Answer:
Step-by-step explanation:
Equation of circle is, (x-h)^2+ (y-k)^2=r .......(eqn1)
where, (h,k) is the center and r is the radius.
therefore, from the question by rearranging the equation,
x² + y² + 4x − 6y + 12=0
viz, (x² +4x+4) + (y²-6y+9)-1=0
(x+2)^2 + (y-3)^2=1
therefore from eqn1, (-2,3) is the center and radius is 1
For how many values of x is h(x) = 0? Justify you answer.
Answer:
the answer for x when h(x) is 2.9
Please help 25 points
The angles that are congruent are as follows:
∠EBF and ∠GBH∠DEA and ∠BEC∠FBG and ∠HBE∠AEB and ∠CEDWhat are vertical angles?Vertical angles are angles that are opposite of each other when two lines cross. In other words, vertical angles are formed when two lines meet each other at a point.
Vertically opposite angles are congruent.
Therefore, let's find the angles that are congruent in the diagram.
When lines intersect angle relationship such as vertically opposite angles are formed.
Therefore, the following angles are congruent because they are vertically opposite angles.
∠EBF and ∠GBH are congruent. ∠DEA and ∠BEC are congruent. ∠FBG and ∠HBE are congruent. ∠AEB and ∠CED are congruent.learn more on vertical angles here: https://brainly.com/question/24460838
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ASAP
10 yellow, 6 green, 9 orange, and 5 red cards facedown. Once a card selected, NOT replaced.
a. P(two cards that are not orange)
b. P(two cards that are neither red nor green)
The probability of selecting two cards that are not orange, is 0.483 and the probability of selecting two cards that are not red and green, is 0.393.
In the given question we have to find the probability.
From the question it is given that,
10 yellow, 6 green, 9 orange, and 5 red cards facedown.
Total number of cards = 10+6+9+5
Total number of cards = 30
Once a card selected, NOT replaced.
a.) Now finding the probability of selecting two cards that are not orange.
There are total orange cards = 9
The number of cards except orange card = 21
Then the probability of selecting one card except orange = 21/30
Then the probability of selecting other card except orange = 20/29
Then the probability of selecting two cards that are not orange is
P(O) = 21/30 * 20/29
P(O) = 420/870
P(O) = 0.483
Then the probability of selecting two cards that are not orange, is 0.483.
(b) Now finding the probability of selecting two cards that are neither red nor green.
The total number of cards except red and green card = 19
Then the probability of selecting one card except red and green card = 19/30
Then the probability of selecting other card except red and green card = 18/29
Then the probability of selecting two cards that are not red and green card is
P(RG) = 19/30 * 18/29
P(RG) = 342/870
P(RG) = 0.393
Then the probability of selecting two cards that are not red and green, is 0.393.
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The equation a = 12850 + 530h gives a hiker's altitude a (in feet), h hours after beginning his hike.
A. At what rate, in feet per hour, is the hiker gaining altitude?
The rate of gaining altitude for the hiker is 530 feet per hour.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as g'(x) = (g(x + h) - g(x)) /(x + h - x).
Its geometric aspect is the slope of the function at a given point.
The given equation for hiker's altitude is as below,
a = 12850 + 530h
Here a is the altitude in feet and h is time in hours.
In order to find the rate of gaining altitude, the equation for altitude has to be differentiated with respect to hours as below,
a = 12850 + 530h
Differentiate the above equation w.r.t h as,
da/dh = 0 + 530
= 530
Hence, the rate of gaining altitude is 530 feet per hour.
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Evaluate the expression when a=5 and b=1/2: 13/2 - 7/2 -b( 2/3) + 4/8 - ab
How would you investigate the complaints from renters who are
unhappy about their monthly rents?
What statistical measurement would be used?
To investigate the complaints from renters who are unhappy about their monthly rents, the mean rents can be collected
The statistical measurement that would be used is the ANOVA.
What is a mean?A dataset's mean (also known as the arithmetic mean, as opposed to the geometric mean) is the sum of all values divided by the total number of values. It is the most widely used measure of central tendency and is frequently referred to as the "average."
ANOVA is an abbreviation for Analysis of Variance. It is a statistical test invented by Ronald Fisher in 1918 that has been in use ever since. Simply said, ANOVA determines whether or not there are statistical differences between the means of three or more independent groups. The most basic type is one-way ANOVA. To know of the meansare the same, the ANOVA can be used.
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There are 121 boys and 116 girls signed up for a trip to an amusement park. The leader first makes groups of 9 students each and then assigns any remaining students to make some of the groups have 10 students. Part A How many groups of 10 students will there be? Explain. Part B How many groups of 9 students will there be? Explain.
The remainder is the amount "leftover" after performing some computation.
Hence,
(A) There are [tex]4[/tex] groups out of [tex]10[/tex] students.
(B) There are [tex]33[/tex] groups of [tex]9[/tex] students.
What is a remainder?
The remainder is the amount "leftover" after performing some computation. In arithmetic, the remainder is the integer "leftover" after dividing one integer by another to produce an integer quotient.
Here given that,
The strength of boys is [tex]121[/tex]
The strength of girls is [tex]116[/tex]
So, the total number of students are
[tex]121+116=337[/tex]
The leader first makes groups of [tex]9[/tex] students and then assigns any remaining students to make some of the groups have [tex]10[/tex] students.
So we divide by [tex]9[/tex] to find out the remainder and the total number of groups are:-
[tex]\frac{337}{9}=37[/tex]
and the remainder value is [tex]4[/tex].
Therefore, there are [tex]37[/tex] groups in the total out of which [tex]4[/tex] are out of [tex]10[/tex]students.
So,
[tex]\frac{37}{4}=33[/tex] groups are of [tex]9[/tex] students.
Hence,
(A) There are [tex]4[/tex] groups out of [tex]10[/tex] students.
(B) There are [tex]33[/tex] groups of [tex]9[/tex] students.
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Z-Grand Shipping Company manufactures boxes in the shape of a cube.
The formula for the surface area of a cube is 6s, where s is the length of one side.
Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is
square feet
The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is
square feet
The surface area of the large box is times larger than the small box.
Please Help?
Answer:
Z-Grand Shipping Company manufactures boxes in the shape of a cube.
The formula for the surface area of a cube is 6s, where s is the length of one side.
Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is 216
square feet
The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is 54
square feet
The surface area of the large box is 4 times larger than the small box.
{So for the first line which is The surface area of each large box is
square feet.}
Ans;216
{The second line which is The surface area of each small box is
square feet.]
Ans;54
{The Third line which is The surface area of the large box is times larger than the small box.}
Ans;4
Thank you So much Hope this helps you! Please Mark Brainleast looking forward to help everyone ty!
Answer:
Z-Grand Shipping Company manufactures boxes in the shape of a cube.
The formula for the surface area of a cube is 6s, where s is the length of one side.
Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is 216
square feet
The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is 54
square feet
The surface area of the large box is 4 times larger than the small box.
{So for the first line which is The surface area of each large box is
square feet.}
Ans;216
{The second line which is The surface area of each small box is
square feet.]
Ans;54
{The Third line which is The surface area of the large box is times larger than the small box.}
Ans;4
Two student groups went to an amusement park on the same day. Group 1 bought 9 tickets and received a $120 discount. Group 2 bought 3 tickets and received a $30 discount. Both groups spent the same total amount of money on tickets. The price of each ticket was the same. What was the cost of each ticket?
The cost of each ticket of the amusement park is $15.
What is the system of equation?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
Two student groups went to an amusement park on the same day.
Group 1 bought 9 tickets and received a $120 discount.
Group 2 bought 3 tickets and received a $30 discount.
Let x be the amount of one ticket and y be the total amount.
According to the question:
We have system of equation,
y = 9x - 120 equation1
y = 3x - 30 equation 2
Subtract the equation 2 to equation 1.
So, 6x = 90
x = 15
Therefore, $15 is the cost of each ticket.
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what are her monthly payments
The interest she is pay total is $2340.822 when Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.
Given that,
For the purpose of buying new equipment for her business of antique restoration, Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.
We have to find will she pay interest at all.
We know that,
i=p×r×t
Here,
i is interest.
p is principal amount.
r is rate of interest
t is time.
So, p is $6490
r is 7.26%
t is 5 years
So,
i= 6490×0.0726×5
i= $2355.87
Therefore, the interest she is pay total is $2355.87 when Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.
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10. Brock bought a bicycle that cost $40.00 when it was new. If he eventually sold it for 10%
of the original cost, how much was it sold for?
Answer:IT WOULD BE 60.00
Step-by-step explanation:
BC 40 = 60
A candidate for mayor in a small town has allocated $40,000 for last-minute advertising in the days preceding the election. Two types of ads will be used: radio and television. Each radio ad costs $200 and reaches an estimated 3,000 people. Each television ad costs $500 and reaches an estimated 7,000 people. In planning the advertising campaign, the campaign manager would like to reach as many people as possible, but she has stipulated that at least 10 ads of each type must be used. Also, the number of radio ads must be at least as great as the number of television ads. How many ads of each type should be used? How many people will this reach?
To maximize the $40,000 allocated to reach the most people, using linear programming, 10 TV ads and 175 radio ads should be used
The number of people reached is 595,000
What is linear programming?Linear programming is a method of maximizing a straight-line or linear function that consists of two or more variables such as the cost and the number of people reached.
Let R represent the number of radio ads and let T represent the number of television ads.
The constraints are;
200·R + 500·T ≤ 40,000
R ≥ 10
T ≥ 10
The maximum value function is 7,000·T + 3,000·R
R ≥ T
R - T ≥ 0
R ≥ T
The equations are therefore;
200·R ≤ 40,000 - 500·T
R ≤ (40,000 - 500·T)/200 = 200 - 2.5·T
R ≤ 200 - 2.5·T
When R = T, we have;
T = 200 - 2.5·T
3.5·T = 200
T = 200 ÷ 3.5 ≈ 57.14
The value of the maximizing function, 7,000·T + 3,000·R, at the vertices of the feasible region are therefore;
(T, R)
At (10, 10); 7,000 × 10 + 3,000 × 10 = 100,000
At (10, 175); 7,000 × 10 + 3,000 × 175 = 595000
At (57.14, 57.14); 7,000 × 57.14 + 3,000 × 57.14 = 571400
The number of adds of each type that will reach the maximum number of people is 10 television ads and 175 radio adsThe number of persons the ads reaches is 595,000Learn more about linear programming or linear optimization here:
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Given mn, find the value of x.
(2x+6) (x+9)"
Answer:
(2x+6) = (x+9) ; x = 3
Step-by-step explanation:
-x both sides ; 2x-x = x and -6 both sides which is x = 3
Considering the Matrix: Give the solution in terms of x. Show work.
1 0 -.05 I 2
0 1 2 I 1
0 0 0 I 0
The solution to the system of equations, in terms of x, considering the augmented matrix, is of:
y = -40x + 81.x = 20x - 40.Augmented matrix of system of equationsThe augmented matrix of a system of equations is built as follows:
Each of the columns before the | represents the coefficients of a variable.The column after the | represents the numeric value of the expression.In this problem, there are three columns before the |, the there are three variables given as follows:
x,y and z.
The expression from the first row is:
x -0.05z = 2.
The expression from the second row is:
y + 2z = 1.
The third row is all zero, meaning that there is a free variable, hence the solution to the system is written as a function of x as follows:
x - 0.05z = 2
0.05z = x - 2.
z = (x - 2)/0.05
z = 20x - 40.
Hence the solution for y is:
y = 1 - 2z
y = 1 - 40x + 80
y = -40x + 81.
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Find the values of x and y.
Answer:
y=60°, x=60°
Step-by-step explanation:
X=60° Angles in a Equaliteral triangles are all 60°
Alternate angle to get the base angle close to y
Y=60° because of Isoceless angles
Which of the following is NOT true about the body mass index? A. uses statistical data of weight and height across the population B. measures the percentage of one's body fat directly C. relies on a correlation between weight and body fat D. does not account for one's body frame size or muscle content Please select the best answer from the choices provided. A B C D Mark this and return
The statement that is not true about body mass index is B. measures the percentage of one's body fat directly
What is Body mass index?The Body Mass Index (BMI) calculates a person's weight in relation to their height. It is not a precise assessment of a person's total body fat, more of an indicative.
The majority of the time, total body fat and BMI are correlated.
The Body mass index (BMI) formula
= weight in kilograms / square of height in meters
BMI Categories values are classified below
Underweight ≤ 18.5
Normal weight = 18.5–24.9
Overweight = 25–29.9
Obesity = BMI of 30 or greater
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Answer:B
Step-by-step explanation:
The time is takes an object to move a certain distance is inversely propotional to the speed that it's travelling at.
it takes a car 12 minutes to travel the length of a road if it goes at an average speed of 60mph
a) How long would it take the car to travel down the same road if it travelled at an average speed of 30mph
B) if it takes the car 36 minutes to drive down the road, what will it's average speed
Answer:
a) 24 minutes
b) 20 mph
Step-by-step explanation:
Speed - distance -time:time= 12 min
[tex]\sf = \dfrac{12}{60} \ hour[/tex]
speed = 60 mph
[tex]\sf \boxed{distance =speed * time}[/tex]
[tex]\sf = 60 * \dfrac{12}{60}\\\\ = 12 \ m[/tex]
a) Speed = 30 mph
[tex]\sf \boxed{time = \dfrac{distance}{speed}}[/tex]
[tex]\sf = \dfrac{12}{30}\\\\ = \dfrac{2}{5} \ hour\\\\ = \dfrac{2}{5}*60\\\\= 2 * 12\\\\= 24 \ minutes[/tex]
It will take 24 minutes.
c) time = 36 minutes
[tex]\sf = \dfrac{36}{60} \hour[/tex]
[tex]\sf \boxed{speed= \dfrac{distance}{time}}[/tex]
[tex]\sf = \dfrac{12}{ \dfrac{36}{60}}\\\\\\ = 12* \dfrac{60}{36}\\\\= 20 \ mph[/tex]
Average speed = 20 mph
(PLEASE OPEN) Need help with triangle proofs.
The missing terms in the two column proof are;
Reason 1; Perpendicular bisector
Reason 2; Definition of perpendicular bisector
Statement 3; CO ≅ BO
Reason 3; Segment division
Reason 4; Reflexive Property of Congruence
Reason 5; Definition of Isosceles Triangle
Reason 6; AAS Congruency Postulate
How to carry out two column proof of triangles?From the given image, we want to use the two column proof to prove that ΔAOB ≅ ΔAOC
Now, we have the two column proof as follows;
Statement 1; AO ⊥ BC
Reason 1; Perpendicular bisector
Statement 2; ∠AOB and ∠AOC are right angles
Reason 2; Definition of perpendicular bisector
Statement 3; CO ≅ BO
Reason 3; Segment division
Statement 4; AO ≅ AO
Reason 4; Reflexive Property of Congruence
Statement 5; AB ≅ AC
Reason 5; Definition of Isosceles Triangle
Statement 6; ΔAOB ≅ ΔAOC
Reason 6; AAS Congruency Postulate
The final proof is AAS Congruency postulate because it has 2 congruent angles and the non-included congruent side.
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(42x³ + 16x² + 46x +42) ÷ (7x + 5)
응
a ski shop sells a pair of skis for $210. for a winter sale, the skis are 30% off. two weeks later, the shop has a clearence sale and sells the skis for 20% off the sale price. what is the clearence price of the skis
Answer: The skis cost $117.60.
Step-by-step explanation:
A pair of skis costing $210 is 30% off.
30% of $210 is $147
Then two weeks later, it will be 20% off THAT price.
20% of $147 is $117.60
Therefore, $117.60 is the clearence price of the skis. Hope this helps!
Identity the a, b, h and k values from the parent function, y = x^2
The values from the parent function are a = 1, b = -6, h = 3, and k = -4.
What is the vertex form of quadratic equations?
The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.
The given parent function is f(x) = (x - 3)² - 4.
comparing with the standard vertex form of the parabola, we get
a = 1, h = 3 and k = -4.
Now to find 'b', we have to simplify the given function in the form of f(x) = ax² + bx + c
f(x) = (x - 3)² - 4
f(x) = (x² - 6x + 9) - 4
f(x) = x² - 6x + 5
Comparing with f(x) = ax² + bx + c we get, c = -6.
Hence, The values from the parent function are a = 1, b = -6, h = 3, and k = -4.
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Janelys is going to invest in an account paying an interest rate of 5.9% compounded daily. How much would Janelys need to invest, to the nearest ten dollars, for the value of the account to reach $1,890 in 12 years?
The amount that should be invested to the nearest ten dollars is $930.
How much should be invested today?When an amount is compounded daily, it means that the investment increases in value everyday over the investment period.
In order to determine how much should be invested today, the present value of $1890 has to be determined.
The formula for determining the present value is:
PV = FV ÷ (1 + r)^nm
Where:
FV = future value of the investment r = daily interest rate = 5.9% / 365 = 0.01616%n = number of years m = number of compoundingPV = 1890 ÷ (1.00016)^(12 x 365) = 930
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Alyssa is signing up for a gym membership with a one-time fee to join and
then a monthly fee to remain a member. Let C represent the total cost of the
gym membership over t months. The table below has select values showing
the linear relationship between t and C. Determine the one-time joining fee.
Answer: $
t
2
4
9
C
200
250
375
Submit Answer
The one time joining fee found from the linear relationship between total cost and the number of months of membership is $250
What is a linear relationship?A linear relationship is a relationship between two variables that has a straight line when graphed.
The total cost of the gym membership = C
The number of months of membership = t
The table in the question is presented as follows;
t (Time in months) [tex]{}[/tex] C (Total cost)
2 [tex]{}[/tex] 200
4 [tex]{}[/tex] 250
9 [tex]{}[/tex] 375
The linear equation that represents the value in the table is found as follows;
Slope of the line, m = (375 - 250)/(9 - 4) = 25
The equation of the line in point and slope form is therefore;
(C - 375) = 25·(t - 9)
C = 25·(t - 9) + 375
C = 25·t - 225 + 375 = 25·t + 250
C = 25·t + 250
The joining fee is the amount paid at the start when t = 0, therefore;
Joining fee = 25 × 0 + 250 = 250
The one time joining fee is $250
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Write an equation of the parabola in vertex form.
Amusement Park Ride
Height (feet)
YA(0, 180)
(1, 164)
160
80
0 2 4
Time (seconds)
Equation:
Equation of parabola in vertex form is :
[tex](x-h)^{2} = 4a(y-k)[/tex]
[tex](x-0)^{2} = 4a(y-180)[/tex]
it passing through (1,164)
∴ [tex](1-0)^2=4a(164-180)[/tex]
[tex]1 = 4a(-16)[/tex]
⇒ [tex]-64a = 1[/tex]
⇒ [tex]a = -\frac{1}{64}[/tex]
∴ [tex](x-0)^2 = 4 \times \frac{1}{-64} (y-180)[/tex]
[tex]x^2 = -\frac{1}{16}(y-180)[/tex]
[tex]-16x^2 = y-180\\y = -16x^2+180\\[/tex]
Here, the equation of parabola in vertex form is:
[tex]y = -16(x^2)+180 ,\ for \ x\geq 0[/tex]
What is Parabola?
A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface.
What is cone?
A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the Centre of base) called the apex or vertex.
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Choose the figure that models 4 divided by 4/3
The required solution to the given expression is 3 which is determined by the division operation.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation.
To determine the evaluation of expression 4 ÷ 4/3
When considering multiplying the fractions together, After that, you would multiply the denominator across and the numerator across, respectively. Your final answer should be 12/4 However, if you simplify it by 4, your final answer will be 3.
Thus, the required solution to the given expression is 3.
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The following number is shown in expanded form:
1 1
4x1+8 x 100 + 9 × 1000
What is the decimal form of the number?
The decimal form of the number is :
9804.0
What is the decimal number?
Decimals are a form of a number in algebra that has a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal number is, for instance, 34.5.
If the question is,
4x1+8 x 100 + 9 × 1000, then simplify it first
4x1+8 x 100 + 9 × 1000=4+800+9000=9804
So, the decimal form is :
9804.0
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Evaluate 4x ÷ y if y = 2 and x = 4
Answer:
18
Step-by-step explanation:
x = 4
4x
= 4 * 4
= 16
y = 2
4x + y
= 16 + 2
= 18
mr colton needs 4.62 cups of flour to make 3 pound of dough.How many cups does she need to make 2 pounds of dough
The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10
Let the number of cups be represented by x.
This will be expressed as:
2/3 = x/4.62
Cross multiply
3x = 2 × 4.62
3x = 9.24
Divide
x = 9.24 / 3
x = 3.08
Therefore, 3.08 cups are needed.
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Answer:
The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.
Step-by-step explanation:
There are 12 red balls and 7 green balls in a
non-transparent black bag. What is the
least number of balls we need to take out to be certain we have taken out the
following?
two green or two red balls
The least number of balls we require to take out to be sure that we have two green or two red balls is 14.
What is the combination of balls?In the bag, there are a total number of balls of;
Total number of balls = 12 + 7 = 19 balls
Inside the bag, we have 12 red balls and 7 green balls.
The balls are selected without replacement, and this means that they are removed from the bag, and replaced back.
In theory, we could pick 12 balls, and all 12 being red, while also 13, with 12 red and 1 green e.t.c
Therefore, at least 14 balls are needed to guarantee that there are at least 2 green or two red balls
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attachment above please
