Answer:
The coordinates of the solution that lies in quadrant IV are (2, -5)
Step-by-step explanation:
We have 2 equations, the first of an ellipse and the second of a circumference.
[tex]2x^2+y^2=33\\x^2+y^2+2y=19[/tex]
To solve the system solve the second equation for x and then substitute in the first equation
[tex]x^2+y^2+2y=19\\\\x^2 = 19 -y^2 -2y[/tex]
So Substituting in the first equation we have
[tex]x^2 = 19 -y^2 -2y\\\\2(19 -y^2 -2y)+y^2=33\\\\38 -2y^2-4y +y^2 = 33\\\\-y^2-4y+5=0\\\\y^2 +4y-5 = 0[/tex]
Now we must factor the quadratic expression.
We look for two numbers that multiply as a result -5 and add them as result 4.
These numbers are -1 and 5.
Then the factors are
[tex]y^2 +4y-5 = 0\\\\(y-1)(y+5) = 0[/tex]
Therefore the system solutions are:
[tex]y = 1[/tex]; [tex]y = -5[/tex]
In the 4th quadrant the values of x are positive and the values of y are negative.
So we take the negative value of y and substitute it into the system equation to find x
[tex]y=-5\\\\2x^2+(-5)^2=33\\\\2x^2 = 33-25\\\\2x^2 = 8\\\\x^2 = 4[/tex]
[tex]x = 2[/tex], and [tex]x= -2[/tex]
In the 4th quadrant the values of x are positive
So we take the positive value of x
the coordinates of the solution that lies in quadrant IV are (2, -5)
Kite WXYZ is graphed on a coordinate plane. What is the area of the kite?
7 square units
8 square units
14 square units
16 square units
Answer:
14 square units
Step-by-step explanation:
There are several ways we can find the area. Probably the easiest is to cut the kite in half vertically and find the area of each triangle. The area of the kite will be double that.
The height of the kite is 7 units, and the width is 4 units. So each triangle will have a base of 7 and height of 2.
A = 1/2 bh
A = 1/2 (7) (2)
A = 7
The area of the kite is double that, so:
2A = 14
The area of kite WXYZ in the coordinate plane given is: C. 14 square units.
What is the Area of a Kite?Area of a kite = pq/2, where p and q are the diagonal lengths of the kite.
The dimensions of the kite are:
p = 4 unitsq = 7 unitsArea of the kite = (7×4)/2
Area of the kite = 14 square units
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Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = (x - 6)2
Answer:
Translate 6 units to the right.
Step-by-step explanation:
The y = x^2 function is a quadratic function with vertex at (0,0). It can be transformed to have a vertex of (6,0) like the function y = (x-6)^2 by shifting it 6 units to the right. It is now the graph of y = (x-6)^2.
The equation y = (x - 6)² represents a transformation of the graph y = x², specifically a horizontal shift 6 units to the right on the 2-dimensional (x-y) plane.
Explanation:To transform the graph of y = x² to the graph of the equation y = (x – 6)², you must understand that these both take the form of a quadratic equation, producing a parabola when graphed. The difference between these two equations is indicated by the term '– 6' in the x of the second equation which corresponds to a horizontal shift in the graph.
In the equation y = (x – 6)², this specifically means that the graph of y = x² is shifted 6 units to the right. This shift doesn't change the shape of the graph, it only moves the location in the 2-dimensional (x-y) plane. So, when you plot data pairs for both y = x² and y = (x – 6)², the second graph would be identical to the first, just moved 6 units to the right.
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Veata is buying a new video game for $45. She has $150 in her checking account and $5 in her wallet. Which is the most reasonable way for Veata to pay for the game?
2 bill of 20 and 3 of 1
Answer:
Debit card
Step-by-step explanation:
The library is 3 miles east of the city hall. The mall is 10 miles west of the library. How far and in what direction is the mall from the city hall?
