Substitute -6x-7 for y in the equation 7x+y=-3 to obtain the value of the of x.
[tex]\begin{gathered} 7x-6x-7=-3 \\ x=-3+7 \\ =4 \end{gathered}[/tex]Substitute 4 for x in the equation y=-6x-7 to obtain the value of the y.
[tex]\begin{gathered} y=-6\cdot4-7 \\ =-24-7 \\ =-31 \end{gathered}[/tex]So solution of the equation is (4,-31).
4. A 5% tax is added onto a $75 online order. How much are the taxes?
We have the following:
We know that 100% is the value of the purchase of $ 75, therefore, if we add 5%, it would be 105%, that is equal to 1.05, so we multiply the value of 75 by 1.05, and we are left with the following
[tex]\begin{gathered} 75\cdot1.05=78.75 \\ 78.75-75=3.75 \end{gathered}[/tex]Total value is $78.75 and taxes are 3.75
find the are and perimeter
L: Length
W: Width
The perimeter of a rectangle is:
[tex]P=2W+2L[/tex][tex]\begin{gathered} P=2(3ft)+2(5ft) \\ P=6ft+10ft \\ P=16ft \end{gathered}[/tex]The area of a rectangle is:
[tex]A=W\cdot L[/tex][tex]\begin{gathered} A=3ft\cdot5ft \\ A=15ft^2 \end{gathered}[/tex]Which of the following are mathematical sentences? Check all that apply. A. 34 B. r + 7 = 4 C. 5g = 9 D. 4x E. 8r = 12 F. x = 1
The mathematical sentences that can be found in the sentence are:
B. r + 7 = 4 C. 5g = 9 D. 4x E. 8r = 12 F. x = 1What are mathematical sentences?A mathematical sentence can be described as the statement that comprises the two expressions nor more than two expression.
It should be noted that these two expressions can make use of the numbers as well as the variables and in some of the cases combination of them however the mathematical sentence do encompass the symbols which could be inform of equals, greater than, as well as less than.
Therefore, the options that are examples of mathematical sentences are option B C D E F.
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The mathematical sentences which can be found in the sentence are;
B. r + 7 = 4, C. 5g = 9, D. 4x, E. 8r = 12 and F. x = 1
What are mathematical sentences?A mathematical sentence can be described as a statement that comprises two expressions or more than two expressions.
Expression can be defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Remember that these two expressions can make use of the numbers as well as the variables and in some cases a combination of them however the mathematical sentence does encompass the symbols which could be in form of equals, greater than, as well as less than.
Hence, the options that are examples of mathematical sentences are ; B. r + 7 = 4, C. 5g = 9, D. 4x, E. 8r = 12 and F. x = 1
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ok my question is math algebra. consider the linear equation y-1=0 and grapthe two points
To find:
We need to find two points on the linear equation y-1=0 and to plot those points on graph.
Step by step solution:
We know that:
General coordinate of any two points on line y = 1:
= (x, 1)
So let us assume any two random points on the line:
= (1,1) and (2,1)
We will now mark them on the graph:
B>DGiven:. E is the midpoint of ADE is the midpoint of BCProve: ΔΑΕΒΑ ΔDECE is the midpoint of ADGiven
We are given a mid-point for segments AD and BC, we have the following:
segments AE and DE are congruent, that is:
[tex]AE\cong DE[/tex]By definition of mid-point.
Segments BE and CE are congruent, that is:
[tex]BE\cong CE[/tex]By definition of mid-point.
We also have that angles AEB and DEC are congruent, that is:
[tex]\angle AEB\cong\angle DEC[/tex]By the vertical angles theorem, which states that when two lines intercept their vertical or opposite angles are equal or congruent.
Now we can conclude that triangles AEB and DEC are congruent, that is:
[tex]\Delta AEB\cong\Delta DEC[/tex]Due to the Side-Angle-Side Theorem, which states that when two triangles have two congruent sides and the angle between the congruent sides also congruent, then the triangles are congruent.
