Starting from the given system of equations:
[tex]\begin{gathered} 9x+y=16 \\ y=7x \end{gathered}[/tex]Since the variable y is already isolated in the second equation, we can use the substitution method to solve the system.
Replace y by 7x on the first equation:
[tex]\begin{gathered} 9x+y=16 \\ \Rightarrow9x+7x=16 \\ \Rightarrow16x=16 \\ \Rightarrow x=1 \end{gathered}[/tex]Then. substitute the value x=1 back into the second equation to find the value of y:
[tex]\begin{gathered} y=7x \\ \Rightarrow y=7(1) \\ \Rightarrow y=7 \end{gathered}[/tex]Therefore, the solution for this system of equations is:
[tex]\begin{gathered} x=1 \\ y=7 \end{gathered}[/tex]A worn, poorly set-up machine is observed to produce components whose length x follows a normal distribution with a mean equal to 14 centimeters and a variance equal to 9. Determine the probability that a component is at least 10 centimeters long. Round your answer to four decimal places.
80.64% probability that a component is at least 10 centimeters long.
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation , the z-score of a measure X is given by:
Z = x - μ / σ
Z-scores are used to measure how far a measure is from the mean. We find the p-value associated with this Z-score by looking at the z-score table after finding the Z-score. The p-value represents the probability that the measure is smaller than X, which is the percentile of X. The probability of the measure being greater than X is calculated by subtracting 1 from the pvalue.
μ = 14
Variance is 9.
The standard deviation is the square root of the variance.
So,
σ = √9 = 3
This is the pvalue of Z when X = 10
z = 10 - 14/3
z = -1.3
z = -1.3 has a p value of0.1936
1-0.1936 = 0.8064
80.64% probability that a component is at least 10 centimeters long.
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Answer:
0.7475
Step-by-step explanation:
The mean is μ=14, and the standard deviation is σ=9‾√=3.Open Excel. Click on an empty cell. Type =NORMDIST(12,14,3,1) and press ENTER.The probability, rounded to four decimal places, is P(X<12)≈0.2525.The desired probability is P(X≥12), so subtract from 1 to get P(X≥12)=1−0.2525=0.7475
What is the slope of the line created by this equation?
Considering the linear equation in slope-intercept form:
[tex]y=11.2x-1[/tex]The y-intercept of the line is the constant of the equation, in this case, the y-intercept is -1.
The slope of the line corresponds to the coefficient of the x-term, i.e. the value that multiplies x. For this line, the slope is equal to 11.2
help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
Answer:
Shorter leg = 2.5 ft
Longer leg = 6.5 ft
Step-by-step explanation:
Pythagorean theorem:Let the shorter leg = x ft
Longer leg = (x + 4) ft
Hypotenuse = 7 ft
[tex]\sf x^2 + (x +4)^2 = 7^2[/tex]
x² + x² + 2*x*4 + 4² = 49
x² + x²+ 8x + 16 = 49
2x² + 8x + 16 - 49 = 0
2x² + 8x - 33 = 0
This is a quadratic equation. We can use the below mentioned formula to find the value of x.
