Answer:
y = - (11/19)x + 8/19==============================
Given Line 11x + 19y = 8To findConvert the equation into slope-intercept formSolutionThe slope-intercept form is:
y = mx + bConvert the given equation to the above form.
11x + 19y = 8 ⇔ Given equation19y = - 11x + 8 ⇔ Make y the subject19y/19 = - 11x/19 + 8/19 ⇔ Divide all terms by 19y = - (11/19)x + 8/19 ⇔ AnswerIn a nearby park, a field has been marked off for the neighborhood Pop Warner football team. If the field has a perimeter of 310 yd and an area of 4950 yd', what are the dimensions of the field?
Answer:
The dimension of the field is ( 110 x 45)
Exolanations:
Perimeter of the field, P = 310 yd
Area of the field, A = 4950 yd²
Note that the shape of a field is rectangular:
Perimeter of a rectangle, P = 2(L + B)
Area of a rectangle, A = L x B
Substituting the values of the perimeter, P, and the Area, A into the formulae above:
310 = 2(L + B)
310 / 2 = L + B
155 = L + B
L + B = 155...............................................(1)
4950 = L x B...............(2)
From equation (1), make L the subject of the formula:
L = 155 - B...................(3)
Substitute equation (3) into equation (2)
4950 = (155 - B) B
4950 = 155B - B²
B² - 155B + 4950 = 0
Solving the quadratic equation above:
B² - 110B - 45B + 4950 = 0
B (B - 110) - 45(B - 110) = 0
(B - 110) ( B - 45) = 0
B - 110 = 0
B = 110
B - 45 = 0
B = 45
Substitute the value of B into equation (3)
L = 155 - B
L = 155 - 45
L = 110
The dimension of the field is ( 110 x 45)
Peri earned $55 for 5 dog walks. If Peri earned $22, how many times did she walk her neighbor's dog?
Answer:
2
Step-by-step explanation:
55÷5=11
22÷11=2
Gourmet Eatery has a policy of automatically adding a 18% tip to every restaurant Bill if a restaurant bill is $12 how much is it
Let:
B = Bill
C = Cost of the meal
T = Tip
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What is this answer?
Answer:
24/25
Step-by-step explanation:
We are dividing 3/10 by 5/16
the length of a rectangle is two more than the width. if the perimeter is 28, find the length and the width of the rectangle, let w represent the width and l represent the length.
You have that the perimeter of a rectangle is 28. In order to find the values of length and width of the rectangle, you take into account the following formula for the perimeter of a rectangle:
[tex]P=2w+2l[/tex]where w is the width and l is the length. You have that the length l is twice the width w of the rectangle, that is l=2w. By replacing this expression for l into theformula for the calculation of the perimeter you obtain:
[tex]P=2w+2(2w)=2w+4w=6w[/tex]Thus, you have that P = 6w. You solve this equation for w, and also replace the value of P, just as follow:
[tex]\begin{gathered} P=6w \\ w=\frac{P}{6}=\frac{28}{6}=\frac{14}{3}=4.66 \end{gathered}[/tex]Then, the width is 4.66. The length is:
[tex]l=2w=2(4.66)=9.33[/tex]length = 9.33
Scientists are conducting an experiment with a gas in a sealed container. The mass of the gas is measured, and the scientists realize that the gas is leaking over time in a linear way. Nine minutes since the experiment started, the gas had a mass of 68.4 grams. Thirteen minutes since the experiment started, the gas had a mass of 61.2 grams. At what rate is the gas leaking? Use g for grams and min for minutes.
the rate is:
[tex]m=\frac{61.2-68.4}{13-9}=-\frac{7.2}{4}=-1.8\frac{g}{\min }[/tex]Triangle UVW, with vertices U(-5,5), V(-4,7), and W(-9,8), is drawn on the coordinate grid below.
