The equation in standard form for the circle will be;
⇒ (x + 2)² + (y - 9)² = 1
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The circle that has a diameter with endpoints (-2,10) and (-2,8).
Now,
Since, The circle that has a diameter with endpoints (-2,10) and (-2,8).
Hence, The radius of circle is the half of the distance between two points of the diameter.
So, Radius = 1/2 (√ (8 - 10)² + (- 2 - (-2))²
= 1/2 √4
= 1/2 × 2
= 1
Thus, Radius (r) of circle = 1
And, The center of circle is midpoint of the endpoints of the diameter.
Hence, Centre = (- 2 + (-2))/2, (10 + 8)/2
= - 4/2 , 18/2
= (- 2, 9)
Hence, The equation of circle with center (-2, 9) and radius 1 is;
⇒ (x - (-2))² + (y - 9) = 1²
⇒ (x + 2)² + (y - 9)² = 1
Thus, The equation in standard form for the circle will be;
⇒ (x + 2)² + (y - 9)² = 1
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In the United States, the common paper size is called letter size and measures 8. 5 by 11 inches. Let
V(x)= (8. 5-2x)(11-2x) (x) be the volume in cubic inches of a box made from a letter size paper
by cutting out squares of side length x in inches from each corner and then folding up the sides.
What is a reasonable domain for V in this context? Explain or show your reasoning.
PLs help
Answer:
0 < x < 4.5
Step-by-step explanation:
You want the reasonable domain of V(x) = (8.5 -2x)(11 -2x).
Reasonable domainThe equation describes volume (V) and cut length (x), so both need to be positive. Volume will be positive when ...
8.5 -2x > 0
4.25 > x
The reasonable domain is 0 < x < 4.5.
(2x^2 - 4x + 3) + (5x - 6x^2 - 1)
Answer:
The answer is (-4x² + x + 2)
Step-by-step explanation:
(2x² - 4x + 3) + (5x - 6x² - 1)
open the brackets
2x² - 4x + 3 + 5x - 6x² - 1
rearrange the priority order
2x² - 6x² - 4x + 5x + 3 - 1
combine like terms
-4x² + x + 2
Thus, The answer is (-4x² + x + 2)
Write the equation of the circle with a radius of 10 and a center at (3,-1)
Answer:
[tex]\textsf{b)} \quad (x-3)^2+(y+1)^2=100[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Given:
center = (3, -1)radius = 10Substitute the given center and radius into the formula to create the equation of a circle with the given parameters:
[tex]\implies (x-3)^2+(y-(-1))^2=10^2[/tex]
[tex]\implies (x-3)^2+(y+1)^2=100[/tex]
Graph the line that passes through the coordinates below and determine which statement is true.
A.
The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
B.
The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin.
C.
The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.
D.
The line that passes through the given coordinates represents a proportional relationship because the line passes
Answer:
The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
Does the picture represent a function?
Yes or No
Answer: Yes
Step-by-step explanation: To determine if this graph represents a function, we use what is called the vertical line test.
In other words, if we can draw a vertical or straight up and down line that passes through more than one point on the graph, the relation is not classified as a function.
In this case, it's impossible to draw such a line that hits more than one point on the graph so the relation is a function.
Write all classifications that apply to the real number −2.
A. natural number, terminating decimal
B. rational, integer, whole number
C. rational, integer, whole number, natural number, terminating decimal
D. terminating decimal, integer, rational
Answer: D
Step-by-step explanation:
-2 is not a repeating decimal.
It is not a fraction
And it is a rational number
Wendy spent 1/4of her paycheck on Monday and
3/7of it on Tuesday. She spent the rest of her
paycheck over the next 3 days. If Wendy spent $18 on each of the 3 days, what was the amount of
her paycheck
Answer:
$56.00
Step-by-step explanation:
Check:
1/4(56) + 3/7(56) + 18 =
14 + 24 + 18 = 56
See the picture below. I wanted to figure out what fraction of the paycheck was the 18.
I took 1 which is the whole pay check and subtracted out the fractions that I knew were spent 1/4 and 3/7. That left me with 9/28. So I knew 9/28 of the paycheck was 18 dollars. I drew out 28 squares. 9 of those squares was worth $18. That meant that each square was worth $2. 2 x 28 = 56
What is 8/15 simplyfied??
Answer:
8/15
Step-by-step explanation:
There is no GCF (greatest common factor) in this. These numbers are relatively prime.
Please check if ur able to help with these Segments OA and OB are radii ofthe semicircle above. Arc AB has length 3n and OA = 5. What is the value of x ?'
OA=5 and the length of arc AB is 3π. The x value is [tex]108[/tex]°.
The circle's radius and arc length are both provided. Finding the angle that the arc occupies on the center O is necessary.
The correct formula is
s=rФ
Where
arc length is measured in radians,
r is the radius, and
Ф is the angle (in radians)
If Ф is in degrees, we apply the formula.
s= Ф[tex]*\frac{\pi }{180} *r[/tex]
In order to determine the value of theta, we must enter the specified values of s and r into the formula above.
[tex]3\pi =[/tex]Ф[tex]*\frac{\pi }{180} *5[/tex]
[tex]3\pi *\frac{180}{\pi } *\frac{1}{5}=[/tex]Ф
Ф=[tex]108[/tex]°
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Marissa's mom purchased coffee from the local coffee shop. The first cup of coffee was $3.95. Each refill is $1.50. She also decided to get a bagel for $3.00. If Marissa's mom had 2 refills and a $0.50 discount as part of the rewards program, how much did she spend at the coffee shop?
$9.95
$9.45
$8.65
$7.95
Answer:
(b) $9.45
Step-by-step explanation:
You want to know how much Marissa's mom spent at the coffee shop for ...
1st cup of coffee: $3.952 refills: $1.50 each1 bagel: $3.00after her rewards program discount of $0.50 was applied.
TotalAdding up the bill, we find it to be ...
$3.95 + 2×1.50 +3.00 -0.50 = $9.45
Marissa's mom spent (b) $9.45 at the coffee shop.
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which choices if multiplied by 0.5 would result in a rational number answer?
If the integer begins through being rational, multiplying by 0.5 would not change whether or not something is rational. It will continue with rational numbers.
What is a rational number?In mathematics, a rational number is a number that can be written as the quotient or fraction p/q of two numbers, an integrand p and a non-zero denominator q.
For instance, −3/7 is a rational number, and so is every integer.
So, in that case, any even number would be 12 * 0.5 = 6.
The solution is reasonable because 12 began as rational (6).
Any odd number also is rational:
23 * 0.5 = 11.5
23 and 11.5: Both rational
1.818181818 is reasonable hence when multiplied by 0.5 the result will be rational 3.636363636.
Therefore, if we begin with an irrational number like π:
π*0.5: Not rational
Therefore, if the integer begins through being rational, multiplying by 0.5 would not change whether or not something is rational. It will continue rational.
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Correct question:
Which number produces a rational number when multiplied by 0.5?
the cdc estimated that 12% of women who have recently given birth suffer from ppd. however, this research only reflected self-reported cases. therefore, one group dedicated to helping women and their families with ppd believes that the true percentage of women who suffer from ppd is much higher. the group conducts a simple random sample of 139 women who had given birth in the last year and discovers that 25 of them report having ppd. based on this evidence, can the group claim that the true percentage of women who have ppd is greater than 12%? use a 0.05 level of significance. step 2 of 3 : compute the value of the test statistic. round your answer to two decimal places.
The actual percentage of female people with ppd is more than 12%.
What is ppd ?Many women experience postpartum depression (commonly known as PPD), which is a medical disorder. After giving delivery, there are intense emotions of sadness, anxiety (concern), and exhaustion that persist for a long time. You may find it challenging to care for both you and your infant as a result of these feelings. PPD can occur at any point following childbirth. Within 1 to 3 weeks of giving birth, it frequently begins. To get better, it need treatment.
What does true percentage mean in statistics?And that's basically what TS% is. A measure of scoring efficiency based on the number of points scored over the number of possessions in which they attempted to score. The actual TS% formula multiplies the denominator by 2 to put the number into a percentage scale, but it's the same result on a different scale
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Triangle ABC is reflected over the x-axis. What are the coordinates of the image of the vertex A?
The image of vertex A will be at point (2,-5).
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The perimeter will be P = sum of all three side.
Point A is located at (2, 5), thus you look at the y-coordinate since you are reflecting it across the x-axis.
Given that it is five above the x-axis, you must travel five below it, or you can simply enter the opposite of five, which is -5.
So, A' is at (2, -5).
Hence, The image of vertex A will be at point (2,-5).
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Andrea is 165 cm tall, correct to the nearest cm. Joel is 170 cm tall, correct to the nearest 10 cm. Calculate the upper and lower bound for each person.
Andrea lower bound =
Andrea upper bound =
Joel lower bound =
Joel upper bound=
Answer:
Step-by-step explanation:
andrea lb: 164.5cm
andrea ub: 165.5 cm
joel lb: 165
joel ub: 175
these are two angles that are formed by two coplanar lines and a transversal. they occupy the same relative positions.
Corresponding angles are two angles that are formed by two coplanar lines and a transversal and they occupy the same relative positions.
What pairs of angles are formed when two parallel lines are cut by a transversal?There are numerous pairs of angles that are created when a transversal cuts any two parallel lines. These angles include consecutive interior angles, alternate interior and exterior angles, and comparable angles.
Which of these pairs of angles is always equal when a transversal cuts two parallel lines?Each set of comparable angles are equal when a transversal cuts two parallel lines.
The angles that occupy the same relative location when a transversal cuts two or more lines are known as corresponding angles. The matching angles are equivalent when the lines are parallel.
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!!!Select all of the true statements that James can use as evidence to support the converse of the Pythagorean theorem.!!!!
James wants to informally prove the converse of the Pythagorean theorem by producing some evidence that supports it.
Recall that the converse of the Pythagorean theorem states:
If a triangle has side lengths a, b, and c such that a^2 + b^2 = c^2 , then that triangle is a right triangle.
James is going to construct several triangles with different side lengths and use a protractor to determine if the triangles turn out to be right triangles.
Select all of the true statements that James can use as evidence to support the converse of the Pythagorean theorem.
The only triangle dimensions that give a right angle triangle are;
3) 15, 36, 39
4) 15, 20, 25
6) 16, 30, 34
How to identify a right angle triangle?We are told that If a triangle has side lengths a, b, and c such that;
a² + b² = c² , then that triangle is a right triangle.
1) Using Pythagoras theorem, we can say that;
15² + 18² ≠ 21²
Thus, this is not a right angle triangle.
2) Using Pythagoras theorem, we can say that;
16² + 20² ≠ 24²
Thus, this is not a right angle triangle.
3) Using Pythagoras theorem, we can say that;
15² + 36² = 39²
Thus, this is a right angle triangle.
4) Using Pythagoras theorem, we can say that;
15² + 20² = 25²
Thus, this is a right angle triangle.
5) Using Pythagoras theorem, we can say that;
16² + 32² ≠ 48²
Thus, this is not a right angle triangle.
6) Using Pythagoras theorem, we can say that;
16² + 30² = 34²
Thus, this a right angle triangle.
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one apple and six bananas cost £2.70
one apple and eight bananas cost £3.50
Work out the cost of an apple and a banana
PLSSS HELP TYSM
Answer:
An apple costs 0.30 pounds and a banana costs 0.40 pounds.
Step-by-step explanation:
Let's think of apples as x and bananas as y.
Using the given information, you can write two equations.
[tex]x+6y=2.70[/tex]
[tex]x+8y=3.50[/tex]
x can also be written as
[tex]x=2.70-6y[/tex]
We can plug this equation into the second one to solve for y, or the cost of a banana.
[tex](2.70-6y)+8y=3.50[/tex]
[tex]2y=0.8[/tex]
[tex]y=0.4[/tex]
Now that we know the cost of a banana, we can go back to the first equation and solve for x, or the cost of an apple.
[tex]x+6(0.4)=2.70[/tex]
[tex]x=0.30[/tex]
Therefore, an apple costs 0.30 pounds and a banana costs 0.40 pounds.
an automobile assembly line runs for 9 3/4 hours each day. employees work 3/4-hour shifts. how many shifts are there in each day
A. 9 shifts
B. 10 shifts
C. 12 shifts
D. 13 shifts
Answer:
D 13 shirt
Step-by-step explanation:
9 [tex]\frac{3}{4}[/tex] ÷ [tex]\frac{3}{4}[/tex]
[tex]\frac{39}{4}[/tex] x [tex]\frac{4}{3}[/tex] = 13
Find the equation of a line parallel to 4x + 4y = -28 that passes
through the point (−4, –4).
Oy-4=x-4
Oy+4= x +4
○y-4=− (x − 4)
Oy+4= (x+4)
Submit Answer
The equation of the line that passes through the point (-4,-4) is y=-x-8.
How to find equation of line?The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y -axis).
What are three equations of line?The three equation of line are slope-intercept form, standard form and point-intercept form.
4x+4y=-28
Taking 4 common and dividing both sides by 4 gives
x+y= -7
y=-x-7
This means slope that is m=-1.
Now to find c in y=mx+c we need to use points (-4,-4).
-4=(-1)(-4)+c
c=-8
So the equation of line is y=-x-8.
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For the following inequality, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that you used to find a solution for the inequality. Be sure to include at least two terms from the word bank.
Answer:
x ≤ -12
Step-by-step explanation:
We solve for x by dividing both sides by 1/4:
[tex]1/4x\leq -3\\x\leq -12[/tex]
Thus, the two sentences you need to have two words from your work bank are (1) "divide" both sides by 1/4 and (2) x is "less than or equal to" -12
Find sin (x - y) if sin x = 3/5 and cos y = 5/13. Assume both triangles are in quadrant 1.
The value of sin (x - y) of the triangles is -33/65
How to find the value of sin (x - y) of the triangle?Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles
Given: sin x = 3/5 and cos y = 5/13. Both triangles are in quadrant 1
(Consider the image attached)
For triangle with angle x
adjacent = √(5²-3²) = 4
cos x = 4/5 (adjacent/hypotenuse)
For triangle with angle y
opposite = √(13²-5²) = 12
sin y = 12/13 (opposite/hypotenuse)
Using the trigonometric identity:
sin(x-y) = sinxcosy - sinycosx
sin(x-y) = (3/5)×(5/13) - (12/13)×(4/5)
sin(x-y) = 3/13 - 48/65
sin(x-y) = -33/65
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Two dice are rolled. Determine the probability of the following. ("Doubles" means both dice show the same number. Enter your probability as a fraction.)
rolling a number greater than 5 or doubles
The probability of rolling a number greater than 5 or doubles will be 0.78.
What is probability? What is a mathematical equation? What do you mean by domain and range of a function?The formula to calculate the probability of occurrence of an event [A] can be written as -P(A) = n(A)/n(S)
where -
n(A) = Number of outcomes favorable to event A.
n(S) = Total number of outcomes.
A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have two dices are rolled.
The sample space for sum greater than 5 will be 26. For doubles, we will add 2 pairs (1, 1) and (2, 2) to 26 to get a total sample space of 28. Remaining doubles are already in 26. So, the probability of rolling a number greater than 5 or doubles will be -
P(A) = 28/36 = 0.78
Therefore, the probability of rolling a number greater than 5 or doubles will be 0.78.
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[Question in english -
From a point on the ground located 4m from a pole, its upper part can be seen with an elevation angle of 37°. What is the height of the pole?]
Do anyone know the answers?
Answer:
e is 9x D is 4x c is 1× and a is 5× and b is 2×
Which of the following equations has the sum of its roots as 3?
A. 2x2-3x+6=0
B. -x2+3x-3=0
C. 3x2-3x+3=0
D. x2+5x+6=0
-x2+3x-3=0 is the equation that has the sum of its roots as 3.
What is meant by sum of roots?A quadratic equation's roots are equal to the second term's coefficient negated, divided by the leading coefficient. The constant term (the third term), divided by the leading coefficient, is equivalent to the product of the roots of a quadratic equation.
Write general formula for the sum of roots.Sum of roots= -b/a
Sum of root is defined as:
Sum of root = -b/a
Consider option B -x^2+3x-3
a=-1 , b=3
Sum of root= - 3/(-1)=3
So B is the correct option of the following question.
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Determine the x and y intercept:
X -3 -2 -1 0 1
y 0 2 4 6 8
what is the quadratic equation in standard form with rational coefficents that has a root of 5+4i?
Answer:
x^2 -10x + 41 = 0
Step-by-step explanation:
They gave you a root. A root is a solution, is a zero, is an x-intercept(if real).
This is a working backwards problem. They gave you an answer and want the equation back again.
x = 5 + 4i
working backwards:
x - (5 + 4i) = 0
x - 5 - 4i = 0
This left side is a factor of your equation.
If 5+4i is a root then 5-4i is also a root. So do the same thing:
x = 5 - 4i
x - (5 - 4i) = 0
x - 5 + 4i = 0
x - 5 + 4i and
x - 5 - 4i are the factors. Multiply them together to find the quadratic equation. Use distributive property or difference of squares or an area model to model. See image.
Answer:
x² - 10x + 41 = 0
Step-by-step explanation:
complex roots occur as a conjugate pair.
given x = 5 + 4i , then x = 5 - 4i is also a root
the corresponding factors are
(x - (5 + 4i) ) , (x - (5 - 4i) ) , that is
(x - 5 - 4i) and (x -5 + 4i)
the quadratic equation is then the product of the factors, that is
(x - 5 - 4i)(x - 5 + 4i) = 0
multiply each term in the second factor by each term in the first factor.
x² - 5x + 4ix - 5x + 25 - 20i - 4ix + 20i - 16i² = 0 ← collect like terms
x² - 10x + 25 - 16i² = 0 [ note i² = - 1 ]
x² - 10x + 25 + 16 = 0
x² - 10x + 41 = 0 ← in standard form
How do you write the equation for a line that passes through points (2,1) and (0,7)?
The equation for a line that passes through points (2,1) and (0,7) is y-7 = -3x or y= -3x+7
To find the equation of a line passing through two points you must first find the slope of the line.
The slope can be found by using the formula: [tex]m=\frac{y2-y1}{x2-x1}[/tex]
Where m is the slope and (x1,y1) and (x2,y2) are the two points. Substituting the two points given in the problem allows us to calculate the slope as:
[tex]m=\frac{7-1}{0-2} \\m= \frac{6}{-2} \\m= -3[/tex]
Next, we have to use the point-slope formula to find the equation for the line passing through these two points.
The point-slope formula states: (y-y1)=m(x-x1)
Where m is the slope and x1, and y1 are points from which the line passes.
Substituting the value of m and x1 and y1 in the given equation,
y-7=-3(x-0)
y-7= -3x-3*0
y-7+-3x
Solving for the slope-intercept form gives:
y-7+7= -3x+7
y-0 + -3x+7
y= -3x+7
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Learning curve: In psychological tests, it is found that students can memorize a list of words after t hours, according to the learning curve y = 50 - 50e^-0.3t, where y is the number of words a student can learn during the t^th hour of study. Find how many words a student would be expected to learn in the ninth hour of study.
A student is expected to learn approximately 46.535 words in the ninth hour of study.
What is the number of words a student would be expected to learn in the ninth hour of study.?Generally, To find the number of words a student is expected to learn in the ninth hour of study, we can substitute 9 for t in the learning curve equation:
y = 50 - 50e^-0.3(9)
Simplifying the exponent, we have:
y = 50 - 50e^-2.7
To calculate the value of e^-2.7, we can use a calculator or lookup the value in a table of common exponent values. The value of e^-2.7 is approximately 0.0693.
Substituting this value back into the equation, we have:
y = 50 - 50(0.0693)
Simplifying, we find:
y = 50 - 3.465
y = 46.535
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the computed t-value of -1.708 for a two-tailed hypothesis test of the difference of two means with sample size of 26 would yield a p-value of 0.10. group of answer choices true false
The computed t-value of -1.708 for a two-tailed hypothesis test of the difference of two means with sample size of 26 would yield a p-value of 0.10.
This statement is a false statement.
How does hypothesis testing work?To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample. First, a hazy assumption about the parameter or distribution is made.
What is a sample of a hypothesis test?The null hypothesis is that 50% is true, while the alternative hypothesis is that 50% is not accurate, for instance, if someone wants to test whether a penny has an exact 50% chance of landing on heads.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
We can rewrite the circle equation as:
(x - 1)^2 + y^2 = 9
Then the two true statements are:
"The center of the circle lies on the x-axis"
" The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."
Which statements are true about the circle?
Remember that a general circle equation with a center (a, b) and radius R is:
(x - a)^2 + (y - b)^2 = R^2
Here the equation is:
x^2 + y^2- 2 x - 8 = 0
We can rewrite this as:
(x^2 - 2x) + y^2 = 8
Adding and subtracting 1 in the left side we can complete squares:
(x^2 - 2x + 1) - 1 + y^2 = 8
(x - 1)^2 + y^2 = 9
Tha is our equation, so the center is (1, 0) and the radius is 3 units.
Then the true statements are:
"The center of the circle lies on the x-axis"
" The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."
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