Answer:
7 miles west of the city hall
Step-by-step explanation:
The city hall on a coordinate plane is at the origin (0, 0). That means that if the library is 3 miles straight east, its coordinates are (3, 0). If the mall is 10 miles straight west of the library, we find its coordinates by subtracting 10 from 3, which puts us at the coordinate (-7, 0). That means that the mall is 7 miles west of the city hall.
Answer:
[tex]\boxed{\text{seven miles west}}[/tex]
Step-by-step explanation:
Think of this as a number line in which city hall is at 0.
East of city hall is the positive direction and west is negative.
Start at city hall and go three miles east to the library. You are at +3.
Then go 10 mi west to the mall. You end up at -7.
+3 – 10 = -7
[tex]\text{The mall is \boxed{\textbf{seven miles west}} of city hall.}[/tex]
The functions f(x) and g(x) in the graph below are most likely which two equations?
Answer:
It's C.
Step-by-step explanation:
The red curve pass through the point (0, 1) and also y = 2 when x = 1 , so this is y = 2^x. The inverse is the reflection of f(x) in x = y so the blue curve is y = log2 x.
The two equation shown in the graph are y = e^x and y = lnx.
What is a function?In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable).
The red line shown in the graph represents y = e^x
The graph of y = e^x will never have a negative value of y, as the value of x increases the value of y will keep on increasing till ∞ . The value of y at x = 0 is 1, so the graph will cross the y-axis at (0,1).
The blue line shown in the graph represents y = lnx
The value of y will be negative when the value of x lies between 0 and 1 after that the value of y will keep on increasing and the point (1,0) satisfies the equation so it will cross the X - axis at (1,0)
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The figure above shows a store’s supply-demand graph for coffee makers. If the store sells $375 worth of coffee makers, which of the following is a valid possible price for them?
a.
$15
b.
$25
c.
$40
d.
$55
Answer:
Answer is B me compadres!
Step-by-step explanation:
Yes indeed
Based on the supply-demand graph, valid possible price for the coffee makers is $25.
What is the supply demand graph?
The supply-demand graph is a graph that is made up of a demand curve and a supply curve. A demand curve relates the price of a good to the quantity demanded. It is downward sloping. A supply curve relates the price of a good to the quantity supplieed. It is upward sloping.
In order to detemine the price, examine the graph and find the region where total worth is about $375. Looking at the graph, price is $15 becuase total worth is $375(25 x 15)
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Find the equation of the tangent line to the curve x^2 + xy + y^2 = 3 at the point (1,1)
Answer:
y = -x + 2
Step-by-step explanation:
We first need to find the derivative of the equation x² + xy + y² = 3. this is done with implicit differentiation
2x + y + xy' + 2yy' = 0
Get terms with y' to one side, and the other terms to the other side of the equals sign...
xy' + 2yy' = -2x - y
Factor out y'...
y'(x + 2y) = -2x - y
Divide both sides by x + 2y
y' = (-2x - y)/(x + 2y)
This is the formula for the slope of the lines tangent to the curve of the original function.
Plug in the given point (1, 1) to find the slope of this
y' = (-2[1] - 1)/(1 + 2([1])
y' = -3/3
y' = -1
To find the equation of the line:
The general form for a linear equation in slope-intercept form is
y = mx + b where m is the slope and b is the y-intercept
Use what we know about our line to solve the rest. By using one of the given points, we have 3 of the 4 variables in the above equation. Pick either point, it doesn't matter which one. We'll use (1, 1), which is (x, y), and we know that
m = -1
The equation becomes...
