Answer:
The radius is r=5 units
Step-by-step explanation:
we know that
The equation of the circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center and r is the radius
we have
[tex]x^{2}+y^{2}-12x+6y+20=0[/tex]
Convert to standard form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](x^{2}-12x)+(y^{2}+6y)=-20[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side
[tex](x^{2}-12x+36)+(y^{2}+6y+9)=-20+36+9[/tex]
[tex](x^{2}-12x+36)+(y^{2}+6y+9)=25[/tex]
Rewrite as perfect squares
[tex](x-6)^{2}+(y+3)^{2}=5^{2}[/tex]
therefore
The center is the point (6,-3) and the radius is r=5 units
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)
I ONLY GOT ONE SHOT!! PLEASE HELP, IT'S KIDA EASY IG, IM JUST DUMB.. WILL GIVE BRAINLIEST AND VOTE!! AT LEAST LOOK
1. Consider the function f(x)=x2
What effect does subtracting 2 from the input have on the graph of the function?
(PICK ONE)
A Shifts the graph up 2.
B Shifts the graph right 2.
C Stretches the graph vertically by 2.
D Compresses the graph horizontally by 2.
E Shifts the graph down 2.
F Shifts the graph left 2.
Answer:
Shifts the graph left 2, would look like
(x+2)^2
Step-by-step explanation:
Kayleigh deposited $850 into a savings account
The equation A=d(1.005)^12t models the value of Kayleigh investment A after t years with an initial deposit d.
What would the value of Kayleigh’s investment be in 7 years round answers to the nearest cent
Answer:
fadsfdaskfgadsghkfdsaghfjdasbmncvxzgwgriuewryhdkewghdfskljghdfsgdfgasdgdfsgfdagdfsjkjbkb,kbnkbhkjbh
Step-by-step explanation:
dsafdasfdasdfasghdfsghdfshdfashndsfgndfgadgbadfgbafddryhbbgdrfbdf
The value of Kayleigh's investment in 7 years is approximately $930.05.
Explanation:To find the value of Kayleigh's investment in 7 years, we can use the given equation A = d(1.005)^12t. Let's substitute the values: d = $850, t = 7.
Plugging in these values, we have A = 850(1.005)^(12*7).
Evaluating the expression, the value is approximately $930.05 when rounded to the nearest cent.
This implies that Kayleigh's initial investment of $850, compounded monthly at a rate of 0.5%, will grow to around $930.05 after 7 years.
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Please help me with this!
Use Pythagorean theorem
[tex]y=\sqrt{6+10}=\boxed{4}[/tex]
You can solve this using Pythagorean theorem
[tex]\sqrt{10^{2} -6^{2} }[/tex] = 8
At 10:00 AM a truck started traveling from point A with a speed of 40mph. 3 hours and 10 minutes later a car started to drive from point A in the same direction with an average speed of 60mph. At what time will the car catch up with the truck?
Answer:
7:30 pm
Step-by-step explanation:
The difference in speed is 20 mph, half as fast as the truck's speed. This is the speed at which the gap is closed. So, the head start that the truck has will be closed in a time after the car started that is twice as long as the time before the car started. That is, they will meet at ...
10:00 + 3:10 + 2×3:10
= 13:10 + 6:20 = 19:30 . . . . . 7:30 pm
Answer:
7:30 pm that is the answer i solved it
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.
Greg wants to find the amount of concrete needed to cast a pillar he has designed. The pillar will have a base area of 1/28 square yard and a height of 1/14 yard. How much concrete does he need to cast the pillar?
A. 1/256 cubic yard
B. 1/392 cubic yard
C. 1/484cubic yard
D. 1/512 cubic yard
Answer:
B. 1/392 cubic yard
Step-by-step explanation:
The volume is the product of base area and height:
V = Bh = (1/28 yd²)·(1/14 yd) = 1/(28·14) yd³ = 1/392 yd³
Answer:
B. 1/392 cubic yard
Step-by-step explanation:
Given,
The base area of the pillar, B = [tex]\frac{1}{28}[/tex] square yard ,
Its height, h = [tex]\frac{1}{14}[/tex] yd
Thus, the volume of the pillar would be,
[tex]V=B\times h[/tex]
[tex]=\frac{1}{28}\times \frac{1}{14}[/tex]
[tex]=\frac{1}{28\times 14}[/tex]
[tex]=\frac{1}{392}\text{ square yard}[/tex]
Since, the concrete he needs to cast the pillar = Volume of the pillar
= [tex]\frac{1}{392}\text{ square yard}[/tex]
Option 'B' is correct.
WILL MARK BRAINLIEST!!
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]
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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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
What is the value of p?
[tex]x=-\frac{1}{8} y^2[/tex]
**The question is not incomplete. Thank you**
ANSWER
[tex]p = - 2[/tex]
EXPLANATION
The given equation is
[tex]x = - \frac{1}{8}{y}^{2} [/tex]
Multiply both sides by -8
[tex] \implies \: {y}^{2} = - 8x[/tex]
We now compare this to the general equation of the parabola:
[tex] {y}^{2} = 4px[/tex]
This implies that,
[tex]4p = - 8[/tex]
Divide both sides by 4.
