Explanation
a linear function must have
dependent and independent variables, ( y and x in this case)and the exponent of the independent vairable must be 1, so
Step 1
Check
a)
[tex]a)\text{ y=x-1}[/tex]this is a linear function
b)
[tex]y=4.5[/tex]this is not a functin, this expression has not x
c)
[tex]3x-4y=2[/tex]this functin has x and y, and the exponent of x is 1, so, this is a linear function
d)
[tex]5x^2=10y[/tex]this function has x and y, but the exponent is 2, so this is not a linear function
e)
[tex]y=\frac{1}{2}x^2+6[/tex]this function has x and y, but the exponent is 2, so this is not a linear function
i hope this helps you
A bucket of green paint 6 teaspoons of blue in it and 8 teaspoons of yellow paint to make a shade of green paint using 18 teaspoons of blue paint how many teaspoons of yellow
Answer:
24 teaspoons of yellow
Step-by-step explanation:
The ratio of blue to yellow is 6 to 8.
[tex] \frac{6}{8} = \frac{18}{y} [/tex]
We see that y = 24 since 18 = 3 × 6 and
24 = 3 × 8.
Find sin ^-1 (-1/2). Write both angles for full credit
sin^-1 (-1/2) is 30 degrees measured from the x-axis in the clockwise direction, that is, in the fourth quadrant.
What is trigonometry ?Trigonometry is one of the important branches in the history of mathematics that studies the relationship between the sides and angles of right triangles. This concept comes from the Greek mathematician Hipparchus. In this article, we will discuss trigonometric functions, ratios, trigonometric tables, Trigonometry is one of the most important branches of mathematics and has wide applications in many fields. The Department of Trigonometry is basically concerned with studying the relationship between the sides and angles of a right triangle. Therefore, trigonometric formulas, functions, or trigonometric identities can help you find missing or unknown angles or sides in right triangles. In trigonometry, angles can be measured in degrees or radians. The most commonly used trigonometric angles for calculations are 0°, 30°, 45°, 60°, and 90°. Trigonometry is further divided into two sub-branches.This article describes six important trigonometric functions, ratios, trigonometric tables, formulas, and identities to help you find the missing angles and sides of right triangles.In light of the question -The below figure serves as a reference for quickly determining the sines (y-value) and cosines (x-value) of angles that are commonly used in trigonometry. As can be seen from the figure, sine has a value of 0 at 0° and a value of 1 at 90°. Cosine follows the opposite pattern; this is because sine and cosine are cofunctions (described later). The other commonly used angles are 30° (), 45° (), 60° () and their respective multiples. The cosine and sine values of these angles are worth memorizing in the context of trigonometry, since they are very commonly used.
One method that may help with memorizing these values is to express all the values of sin(θ) as fractions involving a square root. Starting from 0° and progressing through 90°, sin(0°) = 0 = . The subsequent values, sin(30°), sin(45°), sin(60°), and sin(90°) follow a pattern such that, using the value of sin(0°) as a reference, to find the values of sine for the subsequent angles, we simply increase the number under the radical sign in the numerator by 1, as shown below.
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Write the point-slope form of an equation for the line graphed.
a. y + 1 = -3(x)
b. y - 1 = 3(x)
c. y - 1 = 4(x)
d. y + 1 = 4(x)
The point slope of an equation for the line graphed is y - 1 = 4 ( x + 1).
To find the point slope of an equation for the line graphed:
First you have to find the slope which is 4. To get that you get 2 points and do rise/run. I chose the 2 points (-2,-3) and (-1,1).
Since the formula for point-slope form is:
Here [tex](y-y_{1}) = m(x-x_{1})[/tex], the equation should pass through the point (-1,1)
Therefore, the point-slope form is:
y - 1 = 4 ( x + 1)
Hence the answer is, The point slope of an equation for the line graphed is y - 1 = 4 ( x + 1).
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: Width = 3.4 meters, Length = 6.4 meters
Step-by-step explanation:
If the width is [tex]w[/tex], then the length is [tex]w+3[/tex].
