Let:
(x1,y1) = (0,4)
(x2,y2) = (4,0)
The slope m is:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1}=\frac{0-4}{4-0}=\frac{-4}{4}=-1 \\ \end{gathered}[/tex]Using the point slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-4=-1(x-0) \\ y=-x+4 \\ \text{ In standard form:} \\ x+y=4 \end{gathered}[/tex]Corey is designing a rectangular garden. the garden's diagonal must be 15.6 feet, and the ratio between the garden's base and height must be 12 : 5. find the length of the garden's base and height.
The base of the garden is 14.4 feet.
The height of the garden is 6 feet.
Given,
Corey is designing a rectangular garden;
The diagonal of the garden = 15.6 feet
Ratio between garden's base and height = 12:5
We have to find the length of base and height of the garden.
Here,
Diagonal of a rectangle, d = [tex]\sqrt{base^{2}+ height^{2} }[/tex]
Base = 12x
Height = 5x
Then,
Diagonal, 15.6 = [tex]\sqrt{(12x)^{2} + (5x)^{2} }[/tex]
15.6 = [tex]\sqrt{144x^{2} +25x^{2} }[/tex]
15.6 = √169x²
15.6 = 13 √x²
15.6 = 13x
x = 15.6/13
x = 1.2
Then,
Base of the garden = 12 x 1.2 = 14.4 feet
Height of the garden = 5 x 1.2 = 6 feet
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What is the domain of f(x)?
(-6 , 6)
[-4 , 5]
[-6 , 6]
(-4 , 5)
Answer:
{−6,−4}
Step-by-step explanation:
the domain is all the x- values of the points.
so -6 and -4 are repeated so they are the domain of the points.
What is the perimeter of this 48" by 60" rug?
the admission fee at an amusement park is $2.00 for children and $7.00 for adults. on a certain day, 299 people entered the park, and the admission fees collected totaled $1573. how many children and how many adults were admitted?
Answer:
104 children and 195 adults
Step-by-step explanation:
let a represent number of adults and c represent number of children , then
a + c = 299 → (1)
7a + 2c = 1573 → (2)
multiplying (1) by - 2 and adding to (2) will eliminate c
- 2a - 2c = - 598 → (3)
add (2) and (3) term by term to eliminate c
5a + 0 = 975
5a = 975 ( divide both sides by 5 )
a = 195
substitute a = 195 into (1) and solve for c
195 + c = 299 ( subtract 195 from both sides )
c = 104
104 children and 195 adults were admitted
Graph the following. y=3-4x
Here Ya Go! :D
Hope this helps! If so, please lmk. Thanks and good luck!
The exponential model A = 64.5 e0.020describes the population, A, of a country in millions, t years after
The exponential model A=64.5e^0.02t describes the population, A of a country in millions, t years after 2003. The population of the country will be 108 million in
we have the expression
A=64.5e^0.02t
For A=108
substitute
108=64.5e^0.02t
108/64.5=e^0.02t
Apply ln both sides
ln(108/64.5)=ln(e^0.02t)
ln(108/64.5)=0.02t(ln(e))
ln(108/64.5)=0.02t
solve for t
t=ln(108/64.5)/0.02
t=26 years
therefore
2003+26=2029
answer is
year 2029Maths problem in indices. Pls help
Answer:
x = 9
Step-by-step explanation:
using the rule of indices
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]5^{x}[/tex] = [tex]\frac{5^{8} }{5^{-1} }[/tex] = [tex]5^{(8-(-1))}[/tex] = [tex]5^{(8+1)}[/tex] = [tex]5^{9}[/tex]
since bases on both sides are equal, both 5 , then equate indices
x = 9
Find the circumcenter of the triangle ABC.
A(-5, -6), B(-8,6), C(-5,6).
