To find the point of intersection for two lines, we can use substitution to solve for the coordinates.
Solving the QuestionWe're given:
[tex]3x-2y=5[/tex][tex]x+2y=7[/tex]With these two equations, we can:
First isolate x in the second equationUse substitution to input in second equation into the first and solve for yUse the y-coordinate to find the corresponding x-coordinate using substitutionIsolate x in the second equation:
[tex]x+2y=7\\x =7-2y[/tex]
Substitute the second equation into the first:
[tex]3x-2y=5\\3(7-2y)-2y=5\\21-6y-2y=5\\21-8y=5\\21-8y=5[/tex]
Solve for y:
[tex]21-6y-2y=5\\21-8y=5\\-8y=-16\\y=2[/tex]
Solve for x:
[tex]x+2y=7\\x+2(2)=7\\x+4=7\\x=3[/tex]
AnswerThe point of intersection of the lines is (3,2).
You are choosing between two different cell phone plans. The first plan charges a rate of
24 cents per minute. The second plan charges a monthly fee of $49.95 plus 11 cents per
minute.
Lett be the number of minutes you talk and C₁ and C₂ be the costs (in dollars) of the first
and second plans. Give an equation for each in terms of t, and then find the number of
talk minutes that would produce the same cost for both plans (Round your answer to one
decimal place).
C₁ =____
C₂ =____
If you talk for
_____ minutes the two plans will have the same cost.
If you talk for 384.23 minutes the two plans will have the same cost.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
x is the number of minutes that will be used during a month:
C₁ = 0.24x
C₂ = 49.95 + 0.11x
So, when 1st = 2nd
0.24x = 49.95 + 0.11x
0.24x - 0.11x = 49.95
0.13x = 49.95
x = 49.95/0.13
x = 384.23 minutes
Hence, If you talk for 384.23 minutes the two plans will have the same cost.
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Find the greatest number which divides 6168, 2447, and 3118 leaving the same remainder in each case.
Answer:
Greatest number which divides 6168 is 3084,the greatest number which divides 2447 is1223.5 , and the greatest number which divides 3118 is 1559.
What is the vertex of the quadratic function given in the table?
Answer:
The vertex is (-3,-2)
The vertex is basically the very top or very lowest, so you will notice how values around (-3,-2) are relatively the same in the y coordinate, but -2 is the "highest/lowest" so that's how you know it's a vertex.
If you try picturing the points in your head, you will see it make a U and at the bottom of the U is the vertex.
If you currently makes 425 What is the gross they will earn If they work every week If the year
They will earn If they work every week If the year is $22100.
We have given that,
you currently make 425
We have to determine what is the gross they will earn If they work a week If the year.
We know that
A worker currently makes $425 per week
How many weeks in a year?1year=52 weeks
So by proportion find the amount that the worker will earn in one year
[tex]\frac{425}{x}\times \frac{\$}{weeks}[/tex]
[tex]=\frac{x}{52}\times \frac{\$}{weeks}[/tex]
[tex]x=52\times 425[/tex]
x=22,100
Therefore, The answer is $22100.
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Help please!! I’m stuck with these questions. :)
Answer:
20 elements.
Step-by-step explanation:
Lets say
n(U) = 114
n(A) = 57
n(B) = 79
n(A n B)= 42
Now,
n(A U B) = n(A) + n(B) - n(A n B)
= 57 + 79 - 42
= 94
Now,
n(A U B) compliment = n(U) - n(A U B)
= 114 - 94
= 20
. It costs C(x) = [tex]\sqrt{x}[/tex] dollars to produce x golf balls. What is the marginal production cost to make a golf ball? What is the marginal production cost when x = 25? when x= 100? (Include
units.)
The marginal cost when x = 25 and when x = 100 are $0.1 and $0.05 respectively.
