Answer:
a) 4x -3y ≥ -24
b) 2x +3y ≥ -12
c) 4x -3y ≤ 12
d) 2x +3y ≤ 24
Step-by-step explanation:
All of the given points are on the axes, so it is useful to know the intercept form of the equation for a line is ...
x/a +y/b = 1 . . . . . . where a is the x-intercept and b is the y-intercept.
a)The boundary line for the first side is ...
x/-6 +y/8 = 1
4x -3y = -24 . . . . . . multiply by -24 to put in standard form
The graph shows the quadrilateral is to the right of this line, so its inequality is ...
4x -3y ≥ -24
__
b)The boundary line for side 2 has equation ...
x/-6 +y/-4 = 1
2x +3y = -12 . . . . . multiply by -12
The quadrilateral is to the right of this line, as well, so its inequality is ...
2x +3y ≥ -12
__
c)We can see from the graph that the x-intercept of the boundary line for side 3 is x=3. The equation for that boundary line is ...
x/3 +y/-4 = 1
4x -3y = 12
The quadrilateral is to the left of this line, so its inequality is ...
4x -3y ≤ 12
__
d)Apparently, side 4 is intended to use points already given. We assume it passes through (6, 4) and (0, 8). This boundary is parallel to side 2, so will have the same equation, but with a different constant.
2x +3y = 2(0) +3(8) = 24
The quadrilateral is to the left of this line, so its inequality is ...
2x +3y ≤ 24
__
The second attachment shows a graph of the four inequalities with their shading.
_____
Additional comment
All of the inequalities are written in standard form, so the x-coefficient is positive for all of them. The direction of the inequality symbol can be chosen to select values of x that are greater than or less than those on the boundary line. If the shading is to be to the right, then larger x-values are required, and the inequality will have the form ax + by ≥ c (a > 0). If shading is to the left, then smaller x-values are required, and the inequality symbol points in the other direction.
The figure is a parallelogram, not a rectangle.
19) The x coordinate of a point that lies on the x-axis is negative.
Answer:
false
Step-by-step explanation:
i'm not sure if this is a true or false question, but if so, it is false
the x-axis has a positive side and a negative side, so the coordinate isn't necessarily negative. it could also be zero if the point is at the origin
hope this helps!
(x+2)^2 ≠ 0 ? hihihihihihi
A cafeteria offers oranges, apples, or bananas as its fruit option. It offers peas, green beans, or carrots as the vegetable option. Find the number of fruit and vegetable options. If the fruit and the vegetable are chosen at random, what is the probability of getting an orange and carrots? Is it likely or unlikely that a customer would get an orange and carrots?
i don't know please answer me
A square has an area of 100 m squared. What is the length of each side?
Answer:
10m
Step-by-step explanation:
area of a square =s^2
therefore s^2=100
s= under root 100
= 10
Solve the equation | 7x + 5| = |3x - 13|
I 7X + 5 I = I 3X- 13I
7×+5 = 3x +13
7X-3x = 13-5
4x = 8
X= 8/4
X=2
What is the expected value?
Answer:
2.1
Step-by-step explanation:
The expected value of a probability is given by the formula:
E(x) = Σxp(x)
Therefore from the table showing the winnings of a game, the expected value of the probability distribution is:
E(x) = Σxp(x) = (0 * 0.5) + (2 * 0.2) + (4 * 0.15) + (6 * 0.1) + (10 * 0.05)
E(x) = 0 + 0.4 + 0.6 + 0.6 + 0.5 = 2.1
Hence we can conclude that the expected value of the winnings of the game is 2.1.