1 = -1(1) + b (now solve for b)
1 = -1 + b
2 = b
Plug that value into the general form...
y = -x + 2
See attached photo for the graphs of the original equation, and the graph of the tangent line at (1, 1)
Determine two pairs of polar coordinates for the point (5, 5) with 0° ≤ θ < 360°.
a. (5 square root 2, 225°), (-5 square root 2, 45°)
b. (5 square root 2, 315°), (-5 square root 2, 135°)
c. (5 square root 2, 135°), (-5 square root 2, 315°)
d. (5 square root 2, 45°), (-5 square root 2, 225°)
Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±10).
a. y squared over 81 minus x squared over 100 = 1
b. y squared over 81 minus x squared over 19 = 1
c. y squared over 19 minus x squared over 81 = 1
d. y squared over 100 minus x squared over 81 = 1
Answer:
First part
The answer is (5 square root 2, 45°), (-5 square root 2, 225°) ⇒ answer (d)
Second part
The equation in standard form for the hyperbola is y²/81 - x²/19 = 1 ⇒ answer(b)
Step-by-step explanation:
First part:
* Lets study the Polar form and the Cartesian form
- The important difference between Cartesian coordinates and
polar coordinates:
# In Cartesian coordinates there is exactly one set of coordinates
for any given point.
# In polar coordinates there is an infinite number of coordinates
for a given point. For instance, the following four points are all
coordinates for the same point.
# In the polar the coordinates the origin is called the pole, and
the x axis is called the polar axis.
# The angle measurement θ can be expressed in radians
or degrees.
- To convert from Cartesian Coordinates (x , y) to
Polar Coordinates (r , θ)
# r = ± √(x² + y²)
# θ = tan^-1 (y / x)
* Lets solve the problem
- The point in the Cartesian coordinates is (5 , 5)
∵ x = 5 and y = 5
∴ r = ± √(5² + 5²) = ± √50 = ± 5√2
∴ tanФ = (5/5) = 1
∵ tanФ is positive
∴ Angle Ф could be in the first or third quadrant
∵ Ф = tan^-1 (1) = 45°
∴ Ф in the first quadrant is 45°
∴ Ф in the third quadrant is 180 + 45 = 225°
* The answer is (5√2 , 45°) , (-5√2 , 225°)
Second part:
* Lets study the standard form of the hyperbola equation
- The standard form of the equation of a hyperbola with
center (0 , 0) and transverse axis parallel to the y-axis is
y²/a² - x²/b² = 1, where
• the length of the transverse axis is 2a
• the coordinates of the vertices are (0 , ±a)
• the length of the conjugate axis is 2b
• the coordinates of the co-vertices are (±b , 0)
• the coordinates of the foci are (0 , ± c),
• the distance between the foci is 2c, where c² = a² + b²
* Lets solve our problem
∵ The vertices are (0 , 9) and (0 , -9)
∴ a = ± 9 ⇒ a² = 81
∵ The foci at (0 , 10) , (0 , -10)
∴ c = ± 10
∵ c² = a² + b²
∴ (10)² = (9)² + b² ⇒ 100 = 81 + b² ⇒ subtract 81 from both sides
∴ b² = 19
∵ The equation is y²/a² - x²/b² = 1
∴ y²/81 - x²/19 = 1
* The equation in standard form for the hyperbola is y²/81 - x²/19 = 1
A veterinarian investigating possible causes of enteroliths in horses suspects that feeding alfalfa may be to blame. she wishes to estimate the proportion of horses with enteroliths who are fed at least two flakes of alfalfa per day. in a sample of 62 horses with enteroliths, she finds 42 are fed two or more flakes of alfalfa. she estimates the standard error to be se = 0.0594. 0.2185. 0.0035. 0.4675.
Final answer:
In this Biology question, a veterinarian is investigating the possible causes of enteroliths in horses and suspects that feeding alfalfa may be responsible. She conducted a study to estimate the proportion of horses with enteroliths who are fed two or more flakes of alfalfa per day.
Explanation:
The subject of this question is Biology. The veterinarian is investigating the possible causes of enteroliths in horses and suspects that feeding alfalfa may be to blame. She wants to estimate the proportion of horses with enteroliths who are fed at least two flakes of alfalfa per day.