[tex]w(w+3)=22\\\\w^2 +3w=22\\\\w^2 +3w-22=0\\ \\ w=\frac{-3 \pm \sqrt{3^2 -4(1)(-22)}}{2(1)}\\\\w \approx 3.4 \text{ } (w > 0)\\\\\implies w+3 \approx 6.4[/tex]
Which of the following values are in the domain of the function graphed below? Check all that apply. A. -4 B. -1 C. 4D. 0E. 5 F. -2
Checking the given graph, it can be seen that the range of values of x is
[tex]\begin{gathered} rangeofvaluesofx, \\ -2\leq x\leq4 \end{gathered}[/tex][tex]undefined[/tex]The range of values of x are the values of the domain of the graph function
A. -4; -4 does not satisfy the function of the graph
y=x-7
5x+2y = 7
Use the substitution method.
O (0, -7)
O (-1, -8)
O (7,0)
O (3, 4)
-
Answer:
(3, -4)
Step-by-step explanation:
To solve the system of equations by substitution, start by labelling the 2 given information.
y = x - 7 -----(1)
5x + 2y = 7 -----(2)
Substitute (1) into (2):
5x + 2(x - 7) = 7
Expand:
5x + 2x - 14= 7
7x = 14 + 7
7x = 21
Divide both sides by 7:
x = 21 ÷ 7
x = 3
Substitute into (1):
y = 3 - 7
y = -4
Thus, the solution to the equations is (3 , -4).
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Jordyn and Anya left a 30% tip after having lunch at a restaurant. The amount of the tip was $14.10. Jordyn's lunch cost $22. Write and solve an equation you can use to find x, the cost of Anya's lunch.
The cost of Anya's lunch would be = $25
What is lunch?Lunch is the type of meal that is taken after the noon day or in the afternoon.
The percentage of tip left by Jordyn and Anya = 30%
The amount of the tip = $14.10
If 30% = 14.10
100% = $x
$x = 100 × 14.10/30
$x = 1,410/30
$x = 1,410/30
$x = $47
This is the total amount for the cost of lunch.
To find Anya's cost for lunch would be;
Total cost - Jordyn lunch cost = Anya lunch cost
Anya lunch cost = 47 - 22
= $25
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What conjecture can you make about the sum of the frst 25 positive even numbers?Make a conjecture. Choose the correct answer below.O A. The sum is equal to the number of terms squared.OB. The sum is the product of the number of terms and the number of terms plus one.O C. The sum is the product of the number of terms and twoOD. The sum is the product of the number of terms and the number of terms minus one.
Given:
2+4+6+8+10+.....+50
[tex]2+4+6+10+\cdots+50=2(1+2+3+\cdots+25)[/tex]Let the sum of the first n natural numbers be
[tex]S_n=\frac{n(n+1)}{2}[/tex]Therefore the sum of first 25 positive even numbers is
[tex]2S_n=\frac{2n(n+1)}{2}[/tex][tex]2S_n=n(n+1)[/tex]Therefore,The sum is the product of the number of terms and the number of terms plus one.
Option B is the correct answer.
Solve two and one-third times four-fifths equals blank.
four-sixths
one and twelve-fifteenths
one and thirteen-fifteenths
four and four-sixths
The solution to the fraction two and one-third times four-fifths equals one and thirteen-fifteenths.
The correct answer option is option C
How to solve the product of a fraction?A fraction refers to a part of a whole, especially a comparatively small part. It is also the ratio of two numbers, the numerator and the denominator, usually written as one above the other and separated by a horizontal bar.
A numerator is the number above the horizontal bar while the denominator is the number below the horizontal bar in a fraction.
Two and one-third times four-fifths
= 2 1/3 × 4/5
= 7/3 × 4/5
= (7 × 4) / (3 × 5)
= 28 / 15
= 1 13/15
Therefore, the fraction two and one-third times four-fifths equals one and thirteen-fifteenths.
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Autumn has 55 cups of yogurt to make smoothies. Each smoothie uses 1/3
cup of yogurt. How many smoothies can Autumn make with the yogurt?
The total number of smoothies that Autumn can make with the yoghurt is 165.
We know that the total number of cups of yoghurt that Autumn needs to make smoothies is 55. Each smoothie uses 1/3 cup of yogurt. We need to calculate the total number of smoothies that Autumn can make with the yogurt.
Let the total number of smoothies be represented by the variable "N''. We will use the unitary method. The total number of smoothies that can be made is the ratio of the total number of cups of yoghurt to the fraction of a cup used to make one smoothie.
