We have to solve the equation.
[tex]x=-8y+9[/tex]We have 2 unknowns and one equation, so we can only express one in function of the other.
We already have x in function of y, so we will now express y in function of x:
[tex]\begin{gathered} x=-8y+9 \\ x-9=-8y+9-9 \\ \frac{x-9}{-8}=\frac{-8y}{-8} \\ \\ -\frac{x}{8}+\frac{9}{8}=y \\ \\ y=-\frac{x}{8}+\frac{9}{8} \end{gathered}[/tex]Answer:
y = -x/8 + 9/8
32. Recall the pattern that you found in the diamond problems from Ready, Set, Go #2. Use the pattern you discoveredto complete each diamond below.8-121-724ISet
Answer:
Step-by-step explanation:
6 Equations of parallel and perpendicular lines VEB
The equation for line u can be written as y = -x + 1. Line v, which is perpendicular to line
u, includes the point (-3, 2). What is the equation of line v?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answer:
y = 4/9x +10/3
Step-by-step explanation:
You want the slope-intercept equation of the line through point (-3, 2) that is perpendicular to the line y = -9/4x +1.
Slope-intercept equationThe slope-intercept form of the equation for a line is ...
y = mx + b . . . . . . m is the slope, b is the y-intercept
In order to write the desired equation, we need to know the desired slope and the y-intercept that makes the line go through the given point.
SlopeThe slope of the perpendicular line is the opposite reciprocal of the slope of the given line. The given line equation is in slope-intercept form, so the coefficient of x is the slope of it: -9/4.
The slope of the perpendicular line is the opposite reciprocal of this:
m = -1/(-9/4) = 4/9
Y-interceptSolving the slope-intercept form equation for b, we find ...
b = y - mx
Using the values of x and y for the given point, and the slope we just found, we have ...
b = 2 -(4/9)(-3) = 2 +4/3 = 10/3
Desired equationThe slope-intercept equation for a line with slope 4/9 and y-intercept 2/3 is ...
y = 4/9x +10/3
__
Additional comment
It can also be useful to start from the point-slope equation:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
Your line is ...
y -2 = 4/9(x +3) . . . . . . use m=opposite reciprocal of -9/4; (h, k) = (-3, 2)
y = 4/9x +(4/9)(3) +2 = 4/9x +10/3 . . . . . . add 2 and simplify
Solve by factoring. Be sure to look for a GCF first in case there is one-2x²-4x+70=0
ANSWER
x = 5 and x = -7
EXPLANATION
We want to solve the equation by factoring.
The equation is:
[tex]-2x^2\text{ - 4x + 70 = 0}[/tex]First, there is a greatest common factor that we can use to simplify the equation. That is -2, so, first we divide through by -2.
It becomes:
[tex]x^2\text{ + 2x - 35 = 0}[/tex]Now, factorise:
[tex]\begin{gathered} x^2\text{ + 2x - 35 = 0} \\ x^2\text{ + 7x - 5x - 35 = 0} \\ x(x\text{ + 7) - 5(x + 7) = 0} \\ (x\text{ - 5)(x + 7) = 0} \\ x\text{ = 5 and x = -7} \end{gathered}[/tex]I need to send a picture in order to answers the question because it has a graph.
The dotted plot representing how much a customer spends in a store from the attached diagram is Option D.
Step 1: Write out the frequency distribution of the population in tabular form
x | f
------------------------------------------
5 | 17
------------------------------------------
| 17
------------------------------------------
The difference between two numbers is 28. The sum of the two numbers is 56. Let x be the larger number and y be the smaller number. Which system of equations represents this proble O y - x = 28 I + y = 56 O x=y= 28 x + y = 56 Oy - 2 = 56 x + y = 28 - y = 56
Since x is the larger number and y is the smaller number
Since their sum is 56
That means add x and y then equate them by 56
[tex]x+y=56(1)[/tex]Since the difference between them is 28
That means subtract y from x and equate the answer by 28
[tex]x-y=28(2)[/tex]Look at the answer to find the correct answer
It is B
x - y = 28 and x + y = 56
Hello I could really use help with this problem please!
