Let:
[tex]\begin{gathered} 6x+8y=-10_{\text{ }}(1) \\ 2x-5y=12_{\text{ }}(2) \\ 8x+3y=2_{\text{ }}(3) \\ 12x+16y=-20_{\text{ }}(4) \end{gathered}[/tex][tex]\begin{gathered} (4)=2(1) \\ so\colon \\ 2(6x+8y)=2(-10)\equiv12x+16y=-20 \\ 12x+16y=-20\equiv12x+16y=-20 \end{gathered}[/tex]Therefore, (4) is a Scalar Multiple of (1).
[tex]\begin{gathered} (1)+(2) \\ 6x+2x+8y-5y=-10+12 \\ 8x+3y=2\equiv(3) \\ so\colon_{} \\ (1)+(2)\equiv(3) \end{gathered}[/tex]Therefore, (3) is a linear combination of (1) and (2)
You hit 9) Consider the set of related x and y values. Which value of g would make it impossible for the set to represent a function? {(8. 67), (5, 28), (g. 19), (9,84)}
Remember that for any value on the domain of a function, there can only be one value on the range that assigns to it.
We have the set:
[tex]\mleft\lbrace(8,67\mright),(5,28),(g,19),(9,84)\}[/tex]therefore, a value of g that make it impossible for the set to represent a function can be 8, 5 or 9, since those values already have another value assigned from the range.
Use the diagram to the night to answer questions 1-4 1. Name two points collinear to point K2. Give another name for line b. 3. Name the intersection of line c and plane R. 4. Name a point non-coplanar to plane R
ANSWER
1. L and J
2.
3.
4.
EXPLANATION
1) We want to name two points that are collinear to K. That is two points that lie on the same line as K.
They are points L and J
2) To name line b,
The table shows sereral values of a relation. 12 1 10 8 1 6 3 -4
As we know, "A function relates each element of a set with exactly one element of another set". That means every element in x is related with some element in y. Also there cant be two values of y for one x.
Thus, the correct answer is , option (c)
Use substitution to solve the system of equations. How many solutions are there?1/2x-1/3y=5X=2/3y+10A. There are no solutionsB. There is one solutionC. There are intinitely many solutionsD. It is not possible to determine the number of solutions
In order to solve the system using substitution, we can use the value of x from the second equation in the first one. So we have:
[tex]\begin{gathered} \frac{1}{2}x-\frac{1}{3}y=5 \\ \frac{1}{2}(\frac{2}{3}y+10)-\frac{1}{3}y=5 \\ \frac{1}{3}y+5-\frac{1}{3}y=5 \\ 5=5 \end{gathered}[/tex]Since the final sentence is true, we have an infinite number of solutions for this system, therefore the correct option is C.
Consider the data in the table below. Determine the logarithmic regression model for the data. Round the coefficients in the regression equation to 3 decimal places.
Year 1 2 3 4 5 6 7 8
Average Height 7.4 6 4.9 4.4 4 3.6 3.1 2.7
The regression equation is y
=
The regression equation, y = -0.6155x + 7.282
Given,
Year, x ; 1 2 3 4 5 6 7 8
Average height, y ; 7.4 6 4.9 4.4 4 3.6 3.1 2.7
Logarithms of y values;
log 7.4 = 0.869log 6 = 0.778log 4.9 = 0.690log 4.4 = 0.643log 4 = 0.602log 3.6 = 0.556log 3.1 = 0.491log 2.7 = 0.431The order of xy pairs;
(1, 0.869), (2, 0.778), (3, 0.690), (4, 0.643), (5, 0.602), (6, 0.556), (7, 0.491), (8, 0.431)
There are 8 xy pairs
Using online calculator, the regression equation get as;
y = -0.6155x + 7.282
Learn more about regression equation here;
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Suppose the population of a town is 5,900 and is growing 2% each year. Write an equation to model the growth in population.
The equation/formula to model population growth can be given below;
[tex]\begin{gathered} P=P_0\times e^{rt} \\ \text{where P = total population after time t} \\ P_0=orig\text{inal or starting population} \\ r=\text{ rate of growth in percentage} \\ t=\text{time in years} \\ e=\text{Euler's constant = }2.71828 \end{gathered}[/tex]Therefore, for the question using the same formula, we have the model equation as;
[tex]\begin{gathered} P_0=5000 \\ r=2\text{ \% = 2/100=0.02} \\ \text{Then the equation will be;} \\ P=5000\times2.71828^{0.02t} \end{gathered}[/tex]Hence, P = 5000 x 2.71828^0.02t
2. Write an expression that can be used to calculate how many hours are needed for a party. Then use yourexpression to tell the number of hours needed for a party with 16 participants and 4 escape puzzles.• (Replace this text with your expression)I• (Replace this text with your answer and work)
We know that each escape room is scheduled for 20 minutes. So, if there are 8 participants, then they need 160 minutes, which is equivalent to 2.67 hours.
