Answers
Answer:
Line 1: [tex]y=-x+2[/tex]
Line 2: [tex]y=2x-1[/tex]
Step-by-step explanation:
Line 1
Staring with line one, let's find the slope!
Between the two known points, the rise, or change in y, is 2, and the run, or change in x, is -2. The slope is the rise over the run, so:
[tex]-\frac{2}{2} =-1[/tex]
The slope is negative 1! The line crosses the y-axis at [tex]y=2[/tex], so 2 is the y-intercept. Using the slope-intercept formula, the equation is:
[tex]y=-x+2[/tex]
Line 2
To find the slope of line 2, find the rise and the run between the two known points! The rise is 4, and the run is 2. Simplified, this is:
[tex]\frac{4}{2} =2[/tex]
The slope is 2! The line crosses the y-axis at [tex]y=-1[/tex], so -1 is the y-intercept. Using the slope-intercept formula, the equation is:
[tex]y=2x-1[/tex]
Answer:
y=2x-1 , y=x+2 , the solution of the system is (1,1)
Step-by-step explanation:
Lines can be expressed in the form y=mx+b where m is the slope and b is the y-intercept.
m= rise/run
Looking at the blue line:
m =2/1 =2
The slope is 2 since you rise 2 squares and run to the right one square.
We see that the line crosses the y-axis at (0,-1) so the y-intercept is -1.
Putting it all together: y=2x-1
Looking at the red line:
m = -1 / 1 = -1
We see that the line crosses the y-axis at (0,2) so the y-intercept is 2.
Putting it all together: y=1x+2 or simply y=x+2
The solution to the system is the point that satisfies both equations. Rather than solving it algebraically, we can simply look at the graph and find a point that is on both lines, aka the intersection. In this case, the intersection is (1,1).
Related Questions
Use the Law of Cosines. Find x to the nearest tenth.
B
15
24
16
Answers
Using the Law of Cosines, the value of x is 40.9°.
Cosine formula, cos A [tex]=\frac{b^{2}+c^{2}-a^{2} }{2bc}[/tex].
Here, A = x
a = 16
b = 15
c = 24
cos x [tex]=\frac{15^{2}+24^{2}-16^{2}}{2*15*24}[/tex]
[tex]=\frac{225+576-256}{720}[/tex]
[tex]=\frac{801-256}{720}[/tex]
[tex]=\frac{545}{720}[/tex]
= 0.756
x [tex]= cos^{-1}0.756[/tex]
= 40.9
Hence, value of x is 40.9°.
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Eva bought seven and one-half pounds of chocolate chips. She used three and three-fourths pounds in some cookies and two and five-sixths pounds in some muffins. How many pounds of chocolate chips were left?
three-twelfths pounds
eleven-twelfths pounds
one and two-twelfths pounds
one and seven-twelfths pounds
Answers
The amount of chocolate left is three and seven-twelfths pounds
How to find the amount of chocolate leftThe amount of chocolate left is found by addition and subtraction of fraction
The fraction required are:
Eva bought seven and one-half pounds of chocolate chips = 7 1/2
She used three and three-fourths pounds = 3 3/4
two and five-sixths pounds in some muffins = 2 5/6
total amount used = addition of amount used
3 3/4 + 2 5/6
= 3 11/12
the amount left is gotten by subtraction of amount used from amount Eva bought
= 7 1/2 - 3 11/12
= 3 7/12
this is three seven-twelfths
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Graph the polygon with vertices A(-3,-1), B(2, 2), C(3,-3) and its image after a rotation 90° about the origin
What are the points???
Geometry chapter 4 review
Answers
The image of the polygon after rotation of 90° about the origin is A'(-1, 3) , B'(2 , -2) , C'(-3 , -3) , the graph of the polygon and its image is shown below .
In the question ,
it is given that ,
the vertices of the polygon is A(-3,-1), B(2, 2), C(3,-3) .
the graph of the polygon ABC is shown below .
We know when the point (x , y) is rotated 90° in clockwise direction , it s coordinate change to (y , -x) .
So , image of coordinate A(-3,-1) is
A'(-1,-(-3)) = A'(-1, 3)
image of coordinate B(2, 2) is
B'(2 , -2)
image of coordinate C(3,-3) is
C'(-3 , -3)
So , the graph of the image with coordinates A'(-1, 3) , B'(2 , -2) , C'(-3 , -3) is shown below .
