What is the slope of the line given by the equation below?
y-20 = 5(x-2)
Answers
Answer:
5
Step-by-step explanation:
first you need to simplify this equation and put it in slope intercept form which is y = mx + b
after simplifying you will get y = 5x + 10
since the slope is m , the answer will be 5
Related Questions
A rectangular solid (with a square base) has a surface area of 337.5 square centimeters. Find the dimensions that will result in a solid with maximum volume.
Answers
We are given the following information:
rectangular solid with a square base
surface area = 337.5 cm^2
We are asked to find the dimensions that will give us the maximum volume.
First, we need to represent the dimensions of the given solid. If x = the side of the square base, then we can represent the height as:
\(\begin{gathered} SA=2(lw+lh+wh) \\ SA=2(x^2+xh+xh) \\ SA=2(x^2+2xh) \\ 337.5=2(x^2+2xh) \\ 168.75=x^2+2xh \\ 168.75-x^2=2xh \\ \frac{168.75-x^2}{2x}=h \end{gathered}\)So we can express the volume of the solid figure as:
\(Volume=f(x)=(x)(x)(\frac{168.75-x^2}{2x})\)Simplifying the equation, we get:
\(\begin{gathered} f(x)=\frac{x(168.75-x^2)}{2} \\ f(x)=\frac{1}{2}(168.75x-x^3) \\ \\ f(x)=84.375x-0.5x^3 \end{gathered}\)To find the maximum value of x, we will calculate the derivative of f(x).
\(f^{\prime}(x)=84.375-1.5x^2\)Then, we will find the value of x that will make f'(x) = 0.
\(\begin{gathered} 0=84.375-1.5x^2 \\ -84.375=-1.5x^2 \\ 56.25=x^2 \\ x=\pm7.5 \end{gathered}\)But because x represents the side of the square base, then we can only accept x = 7.5.
That gives us the height of:
\(\begin{gathered} h=\frac{168.75-7.5^2}{2(7.5)} \\ \\ h=\frac{168.75-56.25}{15} \\ \\ h=\frac{112.5}{15} \\ \\ h=7.5 \end{gathered}\)So, the dimensions of the solid figure must be 7.5 cm x 7.5 cm x 7.5 cm.
How many times larger is (1.092 × 101) than (7 × 10−1)?
The answers: A. 0.156 B. 15.6 C. 6.41 D. 6.908
please helpppppppp
Answers
The correct option is A. 0.156. The number (1.092×10¹) is 156 times larger than number (7×10⁻¹).
What is defined as the scientific notations?Scientific notation is a method of writing extremely large or extremely small numbers. Whenever a number among 1 and 10 is multiplied by a power of 10, it is written in scientific notation. 650,000,000, for example, can be composed in scientific notation as 6.5× 10⁸.Scientific notation is a method of writing extremely large or extremely small numbers in a way that makes them easier to read as well as work with. A number is expressed as the product of an amount that is equal to one but less than ten and an integral power of ten.For the given number;
The number 1.092×10¹ can be written as; 10.92 after multiplication with 10.
Similarly, the number 7×10⁻¹ can be written as 0.7 after diving with 10.
Now, divide larger number by 0.7
= 10.92/0.7
= 156
Thus, the number 1.092×10¹ is almost 156 time greater than (7×10⁻¹).
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The annual rate, r, it takes for 1 dollar to grow to X dollars in 2 years is given by the formula X = (1+r) ².
Find the rate necessary for a dollar to triple in 2 years.
Answers
The rate of interest is 73%.
What is the annual rate?
The term annual percentage rate of charge refers to the interest rate for an entire year rather than just a monthly fee or rate as applied on a loan, mortgage loan, credit card, etc. It can also be referred to as a nominal APR or an effective APR. It is an annual rate of a finance charge.
Given that 1 dollar to grow to X dollars in 2 years is given by the formula X = (1+r) ².
A dollar to triple in 2 years.
Thus putting X = 3 in X = (1+r) ²
3 = (1+r) ²
Take square root on both sides:
√3 = 1 + r
Subtract 1 from both sides:
r = √3 - 1
r = 0.73
r = 73%
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if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30
i need helppppp plzzzzz ?!
Answers
Answer:
157 cm³
Step-by-step explanation:
Given
height (h) = 6 cm
radius (r) = 5 cm
π = 3 . 14
Now
Volume of cone
= 1/3hπr²
= 1/3 * 6 * 3.14 * 5²
= 2 * 3.14 * 25
= 157 cm³
Hope it will help :)
The winner of a 100 mile race drove his car to victory at a rate of 120.1229 mph. What was his time to the nearest thousandth of an hour)?
His time was hours.
(Round to the nearest thousandth.)
Answers
Answer:
\(t=1.201\ \text{hour}\)
Step-by-step explanation:
Given that,
Distance, d = 100 mile
Velocity of the winner, v = 120.1229 mph
We know that velocity of an object is equal to distance per unit time. Let t is the time. So,
\(v=\dfrac{d}{t}\\\\t=\dfrac{d}{v}\\\\t=\dfrac{120.1229}{100 }\\\\t=1.201229\ \text{hour}\\\\\text{Round to the nearest thousandth}\\\\t=1.201\ \text{hour}\)
Hence, 1.201 hour is taken by the winner.
. At a certain airport, 75% of the flights arrive on time. A sample of 10 flights is studied. a. Find the probability that all 10 of the flights were on time.
Answers
Answer:
0.5256
Step-by-step explanation:
X ~ B(10,0.75)
q = 1 - 0.75 = 0.25
A function is shown in the table. which equation represents this function?
X: 0,5,10,15
Y: 8,-7,-22,-37
Answers
The equation that represents this function is y = -3x + 8
How to determine which equation represents this function?From the question, we have the following parameters that can be used in our computation:
X: 0,5,10,15
Y: 8,-7,-22,-37
A linear relation is represented as
y = mx + c
Where
c = y when x = 0
Using the above as a guide, we have the following:
c = 8
So, we have
y = mx + 8
Using the points on the table, we have
5m + 8 = -7
This gives
5m = -15
m = -3
So, the function is
y = -3x + 8
Hence, the function is y = -3x + 8
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-2|10 + 5x|-8=-16
How do I solve?
Answers
Answer:
so the answer is
x = -6/5, - 14/ 5
Step-by-step explanation:
i hope this is what your looking for
Answer:
5/6 and -26/5
Step-by-step explanation:
-16 divide -2 = 8
Add 8 = 16
Remove absolute value
Positive 16 - 10 = 6
Divide 5 = 6/5
Negative -16 - 10 = -26
Divide 5 = -26/5
PLZ HELP ME WHAT IS THE ANSWER FOR THIS PLZ I WILL MARK BRAINLIEST!!!
Answers
Answer:
B.Andrew will have 0 points
C.4+(-4) is an expression showing how Andrew gained 4 points but lost 4 points
Step-by-step explanation:
If you add 4 for the first round then take away 4 from the second round you get 0.
The 4+ shows that Andrew gained 4 points in the first round but in the second he lost 4 points.
Let f(x) = −x^2 and g(x) = 1/√x. Find formulas for f ◦g and g◦f and state the domain of each composition. I only need the domains if possible.
Answers
Answer: see below
Step-by-step explanation:
\(f(x)=-x^2\qquad g(x)=\dfrac{1}{\sqrt x}\)
\(f og(x)=f\bigg(\dfrac{1}{\sqrt x}\bigg)\\\\.\qquad =-\bigg(\dfrac{1}{\sqrt x}\bigg)^2\quad \\\\.\qquad =-\dfrac{1}{x}\\\\\text{Domain:}\ x>0\)
\(gof(x)=g(-x^2)\\\\.\qquad =\dfrac{1}{\sqrt{-x^2}}\\\\.\qquad =\dfrac{1}{xi}\\\\\text{Domain: Does Not Exist since result is an imaginary number}\)
A package of self-sticking notepads contains 6 yellow, 6 blue, 6 green, and 6 pink notepads. An experiment consists of randomly selecting one of the notepads and recording its color. Find the sample space for the experiment.
Answers
Answer:
24
Step-by-step explanation:
becuse 6+6+6+6=24
A student purchased 9 binders for $11.07.
Use the drop down to answer the question.
Which equation can be used to find the cost of each binder, b, in dollars?
Answers
Answer:
11.07/9
Step-by-step explanation:
Math
(Diversifying Portfolios MC)
worth points)
Name of Stock Symbol High Low Close
Stock A
105.19 103.25 103.38
Stock B
145.18 143.28 144.05
A
B
Last year, an investor purchase
difference in overall loss or ga
O The difference in overall gain is $207.00.
O The difference in overall loss is $207.00.
O The difference in overall loss is $200.70.
O The difference in overall gain is $200.70.
shares of stock A at $90 per share and 75 shares of stock B at $145 per share. What is the
ween selling at the current day's high price or low price?
Answers
The difference in overall gain between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price is $239.50.
To determine the difference in overall gain or loss between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price, we need to calculate the selling prices of the stocks.
Stock A:
High price = $105.19
Low price = $103.25
Close price = $103.38
Stock B:
High price = $145.18
Low price = $143.28
Close price = $144.05
The investor purchased 50 shares of stock A at $90 per share and 75 shares of stock B at $145 per share.
To calculate the selling prices, we need to multiply the number of shares by the respective selling price.
Selling price of stock A at the high price: 50 shares \(\times\) $105.19 = $5,259.50
Selling price of stock A at the low price: 50 shares \(\times\) $103.25 = $5,162.50
Selling price of stock B at the high price: 75 shares \(\times\) $145.18 = $10,888.50
Selling price of stock B at the low price: 75 shares \(\times\) $143.28 = $10,746.00
Now, let's calculate the difference in overall gain or loss:
Difference in overall gain = Selling price at the high price - Selling price at the low price
= ($5,259.50 + $10,888.50) - ($5,162.50 + $10,746.00)
= $16,148.00 - $15,908.50
= $239.50
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The value of a machine depreciates at the rate of 10% per annum. It was purchased 3 years ago. If its present value is Rs 43740, find its purchase price.
pls anwer in details! no spam...
Answers
Given
present value of the machine : Rs 43,740Rate of depreciation per annum : 10%To find
Purchase value of the machine ( 3 years before )Let the purchase value be P,
ATQ,
P -3 x 0.1P = Rs 43,740
P-0.3P = Rs 43,740
0.7P = Rs 43,740
P = Rs 43,740/0.7
P = Rs 62,486 (approx)
Hence, the purchase value of the machine would be Rs 62,486
Part 2: Identify key features and graph a circle from general form.
Answer the following questions to determine the key features of the circle whose equation is shown
and then graph it.
x2 + y2 + 12x-2y - 12 = 0
a) Write the equation of the circle in standard form. (3 points)
b) What is the center of the circle? (1 point)
c) What is the radius of the circle? (1 points)
d) Sketch a graph of the circle and label the center and the endpoints of the horizontal and
vertical diameter. (4 points)
Answers
Answer:
Subtract
12
from both sides of the equation.
x
2
+
y
2
−
12
x
+
2
y
=
−
12
Complete the square for
x
2
−
12
x
.
Tap for more steps...
(
x
−
6
)
2
−
36
Substitute
(
x
−
6
)
2
−
36
for
x
2
−
12
x
in the equation
x
2
+
y
2
−
12
x
+
2
y
=
−
12
.
(
x
−
6
)
2
−
36+y2+2y=−12
Move
−36
to the right side of the equation by adding
36
to both sides.
(x−6)2+y2+2y=−12+36
Complete the square for
y2+2y.
Tap for more steps...
(y+1)2−1
Substitute
(y+1)2−1
for
y2+2y
in the equation
x2+y2−12x+2y=−12.
(x−6)2+(y+1)2−1=−12+36
Move
−1
to the right side of the equation by adding
1
to both sides.
(x−6)2+(y+1)2=−12+36+1
Simplify
−12+36+1.
Tap for more steps...
(x−6)2+(y+1)2=25
This is the form of a circle. Use this form to determine the center and radius of the circle.
(x−h)2+(y−k)2=r2
Match the values in this circle to those of the standard form. The variable
r
represents the radius of the circle,
h
represents the x-offset from the origin, and
k
represents the y-offset from origin.
r=5 h=6 k=−1
The center of the circle is found at
(h,k).
Center:
(6,−1)
These values represent the important values for graphing and analyzing a circle.
Center: (6,−1)
Radius:
5
image of graph
Step-by-step explanation:
Answer:
A) (x+6)^2 + (y-1)^2 =49
B) (-6, 1)
C) Radius of 7
D) I’ll try to add picture
Step-by-step explanation:
hotomath
Part A : 5x+3 = 7x-1
Part B: 5x + 2(x+7) = 14x -7
Part C: 5(z+1) = 3(z+2) + 11
Answers
2.) 3
3.) 6
mark me please !
Answer:
Part A: x=2
Part B: x=3
Part C: z=1
Step-by-step explanation:
Part A:
like terms...
5x+3=7x-1
-5x -5x
solve...
3=2x-1
+1 +1
4=2x
/2 /2
2=x
Part B:
use distributive property first...
5x+2x+14=14x-7
like terms...
7x+14=14x-7
-7x -7x
Solve...
14=7x-7
+7 +7
21=7x
/7 /7
3=x
Part C:
use distributive property first...
5z+5=3z+17
like terms...
5z+5=3z+17
-3z -3z
solve...
2z+5=17
-5 -5
2z =2
/2 /2
z=1
the graph below has the same shape as the graph g(x)=x^2 but it is shifted down 3 units and to the left 2 units what is this equation
Answers
Answer:
Option (C)
Step-by-step explanation:
Parent function g(x) = x² [Vertex at the origin (0, 0)]
When this function is shifted 3 units down,
Rule to be followed,
g(x) → g(x) - 3
So, g'(x) = x² - 3
Followed by 2 units shift to the left,
Rule to be followed,
g'(x) → g'(x + 2)
F(x) = (x + 2)² - 3
Therefore, Option (C) will be the answer.
step 1: find the factors of ac that add up to b. ac=6(−10)=−60 b=−11 the factors of −60 that add up to −11 are and . step 2: rewrite the trinomial with the x-term expanded, using the two factors from step 1. 6x2−11x−10 (6x2− )+( −10) step 3: group the first two and second two terms together, find the gcf and factor again. (2x−5)+ (2x−5
Answers
Answer:
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=6⋅−10=−60 and whose sum is b=−11
.
6x2+4x−15x−10
Factor out the greatest common factor from each group.
2x(3x+2)−5(3x+2)
Factor the polynomial by factoring out the greatest common factor, 3x+2
.
(3x+2)(2x−5)
Put the following equation of a line into slope-intercept form, simplifying all fractions. 3y-9x=-6
Answers
Answer: y=3x-2
Step-by-step explanation:
3y-9x=-6
First you will need to add 9x to the other side so your equation will look like 3y=9x-6. Then you need to divide all the numbers by 3. So 3y divided by 3 and 9 divided by 3 and -6 divided by 3. Your final answer should be y=3x-2.
Answer:
This equation in slope intercept form would be y = 3x - 2
Step-by-step explanation:
The following is how to solve this equation:
3y - 9x = -6
+9x +9x
----------------------
3y = 9x - 6
divide each of the numbers by 3
So the answer is y = 3x - 2
Find a function of the form
or whose graph matches this one:
Answers
The function whose graph matches this one y= 4 sin (π/7 x) - 2
As, The general form of a sine function is
y= A sin (kx) + C........(1)
From the given graph the maximum value of the function is 2 and minimum value of the function is -6.
So, Amplitude= (Max- Min)/2
A = (2- (-6))/2
A= 8/2
Amplitude= 4
Now, The function complete a cycle in 14 units, so period of the function is 14.
2π/k= 14
k = π/7
and, Midline= (Min + Max)/2 = (2-6)/2 = -2
So, the function is
y= A sin (kx) + C.
y= 4 sin (π/7 x) - 2
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Perform the following operation
and express the answer in
scientific notation.
4.0x105 x 3.0x103
[ ? ]x10!?)
![Perform the following operationand express the answer inscientific notation.4.0x105 x 3.0x103[ ? ]x10!?)](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/vCP9NkRFpIeva1cBbV1pNpUtGHuwVL71.png)
Answers
Answer:
Step-by-step explanation:
first step, multiply 4 and 3
4x3=12 , we write is 1.2x10
10^5 x10^3=10^8
4 x10^5 x 3 x 10^3= 1.2x10^9
The required answer is 1.20 x 10⁹ in scientific notation.
What is scientific notation?Scientific notation is a method of writing extremely large or extremely small numbers. When a number between 1 and 10 is multiplied by a power of 10, it is written in scientific notation.
Here,
To multiply two numbers in scientific notation, we multiply their coefficients and add their exponents. Applying this rule, we get:
= (4.0 x 10⁵) x (3.0 x 10³)
= (4.0 x 3.0) x (10³ x 10⁵)
= 12.0 x 10⁵⁺³
= 12.0 x 10⁸
However, the answer is not yet in proper scientific notation form because the coefficient 12.0 is not between 1 and 10. To express the answer in scientific notation, we need to adjust the coefficient and exponent so that the coefficient is between 1 and 10. We can do this by dividing the coefficient by 10 and increasing the exponent by 1. Doing this, we get:
12.0 x 10⁸ = 1.20 x 10⁹
Therefore, the answer is 1.20 x 10⁹ in scientific notation.
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Triangle ABC, shown in the diagram below, is an isosceles triangle
If the measure of <ABC is 42.5°, what is the measure of <ABC?
Answers
Answer:
A. 42.5
Step-by-step explanation:
The triangle shown is an isosceles triangle. An isosceles triangle haas two of its sides and base angles equal. Hence;
<ACB = <ABC (Base angles are equal)
Given
<ACB = 42.5°
Required
<ABC
According to the law above which says <ACB = <ABC , hence <ABC is also equal to 42.5°
Poindexter's uncle is building a house on land that has been devastated by hurricanes 160 times in the past 200 years. However, there hasn't been a major storm there in 13 years, so his uncle says this is a safe investment. His nephew argues that he is wrong because a hurricane must be due soon. What are the fallacies in the reasoning of both men?
Answers
Both men are committing fallacies in their reasoning. The occurrence of a hurricane on that land cannot be predicted with certainty, and making decisions based on fallacious reasoning can lead to poor outcomes.
What are the fallacies in the reasoning of both men?A fallacy refers to the statement in an argument that makes an error in logic. Fallacies are very dangerous because they lead to incorrect thinking about certain topics and may lead to an incorrect conclusion about that topic most of the time.
The fallacy in Poindexter's uncle's reasoning is known as the fallacy of induction. This fallacy occurs when someone assumes that because a certain event has happened in the past, it is likely to happen again in the future. While it is true that the land has been hit by hurricanes 160 times in the past, it doesn't necessarily mean that it will happen again in the near future.
On the other hand, Poindexter's nephew is committing the fallacy of the Gambler's Fallacy. This fallacy occurs when someone assumes that because something hasn't happened in a while, it is more likely to happen soon. In this case, the nephew assumes that a hurricane must be due soon simply because it hasn't happened in the past 13 years. However, the occurrence of a hurricane is not influenced by the time that has passed since the last one. Each hurricane is a unique event that is not influenced by previous occurrences.
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25.3 + x= 32 what is the answer to this problem
Answers
Answer:
6.7
Step-by-step explanation:
Answer:
6.700
Step-by-step explanation:
hope this helped
The sum of two numbers is 12. The difference of the two numbers is 6. What are the two numbers?
Answers
Answer:
3 and 9
Step-by-step explanation:
x+y=12
y-x=6
y-x=6
+x. +x
y=6+x
x+(6+x)=12
6+2x=12
-6. -6
2x=6
/2. /2
x=3
3+y=12
-3. -3
y=9
Hopes this helps please mark brainliest
Can some one help with this problem
Answers
Step-by-step explanation:
Area of the trapezoid = height x average of bases
area = 4 x (8+13)/2) = 42 in^2
Area of triangle = 1/2 base * height = 1/2 (13-8) * 4 = 10 in^2
4/11 divided by 5/8
Answers
Answer:
4/11 divided by 5/8 is 0.58181818181
Step-by-step explanation:
Answer:
\( \frac{32}{55} \)
= 0.582
Step-by-step explanation:
\( \frac{4}{11} \div \frac{5}{8} = \frac{4}{11} \times \frac{8}{5} = \frac{32}{55}\)
I need the answer fast pls
Answers
amount of money earned last week
arm span
amount of minutes exercised daily
height in inches
hours slept per night
travel time in minutes to school
minutes to cook pasta
school zip id
Tomas is paid $200 for 5 days of work. How much is he paid per day?
Answers
$200/5
40 dollars per day imk if I'm wrong