a = 2 ; b = 8 ; c = -33
b² - 4ac = 8² - 4 * 2 * (-33)
= 64 + 264
=328
[tex]\sf x = \dfrac{-b \± \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\sf x = \dfrac{-8 \±\sqrt{328}}{2*2}\\\\\\x= \dfrac{-8 \±18.11}{4}\\\\\\x =\dfrac{-8+18.11}{4} ; \ x=\dfrac{-8-18.11}{4} > > \text{this is rejected because sides of } \\\\ \text{a triangle cannot be measured in negative value}[/tex]
[tex]\sf x = \dfrac{-8+18.11}{4}[/tex]
[tex]\sf x = \dfrac{10.11}{4}\\\\x =2.5275[/tex]
x+ 4 = 2.5275 + 4 = 6.5275
Shorter leg = 2.5 ft
Longer leg = 6.5 ft
Answer: the length of the shoter leg is 2,5 feet
the length of the longer leg is 6.5 feet
Step-by-step explanation:
Let the length of the shoter leg is x feet
Than the length of the longer leg is (x+4) feet
We use Pythagoras' theorem:
[tex]\displaystyle\\x^2+(x+4)^2=7^2\\\\x^2+x^2+2(x)(4)+4^2=7(7)\\\\2x^2+8x+4(4)=49\\\\2x^2+8x+16-49=49-49\\\\2x^2+8x-33=0\\\\D=b^2-4ac\\\\Hence,\\\\D=8^2-4(2)(-33)\\\\D=8(8)+8(33)\\\\D=64+264\\\\D=328\\\\\sqrt{D}=\sqrt{328} \\\\x=\frac{-bб\sqrt{D} }{2(a)} \\\\x=\frac{-8б\sqrt{328} }{2(2)} \\\\x=-6.5277\notin (x > 0)\\\\x=2.5277\ feet\\\\x+4=2.5277+4\\\\x+4=6.5277\ feet[/tex]
Can someone please help me?
Graph the image of this figure after a dilation with a scale factor of centered at the origin.
Use the polygon tool to graph the dilated figure.
Answer:the real answer is (-2,1), (-1,4), (1,2)
Step-by-step explanation:
pls mark brainliest
Write the equation of the line that it is perpendicular to [tex]y = 7x - 3[/tex]and passes through the origin
Answer
The equation of the line is
y = (-x/7)
We can cross multiply and write it in the form of
7y = -x
OR
x + 7y = 0
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
The relationship between the slopes of two lines that are perpendicular to each other is
m₁m₂ = -1
m₁ = Slope of line 1
m₂ = Slope of line 2
For the given equation, if we compare its equation with y = mx + b,
y = 7x - 3
y = mx + b
m = 7, b = -3
We can now find the slope of the line we want.
m₁m₂ = -1
m₁ = 7
m₂ = ?
m₁m₂ = -1
(7)m₂ = -1
7m₂ = -1
Divide both sides by 7
(7m₂/7) = (-1/7)
m₂ = (-1/7)
Then we can find the equation of the line we want.
For that line,
m = slope = (-1/7)
b = y-intercept (where the line crosses the y-axis) = 0
This is obtained from the point given that the line passes through the origin, (0, 0)
So, we can write y = mx + b
y = (-1/7)x + 0
y = (-x/7)
We can cross multiply and write it in the form of
7y = -x
OR
x + 7y = 0
Hope this Helps!!!
Use the graph to answer the question.The vector u is graphed. Which of the vectors below would be orthogonal to vector u?
We can find the orthogonal vector when we use the dot product.
Then, the result must be equal to zero.
The vector u is given by coordinates <-7,-4>
Then, we need to find a vector in which their dor product will be equal to zero:
<-7,-4>*<1/7,-1/4> =-7*1/7 +(-4)*-1/4 = -1+1 =0
Therefore, the orthogonal vector is <1/7,-1/4>
The correct answer is option B
Answer:
Step-by-step explanation:
1.c
2.c
3.a
4.d
5.d
6.c
7. they are equal
8 A.a
8 B.d
9 A. c
9 B. b
10 A.c
10 B. b
11.b
12.d
13.b
14.b
15. a
16.d
17.c
18. 26.56 degrees
A scuba diver descends below the surface of a lake at a rate of 12 feet per minute. What is the depth of the diver after 4 minutes?
The depth of the diver after 4 minutes when a scuba diver descends below the surface of a lake at a rate of 12 feet per minute is 48 feet.
What is a rate?The concept that is used in the solution is the concept of rate in mathematics. A rate can be described as a special ratio having two terms that are in different units.
