The true statements about the circle are the radius of the circle is 3 units, the center of the circle lies on the x-axis and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9
How to determine true statements about the circle?Given: the equation is x²+y²–2x–8 = 0
In order to determine true statements about the circle, we have to rewrite the given equation and compare it with the standard form of the equation of a circle.
The standard form of the equation of a circle is
(x-a)² + (y-b)² = r²
where (a, b) is the center and r is the radius
using the completing square method on the given equation:
x²+y²–2x–8 = 0
x²-2x + (-1)² + y² + (0)²= 8 + (-1)²
(x-1)² + (y-0)² = 9
(x-1)² + (y-0)² = 3²
Thus, the center is (0, 1) and the radius is 3
Therefore, the options are the radius of the circle is 3 units, the center of the circle lies on the x-axis and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9
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Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −3, ordered pair: (−5,3)
Answer:
[tex] \huge{ \boxed{y = - 3x - 12}}[/tex]
Step-by-step explanation:
Equation of a line in slope-intercept form is given by
[tex]y = mx + c[/tex]
where
m is the slope
c is the y intercept
From the question
m = -3
In order to find c we substitute the point (−5,3) into the equation y = mx + c
We have
[tex]3 = - 3( - 5) + c \\ 3 = 15 + c \\ c =3 - 15 \\ c = - 12 [/tex]
We now substitute c and m into the main equation
We have the final answer as
[tex]y = - 3x - 12[/tex]
Hope this helps you
Use the following model to answer the question.
Which division problem is shown by the model?
OA. 0.66÷3= 0.22
O B. 0.663 = 0.26
OC. 0.78÷3= 0.62
www
D. 0.78÷3= 0.26
D
G
Option D is correct answer, The given model in the picture shows the division problem as: 0.78 ÷ 3 = 0.26.
What is division?
Along with addition, multiplication, and subtraction, division is one of the four basic mathematical operations. The act of separating anything into smaller groups so that each one has the same amount of items is known as division. It is a mathematical operation that is used to distribute and group things equally.
we can count that, there are 26 cubic blocks in each square in the picture,
10 each are vertically in two rows and 6 are horizontally present.
And there are total of 3 such squares present each with 26 cubic blocks.
So these all totals to 78 cubic blocks which is divided in 3 squares and in each squares there are 26 cubic blocks.
Therefore, the division problem representing this can be written as:
0.78 ÷ 3 = 0.26
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Tricia made a 72% on her science test. if she got 18 problem correct, how many questions were on the test?
Answer: 25 questions
Step-by-step explanation:
The following angles are supplementary to each other.
mzA= (4x + 30) and mzB = (2x - 30)°
Determine x.
15
20
30
60
Answer:
30
Step-by-step explanation:
Supplementary angles add to 180°.
[tex]4x+30+2x-30=180 \\ \\ 6x=180 \\ \\ x=30[/tex]
(100 POINTS AND BRAINLYEST JUST PLEASE ANSWER)
1.) An algae bloom is threatening to cover Grand Lake St. Mary’s near Celina, Ohio. The EPA needs to calculate the surface area of the lake to treat the algae bloom. Estimate the area of the irregular shape.
A) Draw on the map to show what method was used to find the area of the lake. (2 points)
B) Show work to estimate the area of the lake in square units. Attach additional paper if necessary. (2 points)
C) Each unit on the grid is 0.25 miles. Find the actual estimate of the area of the lake. (2 points)
The area of the irregular shape is 288 sq. units
Given,
An algae bloom is threatening to cover Grand Lake St. Mary’s near Celina, Ohio.The EPA needs to calculate the surface area of the lake to treat the algae bloomWe have to estimate the area of the irregular shape;
Here,
The shape can be broken down into a trapezoid, a rectangle, and a triangle
The area of the trapezoid = 1/2 × 12 × 9 × (7 + 10) = 76.5 sq. unitsThe area of the rectangle = 7 × 20 = 140 sq. unitsThe area of the triangle = 1/2 × 11 × 13 = 71.5 sq. unitsThe total area = 76.5 + 140 + 71.5 = 288 sq. units
Therefore,
The area of the irregular shape is 288 sq. units
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Consider the function f, where f(x) = 2x2 - x+ 3. Part A Complete the equation to represent f(x + 1). X+Y Select and drag numbers into the empty boxes to correctly complete the equation.
The numeric value of the function f(x) = 2x² - x + 3 at x = x + 1 is given as follows:
f(x + 1) = 2x² + 3x + 4.
How to obtain the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
In this problem, the function is defined as follows:
f(x) = 2x² - x + 3.
The point at which the numeric value is calculated as given by:
x = x + 1.
Hence the numeric value is obtaining replacing the two instances of x in the function by x + 1, as follows:
f(x + 1) = 2(x + 1)² - (x + 1) + 3
f(x + 1) = 2(x² + 2x + 1) - x - 1 + 3
f(x + 1) = 2x² + 4x + 2 - x - 1 + 3
f(x + 1) = 2x² + 3x + 4.
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Question
A farmer notices that there is a linear relationship between the number of bean stalks, n, she plants and the yield, Y. When
she plants 3 stalks, each plant yields 115 ounces of beans. When she plants 8 stalks, each plant yields 190 ounces of beans.
Write the linear equation, Y(n), that correctly represents this situation.
Provide your answer below:
Y(n)=
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The equation that represent the given situation is y = 15x + 70
When she plants 3 stalks, each plant yields 115 ounces of beans
The first point = (3, 115)
When she plants 8 stalks, each plant yields 190 ounces of beans
The second point = (8, 190)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line m = (190-115) / (8-3)
= 75/5
= 15
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Choose one point and substitute the values in the equation
y - 115 = 15(x - 3)
y - 115 = 15x - 45
y = 15x - 45 + 115
y = 15x + 70
Hence, the equation that represent the given situation is y = 15x + 70
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2x < 15
answer and how to solve please
Answer:
×= -7½
Step-by-step explanation:
2x<15
2x<15=0
2x= -15
x= -15/2
x= -7½
How many seven-digit numbers can be formed with the digits of 2201213?
There are 420 arrangements for seven-digit numbers that can be formed with the digits of 2201213 by permutation.
What is permutation?The term permutation is simply the process of arrangement or selection of objects. It involves each of several possible ways in which a set or number of things can be ordered or arranged.
We can apply the formula for permutation;
[tex]p(n,r) = \frac{n!}{(n - r)!}[/tex]
where n = total number of object and r = number of objects selected.
Total number of digits = 7
number of the digit 2 = 3
number of the digit 1 = 2
number of the digit 0 = 1
number of the digit 3 = 1
so the permutation for the digits 2201213 is calculated as;
7!/(3! × 2! × 1! × 1!)
(7 × 6 × 5 × 4 × 3!)/(2 × 3!) {cancel out 3! with 3! and 4 with 2}
7 × 6 × 5 × 2
420 arrangements
Hence, by permutation, we can say that there are 420 arrangement for which seven-digit numbers can be formed with the digits of 2201213
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Emma recorded the weight of her kitten in ounces on certain days for 24 days. The data are shown in the scatterplot.
Answer:
can you show me it so i can help
Step-by-step explanation:
Which point below is a solution to the equation y = 2x − 5?
(1, -3)
(4, 2)
(-1, -5)
(2, 0)
Sorry I don't have the answer but I can rule out 2.
Step-by-step explanation:
4,2 and 2,0 are not going to be correct because I got them wrong on a quiz I had 2 attempts to take.
So its either 1,-3 or -1,-5.
Hope this helps you.
Lim x->1 sinx - sin1/x-1
The limit Lim x→1 (sinx - sin1)/(x - 1) = cos1
What is the limit of a function?The limit of a function f(x) as x tends to a is the value of the function f(x) as x tends to a. It is written as [tex]\lim_{x \to a} f(x) = L[/tex]
How to find the given limit of the function?GIven that we require the limit given as [tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1}[/tex]
So, substituting the value of x = 1 into the given equation, we have that
[tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = \frac{sin1 - sin1}{1 - 1} \\= \frac{0}{0}[/tex]
Since 0/0 is one of the inderterminate forms, we use the L'hopital's rule to find the limit of the given function.
What is L'hopital's rule?L'hopital's rule states that if [tex]\lim_{x \to a} f(x) = \lim_{x \to a} g(x) = 0[/tex] and f'(x) and g'(x) exist then [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]
Let the variables be
f(x) = sinx - sin1 and g(x) = x - 1So, since we know that
[tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = \frac{0}{0}[/tex],
So, [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]
So, we differentiate both the numerator and denominator and find the limit.
So,
[tex]\lim_{x \to 1} \frac{f'(x)}{g'(x)} = \lim_{x \to 1} \frac{\frac{d(sinx - sin1)}{dx} }{\frac{d(x - 1)}{dx} } \\= \lim_{x \to 1} \frac{cosx - 0}{1 - 0} \\= \lim_{x \to 1}cosx \\= cos1[/tex]
So, [tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = cos1[/tex]
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write the mixed number 4 2/5 as an improper fraction
Answer:
[tex]\frac{22}{5}[/tex]
Step-by-step explanation:
To write a mixed number as an improper fraction, you start by converting the "number part" into a fraction.
For example, in this problem 4 is the number part, and we want to rewrite 4 as fraction with a denominator of 5. To do this, we multiply four by 5, which is twenty and put this over 5: [tex]\frac{20}{5}[/tex]. This would be a fraction representing 4(you can check through division).
Next, we need to add [tex]\frac{2}{5}[/tex] to this. [tex]\frac{2}{5} +\frac{20}{5}[/tex] would just be [tex]\frac{22}{5}[/tex] because 20 + 2 = 22.
calculate the area of this trapezium
Answer:
Step-by-step explanation:
Let the trapezium be B.
Draw a line from the top of the trapezium to it's base and call the triangle formed B.
The base of is 2cm (8cm - 6cm
The area of the triangle = 40cm² ( 5cm x 4cm x 2cm)
Area of the trapezium =. ½ (base x height)
. = 18cm²
Add area of trapezium and triangle.
= 40cm² + 18cm² = 58cm²
.
3) Karen, her brother Dan, Dana, and her sister Randi own a pizza restaurant, Karen and Dan each own 2/7 of the
restaurant. The remaining share is owned equally by Dana and Randi. Exactly what fraction of the business
does Dana own?
Dana owns [tex]\frac{3}{14}[/tex] fraction of the business
How to calculate the fractions?
*Identify a fraction: When writing fractions, one number is placed above the dividing line and one number is written underneath it.
*Find the numerator: The numerator—the number at the top—indicates the number of elements that make up the fraction.
*find the denominator: The denominator is the figure at the bottom. This number reveals how many components there are in the total number.
Let us take the fraction shared by Dana and Randi as x
So the equation becomes
[tex]\frac{2}{7} +\frac{2}{7} +x+x=1[/tex]
⇒ [tex]\frac{4}{7}+2x=1[/tex]
⇒2x=1-[tex]\frac{4}{7}[/tex]
⇒[tex]2x=\frac{7-4}{7}[/tex]
⇒[tex]2x=\frac{3}{7}[/tex]
⇒[tex]x=\frac{3}{7*2}[/tex]
⇒[tex]x=\frac{3}{14}[/tex]
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Which graph represents the function f(x) = 4/x
Answer:
Step-by-step explanation:
On December 13,2007 one U.S. dollar was worth 0.69 euro
On that date, how many dollars was 110.66 euro worth?
Round your answer to the nearest hundredth of a dollar.
-----need a response back ASAP!----------
On that date, how many euro was 77.65 dollars worth?
Round your answer to the nearest hundredth of a euro.
On that date, 110.66 euro was worth 160.38 dollars.
On that date, 77.65 dollars was worth 53.58 euro.
How to calculate the value?Given that one U.S. dollar was worth 0.69 euro, the dollar that was 110.66 euro worth will be:
= Amount of euro / Rate
= 110.66 / 0.69
= 160.38 dollars
The euro that 77.65 dollars was worth will be:
= 77.65 × 0.69
= 53.58 euro
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1. Fourteen cars were randomly chosen at a used car lot. The age of each car and its sale price are shown in
the following table.
Answer: $10,252.87
Step-by-step explanation:
Based on the linear model of data, the price of the car that is 10 year old is approximately 10,000.
Linear model.
Basically, the linear model describes the relationship between a dependent variable, y, and one or more independent variables, X. Where the dependent variable is also called the response variable. And the independent variables are also called explanatory or predictor variables.
Given,
Here we have the table of data that contains the fourteen cars were randomly chosen at a used car lot and the age of each car and its sale price.
Now, we have to find the sale price for the 10 year old car.
In order to find the price of the 10 year old car, we have to plot these given table on the graph.
Then we get the graph like the following.
By looking at the graph, the sales price of the 10 year old car is predicted as approximately 10,000,
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The following inequalities form a system.
y is greater than or equal to two-thirds times x plus 2
y is less than negative one-third times x plus 1
Which ordered pair is included in the solution to this system?
(−6, −3)
(−6, −2)
(−6, 3)
(−6, 4)
From the graph, the ordered pair that is included in the solution to the given system is (-6, -2). The correct option is the second option (−6, −2)
Solving system of linear inequalities using graphFrom the question, we are to determine the ordered pair that is included in the solution to the given system of inequalities
The given system of inequalities is
y ≥ 2/3(x) + 2
y < -1/3(x) + 1
To determine the ordered pair that is included in the solution, we will graph the given system of linear inequalities.
The graph of the system of linear inequalities is given below.
From the graph, we can observe that (-6, -2) is a solution to the given system of linear inequalities.
Hence, the ordered pair that is a solution is (-6, -2)
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Answer:
Option B: (-6, -2)
Step-by-step explanation:
i took the test xx
Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph. What are the coordinates of pre-image point H?
The coordinates of pre-image point H is (c) (3, 2)
How to determine the coordinates of pre-image point H?The graph represents the given parameter
On the graph, we have the coordinate of point H' (i.e. the image) to be
H' = (-3, -2)
The transformation rule is given as
Rotation 180° about the origin
Mathematically, this is represented as
(x, y) = (-x, -y)
This implies that:
H = (3, 2)
So, the coordinates are (3, 2)
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Hunter is going to see a movie and is taking his 4 kids. Each movie ticket
costs $12 and there are an assortment of snacks available to purchase for $5
each. How much total money would Hunter have to pay for his family if he
were to buy 4 snacks for everybody to share? How much would Hunter have
to pay if he bought a snacks for everybody to share?
Answer:
$80
Step-by-step explanation:
hunter+ kid 1+kid 2+kid 3+kid 4= 60 dollars just for tickets
4 snacks= 20 dollars for snacks
$60+$20=$80
PLEASE MARK BRAINIEST
ACTIVITY 7
In a pack of cards, there are 52 cards. There are 4 suits diamonds, hearts, spades and
clubs. Each suit has a King, a Queen, a Jack and an Ace. It also has cards for 2. 3. 4.
5, 6, 7, 8, 9 and 10 If the pack has been shuffled so that the cards are in no particular
order, and you select one card from the pack without looking, what is the probability of
selecting
a) a Queen
b) a red Queen
c) a Jack of Hearts
d) a Jack of Hearts or Diamonds
e) any club
f) a six or a seven
g) a black six
h) a picture card (Jack, Queen or King)
Answer:
Step-by-step explanation:
abcdefgh
NO LINKS!! Please help me with the Angle Proofs Part 3
Answers in bold
GivenDefinition of complementaryGivenDefinition of congruenceVertical anglesDefinition of congruenceSubstitution propertyDefinition of complementary==============================================
Explanation:
Always start with what is given. The last statement is the thing we want to prove.
Complementary angles add to 90 degrees. They form a right angle.
When "definition of congruence" is mentioned, we go from two angles being congruent to having them be of the same measure. It's a slight change of notation.
Vertical angles form whenever we cross two lines to form an X shape. The vertical angles are opposite one another, and always congruent.
The substitution property is the idea of replacing one thing with something it is equivalent to. In other words, we plug in the item.
Notice on line 2, if we replace "angle 1" with "angle 4" (valid because the two angles are congruent), and then replace "angle 2" with "angle 3", then we get the result on line 7.
Answer:
1. Given.
2. Definition of complementary angles.
3. Given.
4. Definition of congruent angles.
5. Vertical Angles Theorem.
6. Definition of congruent angles.
7. Substitution Property of Equality.
8. Definition of complementary angles.
Step-by-step explanation:
Statement 1
∠1 and ∠2 are complementary.
Reason: Given.
Statement 2
m∠1 + m∠2 = 90°
Reason: Definition of complementary angles.
Complementary angles are two angles that sum to 90°. Therefore, if ∠1 and ∠2 are complementary, then their measures must sum to 90°.
Statement 3
∠1 ≅ ∠4
Reason: Given.
Statement 4
m∠1 = m∠4
Reason: Definition of congruent angles.
Congruent angles are angles with exactly the same measure. As angle 1 is congruent to angle 4, then their measures are equal.
Statement 5
∠2 ≅ ∠3
Reason: Vertical Angles Theorem.
Vertical angles are always congruent.
Statement 6
m∠2 = m∠3
Reason: Definition of congruent angles.
Congruent angles are angles with exactly the same measure. As angle 2 is congruent to angle 3, then their measures are equal.
Statement 7
m∠4 + m∠3 = 90°
Reason: Substitution Property of Equality.
For all numbers a and b, if a=b, then a may be replaced by b in any equation or expression.
As m∠2 = m∠3 and m∠1 = m∠4, replacing them in m∠1 + m∠2 = 90° gives m∠4 + m∠3 = 90°.
Statement 1
∠3 and ∠4 are complementary.
Reason: Definition of complementary angles.
Complementary angles are two angles whose sum is 90°. Therefore, if the sum of m∠4 and m∠3 is 90°, this means that ∠4 and ∠3 must be complementary.
HELP PLEASE! 66pts!
Solve for x. SHOW WORK!
2^(3x+1)=1/4
The solution of the exponential equation is x = -1
How to find the value of x?
We want to solve the exponential equation:
2^(3x + 1) = 1/4
If we apply the natural logarithm in both sides of that equation, we will get:
ln( 2^(3x + 1) ) = ln( 1/4)
(3x + 1)*ln(2) = ln(1/4)
3x*ln(2) = ln(1/4) - ln(2)
x = (ln(1/4) - ln(2))/(3*ln(2)) = -1
The value of x is -1
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Naomi is going to invest $78,000 and leave it in an account for 7 years. Assuming the
interest is compounded daily, what interest rate, to the nearest hundredth of a
percent, would be required in order for Naomi to end up with $91,000?
In order to get the total amount $91,000 at the end of the 7 year, the interest rate is 2.2% on compound interest basis.
Compound Interest:
The general form to calculate the compound interest is written as,
A = P(1 + r/n)ⁿˣ
where
A = Accrued amount (principal + interest)
P = Principal amount
r = Annual nominal interest rate as a decimal
n = number of compounding periods per unit of time
x = time in decimal years
Given,
Naomi is going to invest $78,000 and leave it in an account for 7 years. Assuming the interest is compounded daily.
Here we need to find the nearest hundredth of a percent, would be required in order for Naomi to end up with $91,000.
Here we have to solve for rate r as a decimal
[tex]r = n[(A/P)^{1/nt} - 1][/tex]
r = 365 × [(91,000.00/78,000.00)1/(365)(7) - 1]
r = 0.022022202
Then convert r to R as a percentage
R = r * 100
R = 0.022022202 * 100
R = 2.202%/year
Therefore, the interest rate required to get a total amount of $91,000.00 from compound interest on a principal of $78,000.00 compounded 365 times per year over 7 years is 2.202% per year.
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find the area between the curve y=x^2-3x for x between 1 and 8
The area between the curve y = x^2 - 3x for x between 1 and 8 is 1343 / 3 square units.
First, let us understand the area under the curve:
A definite integral between two points is used to calculate the area under a curve between them. Integrate y = f(x) between the limits of a and b to determine the area under the curve y = f(x) between x = a and x = b. This area can be estimated by integrating with specified limitations.
We are given:
y = x^2 - 3x
We need to find the area between the curve y = x^2 - 3x for x between 1 and 8.
Now,
Integrate the given function:
Integration y = Integration x^2 - Integration 3x
y = [x^(2 + 1) / (2 + 1)] ^ 8 _1 - [3x^(1 + 1) / (1 + 1)] ^ 8 _1
y = [x^3 / 3] ^ 8 _1 - [3x^2 / 2] ^ 8 _1
y = [8^3 / 3 - 1^3 / 3] - [3 * 8^2 / 2 - 1 * 8^2 / 2]
y = [512 / 3 - 1 / 3] - [96 - 32]
y = 1535 / 3 - 64
y = 1535 - 192 / 3
y = 1343 / 3 square units.
So, the area is 1343 / 3 square units.
Thus, the area between the curve y = x^2 - 3x for x between 1 and 8 is 1343 / 3 square units.
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What is the equation for the parabola graphed below
Answer:
[tex]y = x^2 - 2x -1[/tex]
Step-by-step explanation:
General Form of a parabola :
[tex]y = a (x - h)^2 + k[/tex]
Solving :
h and k refer to the point of the vertex. In this case, it's (1, -2), so :
[tex]y = a(x - 1)^2 - 2[/tex]
Plug in values for x and y. In this case, they're (0, -1), so :
[tex]-1 = a(0 - 1)^2 - 2\\-1 =a(1) - 2\\1 = a[/tex]
Plug in all values :
[tex]y = ( x - 1)^2 -2[/tex]
Further simplifying :
[tex]y = ( x - 1 )^2 - 2 \\y = (x^2-2x + 1) - 2\\y = x^2 - 2x -1[/tex]
PLEASE ANSWER!!!! WILL GIVE BRAIN THINGY
Answer:
No solutions
Step-by-step explanation:
-5y+7/2y=-5-3/2y-4
+3/2y. +3/2y
-5y+3/2y+7/2y=-5-4
-5y+10/2y=-9
-5y+5y=-9
0=-9
No solutions
Hopes this helps please mark brainliest
What expression represents the verbal phrase?
one-half times a number m plus twenty-five
The expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.
According to the question,
We have the following information,
The given verbal phrase is one-half times a number m plus twenty-five.
Now, we will solve it step by step.
Now, we will first find one-half times a number m. We know that we will replace the word times with multiplication. So, we have the following expression:
m/2
Now, adding 25 to this term, we have the following final expression:
m/2+25
Hence, the expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.
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You invest $6000 in a restaurant. The investment has a return of 12%. How
much do you receive for your investment after 30 months?
The return received after 30 months on an investment of $6000 will be $1800.
According to the question,
We have the following information:
You invest $6000 in a restaurant. The investment has a return of 12% per year.
We know that the following formula is used to find the simple interest on the amount:
Simple interest = principal*rate*time/100
Now, we have the following values in this case which we will put in the formula:
Principal = $6000
Rate = 12%
Time = 2.5 years
Simple interest = (6000*12*2.5)/100
Simple interest = $1800
Hence, the amount received after 30 months on an investment of $6000 will be $1800.
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