Answer:
C
[tex]A=2\pi\text{ square units; }h=2\text{ units}[/tex]Explanation:
Given:
Volume of a cylinder (V) = 4pi cubic units
To find:
Base area(A) and height(h)
Recall that the volume of a cylinder(A) is usually given as;
[tex]\begin{gathered} V=A*h \\ \end{gathered}[/tex]So let's go ahead and try each of the options and see which gives us 4pi on the left-hand side as we have on the right-hand side for Volume.
For option A;
We have that A = 1 and h = 2, so we'll have;
[tex]\begin{gathered} V=A*h \\ 4\pi=1*2 \\ 4\pi\ne2 \end{gathered}[/tex]For option B;
We have A = 2pi and h = 1, so we'll have;
[tex]\begin{gathered} 4\pi=2\pi *1 \\ 4\pi\ne2\pi \end{gathered}[/tex]For option C;
We have A = 2pi and h = 2, so we'll have;
[tex]\begin{gathered} 4\pi=2\pi *2 \\ 4\pi=4\pi \end{gathered}[/tex]We can see from the above that option C is the right option.
Kimberly has an empty cardboard box that weighs 0.5 pounds. She puts 10 loaves of bread and a 4-pound jar of peanut butter in the box. The total weight of the box and its contents is 19.5 pounds. One way to represent this situation is with the equation 0.5 - 106 + 4 = 19.5 In this situation, what does the solution to the equation represent? In other words, if you solved for b. what would the value of b tell you? You do not have to find the solution to answer the question
The equation is represented by:
0.5 + 10b + 4 = 19.5
In which 19.5 is the total weight of the box and it's contents.
0.5 is the weight of the cardboard box.
4 is the weight of the jar of peanut butter.
10b is the weight of all loaves of bread.
And b is the weight of a single loaf of bread
The answer is:
The solution of the equation, which is the value of b, represents the weight of a single loaf of bread.
If the number of college professors is P and the number of students S, and there are 20 times more students as professors, write an algebraic equation that shows the relationship
Answer
Algebraic equation that shows the relationship is
P = 20S
Explanation
Number of college professors = P
Number of students = S
There are 20 times as many students as professors.
P = (S) (20)
P = 20S
Hope this Helps!!!
find the ranges of values for which x²-5+6<0
Answer:
The range of values of x for which the function is < 0 is:
2<x<3.
Step-by-step explanation:
x²-5x+6<0
First find the critical points:
x^2 - 5x + 6 = 0
(x - 2)(x - 3) = 0.
x = 2, 3.
The critical points are 2 and 3.
Make a table of values:
x x<2 2<x<3 x >3
x -2 < 0 >0 >0
x -3 <0 <0 >0
(x - 2)(x - 3) >0 <0 >0
Three times a number decreased by 1 is 10 Three times the difference of a number is 1 is 10One less than three times a number is 10The quotient of a number and 3 is 10
Three times a number decreased by 1 is 10:
X is the number.
3x = three times a number.
3x - 1 = 10 (Three times a number decreased by 1 is 10)
3x = 10 + 1
3x = 11
x = 11/3
I need help answering this question The other values of x are 8 and 13
Given the modulus function expressed as:
[tex]y=|x-8|[/tex]Since the function is a modulus function, the dependent variables "y" will all be a positive value
Using the values of x to be -5, 8, and 13 to determine the ordered pairs
When x = -5
y = |-5 - 8|
y = |-13|
y = 13
The first ordered pair will be (-5, 13)
If x = 8
y = |8 - 8|
y = |0|
y = 0
The second ordered pair will be (8, 0)
If x = 13
y = |13 - 8|
y = |5|
y = 5
The third ordered pair will be at (13, 5)
The graph of the function is as shown below:
which of the following describe ✓2) Irrational number) Whole number ) Integer) Real number
Okay, here we have this:
Considering that a real number is said to be irrational if it cannot be expressed as a quotient of whole numbers. ✓2 is an irrational number, and as all the irrational number are real numbers ✓2 is also a real number.
what is 9=-1/4x+4 in standard form
The standard form in which the equation must be written is -1/4x = 5
Standard Equation FormStandard form is just another way to write a linear equation equation along with slope intercept form and point slope form.
Standard form appears in the form ax + by = c
Where a, b and c are integers and a must be positive
In the given equation 9 = -1/4x + 4, we can rewrite this into standard equation of line by
-1/4x + 4 = 9
-1/4x + 4 - 9 = 0
-1/4x - 5 = 0
-1/4x = 5
The standard form of the equation is -1/4x = 5
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Translate the sentence into an inequality, the product of c and 9 is greater than 16.
