Answer: Area = 4 square units
Perimeter of the rectangle = 8x - 14 units
Length of the rectangle = x - 5 units
Let the width of the rectangle = x units
Perimeter = 2( length + width)
8x - 14 = 2(x - 5 + x)
Solve the parenthesis for once
8x - 14 = 2(x + x - 5)
8x - 14 = 2(2x - 5)
8x - 14 = 4x - 10
Collect the like terms
8x - 4x = -10 + 14
4x = 4
Divide both sides by 4
4x/4 = 4/4
x = 1
Since, the length is x - 5 units
Length = 1 - 5
Length = - 4units
Length = 4 units
Width = 1 unit
Area = length x width
Area = 4 x 1
Area = 4 square units
The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 17 HCF of water is $32.13 and the cost for using 35 HCF IS 61.83. . What is the cost for using 19 HCF of water?
If the cost for using 35 HCF IS 61.83. . the cost for using 19 HCF of water is :$68.31.
How to find the cost price?Straight line: y=mx+b, m=slope, b=y-intercept
Let y=cost of using 19 HCF water
Let x =amount of water used
m=∆y/∆x =(61.83 - 32.13) / (35-19)
m=∆y/∆x =29.7 /16
m=∆y/∆x = 1.85625
m=∆y/∆x = 1.86 ($/HCF) (approximately)
equation: y=1.86x+b
Solving for b using point (19, 32.13)
32.13 =1.86×19+b
32.13=35.34+b
b=35.34 -32.13
b=3.21
equation:
f(x)=1.86x+3.21
f(25)=1.86×35+ 3.21
= 68.31
Cost of using 35 HCF water= $68.31
Therefore the cost price is $68.31.
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The angle between 0° and 360° and is coterminal with a standard position angle measuring 1652° angle is ______ degrees.
Please help me find the answer for the blank.
Answer:
212°
Step-by-step explanation:
Keep subtracting 360 from 1652 until you get a number under 360
You are offered two different sales jobs. The first company offers a straight commission of 6% of the sales. The second company offers a salary of $ 270 per week plus 2% of the sales. How much would you have to sell in a week in order for the straight commission offer to be at least as good?
One needs to sell $6750 worth of goods to make the straight commission be at least good to the secondary offer
Straight offer = 6% commission on the sales
Second offer = $270 + 2% of the sales
For the straight offer to be competitive with the second offer it should be able to cover the fixed income of $270
Let x be the sales made in the week
Formulating the equation we get the following:
6% of x = 270 + 2% of x
6/100x = 270 + 2/100x
4/100x = 270
x = 6750
So, for sales up to $6750, the second job offer is good, while for sales more than $6750 the first job offer is good
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perfect pizza has 16 Toppings
listed on their menu how many ways can a customer choose a piece of that contains five different toppings
Factorial five. Factorial 16-5. And the response to this question is 4368. There are therefore 4000 368 options for these pizzas with five toppings.
The sum of all positive integers less than or equal to n, indicated by the symbol n!, is the factorial of a non-negative integer n. Additionally, the factorial of n is equal to the sum of n and the subsequent smaller factorial: For instance, According to the convention for an empty product, the value of 0! is 1. The mathematical operation known as a factorial, denoted by the symbol (! ), multiplies a number (n) by each number that comes before it. The factorial function instructs you to multiply all the whole numbers starting at the selected number and going all the way down to one. In further mathematical terms, a number's factorial (n!) equals n (n-1)
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what number is not part of the solution set for the inequality below?3x-18> 1210, 11, 15,8 _
First, let's solve for x in the inequality to find an interval, the options that are not included in the interval are not part of the solution set, we can do it by following these steps:
1. 3x-18> 12 , add 18 on both sides:
3x - 18 + 18 > 12 + 18
3x > 30
2. Divide both sides by 3:
3x/3 > 30/3
x > 10
So, to be a part of the solution, x must be greater than 10, then the interval that represents the solution is (10, ∞). From the given options, the only one that is not included in this interval is 8, because it is less than 10, then the answer is 8.
help!!! please see image, thanks
The smallest whole numbers that makes the statement true are:
(a) 41 - 9 ≡ 2 (mod 5)
(b) 17 + 8 ≡ 4 (mod 7)
Let a, b and m be integers. Then a is said to be congruent to b modulo m if m divided a-b. That is,
a ≡ b(mod m) if and only if m divided a-b.
Also here, if b is the smallest integer satisfying this relation, then b is the remainder when a is divided by m.
(a) So for 41 - 9 ≡ (mod 5)
⇒ 32 ≡ (mod 5)
The smallest whole number satisfying this congruence is the remainder when 32 is divided by 5 which is 2.
