In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
eq1. y = 2x + 3
eq2. 3x + 2y = 34
Step 02:
eq1. in eq2.
3x + 2 (2x + 3) = 34
3x + 4x + 6 = 34
7x = 34 - 6
x = 28 / 7
x = 4
eq1.
y = 2 (4) + 3
y = 8 + 3
y = 11
The answer is:
(4 , 11 )
of the following sets, which numbers in {1, 2, 3, 4, 5) make the inequality 3x + 1 > 4 true?A. {1,2)B. {1, 2, 3)C. {1, 2, 3, 4, 5)D. {2,3,4,5)
Answer:
[tex]D;\text{ \textbraceleft2,3,4,5\textbraceright}[/tex]Explanation:
Here, we want to select the member of the set that makes the inequality true
We simply substitute the values in the set
When x is 1
3(1) + 1 = 4
This is not greater then 4 and as such, it cannot be a soution
However, as x is greater than 1, the values hold
Thus, we have the correct options as:
{2,3,4,5}
the graphing troubles me
The vertices are given as D(-8,4), E(-2,2), and F(-5,9).
Consider that area of the traingle is given by,
[tex]\text{Area}=\frac{1}{2}\lbrack x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\rbrack[/tex]Then the area of triangle DEF is given by,
[tex]\text{Area}=\frac{1}{2}\lbrack-8(2-9)-2(9-4)-5_{}(4-2)\rbrack=\frac{1}{2}\lbrack-8(-7)-2(5)-5(2)\rbrack[/tex]Simplify the terms further as,
[tex]\text{Area}=\frac{1}{2}\lbrack56-10-10\rbrack=\frac{1}{2}(36)=18[/tex]Thus, the area of the triangle is 18 square units.
Find the variance of 101, 102, 100, 100, 110, 109, 109, 108, 109how do i do this
Given the data;
[tex]101,102,100,100,110,109,109,108,109[/tex]We want to find the variance of the given data.
The formula for variance can be written as;
[tex]s^2=\frac{\Sigma(x-\bar{x})^2}{n-1}[/tex]Where;
n = number of data
[tex]\begin{gathered} s^2=variance \\ \bar{x}=\operatorname{mean}\text{ of data} \end{gathered}[/tex]Firstly, let us calculate the mean p
Tell whether each equation represents a direct variation. If so, identify the constant of variation.
The variation of the equation is ; y/x
if y/x = k , where k is constant then the variation is Constant
1) 3y = 4x+1
[tex]\begin{gathered} \text{Simplify it in }\frac{y}{x} \\ \text{Divide equation by x} \\ \frac{3y}{x}=\frac{4x}{x}+\frac{1}{x} \\ \frac{y}{x}=\frac{4}{3}+\frac{1}{3x} \\ \frac{y}{x}\ne\text{ any constant term} \end{gathered}[/tex]So, it does not represent direct variation.
2) 3x = -4y
[tex]\begin{gathered} \text{Simplify it in }\frac{y}{x} \\ 3x=-4y \\ \text{Divide by 3y} \\ \frac{3x}{3y}=\frac{-4y}{3y} \\ \frac{x}{y}=-\frac{4}{3} \\ \frac{y}{x}=-\frac{3}{4} \\ \frac{y}{x}=Cons\tan t\text{ term} \end{gathered}[/tex]It represent direct variation.
3) y + 3x =0
[tex]\begin{gathered} \text{Simplify it in }\frac{y}{x} \\ \text{Divide by x} \\ \frac{y}{x}+\frac{3x}{x}=0 \\ \frac{y}{x}=-3 \\ \frac{y}{x}=\text{ Constant term} \end{gathered}[/tex]It represnt the direct variation.
Answer: 2) 3x = -4y
3) y + 3x = 0
Solve each equation Show steps for credit 10.4+a=13
The given equation is,
[tex]4+a=13[/tex]Subtract 4 from both sides of the equation.
[tex]\begin{gathered} 4+a-4=13-4 \\ a=9 \end{gathered}[/tex]Therefore, the value of a is 9.