In order to write an inequality we can read the original statement in small parts.
In this case, the statement is:
"the product of c and 9 is greater than 16"
We have that "the product" is a multiplication
Then, "the product of c and 9" is the multiplication between c and 9:
9 · c
And, "the product of c and 9 is greater than 16" means that 9 · c is greater than 16:
9 · c > 16
Answer: 9 · c > 16Jim can choose plan A or plan B for his long distance charges. For each plan, cost (in dollars)depende on minutes used (per month) as shown below.(a)If Jim makes 40 minutes of long distance calls for the month, which plan costs more? How much more does it cost than the other plan?(b) For what number of long distance minutes do the two plans cost the same?
Answer:
• Plan B, by $4
,• 140 minutes
Explanation:
Part A
From the graph, at 40 minutes, the costs of the plans are:
• Plan A: $4
,• Plan B: $8
[tex]\begin{gathered} \text{Difference}=8-4 \\ =\$4 \end{gathered}[/tex]Plan B costs more by $4.
Part B
The point where the costs are the same is the time at which the two graphs intersect.
When the number of minutes = 140 minutes
• Cost of Plan A = $14
,• Cost of Plan B = $14
Thus, the two plans cost the same for 140 minutes of long-distance call.
• If the time spent is less than this amount, Plan B costs more.
A one-day admission ticket to a park costs $43.85 for adults and $15.95 for children. Two families purchased nine tickets and spent $338.85 for the tickets. Fill in a chart that
summarizes the information in the problem. Do not solve the problem.
Using mathematical operations we know that total tickets of 2 children ($31.9) and 7 adults ($306.95) were purchased which cost the total amount of $338.85.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).So, a number of adults and children who purchased the tickets:
Let, adults are 'a and children be 'c':Now, the equation can be:
a + c = 9a = 9 - cNow, the second equation will be:
43.85a + 15.95c = 338.85
Now, substitute a = 9 - c in equation (2) as follows:
43.85a + 15.95c = 338.8543.85(9 - c) + 15.95c = 338.85394.65 - 43.85c + 15.95c = 338.85- 27.9c = 338.85 - 394.65- 27.9c = - 55.8c = - 55.8/ - 27.9c = 55.8/27.9c = 2Hence:
a = 9 - ca = 9 - 2a = 7Then:
c = 2 ⇒ 15.95 × 2 = $31.9a = 7 ⇒ 43.85 × 7 = $306.95Sum = $338.85Therefore, using mathematical operations we know that total tickets of 2 children ($31.9) and 7 adults ($306.95) were purchased which cost the total amount of $338.85.
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In health class, Leslie is learning about making healthy food choices. For a lesson on digestive health, her teacher asks everyone to track how much fiber they eat daily. At breakfast, Leslie has a banana. She also has raisin bran cereal, which contains 3.8 grams of fiber. In all, Leslie eats 6.7 grams of fiber at breakfast.
Use an equation to find the amount of fiber in the banana.
The amount of fiber in the banana is 2.9 grams of fiber.
What is a equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
From the. information, she has raisin bran cereal, which contains 3.8 grams of fiber and in all, Leslie eats 6.7 grams of fiber at breakfast.
Let the fiber in banana be b. This will be illustrated as:
b + 3.8 = 6.7
Collect like terms
b = 6.7 - 3.8
b.= 2.9
The fiber is 2.9 grams
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Liz attended class every day since she started school as a kindergarten. She said she has been in school for about 1,000 days.What numbers could be the actual number of school days if Liz rounded to the nearest ten?4 grade student
Solution.
Given that Liz attended class every day since she started school as a kindergarten and that she said she has been in school for about 1000 days (by rounding up the actual number of days to the nearest ten)
The actual number is a number that when rounded up, we would arrive at 1000.
This number falls between the numbers 995 and 1004.