That is, 41 - 9 ≡ 2 (mod 5)
(b) Similarly for 17 + 8 ≡ (mod 7)
⇒ 25 ≡ (mod 7)
The smallest whole number which makes this statement true is the remainder when 25 is divided by 7, which is 4.
Hence, 17 + 8 ≡ 4 (mod 7)
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A school is installing a flagpole in the central plaza. The plaza is a square with side length 100 yards as shown in the figure below. The flagpole will take up a square plot in the middle of the plaza and its base will have an area of x2−10x+25 yd2. Area of the flagpole plot: x2−10x+25 A plaza square with a small flagpole square in the middle. 100 yards100 yards Find the length of the base of the flagpole by factoring. (Hint: Because the area of the flagpole is an expression that involves the variable x, the length of the base will also involve the variable x.) The length of the base of the flagpole is
The area of the flagpole is:
[tex]x^2-10x+25[/tex]This represents a perfect square, because it can be represented as below:
[tex]x^2-2\cdot5+5^2[/tex]Therefore we can use the notable product, square of the difference to factor the expression:
[tex](x-5)^2=(x-5)\cdot(x-5)[/tex]Since the area of the flagpole is the product between it's length and width, then we know that the length and width are equal and are equivalent to:
[tex]\text{length}=\text{width}=(x-5)[/tex]Find the exact value of the indicated trigonometric function of θ.
cos θ = (2/5), tan θ < 0 Find sin θ.
The exact value of indicated trigonometric function, sin θ is -0.92
How to find a sine relation when a cosine relation is given?The sine relation is the ratio of the height to the hypotenuse. Meanwhile, the cosine relation is the ratio of the base to the hypotenuse.
The relation of sine and cosine is given as follows:
[tex]\sin \theta=\pm\sqrt{1-\cos^2\theta}[/tex]
It is given that cos θ = (2/5)
So, the sine value can be obtained from the given value.
[tex]\sin \theta=\pm\sqrt{1-\cos^2\theta}\\=\pm\sqrt{1-(2/5)^2}\\=\pm\sqrt{21}/5\\ =-0.92[/tex]
So, the sine value for the given cosine value is - [tex]\sqrt{21}/5[/tex] or -0.92.
Note that we omitted the positive value because it is given that the tangent value is negative, so the angle lies in the fourth quadrant, where the sine value is also negative.
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A is the point (-6, 5) and B is the point (-2,-3). (a) Find the equation of the straight line, I, that passes through point A and point B. Give your answer in the form y=mx+c.
The linear equation that passes through the point (-6, 5) and B is the point (-2,-3) is:
y = -2x - 7
How to find the linear equation?
A general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:
s = (y₂ - y₁)/(x₂ - x₁)
In this case, we have the points (-6, 5) and (-2,-3), then the slope is:
s = (-3 - 5)/(-2 + 6) = -8/4 = -2
Then we have:
y = -2*x + c
To find the value of the constant we use one of the points, I will use (-2, -3) to get:
-3 = -2*(-2) + c
-3 = 4 + c
-3 - 4 =c
-7 = c
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A pole that is 3.1 m tall casts a shadow that is 1.46 m long. At the same time, a nearby tower casts a shadow that is 38.5your answer to the nearest meter.long. How tall is the tower RoundIM
82 meters
Explanation
Step 1
Draw:
as the angle of the sun´s ligth is the same for both, we have two congruent trianges, then we can make a proportion
[tex]\text{ratio}=\frac{heigth}{\text{shadow}}[/tex]so
[tex]\begin{gathered} \text{ratio}_1=ratio2 \\ \text{replacing} \\ \frac{3.1}{1.46}=\frac{x}{38.5} \\ to\text{ solve, multiply both sides by 38.5} \\ \frac{3.1}{1.46}\cdot38.5=\frac{x}{38.5}\cdot38.5 \\ 81.74\text{ m=x} \\ \text{rounded} \\ x=82 \end{gathered}[/tex]therefore, the heigth of the tower is
82 meters
The perimeter of a rectangular field is 338 yards. If the width of the field is 77 yards, what is its length?
2(l+b)=338 2(l+77)=338
154×l=338 l=338÷154=2ans
Answer:
The length is 92 yards.
Step-by-step explanation:
Just use the rectangle perimeter formula and substitute the given values.
P=2l+2w Rectangle formula
We know the perimeter and the width already.
So, 338=2L+2(77)
Now solve:
338=2L+154
338-154=2L
184=2L
184/2=L
92=L Answer
find x=___°please help
Step 1: We have two triangles with the following information:
• Upper Triangle has two known angles: 29 and 52 degrees
,• Lower Triangle has one known angle: 33 degrees and two unknown: x and the third angle
Step 2: Let's find the third angle of the upper triangle, as folllows:
Third angle = 180 - 29 - 52
Third angle = 99
Step 3: Now we can see that the angle we just found on Step 2 is a congruent angle with the third angle from the lower triangle, which means they are equal.