5. Identify the transformation graphed below. (Remember to include the required information): 6. Answer A 5 2 1 -6 -5 -4 -3 -2 -1 X (-1,-2) -5
From the graph, we have:
Remember, the coach1) needs to buy at least 4 bats and atleast 8 balls2) cannot spend more than $12012-4 8y2880-0x 241215x + 5y s 120Which combination could the coach buy?Click on the correct answer.6 bats, 10 balls3 bats, 10 balls4 bats, 9 balls
x represent the number of bats
y represent the number of balls
The inequalities are
x ≥ 4
y ≥ 8
15x + 5y ≤ 120
To determine the combination that the coach should buy, we would substitute the values of x and y in the different combinations. We have
For x = 6, y = 10
15(6) + 5(10) = 140
This is greater than 120
For x = 3, y = 10,
15(3) + 5(10) = 95
This is less than 120 but x is less than 4
For x = 4, y = 9,
15(4) + 5(9) = 105
The cost is less than 120 and the conditions for x and y are satisfied. Thus, the correct option is
4 bats,
2 In early 2016, there were about 80 devils living on Maria Island. Of that total, 75% are offspring from the previous two breeding seasons. How many are offspring?
Total devils on Maria island = 80
75% are offsprings
75% of 80 = 75/100 x 80 = 60
so 60 where offsprings
In the similarity transformation of ABC to EFD, ABC was dilated by a scale factor of
Find DE = √ 2^2 + 2^2= √8
AB = √1^2+1^2 = √2
Then DE/AB = √8/√2 = √4 = 2
ANSWER IS
OPTION A) 2
Answer:
2
y-axis
Step-by-step explanation:
Lesson 4 Extra Practice Mean Absolute Deviation Determine the mean absolute deviation for e the nearest hundredth if necessary. Then des absolute deviation represents. 1. Number of Sibmas 2 5 8 9 7 6 3 5 1 &
Data set: 2 5 8 9 7 6 3 5 1
Number of data values: 9
Average: (2 + 5 + 8 + 9 + 7 + 6 + 3 + 5 + 1)/9 = 5.11
|2 - 5.11| = 3.11
|5 - 5.11| = 0.11
|8 - 5.11| = 2.89
|9 - 5.11| = 3.89
|7 - 5.11| = 1.89
|6 - 5.11| = 0.89
|3 - 5.11| = 2.11
|5 - 5.11| = 0.11
|1 - 5.11| = 4.11
Mean Absolute Deviation =
(3.11 + 0.11 + 2.89 + 3.89 + 1.89 + 0.89 + 2.11 + 0.11 + 4.11)/9 = 2.12
Solve the system of equations algebraically.5x + y = 93x + 2y = 4
The solution is (2, -1)
Explanation:5x + y = 9 ....(1)
3x + 2y = 4 ....(2)
Using susbtitution method:
from equation 1, we will make y the subject of formula
y = 9 - 5x
substitute for y in equation 2:
3x + 2(9 - 5x) = 4
3x + 2(9) -2(5x) = 4
3x + 18 - 10x = 4
-7x + 18 = 4
-7x = 4 - 18
-7x = -14
Divide both sides by -7:
-7x/-7 = -14/-7
x = 2
substitute for x in equation (1):
5(2) + y = 9
10 + y = 9
y = 9 - 10
y = -1
The solution (x, y) is (2, -1)
If I move the points what are 5 things I would be able to observe about AVB, AVC and BVC
Point V is the focus for AV
Write in number form:nine million one hundred eight thousand one hundred seventy-six
In order to write this expression in number form, let's first separate it and write each corresponding value in number form:
"nine million" = 9,000,000
"one hundred eight thousand" = 108,000
"one hundred seventy-six" = 176
So, adding each piece, we have:
"nine million one hundred eight thousand one hundred seventy-six"
=
9,108,176.
if two lines have slopes of 2/9 and 9/2, are they perpendicular?A. yesB. no
The lines are perpendicular if their slopes are negative reciprocal of the other.
Since 9/2 is just a reciprocal and not the NEGATIVE reciprocal of 2/9, the lines are NOT perpendicular.
Can somebody help me fix my 4 and 5 problem of this exercise?
