The equation of the circle with endpoints of a diameter at the points (3, 8) and (-5, 6) is x² + y² + 2x - 14y + 33 = 0.
How to determine the equation of a circleThese are the specified parameters:
Endpoints of a diameter at the points (3, 8) and (-5, 6).
Determine the center point of the circle (a, b).
(a, b) = ((x₁ + x₂)/2 , (y₁ + y₂)/2)
= ((3 + (-5))/2 , (8 + 6)/2)
= (-2/2 , 14/2)
= (-1, 7)
The center point is (-1, 7).
Determine the radius of the circle (r).
[tex]\begin{aligned} r & = \frac{1}{2} \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\r & = \frac{1}{2} \sqrt{(-5-3)^2 + (6-8)^2} \\ r& = \frac{1}{2} \sqrt{(-8)^2 + (-2)^2} \\ r& = \frac{1}{2} \sqrt{64 + 4} \\ r & = \frac{1}{2} \sqrt{68} \end{aligned}[/tex]
Determine of the equation of the circle
(x - a)² + (y - b)² = r²
(x - (-1))² + (y - 7)² = (1/2 √68)²
x² + 2x + 1 + y² - 14y + 49 = 1/4 × 68
x² + y² + 2x - 14y + 50 = 17
x² + y² + 2x - 14y + 50 - 17 = 0
x² + y² + 2x - 14y + 33 = 0
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evaluate the summation for the indicated value of the variable. 1(1!) 2(2!) 3(3!) 4(4!) m(m!); m
The sum of the indicated variable is 23.
What is variable?
A variable is an alphabet or term that represents an unknown variety or unknown worth or unknown amount. The variables are specially employed in the case of pure mathematics expression or pure mathematics.
MAIN body:
the correct expression is as follows :
1(1!) +2(2!) +3(3!)+ 4(4!) ........+ m(m!) where m = 3
for m= 3
the expression becomes:
=1(1!) +2(2!) +3(3!)
factorial means we need to multiply the number until it reaches 1.
= 1*1 + 2*2*1 + 3*3*2*1
= 1+ 4+ 18
= 23
Hence the sum of expression is 23.
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What number for C would make the equation below a perfect square trinomial.
x^2 +22x+c
(A)121
(B)72
(C)81
(D)96
The expression x^2 + 22x + c becomes a perfect square trinomial if the value of c is 121, so the correct option is A.
What value of C makes the expression a perfect square trinomial?A perfect square trinomial is written as:
(a + b)^2 = a^2 + 2ab + b^2
Here we have the expression:
x^2 + 22x + c
We can rewrite the second term in such a way that we get:
x^2 + 2*11*x + c
comparing this with the form of the general perfect square trinomial we can see that:
a = x
b = 11
Then the value of c must be 11^2 = 121
Then we have:
x^2 + 2*11*x + 121 = (x + 11)^2
The correct option is A.
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An equation in slop intercept form the y intercept -5 the slope -1/2
Answer:
y=-1/2x-5
Step-by-step explanation:
ab³ (5a²-4ab+b²) multiply
Answer: The correct answer is 5a^3b^3 − 4a^2b^4 + ab^5
Step-by-step explanation:
ab^3 (5a^2 − 4ab + b^2)
Multiply together:
(ab^3)*(5a^2 + −4ab + b^2)
(ab^3)*(5a^2) + (ab^3)*(−4ab) + (ab^3)*(b^2)
= 5a^3b^3 − 4a^2b^4 + ab^5
Answer:
[tex]5a^3b^3-4a^2b^4+ab^5[/tex]
Step-by-step explanation:
Given expression:
[tex]ab^3(5a^2-4ab+b^2)[/tex]
Apply the distributive property a(b - c + d) = ab - ac + ad :
[tex]\implies ab^3 \cdot5 a^2-ab^3 \cdot 4ab+ab^3 \cdot b^2[/tex]
Collect like terms:
[tex]\implies 5aa^2b^3-4aabb^3+ab^2b^3[/tex]
Apply the exponent rule a = a¹ :
[tex]\implies 5a^1a^2b^3-4a^1a^1b^1b^3+a^1b^2b^3[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies 5a^{(1+2)}b^3-4a^{(1+1)}b^{(1+3)}+a^1b^{(2+3)}[/tex]
Simplify:
[tex]\implies 5a^3b^3-4a^2b^4+ab^5[/tex]
Anyone know this? Kind of struggling.
Answer:
It's -5 + 3 basicaly because 2 negatives is one positive. So the answer is -2.
Write an equation of a line in slope intercept form with a slope of 3/2 that passes through point (4,7).
Answer:
y
=
−
3
2
x
+
13
Explanation:
First write it using point-slope form:
y
−
7
=
−
3
2
(
x
−
4
)
Now simplify to slope-intercept:
Add 7 to each side:
y
=
−
3
2
(
x
−
4
)
+
7
Distribute
−
3
2
to each term in the parentheses:
y
=
−
3
2
x
+
6
+
7
y
=
−
3
2
x
+
13
hope I helped you:)
Can someone help me with this
Answer:
Step-by-step explanation:
What are you supposed to do?
the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km. what is the difference between these distances?
HELPPPPPPPPPPPP ASAP!!!!
The difference between these distances on the Earth is 3.32 × 10⁴.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.
Given that the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km.
The difference will be:
= 4.00x10^4 km - 6.8x10^3 km.
= 3.32 × 10⁴
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suppose you are testing to see if there is a difference in population mean lifetime of two brands (1,2) of batteries. random samples of batteries are taken for each brand and the following data are recorded: sample 1: n1
The test statistic of two brands of batteries is -2.177.
How to calculate test statistic?[tex]n_1[/tex] = size of sample 1 = 16
[tex]n_2[/tex] = size of sample 2 = 21
[tex]\bar{x_1}[/tex] = mean of sample 1 = 210
[tex]\bar{x_2}[/tex] = mean of sample 2 = 225
[tex]\sigma_{1}[/tex] = standard deviation of sample 1 = 20
[tex]\sigma_{2}[/tex] = standard deviation of sample 2 = 23
T test is test for statistical hypothesis that follows t-distribution table under null hypothesis. T test is used when test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. So, for this case we use t test for test statistic,
t = [tex]\frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}}[/tex]
t = [tex]\frac{210-225}{\sqrt{\frac{20^2}{16}+\frac{23^2}{21}}}[/tex]
t = [tex]\frac{-15}{\sqrt{\frac{400}{16}+\frac{529}{21}}}[/tex]
t = -15 / 7.0845
t = -2.117
Thus, the two brands of batteries have test statistic result is -2.117
Your question is incomplete, but most probably your full question was
Suppose you are testing to see if there is a difference in population mean lifetime of two brands (1,2) of batteries. Random samples of batteries are taken for each brand and the following data are recorded:
Sample 1: n1= 16, X1 = 210, s1= 20
Sample 2: n2= 21, X2 = 225, s2= 23
What is the test statistic assuming unequal population standard deviations?
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Colorful wool is being woven into a scarf in cold, damp Ireland. Wool is used for scarves, sweaters, hats, and gloves because it is a good insulator. If wool is a good insulator, what substance would be a good conductor?
A plastic
B fur
C cotton
D metal
4. Identify each of the following polygons:
Answer:
Step-by-step explanation:
1. Square
2. Rhombus
3. Trapezoid
4. Diamond
5. Octogon
6. Triangle
7. Pentagon
8. Hexagon
9. Triangle?
A baker makes a cake that requires 44 ounces of ingredients. The ratio of flour to sugar is 6:5. She didn’t like how the cake tasted so for the new cake, she changed the flour to sugar ratio to 7:6. If the amount of ounces she used increased to 91, how many more ounces of sugar did she add to the new cake? ( BE FAST PLEASE)
The amount of ounces of sugar she added to the new cake is 22 ounces
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the total ounces of ingredients in the cake be = 44 ounces
The ratio of flour to sugar is = 6 : 5
So , the amount of flour in 44 ounces = 6x
The amount of sugar in 44 ounces = 5x
And , the equation is
6x + 5x = 44
On simplifying the equation , we get
11x = 44
Divide by 11 on both sides , we get
x = 4
So , the total amount of sugar in 44 ounces of ingredients = 5x
Substitute the value for x = 4 , we get
Total amount of sugar in 44 ounces of ingredients = 20 ounces
And ,
Let the total ounces of ingredients in the new cake be = 91 ounces
The ratio of flour to sugar is = 7 : 6
So , the amount of flour in 91 ounces = 7y
The amount of sugar in 91 ounces = 6y
And , the equation is
7y + 6y = 91
On simplifying the equation , we get
13y = 91
Divide by 13 on both sides , we get
y = 7
So , the total amount of sugar in 91 ounces of ingredients = 6y
Substitute the value for y = 7 , we get
Total amount of sugar in 91 ounces of ingredients = 42 ounces
Therefore , the extra ounces of sugar the baker added to the new cake is =
Total amount of sugar in 91 ounces of ingredients - Total amount of sugar in 44 ounces of ingredients
The extra ounces of sugar the baker added to the new cake is = 42 - 20
Extra ounces of sugar the baker added to the new cake is = 22 ounces
Hence ,
The amount of ounces of sugar she added to the new cake is 22 ounces
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if the original recipe calls for 50 portions, 6oz each and the new recipe calls for 100 portions at 5oz each, what is the recipe conversion factor?
By using multiplication and division of integers, it can be calculated that
Conversion factor of the recipe = [tex]\frac{500}{300}[/tex] = 1.6
What is multiplication and division of integers?
At first it is important to know about integers
Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.
Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a word problem where multiplication and division of integers is required
The original recipe calls for 50 portions, 6oz each
Required yield of the original recipe = 50 [tex]\times[/tex] 6 = 300 oz
The new recipe calls for 100 portions at 5oz each
Required yield of the new recipe = 100 [tex]\times[/tex] 5 = 500 oz
Conversion factor of the recipe = [tex]\frac{500}{300}[/tex] = 1.6
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Nancy i making acceorie for the occer team. She ue 566. 28 inche of fabric on headband for 36 player and 3 coache. She alo ue 306. 36 inche of fabric on writband for jut the player. How much fabric wa ued on a headband and writband for each player?
Using some mathematical operations, we know that each player's headband and wristband are made from 16.18 inches of fabric and 8.63 inches of fabric.
What are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.
The quantity of operands affects the operation's arity.
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are collectively referred to as PEMDAS.
So, given that we've done it:
There are 35 players.
There are two coaches.
The cloth on the headbands measures 598.66 inches in length.
Just for the players, the wristbands include 302.05 inches of fabric.
Each player's headband's fabric length is specified by:
= Total inches/Total number of persons
= 598.66/37
= 16.18 inches
Each player's wristband's fabric length is specified by:
= Total inches/Number of persons
= 302.05/35
= 8.63 inches
Therefore, using some mathematical operations, we know that each player's headband and wristband are made from 16.18 inches of fabric and 8.63 inches of fabric.
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Complete question:
Nancy is making accessories for the soccer team. She uses 598.66 inches of fabric on headbands for 35 players and 2 coaches. She also uses 302.05 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
if a cup of diced cucumbers weighs 5.3 ounces, how many pounds of prepped cucumbers will you need for your 140 house salads?
46 pounds of prepped cucumbers are needed for 140 house salads.
It is given that one cup of diced cucumbers weighs 5.3 ounces.
Also, we know that one pound= 16 ounces or 1-ounce measure 1/16 pounds, we can do it in any way.
Thus, firstly, we will convert the ounces into pounds.
thus, 5.3 ounces= 5.3/16 pounds
Now, we need prepped cucumbers for 140 house salads, According to the given question.
thus, pounds needed for 140 house salads= 5.3/16*140
=> 46 pounds (nearly)
Thus, 140 house salads need nearly 46 pounds of cucumbers.
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A given triangle has vertices at (-3,1) (2,4) and (5,-3) . If the triangle were rotated 180 degrees counterclockwise, the new coordinates would be ?
The new coordinates when we rotate the triangle counterclockwise are (3, -1), (-2, -4), (-5, 3).
Define transformations.A function, f, that maps to itself are known as a transformation, or f: X → X. The transformation results in the pre-image X becoming the picture X. This transformation can utilize any operation, or a combination of operations, including translation, rotation, reflection, and dilation.
Given, the triangle vertices (-3, 1) (2, 4), and (5, -3).
When the triangle turned 180 degrees counterclockwise, we must determine the new coordinates;
When we rotate 180 degree counterclockwise, the plane changes not the point.
That is,
(-3, 1) becomes (3, -1)
(2, 4) becomes (-2, -4)
(5, -3) becomes (-5, 3)
Therefore, the new coordinates when we rotate the triangle counterclockwise are (3, -1), (-2, -4), (-5, 3).
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Victoria deposited $15,000 into a savings account that earns an annual simple interest rate of 0.2% to the nearest 10th of a year how long will it take for the account to reach 15,500
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
sus
It will take about 16.7 years to reach $15500.
What is the interest rate?The percentage that a lender adds to the amount of money lent to them is called an interest rate.
Given that, the initial deposited amount is P = $15000, the interest rate is r= 0.2% annually, and the final amount is $15500.
The interest earned is calculated by subtracting the initial amount from the final amount:
15500-15000
=500
Therefore, the interest earned is $500.
Now, the formula for the simple interest is:
interest = P × r × t
Substitute the known values:
500 = 15000 × 0.2% × t
500 = 15000 × 0.2/100 ×t
500 = 30t
t = 500/30
t = 16.7
Hence, It will take about 16.7 years to reach $15500.
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If the nth term of a number sequence is n^2 + 2n,
find the first 3 terms and the 10th term.
Answer:
3, 8, 15 and 120
Step-by-step explanation:
to find the first 3 terms, substitute n = 1, 2, 3 into the nth term rule
n = 1 : 1² + 2(1) = 1 + 2 = 3
n = 2 : 2² + 2(2) = 4 + 4 = 8
n = 3 : 3² + 2(3) = 9 + 6 = 15
the first 3 terms are 3, 8, 15
to find the 10th term , substitute n = 10 into the rule
n = 10 : 10² + 2(10) = 100 + 20 = 120
f(x) = 2x²+ 3x - 14.
Answer:
Step-by-step explanation:
domain = all real numbers
range = {-121/8,∞)x-intercepts (2,0)
y-intercepts (0,-14)
vertex = minimum (-3/1 - 121/8)
Answer: Okay so I got,
1) x intercept = (2, 0), (-7/2, 0) and y intercept (0, -14)
2) 'x' equals to..
-Exact Form: 2, -7/2
-Decimal Form: 2, -3.5
Hope this helps!
in a regression analysis, a(n) is used to predict a(n) . a. ordinal variable, ratio variable b. independent variable, dependent variable c. nominal variable, independent variable d. response variable, explanatory variable
In a regression analysis, a(n) is used to predict a(n) is known as option (b).independent variable, dependent variable.
Regression analysis:
In the concept of statistics, the regression analysis is useful to come up with a predictive model consisting of dependent and independent variables. And the R-squared value for a regression equation indicates the percentage of variability in the dependent variable being expressed by the variability in the independent variables.
Given,
Here we need to find the type of variable for a regression analysis, a(n) is used to predict a(n).
As per the definition of regression analysis, in the given question, we have two variable there are
=> a(n)
After prediction, the predicted value of a(n).
Here the first one is the independent variable because the this value is the based to predict the value of the other one is the dependent variable.
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Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve.
If y = 21 when x = 14, find y when x = 40 .
ur answer should have ,60
Answer:
see explanation
Step-by-step explanation:
given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 21 when x = 14 , then
21 = 14k ( divide both sides by 14 )
[tex]\frac{21}{14}[/tex] = k , that is
k = [tex]\frac{3}{2}[/tex] = 1.5
y = 1.5x ← equation of variation
when x = 40 , then
y = 1.5 × 40 = 60
6(x−2)=−18
due today
Answer: -1
Step-by-step explanation: 6x-12=-18
+12= +12
------------------
-6/6=-1
If line segment AB represents 50%, what is the length of a line segment that is 100%?
Answer:
it would be CD or 50%
Step-by-step explanation:
write the expression as a sum and/or difference of logarithms. express exponents as factors.log5 a3 b
Expression of logarithms is log₅a³b = 3log₅a + log₅b.
Given expression is log₅a³b.
We have to express given expression as a sum or difference of logarithms.
We know the logarithmic formulas which is,
logₐ(PQ) = logₐP + logₐQ
logₐ([tex]P^{Q}[/tex]) = QlogₐP
we will use above formulas and solve the given equation.
log₅a³b = log₅a³ + log₅b
log₅a³b = 3log₅a + log₅b
Logarithms, like exponents, have many helpful properties that can be used to simplify logarithmic expressions ans solve logarithmic equation.
The product property states that to miltiply two powers that have the same base, add the exponents.
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(2+8) + 10 ^2 +60 divided 10
Answer: 17
Step-by-step explanation:
Answer:
Step-by-step explanation:
116
josh was preparing a speech about home real estate and wanted to give an idea how home prices had fallen in all seven recognized neighborhoods in his city. he found that the rounded percentage decreases were 3, 3, 5, 6, 7, 7, and 19. why would using the mean, or average, decrease be misleading?
The mean of the decrease in rounded percentage of home is 7.14 which would used as misleading the about data as raw data very far away from 7.14.
As given in the question,
Given rounded percentage decrease in home price is:
3, 3, 5, 6, 7, 7, 19
Mean of the rounded percentage
= ( Sum of all the values)/ (Number of values)
= ( 3 + 3 + 5 + 6 + 7 + 7 + 19) / 7
= 50 /7
=7.1428
= 7.14
7.14 is very far away from 3 and 19.
Mean is not representing the correct information of the home price.
Using mean is misleading the correct information about percentage decrease.
Therefore, value of the mean is equal to 7.14 which mislead the decrease percentage.
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Use the grid to help you fill in the blank.
0.9 × ___ = 0.27
Answer:
0.3
Step-by-step explanation:
0.9 times 0.3 equals 0.27
if you can notice the difference between 10- and 11-pound weights, which of the following weights could you differentiate from a 100-pound weight?
If we can notice the difference between 10- and 11-pound weight, we can differentiate 110-pound weight from a 100-pound weight.
What is weight?All things close to Earth are constantly subject to the force known as weight. All items are pulled downward toward the Earth's core by the gravity of the planet. On the other hand, weight is a measurement of how much gravity pulls an item downward. The mass of the thing has an impact on this force; the heavier the object, the stronger gravity's pull is. The force of gravity acting on a body is the most typical definition of weight given in introductory physics textbooks. This is sometimes formulated as W = mg, where W is the weight, m is the object's mass, and g is the acceleration due to gravity.
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One angle of a triangle measures 75°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?
well, since a triangle has a total of 180° interior angles, that means 180 - 75 = 105 is leftover for the other two remaining angles.
now, they're in a 2 : 5 ratio, well, let's simply divide 105° by (2 + 5) and distribute accordingly.
[tex]2~~ : ~~5\implies 2\cdot \frac{105}{2+5}~~ : ~~5\cdot \frac{105}{2+5}\implies 2\cdot 15~~ : ~~5\cdot 15\implies \text{\LARGE 30~~ : ~~75 }[/tex]
a shipment of 15 televisions contains 6 regular and 9 deluxe models. the manufacturer failed to mark the model designation on the cartons. if 3 cartons are selected at random, what is the probability that exactly 2 of them are the deluxe model? (round your answer to three decimal places.)
The probability that exactly 2 of them are the deluxe model =0.474
given that
there is a shipment of 15 televisions contains 6 regular and 9 deluxe models
now 3 cartons are selected at random
C(15,3) =[tex]\frac{15!}{(15-3)!3!}[/tex]
C(15,3) = [tex]\frac{13*14*15}{3*2*1}[/tex]
C(15,3) = 455
2 out of 9 deluxe models be picked
C(9,2) = [tex]\frac{9!}{(9-2)!2!}[/tex]
C(9,2) = [tex]\frac{8*9}{2*1}[/tex]
C(9,2) = 36
Each of these can be matched with 1 of 6 regular models
36 × 6 = 216
the probability that exactly 2 of them are the deluxe model
= [tex]\frac{216}{455}[/tex]
=0.474
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