NEED HELP DUE BY WEDNESDAY OR TOMMOROW. Solve each of the equations and select the numbers that represent solutions to more than one of the six equations. Select all that apply. 4x-3=17. 8(x + 1) = 24. 5(x - 2) = 20. 34 - 7x = 20. 31 - x = 29. 3x +6=21. A. x=1. B. x=2. C. x=3. D. x=4.E. x=5. F. X = 6.
We are to solve for x in all the equations and select the ones that occur more than one solution.
Hence,
[tex]\begin{gathered} 4x-3=17 \\ 4x=17+3 \\ 4x=20 \\ x=\frac{20}{4}=5 \\ \therefore x=5 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 5(x-2)=20 \\ x-2=\frac{20}{5} \\ x-2=4 \\ x=4+2=6 \\ \therefore x=6 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 31-x=29 \\ 31-29=x \\ 2=x \\ \therefore x=2 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 8(x+1)=24 \\ x+1=\frac{24}{8} \\ x+1=3 \\ x=3-1=2 \\ \therefore x=2 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 34-7x=20 \\ 34-20=7x \\ 14=7x \\ \frac{14}{7}=\frac{7x}{7} \\ 2=x \\ \Rightarrow x=2 \end{gathered}[/tex]Lastly,
[tex]\begin{gathered} 3x+6=21 \\ 3x=21-6 \\ 3x=15 \\ x=\frac{15}{3}=5 \\ \therefore x=5 \end{gathered}[/tex]Hence, the numbers that represent solutions to more than one of the six equations are
[tex]\begin{gathered} x=2\text{ \lparen Option 2\rparen} \\ x=5\text{ \lparen Option 5\rparen} \end{gathered}[/tex]If y varies directly with x and y = 90 when 3 = 15, then what is y when = 4?y =+
Recall than a direct variation implies the following type of relationship between y and x:
y = k * x
where k is a constant value
Then you have (by dividing by x, the following:
y / x = k (the constant)
then, we are told that when y = 90 , x = 15, so we have:
90 / 15 = k
6 = k
so,now that we know what the constant k is (6), we can answer the question: What is y when x = 4?
so we write:
y = k * x
y = 6 * 4
y = 24
This is the value of y when x is 4 since the constant k is 6 as we found above.
Another example:
We need to find the variation relationship for a case that when y = 6, x = 12
We think the same way we did before, starting with the fact that a direct variation is of the form:
y = k * x
given the info that when x = 12, y = 6, we can find the constant k:
6 = k * 12
divide by 12 both sides:
6/12 = k
1/2 = k
So k is 1/2 (one half)
Then we can write the variation as:
y = (1/2) x
(the product of 1/2 times x)
URGENT!!! help!!!!!!!!!!!!!
Triangles' resemblance is reflected by their congruence. If the matching sides and angles of two triangles match, the triangles are said to be congruent.
For triangles, there are five primary congruency rules: Side-Side-Side is an SSS criterion. The side-angle-side SAS criterion. Angle, Side, Angle is an ASA criterion. Angle-Angle-Side is an AAS criterion.
The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
An isosceles triangle in geometry is one with at least two equal-length sides. It is sometimes stated as having exactly two equal-length sides and other times as having at least two equal-length sides, with the latter version adding the equilateral triangle as one of the possible configurations.
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MP and MN are tangents to the circle.What is the value of x?133M90940NxºР17286
To get x, we will use the equation below:
[tex]\frac{1}{2}\lbrack(360-x)-x\rbrack=94[/tex]open the inner paremthesis
[tex]\frac{1}{2}\lbrack360-2x\rbrack=94[/tex]
open the parenthesis
180 - x = 94
collect like term
180 - 94 = x
86 = x
Property valued at $56,000 is assessed at of itsvalue. If the yearly tax is calculated as $3 per $100 ofassessed value, what is the yearly tax on this property?A. $ 420B. $1.120C. $1,260D. $1,680E $2,240
Since the yearly tax is calculated as $3 per $100 of assessed value, which is 3/4 of $56,000 , the yearly tax on this property can be calculated as: $56,000*3/4*$3/$100 = $ 1260. The answer is option C.
