Answer:
(-1, 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
-2x - y = 0
10x + y = -8
Step 2: Solve for x
Elimination
Combine equations: 8x = -8Isolate x: x = -1Step 3: Solve for y
Define equation: -2x - y = 0Substitute in x: -2(-1) - y = 0Multiply: 2 - y = 0Isolate y term: -y = -2Isolate y: y = 2Answer:
Step-by-step explanation:
-2x -y = 0
10x+ y= -8
8x = -8
x = -1
-10 + y = -8
y = 2
(-1, 2)
Researchers wanted to determine if there was an association between the level of trauma of an individual and their risk
of diabetes. The researchers studied 1544 people over the course of 12 years. During this 12-year period, they
interviewed the individuals and asked questions about their daily lives and the hassles they face. In addition,
hypothetical scenarios were presented to determine how each individual would handle the situation. These interviews
were videotaped and studied to assess the emotions of the individuals. The researchers also determined which
individuals in the study experienced any type of diabetes over the 12-year period. After their analysis, the researchers
concluded that the trauma-free individuals were less likely to experience diabetes. Complete parts (a) through (c).
(a) What type of observational study was this? Explain.
This was a
because information was collected about a group of individuals
The observational study is the Cross-sectional studies.
What is an observational study?It should be noted that an observational study is simply used to answer a research question that is based on what the researcher observes.
This is a cross-sectional studies because it analyzes a population of study at a specific point in time. It should be noted that this involves narrowing previously collected data to one point in time to test the prevalence of a theory.
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Which is the best estimate of 162% of 79?
112
119
128
136
Answer:
nwm zycze powodzenia kolego drogi
What is the graph of this function
A statement, rule, or regulation that establishes the relationship between an independent variable and a dependent variable is known as a function.
A network can be represented mathematically as a graph, which explains the connection between lines and points. A graph consists of some points with connecting lines.
Consider the function,
[tex]f(x)=\frac{||x||+2}{2}[/tex] and 0 ≤ x ≤ 6
To graph the function we will find the points on the graph for different values of x.
When x = 0,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(x)=\frac{||0||+2}{2}=1[/tex]
When x = 1,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(1)=\frac{||1||+2}{2}\\ f(1)=\frac{3}{2}[/tex]
When x = 2,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(2)=\frac{||2||+2}{2}[/tex]
[tex]f(2)=2[/tex]
When x = 3,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(3)=\frac{||3||+2}{2}[/tex]
[tex]f(3)=\frac{5}{2}[/tex]
When x = 4,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(4)=\frac{||4||+2}{2}\\ f(4)=3[/tex]
When x = 5,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(5)=\frac{||5||+2}{2}[/tex]
[tex]f(5)=\frac{7}{2}[/tex]
When x = 6,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(6)=\frac{||6||+2}{2} \\f(6)=4[/tex]
Therefore, the points on the graph of the function [tex]f(x)=\frac{||x||+2}{2}[/tex] are ( 0, 1 ), ( 1, ( 3/2 ) ), ( 2, 2 ), ( 2, ( 5/2 ) ), ( 4, 3 ), ( 5, ( 7/2 ) ), and ( 6, 4).
Hence, the graph of the function is:
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William and his children went into a restaurant where they sell hamburgers for $8 each and drinks for $2.50 each. William has $95 to spend and must buy no less than 18 hamburgers and drinks altogether. If xx represents the number of hamburgers purchased and yy represents the number of drinks purchased, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
95=Xx9 +Yx2.50
Step-by-step explanation:
The inequalities graphically shows the given situation is 95 ≥ +2.50y + 18x. The graph is attached below.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for that equation or inequality might be true. Such values are called solution to that equation or inequality.
Here Set of such values is called solution set to the considered equation or inequality.
We have been given that William and his children went into a restaurant where they sell hamburgers for $8 each and drinks for $2.50 each.
Since William has $95 to spend and must buy no less than 18 hamburgers and drinks altogether.