What is a Marginal Production Cost?A marginal production cost is a derivative of a cost function. From the information given, the total cost is:
C(x) = [tex]\mathbf{\sqrt{x}}[/tex]The marginal production cost can be expressed as:
[tex]\mathbf{C'(x) = \dfrac{d}{dx}(\sqrt{x})}[/tex]
[tex]\mathbf{C'(x) = \dfrac{1}{2\sqrt{x}}}[/tex]
However, when the cost is 25, the marginal production is:
[tex]\mathbf{C'(25) = \dfrac{1}{2\sqrt{25} }}[/tex]
[tex]\mathbf{C'(25) = \dfrac{1}{2\times5}}[/tex]
[tex]\mathbf{C'(25) = \dfrac{1}{10}}[/tex]
C' (25) = $0.1
Also, when the cost is 100, the marginal production is:
[tex]\mathbf{C'(100) = \dfrac{1}{2\sqrt{100} }}[/tex]
[tex]\mathbf{C'(100) = \dfrac{1}{2\times10}}[/tex]
[tex]\mathbf{C'(100) = \dfrac{1}{20}}[/tex]
C' (100) = $0.05
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Select all the correct answers. Function g is a transformation of the parent exponential function. Which statements are true about function g? A Linear graph function where red line g intercepts y-axis at (0, 4) and passes through (minus 10, 3) and (3, 10) Function g is positive over the interval . The domain of function g is . Function g has a y-intercept of . Function g decreasing over the interval . Function g is 4 units above function f. The range of function g is .
The correct statements are:
Function g has a y-intercept of (0,4)
The range of the function g is (3, ∞).
The function g is positive over the interval (-∞ , ∞ ).
The parent function i.e. exponential function is defined by:
y=f(x)=aˣ
From the graph given below,
1. The graph of the function g is 3 units above the graph of the parent exponential function. as the parent exponential function aˣ cuts the y-axis at (0,1) and the child transformed function cut at (0,4) for which g is 4-1=3 units above the parent function
2. The domain of the function is set of all the inputs for which function is defined. From the graph of function g, it is clear tha the domain of the function is (-∞ , ∞ ) as the domain of the parent exponential function is also (-∞ , ∞ ).
3. The y-intercept is the point at which function cut the y-axis. Graph of function g cut the y-axis at (0, 4). Therefore, Function g has the y-intercept at (0,4).
4. From the graph it is clear that Function g increases over the interval (-∞, 0) .
5. The range of the function is the output values of the function. From the graph, it is observed that the range of function g is (3, ∞). as its minimum value is 3 then the maximum value is ∞.
6. As, the graph of function g is drawn above the x-axis. Therefore, Function g lies completely on +ve y-axis, so function g is positive over the interval (-∞ , ∞ ).
Therefore The correct statements are:
Function g has a y-intercept of (0,4)
The range of the function g is (3, ∞).
The function g is positive over the interval (-∞ , ∞ ).
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A hostel has food for 60 days if after 15 days 500 more students joined th hostel and the food lasted for 40days only. How many students were there in hostel
Answer:
625
Step-by-step explanation:
here we are in an inverse proportion situation :
As the number of days increases
when the number of students decreases and vice versa.
__________________
Say n is the original number of students.
___________________________________________
After 15 days, the rest of food is enough for n students for 45 days,
or enough for n+500 students for 25 days.
Then
45n = 25×(n + 500)
Then
45n = 25n + 25×500
Then
45n - 25n = 25×500
Then
20n = 12500
Then
n = 12500÷20
= 625
and thus , there were 625 students in the hostel.
Using Triangle Congruence Theorems
There are a total of five theorems congruent triangles. They are summarized as:
SASSSSAASRHS and ASA.What are the definitions of the Theorems of Congruent Triangles?SAS - Side Angle Side
According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.
SSS - Side Side Side Rule
According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are proportional to the size three sides of the second triangle.
AAS - Angle Angle Side Rule
Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the comparable angles and sides of another triangle.
ASA - Angle Side Angle rule
According to the ASA rule, two triangles are said to be congruent if any two angles and the side contained between the angles of one triangle are proportional to the size two angles and side included in between angles of the second triangle.
RHS - Right Angle- Hypotenuse side Rule
According to the RHS rule, two right triangles are said to be equivalent if their hypotenuses and one of their sides are identical to those of another right-angled triangle.
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Answer:
AD=BC (given)
DC=DC (reflexive property)
DE=CE (converse of isosceles triangle thm)
<BCD=<ADC (given)
<ECD=<EDC (CPCTC)
TriangleADC=TriangleBCD (SAS)
5
сл
Type the correct answer in each box.
A circle is centered at the point (-7, -1) and passes through the point (8, 7).
The radius of the circle is
units. The point (-15,
) lies on this circle.
Part 1: Finding radius
The radius of a circle is defined as the distance from the center to a point on the circle's circumference.