The formula Total cost=C+Shipping cost+Installation is used to find the total cost of a business asset. The formula can be written in symbols as T=C+S+I. Solve the formula for I, the Installation cost of the asset.
Formulas
The formula for the Total Cost is given as:
T = C + S + I
Where C is the shipping cost, I is t
A bus travels 8.4 miles eastand then 14.7 miles north.What is the angle of the bus'resultant vector?Hint: Draw a vector diagram.O[?]
A bus travels 8.4 miles east and then 14.7 miles north.
What is the angle of the bus resultant vector?
see the figure below to better understand the problem
The angle of the bus resultant vector R is equal to
tan(x)=14.7/8.4
mm
Hello, I need some assistance with the following question. Q1.
Given the expression f/g
Which is a rational expression.
The domain is all real numbers of (x) except the zeros of the denominators
The zeros of the denominators can be calculated using the equation g(x)=0
So, the answer will be as follows:
The domain of f/g consists of numbers (x) for which g(x) ≠ 0 that are in the domains of both f and g
Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible Through (15,5) and (5,15)
Given that the required linepasses through the points (15, 5)and (5, 15).
Find the slope of the line using teo-point formula.
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{15-5}{5-15} \\ =\frac{10}{-10} \\ =-1 \end{gathered}[/tex]Substitute the value of m into theslope-intercept form y = mx+c.
[tex]y=-x+c[/tex]Plug in the point (5, 15)to find c, the y-intercept.
[tex]\begin{gathered} 15=-5+c \\ c=20 \end{gathered}[/tex]Thus, y = -x + 20, which is the required equation of line.
A manager measured the number of goods, y, that his company produced in a hours. The
company produces goods at a rate of 5 per hour. At hour 9, the company had produced 45
goods.
Which equation, in point-slope form, correctly represents the goods produced by the company
after x hours?
Oy-45 = 5(x-9)
Oy+9= 5(x +45)
Oy 45= 5(x + 9)
Oy-9=5(x - 45)
Answer:
[tex]y-45=5(x-9)[/tex]
Step-by-step explanation:
Definition of the variables:
y = total number of goods produced.x = time in hours.Given information:
The company produces goods at a rate of 5 per hour. At hour 9, the company had produced 45 goods.As the rate of change is constant and linear, the rate of change is the slope of the line. Therefore, the slope is 5.
At hour 9 (x-value) the company had produced 45 (y-value) goods. Therefore, this can be represented by the point (9, 45).
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and point into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-45=5(x-9)[/tex]
Therefore, the equation that correctly represents the goods produced by the company after x hours is:
[tex]\boxed{y-45=5(x-9)}[/tex]
You have been tracking an adult female Australian flatback sea turtle who weighs 25 kg. How many kilocalories must she consume each day to maintain her body weight?
The kilocalories that she must consume each day to maintain her body weight is 6250 kilocalories.
How to calculate the value?From the information, the person has been been tracking an adult female Australian flatback sea turtle who weighs 25 kg.
It should be noted that the requirements is 250kcal per kilograms.
Therefore, the calories will be:
= Weight × Required calories
= 250 × 25
= 6250 kcaloriies
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What is the slope of the line that passes through (5,4) and (7,10)a.3b. -3 C. 2D.-2
To find a slope of a line we need two points, so we will do it as follows.
[tex]m=\frac{\Delta y}{\Delta x}=\frac{10-4}{7-5}=\frac{6}{2}=3[/tex]Therefore it is (a) the slope is 3.
Answer:
a.3
Step-by-step explanation:
To find the slope, use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 10-4)/(7-5)
= 6/2
= 3
I need help with my pre-calculus homework, the image of the problem is attached. Please show me how to solve this problem, thank you!