The rate that is been given is 12 feet per minute which implies that 12 feet will operate at the time of 1 minute. Then we were now given the depth of the diver after 4 minutes, using the given rate, then ;
12feet = 1mins
X feet = 4mins
where X is the depth of the diver after 4 minutes then we can cross multiply,
X= (4mins *12feet) / 1mins
= 48feets.
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Alejandro has a computer support business. He estimates that the cost to run his business can be represented by X = 48 x + 500, where x is the number of customers. He also estimates that his income can be represented by R = 65 x - 145. How many customers he will need in order to break even?
If Alejandro has a computer support business. The number of customers he will need in order to break even is 38 customers.
How to find the number of customers to break even?Given data:
Cost of business = 48 x + 500
Income = R = 65 x - 145
Let x is the number of customers. He
Income equation
R= 65x- 145
Substitute 48x + 500 for y
48x + 500 = 65x -145
Substract 48x from both side
500 = 17x - 145
Add 145 to each side
645 = 17x
Divide both side by 17x
x =645 /17
x = 37.9
x = 38 customers (Approximately)
Therefore the number or customers is 38 customers.
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i am having trouble with a question on my geometry homework. on how to do it
a) Given the triangle ABC, you have to do a counterclockwise 90º rotation of the figure.
To make said rotation you have to invert the coordinates of each point of the figure and invert the sign of the x-coordinate of the image point.
In general:
Preimage point; Image point
P(x,y) → P'(-y,x)
The y-coordinate turns into the x-coordinate and the x-coordinate turns into the y-coordinate.
The x-coordinate of the image point must have the opposite sing as the original one.
So for triangle ABC:
A to A'
(3,-2) → (-(-2),3)= (2,3)
B to B'
(3,-6) → (-(-6),3)= (6,3)
C to C'
(9,-2) → (-(-2),9)= (2,9)
The coordinates for the 90º counterclockwise rotation are A'(2,3), B'(6,3) and C(2,9)
b) Triange A'B'C' was translated a certain number of units, its new position is given as triangle A''B''C'':
A''(-3,-4)
B''(1,-4)
C''(-3,2)
To determine what kind of translation was done, first step is to draw triangle A''B''C'' and compare it to triangle A'B'C':
As you can see in the graphic, triangle A'B'C' was translated horizontally to the left a k number of units and vertically downwards a m number of units.
Horizontal translation
These translations are made over the x-axis, the translation factor k is added (movement to the rigth) or subtracted (movement to the left) from the x-coordinate of each point:
In this case the translation was made to the left, so:
Preimage point; Image point
P(x,y) → P'(x-k,y)
Vertical translation
These translations are made over the y-axis, this means that the translation factor m will be added (↑up) or subtracted (↓down) from the y-coordinates of each point.
For the example, the movement was downwards so we can express it as:
Preimage point; Image point
P(x,y) → P'(x,y-m)
You can unite both movements in the same expression as:
Preimage point; Image point
P(x,y) → P'(x-k,y-m)
Going a little further you can determine the amount of units the figure was translated by comparing a set of points from the preimage and image:
Given A'(2,3) and A''(-3,-4)
For the horizontal movement compare the x-coordinates. We know that to determine the x-coordinate of A'', k units were subtacted from the x-coordinate of A', so:
2-k=-3
-k=-3-2
-k=-5
k=5
For the vertical movement, compare the y-coordinates of both point. We know that m units were subtracted from the y-coordinate of A' to determine the y-coordinate of A'', so:
3-m=-4
-m=-4-3
-m=-7
m=7
This means that the translation rule for A'B'C' → A''B''C'' is (x-5,y-7)
Select the correct answer.
Consider this equation.
cos(8) = -
If 8 is an angle in quadrant II, what is the value of tanê)?
ОА.