Using the distance formula,
[tex]r=\sqrt{(-7-8)^{2}+(-1-7)^{2}}=\boxed{17}[/tex]
Part 2: Finding the point with x-coordinate -15
Let the y coordinate of the point be y. Then, we have the point (-15, y). Substituting into the distance formula,
[tex]\sqrt{(-15-(-7))^{2}+(-1-y)^{2}}=17\\\\64+(-1-y)^{2}=289\\\\(-1-y)^{2}=225\\\\-1-y =\om 15\\\\y=\boxed{-16, 14}[/tex]
The length of a golden rectangle is 35 cm. Find the width to the nearest centimeter.
17cm
25cm
22cm
29cm
16cm
Answer:
22 cm
Step-by-step explanation:
First we need to know that The golden number
= (1+√(5))÷2
= 1.61803398875 (in decimal)
………………………………………………
We get the length of a golden rectangle
by multiplying its width by the golden number itself.
Then
The width = 35÷ 1.61803398875
=21.631189606245
A company finds that there is a linear relationship between the amount of money that it spends on advertising and the number of units it sells. If it spends no money on advertising, it sells 250 units. For each additional $4000 spent, an additional 25 units are sold. If x is the amount of money that the company spends on advertising, find a formula for y, the number of units sold as a function of x.
The formula for the equation of y, the number of units sold as a function of x is y = 0.00625x + 250
How to illustrate the equation?From the information given, when the company spends no money on advertising, it sells 250 units and for each additional $4000 spent, an additional 25 units are sold.
The formula for y will be:
y = (25/4000)x + 250
y = 0.00625x + 250
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Given the function f(x) = -5|x + 1| + 3, for what values of x is f(x) = -12? O X= -2. x = 1 O x= -2 x = 4 O x = 2. x = 4 O x = 2, x = 4
The values are x= -2 and x =4 of the given function f (x) =-5|x+1| +3
What is function?
Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
According to the question,
The given function is
[tex]f(x) = -5|x + 1| + 3[/tex]
Here f(x) = -12
Substitute f(x) and solve for x
[tex]- 12 = -5|x + 1| + 3[/tex]
By subtracting 3 on both sides
[tex]- 12 - 3 = -5|x + 1| + 3 - 3[/tex]
[tex]- 15 = -5|x + 1|[/tex]
By dividing -5 on both sides
[tex]3 = |x + 1|[/tex]
We get absolute values for the function.
[tex]x + 1 = 3 , x + 1 = -3[/tex]
By subtracting 1 on both sides
[tex]x + 1 - 1 = 3 - 1 = 2\\\\x + 1 - 1 = - 3 - 1 = -4\\\\x = 2 , x = - 4[/tex]
Therefore, the values of x are 2 and - 4 of the given function f (x) =-5|x+1| +3
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The angles of a quadrilateral have measures m∠A = (7x)◦, m∠B = (4x + 5)◦, m∠C =
(6x + 15)◦, m∠D = (6x −5)◦. Find the value of x. If a diagonal bisects ∠B and ∠D, what
type of quadrilateral is ABCD?
The value of x is 15° and the type of quadrilateral is a rhombus.
Quadrilateral
A quadrilateral is a polygon that has four sides.The sum of all angles of a quadrilateral is 360°.
Here, we are given,
m∠A = (7x)◦, m∠B = (4x + 5)◦, m∠C =(6x + 15)◦, m∠D = (6x −5)◦
So, we will have
7x+4x+5+6x+15+6x-5=360°
23x+15°=360°
23x=345°
x=345°/23°
x=15°
Hence, the angles of the quadrilateral are:
m∠A = (7x)◦=105°,
m∠B = (4x + 5)◦ =65°
m∠C =105°
m∠D = (6x −5)◦ =85°
Since the diagonal bisects ∠B and ∠D, we get that the quadrilateral is a rhombus.
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3.8% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?
The conditional probability that the person has the disease given that the test result is positive is of 0.4750 = 47.50%.
What is Conditional Probability?
Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.In this problem, the events are:
Event A: Positive test.Event B: Has the disease.The percentages associated with a positive test is:
93.9% of 3.8%(has the disease).4.1% of 100 - 3.8 = 96.2%(does not have the disease).Hence:
[tex]P(A) = 0.939(0.038) + 0.041(0.962) = 0.075124[/tex]
The probability of both a positive test and having the disease is given by:
[tex]P(A \cap B) = 0.939(0.038) = 0.035682[/tex]
Hence the conditional probability is given by:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.035682}{0.075124} = 0.4750[/tex]
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ASAP!!!!!!!!!!!!
PLEASE GIVE A STEP BY STEP EXPLANATION!!!
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
The two transformations for fx and gx would be to shift by 6 units and also go up by 18.
