation:
Answer:
al la trade la temperature en Seattle
Era de 7c a medical
Step-by-step explanation:
b. Find the change in temperature if the temperature rises from -18°F to 15°F.
The change in temperature is 33°F.
According to the question we have been given that there are two temperature readings which are, -18°F and 15°F.
We need to find the change in temperature that is we need to find the difference. And for that we will use distance formula.
The formula to find the distance between the two numbers p and q is
= |p-q|
Here , p = -18°F and q = 15°F
Putting the required values in the above formula we get
= |-18 - 15| °F
= |-33| °F
= 33°F
Hence the change in temperature is 33°F.
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The function g is defined as follows
g(x)=2x^2-7
If the graph is translated vertically downward by 3 units, it becomes the graph of a function h
FIND THE EXPRESSION OF h(x)
H(X)=
Here is how the function g is defined.
g(x)=2x²-7 The graph becomes the graph of a function h if the graph is translated vertically downward by 3 units. The function of h(x)=2x²-4.
Given that,
Here is how the function g is defined.
g(x)=2x²-7
The graph becomes the graph of a function h if the graph is translated vertically downward by 3 units.
We have to find the function of h(x).
Translation of the quadratic function.
A quadratic function is presented in the form where in its standard form.
f(x)=a(x-h)²+k
Where (h,k) are the vertex. This form is also referred to as the vertex form of a quadratic function because the vertex occurs in the quadratic function's standard form.
h(x)=g(x)+k
Where g(x)=2x²-7 and k=3
h(x)=g(x)+3
h(x)=2x²-7+3
h(x)=2x²-4
Therefore, the function of h(x)=2x²-4.
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how to solve? …………….
Solution:
[tex]3(2x+3)[/tex]
Hope this helps!
Round 3,487,967 to the nearest ten thousands
Answer:
3,490,000
Step-by-step explanation:
3,487,967 = (87967) The 7 rounds up so the 8 would become 9.
j² 5k for j = -4 and k = -1
Answer: -80
Step-by-step explanation:
j = -4 and k = -1
j² 5k=
5kj²=
5(-1)(-4)²=
-5(16)=-80
There are 140 cars in a parking lot. Keisha looks at 15 cars and sees that two of them are red. Aproximately, how many red cars are in the parking garage?
Liam is 3 years older than his little sister Carin. Together they're 31 years old. How old is Liam? Solve the problem with an equation
Answer: Liam is 17
Step-by-step explanation: 17-14= 3. 17 + 14 = 31
Approximate √18 to the nearest tenth and plot
the number on a number
line.
Answer: 4.2
Step-by-step explanation:
√18=
4.24=
4.24=4.2
Example 8
A school received a shipment of laptops and tablets purchased for $35,100 for their new
computer lab. Each tablet cost $375 and each laptop cost $850. If the school ordered 3 times as
many laptops as tablets, then which of the following is the number of laptops in the shipment?
The shipment contained 12 tablets and 36 laptops.
What is an equation?An equation is used to show the relationship between numbers and variables. An equation can be linear, quadratic depending on the degree.
Let x represent the number of tablets and y represent the laptop.
Each tablet cost $375 and each laptop cost $850, hence:
375x + 850y = 35100 (1)
Also:
y = 3x (2)
From both equations:
x = 12, y = 36
The shipment contained 12 tablets and 36 laptops.
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hello ! how's you're day, I hope it's doing good Im proud of ur work !
Answer:
thanks, I needed That
Step-by-step explanation:
brainliest
Write down the inequality described by "negative three groups of x is less than two", and solve for x
Answer:
- 3x < 2
x < - 1
Explanation and Check part below
Explanation and Check part belowHope this helps :)
Step-by-step explanation:
1. To solve, first isolate the variable by doing the inverse operation which is in this case dividing by - 3 on both sides of the equation.
- 3x < 2
- 3 -3
x < - 1
2. Graph it if needed with an open dot because - 1 is not part of the set of solutions.
<--------○
<----l----l-----l----->
-2 -1 0
Check:
1. Substitute x with any number less than - 1 and solve.
- 3 (- 2) < 2
-6 < 2
True statement.