The area formula of a triangle given the coordinates of the vertices :
[tex]U(-5,5),V(-4,7),W(-9,8)[/tex][tex]A=\lvert\frac{U_x(V_y-W_y)+V_x(W_y-U_y)+W_x(U_y-V_y)}{2}\rvert[/tex]Using the formula above, the area will be :
[tex]\begin{gathered} A=\lvert\frac{-5(7-8)-4(8-5)-9(5-7)}{2}\rvert \\ A=\lvert\frac{5-12+18}{2}\rvert \\ A=\lvert\frac{11}{2}\rvert \\ A=\lvert5.5\rvert \\ A=5.5 \end{gathered}[/tex]The answer is 5.5 square units
Part of a manufacturing plant packages tissues in boxes. Each box contains 250 tissues. Part A: Write an algebraic expression that can be used to find the total number of tissues packaged one day. Describe what the variable stands for in your expression. Part B: In one hour, 87,500 tissues are packaged into boxes. How many boxes of tissues are packaged? Show your work. Answer: boxes
Given
A manufacturing plant packages tissues in boxes and each box contains 250 tissues.
Required
We need to find an algebraic expression that illustrates the number of tissues packed per day.
Explanation
Let x be the number of boxes manufactured in one day
Then total number of tissues manufactured on that day is 250x
This answers our first part.
Now in one hour 87500 tissues are manufactured
Let the number of boxes packed in one hour be y
Then
[tex]y=\frac{number\text{ }of\text{ }tissues\text{ }in\text{ }one\text{ }hour}{number\text{ }of\text{ }tissues\text{ }in\text{ }each\text{ }box}=\frac{87500}{250}=350\text{ boxes}[/tex]So the answer to second part is 350 boxes.
If f(x)=2x+1, what is f(2)?
f(2) means that we must substitute the value 2 in the place of x, that is
[tex]f(2)=2\cdot2+1[/tex]which gives f(2)=5.
Here is another riddle:•The sum of two numbers is less than 2.•If you subtract the second number from the first, the difference is greater than 1.What are the two numbers? Explain or show how you know.
Let the two numbers be A and B
Their sum is less than 2
Thus,
[tex]A+B<2[/tex]When the second number is subtracted from the first number, the difference is greater than 1.
Thus,
[tex]A-B>1[/tex]Solve the equation by working backward through the number trick.
x = 3
Explanations:The given equation is:
[tex]\frac{4(x+3)-6}{2}=\text{ 9}[/tex]Step 1: Cross multiply
4 ( x + 3) - 6 = 9(2)
Step 2: Remove the brackets by expanding the equation
4x + 12 - 6 = 18
4x + 6 = 18
Step 3: Collect like terms
4x = 18 - 6
4x = 12
Step 4: Divide both sides by 4
4x / 4 = 12 / 4
x = 3
StatusExam9 ft.15 ft.The volume ofthe figure iscubic feet.15 ft.15 ft.
Step 1:
The figure is a composite figure with a square base pyramid and a cube.
Step 1:
The volume of the composite shape is the sum of the volume of a square base pyramid and a cube.
[tex]\text{Volume = L}^3\text{ + }\frac{1}{2}\text{ base area }\times\text{ height}[/tex]Step 3:
Given data
Cube
Length of its sides L = 15 ft
Square base pyramid
Height h = 9 ft
Length of the square base = 15 ft
Step 4:
Substitute in the formula.
[tex]\begin{gathered} \text{Volume = 15}^3\text{ + }\frac{1}{3}\text{ }\times15^2\text{ }\times\text{ 9} \\ \text{= 3375 + 675} \\ =4050ft^3 \end{gathered}[/tex]A small town has two local high schools. High School A currently has 900 studentsand is projected to grow by 50 students each year. High School B currently has 500students and is projected to grow by 100 students each year. Let A represent thenumber of students in High School A in t years, and let B represent the number ofstudents in High School B after t years. Graph each function and determine whichhigh school is projected to have more students in 4 years.
High School A currently has 900 students and is projected to grow by 50 students each year.
We can write an equation using the above information
[tex]A=900+50t[/tex]Where A represents the number of students in High School A in t years.
High School B currently has 500 students and is projected to grow by 100 students each year.
We can write an equation using the above information
[tex]B=500+100t[/tex]Where B represents the number of students in High School B in t years.
Let us graph these two equations
Determine which high school is projected to have more students in 4 years.
Let us substitute t = 4 into both equations
[tex]\begin{gathered} A=900+50t \\ A=900+50(4) \\ A=900+200 \\ A=1100 \end{gathered}[/tex]High school A is projected to have 1100 students in 4 years.
[tex]\begin{gathered} B=500+100t \\ B=500+100(4) \\ B=500+400 \\ B=900 \end{gathered}[/tex]High school B is projected to have 900 students in 4 years.