Therefore, we know two angles of the lower triangle:
99 and 33
With these measurements, we can calculate x, as follows:
x = 180 - 99 - 33
x = 180 - 132
x = You can calculate the difference now
Determine the intercepts of the line
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
Since the number of years must be non-negative, we can eliminate all the options except for d.
The graph of a function g is shown below.
Find g (-4)
Are the following ratios equivalent?5cookies:9 glasses of milk and 3 cookies :12 glasses of milk
Answer:
No
Step-by-step explanation:
5:9 and 3:12 do not divide with the same number
For example:
3:6 and 9:18 would be equivalent as dividing 9:18 by 3 would give 3:6
What’s the correct answer answer asap for brainlist
Answer:
B
Step-by-step explanation:
Answer: B. Symbolic - the "Queen" represents suppression and deceit.
Express 55 miles per hour in kilometers per hour.km/hr(Round to the nearest whole number as needed.)
Okay, here we have this:
Considering the provided amount in miles per hour, we are going to convert it to kilometers per hour, so we obtain the following:
[tex]\begin{gathered} \frac{55mi}{h}\cdot\frac{1.6km}{1mi} \\ =\frac{55\cdot1.6km}{h} \\ =88\frac{\text{ mi}}{h} \end{gathered}[/tex]Finally we obtain that 55 miles per hour are equivalent to 88 kilometers per hour.
Find the surface area of the prism. 5 m 1 1 4646 om 13 m Not drawn to scale 195 m2 O 48 m2 780 m2 346 m2
Prism surface is formed by
2 rectangles x and 2 rectangles y ,2 rectangles z
then
Area of rectangles for x= 2x13x6 = 156 m2
. For y = 2x5x6= 60 m2
. For z = 2x13x 5 = 130 m2
Then now add all these results
Prism area = 156 + 60 + 130 = 346
Then answer is
OPTION D) 346 m2
What is the rate of return when 12 shares of Stock
A, purchased for $22/share, are sold for $465? The
commission on the sale is $9.
Rate of Return = profit or loss
total cost
First, calculate the total cost.
Hint: 12 shares were purchased for $22
each. So first, we'll multiply 12 - 22.
12- $22= $[?]
The rate of return of the 12 shares purchased by A is 72.72%.
Here, we are given that A purchases 12 shares at $22 per share.
So the cost price of 12 shares will be = 12 × 22
= 264
A sold these shares at $465.
The commission on sale = $9.
Thus, the total cost of the shares will be = 264 + 9
= $273
Hence, the total profit of A will be-
465 - 273
= 192
The rate of return is calculated as-
Rate of return = profit/cost price × 100
Thus, here-
Rate of return = 192/264 × 100
= 0.7272 × 100
= 72.72%
Thus, the rate of return on these 12 shares purchased by A is 72.72%.
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Which term describes the slope of the line below?
•
A. Undefined
B. Zero
• C. Positive
D. Negative
Answer:
D. Negative
Step-by-step explanation:
The slope is negative because the line goes down from left to right. In other words, as x increases, y decreases.
A slope would be positive when the line goes up from left to right. In other words, as x increases, y increases.
A slope would be zero if the line is horizontal, so as x increases, y remains constant.
A slope would be undefined if the line is vertical. It is undefined because x remains constant while y changes. Lines are functions, which mean for every input there is exactly 1 output. If there are multiple y values for 1 x value, then this is not a function and therefore has an undefined slope.
Write in terms of the cofunction of a complementary angle.
given the expression
[tex]sin(\frac{\pi}{15})[/tex]since
[tex]sin(\theta)=\frac{1}{csc(\theta)}=cos(\frac{\pi}{2}-\theta)[/tex]then
[tex]s\imaginaryI n(\frac{\pi}{15})=\frac{1}{csc(\frac{\pi}{15})}=cos(\frac{\pi}{2}-\frac{\pi}{15})[/tex][tex]s\imaginaryI n(\frac{\pi}{15})=\frac{1}{csc(\frac{\pi}{15})}=cos(\frac{(15-2\pi)}{30})[/tex][tex]s\imaginaryI n(\frac{\pi}{15})=cos(\frac{13\pi}{30})[/tex]ten the correct answer is
Option C
Choose the function whose graph is given below. 1 į į NA 5 in A. Y= CSC X B. y= tan x O c. y = sec x OD. y = cotx
In the picture there is graph. The graph has a function is y=secx. The option c is correct.