Which expression can be used to convert 80 dollars (USD) to Australian dollars (aud) 1 USD=1.0343 AUD 1 AUD 0.9668 USD
Answer: [tex]1\ \text{USD}\equiv 1.35\ \text{AUD}[/tex]
Step-by-step explanation:
1 USD is equivalent to 1.35 AUD
Therefore, 80 USD is equivalent to
[tex]\Rightarrow 80\ \text{USD}\equiv 80\times 1.35\\\\\Rightarrow 108\ \text{AUD}[/tex]
please help me! anyone pls
Answer:
Option c is the correct answer
Step-by-step explanation:
Reason : -
When,
x = 6, y = 3
x / y
= 6 / 3
= 2 / 1
= 2
When,
x = 10, y = 5
x / y
= 10 / 5
= 2 / 1
= 2
When,
x = 14, y = 7
x / y
= 14 / 7
= 2 / 1
= 2
These ordered pairs represents a proportional relationships.
Which expression is equivalent to 206.230?
O a. 2 x 100 + 6 x 10 + 2 x 1 + 3 < 1/10
O b. 2 x 100 + 6 x 1 + 2 x 1/10 + 3 < 1/100
O c. 2 × 10 + 6 x 1 + 2 x 1/10 + 3 * 1/100
Answer:
b.
Step-by-step explanation:
hsgusuhsghshjsuhsyh
Determine whether the statement below is true or false boxy is rectangle
Find the distance between points M(-1,-10) and P(-12,-3). Round to the nearest tenth
Answer: Distance = √170
Step-by-step explanation:
Concept:
Here, we need to know the concept of the distance formula.
The distance formula is the formula, which is used to find the distance between any two points.
If you are still confused, please refer to the attachment below for a clear version of the formula.
Solve:
Find the distance between M and P, where:
M (-1, -10)P (-12, -3)[tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]Distance = \sqrt{(-3+10)^2+(-12+1)^2}[/tex]
[tex]Distance = \sqrt{(7)^2+(-11)^2}[/tex]
[tex]Distance = \sqrt{49+121}[/tex]
[tex]Distance = \sqrt{170}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
Step-by-step explanation:
(x₁ , y₁) = (-1 , -10) & (x₂,y₂)=(-12,-3)
Distance = [tex]\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]
[tex]= \sqrt{(-12-[-1])^{2}+(-3-[-10])^{2}}\\\\= \sqrt{(-12+1)^{2}+(-3+10)^{2}}\\\\=\sqrt{(-11)^{2}+(7)^{2}}\\\\= \sqrt{121+49}\\\\=\sqrt{170}[/tex]
= 13.03
= 13
please help (picture) 25 points
Answer:
1) perimeter = sum of all the sides = 3y+9+2y+4+y+3+2y+4 = 8y+20
2) P = 4(5x-2) = 20x-8
in a survey of 850 students in a school 90% reported having pets at home. if the margin of error is +3.4%, what is the interval that is likely to contain the exact percent of all people who have pets at home
Answer:
86.6% ; 93.4%
Step-by-step explanation:
To obtain the population proportion from the sample, we calculate the confidence interval ;
Confidence interval = phat ± margin of error
Phat = 90% ; margin of error = +3.4%
Hence,
90% ± 3.4%
(90 - 3.4)% ; (90 + 3.4)%
86.6% ; 93.4%
can a right triangle be obtuse?
ok so this... is confusing the hell outta me any help?
Answer:
y = 24
Step-by-step explanation:
The sum of the angles of a triangle is 180
A+B+C = 180
ABC = 60
We know 2x-4 = 60
2x -4+4 = 60+4
2x = 64
x = 64/2 = 32
A = 3x = 3(32) = 962x-4 = 60
B = 60
Using the first equation
96+ 60 +y = 180
156 +y =180
y = 180-156
y = 24
dilations geometry!
Answer:
A' (0,20)
B' (30,-20)
C' (-10,-40)
Answered by GAUTHMATH
find the missing length indicated
Answer:
x = 240
Step-by-step explanation:
Apply the leg rule to find the value of x.
