Answer:
Step-by-step explanation:
A=(-1,5)
B=(5,2)
P=(x,y)
AP²=(x+1)²+(y-5)²=x²+2x+1+y²-10y+25
BP²=(x-5)²+(y-2)²=x²-10x+25+y²-4y+4
AP²=BP² ==> 12x-6y=3 or y=2x-1/2
Proof:
[tex]AB\ slope=\dfrac{2-5 } { 5+1 } =-\frac { 1 } { 2 } \\\\perpendicular\ slope =2\\\\middle\ of\ AB=(2, \frac{7}{2} )\\\\perpendicular\ bisector:\ y-\frac{7}{2} =(x-2)*2\\\\y=2x-\dfrac{1}{2} \\\\[/tex]
Functions f and g are defined for all real
numbers. The function f has zeros at -2, 3, and 7:
and the function g has zeros at -3, -1, 4, and 7.
How many distinct zeros does the product
function f g have?
9514 1404 393
Answer:
6
Step-by-step explanation:
The number of distinct zeros in the product will be the union of the sets of zeros. Duplicated values are not distinct, so show in the union of sets only once.
F = {-2, 3, 7}
G = {-3, -1, 4, 7}
F∪G = {-3, -2, -1, 3, 4, 7} . . . . . . a 6-element set
The product has 6 distinct zeros.
_____
As you may notice in the graph, the duplicated zero has a multiplicity of 2 in the product.
log_c(A)=2
log_c(B)=5,
solve log_c(A^5B^3)
We know that [tex]\log_a(bc)=\log_a(b)+\log_a(c)[/tex].
Using this rule,
[tex]\log_c(A^5B^3)=\log_c(A^5)+\log_c(B^3)[/tex].
We also know that [tex]\log_c(a^b)=b\log_c(a)[/tex].
Using this rule,
[tex]\log_c(A^5)+\log_c(B^3)=5\log_c(A)+3\log_c(B)[/tex]
Now we know that [tex]\log_c(A)=2,\log_c(B)=5[/tex] so,
[tex]5\cdot2+3\cdot5=10+15=\boxed{25}[/tex].
Hope this helps :)
Michelle ate a watermelon with 81 seeds. She picked out 1/9 of all the seeds to plant in her backyard. But her mother said there is no room for that many watermelon plants, so her mom only let her plant 1/3 of the seeds she had chosen. How many watermelon seeds was she allowed to plant in her backyard?
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Answer:
3
Step-by-step explanation:
1/3 of 1/9 of 81 is ...
81×1/9×1/3 = 9×1/3 = 3
Michelle was allowed to plant 3 seeds.
Help me with this please
9514 1404 393
Answer:
B. √6
Step-by-step explanation:
The circles are not tangent to one another. If they were, the distance between their centers would be the sum of their radii: 1 +1 = 2.
__
The center of the first circle is (√3, √3), and the center of the second is the origin. The distance between these two centers is given by the distance formula:
d = √((x2 -x1)^2 +(y2 -y1)^2)
d = √((√3 -0)^2 +(√3 -0)^2) = √(3+3) = √6 . . . . matches choice B
Solve this inequality:
-9 > 3b + 6
Answer:
- 5 > b
Step-by-step explanation:
- 9 > 3b + 6
- 9 - 6 > 3b
- 15 > 3b
Divide 3 on both sides,
- 5 > b
Answer:
-5 >b
Step-by-step explanation:
-9 > 3b + 6
Subtract 6 from each side
-9-6 > 3b + 6-6
-15 > 3b
Divide each side by 3
-15/3 > 3b/3
-5 >b
You work as an assistant to a carpenter who designed the tabletop below. He tells you that each shape is a right triangle, and each is the same size. You now need to calculate the area of one triangle so that you can begin building the tabletop. What is the area of each triangle in square inches? 28 1/4" and 20"
Answer:
A. 200 square inches
Step-by-step explanation:
First, use Pythagorean Theorem to find the base of each triangle.
[tex]a^2+b^2=c^2\\20^2+b^2=(28\frac{1}{4})^2\\400+b^2=798.0625\\b^2=398.0625\\b=\sqrt{398.0625}\\b=19.9515037[/tex]
Finally, use the area of a triangle formula to find the area of each triangle.
[tex]A=\frac{1}{2}bh\\A=\frac{1}{2}(19.9515037)(20)\\A=199.515037[/tex]
Therefore, the area of each triangle is approximately 200 in².
The area of each triangle in square inches is 200 square inches.
What is the area of triangle?The area of triangle is defined as the region enclosed by its perimeter or the three sides of triangle.
Mathematically,
Area of triangle = 1/2(base*height)
Now given that,
Base of the triangle, B = 20''
Hypotenuse of the triangle, H = 28(1/4)'' = 28.25''
So, Height of the triangle, P = [tex]\sqrt{H^2 - B^2}[/tex]
or, Height of the triangle, P = [tex]\sqrt{28.25^2 - 20^2}[/tex]
or, Height of the triangle, P = [tex]\sqrt{398.0625} }[/tex]
or, Height of the triangle, P = 19.95 inches
Finally, use the area of a triangle formula to find the area of each triangle.
Area of triangle = 1/2*(BasexHeight)
⇒Area of triangle = 1/2*(20x19.95)
⇒Area of triangle = 1/2*399
⇒Area of triangle = 199.5 square inches
or, Area of triangle ≈ 200 square inches.
Hence, The area of each triangle in square inches is 200 square inches.
More about triangle :
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7) Ten times the sum of -150 and a number yields -110.
Answer:
the answer to that is 10(N+14)=9N
Let the number = x
Set up an equation:
10(-150 + x ) = -110
Simplify:
-1500 + 10x = -110
Add 1500 to both sides
10x = 1390
Divide both sides by 10
X = 139
The number is 139
This graph describes which of the expressions given?
8. Find the area of the following triangle.
h=8m
b= 6.5
Answer:
26m^2
Step-by-step explanation:
Area of triangle=1/2b*h
We have,
b=6.5
h=8m
Now,
Area=1/2b*h=1/2*6.5*8=26m^2
i nedd help due today plzzzz answer fast
Answer:
Option A, m⁴/n²
Multiply the exponent 6 with the exponents of m and n
1106.666667 To the nearest whole number
Answer:
1107.
You are rounding up because the number in the tenths slot is over 5.
Researchers wanting to assess skin irritation associated with a new sunscreen developed for those with photosensitivity. They randomly sample 240 men with a history of photosensitivity and 240 men without a history of photosensitivity and ask them to apply the cream and report the level of skin irritation they experience after spending 20 minutes in the sun using a scale of 0-10. The average skin irritation score for the group with a history photosensitivity was 1.2 and the average skin irritation score for the group without a history of photosensitivity was 1.4. The Levene's test for equality of variances had a p value of 0.08. You know this means:
A. The researchers should report the t test results assuming equal variances. Select The researchers should report the t test results NOT assuming equal variances. as your answer
B. The researchers should report the t test results NOT assuming equal variances.
C. The researchers should reject the null hypothesis and report there is a difference in the average skin irritation score.
D. The researchers should fail to reject the null hypothesis and conclude there is NOT a difference in the average skin irritation score.
Answer:
Blablabka
Step-by-step explanation:
Blablabla
Solve the word problems. The price of a bed was $2600. MDM Yap bought the bed and had to pay an additional 7% GST. (a) What was the amount of GST she had to pay? (b) What was the price of the bed including GST?
Answer:
Step-by-step explanation:
I have know idea how to do this problem and teach my child
k(t)=13t-2
Answer:
K(t)=37
Step-by-step explanation:
k(t) = 13t - 2
k(3) = 13(3) - 2
k(3) = 39 - 2
k(3) = 37 <===
If Logx (1 / 8) = - 3 / 2, then x is equal to what?
Answer:
Logx(1/8) = -3/2
x = 4
Answered by GAUTHMATH
Use the distributive property to find the product of the rational number.
5/2 (- 8/5 + 7/5)
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Answer:
-1/2
Step-by-step explanation:
The factor outside parentheses multiplies each term inside.
5/2(-8/5 +7/5)
= (5/2)(-8/5) +(5/2)(7/5)
= -8/2 +7/2 = -1/2
Sharla invests $275 in a simple interest bearing account for 16 years. The annual interest rate is 8%. Using the simple
interest formula, / -Prt, how much interest will Sharla's initial investment earn over the 16 year period?
$297
$319
$352
$627
Answer:
352
Step-by-step explanation:
I = PRT where P is the principle, I is the interest rate, T is the time
I = 275 ( .08) ( 16)
I = 352
Determine the degree of the term 2^3x2yz4
Answer:
7
Step-by-step explanation:
It looks like the term is [tex]2^3}x^2}yz^4[/tex]
First simplify
[tex]8x^2}yz^4[/tex]
[y has an exponent of 1 btw]
Then to find the degree of a term, just add up the values of all the exponents
2+1+4=7
I hope this helps!
Give a vector parametric equation for the line through the point (−2,−4,0) that is parallel to the line ⟨−2−3t,1−4t,−5t⟩:
The tangent vector for the given line is
T(t) = d/dt ⟨-2 - 3t, 1 - 4t, -5t⟩ = ⟨-3, -4, -5⟩
On its own, this vector points to a single point in space, (-3, -4, -5).
Multiply this vector by some scalar t to get a whole set of vectors, essentially stretching or contracting the vector ⟨-3, -4, -5⟩. This set is a line through the origin.
Now translate this set of vectors by adding to it the vector ⟨-2, -4, 0⟩, which correspond to the given point.
Then the equation for this new line is simply
L(t) = ⟨-3, -4, -5⟩t + ⟨-2, -4, 0⟩ = ⟨-2 - 3t, -4 - 4t, -5t⟩
The vector parametric equation for the line through the point is [tex]r = (-2, \ -4, \ 0) +(-3, \ -4, \ -5)t\\\\[/tex].
GivenGive a vector parametric equation for the line through the point (−2,−4,0) that is parallel to the line ⟨−2−3t,1−4t,−5t⟩.
What is a parametric equation vector?Parametric equations of the line segment are defined by its endpoints.
To find the vector equation of the line segment, we’ll convert its endpoints to their vector equivalents.
Two lines are parallel if they have the same direction, and in the parametric form, the direction of a line is always the vector of constants that multiply t (or the parameter).
The vector equation of a line is given by:
[tex]\rm v = r_0+tv[/tex]
Where v is the direction vector and [tex]\rm r_0[/tex] is a point of the line.
The tangent vector for the given line is
T(t) = d/dt ⟨-2 - 3t, 1 - 4t, -5t⟩ = ⟨-3, -4, -5⟩
Here,
[tex]\rm r_0 = (-2,-4,0) \ and \ v=(-3, \ -4, \ -5)t\\\\[/tex]
Then,
[tex]r = (-2, \ -4, \ 0) +(-3, \ -4, \ -5)t\\\\[/tex]
x = -2-3t, y = -4-4t, and z = 0-5t
To know more about the Parametric equation click the link given below.
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What type of function is represented by the following table?
Number of weeks
1 2 3 4 5
Cost of rental car 79,
158,
237,
316,
395
Answer:
Linear
Step-by-step explanation:
cost = 79 * weeks
79*1=79
79*2=158
etc.
At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute. The resulting data were grouped by month of birth: January, May, and September:
Answer:
Babies learn to crawl between age of 6 to 10 months.
Step-by-step explanation:
It may take longer for babies to crawl in winter season since the climate restricts the babies movement due to extra clothes. The babies who are born in summer will learn crawling earlier than those who are born in winter season.
[tex]\sqrt{25}[/tex]=?
[tex]Hello[/tex] [tex]There[/tex]
The answer is...
[tex]5.[/tex]
[tex]HopeThisHelps!![/tex]
[tex]AnimeVines[/tex]
A local rectangular shaped pool used by lap swimmers has dimensions 25 yd by 30 yd and is 5.1 feet deep. Find the cost for filling the pool if the city charges $1.50 per 1000 gallons. Use the conversion 1 gallon
Answer:
the cost of filling the pool is $386.3
Step-by-step explanation:
Given;
dimension of the rectangular pool, = 25 yd by 30 yd by 5.1 ft
covert the given dimensions to feet;
1 yd = 3 ft
25 yd = 25 x 3 ft = 75 ft
30 yd = 30 x 3 ft = 90 ft
The volume of the rectangular pool in cubic feet (ft³);
Volume = 75 ft x 90 ft x 5.1 ft
Volume = 34,425 ft³
Convert the volume to gallons;
1 ft³ = 7.481 gallons
10,125 ft³ = 34,425 x 7.481 gallons
= 257,533.425 gallons
The cost per a 1000 gallons is $1.50, then cost of the 257,533.425 gallons is calculated as;
[tex]cost = \frac{\$ 1.50}{1000 \ gallons} \times 257,533.425 \ gallons = \$ 386.3[/tex]
Therefore, the cost of filling the pool is $386.3
Find the missing side of the triangle
Answer:
x = 2[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Pytago:
[tex]2^2 + 4^2 = x^2\\x = \sqrt{2^2 + 4^2} \\x = 2\sqrt{5}[/tex]
Answer:
4.47
Step-by-step explanation:
x²= 2² + 4²
x² = 4 + 16
x²= 20
x = √20
x= 4.47
Suppose a professional baseball player hit 55 home runs his first season, 58 his second,
and 69 his third. How many home runs would he need to hit in the current season so that
his average for the 4 years is no less than 59?
Answer:
About 54
Step-by-step explanation:
To work backwards from average, you need to multiply the average by the total number of cases, which is 4, since there are 3 current cases/seasons and you want the 4th.
59 * 4 = 236
You then subtract the total home runs that you know of from 236.
236 - 55 - 58 - 69 = 54
To find average, you are adding to the total and then dividing by the number of groups, which is essentially mean (mean is basically the average).
2. What amount of money must Kurt Blixen invest at 4.75% to have it earn $10,000 in 90 days?
Kurt Blixen must invest $85,2296.94.
Given the following data;
Interest rate = 4.75%Simple interest = $10,000Time = 90 daysTo find how much money Kurt Blixen must invest;
Mathematically, simple interest is given by the formula;
[tex]S.I = \frac{PRT}{100}[/tex]
Where:
S.I is the simple interest.P is the principal amount.R is the interest rate.T is the time measured in years.First of all, we would convert the time in days to years.
Conversion:
365 days = 1 year
90 days = x year
Cross-multiplying, we have;
[tex]365 * x = 90\\\\x = \frac{90}{365}[/tex]
x = 0.247 year
Making P the subject of formula;
[tex]P = \frac{S.I(100)}{RT}[/tex]
Substituting the values into the formula, we have;
[tex]P = \frac{10000(100)}{4.75*0.247}\\\\P = \frac{1000000}{1.1733}[/tex]
P = $85,2296.94
Therefore, Kurt Blixen must invest $85,2296.94.
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Mary spent $4 more than 1/8 of her original amount of money on a bag. She then
Spent $12 more than 2/3 of her remaining money on groceries.Given that Mary had $24 left,how much did the bag cost?
Answer:
464 $
Step-by-step explanation:
Please answer ASAP!!!!
Answer:
0
Step-by-step explanation:
0
HELP I NEED TO FIND THE COORDINATES OF THE POINTS
Answer:
The coordinate of any given point can be written as (x, y), where x is the x coordinate, and y is the y coordinate.
For example, point A has an x coordinate (horizontal) of 5, and a y coordinate (vertical) of 6. So the ordered pair is (5, 6).
Similarly, for the rest we have:
B: (-5,5)
C: (-2,3)
D: (-2,-2)
E: (3,-4)
F: (3,-6)
How many numbers multiple of 3 are in the range [2,2000]?
Answer: so there are 666 multiples of 3 between 2 and 2000.
Step-by-step explanation:
the smallest number = 3 which is 3*1. The largest number is = 1998 = 3*666
multiples of 3 between {2,2000} = 666-1+1 = 666