Given the following equation:
[tex]\text{ }\frac{\text{ 2}}{5x}\text{ + 4 = }\frac{2}{x}[/tex]Let's find x,
[tex]\text{ }\frac{\text{ 2}}{5x}\text{ + 4 = }\frac{2}{x}[/tex][tex]\text{ 5x( }\frac{\text{ 2}}{5x}\text{ + 4) = (}\frac{2}{x})5x[/tex][tex]\text{ 5x(}\frac{\text{ 2}}{5x})\text{ + 5x(4) = (}\frac{2}{x})5x[/tex][tex]\text{ 2 + 20x = 10}[/tex][tex]\text{ 2 + 20x - 2 = 10 - 2}[/tex][tex]\text{ 20x = 8}[/tex][tex]\text{ }\frac{\text{20x}}{20}\text{ = }\frac{\text{8}}{20}[/tex][tex]\text{ x = }\frac{8}{20}[/tex][tex]\text{ x = }\frac{\frac{8}{4}}{\frac{20}{4}}\text{ = }\frac{2}{5}[/tex]Therefore, the answer is letter A: 2/5
In the accompanying diagram, three vertices of parallelogram ORST are O(0,0), R(b,d), and T(a,0). What are the coordinates of S?A. (a, b)B. (a+b, d)C. (a+b, b)D. (a, d)
In a parallelogram, the opposite sides are parallel.
This means that RS is parallel to OT. So, the y value of S is the same as the y value of R, which is d, so y = d. Thus:
[tex]S=(x,y)=(x,d)[/tex]Now, we need to find x.
Since the sides RO and ST are also parallel, the x distance from O to R is the same as the x distance from T to S.
The x distance from O to R is
[tex]b-0=b[/tex]The x distance from T to S is
[tex]x-a[/tex]Since these x distances are equal, then:
[tex]\begin{gathered} b=x-a \\ x=a+b \end{gathered}[/tex]Then, the coordinates of S are:
[tex](a+b,d)[/tex]Which corresponds to option B.
The electronics company makes two types of switches. Type a takes 4 minutes to make and requires $3 worth of materials.Type b takes 5 minutes to make and requires $5 of materials. In the latest production bath, it took 32 hours to make these switches and the materials cost 1740. How many of each type of switch was made?
Let
x ------> number of switch type A
y -----> number of switch type B
so
Remember that
1 hour=60 min
32 hours=32*60=1,920 minutes
4x+5y=1,920 -------> equation 1
3x+5y=1,740 ------> equation 2
Solve the system of equations
Solve by graphing
using a graphing tool
see the attached figure
Solution is
x=180
y=240
therefore
the number of switch type A was 180the number of switch type B was 240Identify the word described by the following statement.The type of rule in which you can find any number of term in the sequence without knowing the first or previous term.
Recursive is the type of rule in which you can find any number of term in the sequence without knowing the first or previous term.
Hence, the answer is Recursive.
based on the data provided what was the rent expenses each month
From the table it can be observed that rate expense for a month is -$1,120.00. The negative value means that amount is reduced.
So rent expense is -$1,120.00, where negative sign is for decrease in amount.
A spinner can land on either red or blue You spin seven times and then roll a six sided die. Find the number of possible outcomes in the sample space?
If we spin the spinner once, we can get two possible outcomes (red or blue).
If we spin it twice, the outcomes can be (blue, blue), (blue, red), (red, blue), (red, red); this is, 4 different results.
Then, if we spin the spinner 7 times, there are 2^7=128 possible outcomes.
Finally, we can get any of the 128 possible outcomes from the spinner and rolling a 1; similarly, for rolling a 2, 3,..., 6.
Therefore, the number of possible outcomes of spinning the spinner seven times and rolling a die is
[tex]2^7\cdot6=128\cdot6=768[/tex]There are 768 possible outcomes in the sample space.