Therefore , The image of the polygon after rotation of 90° about the origin is A'(-1, 3) , B'(2 , -2) , C'(-3 , -3) , the graph of the polygon and its image is shown below .
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a. Create a quadratic expression in standard form. An expression does NOT have an equal sign. Quadratic has the form ax^2+bx+c where you pick numbers for a, b, and c. You will need to find (b/2)^2; what will make that easier? LOOK (Links to an external site.)Links to an external site. here is a short video that demonstrates how to do this, please do not use x2 +16x in your example.
b. Rewrite the expression by completing the square. Explain your work using complete sentences.
Use the order of operations to turn the expression back into standard form. Explain your work using complete sentences.
Explain why completing the square will always result in a perfect square trinomial.
Answers
f(x) = ax? + bx + c
(b) To complete the square:
Divide the equation through by a , the equation then becomes
At this point, you are require to
(i) multiply the coefficient of x by 1/2
(I) square the result
(ili) add the result to both sides , we have
4(x) =27+ + (2) + + (2a) by completing the square, we have
4x) = (a + da) + & - *. We did this in order to make the expression balance
(c) Using the order of operation to turn the expression back into standard
form
What is the equation of the line that passes through the point (5, 3) and has a slope of 3/5?
Answers
Answer:
y -3 = 3/5(x -5) . . . . point-slope formy = 3/5x . . . . . . slope-intercept formStep-by-step explanation:
You want the equation of the line with slope 3/5 that passes through point (5, 3).
Point-slope formThe point-slope form of the equation of a line with slope m through point (h, k) is ...
y -k = m(x -h)
You have m=3/5, (h, k) = (5, 3), so your equation is ...
y -3 = 3/5(x -5) . . . . point-slope form of desired equation
Slope-intercept formThis can be simplified to ...
y -3 = 3/5x -3
y = 3/5x . . . . . . . add 3
A scale drawing of a rectangular blacktop
is 21 inches by 12 inches. If the actual
blacktop is 126 feet by 72 feet, which is
the scale used for the drawing?
Answers
Answer:The area A of a rectangle is represented by the formula A=lw where l is the length and w is the width. The length of the rectangle is 5.
Write an equation that makes it easy to find the width of the rectangle if we know the area and the length.
Step-by-step explanation:
Determine the convergence of divergence of the sequence. If the sequence converges, find its limit.
Answers
The sequence converges and its limit is zero
What is a sequence?A sequence is an ordered set of numbers governed by a rule.
What is the limit of a sequence?The limit of a sequence is the value the sequence approaches
What is convergence of a sequence?The convergence of a sequence is when the sequence approached a definite value
What is divergence of a sequence?The divergence of a sequence is when the sequence does not approach a definite value.
How to determine the convergence of divergence of the sequence?Since we have the sequence (√3 - √1), (√4 - √2), (√5 - √3), (√6 - √2), We need to find the general term of the sequence.
Observing this, we find that the general term Uₙ = √(n + 2) - √n
To determine if the limit converges or diverges, we take the limit of the sequence as n → ∞.
So,
[tex]\lim_{n \to \infty} U_n = \lim_{n \to \infty} \sqrt{n + 2} - \sqrt{n} \\= \lim_{n \to \infty} \sqrt{n + 2} - \lim_{n \to \infty} \sqrt{n} \\= \sqrt{\infty - 2} - \sqrt{\infty} \\= \sqrt{\infty} - \sqrt{\infty} \\= \infty -\infty[/tex]
Since this is an indeterminate form, we use L'hopital's rule to find the limit.