So, the expression would be
[tex]\frac{20\times8}{60}[/tex]On the other hand, if there are 16 participants, then the hours needed are
[tex]2\cdot\frac{20\times8}{60}\approx5.33[/tex]Question 3 of 10Which output in this table is incorrect?Cost ofItemTax onItem.081.002.00 .163.00 .248.50 .6410.00 .80Note: all entries are in dollarsA. 0.80B. 0.64C. 0.16D. 0.24
Solution:
Given:
The table;
where;
[tex]\begin{gathered} \text{the input=cost of item} \\ \text{the output=tax on item} \\ \text{Let the input be represented by x} \\ \text{Let the output be represented by y} \end{gathered}[/tex]From the data given in the table, the relationship between the input and output can be given as;
[tex]y=0.08x[/tex][tex]\begin{gathered} \text{When the cost = \$1.00, x = 1} \\ y=0.08\times1 \\ y=\text{ \$0.08} \\ \\ \text{When the cost = \$}2.00,\text{ x = 2} \\ y=0.08\times2 \\ y=\text{ \$0.16} \\ \\ \text{When the cost = \$3.00, x = 3} \\ y=0.08\times3 \\ y=\text{ \$0.24} \\ \\ \text{When the cost = \$8.50, x = 8.5} \\ y=0.08\times8.5 \\ y=\text{ \$0.68} \\ \\ \text{When the cost = \$10.00, x = 10} \\ y=0.08\times10 \\ y=\text{ \$0.80} \end{gathered}[/tex]From the above, it can be seen that when the cost of the item was $8.50, the tax on the item should be $0.68 but on the table, it was written as $0.64
Therefore, the output in the table that is incorrect is $0.64
The correct answer is OPTION B
will swims a total of 45.6 laps iin 2.85 hours how many laps does he swim each hour
Monica, this is the solution to the problem:
Total laps that Will swims = 45.6
Time it takes Will to swim this distance = 2.85 hours
Let's calculate the number of laps Will swims each hour, using Direct Rule of Three, as follows:
Laps Time
45.6 2.85
x 1
____________
2.85 * x = 45.6 * 1
2.85x = 45.6
Dividing by 2.85 at both sides:
2.85x/2.85 = 45.6/2.85
x = 16
Will swims 16 laps per hour
Luis has a recipe that requires 2 cups of milk. He knows that 1 cup = 8 ounces.How many ounces of milk does Luis need for the recipe?
1 cup is equivalent to 8 ounces.
To find how many ounces are equivalent to 2 cups, we can use the next proportion:
[tex]\frac{1\text{ cup }}{2\text{ cups}}=\frac{8\text{ ounces}}{x\text{ ounces}}[/tex]Solving for x,
[tex]\begin{gathered} 1\cdot x=8\cdot2 \\ x=16\text{ ounces} \end{gathered}[/tex]Find the solution to the following system using the elimination method . SEE ATTATCHED PHOTO .
System
[tex]\begin{gathered} 5x-2y=-13 \\ 2x+y=11 \end{gathered}[/tex]Using elimination
We will operate the equations in the following way
(1) + 2 (2)
[tex]\begin{gathered} 5x-2y+2(2x+y)=-13+2\cdot11 \\ 5x-2y+4x+2y=-13+22 \\ 5x+4x-2y+2y=9 \\ 9x=9 \\ x=1 \end{gathered}[/tex]Now for y, using (2)
[tex]\begin{gathered} y=11-2x \\ y=11-2 \\ y=9 \end{gathered}[/tex]The solution of the system would be x = 1 and y = 9
Figure B is a dilation of Figure A.Which is the scale factor in the dilation?
Answer:
1/2
Explanation:
If B is a dilation of figure A, the length of a given side in B will be equal to the scale factor times the corresponding side in A.
So, if 10 in figure A is corresponding to 5 in figure B, we get:
5 = k(10)
Where k is the scale factor.
Then, solving for k, we get:
5/10 = k(10)/10
1/2 = k
Therefore, the scale factor in the dilation is 1/2.
We can also say that B is smaller than A, so the scale factor should be a number lower than 1. Since 5 is half 10, we can say that the scale factor is one-half or 1/2.
Find the equation of the line that passes through the given points. (Use x as your variable.)(2, 0), (0, −1)
Find the equation of the line that passes through the given points. (Use x as your variable.)
(2, 0), (0, −1)
step 1
Find out the slope
m=(-1-0)/(0-2)
m=-1/-2
m=1/2
step 2
Find out the equation of the line in slope-intercept form
y=mx+b
where
m is the slope
b is the y-coordinate of the y-intercept
we have
m=1/2
the y-intercept is given -----> (0,-1)
so
b=-1
substitute
y=(1/2)x-1Rewrite the exponential function v" = 94 in logarithmic form.