Eliza had $14 and Emma had $64 more than Eliza how much did Emma have?
Given
Eliza had $14
Emma had $64 more than Eliza
Find
how much did Emma have
Explanation
as we have given
Eliza has $14
so , Emma = $64 + $14 = $78
Final Answer
Therefore , the Emma had $78
1. Evaluate the following expressions if a = 2. b = 3, x = 4, and y = 5.+3(27-»
When a=2, b=3, x=4, and y=5,
evaluate:
[tex]b^2+3(2x-y)[/tex]Let's replace b, x and y by the appropriate values:
[tex](3)^2+3(2(4)-5)[/tex]now let's solve what is inside the parenthesis:
[tex]9+3(8-5)[/tex]again more solving inside the second parenthesis:
[tex]9+3(3)[/tex]and again, first multiplying what is indicated. Recall that the rule PEMDAS for order of operations indicates that Parenthesis have to be solved first, then exponents, then multiplications and divisions, and the VERY LAST is additions and subtractions:
[tex]9+9=18[/tex]You do the same type of replacement of variables wit numbers, and then use of the rules for order of operations to evaluate the rest.
Like:
[tex]ab+ya^3[/tex]and then evaluate:
[tex]\frac{y+ab}{b+x}[/tex]Hello! I need some assistance with this homework question, pleaseQ12
Answer:
A(-1,4) and B(2,0)
Step-by-step explanation:
The quadratic parabola equation is represented as;
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the vertex of the parabola} \end{gathered}[/tex]Therefore, if the given vertex (2,-5) and the other given point (-1,-1), substitute into the equation and solve for the constant ''a'':
[tex]\begin{gathered} -1=a(-1-2)^2-5 \\ -1=9a-5 \\ 9a=4 \\ a=\frac{4}{9} \end{gathered}[/tex]Hence, the equation for the parabola:
[tex]f(x)=\frac{4}{9}(x-2)^2-5[/tex]Now, for the line since it is a horizontal line, the equation would be:
[tex]g(x)=5[/tex]Then, for (f+g)(x):
[tex]\begin{gathered} (f+g)(x)=\frac{4}{9}(x-2)^2-5+5 \\ (f+g)(x)=\frac{4}{9}(x-2)^2 \end{gathered}[/tex]Then, the graph for the composite function and the points that lie on the graph:
A(-1,4) and B(2,0)
complete the equation of the line through (-1,6) and (,7-2)
The two points given are
A(-1, 6)
B(7, -2)
We shall start by calculating the slope of the line, since we've been given two points.
[tex]\begin{gathered} \text{The slope which is m, is derived as;} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-2-6}{7-\lbrack-1\rbrack} \\ m=\frac{-8}{7+1} \\ m=\frac{-8}{8} \\ m=-1 \end{gathered}[/tex]Next we shall derive the y-intercept, by inserting the known values into the equation in slope-intercept form.
[tex]\begin{gathered} y=mx+b \\ We\text{ shall use the first set of coordinates, that is (-1, 6)} \\ 6=-1(-1)+b \\ 6=1+b \\ 6-1=b \\ b=5 \end{gathered}[/tex]Having calculated the values of m (the slope) and b (the y-intercept), the equation is now;
[tex]\begin{gathered} y=mx+b \\ y=-1x+5 \\ y=-x+5 \end{gathered}[/tex]Write an equation and solve to find the value of your variable. 7.3 less than -2 times a number is the same as 16 1/2. n=?
The equation is -2n - 7.3 = 16 1/2
The value of the variable n = -11.9
STEP - BY - STEP EXPLANATION
What to find?
• Write the equation of the given statement.
,• The value of n.
Given:
find the value of your variable. 7.3 less than -2 times a number is the same as 16 1/2. n=?
To solve follow the steps below:
Step 1
Translate the given statement into equation.
Let n be the number.
-2n - 7.3 = 16 1/2
Step 2
Convert 16 1/2 to decimal.