N = 55/(1/3)
N = 55*3
N = 165
Hence, Autumn can make 165 smoothies from 55 cups of yogurt.
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Find the value of X express each answer as a decimal rounded to the nearest 10th
x = 11.1
Explanations:Note that the Pythagora's theorem is applied in solving this exercise
The Pythagora's theorem states that "the square of the hypotenuse equals the sum of the squares of the other two sides"
Hypotenuse is the longest side of the right-angled triangle:
Hypotenuse = 22
[tex]\begin{gathered} 22^2=19^2+x^2 \\ 484\text{ = }361+x^2 \\ x^2\text{ = 484 - 361} \\ x^2\text{ = }123 \\ x\text{ = }\sqrt[]{123} \\ x\text{ = }11.1 \end{gathered}[/tex]help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
A liniar equation has no solutions when the equation makes a false statement
Answer:
True
Step-by-step explanation:
Match the pair of points with the slope of the line that joins them. (4,7) and (6,2)
We need to find the equation of the line that joins the points ( 4 , 7 ) and ( 6 , 2 )
The general equation of the line is ;
[tex]y=m\cdot x+b[/tex]where m is the slope and b is y - intercept
the slope = Rise/Run
Rise = 7 - 2 = 5
Run = 4 - 6 = -2
so, the slope :
[tex]m=\frac{5}{-2}=-2.5[/tex]So, the equation of the line :
[tex]y=-\text{2}.5x+b[/tex]Using any point from the given points to find the value of b
So, using ( 4 , 7 )
when x = 4 , y = 7
[tex]\begin{gathered} 7=-2.5\cdot4+b \\ 7=-10+b \\ b=7+10 \\ b=17 \end{gathered}[/tex]So, the equation of the line is:
[tex]y=-2.5x+17[/tex]Two ships leaving the same marina at the same timeare 3.2 miles apart after sailing 2.5 hours. If theycontinue at the same rate and direction, how farapart will they be 2 hours later?2.56 miles3.52 miles5.76 miles6.08 miles
To answer this question, we need to take into account that the two ships continue sailing at the same rate and direction, and we can solve this using the unit rate concept, as follows:
[tex]\frac{3.2}{2.5}\frac{miles}{h}=1.28\frac{miles}{h}[/tex]If they continue sailing at this same rate, then, after two hours they will be:
[tex]1.28\frac{miles}{h}\cdot2h=2.56miles[/tex]They will have 2.56 miles more distance between them.
Then, they will be separated by a distance of:
[tex]3.2\text{miles}+2.56\text{miles}=5.76\text{miles}[/tex]In summary, we have that the answer is 5.76 miles.
Need some help with this question I’ve been stuck on it for a bit
Answer: L BOZO
Step-by-step explanation:
L+RATIO=BOZO
8 squares and 10 triangles. What is the simplest ratio
The ratio for 8 squares and 10 triangles is 4:5.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them.
A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this case, the ratio for 8 squares and 10 triangles will be:
= Number of square / Number of triangle
= 8/10
= 4/5
The ratio is 4:5.
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Select the transformations of g(x) = |1-2x+6| in relation to the parent function. HURRY PLEASE!!!
Answer:
Translated right [tex]\frac{7}{2}[/tex] units and vertical stretch
OR
translated right 3.5 units and vertical stretch
bcz
[tex]\frac{7}{2} =3.5[/tex]
Step-by-step explanation:
The absolute function is given as:
[tex]g(x) = |1-2x+6|[/tex]
If we simplify the equation, then we have
[tex]g(x) = |1-2x+6|\\g(x)=|-2x+6+1|\\g(x)=|-2x+7|\\g(x)=2|x-\frac{7}{2} |[/tex]
Now we can say that the transformation of g(x) to the parent function will be translated right [tex]\frac{7}{2}[/tex] units and vertical stretch (bcz you have a number (2) multiplying the function).
If the sign of the number that adds to the independent variable is negative, the transformation will be translated to the right, and if it is positive, it will be translated to the left.