Hello
To solve this question, we were given a particular function and asked to evalute when the function is defined with a particular variable
[tex]\begin{gathered} f(x)=3-4x \\ g(x)=3x+4x^2 \end{gathered}[/tex]For f(-6)
[tex]\begin{gathered} f(x)=3-4x^{} \\ f(-6)=3-4(-6) \\ f(-6)=3-4(-6) \\ f(-6)=27 \end{gathered}[/tex]For g(-9)
[tex]\begin{gathered} g(x)=3x-4x^2 \\ g(-9)=3(-9)+4(-9)^2 \\ g(-9)=297 \end{gathered}[/tex]For f(-9) + g(-9)
[tex]\begin{gathered} f(x)=3-4x \\ g(x)=3x+4x^2 \\ f(-9)+g(-9)=3-4(-9)+3(-9)+4(-9)^2=336 \end{gathered}[/tex]for g(-6) - f(-9)
[tex]\begin{gathered} g(x)=3x+4x^2 \\ f(x)=3-4x \\ g(-6)-f(-9)=3(-6)+4(-6)^2-(3-4(-9))=87 \end{gathered}[/tex]For f(-9).g(-7)
[tex]\begin{gathered} g(x)=3x+4x^2 \\ f(x)=3-4x \\ f(-9).\text{g}(-7)=3-4(-9)\times3(-7)+4(-7)^2=39\times175=6825 \end{gathered}[/tex]For f(-6) / g(-7)
[tex]\begin{gathered} f(x)=3-4x \\ g(x)=3x+4x^2 \\ \frac{f(-6)}{g(-7)}=\frac{3-4(-6)}{3(-7)+4(-7)^2}=\frac{27}{175} \end{gathered}[/tex]From the calculations above, i believe you must've seen your mistaken and taken the necessary correction.
Therefore the answers are
1 = 27
2 = 297
3 = 336
4 = 87
5 = 6825
6 = 27/175
In the figure below, k || 1 and m || n. Find the values of x and z.
As shown in the figure m // n
the angles x and 63 are exterior supplementary angles
So, x + 63 = 180
so, x = 180 - 63 = 117
and the angles 63 and ( 4z - 29 ) are congruent
so,
[tex]\begin{gathered} 4z-29=63 \\ 4z=63+29 \\ 4z=92 \\ \\ z=\frac{92}{4}=23 \end{gathered}[/tex]So, the answer is :
[tex]\begin{gathered} x=117 \\ \\ z=23 \end{gathered}[/tex]Write each function in vertex form, and identify its vertex.f(x)=x^2–14x+50
Problem
Write each function in vertex form, and identify its vertex.f(x)=x^2–14x+50
Solution
For this case we need to write the expression like this:
f (x) = a(x - h)^2 + k
f(x) = x^2 -14 x +50
We cna complete the square on the following way:
f(x)= x^2 -14x + (14/2)^2 +50 - (14/2)^2
f(x) = x^2 -14x+49 + 50 -49
f(x)= (x-7)^2 +1
Then the final solution would be:
f(x)= (x-7)^2 +1
And the vertex is given by V=(7,1)
i really need help i want the answer just the answer please
The given figure is :
In the given figure, there are three triangles that are lie on the triangular base
The dimension of triangular base :
Height = 10.4 ft, Base = 12 ft
[tex]\begin{gathered} \text{ Area of triangle = }\frac{1}{2}\times Base\times Altitude \\ \text{ Area of triangle=}\frac{1}{2}\times10.4\times12 \\ \text{ Area of trianglur base=}62.4ft^2 \end{gathered}[/tex]The dimension of the side triangular is :
Height = 9ft, base = 12ft
[tex]\begin{gathered} \text{ Area of triangle= }\frac{1}{2}\times9\times12 \\ \text{ Area of triangle=}54ft^2 \\ \text{ Area of thr}ee\text{ triangle=3}\times54 \\ \text{ Area of thre}e\text{ triangle= }162ft^2 \end{gathered}[/tex]The surface area of the pyramid = Area of three triangles + Area of triangular base
The surface area of the pyramid=162 + 62.4
The surface area of the pyramid = 224.4 ft²
Answer : 224.4 ft²
Translate and solve: Three less than y is - 19
The statement given is:
Three less than y is - 19.
Three less than y can be translated as:
[tex]y-3[/tex]Three less than y is - 19 can be translated as:
[tex]y-3=-19[/tex]Solve the above equation by adding three to both sides of the equation.
[tex]\begin{gathered} y-3+3=-19+3 \\ y=-16 \end{gathered}[/tex]Therefore, the solution is y=-16.
Hello, I really need help on this assignment. A swimming pool is being drained for maintenance. The volume of water in the pool changes by −12 gallons every minute.What is the change in volume over 90 minutes?Enter the your answer in the box.