-2n - 7.3 = 16.5
Step 3
Add 7.3 to both-side of the equation.
-2n = 16.5 + 7.3
Step 4
Simplify the right-hand side of the equation.
-2n =23.8
Step 5
Divide both-side of the equation by -2.
[tex]\frac{\cancel{-2}n}{\cancel{-2}}=\frac{23.8}{-2}[/tex]n = -11.9
Therefore, the value of the variable n = -11.9
Cynthia wants to buy a rug for a room that is 18ft wide and 28ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 264 square feet of carpeting. What dimensions should the rug have ?
SOLUTION
Let us use a diagram to illustrate the information, we have
Now, from the diagram, let the length of the uniform strip of floor around the rug be x, So, this means the length and width of the rug is
[tex]\begin{gathered} \text{length = 2}8-x-x=28-2x \\ \text{width = }18-x-x=18-2x \end{gathered}[/tex]Now, since she can afford to buy a rug of 264 square feet for carpeting, this means that the area of the rug is 264, hence we have that
[tex]\begin{gathered} \text{area of rug = (2}8-2x)\times(18-2x) \\ 264=\text{(2}8-2x)(18-2x) \\ \text{(2}8-2x)(18-2x)=264 \end{gathered}[/tex]Solving for x, we have
[tex]\begin{gathered} \text{(2}8-2x)(18-2x)=264 \\ 504-56x-36x+4x^2=264 \\ 504-92x+4x^2=264 \\ 4x^2-92x+504-264=0 \\ 4x^2-92x+240=0 \end{gathered}[/tex]Dividing through by 4 we have
[tex]\begin{gathered} x^2-23x+60=0 \\ x^2-20x-3x+60=0 \\ x(x-20)-3(x-20)=0 \\ (x-3)(x-20)=0 \\ x=3\text{ or 20} \end{gathered}[/tex]So from our calculation, we go for x = 3, because 20 is large look at this
[tex]\begin{gathered} \text{From the length which is (2}8-2x) \\ 28-2(20) \\ =28-40=-12 \end{gathered}[/tex]length cannot be negative, so we go for x = 3.
Hence the dimensions of the rug becomes
[tex]\begin{gathered} \text{(2}8-2x) \\ =28-2(3) \\ =28-6=22 \\ \text{and } \\ 18-2x \\ 18-2(3) \\ 18-6=12 \end{gathered}[/tex]So the dimension of the rug should be 22 x 12 feet
In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.11. What is the probability that the mixture will test positive?
From the information available, the mixture will test negative if all 6 samples are negative.
The probability of each is independent of the other for all 6 samples.
The probability of a sample testing positive is 0.11. That means the probability of a sample testing negative would be
[tex]\begin{gathered} P\lbrack neg\rbrack=1-P\lbrack pos\rbrack \\ P\lbrack\text{neg\rbrack}=1-0.11 \\ P\lbrack\text{neg\rbrack}=0.89 \end{gathered}[/tex]However, for all 6 samples, the probability of having a negative result would be a product of probabilities, that is;
[tex]\begin{gathered} P\lbrack tests\text{ negative}\rbrack=0.89\times0.89\times0.89\times0.89\times0.89\times0.89 \\ P\lbrack\text{tests negative}\rbrack=0.89^6 \\ P\lbrack\text{tests negative\rbrack}=0.4969 \end{gathered}[/tex]Therefore if we have the probability of the mixture testing negative as
[tex]P_{\text{neg}}=0.4969[/tex]The probability of the mixture testing positive would be;
[tex]\begin{gathered} P_{\text{pos}}=1-P_{\text{neg}} \\ P_{\text{pos}}=1-0.4969 \\ P_{\text{pos}}=0.5031 \end{gathered}[/tex]ANSWER:
The probability that the mixture will test positive is 0.5031
Rounded to 2 decimal places,
[tex]P_{\text{pos}}=0.50[/tex]