If x represents the number of hamburgers purchased and y represents the number of drinks purchased then;
95 ≥ +2.50y + 18x
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Ritzie has 80 metres of fencing wire which she wants to use to fence a rectangular plot for gardening. She wished to get the right length and width such that the area enclosed is the maximum. Let x to represent length and y to represent width.
1) Write two equations one for perimetre and the other for area using X and Y
2)Obtain only one equation in terms of area from the equations in 1
Step-by-step explanation:
1)
the perimeter P
P = 2x + 2y = 80 m
the area A
A = x × y
2)
2x + 2y = 80
2y = 80 - 2x
y = 40 - x
and we use that in the equation for area
A = x × (40 - x) = 40x - x²
we find the maximum (or minimum) of a function by finding the 0s of the first derivative.
A' = 40 - 2x = 0
40 = 2x
x = 20
y = 40 - x = 40 - 20 = 20
and just to be sure :
if the second derivative at that point x is negative, we have a maximum, if it is positive, we have a minimum.
A'' = -2
so, it is negative for all x incl. x = 20.
therefore, we have a maximum.
the rectangle with perimeter of 80 m and the max. area is a square of 20 m side length.
In a recent year, a university had an enrollment of 15,363 male and 19,512 female undergraduate students. The total number of full-time instructional faculty was 1,849. Find the ratio of students to full-time instructional faculty as a unit ratio. Round to the nearest whole number.
The required ratio of students to teachers is 19: 1.
Given that,
The total enrollment of male students and female students is 15,363 male and 19,512 female respectively.
The total number of full-time instructional faculty was 1,849.
To determine the ratio of students to teachers.
Here,
Total students = 15363 + 19512 = 34875
Number of teachers = 1849
Now,
Ratio = total students / teacher
Ratio = 34875 / 1849
Ratio = 19 : 1
Thus, the required ratio of students to teachers is 19 : 1.
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A chord of a circle 9cm long if it's distance of the centre of the circle is 5 cm calculate the radius of the circle
considering the distance between the center of the circle and the chord is perpendicular, pythagorean theorem can be applied to calculate the radius of the circle.
[tex]r^2=a^2+b^2[/tex] , r=radius, a=half of the chord length, b the distance between the center of the circle and the center of the chord
[tex]r^2=(4.5cm)^2+(5cm)^2\\r^2=20.25cm^2+25cm^2\\r^2=45.25cm^2\\r=\sqrt{45.25cm^2}\\r=6.7268cm[/tex]
The bill for dinner was $77.12. You left $15.88 for the tip. What percentage of the original bill was the tip?
Answer:
The tip was 20.6% or 20.59% of the original bill
Step-by-step explanation:
Question: The bill for dinner was $77.12. You left $15.88 for the tip. What percentage of the original bill was the tip?
Step-by-step:
To find the percentage of how much a part ($15.88) is or a whole ($77.12), the formula of part = percentage * whole is used.
It is usually written as a = p*w
In this case, $15.88 is a and $77.12 is w.
so, 15.88 = p*77.12
However, we need to find p. To do so, we need to get p by itself. Divide 77.12 on both sides so that it cancels out on the right side.
15.88 divided by 77.12 is about 0.2059
We need to make the decimal a percentage by multiplying 100
0.2059 * 100 = 20.59%
You could probably round it up to 20.6% if you wanted to
Therefore, the tip was 20.6% or 20.59% of the original bill.