What is a transformation?This is the term that is used in mathematics to describe the manipulation of a line or a shape.
a. The possible transformations that can be gotten here would be to shift to the left by 6 units from what we have in the graph and also shift to the top by 18.
b. How to solve for K in the transformationg of x = f(x - k) then
g(x)= f(x) + k
C. The value of k should be based on the way it changes based on the given points.
Vertically, g(x)=f(x) +18
Horizontally , g(x)=f(x-6)
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P, Q and R are points in the same
horizontal plane. The bearing of
Q from P is 150° and the bearing
of R from Q is 060°.
If |PQ| = 5m and QR = 3m,
Find the bearing of R from P.
correct to the nearest degree./
Answer: 119°
Step-by-step explanation:
From the positive y-axis, all angles are measured clockwise
PR = PQ + QR = 5[150°] + 3[60°]
X = 5*sin150 + 3*sin60 = 5.1
Y = 5*Cos150 + 3*Cos60 = -2.83
TanA = X/Y
A = -61° = 61° East of South = 119° Clockwise
Therefore, the bearing of R from P is 119°
At a certain time of day, the angle of elevation of the sun is 80degree. Find the height of a tree whose shadow is 44 feet long.
The height of the tree is 249.5 feet
How to determine the height of the tree?The given parameters are:
Elevation angle = 80 degreesShadow length (L) = 44 feetLet the height of the tree be x.
So, we have:
tan(80) = x/44
Multiply both sides by 44
x = 44 * tan(80)
Evaluate
x = 249.5
Hence, the height of the tree is 249.5 feet
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Suppose that an examination consists of 10 questions with the choice A, B, C, and D. Assume that a student has no knowledge of the subject matter. Then what is the probability that: Guessing at most two correct answers? Guessing at least seven correct answers? Which type of probability distribution it has? Why? average five smokers pass a crain traat B. C. Suppose that an examination consists of 10 questions with the choice A , B , C , and D. Assume that a student has no knowledge of the subject matter . Then what is the probability that : Guessing at most two correct answers ? Guessing at least seven correct answers ? Which type of probability distribution it has ? Why ?
The probability of getting two correct answers will be 0.0625.
How to calculate the probability?The probability of getting two correct answers will be:
Probability of getting the correct answer will be:
= 1/4 = 0.25
The probability of getting two correct answers will be:
= 0.25 × 0.25
= 0.0625
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Can someone answer this
The order of the graphs from largest to lowest correlation coefficients is:
Graph D, Graph A, graph C, graph B.
Which graph has the largest correlation coefficient?The correlation coefficient between two variables is a coefficient that tells us "how much" these variables relate.
So, in the case for linear correlation, as "more linear" the data appears to be, a large correlation is between the two variables.
With that in mind, we conclude that the order of the graphs (going for larger correlation coefficient to smaller correlation coefficient) is:
Graph D, Graph A, graph C, graph B.
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x + 4 = x2? Assume x greater-than 0
Answer:
The value comes out to be
[tex]x=\frac{1}{2}+\frac{\sqrt{17}}{2}[/tex]
Step-by-step explanation:
The quadratic equation is an equation containing a single variable of degree [tex]2[/tex]. Its general form is [tex]ax^{2} +bx + c=0[/tex].
The discriminant is the part of the quadratic formula underneath the square root symbol: b²- 4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
The equation we are given is :[tex]x+4=x^{2} \\x^{2} -x-4=0\\[/tex]
We know the formula as :
[tex]x=[-b[/tex]±[tex]\sqrt{b^{2}-4ac}][/tex] ×[tex]\frac{1}{2a}[/tex]
[tex]x=[-(-1)[/tex]±[tex]\sqrt{(-1)^{2} -4(1)(-4)}][/tex]×[tex]\frac{1}{2(1)}[/tex]
[tex]x=\frac{1}{2}[/tex] ±[tex]\frac{\sqrt{17} }{2} }[/tex]
Since [tex]x[/tex]≥[tex]0[/tex]
Other negative option is neglected
[tex]x=\frac{1}{2}+\frac{\sqrt{17}}{2}[/tex]
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What is the product of (x² + x + 2) and (x² − 2x + 3)
Answer:
[tex]x^4-x^3+3x^2-x+6[/tex]
Step-by-step explanation:
Multiply each term in the first equation by all the terms in the second and add them together.
Find the sine and the cosine of 30°.
A. sin 30° =1/2, cos 30°= √3
B. sin 30°=1/2, cos 30° = √3/2
C. sin 30° = √3/3, cos 30°= √3/4
D. sin 30° = √3/3, cos 30° = √3/2
Answer:
Option B is correct.