Uₙ = √(n + 2) - √n
= √n{√[(n + 2)/n] - 1}
= √n÷ 1/{√[(1 + 2/n] - 1}
Differentiating, we have
lim n → ∞ Uₙ = lim n → ∞ d√n/dn ÷ d(1/{√[(1 + 2/n] - 1})/dn
= 1/(2√n)/-√[(1 + 2/n] - 1})⁻² × 1/2√(1 + 2/n] × (-2/n²)
= n²[√(1 + 2/n] - 1})²/(2√n)√(1 + 2/n]
= n²[√(1 + 2/n] - 1})²/(2√n)√(1 + 2/n)]
Dividing through by n², we have
= n²[√(1 + 2/n] - 1})²/n² ÷ (2√n)√(1 + 2/n)]/n²
= [√(1 + 2/n] - 1})² ÷ (2(√n)³√(1 + 2/n³)]
Dividing both the numerator and denominator by (√n)³, we have
= [√(1 + 2/n] - 1})²/(√n)³ ÷ (2(√n)³√(1 + 2/n³)]/(√n)³
= (1 + 2/n] - √(1 + 2/n] + 1)/(√n)³ ÷ [2√(1 + 2/n³)]
= (1(√n)³ + 2/n²] - √{(1 + 2/n]/n)³} + 1/(√n)³) ÷ [2√(1 + 2/n³)]
= (1(√n)³ + 2/n²] - √{(1/n³ + 2/n⁴} + 1/√n)³) ÷ [2√(1 + 2/n³)]
So, lim n → ∞ Uₙ = lim n → ∞ (1(√n)³ + 2/n²] - √{(1/n³ + 2/n⁴} + 1/√n)³) ÷ [2√(1 + 2/n³)]
= (1(√∞)³ + 2/∞²] - √{(1/∞³ + 2/∞⁴} + 1/√∞)³) ÷ [2√(1 + 2/∞³)]
= (0 + 0] - √{(0 + 0} + 0) ÷ [2√(1 + 0)]
= (0 - 0 + 0)/2
= 0/2
= 0
The sequence converges and its limit is zero
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The three angles of a quadrilateral are 60 degrees, 90 degrees and 110 degrees. Determine the fourth angle
Answers
Answer:
100°
Step-by-step explanation:
The sum of any polygon angles add to ( n-2)(180) where n is the number of sides ......for a quadrlateral ( 4-2)(180 ) = 360
60 + 90 + 110 + x = 360 shows x = 100 °
Answer:
sin75^°-sin15^°=1/√2
A prefect is to be chosen from 15 girls and 8 boys. What is the probability that the prefect is a girl?
Answers
Answer:
0.6522 or 65.22%Step-by-step explanation:
Total number of candidates is:
15 + 8 = 23Probability of a girl to be chosen as prefect:
P(girl) = number of girls / total number of candidatesP(girl) = 15/23 = 0.6522 or 65.22%Answer:
Probability = 15/23
Step-by-step explanation:
Now we have to,
→ find probability that prefect is a girl.
The total members are,
→ 15 girls + 8 boys
→ s = 15 + 8
→ [ s = 23 ]
Then the probability will be,
→ P = 15/s
→ [ P = 15/23 ]
Hence, the answer is 15/23.
HELP! PLEASE ASAP!!!!!!
Answers
The sales tax is $2 and the total cost of the item is $42.
Given:
selling price = $40
rate of sales tax = 5%
sales tax = 40*5%
= 40*5 / 100
= 200/100
= $2
Total cost = 40+2
= $42.
Therefore the sales tax is $2 and the total cost of the item is $42.
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Divide usando un modelo de área
6426 ÷ 9
Answers
Find the common difference of the arithmetic sequence -13, -22, -31,.
Answers
The common difference of the arithmetic sequence -13, -22, -31, is -9.
What is an arithmetic sequence?An arithmetic sequence is a set of numbers that are ordered and have a common difference between each consecutive term. In the arithmetic sequence 3, 9, 15, 21, 27, for example, the common difference is 6. An arithmetic progression is another name for an arithmetic sequence.
To find a specific term in an arithmetic sequence, we use the nth term formula. Step 1: An = a + (n - 1)d gives the nth term of an arithmetic sequence.
Some arithmetic sequence examples using this expression are:
1, 5, 9, 13, 17, 21, 25, 29, 33, ...
2, 4, 6, 8, 10, 12, 14, 16, 18,...
In this case, the difference will be:
= 2nd term - 1st term
= -22 - (-13)
= -22 + 13
= -9
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What is the equation of the trend line in the scatter plot?
Use the two yellow points to write the equation in slope-intercept form. Write any coefficients
as integers, proper fractions, or improper fractions in simplest form.
PLS RN!!
Answers
The equation of the trend line in the scatter plot is y = - 4x + 24
What is the slope-intercept form?
Writing the equation of a line in the slope-intercept form simply makes the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) obvious.
Here, we have
The yellow points are located at points (6, 0) and (4, 8)
For a linear equation that passes through the points (x₁, y₁) and (x₂, y₂), the slope is:
s = (y₂ - y₁)/(x₂ - x₁)
Then, for the equation, the slope is
s = (8-0)/(4-6) = -4
Then the linear equation become
y = -4x + b
where b is the y-axis intercept.