Answer: Any of the numbers below could be the actual number:
995, 996, 997, 998, 999, 1000, 1001, 1002, 1003, 1004
Find the area to the right of x=71 under a normal distribution curve with the mean=53 and standard deviation=9
Answer:
[tex]Area=0.0228\text{ or 2.28\%}[/tex]Explanation:
We were given the following information:
This is a normal distribution curve
Mean = 53
Standard deviation = 9
We are to find the area right of x = 71
This is calculated as shown below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ x=71 \\ \mu=53 \\ \sigma=9 \\ \text{Substitute these into the formula, we have:} \\ z=\frac{71-53}{9} \\ z=\frac{18}{9} \\ z=2 \end{gathered}[/tex]We will proceed to plot this on a graph as sown below:
The area to the right of x = 71 (highlighted in red above) is given by using a Standard z-score table:
[tex]\begin{gathered} =1-0.9772 \\ =0.0228 \\ =2.28\text{\%} \end{gathered}[/tex]Therefore, the area that lies to the right of x = 71 is 0.0228 or 2.28%
The table below shows possible outcomes when two spinners that are divided into equal sections are spun. The first spinner is labeled with five colors, and the second spinner is labeled with numbers 1 through 5. Green Blue Pink Yellow Red 1 Gi B1 P1 Y1 R1 1 2 . G2 B2 P2 Y2 R2 3 G3 B3 P3 Y3 R3 4 G4 B4 P4 Y4 R4 5 G5 B5 P5 Y5 R5 According to the table, what is the probability of the first spinner landing on the color pink and the second spinner landing on the number 5?
Answer:
P = 0.04
Explanation:
The probability is equal to the number of options where the first spinner is landing on the color pink and the second spinner is landing on the number 5 divided by the total number of options.
Since there is only one option that satisfies the condition P5 and there are 25 possible outcomes, the probability is:
[tex]P=\frac{1}{25}=0.04[/tex]So, the answer is P = 0.04
the table shows the number of jeans sold at a store at different prices
To make a plot of the data you first must choose your axis. In this case we've chosen the X axis to be the average cost of the jeans and the Y axis to be the number of copies sold. To graph the data we match the information we're given in the table as shown in the drawing.
The dimensions and the weight of several solids are given. Use the density information to determine what element is the solid made up of.
Given:
Dimensions and weight of a solid is given.
Height (h) of a cylinder (in cm) =
[tex]h=5[/tex]Radius (r) of a cylinder (in cm) =
[tex]r=5[/tex]Mass (m) of solid (in grams)=
[tex]m=3090.5[/tex]Density of several elements is given.
Cobalt=8.86, Copper=8.96, Gold=19.3, Iron=7.87, Lead 11.3, Platinum=21.5, Silver=10.5, Nickel=8.90.
Required:
What element is the solid made up of.
Answer:
Let us find the volume (V) of cylinder (in cubic cm).
[tex]\begin{gathered} V=\pi\times r^2\times h \\ V=3.14\times\left(5\right)^2\times5 \\ V=3.14\times25\times5 \\ V=392.5 \end{gathered}[/tex]Using formula of density (D), we get,
[tex]\begin{gathered} D=\frac{m}{V} \\ D=\frac{3090.5}{392.5} \\ D=7.87 \end{gathered}[/tex]Hence, the density of the solid is 7.87 grams per cubic cm.
From the given information of density of several elements, we see that the solid is made up of Iron.
Final Answer:
The solid is made up of Iron.
Is the prime factor of 85 17x5
Given data:
The given number is 85.
The given number 85 can be expressed in terms of their prime factors as,
[tex]85=5\times17[/tex]Thus, yes 85 can be expressed in terms of their prime factors as 17x5.
y−10=2(x−8)Write in Standard Form
The standard form of a linear equation in two variables is given by the expresssion:
[tex]Ax+By=C[/tex]So, rewriting the equation:
y-10=2x-16
y-2x=-16+10
y-2x=-6
2x-y=6
the square root of 31 is closer to which number? 6 or 5.
Answer:
6
Explanation:
First, we find the squares of 5 and 6.
[tex]\begin{gathered} 5^2=25 \\ 31-25=6 \end{gathered}[/tex][tex]\begin{gathered} 6^2=36 \\ 36-31=5 \end{gathered}[/tex]We conclude therefore that the square root of 31 is closer to 6 since it has a smaller difference.
пеу Fabric Sale At a fabric store, fabrics are sold by the yard. A dressmaker spent $46 on 5 yards of silk and cotton fabrics for a dress. 1 x + y = 5 117x + 4y = 46) Silk is $17 per yard and cotton is $4 per yard. Here is a system of equations that represent the constraints in the situation. What does the solution to the system represent?