15
8
ов. 15
ос. -
✓15
8
OD. 15
Given that:
[tex]\cos \theta=\frac{adjacent}{hypothenus}[/tex]and we are given that:
[tex]\cos \theta=-\frac{7}{8}[/tex]we can say that:
adjacent = 7, hypothenus = 8
And we can apply the Pythagorean theorem which is:
[tex]\text{hypothenus}^2=opposite^2+adjacent^2[/tex]Thus, we have that:
[tex]undefined[/tex]Write the number below in expanded notation. 14,422 A. 10,000 + 400 + 400 + 20 + 2 B. 10,000 + 4,000 + 400 + 20 + 2 C. 1,000 + 4,000 + 4 + 20 + 2 D. 1,000 + 400 + 40 + 2 + 2
Let's begin by listing out the information given to us:
[tex]14,422[/tex]Expanded notation is a form of writing in which the value of each digit; it arranges the digit in their values of tens, hundreds, tens etc.
[tex]\begin{gathered} 14,422\Rightarrow1\cdot10,000+4\cdot1,000+4\cdot100+2\cdot10+2\cdot1 \\ \Rightarrow10,000+4,000+400+20+2 \end{gathered}[/tex]Hence, option B is the correct answer
for each of the 7 you have to determine whether its alternative exterior angles, same side interior angles, vertical angles, alternate interior angles, definition of a parallelogram, SAS, Or Given
Statement Reason
WXYZ is a parallelogram Given
WX || ZY and WZ || XY Definition of a parallelogram
∠ZYW ≅ ∠XWY Alternate interior angles
WX ≅ YZ Definition of a parallelogram
WY ≅ WY Reflexive property of congruence
ΔWXY ≅ ΔZYW SAS
∠X ≅ ∠Z CPCTC
I have took a picture of the question and attached it here.
Given:
[tex](3-4i)(6i+7)-(2-3i)[/tex]1. Arrange the expression, with the variables are written first
[tex](-4i+3)(6i+7)-(-3i+2)[/tex]2. Distribute the "minus" operation
[tex](-4i+3)(6i+7)+3i-2[/tex]3. Expand by multiplying the first two expressions
[tex](-4i+3)(6i+7)[/tex]*multiply the first terms
[tex](-4i)(6i)=-24i^2[/tex]*multiply the outer terms
[tex](-4i)(7)=-28i[/tex]*multiply the inner terms
[tex](3)(6i)=18i[/tex]*multiply the last terms
[tex](3)(7)=21[/tex]This will give us:
[tex](-24i^2-28i+18i+21)[/tex]*combine like terms
[tex](-24i^2-10i+21)+3i-2[/tex]*Remove the parenthesis
[tex]-24i^2-10i+21+3i-2[/tex]4. Combine like terms
[tex]-24i^2-7i+19[/tex]The final answer would be:
[tex]-24i^2-7i+19[/tex]4x 3y2 Evaluate the expression for x = 3 and y = 4.
Explanation
[tex]-\frac{4x^3}{3y^2}[/tex]Step 1
to find the answer just replace the values for x and y
for x=3 and y =4
[tex]\begin{gathered} -\frac{4x^3}{3y^2} \\ -\frac{4(3)^3}{3(4)^2}=-\frac{4\cdot(3\cdot3\cdot3)}{3\cdot(4\cdot4)}=-\frac{4\cdot27}{3\cdot16}=-\frac{27}{12}=-\frac{9}{4} \end{gathered}[/tex]I hope this helps you
PLEASE HELP ASAP!!!!!
Answer the answer is 12 units:
Step-by-step explanation:
A cat of mass 4kg jumps on a dining table of mass 28kg. As the cat walks around on the table, what is the average force that the table applies to the cat? (gravity is 10 meters per second-squared)
*
1 point
7N
280N
.4N
40N
2.8N
The average force that the table applies to the cat is 40N, by using newton's law.
What is the meaning of acceleration?
Acceleration: the rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting.
Given that the mass of the cat is 4 kg. The gravity is 10 meters per second-squared.
Force is the product mass and acceleration.
Mass = 4 kg
Acceleration = 10 ms⁻².