Leg rule is given as:
Hypotenuse/leg 1 = leg 1/part 1
Hypotenuse = 400
Leg 1 = x
Part 1 = 144
Plug in the known values into the formula
400/x = x/144
Cross multiply
x*x = 144*400
x² = 57,600
Take the square root of both sides
√x² = √57,600
x = 240
PLSSS HELPPP
give me the answers and explain
What is the y-intercept of the line whose equation is y = –2x + 8?
Answer:
(0,8)
Step-by-step explanation:
y = –2x + 8
The y intercept is found when x =0
y = –2*0 + 8
y = 8
The y intercept is
(0,8)
Please help me to solve this two questions
Answer:
c.8,625grams of flour
4a. X=12
Y=30
Z=60
Step-by-step explanation:
For c. , You have to convert the mixed numbers to fractions.
2¾ cups of flour= 2×4=8
8+3=11
Answer: 11/4 (11 over 4)
You multiply the 2 (whole number) by the 4 (bottom number) and then you get *8*
You then take the 8 (which was your answer) and add 3. This will give you 11
You take the 4 and use it as your denominator (bottom number) for the 11. So no need to find a denominator, because you just use the 4
For the fruit cake, she uses *1½* cups of flour more than carrot cake
Calculation:
1½ converted to an improper fraction= 1×2=2
2+1=3
Answer: 3/2 (3 over 2)
"Customer orders *3* carrot cakes and *4* fruit cakes
How many cups of flour are required to bake for the cakes ordered by the customer?"
11/4÷3= 8,25grams
3/2÷4= 0,375grams
8,25+0,375=8,625grams in total
*Feel free to correct me as I might be wrong!*
Which graph corresponds to the function f(x) = x2 + 4x – 1?
Answer:
1
Step-by-step explanation:
I graphed it to check. x^2+4x-1 has a vertex of (-2,-5).
1000000+200000=?
fun for me
Answer:
1,200,000
Step-by-step explanation:
hope i helped
Answer:
1.200.000
Step-by-step explanation:
[tex]thankyou[/tex]
if possible help me in this. I need to find the two odd numbers...
Part (a)
Consecutive odd integers are integers that odd and they follow one right after another. If x is odd, then x+2 is the next odd integer
For example, if x = 7, then x+2 = 9 is right after.
Answer: x+2========================================================
Part (b)
The consecutive odd integers we're dealing with are x and x+2.
Their squares are x^2 and (x+2)^2, and these squares add to 394.
Answer: x^2 + (x+2)^2 = 394========================================================
Part (c)
We'll solve the equation we just set up.
x^2 + (x+2)^2 = 394
x^2 + x^2 + 4x + 4 = 394
2x^2+4x+4-394 = 0
2x^2+4x-390 = 0
2(x^2 + 2x - 195) = 0
x^2 + 2x - 195 = 0
You could factor this, but the quadratic formula avoids trial and error.
Use a = 1, b = 2, c = -195 in the quadratic formula.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(1)(-195)}}{2(1)}\\\\x = \frac{-2\pm\sqrt{784}}{2}\\\\x = \frac{-2\pm28}{2}\\\\x = \frac{-2+28}{2} \ \text{ or } \ x = \frac{-2-28}{2}\\\\x = \frac{26}{2} \ \text{ or } \ x = \frac{-30}{2}\\\\x = 13 \ \text{ or } \ x = -15\\\\[/tex]
If x = 13, then x+2 = 13+2 = 15
Then note how x^2 + (x+2)^2 = 13^2 + 15^2 = 169 + 225 = 394
Or we could have x = -15 which leads to x+2 = -15+2 = -13
So, x^2 + (x+2)^2 = (-15)^2 + (-13)^2 = 225 + 169 = 394
We get the same thing either way.
Answer: Either 13, 15 or -15, -13Find the reciprocal of I
Answer:
the reciprocal of 1 is 1
Step-by-step explanation:
1/1 flipped is still equal to 1
Select an expression that can be used to find the total number of points Simone can earn
Answer:45
Step-by-step explanation:
Find the length of the arc with central angle of 205° and radius of 7 cm. Use 3.14 for pi(π) and round to the nearest hundredth.