Let's see the logarithm definition to solve the question
[tex]\log_ba=c[/tex]Rewriting in exponential form
[tex]b^c=a[/tex]So in our case b=v, c=u, and a=94
In log form
[tex]\log_v94=u[/tex]Answer: Option B
State whether the equation has one solution, or infinitely many solutions.
Given:
The expression 8y - 3 = 17 - 2y.
Required:
State whether the equation has one solution, or infinitely many solutions.
Explanation:
The calculation is as:
[tex]\begin{gathered} 8y-3=17-2y \\ 10y=20 \\ y=2 \end{gathered}[/tex]Answer:
System has only one solution.
The graph of a function f is shown below.Find one value of x for which f(x)=-3 and find f(0).Hey
One value of x for which f (x ) = -3 is -2 .Therefore,
f(-2) = - 3
f (0) = 1
1- A given line as a slope of – and y-intercept of 8. Which equation represents a line4that is parallel to the given line and passes through the point (-8,-2)?
Answer:
y=(1/4)x.
Explanation:
Two lines are parallel if their slopes are equal.
The slope of the given line is 1/4, therefore:
• The slope of the new line = 1/4
Thus, the goal is to find the equation of a line with a slope of 1/4 that passes through (-8,-2).
Using the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=\frac{1}{4}(x-(-8)) \\ y+2=\frac{1}{4}(x+8) \\ y+2=\frac{1}{4}x+2 \\ y=\frac{1}{4}x+2-2 \\ y=\frac{1}{4}x \end{gathered}[/tex]The equation of the line is y=(1/4)x.
The 3rd choice is correct.
name the postulate or theorem you can use to prove the triangles
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
Theorem 12.2: The AAS Theorem. If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of a second triangle, then the triangles are congruent.
CONCLUSION:
The final answer is:
[tex]AAS\text{ Theorem \lparen OPTION D \rparen}[/tex]In the playing card deck below what is the chance of pulling 5 face cards without replacing the cards in between pulls? Answer in decimal form.
Solve the system of equations by graphing:62 - 7Answer: (2, y) =32 + 11Question Help: Video Message instructorSubmit QuestionJump to Answer
Step 1 : Let's graph the equations, as follows:
y = - 6x - 7
y = 3x + 11
Step 2: Let's find x-intercept and y -intercept for both equations:
y = -6 * 0 - 7
y = -7, therefore, y-intercept = (0, -7)
0 = - 6x - 7
6x = -7
x = -7/6, therefore x-intercept = (-7/6, 0)
y = 3 * 0 + 11
y = 11, therefore, y-intercept = (0, 11)
0 = 3x + 11
-3x = 11
3x = -11
x = -11/3, therefore, x-intercept = (-11/3, 0)
Step 3: Now let's graph the system of equations:
As we can see, the point of intersection is (-2, 5), therefore, the solution is:
x = -2
y = 5
ablished Mr. Allen estimated that 50 people at a basketball game were cheering for the visiting team. Select all of the statements that could represent this estimate. 6.RP.3, 6.RP.30 0 24% of 195 people 18% of 487 people O 62% of 148 people O 67% of 77 people O 11% of 512 people
We are asked to determine what percentage is 50 of the given ones.
We have that:
[tex]undefined[/tex]I want to see if I solved a problem correctly
The problem gives us two expressions:
[tex]\begin{gathered} y=9x-18 \\ y=18x \end{gathered}[/tex]And we need to solve for x. For that, the first step is to replace "y" on the first expression by the right side of the second expression:
[tex]18x=9x-18[/tex]Now we need to isolate the "x" variable on the left side:
[tex]\begin{gathered} 18x-9x=-18 \\ 9x=-18 \\ \frac{9x}{9}=\frac{-18}{9} \\ x=-2 \end{gathered}[/tex]We can now find "y" by replacing the value of "x" on the second expression:
[tex]y=18\cdot(-2)=-36[/tex]The value of x is equal to -2, and the value of y is equal to -36.
5x + 4y if x=3 y=7 ?
In order to evaluate this expression for x = 3 and y = 7, let's use these values in the expression and calculate its final value. So we have:
[tex]\begin{gathered} 5x+4y \\ =5\cdot3+4\cdot7 \\ =15+28 \\ =43 \end{gathered}[/tex]So the value of this expression for x = 3 and y = 7 is 43.
a spinner with 10 equally sized slices has3 Blue slices2 Yellow slices5 Red slicesthe dial is spun & stop at random what is the Probability that the dial Stops on a slice that is NOT blue? write the fraction in the simplest form
Solution
The number of possible outcomes is 10
We need to find the probability that it is blue
Probability is given as = number of required outcomes/ number of the possible outcome
The probability that the dial Stops on a slice that is blue = 3/10
The probability that the dial Stops on a slice that is NOT blue = 1 - Probability that the dial Stops on a slice that is blue = 1 - 3/10
Given the following formula, solve for v.s = 1/2a2v + cs + cA. v = -------2a22(s - c)B. v = --------a2s -- cC. v = --------2a22( s + c)D. v = ----------a2
Given data:
The given expression is s=1/2 a^(2)v +c.