Therefore, high school A is projected to have more students (1100) as compared to high school B (900) in 4 years.
the sum of the reciprocal of two consecutive positive integers is 17/72. Write an equation that can be used to find the two integers. What are the integers?
Answer:
[tex]\frac{1}{x}+\frac{1}{x+1}=\frac{17}{72}[/tex]The two consecutive positive integers are 8 and 9.
Explanation:
Let the 1st positive integer be x and the 2nd be x + 1, so their reciprocal will be 1/x and 1/x+1.
The equation can then be written as;
[tex]\frac{1}{x}+\frac{1}{x+1}=\frac{17}{72}[/tex]To solve for x, the 1st step is to find the LCM of the left-hand side of the equation;
[tex]\begin{gathered} \frac{(x+1)+x}{x(x+1)}=\frac{17}{72} \\ \frac{2x+1}{x(x+1)}=\frac{17}{72} \end{gathered}[/tex]We can equate the numerators and solve for x as shown below;
[tex]\begin{gathered} 2x+1=17 \\ 2x=17-1 \\ x=\frac{16}{2} \\ x=8 \end{gathered}[/tex]If the 1st positive integer, x, is 8, therefore the 2nd integer, x + 1, will be;
[tex]x+1=8+1=9[/tex]Is the following sequence arithmetic, geometric, or neither?1, 5, 25, 125, 625
This is a geometric sequence
This is because we can find the common ratio and not common difference
A normal distribution has a mean of 101 and a standard Deviation of 12. find the probability that a value selected at random is in the following interval.at most 13
Answer:
84.134%
Explanation:
First, determine the value of the z-score.
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ =\frac{113-101}{12} \\ =\frac{12}{12} \\ z-score=1 \end{gathered}[/tex]Next, we determine the probability that a value selected at random is at most 113:
[tex]\begin{gathered} P(X\le113)=P(x\le1)_{} \\ =0.84134 \\ =84.134\% \end{gathered}[/tex]Thus, the probability that a value selected at random is in the given interval is 84.134%.
What is the slope and y-intercept?
y=3x-2
Options:
Blank # 1
Blank # 2
The value of slope is 3 and the value of y - intercept is -2.
Slope and y intercept:
The slope refers the rate of change in y per unit change in x.
The y-intercept states the y-value when the x-value is 0.
Given,
Here we have the equation
y = 3x - 2
Now, we need to find the slope and y intercept of the equation.
We know that, the standard form of the equation of the line is,
y = mx + b
Where
m represents the slope
b represents the y-intercept.
So, we have to rewrite the given equation as,
y = 3x + (-2)
So, while comparing the given equation with standard form, then we get,
the value of the slope is 3 and the value of the y intercept is -2.
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How would the fraction71-√√√5using difference of squares?OA. 7-7√56OB. 7+7√56O c. 7+7√5OD. -7+7√5← PREVIOUSbe rewritten if its denominator is rationalizedSUBMIT
1) Examining that ratio, we can perform the following:
[tex]\begin{gathered} \frac{7}{1-\sqrt{5}} \\ \\ \frac{7\left(1+\sqrt{5}\right)}{\left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right)} \\ \\ \frac{7+7\sqrt{5}}{1^2-(\sqrt{5})^2} \\ \\ \frac{7(1+\sqrt{5})}{-4} \\ \\ -\frac{7(1+\sqrt{5})}{4} \end{gathered}[/tex]2) Note that when we multiply that ratio by their conjugates, that yields a difference between two squares. Note that on the top, there is the expanded version of this expression.
Thus, the answer is D
Angelina has 10 yards of fabric. She needs ⅓ yard of fabric for each purse she will sew. How many purses will she be able to make?
Divide the total amount of fabric by the amount needed to create a purse to find how many purses will she be able to make.
Since she has 10 yards of fabric and each purse requires 1/3 of a yard, then, divide 10 over 1/3:
[tex]10\div\frac{1}{3}=\frac{10}{1}\div\frac{1}{3}=\frac{10\times3}{1\times1}=\frac{30}{1}=30[/tex]Therefore, Angelina will be able to make 30 purses using 10 yards of fabric.
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subtract (7u^2+10u+6) from (3u^2_5u+4).
Given:
[tex]\mleft(3u^2-5u+4\mright)-(7u^2+10u+6)[/tex]The objective is to subtract both the terms.