The circumcenter is
(Type an ordered pair)
Answer: a b C D
Step-by-step explanation:
I'm stuck with my math word problem pls helped me
2/2
Answer:
A. [tex]\frac{c}{11} *7-48[/tex]
Step-by-step explanation:
Rectangle TUVW with vertices
T(-3,-1), U(0, -2), V(-2, -8), and
W(-5, -7): 90° counterclockwise
T':
U':
V':
W':
for given rectangle TUVW with vertices T(-3,-1), U(0, -2), V(-2, -8), and W(-5, -7): 90° counterclockwise rotation would be,
T': (1, -3)
U': (2, 0)
V': (8, -2)
W': (7, -5)
In this question, we have been given a rectangle TUVW with vertices
T(-3,-1), U(0, -2), V(-2, -8) and W(-5, -7)
We know that for 90° counterclockwise rotation is (x, y) becomes (-y, x)
so, the coordinates of T' would be,
T' = (1, -3)
the coordinates of U' would be,
U' = (2, 0)
the coordinates of V' would be,
V' = (8, -2)
the coordinates of W' would be,
W' = (7, -5)
Therefore, for given rectangle TUVW with vertices T(-3,-1), U(0, -2), V(-2, -8), and W(-5, -7): 90° counterclockwise rotation would be,
T': (1, -3)
U': (2, 0)
V': (8, -2)
W': (7, -5)
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a. cos x b. tan x c. sec x d. cot x Simplify the expression
First, multiply by 1:
cos x * 1 + cos x tan^2 x
Factor cos x out of cos x tan^2 x
cos x * 1 + cos x (tan ^2 x)
Factor again
cos x (1+ tan^2 x)
Rearrange:
cos x (tan^2 x +1 )
Apply Pythagorean identity:
cos x * sec ^2 x
Rewrite Sec x in terms of sin and cos
cos x * (1 / cos x )^2
Apply product rule:
cos x * 1^2 / cos^2 x
cos x * (1/ cos^2 x )
Cancel common factor cos x
1 / cos x
1/cosx = sec x
Answer : sec x (option c)
Y(x)=11 and y(x)=7
1 2
Answer: .63
Step-by-step explanation: y(11)=7
y(11)/11=7/11
2x+y = 2
Step 1 of 2: Determine the missing coordinate in the ordered pair (4, ?) so that it will satisfy the given equation.
Answer:
Substitute x = 4 into the equation to find y.
2(4) + y = 2
8 + y = 2
y = -6
To check if it satisfies the equation, substitute values of x and y into the equation.
2(4) + (-6) = 2
8 - 6 = 2
Since, it satisfies the equation, the missing coordinate is -6.
A technical machinist is asked to build a cubical steel tank that will hold 415 L of water.Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.001 m.
we have
1 cubic meter = 1000 L
x cubic meter = 415 L
then:
[tex]\begin{gathered} 1000\times x=415\times1 \\ 1000x=415 \\ \frac{1000x}{1000}=\frac{415}{1000} \\ x=0.415 \end{gathered}[/tex]The volume of a cube with length x is:
[tex]\begin{gathered} x^3=0.415 \\ \sqrt[3]{x^3}=\sqrt[3]{0.415} \\ x=0.746 \end{gathered}[/tex]answer: The smallest possible inside length of the tank is 0.746 m
i need help with my homework PLEASE CHECK WORK WHEN DONE NUMBER 7
Given:
[tex]\begin{gathered} mean(\mu)=28mpg \\ Standard\text{ }deviation(\sigma)=2mpg \end{gathered}[/tex]To Determine: The percentage with greater than 24mpg
Solution
[tex]Z=\frac{x-\mu}{\sigma}[/tex][tex]\begin{gathered} P(x>Z)=P(x>\frac{24-28}{2}) \\ P(x>Z)=P(x>-2) \end{gathered}[/tex]When you open credit cards at a bank, you initiate a hard inquiry once you apply for credit. If you are approved for a credit card, this counts as a new account. Having too many hard inquiries and new accounts on your credit report lowers your credit score, so you’ll want to be judicious when you apply for additional lines of credit. Let’s say you’re interested in the following credit cards: •Chase Sapphire Reserve•Wells Fargo Propel Card•American Express Blue Cash Everyday •Citi Double Cash Card•Chase Freedom•Chase Amazon Prime Rewards Card•Bank of America Cash Rewards Visa•American Express Platinum Answer the following questions below (show work as applicable, using factorial notation if necessary):Scenario 2: Imagine you would like to apply for three of these credit cards. How many different ways could you apply for three credit cards out of this group, without taking order into account? _____________
Given the credit card options:
• Chase Sapphire Reserve
• Wells Fargo Propel Card
• American Express Blue Cash Everyday
• Citi Double Cash Card
• Chase Freedom
• Chase Amazon Prime Rewards Card
• Bank of America Cash Rewards Visa
• American Express Platinum
Then, there are 8 options.