The given expression can be written as,
[tex]\begin{gathered} s=\frac{1}{2}a^2v+c \\ \frac{1}{2}a^2v=s-c \\ v=\frac{2(s-c)}{a^2} \end{gathered}[/tex]Thus, the option (A) is correct.
A friend tells you that he can run three miles in half an hour. You want to calculate his speed in miles per hour. The ratio is: 3miles------------1---2 hours converts this ratio to a unit cup
Given:
The ratio of speed is given as.
[tex]\frac{3\text{ mies}}{\frac{1}{2}\text{ hours}}[/tex]The objective is to convert the ratio into unit ratio.
The unit ratio can be calculated by multiplying 2 on numerator and denominator, so that the denominator will become one.
[tex]\begin{gathered} \frac{3\times2\text{ miles}}{\frac{1}{2}\times2\text{ hour}} \\ \frac{6\text{ miles}}{1\text{ hour}}\text{ } \\ 6\text{ miles/hour} \end{gathered}[/tex]Hence, the unit ratio is 6 miles/hour.
Justify each step in the equation solution below with either a property of real numbers (associative, commutative, distributive) or a property of equality (addition or multiplication). 5(x+2)=30 Step 1: 5x+10=30 Justification: Justification Step 2: 5x+10+-10 = 30+-10 5x= 20 Step 3: Justification: 5 x 20 5 5 x=4
You have the following equation:
[tex]5(x+2)=30[/tex]with the following steps to find the value of x:
5x + 10 = 30 distributive property
5x = 20 addition property of equality (it has added -10 both sides)
x = 4 division property of equality (it has divided by 5 both sides)
please help!!! listing the second half in the comments too big to put in one pic
a) From the graph, when x = -2, the value of the function is 0, that is, h(-2) = 0. Similarly, when x = 0, h(0) = -2; when x = 2, h(2) = 2; when x = 3, h(3) = 3.
b) The domain is the set of all possible x-values.
The range is the set of all possible y-values.
From the graph, the domain is [-3, 4]. And the range is [-2, 3].
c) h(x) = 2 corresponds to the next x-values: -3, 2, 4
d) The value of the function is less than or equal to 2 between -3 and 2, both values included, and when x is equal to 4. Then, the correct option is [-3, 2] and 4.
e) The net change of the function between x = -3 and x = 3 is calculated as follows:
Net change = h(3) - h(-3)
Net change = 3 - 2
Net change = 1
A river has a current flowing with a velocity of 2.0 meters per second due east. A boat travels at 3.0 meters per second relative to the river and is headed due north. In the adjacent diagram, the vector starting at point P represents the velocity of the boat relative to the river water. What is the direction of the resultant velocity relative to the south riverbank? 12 degrees34 degrees56 degrees78 degrees
First let's draw the vectors that correspond to the boat speed and the river speed.
The river speed is 2 m/s due east, and the boat speed is 3 m/s due north, so we have:
Addind these vectors, the resultant is:
In order to calculate the angle x, we can use the tangent relation, which is the opposite side to the angle over the adjacent side to the angle:
[tex]\begin{gathered} \tan (x)=\frac{3}{2} \\ \tan (x)=1.5 \\ x=56.31\degree \end{gathered}[/tex]So the direction of the resultant is 56 degrees.
I need help with this I also need to show my work in order to get credit
We want to find the measure of arc AD. We would need to find x first as this would guide us toward finding AD.
We know from a circle geometry theorem that;
I. Angles in the same segment are equal. In this case,
[tex]\angle ABD\approx\angle ACD[/tex]Therefore, we can equate them, equating them we obtain;
[tex]\begin{gathered} 11x-3=8x+15 \\ 11x-8x=15+3 \\ 3x=18 \\ x=6 \end{gathered}[/tex]We could use this to obtain the measures of angle ABD or ACD, obtaining one is enough as they are congruent, let us use [tex]\begin{gathered} \angle ABD=11x-3 \\ =11(6)-3_{} \\ =66-3 \\ =63^o \end{gathered}[/tex]We can therefore find the measure of angle AD, by using the circle geometry theorem;
ii. Angles subtended at the centre of a circle is twice that subtended at the circumference;
Thus;
[tex]\begin{gathered} \angle AED=2\angle ACD \\ \angle AED=2(63) \\ \angle AED=126^o \end{gathered}[/tex]Therefore, the measure of arc AD is 126 degrees.