Find the coordinates of the point 3/10 of the way from A to B. The points given are A(-3,-5) , B(9,6)
[tex]\displaystyle\\Answer:\ (-\frac{3}{13},-2\frac{6}{13} )[/tex]
Step-by-step explanation:
[tex]\displaystyle\\\frac{3}{10} =0.3\\\\(-3,-5)\ \ \ \ \ (9,6)\\\\\boxed {x=\frac{x_1+\lambda x_2}{1+\lambda} }\ \ \ \ \ \ \ \ \ \ \ \boxed {y=\frac{y_1+\lambda y_2}{1+\lambda} }\\\\x_1=-3\ \ \ \ \ x_2=9\ \ \ \ \ y_1=-5\ \ \ \ \ \ \ y_2=6\\\\x=\frac{-3+0.3*9}{1+0.3} \\\\x=\frac{-3+2.7}{1.3} \\\\x=\frac{-0.3}{1.3}\\\\ x=-\frac{0.3*10}{1.3*10}\\\\ x=-\frac{3}{13} \\\\[/tex]
[tex]\displaystyle\\y=\frac{-5+0.3*6}{1+0.3} \\\\y=\frac{-5+1.8}{1.3} \\\\y=\frac{-3.2}{1.3} \\\\y=-\frac{3.2*10}{1.3*10} \\\\y=-\frac{32}{13} \\\\y=-2\frac{6}{13} \\[/tex]
The slope of the parabola
The equation of the line tangent to the parabola at x = 4 is y = 13 · x - 27. The tangent line has a slope of 13 and a intercept of - 27.
How to determine the equation of a line tangent to a parabola
Parabolae are defined by quadratic equations, that is, equations whose form is y = a · x² + b · x + c. The slope of a line tangent to a point of the curve is defined by a linear equation, that is, an equation of the form y = m · x + b. By derivative rules, the slope of the tangent line can be found by using the following expression:
m = 2 · a · x + b
Then, if we know that y = 2 · x² - 3 · x + 5 and x = 4, then the equation of the tangent line is:
Slope
m = 4 · x - 3
m = 4 · 4 - 3
m = 13
Intercept
b = y - m · x
y = 2 · 4² - 3 · 4 + 5
y = 32 - 12 + 5
y = 25
b = 25 - 13 · 4
b = 25 - 52
b = - 27
The equation of the line tangent to the parabola at x = 4 is y = 13 · x - 27. The tangent line has a slope of 13 and a intercept of - 27.
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A label for a drug indicates that each milliliter contains 7 milligrams of the drug. How many milligrams are in 8 milliliters?
There are 56 milligrams in 8 milliliters of the drug if the drug's label says each milliliter contains 7 milligrams of the substance.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Let x milligrams would in 8 milliliters.
We can write this as a ratio as
As per the given information,
1 milliliter : 7 milligrams = 8 milliliter : x milligrams
⇒ 1 / 7 = 8 / x
⇒ x = 8 × 7
⇒ x = 56 milligrams
Hence, there are 56 milligrams in 8 milliliters of the drug.
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Suppose [tex]f[/tex] is an even function and [tex]\int\limits^7_{-7} {f(x)} \, dx =18[/tex].
a. Evaluate [tex]\int\limits^7_0 {f(x)} \, dx[/tex]
b. Evaluate [tex]\int\limits^7_{-7} {xf(x)} \, dx[/tex]
a. Because [tex]f[/tex] is even,
[tex]\displaystyle \int_{-7}^7 f(x) \, dx = 2 \int_0^7 f(x) \, dx = 18 \\\\ ~~~~ \implies \int_0^7 f(x) \, dx = \frac{18}2 = \boxed{9}[/tex]
b. The product of an even function [tex](f)[/tex] by an odd function [tex](x)[/tex] is an odd function, whose integral over a symmetric interval is zero.
[tex]\displaystyle \int_{-7}^7 xf(x) \, dx = \boxed{0}[/tex]
Study the red pre-image and the associated blue dilation image. The center of dilation is (2, 2). What is the scale factor of the dilation? 1/3 StartFragment, 1/3, 8 StartFragment, 8, 12 StartFragment, 12, 3
Answer: 3
Step-by-step explanation:
The required scale factor of the given dilation is 3. Option D is correct.
Given that,
The center of dilation is (2, 2).
To determine the scale factor of the dilation.0
The scale factor is defined as the ratio of modified change in length to the original length.