She conducted a study where she sampled 62 horses with enteroliths and found that 42 of them are fed two or more flakes of alfalfa. She estimates the standard error to be 0.0594.
sand is falling at the rate 27 cubic feet per minute onto a conical pile whose radius is always equal to its height. how fast is the height of the pile growing when the height is exactly (a) 3 feet (b) 6 feet (c) 9 feet.
Answer:
Step-by-step explanation:
The formula for the volume of a cone is V = (1/3)(area of base)(height). If the radius is always equal to the height of the cone, then V = (1/3)(πh²)(h), where we have eliminated r. Shortened, this comes out to V = (1/3)(π)(h³).
We want to know how fast h is increasing when h = 3 ft.
Taking the derivative dV/dt, we get dV/dt = (1/3)π(3h²)(dh/dt), or, in simpler terms, dV/dt = πh²(dh/dt). Set this derivative = to 27 ft³/min and set h = 3 ft.
Then 27 ft³/min = π(3 ft)²(dh/dt) and solve for dh/dt: (3/π) ft/min = dh/dt when h = 3 ft.
What is the volume of the cylinder below?
Answer: hey, the answer will be choice number 2 or b
Step-by-step explanation:
For this case we have that, by definition, the volume of a cylinder is given by the following formula:
[tex]V = \pi * r ^ 2 * h[/tex]
Where do we have to:
A: It's the radio
h: It's the height
We have to:
[tex]h = 3\\r = 8[/tex]
Substituting the values we have:
[tex]V = \pi * (8) ^ 2 * 3\\V = \pi * 64 * 3\\V = 192 \pi \ units ^ 3[/tex]
Answer:
Option C
A jeweler needs 50 ounces of a 21% silver alloy. Find the amount of a 12% silver alloy and the amount of a 24% silver alloy he should mix. Solve using a system of equation.
Need by today!! please show formula and work!!!!
Answer:
12.5 ounces of 12% alloy37.5 ounces of 24% alloyStep-by-step explanation:
Let x represent the amount (in ounces) of 24% alloy in the mix. Then the amount of 12% alloy is (50 -x). The amount of silver in the mix is ...
24%·x + 12%·(50 -x) = 21%·50
12x = 450 . . . . . . simplify, multiply by 100 (to eliminate %), and subtract 600
x = 37.5 . . . . . . . divide by 12
The jeweler needs to mix 37.5 ounces of 24% silver alloy with 12.5 ounces of 12% silver alloy to make 50 ounces of 21% silver alloy.
Lewis fills his thermos with 2 liter of water. Garret fill his thermos with 1 of water. How many more milliliter of water does lewis have than Garret?
For this case we have to:
Lewis carries 2 liters of water
Garret carries 1 liter of water
So, Lewis has 1 liter of water more than Garret.
By definition we have that 1 liter equals 1000 milliliters.
Thus, Lewis carries 1000 milliliters more water than Garret.
Answer:
1000 milliliters
Simplify -8 + 6(b - 1). answer
Answer:
Step-by-step explanation:
-8 + 6(b - 1) = -8 +6b-6 = 6b -14
The simplified expression is now 6b - 14.
To simplify the expression -8 + 6(b - 1), you need to distribute the 6 to both terms inside the parentheses and then combine like terms. Here's the step-by-step process:
Multiply 6 by both b and -1 inside the parentheses: 6 * b gives 6b, and 6 * -1 gives -6.
Write out the new expression without the parentheses: -8 + 6b - 6.
Combine the like terms, which are the constants -8 and -6: -8 - 6 equals -14.
The simplified expression is now 6b - 14.
Find the parabola of the form y=ax2+b that best fits the points (1,0), (3,4), (4,5) by minimizing the sum of squares, s, given by s=(a+b)2+(9a+b−4)2+(16a+b−5)2
Answer: your mum gay
Step-by-step explanation:
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The frequency table was made using a deck of cards in which each card is numbered 1, 2, 3, or 4.