If you want to apply for 3 credit cards and the order does not matter, you can use combination to see how many options you have.
The formula for combination of r elements out n elements is:
[tex]C(n,r)=\frac{n!}{(n-r)!*r!}[/tex]In this question:
n = 8
r = 3
[tex]\begin{gathered} C(n,r)=\frac{8!}{(8-3)!*3!} \\ C(n,r)=\frac{8!}{5!*3!} \\ C(n,r)=\frac{8*7*6*5!}{5!*3*2} \\ C(n,r)=\frac{8*7*6}{3*2} \\ C(n,r)=56 \end{gathered}[/tex]Answer: 56 ways.
Find the value of x in each case. Please put statement reasons.
Answer:
x = 10°
Step-by-step explanation:
Given the figure with angles 2x, 4x, 5x, and 50° marked, you want to find the value of x.
Development∠HAC = ∠HCA . . . . base angles of isosceles triangle HAC
2(∠HAC) = 4x . . . . . exterior angle 4x is equal to the sum of the equal remote interior angles HAC and HCA
∠HAC = 2x . . . . . . . divide by 2
∠AED = 180° -2x -2x = 180° -4x . . . . sum of angles in ∆AED is 180°
∠AHC = 180° -4x . . . . angles at H are a linear pair
HC ║ ED . . . . converse of corresponding angles theorem
∠FEG = ∠FCH = 50° . . . . . corresponding angles theorem
5x = 50° . . . . . substitute value of ∠FEG
x = 10° . . . . . divide by 5
Using this value for the marked angles, we get the measures shown in the attachment.
What angle does a 3.8 m ladder make with the ground if it reaches 2.1 m up the wall? How far is the foot of the ladder from the wall? (Give your answers to the nearest degree and the 1 decimal place of the metre.)
Answer:
here is the answer hop it helps mark me the brainliest
Which set of points would NOT define a function? A) {(-2,-2), (-1,-1), (0, 0), (1, 1), (2, 2)} B) {(-2,9), (0, 1), (1,0), (3, 4), (4,9)} C) {(-1,0), (0, 1), (0, -1), (3, 2), (3,-2)} D) {(-6, 2), (-5, 1), (-4,0), (-3, 1), (-2, 2)}
In order to a set o points define a function, a value of x can't have two different values of y.
Looking at every option, we have in the option C that the value of x = 0 has two different values of y (1 and -1), therefore this set of points do not define a function.
So the answer is C.
Ken wants to install a row of ceramic tiles on a wall that is 21 3/8 inches wide each tile is 4 1/2 inches wide how many whole dose he need
the width of the wall is 21 3/8 = 171/8
the width of a tile is 4 1/2 = 9/2
so the number of tiles is
(171/8) / (9/2) = 171x2 / (9 x8) = 4.75
so the no of tiles needed is 5.
the altitude of an airplane is decreasing at a rate of 45 feet per second what si the change in altitude of the airplane over a period of 34 seconds
a -1,530
b 79
c -79
d 1530
Answer:
Step-by-step explanation:
d that the answer pls mark me brianlest
URGENT 50 points
WRITE AS AN ORDER OF OPERATIONS EXPRESSION, THEN SIMPLIFY IT.
Chloe owed the bank $3500 after taking out a small loan. She currently works and
makes $24 per hour. She works for 6 hours a day. After 25 days, will Chloe still owe the
bank money?
Answer:
She will no longer owe the bank any money. She will have 100 dollars in profit.
Step-by-step explanation:
$24 x 6 hours a day means she makes 144 dollars a day.
144 dollars times 25 means she makes 3600 dollars over the 25 day period.
3600-3500(the amount she owed) is 100 dollars
what’s the answer to this?
The correct option is B: They both are correct. The function g is the function f translated 4 units and it is also the function f translated 4 units to the left.
What is referred as the translation?In geometry, translation refers to a function that shifts an object a specified distance. The component is not otherwise altered. It has not been rotated, mirrored, or resized.When performing a translation, this same initial object is referred to as the pre-image, as well as the object after translation is referred to as the image.for the given question.