If it takes someone t minutes to drive run or walk a mile then their averages speed
EXPLANATION
Since the average speed is given by the equation:
[tex]s(t)\text{ = }\frac{60}{t}[/tex]Computing s(10) and s(12):
[tex]s(10)\text{ = }\frac{60}{10}=6[/tex]Now, computing s(12):
[tex]s(12)=\frac{60}{12}=5[/tex]In conclusion, the solutions are:
s(10) = 6 miles per hour
s(12) = 7 miles per hour
Which sum or difference is modeled by the algebra tiles?-1OA (x2 - 2x + 3) - (-x2 - 4x - 2) = 2x - 1OB. (x2 - 2x - 3) + (x2 - 4x + 2) = 2x - 1OC. 02 - 2x - 3) - (x2 + 4x + 2) = 2x - 1OD. (x2 - 2x-3) + (-x2 + 4x + 2) = 2x - 1© 2021 Edmentum. All rights reserved.
Okay, here we have this:
We will take as the first term the upper squares and as the second term the lower ones, and we obtain that:
[tex]\begin{gathered} (x^2-x-x-1-1-1)+(-x^2+x+x+x+x+1+1) \\ =(x^2-2x-3)+(-x^2+4x+2) \\ =2x-1 \end{gathered}[/tex]Here we obtain that the correct answer is the option D.
I bought
5) Calculate the area and perimeter of the compound shape:
Area =
Perimeter =
Answer:
A = 48 cm^2
P = 38
Step-by-step explanation:
Area:
We can calculate the area of the more left shape first. We know that one side is 9 cm, but the second side is trickier. For the second side, we need to take the total measurement of the bottom area and subtract it from 6, because that is the part of the 10 cm we don't need. This gives us the first box is 9 cm x 4 cm = 36 cm^2. Then for the second box, we take the 6 cm and 2 cm giving us 6 cm x 2 cm = 12 cm^2. 36 cm^2 + 12 cm^2 = 48 cm^2.
Perimeter:
We will take all of the easy measurements first. We take 9 + 10 + 2 + 6 = 27 cm. Then we need to take 6 away form 10 again giving us 4, and 2 away from 9, giving us 7. 27 + 4 cm + 7 cm = 38 cm.
In Triangle FGH, GJ is an angle bisect or of G and perpendicular to FH. What is the length of FH in units?
Using the perpendicular bisector theorem, we have the following:
[tex]GF=GH[/tex]then we can write the following equation:
[tex]3x-8=16[/tex]solving for x, we have:
[tex]\begin{gathered} 3x-8=16 \\ \Rightarrow3x=16+8=24 \\ \Rightarrow x=\frac{24}{3}=8 \\ \\ x=8 \end{gathered}[/tex]we get x = 8. Then, the length of FH is:
[tex]\begin{gathered} FH=FJ+JH=8+8=16 \\ \Rightarrow FH=16 \end{gathered}[/tex]therefore, FH = 16
I need help with problem number 3 It’s about evaluating the composition of functions in different representations correctly
Given g(x) = 3x - 5 and h(x) = 2x - 4.
We need to find (g o h)(x).
The composition of function is as follows:
[tex]\begin{gathered} (g\circ h)(x)=g(h(x)) \\ =g(2x-4) \\ =3(2x-4)-5 \\ =6x-12-5 \\ =6x-17 \end{gathered}[/tex]Thus, the answer is 6x - 17.
Determine the y-intercept of the equation -x + 2y = 10a. 1b.-10C. 5d. 2
Determine the y-intercept of the equation -x + 2y = 10
a. 1
b.-10
C. 5
d. 2
__________________________________________
y-intercept is (0, b)
y = mx +b
-x + 2y = 10
2y = x +10
y = 1/2 x + 5
______________
if x= 0
y= 1/2 *0 +5
y= 5
____________________
The y-intercept is (0, 5 )
The answer is c
what is the constant term of p(x)=(x+3)(x+2)(x+1)?
(PAHELP PLEASE)
Answer:
constant term = 6
Step-by-step explanation:
if you multiply the constant terms within each factor together you get the constant term of the expansion of p(x) , that is
constant term = 3 × 2 × 1 = 6
Maria spends $22 dollars on lottery tickets every week. shen also spends $133 per month on food. On an (annual) basis ,the money spent on lottery tickets is what percent of the money spent to buy food?