ANSWER:
-1080 gallons
STEP-BY-STEP EXPLANATION:
If the volume of water in the pool changes by -12 gallons per minute, what we must do is multiply -12 by the elapsed time, in this case it would be 90 minutes to determine how much it will change after 90 minutes. Just like that:
[tex]\Delta v=90\cdot-12=-1080[/tex]Which means that the change in volume after 90 minutes is 1080 less gallons.
You have a bag of gummy worms. 12 are green, 3 are blue, 6 are red and 2 are orange. What is the probability that you will reach into the bag and pull a red worm, eat it, and then pull a green worm?answer choices:18/23 36/253 1/529. 72/529
To answer this question, we can proceed as follows:
1. Count the total of gummy worms into the bag:
12 green + 3 blue + 6 red + 2 orange = 23 gummy worms.
2. In the first event (pull a red worm), we have that the probability of it is:
[tex]P(R)=\frac{6}{23}[/tex]Since we have 6 red gummy worms from a total of 23.
3. Now, the probability of the second event is a little different. You have eaten one of the red gummy worms. Then, we have a total of 23 - 1 = 22 gummy worms.
The probability, now, of getting a green worm is (there are 12 green gummy worms):
[tex]P(G)=\frac{12}{22}\Rightarrow P(G)=\frac{6}{11}[/tex]4. Finally, the probability of these two events is, applying the multiplication rule:
[tex]P(R\cap G)=\frac{6}{23}\cdot\frac{6}{11}\Rightarrow P(R\cap G)=\frac{36}{253}[/tex]Then, the answer is 36/253 (second option.)
This is a case of conditional probability. We see that the probability of the second event was influenced by the first event.
suppose U={1, 2, 3, 4, 5} is the universal set and A={1, 5}. What is A’?
U defines the whole sample space for a determined set of numbers (all possible outcomes), A represents an event defined in said space, is a subset that involves one or more possible outcomes of the sample space.
what is the product of 50 × 0.8
Explanation
[tex]50\cdot0.8[/tex]To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product
then
Step 1
[tex]\begin{gathered} 50\cdot0.8=500\cdot8\rightarrow1\text{ decimal position} \\ \\ \end{gathered}[/tex]Step 2
[tex]500\cdot8=400[/tex]put the same number of digits behind the decimal in the product (1 )
[tex]400\rightarrow40.0[/tex]Hence
Given triangle ABC is congruent to triangle HJR. What is the length of side AB? 59 63 1.143 5.143
Answer:
AB=5.143 units
Explanation:
Given that:
[tex]\text{Triangle ABC}\cong\text{Triangle HJR}[/tex]Then:
[tex]\frac{AB}{HJ}=\frac{AC}{HR}=\frac{BC}{JR}[/tex]Substituting the given values, we have:
[tex]\begin{gathered} \frac{x+4}{18}=\frac{6}{21} \\ 21(x+4)=6\times18 \\ 21x+84=108 \\ 21x=108-84 \\ 21x=24 \\ x=\frac{24}{21} \end{gathered}[/tex]Therefore, the length of side AB is:
[tex]\begin{gathered} AB=x+4 \\ =\frac{24}{21}+4 \\ =5.143 \end{gathered}[/tex]iced tea costs $1.75 a glass and a taco costs $0.79. you have $6.00 to spend. let x represent the number of glasses of iced tea and y represent the number of tacos. choose he inequality that represents what you can buy with $6.00. a) 0.79x+1.75y ≤ 6.00b) x+y ≤ 6c) 1.75x+0.79y>6.00d) 1.75x+0.79y ≤ 6.00
From the information available, we have a total of $6.00 to buy 2 items, iced tea and tacos.
The costs are given as;
[tex]\begin{gathered} \text{Iced teas}=1.75 \\ Ta\cos =0.79 \end{gathered}[/tex]The conditions given are such that we can spend $6 to buy both items. If we buy only iced teas, we would be having;
[tex]1.75x=6.00[/tex]If we buy only tacos, we would have;
[tex]0.79y=6.00[/tex]However, we are buying both which means we would be having the following equation;
[tex]1.75x+0.79y=6.00[/tex]Remember however that we have only $6 to spend and nothing more, but we can spend a litle less than $6. That means we can spend $6 or less, but nothing that exceeds that amount. Thats why we can now re-write this as an inequality in the form of "less than or equal to."