The force that the table applies to the cat is (4 kg × 10 ms⁻²) = 40 N.
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Jack earns $5250 per month. Jill earns $1143.50 a week. Who earns more per year, and by how much?
A square measures 8cm to the nearest
cm. What is the largest and smallest
possible area of the square?
Answer: smallest area- 56.25cm2 largest area- 70.56cm2
find the equation in point slope form of the line that lasses through the point (1,2) with the slope m=2/3
Input data
Point = (1, 2)
m = 2/3
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
[tex]\begin{gathered} b=y-mx \\ b=2-\frac{2}{3}1 \\ b=2-\frac{2}{3} \\ b=\frac{4}{3} \end{gathered}[/tex]The equation of the line that passes through the point (1,2) with a slope of 2/3
[tex]y=\frac{2}{3}x+\frac{4}{3}[/tex][tex]y-2=\frac{2}{3}(x-1)[/tex]Help! graph the systems of equations. {2x+y=8 −x+2y=6
A system of equations is simply a collection of equations that can be dependent, independent, consistent, or inconsistent.
2x + y = 8x - 2y = -6 is x,y = 2,4
How are equations graphed?To graph the equation, choose three x values and list them in a table. (Hint: choose values that are easy to calculate, such as 1, 0 and 1). Simplify the equation by substituting each value to find the associated y-coordinate. Draw a line between each point on a graph with the sorted pairings.A system of equations is simply a collection of equations that can be dependent, independent, consistent, or inconsistent.Given equation,
2x + y = 8x - 2y = -6
x,y = 2,4
[1] 2x + y = 8
[2] x - 2y = -6
Solve [2] for the variable x
[2] x = 2y - 6
Plug this in for variable x in [1]
[1] 2•(2y-6) + y = 8
[1] 5y = 20
Solve [1] for the variable y
[1] 5y = 20
[1] y = 4
By now we know this much
x = 2y-6
y = 4
Use the y value to solve for x
x = 2(4) -6 = 2
Hence, {x,y} = {2,4}
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A contractor bought 8.2 ft² of sheet metal. He has used 4.9 ft² so far and has $52.80 worth of sheet metal remaining. The
equation 8.2x -4.9x = 52.8 represents how much sheet metal is remaining and the cost of the remaining amount. How much
does sheet metal cost per square foot?
Sheet metal costs : per square foot.
1
The cost of the sheet metal per square foot is $30.
The first step is to determine the square feet that the contractor used. This can be determined by subtracting the square feet of sheet she bought from the sheet metal she has used so far.
Sheet metal used = 8.2 - 2.1 = 6.1 square feet.
This means that 6.1 square feet costs $183.
The second step is to determine the cost of one square feet of sheet metal. This can be determined by dividing $183 by 6.1
$183 / 6.1 = $30
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Lena uses 2 cups of flour for a batch of cookies, 2 1/2 cups for loaf of bread, and 1/2 cups for dusting her workbench. Let c be the number of cookie batches and b be the number of bread loaves Lena makes. Which of the following expressions could represent how much flour she uses?
The expression that could represent how much flour Lena uses for baking cookies and bread is 2c + 2 1/2b + 1/2.
What is an algebraic expression?
An algebraic expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.
For example 2x + 4, 58m + 2n, 100p + 3q + r.
According to the given question:
(Question with options is attached below)
Let c be the number of cookie batches and b be the number of bread loaves Lena makes.
Lena makes 2 cups of flour for a batch of cookies
∴ Flour used to make cookie batches = 2c
She uses 2 1/2 cups for loaf of bread
∴ Flour used for bread loaves = 2 1/2 b
Ans 1/2 cup flour is used for dusting workbench
Hence expression for the amount of flour used is sum of flour used for making batches of cookies, bread loaves and for dusting.
The expression is 2c + 2 1/2b + 1/2
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3. If the length of a rectangular garden is 2 feet less than the length of a house and the
width of the garden is 5 feet less than half the length of the house, what is the
expression for the area of the garden?