The parent function is f(x) = x + 1.
The translated function is g(x).
As, it is shown in the graph that there is a shift of 4 units up as well as 4 units to the left of the original line.
It mean both Veronica and Drawn are correct.
Thus, The function g is the function f translated 4 units and it is also the function f translated 4 units to the left.
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1.2.1 The number of pieces of ropes for FIVE cuts. 1.2.2 The general formula (Ta), for the number of rope pieces. 1.2.3 How many rupe cuttings will make up 153 rope pieces? 1.2.4 How many ropes pieces will result from 11 cuttings? 5 Please tu
Step 1
The number of pieces for 5 cuts is
[tex]7+4=11[/tex]Step 2
The general formula Tn, for the number of rope pieces is
[tex]\begin{gathered} a=3 \\ d=2 \\ T_n=3+(n-1)2 \\ T_n=2n+1 \end{gathered}[/tex]Step 3
How many rope cuttings will make up 153 rope pieces
[tex]\begin{gathered} 153=2n+1 \\ 152=2n \\ \frac{152}{2}=\frac{2n}{2} \\ n=76\text{ rope cuttings} \end{gathered}[/tex]Step 4
How many ropes pieces will result from 11 cuttings
[tex]\begin{gathered} T_n=2(11)+1 \\ T_n=23\text{ rope pieces} \end{gathered}[/tex]the difference between 5 more than x and twice x is 17
Answer:
x = -12
Step-by-step explanation:
Hello!
The sentence can be represented as (x + 5)-(2x) = 17.
We can solve for x by isolating the variable.
Solve for xx + 5 - 2x = 17-x + 5 = 17-x = 12x = -12The value of x is -12.
the registrar of a college examined the grade point averages of different categories of students. the results showed that the probability of a meaningful difference between men and women was .27. using the most common standard, is this a statistically significant difference?
The difference of 0.27 is not statistically significant.
A statistically significant difference indicates if the responses of one group differ significantly from those of another when using statistical testing.
The statistically significant differences between the numbers really aid in your data analysis. It is up to you how to interpret or act on your results, therefore you should also think about if they are significant.Let's imagine, for instance, that you get more consumer complaints from women than from men. How do you know that this is a genuine issue that has to be addressed? To find out if your male consumers are significantly more satisfied with your goods, doing a poll is a terrific technique. Our statistical significance tool can assist you in determining whether males are considerably more satisfied with your goods than women using a statistical formula. This enables you to base decisions on facts rather than anecdotes.Now we know that any data of t-statistic that is greater than 1.96 is statistically significant.
Now the difference is 0.27. Hence it is not statistically significant.
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Which of the following could be the first step when solving the equation 4-3(x+6)=28
Answer:
I don't know the options, but the first step would definitley be distributing the -3 over the parantheses --> -3x - 18
If you love codes answer this question!
Answer:
Is it B
Step-by-step explanation:
Question 19:
1 2 2 4 8 32 ?
Answer:
256
Step-by-step explanation:
1,2,2,4,8,32
1*2=2
2*2=4
4*2=8
8*4=32
632*8=256
Create an equivalent expression for 17^-7 • 17^5.
1/17²
1/17-²
17²
-17²
Please please pleaseee! I’m so dead if I don’t get this!
The equivalent expression for the indices is 17⁻⁷ × 17⁵ is 1/17²
How to create an equivalent expression for 17⁻⁷ × 17⁵?Index is the power or exponent which is raised to a number or a variable e.g in number 3⁵, 5 is the index of 3. The 3 is called the base. The plural form of index is indices.
We have different Laws of Indices, but the one applicable to this question is the product law and reciprocal law.
Product law: To multiply two variables or numbers with the same base, we need to add their powers and raise them to that base": 5² x 5³ = 5²⁺³ = 5 and P⁴ + P⁶ = P¹⁰
Reciprocal Law: If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable:
8⁻² = 1/8² and b⁻⁶ = 1/b⁶
Let's use the two laws to create an equivalent expression for 17⁻⁷ × 17⁵:
17⁻⁷ × 17⁵ = 17⁻⁷ ⁺ ⁵ = 17⁻² = 1/17²
Therefore, the equivalent expression for 17⁻⁷ × 17⁵ is 1/17². The 1st option is the answer.
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