Here,
Length of one side of triangle former dilation = 2 units
Length of one side of triangle later dilation = 6 units
Scale factor = later dimensions / former dimensions = 6 / 2 = 3
Thus, the required scale factor of the given dilation is 3. Option D is correct.
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simplify 18/42 to lowest terms
Answer: 3/7
The factors of 18 are 1,2,3,6,9,18;
The factors of 42 are 1,2,3,6,7,14,21,42.
A salesperson earns a commission of $510 for selling $3000 in merchandise find the commission rate
Step 1) : Based on the given conditions, formulate
[tex] \large\bf \longrightarrow \frac{510}{3000} [/tex]
Step 2) : Calculate
[tex] \bf \longrightarrow\frac{51 \cancel{0}}{{300 \cancel{0}} } \: = \frac{51 \div 3}{300 \div 3} = \frac{17}{100} [/tex]
Step 3) : Convert to percentage
[tex] \bf\longrightarrow{\frac{17}{100} = 0.17}[/tex]
Hence, the commission rate is 17%.The side-by-side stemplot below displays the arm spans, in centimeters, for two classes.
A stemplot titled Arm Span (centimeters). For Class A, the values are 148, 151, 153, 155, 156, 159, 161, 162, 164, 165, 169, 169, 170, 171, 175, 176, 179, 179, 180, 182, 183, 186, 186, 190. For Class B, the values are 153, 155, 16, 160, 162, 162, 162, 163, 163, 165, 166, 167, 170, 173, 180, 181, 182, 189, 192, 202.
Which statement correctly compares the arm spans for Class A to those of Class B?
The mean arm span for Class A is much lower than Class B’s.
The mean arm span for Class B is much lower than Class A’s.
The mean arm span for Class A is much higher than Class B’s.
The mean arm span for Class B is about the same as Class A’s.
Answer:
D
Step-by-step explanation:
I got it right!
Answer:
d
Step-by-step explanation:
took the test
Let F(x)=x2-19 and G(x) = 14-x
Find (F/G)(-3)
Value of (F/G)(-3) with the given functions F(x)=x² -19 and G(x) = 14 - x is equal to (-10/17).
As given,
Given functions
F(x)=x² -19
G(x)=14 - x
Substitute the values in the required function:
( F/G )(x)=( x² -19 )/( 14 - x)
Now substitute x= -3
( F/G )( -3) =[ (-3)² -19 ] /[ 14 - (-3) ]
⇒ ( F/G )(-3) =( 9-19) / (14+ 3)
⇒ ( F/G )(-3) =( -10/17)
Therefore, value of (F/G)(-3) with the given functions F(x) = x² -19 and G(x) = 14 - x is equal to (-10/17).
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HELP PLEASEEEEEEEEEEEEEE
Answer:
Step-by-step explanation:
Solve parts of equation in order:
Brackets
Indices
Division
Multiplication
Addition
Subtraction
8 + 2 x 7 - 9 = 63
8 + (2 x 7) - 9 not = 63 (multiplication is the first thing that applies to this equation)
(8 + 14) - 9 not = 63
22 - 9 = 13
So the error would be it equals 13 not 63
Answer:
9 is supposed to be 7
Step-by-step explanation:
8 + 2 = 10
10 × 7 = 70
70 - 7 = 63
Amazon is offering a $17.95 discount on a pair of wireless headphones. You pay $71.80 for the headphones after the discount. Write and solve an equation to find the original price of the headphones.
Use "x" for your variable
Answer:
x - 17.95 = 71.80
Use the commutative property of addition
71.80 + 17.95 = 89.75
$89.75 was the original price.
Step-by-step explanation:
Hope it helps! =D
Find the slope of the line graphed below.
GUYS WHAT HELPPP MEEE
Points A and B lie on plane M. Does line AB lie in plane M? Justify your answer using a postulate.