To find b, we use that when x = 6, y = 0
0 = 6×(-4) + b
b = 24
Then equation become y = - 4x + 24
Hence, the equation of the trend line in the scatter plot is y = - 4x + 24
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What is the y-intercept, b, of the following linear equation? y = 2x+4 b=
Answers
Answer:
4
Step-by-step explanation:
you can use the formula y=mx+b where b is 4
-3+-u=-4 Please help!!!!!
Answers
Increasing intervals for cubic function
Answers
Answer:
it is basic and .........
a survey is to be administered to recent graduates of a certain nursing school in order to compare the starting salaries of women and men. for a random sample of graduates, three variables are to be recorded: sex, starting salary, and area of specialization. which of the following best describes a conclusion that can be drawn from this study?
Answers
Answer: based on the information that you gave me, I think the answer is :
A. sex is an explanatory variable; starting salary is the response variable ;area of specialization is a possible confounding variable
hope this helps
Step-by-step explanation:
Help meeeeeeeeeeee pleaseee
Answers
Answer:
25%
Step-by-step explanation:
Please help please please
Answers
Answer: 44
Step-by-step explanation:
since OPN and RPQ are similar triangles, you can use ratios to find their sides
[tex]\frac{24}{15} =\frac{x}{15+12.5}[/tex] or [tex]\frac{24}{15} =\frac{x}{27.5}[/tex]
cross multiply to get: 24*27.5 = 15x
660/15 = x
x = 44
The product of 9 and the sum of a number x and 4 is 6
Answers
Answer:
9(x+4)= 6
Step-by-step explanation:
I could be wrong but im not sure
If the line in a linear-quadratic system of equations is a vertical line, how many solutions are there?
Answers
The number of solutions in the system is 1
How to determine the count of the solutions?From the question, the system of equations is given as
A linear equationA quadratic equationAlso, we understand that the linear equation is a vertical straight line.
So, we have the system to be
A vertical-line linear equationA quadratic equationA vertical line can only intersect with a quadratic line at one point
Hence, there is only one solution in the system
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The equation y = 4.3x can be used to determine the total cost, y, in dollars, of x pounds
of apples. What does the number 4.3 represent in the equation?
Answers
the 4.3 represents The number of apples in 1 pound
The 4.3 in the equation represents the number of apples in 1 pound
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
We are given equation y = 4.3x can be used to determine the total cost, y, in dollars, of x pounds of apples.
Here we can see that y = 4.3x
4.3 = y/x
then we can say that 4.3 is slope of striaght line in term os linear equation.
4.3 in the equation represents the number of apples y, in dollars, of x pounds.
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The acute angle meaure of a triangle are (x 20)°, (2x 10)°,
and (4x - 60)°. What are the angle meaure of the triangle?
A. 45°, 65°, 70° C. 40°, 60°, 80°
B. 50°, 60°, 70° D. 60°, 60°, 60°
Answers
The angles of the triangle will be 50°, 70°, 60° .
let the 3 angles of a triangle be A, B and C
The first acute angle A is given by = x + 20
The second acute angle B is given by = 2x + 10
The third acute angle C is given by = 4x - 60
Now we know that the sum of the angles of a triangle is 180°
So ,
A + B + C + = 180°
x + 20 + 2x + 10 + 4x - 60 = 180°
7x - 30 = 180°
7x = 210°
x = 30°
So, from the value of x , we can calculate the value of each angle
Therefore, the required angles are :
angle A = (x + 20)° = 30° + 20° = 50°
angle B = (2x + 10)° = 60° + 10° = 70°
angle C = (4x - 60)° = 120° - 60° = 60°
verification : sum of the angles = 50° + 70° + 60° = 180°
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Write the equation of a line that has a slope of -3/5 and passes through the point (10,4) in slope intercept form.
Answers
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{3}{5}}(x-\stackrel{x_1}{10}) \\\\\\ y-4=- \cfrac{3}{5}x+6\implies {\Large \begin{array}{llll} y=- \cfrac{3}{5}x+10 \end{array}}[/tex]
waste management company wants to construct a dumpster in the shape of a rectangular solid with no top whose length is four times its width. its volume is fixed at 25.6 yd3. find the dimensions of the dumpster that will minimize its surface area.