12.52 cm
25.03 cm
87.61 cm
153.86 cm
The length of the arc with a central angle of 205° is 25.03 cm
Length of an arcThe formula for calculating the length of an arc is expressed as:
L = rtheta
Given the following parameters
r = 7cm
theta = 205° = 3.57792 radians
L = 7(3.57792)
L = 25.04544
Hence the length of the arc with a central angle of 205° is 25.03 cm
Learn more on length of an arc here: https://brainly.com/question/2005046
8.52 The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches. Pediatricians regularly measure the heights of toddlers to determine whether there is a problem. There may be a problem when a child is in the top or bottom 5% of heights. Determine the heights of 2-year-old children that could be a problem.
Answer:
Heights of 29.5 and below could be a problem.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches.
This means that [tex]\mu = 32, \sigma = 1.5[/tex]
There may be a problem when a child is in the top or bottom 5% of heights. Determine the heights of 2-year-old children that could be a problem.
Heights at the 5th percentile and below. The 5th percentile is X when Z has a p-value of 0.05, so X when Z = -1.645. Thus
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 32}{1.5}[/tex]
[tex]X - 32 = -1.645*1.5[/tex]
[tex]X = 29.5[/tex]
Heights of 29.5 and below could be a problem.
Solve the equation.
8-2x = -8x + 14
O x=-1
Ox=-3/5
Ox= 3/5
Ox=1
The solution to the algebraic equation is x = 1. The last option is correct.
How do we solve a linear algebraic equation?The solution to a linear algebraic equation can be achieved by finding the like terms and equating them to the constant variable.
From the given information:
8 - 2x = -8x + 14
Collecting the like terms, we have:-2x + 8x = 14 - 8
6x = 6
Divide both sides by 6, we have:x = 1
Learn more about solving linear algebraic equations here:
https://brainly.com/question/1365672
#SPJ1
x-1 = [tex]\sqrt{x} -1[/tex]
Answer:
[tex]x = 0[/tex] or [tex]x = 1[/tex].
Step-by-step explanation:
Start by adding [tex]1[/tex] to both sides of this equation:
[tex](x - 1) + 1 = (\sqrt{x} - 1) + 1[/tex].
[tex]x = \sqrt{x}[/tex].
If two numbers are equal, their square should also be equal. Therefore, since[tex]x = \sqrt{x}[/tex], it must be true that [tex]x^{2} = (\sqrt{x})^{2}[/tex]. That is: [tex]x^{2} = x[/tex].
Notice that since [tex]x[/tex] is under a square root, the result must ensure that [tex]x \ge 0[/tex].
Subtract [tex]x[/tex] from both sides of the equation:
[tex]x^{2} - x = x - x[/tex].
[tex]x^{2} - x = 0[/tex].
Factor [tex]x[/tex] out:
[tex]x\, (x - 1) = 0[/tex].
Hence, by the Factor Theorem, [tex]x = 0[/tex] and [tex]x = 1[/tex] would satisfy this rearranged equation. Because of the square root in the original equation, these two value must be non-negative ([tex]x \ge 0[/tex]) to qualify as actual roots of that equation.
In this example, both [tex]x = 0[/tex] and [tex]x = 1[/tex] qualify as roots of that equation.
x-1 = \sqrt{x} -1
Math For Solution#BrainliestBunch
Jacob earned $80 babysitting and deposited the money into his saving account. The next week he spent $85 on video games. Use integers to describe the weekly changes in Jacob's savings account balance.
Answer:
Net change in money: decrease of $5
Step-by-step explanation:
supposing Jacob started with x dollars:
He gained $80 from babysitting: x+80
Lost 85: x + 80 - 85
--> x - 5
Therefore, at the end of the week, Jacob lost 5 dollars