Maria spends $22 on lottery tickets every week and $133 every month on food yearly
This means that in a year
there are 52 weeks and she spends 22 x 52 = $1,144 on Lottery tickets
and there are 12 months in a year, so she spends 133 x 12 = $1,596 on food
The money spent to buy lottery tickets in relation to the money spent on food yearly in percentage is
[tex]\begin{gathered} \frac{1144}{1596}\times100 \\ =71.68\text{ percent approximately} \end{gathered}[/tex]A box contains four tiles numbered 1,4,5 and 8 as shown . Kelly randomly chooses one tile , places it back in the box, then choose a second tile. what is the probability that the sum of two chosen tiles is greater than 7? A. 1/4 B. 5/16 C. 2/3 D. 11/16
Since Kelly chooses one tile, places it back in the box, and then choose another tile, we have that the total outcomes are 4x4 = 16.
Now, we can write easily all the outcomes :
[tex]\begin{gathered} \Omega=\mleft\lbrace(1,1\mright),(4,1),(5,1),(8,1), \\ (1,4),(4,4),(5,4),(8,4), \\ (1,5),(4,5),(5,5),(8,5), \\ (1,8),(4,8),(5,8),(8,8)\} \end{gathered}[/tex]notice that on the first row, only the event (8,1) gives us that the sum is greater than 7.
On the second row,we have the same for events (4,4),(5,4) and (8,4)
On the third row only (1,5) gives us a sum lesser than 7, then here we have 3 more events that fit our criteria.
On the last row, all events gives us a sum greater than 7,then we have another 4 events.
Then, the probability that the sum of two chosen tiles is greater than 7 is:
[tex]\frac{1}{16}+\frac{3}{16}+\frac{3}{16}+\frac{4}{16}=\frac{11}{16}[/tex]A ski resort rents snowshoes in the winter. the resort charges $1 per day and a flat fee of $3 to cover cleaning. write an equation that shows how the cost y, depends on the length of the rental in the day, x.
Answer:
3+ 1x = y
Step-by-step explanation:
a flat rebate means no matter how many days it will only be $3 so you add the 3 and you don’t know how many day you’ll rent the shoes so you put a variable next to the 1 and the 1 times however many days plus 3 will be your cost
based on this relationship which could be the correlation coefficient?
Based on the relationship in the given table the correlation coefficient is -0.9985 .
Let us define a few variables first.
X: X Values
Y: Y Values
Mx: Mean of X Values
My: Mean of Y Values
Deviation scores = X - Mx , Y - My
Deviation Squared = variance = (X - Mx)² , (Y - My)²
Product of Deviation Scores = (X - Mx)(Y - My):
Now we will use the defined variables to calculate the correlation coefficient
X Values
∑ = 118.5
Mean = 11.85
∑(X - Mx)² = Sx = 1283.705
Y Values
∑ = 206
Mean = 20.6
∑(Y - My)² = Sy = 16804.4
X and Y Combined
N = 10
∑(X - Mx)(Y - My) = -4637.7
R Calculation
r = ∑((X - My)(Y - Mx)) / √((Sx)(Sy))
r = -4637.7 / √((1283.705)(16804.4)) = -0.9985
The correlation coefficient is the only statistical measure of the given strength of a linear relationship that is amongst the two variables. Its values normally range from -1 to 1.
Based on a correlation coefficient of 1, which indicates a completely negative or inverse relationship, values in one series increase as those in the other decline, and vice versa.
Hence the correlation coefficient is -0.9985
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Ng one-step equations with rational numbers lc) determine the value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths. 3.4 8.0 11.4 13.11
The value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths is 13.11.
What are one-step equations?In algebra, we often deal with equations with unknown values represented by variables. To solve such an equation, we need to find the values of the variables.
A one-step equation is an algebraic equation that can be solved in just one step. Solve it and you've found the values of the variables that make the equation true. To solve a one-step equation, perform the inverse (reverse) of the operation performed on the variable to get the variable itself.
For the given case, the equation can be written as follows:
[tex]\frac{x}{5\frac{7}{10} }[/tex] = [tex]2\frac{3}{10}[/tex]
x = [tex]5\frac{7}{10}[/tex] × [tex]2\frac{3}{10}[/tex]
x = 5.7 × 2.3
x = 13.11
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