[tex]\begin{gathered} \mleft(3u^2-5u+4\mright)-(7u^2+10u+6) \\ 3u^2-5u+4-7u^2-10u-6 \\ -4u^2-15u-2 \end{gathered}[/tex]Hence the subtraction of the given term is,
[tex]-4u^2-15u-2[/tex]Tran is in charge of the school's Awards Dinner. She set up the multi-purpose room with a stage in front and round tables for parents, students, and family members to sit around for dinner. Below is the floorplan that she drew for the eventStageHow many people can be seated as the tables are arranged right now? (In the box below, type your answer as a number only
Tran has made a plan with 12 tables for 8 people each of them. Then, we have 12 tables * 8 ( amount of chairs each of them) = 96. So 96 people can be seated.
Jerry takes out a 30-year mortgage for $170,000.00 to buy a condo. His monthly mortgage payment is $939.00. How much interest will he pay over the life of the loan? Round your answer to the nearest whole dollar.
Okay, here we have this:
Considering the provided information we obtain the following:
Mortgage capital=$170,000
Total payment = Monthly payment * 12 months of the year * number of years
Total payment = $939*12*30
Total payment = $338,040
Total payment = Mortgage capital + Interest
Replacing we obtain:
Total payment = Mortgage capital + Interest
$338,040=$170,000+interest
Interest= $338,040-$170,000
Total Interest=$168,040
Finally we obtain that the total interest is $168040.
From 1999 to 2009, the number of dogs [tex]D[/tex] and the number of cats [tex]C[/tex] (in hundreds) adopted from animal shelters in the United States are modeled by the equations [tex]D = 2n+3[/tex] and [tex]C = n +4[/tex], where [tex]n[/tex] is the number of years since 1999.
a. Write a function that models the total number [tex]T[/tex] of adopted dogs and cats in hundreds for that time period.
b. If this trend continues, how many dogs and cats will be adopted in 2013?
The functions that models the number of adopted dogs and cat is T = 3n + 7.
If the trend continues, the number of cats and dog that will be adopted by 2013 is 4600.
How to find the function that models a problem?From 1999 to 2009, the number of dogs D and the number of cats C (in hundreds) adopted from animal shelters in the United States are modelled by the equations D = 2n + 3 and C = n + 4, where n is the number of years since 1999.
Therefore, the functions that models the total number T of the adopted dogs and cats in hundreds for that time period can be represented as follows:
T = D + C
where
D = 2n + 3
C = n + 4
where
n = number of yearsT = 2n + 3 + n + 4
T = 3n + 7
b. If the trends continues the number of cats and dogs that will be adopted in 2013 can be calculated as follows:
n = 2013 - 1999 = 13Hence,
T = 3(13) + 7
T = 39 + 7
T = 46
Recall it's represented in hundred's
Therefore, 4600 dogs and cat will be adopted by 2013
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complete the square to writey= x2 + 4x +9 in graphing form.
In order to express y = x² + 4x +9 in graphing form and graphing it we can follow these steps:
1. complete squares to express the equation in the form y = (x - p)² + q
We have to add and subtract (b/2)² on the right, where b is the coefficient of the second term of the equation
y = x² + 4x +9 + (4/2)² - (4/2)²
y = x² + 4x +9 + (2)² - (2)²
We can gorup and factor some terms of the equation by applying the following formula:
(x + a)² = x² + 2ax + a²
then by writing 4x as 2×2x we get:
y = x² + 2×2x + (2)² - (2)² +9
y = (x + 2)² - (2)² + 9
y = (x + 2)² - 4 + 9
y = (x + 2)² + 5
For an equation of the form y = (x - p)² + q, the vertex is (q, p), then, the vertex of the parabola is (-2, 5)
2. Determine the x-intercepts by replacing 0 for y and solving for x, like this:
0 = (x + 2)² + 5
0 - 5 = (x + 2)² + 5 - 5
-5 = (x + 2)²
±√-5 = √(x + 2)²
±√-5 = x + 2
x = -2 ± √-5
As you can see, on the right side the argument of the square root is a negative number, which makes the solution of this equation a complex number, then which means that the parabola won't intercept the x-axis.