Our inequality for this situation therefore would be;
[tex]1.75x+0.79y\le6.00[/tex]ANSWER:
The correct answer is option D
You spin the spinner twice.6789What is the probability of landing on a 6 and then landing on a prime number?Simplify your answer and write it as a fraction or whole number.
Given,
The number of section in the spinner is 4.
Required
The probability of landing on a 6 and then landing on a prime number.
The probability of spinner lands on 6 is,
[tex]\begin{gathered} P(6)=\frac{n(6)}{total\text{ section}} \\ =\frac{1}{4} \end{gathered}[/tex]The probability of spinner lands on prime is,
[tex]\begin{gathered} P(prime)=\frac{n(prime)}{total\text{ section}} \\ =\frac{1}{4} \end{gathered}[/tex]The probability of landing on a 6 and then landing on a prime number.
[tex][/tex]From 2010 to 2012, the average selling price of tablets decreased by 20%. This percent reduction amounted in a decrease of $122. Find the average selling price of tablets in 2010 and in 2012.
Let the original price of tablets be represented by x.
The average selling price decreased by 20% (or 0.2).
The decrease now was calculated as $122. That means the figure 122 is 20% of x. Therefore, what we have is;
[tex]\begin{gathered} \text{Original price=x} \\ \text{Decrease}=122 \\ \text{New price=x-122} \\ \text{Note that 20\% (0.2) is also 122, hence} \\ \frac{20}{100}=\frac{122}{x} \\ \text{Cross multiply and we'll have} \\ x=\frac{122\times100}{20} \\ x=610 \\ \text{The original price in 2010 is \$610} \\ \text{If the price reduced by \$122 in 2012, then } \\ \text{The price in 2012 would be }610-122=488 \\ \end{gathered}[/tex]The price in 2010 would be $610
The price in 2012 would be $488
Find the value for x(1.003)(sin(x))=(1.33)(sin(35))
Given:
Expression is
[tex]1.003\times sin(x)=1.33\times sin(35)[/tex]Required:
Find the value for x.
Explanation:
We will solve given expression as:
[tex]\begin{gathered} 1.003\times sin(x)=1.33\times sin35 \\ sin(x)=\frac{1.33\times sin35}{1.003} \\ sin(x)=0.76 \\ x=sin^{-1}(0.76) \end{gathered}[/tex]Answer:
Hence, value of x is above.
In ∆HIJ, i=99 inches and < H=9°. Find the length of h, to the nearest inch.
ANSWER
h = 16 in
EXPLANATION
We can solve this using the law of sines:
In this case, the relation is:
[tex]\frac{i}{\sin I}=\frac{j}{\sin J}=\frac{h}{\sin H}[/tex]WIth the first two ratios we have:
[tex]\frac{99}{\sin I}=\frac{99}{\sin J}[/tex]We can find that angles I and J are equal:
[tex]\begin{gathered} \frac{\sin J}{\sin I}=\frac{99}{99} \\ \frac{\sin J}{\sin I}=1 \\ \sin J=\sin I \\ J=I \end{gathered}[/tex]Therefore, they measures - because the interior angles of a triangle add up 180º- are:
[tex]\begin{gathered} m\angle H+m\angle J+m\angle I=180º \\ 9º+2m\angle J=180º \\ m\angle J=\frac{180º-9º}{2} \\ m\angle J=m\angle I=85.5º \end{gathered}[/tex]Now, using the law of sines, we can find h:
[tex]\begin{gathered} \frac{i}{\sin I}=\frac{h}{\sin H} \\ \frac{99}{\sin85.5º}=\frac{h}{\sin 9º} \\ h=99\cdot\frac{\sin 9º}{\sin 85.5º} \\ h=15.535in \end{gathered}[/tex]Rounded to the nearest inch, h = 16 in
assume that a randomly selected subject is given a bone density test and those scores are normally distributed with a mean of 0 and a standard deviation of 1 Find the probability that a given score is less than 2.01 and draw a sketch of the region
EXPLANATION
The normal probability Table contains the probabilities to the left of z-scores.
The probability to the left of 2.01 is given in the row with 2.00 and in the column of 0.01 in the normal probability table:
P(Z<2.01) =0.9778.
The answer is 0.9778.