9. Bus A arrives every 12 minutes and Bus B arrives every 15 minutes. Both buses arrive
together at 9am, what time do they next arrive together
============================================================
Explanation:
12 = 3*4
15 = 3*5
The GCF of 12 and 15 is 3
LCM of x and y = (x*y)/(GCF of x and y)
LCM of 12 and 15 = (12*15)/(GCF of 12 and 15)
LCM of 12 and 15 = (12*15)/(3)
LCM of 12 and 15 = 60
-------------------
We can confirm this by listing out the multiples of each
multiples of 12 are: 12, 24, 36, 48, 60, 72, ...
multiples of 15 are: 15, 30, 45, 60, 75, ...
-------------------
Since the LCM is 60, this means their schedules line up every 60 minutes, aka 1 hour.
If they arrive together at 9 AM, then their next arrival time together is 10 AM which is the final answer.
Find the coordinates of the centroid of the triangle with the given vertices. (Lesson 5-2)
X(-11,0), Y(-11,-8), Z(-1,-4)
The triangle with vertices located at X(-11 , 0), Y(-11 , -8), and Z(-1 , -4) has its centroid located at (-23/3 , -4).
The centroid of a triangle is the point inside the triangle where the three medians intersect. The median of a triangle is the line the connects the midpoint of a side and the opposite vertex.
To get the centroid of a triangle, use the formula given by:
C(x , y) = [(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]
where C is the centroid of the triangle located at (x , y)
x1, x2, and x3 are the x-coordinate of the vertices of the triangle
y1, y2, and y3 are the y-coordinate of the vertices of the triangle
Let Point 1(x1 , y1) = X(-11 , 0)
Point 2(x2 , y2) = Y(-11 , -8)
Point 3(x3 , y3) = Z(-1 , -4)
Plug in the values in the formula.
C(x , y) = [(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]
C(x ,y) = [(-11 + -11 + -1)/3 , (0 + -8 + -4)/3]
C(x ,y) = (-23/3 , -12/3)
C(x ,y) = (-23/3 , -4)
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URGENT!! ILL GIVE BRAINLIEST! 100 POINTS
Maria wanted to bring back 5 million grams of sand from her trip to the beach. Each grain of sand weighs approximately 6.7 x 10^-7 kg. How heavy is the bag of sand that Maria brings home?
Answer:
3.35kg
Step-by-step explanation:
Answer:
Multiply (5,000,000 x 6.7 x 10^-7) = (5 x 10^6) x (6.7 x 10^-7) = (5 x 6.7) x (10^(6 + - 7)) = 33.5 x 10^-1 = 3.35 kg
Step-by-step explanation:
estimate the square root of 60 to one decimal place
Algebra 1
1.1 Evaluating Expressions
Evaluate each using the values given.
1) z−5+ x; use x = 1, and z = -3
Evaluating Expressions-
z−5+ x= -7
x = 1, and z = -3
z−5+ x=-3 + (-5) + 1
= -3-5+1=-7
to assess an algebraic expression way to find the price of the expression while the variable is changed by using a given range.
to evaluating expression, we replacement the given range for the variable within the expression and then simplify the expression the use of the order of operations
What does “Evaluating Expressions” suggest?
Simplification of expressions can be performed with the help of operations’ order. It consists of changing the variable to discover the expression’s fee. The given number is substituted to evaluate expressions. After this, one needs to simplify it primarily based at the order of the operations
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multiply or divide write your answer in simplest form 3/6 x 7/10
Answer:
0.35
Step-by-step explanation:
3/6=1/2
7/10=0.7
1/2=0.5,0.5×0.7
=0.35
Answer: 7/20
Step-by-step explanation:
3/6*7/10= 0.35
First write down the decimal number divided by 1 like this:
0.35
1
As we have 2 digits after the decimal point in the numerator, we need to multiply both the numerator and denominator by 102 = 100, so that there is no decimal point in the numerator
0.35 × 100
1 × 100
=
35
100
Since the greatest common factor of 35 and 100 is 5, we can simplify the fraction and show the same amount
35 ÷ 5
100 ÷ 5
=
7
20
Therefore, 0.35 as a fraction is 7/20
8 as a product of three primes
Answer: 2x2x2 or 2 cubed
Step-by-step explanation: 2x2=4 2x4=8