The line AB joining the points A and B on the plane M lies in plane M.
Say there are two points A and B which lies on the plane M.
Through any two points, there is only one line. Then there is exactly one line joining the two points A and B which is the line AB
Since both the points lies on the plane M, the line joining them should also lie on the plane M.
The postulate which verifies this is:
If two points lie on a plane, then the line joining the points also lies on the same plane.
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ILL LOVE YOU FOREVER PLEASEHELP MEE
Answer:
75°
Step-by-step explanation:
[tex]m\angle KLM=m\angle KLQ+m\angle QLM \\ \\ 173=x+105+x+82 \\ \\ 173=2x+187 \\ \\ 2x=-14 \\ \\ x=-7 \\ \\ \implies m \angle QLM=-7+82=75^{\circ}[/tex]
Answer:
75
Step-by-step explanation:
7 + (4 + 8) = (7 + 4) + 8
Answer:
true
Step-by-step explanation:
what is 50 pounds in kilograms
Answer:
22.6796 kg.
Step-by-step explanation:
The answer is 22 i am sure about this
through: (3,-4), perp. to y=-7x
Answer:
y = x/7 + 31/7
or 7y = x + 31
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other so slope will be 1/7
m = 1/7, y = -4, x = 3
y = mx + b
-4 = 1/7(3) + b
b = 3/7 + 4
b = 3/7 + 28/7
b = 31/7
so
y = x/7 + 31/7
or 7y = x + 31
the perimeter of a triangle is 13 cm whose two sides are 4 cm and 5cm . find the area
The area of the Triangle is 7.8 cm².
The perimeter of the triangle is given to be 13cm.
As we know,
perimeter of triangle = sum of length of all sides of the triangle.
13cm = 4cm + 5cm + third side
third side = 4cm.
Hence two side of the triangle are equal to 4cm. We can say that this is an isosceles triangle, with the base length as 5cm and the other two equal sides of length 4cm.
Let say the base length is B and the other sides length is A.
So area of the isosceles triangle can be given by,
Area = 1/2 x B x √(A²-B²/4)
Area = 1/2 x 5 x √(4²-5²/4)
Area = 1/2 x 5 x √(16 - 25/4)
Area = 1/2 x 5 x 3.12
Area = 7.8 cm².
The area of the triangle is 7.8cm².
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Suppose 3
plss helppp
?
A technician repaired 18 laptops and
24 desktops last month. What is the
ratio of laptops to total computers?
Therefore, the ratio of the number of laptops to total computers is 2:7
Number of laptops repaired by a technician = 18
Number of desktops repaired by a technician = 24
Total number of computers = no of laptops + no of desktops
= 18 + 24
= 42
We have to determine the ratio of laptops to total computers as
= no of laptops / total no of computers
= 18 / 42
= 6 / 14
= 2 / 7
Therefore, the ratio of the number of laptops to total computers is 2:7
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What is the vertical distance (Δ`y`) for this slope triangle
What is the horizontal distance (Δ`x`) for this slope triangle?
The vertical distance (Δ`y`) for the slope triangle as indicated is; (4-2) ; 2.
The horizontal distance (Δ`x`) for the slope triangle as indicated is; (4-0) ; 4.
What is the vertical distance (Δ`y`) and horizontal distance (Δ`x`) for this slope triangle?According to the task content, it follows that the vertical and horizontal distance for the slope triangle in discuss are to be determined.
Hence, by observation, Δ`y` can be obtained on the graph from points 4 and 2; we have; 4-2 = 2.
Also, by observation, Δ`x` can be obtained on the graph from points 4 and 0; we have; 4-0 = 4.
Ultimately, the vertical and horizontal distances of the slope triangle are as indicated.
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How you solve this??
Answer:— 36, 20-29 years, 20-29 years, Total confirmed cases in ages 20-29 over the 14 day period ... 707, 01/03/2022, 1151692, 36278, 18031.4286.
Step-by-step explanation: