Point: (3, 4)
Slope: -1
In slope intercept form
y = -x + 7
Step-by-step explanation:Slope-intercept form can give us valuable information about a graph.
Point-Slope Form
There are multiple ways to solve this problem; I am simply showing the way I use most often.
We can plug the known information into point-slope form and then simplify the equation into slope-intercept form. Point-slope is written as:
y - y₁ = m(x - x₁)In this equation, y₁ and x₁ are the y and x values we are given and m is the slope. So, plug in the information.
y - 4 = -1(x - 3)Then, simplify the right side by distributing the -1.
y - 4 = -x + 3Next, add 4 to both sides.
y = -x + 7The equation in slope-intercept form is y = -x + 7.
Slope-intercept Form
Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept. So, our equation, y = -x + 7, shows that the slope is -1 and the y-intercept is 7. Using this information, we can compare the line to other linear functions or graph the line if needed.
Answer:
y = -x + 7 is your correct answer
Step-by-step explanation:
Given the following equation, x^4 -4x^2+10x+13 use synthetic division and show if they are root or not.
Please show steps.
The remainder of the synthetic division of x^4 - 4x^2 + 10x + 13 is 33 which is a non-zero number, x - 2 is not a root of the polynomial.
What is the remainder of the synthetic division?The remainder of the synthetic division of x^4 - 4x^2 + 10x + 13 is obtained as follows:
Using the method of synthetic division x^4 - 4x^2 + 10x + 13 to divide by x - 2 using synthetic division:
2 | 1 0 -4 10 13
| 2 4 0 20
|--------------
| 1 2 0 10 33
The final remainder is 33.
Therefore, by synthetic division:
x^4 - 4x^2 + 10x + 13 = (x - 2)(x^3 + 2x^2 + 10) + 33
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Somebody please help me with this
The measure of angle in degrees is 63 degree
We are given that;
The triangle ABC inscribed in the circle.
Now,
m<BAC-63
From isosceles triangle CBD,
m/CBD=m/BCD = 32
This implies that,
m/BDC+32+32=180
m/BDC+64 = 180
m/BDC=180-64
m/BDC = 126
m/BAC =1/2(m/BDC)
= 1/2(126)
= 63
Therefore, by the triangles the answer will be 63 degrees.
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A solid figure
is separated into two rectangular prisms.
The volume of Rectangular Prism is 80 cubic feet. Rectangular Prism B has
a length of 6 feet and a width of 5 feet.
The total volume of the solid figure is
200 cubic feet. What is the height of
Rectangular Prism B?
Answer:
4 feet
Step-by-step explanation:
Their is one rectangular prison divided into two.
The volume of the first one is
V1= L X H X W=80.
Volume of the second one is
V2= L X H X W
V2= 6 X H X 5
V2 = 30H
Now from the question, the total volume is 200cubic feet which means V1 + V2 = 200, recall that V1=80 and V2=30H, so we say;
80+30H=200, collecting the like term we have, 30H=200-80.
30H=120, divide both side by 30
30H/30=120/30
H= 4feet.
Height is 4feet.
What is a coterminal angle of 23 times pi over 3
60°
120°
240°
300°
240° is the coterminal angle of 23×π÷3.
First, we can simplify 23 times π over 3 by noticing that 2π is equivalent to 6 pi over 3, so we can add 2π to 23 times pi over 3 until we get an angle between 0 and 2π (or 0 and 360 degrees).
23 times π over 3 is equivalent to an angle of 360 degrees times (23 times π over 3)/(2π), which simplifies to 360 degrees times 23/2, or 4140 degrees.
To find a coterminal angle between 0 and 360 degrees, we can subtract 360 degrees until we get an angle in that range.
4140 - 360(11) = 240
Therefore, a coterminal angle of 23 times pi over 3 between 0 and 360 degrees is 240 degrees.
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Which of the following is a quadratic function? Help ASAP!
Answer:
B. f(x) = 4x² + x - 3
Step-by-step explanation:
A quadratic is a second-degree polynomial. This means that the highest power that x is raised to is 2.
We can see that option B is the only one that meets this requirement. Option A is a third-power monomial, so it is not a quadratic. Option C is a linear function, so it is not a quadratic.
Find the slope of a line perpendicular to the line whose equation is x + 6y = -24.
Fully simplify your answer.
Answer:
[tex]m_{perpendicular}[/tex] = 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
x + 6y = - 24 ( subtract x from both sides )
6y = - x - 24 ( divide through by 6 )
y = - [tex]\frac{1}{6}[/tex] x - 4 ← in slope- intercept form
with slope m = - [tex]\frac{1}{6}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{6} }[/tex] = 6
PLS HELP MARKING AS BRAINLIST!!
Answer:
C = 117.92° or 118°
Step-by-step explanation:
Law of Cosine: [tex]c^2=a^2+b^2-2ab*cos(C)[/tex]
Plug in your values to solve for C°
A = 50 , B = 55 , C = 90
[tex]90^2=50^2+55^2-(2*50*55)*cos(C)[/tex]
[tex]8100=2500+3025-5500*cos(C)[/tex]
Subtract 2500 and 3025 to move to other side.
[tex]8100-2500-3025=-5500*cos(C)[/tex]
[tex]2575=-5500*cos(C)[/tex]
Divide -5500 to leave cos(C) byitself
[tex]-\frac{2575}{5500} =cos(C)[/tex]
Inverse Cos(C) to get C byitself solving it in degree.
[tex]C=cos^{-1}(-\frac{2575}{5500} )[/tex]
C = 117.916339°
Round to Hundredths place or Whole Degree.
C = 117.92° or 118°
Roger is paid $50 to sell videos of a play to an audience after the play is performed.
He also receives $2 for each video he sells. The equation E = 50 + 2v models
the amount of money Roger earns selling videos. The play's audience consists of 230 people. What is the practical range?
The range of the function, in dollars, is
R: [50, 510]
What is the practical range?The range of a function is the set of possible outputs of said function. In this case, we know that the function is:
E = 50 + 2v
Where v is the number of games sold.
Here the domain will go from v = 0 (no games sold)
to v = 230 (the number of the play's audience)
Then the range is:
E = 50 + 2*0 = 50
E = 50 + 2*230 = 510
R: [50, 510]
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The table below represents a linear relationship. What is the Y intercepts? X-3 4 5 6
Y-7 10 13 16
the y intercept of the linear function in the table is
-2How to find the y interceptA linear function is represented using the equation
y = mx + c
the parameters are defined as
y = out put values
m = slope
x = input variable
c = y - intercept
Solving for slope using values in the table
m = (y2 - y1) / (x2 - x1)
m = (10 - 13) / (4 - 5)
m = -3 / -1
m = 3
Using point slope formula
y - y1 = m(x - x1)
y - 13 = 3(x - 5)
y = 3x - 15 + 13
y = 3x - 2
hence the y intercept is -2
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Decompose the following figure into separate pieces draw the pieces
The question's single element is divided into
three triangles and a rectangle.What is a composite shapeA composite shape is a geometrical figure formed from two or multiple elementary shapes layered and intermixed.
These simpler elements may comprise of
polygons such as triangles, rectangles, or pentagons)circles, or other geometric figures.As the base forms are overlapped or mixed to create an entirely new shape, they form a composite figure with a combined outline more intricate than any single component.
The single element in the question is separated to form
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1. An account is opened with an initial deposit of $6,500
and earns 3.6% interest compounded semi-annually.
What will the account be worth in 20 years?
The account will be worth approximately $13,268.58 in 20 years if it is opened with an initial deposit of $6,500 and earns 3.6% interest compounded semi-annually.
What is the accrued amount in 20 years?The formula accrued amount in a compounded interest is expressed as;
A = P( 1 + r/n )^( n × t )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $6,500
Compounded semi-annually n = 2
Time t = 20 years
Interest rate r = 3.6%
Accrued amount A = ?
First, convert R as a percent to r as a decimal
r = R/100
r = 3.6/100
r = 0.036
Plug in the given values into the above formula.
A = P( 1 + r/n )^( n × t )
A = $6,500( 1 + 0.036/2 )^( 2 × 20 )
A = $6,500( 1 + 0.036/2 )^( 40 )
A = $6,500( 1 + 0.018 )^( 40 )
A = $13,268.58
Therefore, the accrued amount in 20 years is $13,268.58.
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If 5 + 5 is 9 what is 10 + 10
Answer: 20
Realistically : In this hypothetical scenario, if 5 + 5 equals 9, then the basic principles of mathematics are no longer applicable, and any further calculations cannot be accurately determined. However, in the real world, 5 + 5 equals 10, and therefore 10 + 10 would equal 20.
Answer:
20
Step-by-step explanation:
5. Select all the statements that are true about AJKL and ALMN. (20 pts) The have only one pair of congruent angles. They have two pairs of congruent angles. AJKL has angles 50°, 60°, and 70°. ALMN has angles 50°, 60°, and 70°. AJKL and ALMN are similar.
Answer:
Step-by-step explanation: A. ΔJKL and ΔLMN have only one pair of angles that are congruent
C. ΔJKL has angles that measure
step 1
Find the value of x
we know that
----> by vertical angles
substitute the given values
solve for x
step 2
Find the measure of the interior angles of triangle JKL
we have
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
therefore
Triangle JKL has angles that measure
step 3
Find the measure of the interior angles of triangle LMN
we have
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
Triangle LMN has angles that measure
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
The corresponding angles of triangle JKL and LMN are not congruent
therefore
The triangles are not similar
Verify each statement
Part a) ΔJKL and ΔLMN have only one pair of angles that are congruent
The statement is true (see the explanation)
Part b) ΔJKL and ΔLMN have two pairs of angles that are congruent
The statement is false
Because have only one pair of angles that are congruent
Part c) ΔJKL has angles that measure
The statement is true (see the explanation)
Part d) ΔLMN has angles that measure
The statement is false
Because, Triangle LMN has angles that measure
Part e) ΔJKL and ΔLMN are similar
The statement is false
Because, the corresponding angles are not congruent
We often use the phrase "to the power of" when talking about exponents. For example, x¹³ is
referred to as x to the power of 13. Why do you think that they would name it like this? How does
increasing the exponent of a number increase its "power"?
Hint: Use a number as an example. (for instance 2) if you keep increasing the power, what happens
to the answer? (i.e. compare 2¹, 22, 23, 24, ..., 213, 214, ... until you see the answer you are looking
for!)
The phrase, raise to the power of is used when referring to exponents because the power or strength increases with the addition of more numbers. For instance, 2 raised to the power of 1 is not as strong as 2 raised to the power of 100.
Why the phrase is used?The usage of this phrase stems from the fact that numbers tend to increase in strength as they are raised to an increasing number of figures.
The strength that numbers carry differs as they increase or decrease. Just as 10 is greater than 1 or 2, so will different powers of exponents differ in strengths.
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What is the volume? round to the nearest thousandth
The volume of the pyramid is determined as 433.33 mm³.
What is the volume of the right square pyramid?The volume of the right square pyramid is calculated by applying the following formula.
V = ¹/₃a²h
where;
a is the base of the pyramidh is the height of the pyramidThe volume of the pyramid is calculated as follows;
V = ¹/₃ (10 mm)² x ( 13 mm )
V = 433.33 mm³
Thus, the volume of the pyramid is calculated from the formula stated.
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I NEED HELP FAST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]\huge\boxed{\sf 1}[/tex]
Step-by-step explanation:
Given expression:= [tex]\displaystyle (\frac{1}{4} )^0[/tex]
Using exponent rule:
[tex]a^0=1[/tex]So,
[tex]\displaystyle (\frac{1}{4} )^0=1[/tex]
[tex]\rule[225]{225}{2}[/tex]
if A C B, then
1) A U B = B
2) A n B = 0
3) A n B =B
If in the set A ⊂ B then the statement A U B = B
What is a set?A set is a collection of well defined items.
Since we have A ⊂ B, we want to determine which statement of the set is true. To determine that, we proceed as follows.
Given that A ⊂ B which means that A is a subset of B. which implies that all the elements of the set A are in set B, then this implies that A U B = B.Since all the elements in set A are in set B.The statement A n B = 0 is false since all elements in A are in BAlso, the statement A n B = B is false since all elements in set A are in BSo, if A ⊂ B then the statement A U B = B
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Use the bag of counters from the Review.
Find the probability of each compound event.
Answer:
its one and three
Step-by-step explanation:
Write an inequality to represent the domain of the situation :
Write an inequality to represent the range of the situation :
If the equation of the function is c (x) = n (1.35)^x, the value of n is :
An inequality to represent the domain of the situation: 0 ≤ x ≤ 6
An inequality to represent the range of the situation: 4 ≤ y ≤ 24
If the equation of the function is [tex]c(x) = n(1.35)^x[/tex], the value of n is: 4.
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.
Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of this logarithmic function shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [0, 6] or 0 ≤ x ≤ 6.
Range = [4, 24] or 4 ≤ y ≤ 24.
Next, we would determine the value of n by using the y-intercept (0, 4);
[tex]c(x) = n(1.35)^x\\\\4=n(1.35)^0[/tex]
n = 4.
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Need help on this please
The line of reflection between pentagons PQRST and P'Q'R'S'T' include the following: A. x = 0.
What is a reflection over the y-axis?In Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).
By applying a reflection over the y-axis to the coordinate of the given pentagon PQRST, we have the following coordinates:
Coordinate P = (-4, 6) → Coordinate P' = (-(-4), 6) = (4, 6).
In this scenario and exercise, a line of reflection that would map pentagon PQRST onto itself is an equation of the line that passes through the origin.
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Change to vertex form, with step by step. Thanks
The quadratic function x² - 10x + 20 in vertex form is f(x) = (x - 5)² -5. The vertex of this parabola is (5, 15).
To convert the quadratic function in standard form, f(x) = ax² + bx + c, to vertex form, f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola, follow these steps:
Complete the square by adding and subtracting (b/2a)²inside the parentheses:
f(x) = x² - 10x + 20
f(x) = (x²- 10x + 25) - 5
Factor the expression inside the parentheses as a perfect square:
f(x) = (x - 5)² -5
Write the function in vertex form by pulling out the value of a from the perfect square:
f(x) = 1(x - 5)² -5
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15 mor than twice a number
If we use the variable n to represent the unknown number, then "15 more than twice a number" can be written as:
2n + 15
Answer:
The answer is 15+2n
Step-by-step explanation:
15 more than twice a number =15+2n
Which of the following are more precise than a weight of 1,000 pounds? Check all that apply.
I WILL GIVE 35 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE
Answer:
If im not mistakeing
Step-by-step explanation:
(-15,2)
OR
2,15
or 2,-15
it's one of those three. im srry
31, 92, 25, 69, 80, 31, 29
Median
Mode
Range
Answer:
Median: 31
Mode: 31
Range: 67
Step-by-step explanation:
Median: To find the median, we first need to arrange the numbers in order from smallest to largest:
25, 29, 31, 31, 69, 80, 92
The middle number is 31, so the median is 31.
Mode: The mode is the number that appears most frequently in the set. In this case, the number 31 appears twice, which is more than any other number. So, the mode is 31.
Range: The range is the difference between the largest and smallest numbers in the set. The smallest number is 25 and the largest number is 92, so the range is:
92 - 25 = 67.
Therefore, the median is 31, the mode is 31, and the range is 67.
Answer:
The median of the given set of numbers is 31, the mode is 31, and the range is 67.
Step-by-step explanation:
To find the median, we need to first arrange the numbers in order from smallest to largest:
25, 29, 31, 31, 69, 80, 92
There are seven numbers in the list, which means the middle number will be the fourth number: 31.
Therefore, the median is 31.
To find the mode, we need to determine which number appears most frequently in the list.
In this case, the number 31 appears twice, which is more than any other number in the list.
Therefore, the mode is 31.
To find the range, we need to subtract the smallest number from the largest number. The smallest number is 25 and the largest number is 92, so the range is:
92 - 25 = 67
Therefore, the range is 67.
Find the focus, directrix, focal diameter, vertex and axis of
symmetry for the parabola:
18.8y x²
=
The focus is
The directrix is
The focal diameter is
The vertex is
The axis of symmetry is
[tex] \\ 7 \sqrt{ \\ + 45)4} [/tex]
Samir:
-My parents never invested because they said it was too risky and you should try to avoid risk at all costs when it comes to your money. They want me to just keep my money in a savings account because it's FDIC insured.
-I have a part-time job. After I pay for necessities, save for my emergency fund, and save for senior graduation dues, I only have about $30 left that I could invest per month. I'm thinking I should wait until I'm older and make some more money before I really start investing.
-I don't know anything to invest IN! Could you help me understand some of my options about where to invest?
-I have never been a very risky guy (I always order vanilla ice cream at the shop), so the idea of putting all my investments at risk makes me a little nervous. Is there any way to avoid that feeling?
-How do I know what investments to choose for my portfolio? There are so many options, and I don't want to make the wrong choice!
Outline your advice to Samir. Be sure to address the needs and concerns he brought up and to include the following...
A. WHY could investing be a good idea for Samir? Support your advice with at least one graph or mathematical example demonstrating how his investments could grow.
B. WHAT types of products could Samir invest in?
C. How can Samir go about CHOOSING investments?
Investing could help you grow your funds over time. For example, if you were to invest $30 per month in a stock mutual fund that has a long-term average annual return of 8%, after 10 years, your investment could grow to about $5,000.
This could provide you with more financial security and give you the opportunity to reach your financial goals faster than keeping your money in a savings account.
Some investment products that you could consider are stocks, bonds, mutual funds, and exchange-traded funds (ETFs). You could also consider robo-advisors, which use algorithms to create and manage investment portfolios for you based on your goals and risk tolerance.
When it comes to choosing investments, there are a few things you can consider. First, think about your financial goals and your time horizon. This will help you determine how much risk you can afford to take on.
Thus, if you have a long-term goal, such as saving for retirement, you may be able to afford to take on more risk than if you have a short-term goal, such as saving for a down payment on a house.
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5. Select all expressions that are equivalent to 3^8.
A. 3^2x3^4
B. 3²x3^6
C. 3^16/3^2
D. 3^12/3^4
E. (3^4)²
F. (3¹)^7
The expressions that are equivalent to 3^8 are:
B 3²x3^6D. 3^12/3^4E. (3^4)²How to solve the expressionsWe have to solve these out
3^8. = 6561
From the options
A. 3^2x3^4
= 9 x 81
= 729
B 3²x3^6
= 9 x 729
= 6561
C. 3^16/3^2
= 43046721/9
= 4782969
d. 3^12/3^4
= 531441 / 81
= 6561
E. (3^4)²
= 3⁴ x 3⁴
= 3⁴⁺⁴
= 3⁸
= 6561
F. (3¹)^7
= 3⁷
= 2187
The expressions that are equivalent to 3^8 are:
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Write a doubling equation for the information in question 4 that will find the number of Covid 19 related deaths for any given day. Then calculate the number of deaths expected 240 days from the 100,000-death mark.
Note that the doubling equation can be written as: y = 1000 * 2⁽ˣ/⁷*⁹⁵⁾
The doubling equation for the information given in question 4 can be written as:
y = 1000 * 2⁽ˣ⁺k⁾
To solve for k, we will use the fasts that:
on 240 days after the 100,000- death mark, there will be 2 million deaths.
2000,000 = 100 * x ^(240/k)
Takin the log of both sides we have:
Log 2 (2,000) =log2 (2^240/k))
⇒ Log 2 (2,000) =240/k * log 2(2)
⇒ log 2 (2000) = 240/k
Making k subjet of the formula, we have
k = 240/log2 2000)
k [tex]\approx[/tex] 7.95
Thus, the doubling equation is y = 1000 * 2⁽ˣ/⁷*⁹⁵⁾
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Full Question:
Although part of your question is missing, you might be referring to this full question:
- We know that the number of deaths is growing exponentially, so we can use the exponential function y = a * bnx to model it. - We also know that on day O, there were 1,000 deaths, and on day 240 after the 100,000-death mark, there will be 2,000,000 deaths. - We can use these two points to solve for a and b.
Write a doubling equation for the information in question 4 that will find the number of Covid 19 related deaths for any given day. Then calculate the number of deaths expected 240 days from the 100,000-death mark.