Select the inequality that corresponds to the given graph. graph of an inequality with a dashed line through the points negative 3 comma 0 and 0 comma 4 and shading below the line
A. 4x-3y>-12
B. x+4y>4
C. 4x-2y<-8
D. 2x+4y=>-16
Answers
The detail about dashed line is important because it expresses an equality with a symbol < or >. The data points that coincide with that line is not part of the solution but just stand as a boundary, hence, I used dashed line and hollow points. If it were ≥ or ≤, then we use solid lines and dots. With that, we can already eliminate choice D.
Next, we test the inequality. Let's choose a point within the shaded region. Suppose the point is (1,0) denoted by the red dot. If it is part of the solution, then the inequality will be proven true.
A. 4x-3y>-12
4(1) - 3(0) > -12
4 > -12, this is true
B. x+4y>4
1 + 4(0) > 4
1 > 4, this is not true
C. 4x-2y<-8
4(1) -2(0) < -8
4 <-8, this is not true
∴The answer is A.
Answer:
b
Step-by-step explanation:
i took the test
Related Questions
The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6.
Applying Newton's cooling model, the temperature of the tea after 2 hours will be ___
ºF. round to the nearest integer.
Answers
Newton's Law of Cooling states that the change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature over time.
Therefore when expressed mathematically, this is equivalent to:
dT = - k (T – Ts) dt
dT / (T – Ts) = - k dt
Integrating:
ln [(T2– Ts) / (T1– Ts)] = - k (t2 – t1)
Before we plug in the values, let us first convert the temperatures into absolute values R (rankine) by adding 460.
R = ˚F + 460
T1 = 200 + 460 = 660 R
Ts = 70 + 460 = 530 R
ln [(T2– 530) / (660 – 530)] = - 0.6 (2 - 0)
T2 = 569.16 R
T2 = 109 ºF
Answer: After 2 hours, it will be 109 ºF
Answer:
109 degrees
Step-by-step explanation:
Solve the quadratic equation by completing the square.
x^2-10x+15=0
First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Form:
( x + _ )^2 = _
or
( x - _ )^2 = _
Solution:
x = _
^ Please use the template above to answer ^
Answers
To solve the quadratic equation x^2 - 10x + 15 = 0 by completing the square, we manipulate it to the form (x - 5)^2 = 10, then solve for x to get two solutions: x = 8.16 and x = 1.84.
Explanation:To solve the quadratic equation by completing the square, we need to manipulate the equation x^2 - 10x + 15 = 0 so it takes the form of (x - a)^2 = b, where a is half of the coefficient of x, and b is a constant.
First, we move the constant to the other side of the equation:
x^2 - 10x = -15
Next, we find the value that completes the square. This value is (10/2)^2 = 25.
Adding 25 to both sides, we get:
x^2 - 10x + 25 = 25 - 15
Now the equation is a perfect square:
(x - 5)^2 = 10
To find the solution for x, we take the square root of both sides:
x - 5 = ±10√10
x = 5 ± √10
Thus, the solutions rounded to the nearest hundredth are:
x = 5 + √10 ≈ 8.16
x = 5 - √10 ≈ 1.84
The complete answer in the template is:
Form:
( x - 5 )^2 = 10
Solution:
x = 8.16, 1.84
Which equation is not equivalent to the formula m = ca?
A: [tex]c = \frac{m}{a} [/tex]
B: [tex]a = \frac{c}{m} [/tex]
C: [tex]a = \frac{m}{c} [/tex]
D: m = ac
Answers
If we find a, we must do c = m/a and if we find c we must do a = m/c
The bigger measure over the known one.
Answer B
Answer:m=ca i remember my teacher telling me how to do this.
Step-by-step explanation:
The velocity of a train, measured in meters per second, is described by vector t=(-1,-4). Find the direction the train is traveling using standard position
Answers
Answer:
inverse tangent 4/1
75.96 + 180 bc 3rd quadrant which equals 255.96 degrees.
Step-by-step explanation:
round 256 degrees
The end points of AB are A(-2,-3) , B(3,2) point C lies on AB and is 2/5 of the way from A to . What is the coordinates of point C? Explain how you find your answer
Answers
[tex]\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ A(-2,-3)\qquad B(3,2)\qquad \qquad 2:5 \\\\\\ \cfrac{AC}{CB} = \cfrac{2}{5}\implies \cfrac{A}{B} = \cfrac{2}{5}\implies 5A=2B \\\\\\ 5(-2,-3)=2(3,2)\\\\ -------------------------------\\\\[/tex]
[tex]\bf { C=\left(\cfrac{\textit{sum of "x" values}}{r1+r2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{r1+r2}\right)}\\\\ -------------------------------\\\\ C=\left(\cfrac{(5\cdot -2)+(2\cdot 3)}{2+5}\quad ,\quad \cfrac{(5\cdot -3)+(2\cdot 2)}{2+5}\right)[/tex]
To find the coordinates of point C which divides line AB into a 2:5 ratio, use the section formula. Therefore, the coordinates are (-4/7, -11/7). This provides point C's location on the line segment AB.
Explanation:The coordinates of C are determined through the section formula, which finds the coordinates of a point dividing a line segment into a specific ratio. In this case, the ratio is 2:5. To solve for the x-coordinate of C, the formula [(m*x2) + (n*x1)] / (m+n) is used, where m and n are the ratio values, x1 and x2 are the x-coordinates of points A(-2, -3) and B(3, 2). Using these, the x-coordinate of C is found to be (2*3 + 5*(-2)) / (2+5) = -4/7.
Similar calculations apply to solving for the y-coordinate of C: [(m*y2) + (n*y1)] / (m+n) = (2*2 + 5*(-3)) / (2+5) = -11/7.
Therefore, the coordinates of point C are (-4/7, -11/7). This is the point C on the line segment AB that is 2/5 of the way from point A to point B.
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There are (72)3 ⋅ 70 lambs on a farm. What is the total number of lambs on the farm?
Answers
216(70)= 15,120
15,120 lambs
Heyyy guys just thought I’d let y’all know the answer is *117649* if you (7^2)^3 that’s the answer and 7^0 is 0 soooo yeah!
I need help with #18 c-i
Answers
d - x intercepts
e - it's 4 due to that 4 is shown where x=0 on the graph
f - y intercept
g - Since x>0, we do 4-x^2. x=1, and 1^2=1, so 4-1=3. 1 is x and 3 is f(x), or y, so the coordinates are (1,3)
h - Since it's <0, -1+4=3, and since 3 is the output the coordinates are (-1,3)
i - Since -3 <0, we do -3+4=1
Find the greatest common factor of the following monomials 28g5h2 12g6h5
Also explain step by step how to solve these problems please
Answers
first, we find the GCF of the coefficients 28 and 12. What is the highest number that will go into both 28 and 12 evenly ? That number is going to be 4.
now, we look at our variables....to find the GCF of the variables, pick the lowest exponent.
another words, the lowest exponent of ur variable h is h^2...and the lowest exponent of ur variable g is g^5
therefore, the GCF of these monomials is : 4h^2g^5
Using the graph, find this information about the child’s movement in the vertical (y) direction:
1. the best trigonometric function to start with
2. the amplitude
3. the period
4. any horizontal displacement of the graph.
5. any vertical displacement of the graph.
Type your response here:
Answers
2. The amplitude is the measure from crest to crest, or from trough to trough. The amplitude in the graph is 1.5.
3. The period is the reciprocal of amplitude. Therefore,itis 1/1.5 or 2/3.
4. There is no horizontal displacement because the wave only moves in a vertical direction.
5. The vertical displacement is from crest to trough which is 1 unit.
3. Simplify log3 20 - log3 5
Answers
If four times a number plus 3 is 11, what is the number
Answers
4x = 11 -3
4x = 8
x =8/4
x =2
answer
the number is 2
4x = 11-3 = 8
x = 2
number is 2
Quadrilateral ABCD is a parallelogram. ,  bisects , and . What is the best name for quadrilateral ABCD?
A.
rectangle
C.
isosceles trapezoid
B.
rhombus
Answers
A line passes through the point (-8,3) and has a slope of 5/4.
Write an equation in slope-intercept form for this line.
Answers
3 = 5/4(-8) + b
3 = -10 + b
b= 13
equation
y = 5/4x + 13
y - 3 = (5/4) ( x + 8)
y - 3 = 5/4x + 10
add 3 to both sides
y = 5/4 x + 13
HELP! Type the correct answer in each box. Use numerals instead of words, if necessary, use / for the fractions bar(s)
Answers
The piecewise function is:
[tex]\[ f(x) = \begin{cases} 4 & \text{if } -1 \leq x \leq 1 \\ x - 1 & \text{if } 3 \leq x \leq 5 \end{cases} \][/tex]
To determine the piecewise function represented by the given coordinates, let's examine the points and their corresponding intervals.
The coordinates are (-1, 4), (1, 4), (3, 2), and (5, 4).
The points (-1, 4) and (1, 4) have the same y-coordinate, indicating that on the interval [tex]\(-1 \leq x \leq 1\)[/tex], the function has a constant value of 4. Therefore, the piecewise function for this interval is f(x) = 4 for [tex]\(-1 \leq x \leq 1\).[/tex]
The points (3, 2) and (5, 4) indicate that on the interval [tex]\(3 \leq x \leq 5\)[/tex], the function is a line passing through these two points. We can find the slope (m) and y-intercept (b) for this line.
[tex]\[ m = \frac{\text{change in } y}{\text{change in } x} = \frac{4 - 2}{5 - 3} = \frac{2}{2} = 1 \][/tex]
Using the point (3, 2), we can find the y-intercept:
2 = 1(3) + b
b = -1
Therefore, the equation for the line on the interval [tex]\(3 \leq x \leq 5\) is \(f(x) = x - 1\) for \(3 \leq x \leq 5\).[/tex]
Putting it all together, the piecewise function is:
[tex]\[ f(x) = \begin{cases} 4 & \text{if } -1 \leq x \leq 1 \\ x - 1 & \text{if } 3 \leq x \leq 5 \end{cases} \][/tex]
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The measure of an inscribed angle is 110°. What is the measure of the intercepted arc? 55° 110° 220°
Answers
the measurement of an inscribed angle is half of the measure of the intercepted arc.
the inscribed angle is 110 degrees, so we multiply 110 by 2.
110*2 = 220 degrees
The measure of the intercepted arc is 220 degrees
220° is the measure of the intercepted arc
PLEASE ANSWER ASAP!!! WORTH 13 POINTS! I need help D:
Lucy's goal for her cycling class at the gym is to burn 450 calories in one hour. The number of calories (c) she actually burns in one hour varies no more than 45 calories. Which inequality below represents this scenario?
A) |c − 450| less than or equal to 45
B) |c + 450| greater than or equal to 45
C) |c − 45| less than or equal to 450
D) |c − 45| greater than or equal to 450
Answers
A surface on which all points are at the same potential is referred to as
Answers
Quadrilateral $abcd$ is a trapezoid with $ab$ parallel to $cd$. we know $ab = 20$ and $cd = 12$. what is the ratio of the area of triangle $acb$ to the area of the trapezoid $abcd$? express your answer as a common fraction.
Answers
The area of triangle acb is
A₁ = (1/2)*20*h = 10h
The area of trapezoid abcd is
A₂ = (1/2)*(20+12)*h = 16h
The ratio A₁/A₂ is
A₁/A₂ = (10h)/(16) = 5/8
Answer:
The ratio of triangle acb to the area of trapezoid abcd is 5/8.
Determine the common ratio and find the next three terms of the geometric sequence.
3/4,3/10,3/25,...
Answers
(3/10) / (3/4) = 3/10 * 4/3 = 12/30 = 2/5 <==
In a geometric sequence, the next term is found by multiplying the term by the common ratio.
3/25 * 2/5 = 6/125 <==
6/125 * 2/5 = 12/625 <==
12/625 * 2/5 = 24/3125 <==
The next three terms of the sequence are 6/125, 12/625 and 24/3125
Geometric sequenceThe nth term of a geometric sequence is given as:
Tn = ar^n-1
Given the geometric sequence
3/4,3/10,3/25,...
Find the common ratio
r = 3/10 * 4/3
r = 2/5
Find the 4th, 5th and 6th terms
T4 = (3/4)(2/5)^3
T4 = 3/4 * 8/125
T4 = 6/125
T5 = (3/4)(2/5)^4
T5 = 3/4 * 16/625
T5 = 12/625
T6 = (3/4)(2/5)^5
T6 = 3/4 * 32/3125
T6 = 24/3125
Hence the next three terms of the sequence are 6/125, 12/625 and 24/3125
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A caterer expects a minimum of 160 but no more than 192 people at a wedding. One fruit tray serves 16 people. The compound inequality represents x, the number of fruit trays the caterer should bring to the wedding.
160 ≤ 16x≤ 192
Which is a possible number of fruit trays the caterer might bring to the wedding?
A. 8
B. 10
C. 14
D. 16
Answers
This is because once x is replaced with 16 in the equation, it becomes the number 160, which fits the equation. (it is equal to 160 and less than 192).
All the other numbers are either too large or too small to fit the equation.
Answer:
b. 10
Step-by-step explanation:
I did the test
Find the exact values of sin A and cos A. Write fractions in lowest terms. A right triangle ABC is shown. Leg AC has length 15, leg BC has length 20, and hypotenuse AB has length 25.
Answers
cos A = adjacent / hypotenuse = AC/AB = 15/25 = 3/5
In the right triangle with sides 15, 20, and 25, the exact values of sin A and cos A are 4/5 and 3/5, respectively.
In the right triangle ABC, we can use the given side lengths to find the trigonometric ratios for angle A. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AB) is equal to the sum of the squares of the lengths of the legs (AC and BC).
Let's denote the angle A as angle A:
Find sin A:
sin A = (opposite / hypotenuse) = BC / AB = 20 / 25 = 4/5.
Find cos A:
cos A = (adjacent / hypotenuse) = AC / AB = 15 / 25 = 3/5.
So, the exact values are sin A = 4/5 and cos A = 3/5.
In summary, in the right triangle ABC with side lengths AC = 15, BC = 20, and AB = 25, the exact values of sin A and cos A are 4/5 and 3/5, respectively.
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How many 3 digit numbers can be made if no digit is repeated and the number can not begin with a zero?
Answers
digit #1 - 9 numbers (1-9)
digit #2 = 9 numbers (0-9 minus the first digit)
digit #3 = 8 numbers ( 0-9 minus the first 2 digits)
9*9*8 = 648 combinations
1) It can't start with 0
2) repetition is not allowed.
Let ABC this number:
A = 9 choices (out of 10, excluding 0, because it can't be 0)
B = 9 choices (out of 10 including 0, because it can be 0)
C= 8 choices (out of 10 because 2 digits already selected)
The total ways to write this number are:
9 x 9 x 8 = 648 ways
Another method:
A can be written in ⁹C₁
B can be written in ⁹C₁
C can be written in ⁸C₁
Total ways: ⁹C₁ x ⁹C₁ x ⁸C₁ = 648 ways
Help with these three problems? Please
Answers
6. add the averages then take that average
50+74 = 124, 124/2 = 62
answer: 62
8. first put all the numbers in order
4, 5 ,6 ,8 11, 12,14, 15, 23 ,23
Find the middle number, since there are 10 numbers find the average of the 2 middle numbers
11+12 =23/2 =11.5
Lower half data = 4, 5, 6, 8, 11
The middle number of that set is Q1,
Q1=6
9
9, find q3
1, 2, 3, 5, 5, 6, 9
Find middle number (5)
upper half data = 5, 6, 9
Q3= 5 , 6, 9 = 5+10 +15 = 30
so answer is $30
Can you use the ASA Postulate or the AAS Theorem to prove the triangles congruent?
Answers
Answer:
ASA only
Step-by-step explanation:
Given is a picture of two triangles with one side and one angle congruent.
Comparison of these two triangles given
side = side
one angle = one angle (given)
Second angle = second angle (Vertically opposite angles)
Thus we find here that two angles and one corresponding side are congruent.
HEnce we say that these two triangles are congruent by ASA theorem
ASA theorem can be applied here because the equal side is between the two congruent angles.
Instead if the side is not between the congruent angles but corresponding side then we can only use AAS
SO here ASA is correct.
Answer:
ASA only
Step-by-step explanation:
We are given that two triangles in which
An angle of triangle is equal to its corresponding angle of second triangle.
One side of a triangle is equal to one side of other triangle.
ASA postulate: It states that two angles and included side of one triangle are congruent to its corresponding angles and corresponding side of other triangle , then the two triangles are congruent.
AAS postulate: It states that two angles and non- included side of one triangle are congruent to its corresponding two angles and its corresponding side of another triangle, then the triangles are congruent by AAS postulate.
In triangle AOB and COD
[tex]\angle AOB= \angle COD[/tex] (Vertical angles are equal )
[tex]\angle ABO=\angle CDO[/tex] ( Given )
[tex]OB=OD[/tex] (Given )
[tex]\triangle AOB\cong \triangle COD[/tex] ( ASA Postulate )
Answer: ASA only
A gardener has 27 pansies and 36 daisies. He plants an equal number of each type of flower in each row.What is the greatest possible number of pansies in each row?
Answers
The factors of 27 are (3,9)
Therefore,
Either (a) plant 3 pansies in 9 rows, or
(b) plant 9 pansies in 3 rows.
There are 36 daisies.
The factors of 36 are (3,12), (6,6) or (9,4).
Therefore
Either (a) plant 3 daisies in 12 rows, or
(b) plant 12 daisies in 3 rows, or
(c) plant 6 daisies in 6 rows, or
(d) plant 9 daisies in 4 rows, or
(e) plant 4 daisies in 9 rows.
Because each row has an equal number of pansies and daisies, the only common arrangements are
(a) 9 pansies and 12 daisies in 3 rows, or
(b) 3 pansies and 4 daisies in 9 rows.
To have the greatest number of daisies in each row means planting 9 pansies and 12 daisies in 3 rows.
Answer:
The greatest number of pansies per row is 9.
Plant 9 pansies and 12 daisies in 3 rows.
Parallel to the line 2x-3y=9 and having a y intercept of 3
Answers
The variable Z is inversely proportional to X. When X is 6, Z has the value 2. What is the value of z . When x = 13
Round to at least the thousandths place if needed.
Answers
z α 1/x
hence;
z=k/x
where:
k is the constant of proportionality;
when x=6, z=2
therefore;
2=k/6
hence;
k=2*6=12
Therefore:
z=12/x
the value of z when x=13 will be:
z=12/13
the answer is 12/13
Two containers, one for 3 liters and one for 5 liters, how would you measure 4 liters
Answers
Empty the 3-liter container, and then transfer the 2 liters from the 5-liter container into it.
Now fill the 5-liter container again, then pour water carefully from the 5-liter container into the 3-liter container until it is full - exactly one more liter.
The 5-liter container now has 4 liters in it.
Three out of four students in a school said they would vote for nuncio for class president. Predict how many of the 340 students would vote for nuncio
Answers
cross multiply
(4)(x) = (3)(340)
4x = 1020
x = 1020/4
x = 255 <==
or this way.....
3 out of 4 students.....3/4 = 75%
so 75% of 340 = 0.75(340) = 255 <=
In the diagram below, what is the approximate length of the minor arc ?
Answers
arc length = given angle/360 x 2 x PI x radius
120/450 x 2 x 3.14 x 23 = 48.17
round to 48 cm
Answer:
Option A is correct
the approximate length of the minor arc is, 48 cm
Step-by-step explanation:
Length of an arc is given by:
[tex]l = r \theta[/tex] .....[1]
here r is the radius of the circle from the center and [tex]\theta[/tex] is the angle in radian.
From the given figure, we have;
r = 23 cm
Use conversion:
1 degree = 0.0174533 radian
then
120 degree = 2.094396
[tex]\theta = 2.094396[/tex] radian.
Substitute these in [1] we have;
[tex]l = 23 \cdot 2.094396 = 48.171108[/tex] cm
Therefore, the approximate length of the minor arc is, 48 cm