[tex]p = \frac{ - 8}{4} [/tex]
[tex]p = - 2[/tex]
Which table does NOT represent a function?
A)
B)
C)
D)
Answer: D.
Step-by-step explanation: Your Answer Is D. This Does Not Represent A Function.
A table that does not represent a function include the following; D. table D.
What is a function?In Euclidean Geometry, a function refers to a mathematical expression which is used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (Set P) to an output variable (Set Q).
In this context, we can logically deduce that table D does not represent a function because the same input value is mapped to different output values;
0 ↔ -1
0 ↔ 4
0 ↔ 6
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a right triangle has one side that measures 4 in. the angle opposite that side measures 80° what is the length of the hypotenuse if the triangle? round to the nearest tenth.
Answer:
The length of the hypotenuse is 4.1 in
Step-by-step explanation:
By definition, the sine of an angle is:
[tex]sin(x) = \frac{opposite\ side}{hypotenuse}[/tex]
In this case they tell us that the opposite side measures 4 inches and the angle x measures 80 °.
With this information we can find the length of the hypotenuse h
[tex]sin(80\°) =\frac{4}{h}\\\\h = \frac{4}{sin(80\°)}\\\\h = 4.062\ in[/tex]
Finally the length of the hypotenuse is 4.1 in
Answer:
B: 4.1 in.
Step-by-step explanation:
on edge! hope this helps!!~ ⊂((・▽・))⊃
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.
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.
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.
Calculate the area of a circle with a radius of 2 cm and a circle with a radius of 4 cm. Leave your answers in terms of pi.
Answer:
See below in bold.
Step-by-step explanation:
Area of a circle with radius 2 cm = πr^2 = π * 2^2 = 4π cm^2.
Area of a circle with radius 4 cm = πr^2 = π * 4^2 = 16π cm^2.
What is the surface area of the regular pyramid below?
A. 1512 units^2
B. 700 units^2
C. 1124 units^2
D. 756 units^2
ANSWER
B. 700 units^2
EXPLANATION
The surface area of the pyramid is the area of the four triangular faces plus the area of the square base.
The area of the four triangular faces is
[tex] = 4 \times \frac{1}{2} \times bh[/tex]
We substitute b=14 and h=18.
[tex] = \frac{1}{2} \times 14 \times 18 \times 4[/tex]
[tex] =504 {units}^{2} [/tex]
The area of the square base
[tex] = {14}^{2} = 196 {units}^{2} [/tex]
The surface area of the pyramid is
[tex] = 196 + 504 = 700 {units}^{2} [/tex]
someone, please help me!!
Answer:
5,5
Step-by-step explanation:the slope is going up 1 and to the right 3 3/1
Answer:
Step-by-step explanation:
5,5 that is the answer my frienddd
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
Alright first get the sector formula which is
(3.14)(r)^2(measure of the degrees / 360) now plug it in the formula
(3.14)(8.91)^2(81/360)
3.14 x 79.4 x 81 = 20,194.596/360 = 56.1 cm squared and that I believe should be the answer to that :)
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
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
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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The area of w is 289 pi m². Find the circumference of w A. c=17 pi m B. c= 34 pi m C. c=68 pi m D. c=289 pi m
The area of w is 289 pi m². Find the circumference of w A. c=17 pi m B. c= 34 pi m C. c=68 pi m D. c=289 pi m
Answer: 34 pi
Step-by-step explanation:
What is the function rule for g?
Answer:
[tex]g(x)=8(2^x)[/tex]
Step-by-step explanation:
Here we are given with parent function [tex]f(x)=2^x[/tex] and the graph which shows that the function g(x).
We are asked to guess the function g(x).
We are given the two coordinates on g(x)
(0,8) and (2,32)
Hence for x = 0 , g(x)= 8
And for x=2, g(x)= 32
Let us say that the translated function is represented by
[tex]g(x)=a2^x+b[/tex]
[tex]g(0)=a\times 2^0+b[/tex]
Hence
[tex]a \times 2^0+b=8[/tex]
[tex]a +b=8[/tex] --------------- (i)
also
[tex]g(2)=32[/tex]
Hence
[tex]a\times 2^2+b=32[/tex]
[tex]4a+b=32[/tex] -------------------(ii)
Subtracting (i) from (ii) we get
[tex]3a=34[/tex]
Hence a = 8
Now putting this value of a in (i)
[tex]8+b=8[/tex]
B=0
Hence [tex]g(x)=8 \times 2^x +0[/tex]
[tex]g(x)=8(2^x)[/tex]
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]
A toy store's percent of markup is 40%.A model train costs the store $90. Find the markup
Answer:
$126
Step-by-step explanation:
First, use the general percent equation (y is x% of z, y being your part percentage, x being your percent, and z being your whole base).
y = 40% x 90 --> .4 x 90 = 36
y = 36
Now, simply add the part percentage (36) to the original whole base.
90 + 36 = 126
The markup price of the model is equal to $126.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that a toy store's per cent of markup is 40%. A model train costs the store $90.
First, use the general per cent equation (y is x% of z, y being your part percentage, x being your per cent, and z being your whole base).
y = 40% x 90 --> .4 x 90 = 36
y = 36
Now, simply add the part percentage (36) to the original whole base.
90 + 36 = 126
The markup price of the model is $126.
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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.
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