It is said that the dressmaker bought 5 yards of cotton and silk. Let's see the first equation of the system:
[tex]x+y=5[/tex]And that he spent $46 on those 5 yards. Also, it is said that silk costs $17 per yard and cotton $4 per yard. Let's see the second equation of the system:
[tex]17x+4y=46[/tex]If 46 is how much the dressmaker spent, and 17 and 4 represent how much silk and cotton cost PER YARD then we know that x and y represent how much of each fabric did the dressmaker bought. Also, in the first equation you see that the total is 5 yards. So, if you solve this system you will find that 'x' is how many yards of silk the dressmaker bought and 'y' is how many yards of cotton he bought.
In summary, the solution of this system represents how may yards of silk (x) and cotton (y) the dressmaker bought.
what is the slope formula of (4,2) and (7, 6.5)
Suppose the given coordinates are represented as,
[tex]\begin{gathered} (x_1,y_1)=(4,2) \\ (x_2,y_2)=(7,6.5) \end{gathered}[/tex]Then, the formula for slope can be expressed as,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{6.5-2}{7-4} \end{gathered}[/tex]Solving it,
[tex]m=\frac{4.5}{3}=1.5[/tex]The slope is 1.5.
The formula of (10, 8) anjd (-5,8) is
[tex]m=\frac{8-8}{-5-10}[/tex]Rewrite each equation in slope intercept form . Then determine whether the lines are perpendicular . Explain your answer .. y - 6 = - 5/2 (x + 4) 5y = 2x + 6
y - 6 = - 5/2 (x + 4)
To write in slope-intercept form means to write in the form;
y= mx + b
where m is the slope and b is the intercept
y - 6 = - 5/2 (x + 4)
open the parenthesis
y - 6 = -5/2 x - 10
add 6 to both-side of the equation
y = - 5/2 x - 10 + 6
y = -5/2 x - 4
[tex]y=-\frac{5}{2}x\text{ - 4}[/tex]Next is to check whether 5y = 2x + 6 is perpendicular to the above
To do that, we have to make the equation to be in the form y=mx+ b
5y = 2x + 6
Divid through by 5
y = 2/5 x + 6/5
[tex]y\text{ = }\frac{2}{5}x\text{ + }\frac{6}{5}[/tex]The slope of perpendicular equation, when multiply gives minus one (-1)
The slope of the first equation = -5/2
The slope of the second equation is 2/5
Multiplying the two slopes;
(-5/2) (2/5) = -1
Hence the lines are perpendicular
What is the slant height and surface area of the pyramid
we have that
The surface area of the pyramid is equal to the area of its square base plus the area of its four triangular faces
step 1
Find out the area of the square base
A=15^2
A=225 ft2
step 2
Find out the area of one triangular face
the area of a triangle is equal to
A=(1/2)(b)(h)
we have
b=15 ft
h ----> is the slant height
To find out the slant height, apply the Pythagorean Theorem
h^2=10^2+(15/2)^2
h^2=100+56.25
h=12.5 ft
therefore
A=(1/2)(15)(12.5)
A=93.75 ft2
step 3
The surface area is equal to
SA=225+4(93.75)
SA=600 ft2 and the slant height is 12.5 ftDylan invested $93,000 in an account paying an interest rate of 3% compoundedquarterly. Assuming no deposits or withdrawals are made, how much money, to thenearest cent, would be in the account after 17 years?
The formula to calculate compound interest is given to be:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where:
[tex]\begin{gathered} A=\text{ final amount} \\ P=\text{ initial amount (principal)} \\ r=\text{ interest rate} \\ n=\text{ number of times interest applied per time period} \\ t=\text{ number of time period elapsed} \end{gathered}[/tex]The following parameters are given in the question:
[tex]\begin{gathered} P=93000 \\ r=\frac{3}{100}=0.03 \\ n=4(quarterly) \\ t=17\text{ years} \end{gathered}[/tex]We can substitute these values into the formula to calculate the final amount as follows:
[tex]A=93000(1+\frac{0.03}{4})^{4\times17}[/tex]Solving, we get:
[tex]\begin{gathered} A=93000\times1.0075^{68} \\ A=154,577.64 \end{gathered}[/tex]The amount after 17 years is $154,577.64