Answers
the dimensions of the dumpster that will minimize its surface area
length l = 6.32
width w = 1.58
height h = 0.39
Length = l
width = w
height = h
given that length is four times its width
l = 4w
Now, the formula for the surface area of a cube is;
S = 2lh + 2lw + 2wh
substitute l = 4w in the above equation
S = 2(4w)h+2(4w)w+2wh
S = 8wh+8[tex]w^{2}[/tex]+2wh
S = 10wh + 8[tex]w^{2}[/tex]
formula for the volume of a cube is;
V = lwh
now substitute l=4w in the above equation
V = (4w)wh
V = 4[tex]w^{2}[/tex]h
h = 4[tex]w^{2}[/tex]/V
Put V/2w² for h in the surface area equation to get;
S= 8w² + 10w(V/4w²)
= 8w² + 5V/2w
given that volume V = 25.6 substitute that in the above equation
S = 8w² + 5(25.6)/2w
= 8w² + 128/2w
Since we want to minimize the surface area, let us find the first derivative of S to get;
S' = 16w - 128/2w²
At S' = 0
0 = 16w- 128/2w²
16w = 128/2w²
32w³ = 128
w³ = 128/32
w³ = 4
w = [tex]\sqrt[3]{4}[/tex]
w = 1.58 yds
since l = 4w substitute the value of w in that
l = 4(1.58) = 6.32
h = 4[tex]w^{2}[/tex]/V = 4([tex]1.58^{2}[/tex])/25.6
h = 0.39
the dimensions are
length l = 6.32
width w = 1.58
height h = 0.39
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what is the probability that a family of two children has two boys given that the first child is a boy
Answers
Since the first child is a boy, this means we need to find the probability of another boy. This is 1/2 since we assume each gender has the same chance of happening.
the graph below represents the total number of cups of coffee and the total amount of sugar required to make coffee what is the constant of proportionality'
Answers
a. Constant of proportionality is equal to 5.
b. Point (12, 60) represents that 12 pounds of sugar required to make 60 cups of coffee.
What is graph ?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that varies over time is represented with a line graph.
Given:
We have the relation between total number of cups of coffee and the total amount of sugar:
Let y represents the number of cups of coffee
and, x represents the amount of sugar
y ∝ x
y = kx
a. 'k' is the constant of proportionality
When y = 20 , x = 4
20 = k × 4
k = 20/ 4
k = 5
b. From the graph point (12, 60) represents 12 is on the x-axis and y is on the y-axis.
12 represents amount of sugar and 60 represents the number of cups of coffee.
Hence, the Constant of proportionality is equal to 5.
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A man has extra digits (six fingers on each hand and six toes on each foot). His wife and their daughter have a normal number of digits. Having extra digits is a dominant trait. The couple's second child has extra digits. What is the probability that their next (third) child will have extra digits?.
Answers
The probability that their next (third) child will have extra digits is 0.5
Polydactyly refers to the presence of extra fingers in the human body. It is a hereditary condition that is passed down from parents to children. The thumb, middle, and little fingers are the most commonly affected by this condition. Polydactyly refers to the presence of extra fingers in the human body. It is a hereditary condition that is passed down from parents to children. The thumb, middle, and little fingers are the most commonly affected by this condition.
A trait is a distinguishing characteristic that a person possesses. Dominant traits are defined as having only one copy of a gene on a chromosome that expresses a specific trait.
Individuals exhibit the dominant traits most prominently. Polydactyly is the dominant condition in this case.
The father has six fingers and six toes, while the mother is in normal condition. In this particular condition, polydactyly is a dominant trait. Twelve percent of the couple's children are expected to have extra digits.
Because the father has the dominant trait and the mother is in normal condition, there is a 50% chance that this deformity will be passed down to children.
The probability that their next child will have extra digits is 0.5
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Which is the better buy?
6 pounds of kitty litter for $3.84
231 ounces of kitty litter for $6.93
Answers
Can I pls get sum help
Answers
The values of the variables "a", "b", and "c" are 3.06, 169.74, and 0, respectively. The total amount Gary will pay is $769.74.
Gary purchased a S750 TV on a credit card with a 22% annual percentage rate, and he wants to pay it off in payments of $200 per month. The table shows the information for the first four months after Gary used his credit card. We need to calculate the values of the missing variables and the total amount he will pay.
The variable "a" is the interest charged on the left amount in the third month.
a = (366.68 - 200)*0.018333 = 3.06
The variable "b" is the monthly amount paid by Gary. It is less than or equal to $200, depending on the payment amount. Since the amount to be paid is $169.74, which is less than $200, he will pay the whole amount in one go.
b = 169.74
The variable "c" is the interest charged on the left amount in the fourth month. Since then, the entire amount has been paid.
c = 0
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