3. Find the y-intercept by replacing 0 for x:
y = (0 + 2)² + 5
y = (2)² + 5
y = 4 + 5
y = 9
Then, the y-intercept of this parabola is (0, 9)
By graphing the vertex (-2, 5) and the y-intercept (0, 9) and joining them with the parabola we get the following graph:
The area of the unshaded region is 22.5cm2 . What is the area of the rectangle?A) 11.25cm2B) 22.5cm2C) 45cm2D) 90cm2
Let's use the variable b to represent the white triangle base (which is the width of the rectangle), and the variable h to represent the white triangle height (which is the length of the rectangle).
The white triangle area is given by:
[tex]A=\frac{b\cdot h}{2}=22.5\text{ cm}^2[/tex]The area of the rectangle is given by the product of its length and its width, so we have:
[tex]A_2=b\cdot h=2\cdot(\frac{b\cdot h}{2})=2\cdot A=2\cdot22.5=45\text{ cm}^2[/tex]Therefore the correct option is C.
Solve. 2x – 5=-3x + 15
Explanation:
First we have to add 3x on both sides of the equation:
[tex]\begin{gathered} 2x-5+3x=-3x+3x+15 \\ 5x-5=15 \end{gathered}[/tex]Now add 5 on both sides:
[tex]\begin{gathered} 5x-5+5=15+5 \\ 5x=20 \end{gathered}[/tex]And finally divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{20}{5} \\ x=4 \end{gathered}[/tex]Answer:
x = 5
Answer:
[tex] \sf \: x = 4[/tex]
Step-by-step explanation:
Given equation,
→ 2x - 5 = -3x + 15
Now the value of x will be,
→ 2x - 5 = -3x + 15
→ 2x + 3x = 15 + 5
→ 5x = 20
→ x = 20 ÷ 5
→ [ x = 4 ]
Hence, the value of x is 4.
A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings
below:
Pepperoni
Sausage
Chicken Green pepper
Mushroom Pineapple
Ham
Onion
Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is
going to randomly choose 2 different toppings.
What is the probability that Rosa's mom chooses sausage and onion?
Choose 1 answer:
The Probability that Rosa's mom chooses sausage and onion is [tex]\frac{1}{^{8} C_{2} }[/tex]
What is Probability?Probability is the likelihood of an event occurring, measured by the ratio of the favorable cases to the whole number of cases possible.
The probability of an event happening = number of possible outcomes/total number of outcomes.
The number of possible outcomes is 8 exactly 1 of the total possible groups of toppings is sausage and onion.
The total number of outcome is 8 ways, because she has to choose the 2 toppings from possible 8 toppings
So the probability that Rosa's mom will chooses sausage and onion is [tex]\frac{1}{^{8} C_{2} }[/tex]
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Camera has Alyssa price of $768.95 before tax the sales tax rate is 8.25% final total find the total cost of the camera with sales tax included round your answer to the nearest cent as necessary
We know that the listed price of the camera is $768.95 and the tax rate is 8.25%.
To find the total cost we must use the next formula
[tex]\text{Total cost }=\text{listed price before tax+(listed price before tax }\cdot\text{rate tax)}[/tex]Now, we must replace the values in the formula using that 8.25% = 0.0825
[tex]\text{Total cost}=768.95+(768.95\cdot0.0825)[/tex]Simplifying,
[tex]\text{Total cost}=832.39[/tex]ANSWER:
$O32
The perimeter of a rectangular poster is 14 feet and the length is 4 feet. Describe how to use the perimeter formula to find the width.This calculator has a tray why the answer is not 3.2
Explanation
We are told that the perimeter of a rectangular poster is 14 feet and the length is 4 feet.
Perimeter simply means the total sum of all the sides of the rectangle
[tex]\begin{gathered} From\text{ the above} \\ let\text{ the length = y} \\ width\text{ =x} \end{gathered}[/tex]So, the perimeter is
[tex]x+x+y+y=2x+2y[/tex]Since the perimeter is 14 then
[tex]2x+2y=14[/tex]Also, the length is 4 feet
Therefore y = 4, so that
[tex]\begin{gathered} 2x+2(4)=14 \\ 2x+8=14 \\ collecting\text{ like terms} \\ 2x=14-8 \\ 2x=6 \end{gathered}[/tex]Making x the subject of the formula
[tex]\begin{gathered} x=\frac{6}{2}=3 \\ \\ x=3 \end{gathered}[/tex]Therefore, the width of the rectangle is 3 feet
The rectangle is
[tex]4+3+4+3=14[/tex]