Create a bar graph by dragging the sliders on the horizontal axis to represent the probability distribution.
Answer: 1) 0.10
2) 0.60
3) 0.20
4) 0.10
Step-by-step explanation:
The total frequency is 20+120+40+20 = 200. This means they ran the experiment 200 times. The probability distribution is calculated by the satisfactory number of outcomes (frequency) divided by the total number of experiments/outcomes (total frequency):
[tex]\begin{array}{c|c||lc}\underline{x}&\underline{f}&\underline{f\div 200}&\underline{\text{Probability Distribution}}\\1&20&20\div200=&0.10\\2&120&120\div 200=&0.60\\3&40&40\div 200=&0.20\\4&20&20\div 200=&0.10\end{array}\right][/tex]
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Charles had $15.00. He spent $3.00 on a hot dog. What percent of his money did he spend on the hot dog?
Answer:
Charles spend [tex]20\%[/tex] of his money on the hot dog
Step-by-step explanation:
In this problem we have that
$15 represent the 100% o the money
so
using proportion
Find out what percentage 3 dollars represents
[tex]\frac{15}{100}=\frac{3}{x}\\ \\x=100*3/15\\ \\x=20\%[/tex]
What’s the slope of the line?
Answer:
Y=-3x+4
Step-by-step explanation:
The Slope is -3 and the Y intercept is +4
Answer:
-3
Step-by-step explanation:
We can find the slope of a line by finding 2 points
(0,4) and (2,-2) are two points on the line
m = (y2-y1)/(x2-x1)
= (-2-4)/(2-0)
= -6/2
=-3
A sphere has a diameter of 14 ft. What is its surface area? The surface area of the sphere is ft squared. (Type an exact answer in terms of pi.)
Answer:
196
Step-by-step explanation:
edg 21
The formula for the surface area of a sphere is explained step by step using the given diameter to calculate the surface area in terms of pi. The result is that the surface area of the sphere with a 14 ft diameter is 196π ft².
To calculate the surface area of a sphere:
Identify the diameter of the sphere, which is given as 14 ft.Use the formula for surface area of a sphere: 4πr², where r is the radius (half of the diameter).Calculate the surface area by substituting the radius value (7 ft) into the formula: 4π(7 ft)².Therefore, the surface area of the sphere with a diameter of 14 ft is 196π ft².
The longest river in the UK is the river Severn which has a length of 24 cm on a map. If the map is drawn at a scale of 1:1,500,000, then how many kilometers is the river actually?
Answer:
360 km
Step-by-step explanation:
The length on the ground will be ...
(24·10^-2 m)·(1.5·10^6) = 36·10^4 m = 360·10^3 m = 360 km
Answer:
The length of river is 360km
Explanation:
Length on the map of Severn river = 24cm
Scale on the map = x:y axis
=1:1500000
Where y is the length
Hence 1 cm= 15 km
Therefore
Length of the river
=24[tex]\times[/tex]15
=360 km
Hence the length of river is 360 km
Hey,can you find an area of a trapezoid that has 0.2 for base 1 and 0.6 for base 2 and also 0.2 for its height
Answer:
Trapezoid area = ((sum of the bases) ÷ 2) • height
Trapezoid area = (.2 + .6 / 2) * .2
Trapezoid area = (.8 / 2) * .2
Trapezoid area = .4 * .2 = .08
Step-by-step explanation:
The total cost for 9 bracelets including shiping is $72.00
The shipping charge is $9.00
How much are the bracelets?
Please show your work (and dont guess this is an important test!)
Answer it depends
Step-by-step explanation: how much are there a pice or how much are all 9 . 72-9= 63
But the cost of 1 bracelet is $7
Dan, Gordon and Malachy share some sweets in the ratio 4:3:5. Dan gets 48 sweets. How many sweets are there altogether?