Given that,
In the picture there is graph.
We have to find the graph has a function.
The graph is of y=secx.
Secant will not present at
x = - 5∏/2 , - 3∏/2 , -∏/2 , ∏/2, 3∏/2 , 5∏/2
At certain places, the graph will also include asymptotes. The graph of the secant on the range of - 5∏/2 is shown below. - 5 ∏/2
The graph also always has a value greater than 1 and less than -1. It shouldn't come as a huge surprise. Keep in mind that -1≤ cos (x)≤ 1. One will be more than one when divided by a number that is less than one. Additionally, 1 / ±1 = ±1, therefore we obtain the following secant ranges.
We can write as sec(x)≥1 and sec(x)≤-1
Therefore, the graph has a function is y=secx. The option c is correct.
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HELPPPPP. will give brainliest
Answer:
The maximum value is the same for both functions
Step-by-step explanation:
f(x) maximum is (0,5)
g(x) maximum is (2,5)
Answer:
The maximum value is the same for both functions.
Please give me brainlist!!!
Hypothesis p is false and conclusion q is false. So, the statement
∼q⟶p
True or false
If the Hypothesis p is false and conclusion q is false then the disjunction ∼q⟶p is false.
What is conjunction?In classic propositional logic, a conjunction is a binary operator, that is, used to connect two propositions. A conjunction between two propositions is always true if and only if each of the two propositions are also true, otherwise the compound proposition is false.
Logic Disjunction; consider p and q are propositions.
The dis-junction of p and q, is denoted by p ∨ q, is the proposition called "p or q".
The rule for the 'or' operation would be; If any of the propositions are true, then the result is true.
Thus, If the Hypothesis p is false and conclusion q is false then the disjunction ∼q⟶p is false.
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I need to check my answer for number 1 I put C.
Given
[tex]f(x)=3(\frac{1}{2})^x[/tex]Find
Plot the graph
Explanation
To plot the graph we need points ,
let
[tex]undefined[/tex]use the distribution method to solve the system of equations. enter your answer as an ordered pair. y=7x+6 and y=x+20
y = 7x+6
y = x + 20
Substituting the value of y of the second equation into the first equation, we get:
x + 20 = 7x + 6
20 - 6 = 7x - x
14 = 6x
14/6 = x
7/3 = x
Replacing this value into the first equation, we get:
[tex]\begin{gathered} y=7\cdot\frac{7}{3}+6 \\ y=\frac{49}{3}+6 \\ y=\frac{49+6\cdot3}{3} \\ y=\frac{67}{3} \end{gathered}[/tex]The solution as an ordered pair is (7/3, 67/3)
The weight of a goat increased by 12 pounds is 38 pounds. Which equation represents the situation?
Given that the weight of goat increased by 12 pounds to be 38 pounds.
It means that the weight became 38 pounds after attaining an extra 12 pounds to its initial weight.
Suppose that 'x' is the initial weight of the goat, then adding 12 to is will become 8,
[tex]x+12=38[/tex]Therefore, the third option is the correct choice.
How do I solve for the role of 0 in this equation?(x²-9)(x³-8)=0
Given the equation
[tex](x^2-9)\cdot(x^3-8)=0[/tex]you should have in mind that the expression x^2-9 and x^3-8 are "numbers" and that the product of two numbers is zero if and only if one of the numbers is zero. Then, by using this, you get the following auxiliary equations
[tex]x^2-9=0[/tex]which is equivalent to
[tex]x=\sqrt[]{9}[/tex]so x=3 o x=-3.
Finally, for the other case
[tex]x^3-8=0[/tex]So
[tex]x=\sqrt[3]{8}=2[/tex]so the three possible solutions for the equation are x=3, x=-3 and x=2
Which expression is missing from step 7?
OA.(d- e)²
OB. -2de
OC. (A+B)2
OD. A²+ B²
The correct option A. (d- e)², is the expression is missing from step 7.
What is termed as the Pythagorean theorem?The Pythagorean theorem, or Pythagorean theorem, tries to explain the relationship among the three sides of such a right-angled triangle. The square on the hypotenuse is equal to the total of the squares of the remaining two sides of a triangle, according to Pythagoras' theorem. According to Pythagoras' theorem, when a triangle has been right-angled (90 degrees), the square of the hypotenuse equals the sum of the squares of the remaining two sides.For the given question.
The missing value of the 7th term is -
(√1 + d²)² + (√e² + 1)² = (d- e)²
Such that the 8th terms becomes after squaring the both sides are;
(1 + d²) + (e² + 1) = d² + e² - 2de.
Thus, the missing term in the step 7 is (d- e)².
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