Step-by-step explanation:
Trigonometry is defined as the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles. There are three basic trigonometric ratios: sine, cosine, and tangent. Trigonometry and its functions have an enormous number of uses in our daily life. For instance, it is used in geography to measure the distance between landmarks, in astronomy to measure the distance of nearby stars and also in the satellite navigation system.
The trigonometric function of sine for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse while the cosine is the ratio of the base and the hypotenuse.
Here, [tex]sin 30[/tex]° [tex]=\frac{4}{8}[/tex]
[tex]sin 30[/tex]° [tex]=\frac{1}{2}[/tex]
[tex]cos 30[/tex]° [tex]=\frac{4\sqrt{3}}{8}[/tex]
[tex]cos30[/tex]°[tex]=\frac{\sqrt{3} }{2}[/tex]
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Solve the system of equation for y using Cramer's rule. Hint: The determinant of the coefficient matrix is -23.
Answer:
-4 option (c)
Step-by-step explanation:
Cramer rule : In this method, the values of the variables in the system are to be calculated using the determinants of matrices
if , D :determinant of the coefficient matrix
[tex]{D}_{x}:[/tex]determinant of the matrix with coefficients except x
then,
[tex]x=\frac{{D}_{x}}{D}[/tex]
similarly,
[tex]y=\frac{{D}_{y}}{D}[/tex]
[tex]z=\frac{{D}_{z}}{D}[/tex]
given,
D = -23
[tex]D_{y}[/tex] = [tex]det\left[\begin{array}{ccc}5&7&-1\\2&6&-2\\3&-7&2\end{array}\right][/tex]
[tex]D_{y}[/tex] = 92
therefore, y = 92/(-23)
y = -4 answer
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Answer please! I need this!
Step-by-step explanation:
The top has been multiplied by 5 so multiply the bottom by 5, 2 x 5 = 10. also why is there a pig lol
B is the set of odd numbers greater than 5 and less than 21
Answer:
List method: {7,9,11,13,15,17,19}
Set method: {X:N where N is odd, N>5 and N<21}
The odd numbers greater than 5 and less than 21 are {7, 9,11,13,15,17,19}.
What are odd numbers?Odd numbers are the numbers that cannot be divided by 2 evenly. It cannot be divided into two separate integers evenly.
Odd numbers are opposite to even numbers this means that even numbers are numbers that can be divided by 2.
When we say numbers greater than 5 and less than 21 this means 5< x < 21
The odd numbers greater than 5 and less than 21 are ;
{7, 9,11,13,15,17,19}. These odd numbers are greater than 5 and less than 21.
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There are 192 pencils in 8 Super Saver packs. If there are the same number of pencils in each Super Saver pack, how many pencils are in 5 packs?
the length of a cell is 2/3 mm. If the area of the cell is 1/12 square mm, whtat is the width of the cell
Answer:
0.125 mm
Step-by-step explanation:
A/L=W
W=0.125
An open rectangular box with a volume of 12 cubic meters has a length that is 5 times the width. Express the surface area of the box as a function of the length of a side of the base, x.
The area of a 2D form is the amount of space within its perimeter. The surface area of the prism is 5x²+(24/5x)+(24/x).
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Let the width of the rectangular box be x. Therefore, the length of the box is 5x. Now, the height of the box can be written as,
Volume of the box = length × width × Height
12 = 5x² × H
H= 12 / 5x²
Further, the surface area of the open box is,
Surface area of the box
[tex]= (5x \times x) + 2(h \times x) + 2(5x \times h)\\\\= (5x^2) + 2(\dfrac{12}{5x^2} \times x) + 2(5x \times \dfrac{12}{5x^2})\\\\\\= 5x^2 + \dfrac{24}{5x} + \dfrac{24}{x}[/tex]
Hence, the surface area of the prism is 5x²+(24/5x)+(24/x).
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Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 324 minus quantity y minus 90 end quantity squared over 1600 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.
36 meters
48 meters
80 meters
89 meters
The width of the cooling tower at the base of the structure will be A. 36 meters.
How to calculate the width?From the information given, the towers walls are modeled by x²/324 - (y² - 90)²/1600.
Therefore, the width of the cooling tower at the base of the structure will be:
= 2 × ✓324
= 2 × 18
= 36
In conclusion, the width is 36 meters.
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Answer:
It is actually D
Step-by-step explanation:
