Answer:
{y = 1/4x^2 − 2 y = −1/2x}
(0,0)
(-6,3)
Step-by-step explanation:
Rewrite as system of equations
y=-1/2x
1/4x^2-2y=-1/2x
Move expression to left and change its sign
y+1/2=0
1/4x^2-2y+1/2x=0
Multiply both sides of equation by 2
2y+x=0
1/4x^2-2y+1/2x=0
Sum the equation vertically and eliminate variable (2y)
3/2x+1/4x^2=0
Solve the equation
x=0
x=-6
Substitute the value of x into equation
y+1/2*0 = 0
y+1/2*(-6) = 0
Solve equation for y
y=0
y=3
so the solution is
(x1,y1)=(0,0)
(x2,y2)=(-6,3)
A recently published research study looked at 3000 people over a period of 15 years and determined that those people who ate fast food two or more times per week had gained an average of 10 pounds more than the group who ate fast food less than twice a week. a) Would the 3000 people constitute a census or a sample? b) Was the data qualitative or quantitative?
Answer: a) sample
b) quantitive.
Step-by-step explanation:
Given: A recently published research study looked at 3000 people over a period of 15 years and determined that those people who ate fast food two or more times per week had gained an average of 10 pounds more than the group who ate fast food less than twice a week.
Here, population = "people who ate fast food two or more times per week"
Since a census is the data of all members in a population whereas a sample is a subset of it.
Then, 3000 people constitute a sample as it is a subset of the population.
Since the researcher's point of interest it to measure average weight gain which is a quantitive measure.
So, the data is quantitative.
Identify an equation in point-slope form for the line perpendicular to
y=-2x + 8 that passes through (-3,9).
O A. y - 9 =-2(x+3)
O B. y+3 (x-9)
O C. y-9 - (x+3)
O D. y + 9 = 2(x-3)
Answer:
[tex]y - 9 = \frac{1}{2}(x +3)[/tex]
Step-by-step explanation:
Given
Function; [tex]y = -2x + 8[/tex]
Required
Find an equation perpendicular to the given function if it passes through (-3,9)
First, we need to determine the slope of: [tex]y = -2x + 8[/tex]
The slope intercept of an equation is in form;
[tex]y = mx + b[/tex]
Where m represent the slope
Comparing [tex]y = m_1x + b[/tex] to [tex]y = -2x + 8[/tex];
We'll have that
[tex]m_1 = -2[/tex]
Going from there; we need to calculate the slope of the parallel line
The condition for parallel line is;
[tex]m_1 * m_2 = -1[/tex]
Substitute [tex]m_1 = -2[/tex]
[tex](-2) * m_2 = -1[/tex]
Divide both sides by -2
[tex]m_2 =\frac{ -1}{-2}[/tex]
[tex]m_2 =\frac{1}{2}[/tex]
The point slope form of a line is;
[tex]y - y_1 = m_2(x - x_1)[/tex]
Where [tex](x_1,y_1) = (-3,9)[/tex] and [tex]m_2 =\frac{1}{2}[/tex]
[tex]y - y_1 = m_2(x - x_1)[/tex]becomes
[tex]y - 9 = \frac{1}{2}(x - (-3))[/tex]
Open the inner bracket
[tex]y - 9 = \frac{1}{2}(x +3)[/tex]
Hence, the point slope form of the perpendicular line is:
[tex]y - 9 = \frac{1}{2}(x +3)[/tex]
What solid figure has five faces and five vertices? rectangular prism cone triangular prism square pyramid
Answer:
Square pyramid
Step-by-step explanation:
The flat square on the bottom is 1 face and there are 4 triangle faces.
The flat square on the bottom has 4 vertices and there is the pointy 1 at the top that holds the 4 triangles.
Hope dis helps,
Have a great day.
Answer:
Square Pyramid
Step-by-step explanation:
Only a square Pyramid has 5 faces and 5 vertices. The right one!
A rectangular prism has 6 faces and 8 vertices. Wrong
A cone has 1 face and 0 vertices. Wrong
A triangular prism has 5 faces and 6 vertices. Wrong
A plane is heading in a direction of 045 degress and changes course in a clockwise direction to 135 degrees. The angle though which the plane turn is?
Answer: 90 degrees clockwise
Subtract the angles to get the answer
135 - 045 = 90
In terms of compass bearings, 045 degrees is directly pointed at northeast while 135 degrees is pointed directly at southeast. We have 0 degrees pointed straight north.
Lewis needed to find the difference in lengths between the hypotenuse and the longest leg of this triangle. His work is shown below.
What errors did Lewis make? Check all that apply.
He simplified incorrectly. It should be 20 instead of 200.
He found the difference between the hypotenuse and the short leg instead of the long leg.
He evaluated incorrectly. It should be .
He evaluated incorrectly. It should be .
He should not have taken the square root of each side to get rid of the exponent.
*see the attachment below showing Lewis' work
Answer:
*He simplified √400 incorrectly. It should be 20 instead of 200.
*He found the difference between the hypotenuse and the short leg instead of the long leg
Step-by-step explanation:
=>Going through the work of Lewis, you'd observe that in the 5th line where Lewis was supposed to simplify √400, he made a mistake by writing 200 instead of 20. The square root of 400 is 20 not 200.
=>Also, the length of the longest leg of the right angled triangle that Lewis is supposed to subtract from the length of the hypothenuse is 16 NOT 12.
The difference between the length of the hypothenuse and the length of the longest Leg = 20 - 16 = 4
Answer: A & B homies...
person up top is correct also...
Step-by-step explanation: on edg 2020
suppose y varies inversely with x, and y = 6 when x = 3. Find x when y = 12.
Answer:
1.5
Step-by-step explanation:
[tex]y \: \alpha \: \frac{1}{x} [/tex]
y = k ÷ x
yx = k
y = 6 , x = 3
6 • 3 = k
18 = k
when y = 12 , x = ?
yx = k
12x = 18
x = 18÷12
x = 3/2
x = 1.5
Determine the points of intersection of the equation circumference x² + (y-3) ² = 25 with the coordinate axes.
Answer:
(4, 0), (-4, 0), (0, -2), (0, 8)
Step-by-step explanation:
Answer:
(0, -2), (4, 0), (0, 8), (-4, 0)
Step-by-step explanation:
The y-intercepts are found by solving for y when x=0.
(y -3)² = 25
y -3 = ±5 . . . . . take the square root
y = 3 ± 5 = {-2, 8}
The x-intercepts are found by solving for x when y=0.
x² +(0-3)² = 25
x² = 16 . . . . . . . . subtract 9
x = ±4 . . . . . . . . .take the square root
The y-intercepts are (0, -2) and (0, 8).
The x-intercepts are (-4, 0) and (4, 0).
Which of the following theorems verifies that WVU = RST?
А. НА
B. HL
C. LA
D. LL
The correct theorems which verifies that, WVU = RST is,
⇒ HL
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
To find correct theorems which verifies that, WVU = RST
Now, We know that;
The Hypotenuse-Leg Theorem is the only viable way to determine congruency between 2 right triangles.
Here, By both triangles;
⇒ ∠VUW = 90°
⇒ ∠STR = 90°
Thus, The correct theorems which verifies that, WVU = RST is,
⇒ HL
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(06.01 MC)What is the value of the expression 2 + 3^2 ⋅ (3 − 1)?
Answer:
Step-by-step explanation:
2 + 3² * ( 3 -1) = 2 + 9 * 2
= 2 + 18
= 20
Answer:
20
Step-by-step explanation:
2 + 3² · (3 - 1)
= 2 + 3² · 2 -- (3 - 1 = 2)
= 2 + 9 · 2 -- (3² = 9)
= 2 + 18 -- (2 · 9 = 18)
= 20
solve as many as you can please
Answer:
1. 5²
2. 6p⁵
3. y⁶
4. 1/5w²
5. n⁶/9p⁷
7. 12²
8. 2/5
What is the domain of this function graphed above?
Answer:
domain: x cant be equal to 3.75
Step-by-step explanation:
I don't know if the problem is in my calculations or the question itself, but the result I got is irrational.
Anyway, here are my calculations. If the help you somehow to solve the question - great!
If not,srry to disappoint you
Given: Circle k (O), OA and OC -radii, AP and CP - tangents, m∠AOC=150° Find: m∠APC
Answer:
m∠APC = 30°
Step-by-step explanation:
To solve for the above question, we would be making use of circle theorems
Looking at the circle, we can see that
m∠APC is an Angle outside the circle
m∠AOC is a smaller arc in the circle.
Therefore, Circle Theorem states that for a circle with two tangents,
The Angle outside the circle + The smaller arc = 180°
Hence,
m∠AOC + m∠APC = 180°
m∠APC = 180° - m∠AOC
m∠APC = 180° - 150°
m∠APC = 30°
Does the function ƒ(x) = 7x + 3 represent exponential growth, decay, or neither?
Answer:
Neither
Step-by-step explanation:
This is a linear function as opposed to an exponential function as there are no x terms in higher powers.
Answer:
I graphed the function and its exponential growth
Step-by-step explanation:
Need help trying to figure out
Answer:
14
Step-by-step explanation:
[tex]\frac{18}{45}[/tex]= [tex]\frac{x}{35}[/tex]
18 x 35= 45x
630=45x
x=14
Please Help ASAP! Will name Brainliest! Question: Minimize the objective function P = 5x + 8y for the given constraints. x ≥ 0 y ≥ 0 2x + 3y ≥ 15 3x + 2y ≥ 15 Answer: 25, 46, 39, 37.5
Answer:
Option D.
Step-by-step explanation:
Minimize the objective function P = 5x + 8y for the given constraints.
[tex]x\geq 0,y\geq 0[/tex]
[tex]2x+3y\geq 15[/tex]
[tex]3x+2y\geq 15[/tex]
The related equations of above inequalities are
[tex]2x+3y=15[/tex]
[tex]3x+2y=15[/tex]
For [tex]2x+3y=15[/tex],
x y
0 5
7.5 0
Plot (0,5) and (7.5,0) and join them by straight line.
For [tex]3x+2y=15[/tex],
x y
0 7.5
5 0
Plot (0,7.5) and (5,0) and join them by straight line.
Check the inequalities for (0,0).
[tex]2(0)+3(0)\geq 15\Rightarrow 0\geq 15[/tex] False
[tex]3(0)+2(0)\geq 15\Rightarrow 0\geq 15[/tex] False
It means both lines are solid lines and shaded region for each lies opposite side of (0,0).
From the below graph it is clear that the vertices of feasible region are (0,7.5), (3,3), (7.5,0).
Point P = 5x + 8y
(0,7.5) P=5(0)+8(7.5)=60
(3,3) P=5(3)+8(3)=15+24=39
(7.5,0) P=5(7.5)+8(0)=37.5 (Minimum)
So, minimum value is 37.5.
Therefore, the correct option is D.
from least to greatest -9, 12/20, 1/5
Answer:
-9, 1/5, 12/20
Step-by-step explanation:
-9 is negative so it will always be the least. It helps to turn the fractions into decimals. To do this, you can just divide 1 by 5 and 12 by 20.
1/5 = .2
12/20 = .6
So, 1/5 is less than 12/20.
This makes the order -9, 1/5, 12/20.
Answer:
-9, 1/5 12/20
Step-by-step explanation:
Use 0 as a border.
All numbers less than 0 on one side the rest on the other.
You will have -9 on less than zero and 1/5, 12/20 on the other side.
So -9 is the least.
Now you have 1/5, and 12/20.
Make the denominators equal.
1/5 x 4/4= 4/20, 12/20 x 1/1 = 12/20
Compare the Numerators.
4 is less than 12.
So the answer is -9, 1/5, 12/20.
Feel free to ask questions.
The cost of a loaf of bread increases by $0.50 for every $1 increase in the cost of 1 pound of flour. Which equation relates the cost of one loaf of bread to the cost of one pound of flour? Cost of One Pound of Flour (x) Cost of One Loaf of Bread (y) $1 $1.50 $2 $2.00 $3 $2.50 $4 $3.00 A. y = 0.5x B. y = 1 + 0.5x C. y = 0.5 + x D. y + 0.5 = x E. 0.5y + 1 = x
Answer:
A. y=0.5x
Step-by-step explanation:
It increases by $.50 for every $1 increase
Multiply.
(2x2 – 3x)(3x2 + 2x - 1)
A. 5x4 - 5x2 - 7x2 – 3x
B. 6x4 + 5x3 - 8x2 + 3x
C. 6x4 - 5x3 - 8x2 – 3x
D. 64 - 5x3 – 8x2 + 3x
Answer:
correct answer is D
Step-by-step explanation:
Which of the following solution sets represent the inequality 3-1/2x ≥10
Answer: x ≤ -14
Step-by-step explanation:
3 - [tex]\frac{1}{2}[/tex]x ≥ 10
1) You want to subtract 3 from both sides of the equation: 3 - [tex]\frac{1}{2}[/tex]x ≥ 10
-3 -3
------------------------
2) Once you subtract 3 from both sides of the equation you'll be able to cancel out 3-3.
3) After, you'll be left with; -[tex]\frac{1}{2}[/tex]x ≥ 7
4) You'll then want to divide both sides by -[tex]\frac{1}{2}[/tex] to isolate x.
5) Divide 7 by -[tex]\frac{1}{2}[/tex]
6) X ≥ -14, but then you'll want to flip the inequality since you divided by a negative.
7) X ≤ -14
What is the equation of the line that is parallel to y = negative two-thirds x + 4 and that passes through (–2,–2)? On a coordinate plane, a line goes through (3, 2), and (6, 0). A point is at (negative 2, negative 2). y = negative two-thirds x minus four-thirds y = negative two-thirds x minus StartFraction 10 Over 3 EndFraction y = negative two-thirds x minus two-thirds y = negative two-thirds x minus StartFraction 17 Over 4 EndFraction
Answer:
Option B.
Step-by-step explanation:
If equation of a line is y=mx+c, then m is the slope of line.
The given equation is
[tex]y=-\dfrac{2}{3}x+4[/tex]
Here, slope of line is [tex]m=-\dfrac{2}{3}[/tex].
We need to find the equation of line that is parallel to given equation and passes through (–2,–2).
We know that, slope of parallel lines are same. So, slope of required line is [tex]m=-\dfrac{2}{3}[/tex]. So, equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-2)=-\dfrac{2}{3}(x-(-2))[/tex]
[tex]3(y+2)=-2(x+2)[/tex]
[tex]3y+6=-2x-4[/tex]
[tex]3y=-2x-4-6[/tex]
[tex]3y=-2x-10[/tex]
Divide both sides by 3.
[tex]y=\dfrac{-2x-10}{3}[/tex]
[tex]y=-\dfrac{2}{3}x-\dfrac{10}{3}[/tex]
Therefore, the correct option is B.
Answer:
B.) y = negative two-thirds x minus StartFraction 10 Over 3 EndFraction
Step-by-step explanation:
The line L is shown on the grid. Find an equation for L. Give your answer in the form y=mx+c
Answer:
y=4x-5
Step-by-step explanation:
y=mx+b,
You can identify that the y-intercept is -5.
Using rise/run, there is a rise of +4 and a run of +1, 4/1=4.
Slope = 4
Y-intercept=-5
Slope-intercept form of equation of line is, y = mx + c
Equation of line L is, y = 5x - 5
From given figure, it is observed that line L is passing through point (0, -5) and (1, 0).
First we have to find slope (m) of line.
[tex]m=\frac{0-(-5)}{1-0} =5[/tex]
So, equation of line becomes,
[tex]y=5x+c[/tex]
Since, line passing through (1, 0). Therefore, substituting point (1, 0) in above equation of line.
We get, c = - 5
Thus, equation of line is, [tex]y=5x-5[/tex]
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Fill in with <, >, or = to
make the statement true.
'
1
12
1
4
14
Answer:
1
1=1 1<12 1=1 1<4 1<14
12
12=12 12>1 12>1 12>4 12<14
1
1=1 1<12 1=1 1<4 1<14
4
4=4 4>1 4<12 4>1 4<14
14
14=14 14>1 14>12 14>1 14>4
The graph shows the function f(x) = |x-hl + k. What is
the value of h?
h = -3.5
h=-1.5
h = 1.5
h = 3.5
the graph show
the value of h is 3.5
The value of h is -1.5.
The correct option is B.
What is Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
We have,
function f(x) = |x - h| + k and the vertex of function is (h, k).
Here, in this question,
the vertex of the point in the graph (-1.5, -3.5).
Thus, the value of h is -1.5.
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In the triangle below, what is the length of EF?
Answer:
EF
Step-by-step explanation:
This triangle is symmetric with respect to a vertical line drawn through the upper vertex. Thus, the length of EF is 12.
Answer:
12
12 is the ans
One student ate 3/20 of all candies and another 1.2 lb. The second student ate 3/5 of the candies and the remaining 0.3 lb. What weight of candies did they each eat? PLEASE HELP!!
Let the total weight of the candy = x
We know the total weight is:
X = 3/20x + 1.2 + 3/5x+ 0.3
Simplify:
X= 3/20x + 1.2 + 12/20x + 0.3
X = 15/20x + 1.5
Subtract 15/20x from both sides:
5/20x = 1.5
Divide both sides by 5/20:
X = 1.5 / 5/20
X = 6
Total = 6 pounds.
HELP NEEDED NOW Measure the difference between the lower quartile of Data Set A and the lower quartile of Data Set B. Round to the nearest tenth when performing all operations.
Answer:
29
Step-by-step explanation:
The formula for lower quartile(Q1) = 1/4(n + 1)th term
Where n = number of terms.
For Data set A = 73, 75, 79, 81, 84, 85, 86, 86, 89, 91, 94, 95
n = 12
Q1 = 1/4 (n + 1) th term
Q1 = 1/4(12 + 1) th term
Q1 = 1/4(13) th term
Q1 = 3.25th term
The 3.25th term is data set A is between the 3rd and 4th term
3rd term = 79
4th term = 81
3.25th term = 79 + 81/2
= 160/2
= 80
For Data set B = 47, 49 , 51, 51, 55, 56, 57, 58, 59, 59, 61, 62
n = 12
Q1 = 1/4 (n + 1) th term
Q1 = 1/4(12 + 1) th term
Q1 = 1/4(13) th term
Q1 = 3.25th term
The 3.25th term is data set A is between the 3rd and 4th term
3rd term = 51
4th term = 51
3.25th term = 51 + 51/2
= 102/2
= 51
The difference between the lower quartile of Data Set A and Data Set B =
80 - 51 = 29
Bryan drives at an average speed of 60 miles per hour.
At this rate, it will take him 3 hours to drive miles.
Answer:
180
Step-by-step explanation:
Multiply 60x3
and you will get 180miles
Answer:
um 60 miles per hour?
Step-by-step explanation:
because if he is going at a speed of 60 and it will take him 3 hours to drive miles per hou- do I even make sense
Make a 3-by-3 logic grid on your own paper. Use it to help you solve the logic
puzzle and answer the question given below.
Tina, Jewel, and Amy have three different pets (dog, goldfish, and ferret).
• Tina is allergic to dogs.
• Jewel does not have the ferret.
• The dog belongs to Amy.
Who owns the ferret?
Answer:
Tina
Step-by-step explanation:
Since Amy owns the dog, she doesn't have the ferret and we know that Jewel doesn't have the ferret so the answer is Tina.
FIRST GETS BRAINLLEST A unicycle wheel has a diameter of 30 inches. How many inches will the unicycle travel in 6 revolutions? Use π = 3.14 and round your answer to the nearest hundredth of an inch.
Answer:
565.2 inches
Step-by-step explanation:
circumference = 2pi r
=2x3.14x15
=94.2
6 revolutions =6x94.2=565.2
What is 21 multiplied by 80
Answer:
1680
Step-by-step explanation:
you can use a calculator or do the normal operation