A. 0.5x² - 6x + 10
B. 0.5x²+6x-7
C. 0.5x+10
D. 1.5x² - 6x + 10
E. 1.5x²-6x + 10
Answer:
A. 0.5x² - 6x + 10
hope you get a point
What equation is graphed in this figure? y+2=(x - 2) y+1=(x − 3) y -4 = (x+2)y-3 =3/2 (x+1)
the Answer:is y=-3x+1 so it would b c:)
is y= -4 a linear equation?
Answer:
Yes
Step-by-step explanation:
Answer: yes it is linear
Step-by-step explanation: linear line is a straight line and y=-4 is 1 line so it is linear
identify which are functions (2, 3) , (2,4), (3,6)
ok
Could you send me all the options?
A function is a relationship between two magnitudes (x, y). In which, each value of the first corresponds to a single value of the second
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 2.5, 5.4
Step-by-step explanation:
[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]
Andrea is 108 miles away from Destiny. They are traveling towards each other. If Destiny travels 9 mph faster than Andrea and they meet after 4 hours, how fast was each traveling?
The given information is:
Andrea is 108 miles away from Destiny.
Destiny travels 9 mph faster than Andrea.
They meet after 4 hours.
Let's convert that information into equations:
Let's call x the distance that Destiny travels to find Andrea and y the distance Andrea travels to find Destiny, then:
[tex]x+y=180\text{ Eq. (1)}[/tex]If they meet after 4 hours, the equation for the distance Destiny traveled is:
[tex]\text{velocity}\cdot\text{time}=\text{distance}[/tex]But the problem also says that Destiny travels 9 mph faster than Andrea, then let's call z the mph that Andrea is traveling, thus:
[tex](z+9)\cdot4=x\text{ Eq. (2)}[/tex]And the equation for the distance Andrea traveled is:
[tex]z\cdot4=y\text{ Eq.(3)}[/tex]Then you have a system of 3 equations and 3 variables.
Let's solve it to find how fast each was traveling.
From equation 3 you know that y=4z. You can replace the y-value into equation 1, you will obtain:
[tex]x+4z=180\text{ Eq. (4)}[/tex]Next, you can solve for x in terms of z, from equation 4:
[tex]x=180-4z\text{ Eq.(5)}[/tex]Replace the x-value into equation 2 and solve for z:
[tex]\begin{gathered} (z+9)\cdot4=180-4z \\ \text{Apply distributive property} \\ 4z+36=180-4z \\ \text{Add 4z to both sides} \\ 4z+36+4z=180-4z+4z \\ 8z+36=180 \\ \text{Subtract 36 from both sides} \\ 8z+36-36=180-36 \\ 8z=144 \\ \text{Divide both sides by 8} \\ \frac{8z}{8}=\frac{144}{8} \\ z=18 \end{gathered}[/tex]Then if z=18 mph, this is how fast Andrea is traveling.
And Destiny travels 9 mph faster than Andrea, then Destiny travels at (z+9)=18+9=27 mph
Express the integral as a limit of Riemann sums using right endpoints. Do not evaluate the limit.
Answer:
23,207/210
Step-by-step explanation:
[tex]\int\limits^7_4 {x^{2}+\frac{1}{x} } \, dx \\[/tex]
Right endpoints start at 7
It doesn't say how many so I will assume there are 3.
7, 6, 5
Plug in those values into the integrand:
7^2+ 1/7=
49+1/7
6^2+1/6=
36+1/6
5^2+1/5=
25+1/5
1(49+1/7+36+1/6+25+1/5)
110+1/7+1/6+1/5 The least common factor of 7,6,5 is 210
[tex]110 + \frac{30+35+42}{210} \\110 + \frac{107}{210} \\\frac{23,100+107}{210} \\\\\frac{23,207}{210} \\[/tex]