Answer:
144 sweets
Step-by-step explanation:
Let
x----> number of sweets that Dan has
y----> number of sweets that Gordon has
z----> number of sweets that Malachy has
we know that
x=48
x/y=4/3----> y/x=3/4 ----> y=(3/4)x
Substitute the value of x
y=(3/4)48=36
x/z=4/5 ----> z/x=5/4 ----> z=(5/4)x
Substitute the value of x
z=(5/4)48=60
therefore
altogether there are x+y+z=48+36+60=144 sweets
Ana preparo chicha morada con 30 porciento de maiz concentrado y 70 porciento de agua.Si bebio el 30 porciento de la chicha morada y reemplazo esa cantidad de agua .Que porcentaje de la nueva mezcla es concentrado de maiz morado?
Answer:
No se, lo siento
Step-by-step explanation:
Answer:
noswe:C perdon
Step-by-step explanation:
Please help me out please:)
Answer:
56.1 cm²
Step-by-step explanation:
In any circle the area (A) of a sector is
A = area of circle × fraction of circle
= πr² × [tex]\frac{81}{360}[/tex]
= π × 8.91² × [tex]\frac{81}{360}[/tex]
= [tex]\frac{8.91^2(81)\pi }{360}[/tex] ≈ 56.1 cm²
What is the solution to the equation below?
3log4x=log432+log42
X=-8
X=-4
X=4
X=8
Answer:
[tex]\large\boxed{x=4}[/tex]
Step-by-step explanation:
[tex]3\log_4x=\log_432+\log_42\qquad\text{use}\ \log_ab^c=c\log_ab\ \text{and}\ \log_ab+\log_ac=\log_a(bc)\\\\\log_4x^3=\log_4(32\cdot2)\\\\\log_4x^3=\log_464\iff x^3=64\to x=\sqrt[3]{64}\\\\x=4[/tex]
Answer: 4
Step-by-step explanation: Its on EDG
The volume of a cone with a height of 9 inches and a base area of 7 square inches is 21 cubic inches.
True
False
Answer:
True
Step-by-step explanation:
we know that
The volume of a cone is equal to
[tex]V=\frac{1}{3}BH[/tex]
where
B is the area of the base
H is the height of the cone
we have
[tex]B=7\ in^{2}[/tex]
[tex]H=9\ in^{2}[/tex]
substitute
[tex]V=\frac{1}{3}(7)(9)[/tex]
[tex]V=21\ in^{3}[/tex]
therefore
The answer is True
A box contains 17 nickels, 11 dimes and 19 pennies. if a coin is picked at random from the box, what is the average value of the draw in dollars?
Answer: its not possible
Step-by-step explanation: there are 17 nickels, 11 dimes and 19 pennies, NO dollars
Find the circumference and the area of a circle with diameter 6 cm Use the value 3.14 for pie , and do not round your answers. Be sure to include the correct units in your answers.
The circumference of the circle is 18.84 cm and the area is 28.26 cm².
Explanation:To find the circumference of a circle, we use the formula C = πd, where d is the diameter. In this case, the diameter is 6 cm, so the circumference is:
C = 3.14 × 6 = 18.84 cm
To find the area of a circle, we use the formula A = πr², where r is the radius. Since the radius is half the diameter, the radius in this case is 6/2 = 3 cm. So the area is:
A = 3.14 × 3² = 28.26 cm²
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PLEASE HELP ASAP
y coordinate
show work
-3x+2y=6 and 4x-y=2
A. -6
B. 1
C .2
D. 6
ANSWER
D. 6
EXPLANATION
We want to find the y-coordinate of the point of intersection of
-3x+2y=6
and
4x-y=2
Solve for y in equation (2) to get:
y=4x-2
Put y=4x-2 into the first equation:
-3x+2(4x-2)=6
-3x+8x-4=6
-3x+8x-4=6
[tex]5x=10[/tex]
Divide both sides by 5 to get
x=2
This implies that:
y=4(2)-2
y=8-2=6