we have, the equation is of the form
[tex](x-h)^2+(y-k)^2=r^2[/tex]then, first calculate the radius of the circle
[tex]\begin{gathered} r=\sqrt[]{(x2-x1)^2+(y2-y1)} \\ r=\sqrt[]{(14-14)^2+(-8-1)^2} \\ r=\sqrt[]{0+(-9)^2} \\ r=\sqrt[]{81} \\ r=9 \end{gathered}[/tex]so, (h,k) is the center and the equation is
[tex]\begin{gathered} (x-14)^2+(y-(-8))^2=9^2 \\ (x-14)^2+(y+8)^2=81 \end{gathered}[/tex]find the ratio of the primeter to the area of the square
Given data:
The given figure of square.
The perimeter of the square is,
[tex]P=4(x+3)[/tex]The area of the square is,
[tex]A=(x+3)\times(x+3)[/tex]The ratio of the perimeter to the area of the given square is,
[tex]\begin{gathered} \frac{P}{A}=\frac{4(x+3)}{(x+3)(x+3)} \\ =\frac{4}{x+3} \end{gathered}[/tex]Thus, the ratio of the perimeter to the area of the given square is 4/(x+3).
A 7m long ladder leans against a wall such that the foot of the ladder is 4.5m away from the wall. What is the angle of elevation of the ladder?
Given:
• Height of ladder = 7 m
,• DIstance of foot of ladder to the wall = 4.5 m
Let's find the angle of elevation of the ladder.
First sketch the figure representing this situation.
Where x is the angle of elevation of the ladder.
Let's solve for x.
To solve for x, apply the Trigonometric ratio formula for cosine.
[tex]\cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]Where:
• Adjacent side is the side adjacent to the angle x = 4.5
,• Hypotenuse is the longest side = 7
,• θ is the angle = x
Hence, we have:
[tex]\cos x=\frac{4.5}{7}[/tex]Take the cos inverse of both sides:
[tex]\begin{gathered} x=\cos ^{-1}(\frac{4.5}{7}) \\ \\ x=49.9\approx50^o \end{gathered}[/tex]Therefore, the angle of elevation of the ladder is 50 degrees.
ANSWER:
c. 50 degrees
for the function what are the possible values for B if the function is an exponential decay function select the two right answers
In order for the function to represent an exponential decay, the value of b needs to be a value between 0 and 1.
So analysing each value, we have:
√(0.9)
Since 0.9 is lesser than 1, its square root is also lesser than 1, so this is a valid option.
1 1/5
This value is greater than 1, so it's not a valid option.
√e
The value of e is approximately 2.71, so its square root is greater than 1, so it's not a valid option.
2^-1
This value is equal to 1/2, that is, 0.5, so it's lesser than 1, therefore it's a valid option.
2-0.9999
This exp
add.(7k + 3) + (3k + 2)
The rectangle has side length r and s for each expression determine whether it gives the perimeter of the rectangle the area of the rectangle or neither select the correct choice in each row r+s r times s 2r+2a r2+s2
we have the following:
[tex]\begin{gathered} P=2r+2s \\ A=r\cdot s \end{gathered}[/tex]there P is perimeter and A is area
therefore, r + s and r^2 + s^2 are neither
linear equations in deletion method2x + 2y − z = 04y − z = 1−x − 2y + z = 2
The given system is:
[tex]\begin{gathered} 2x+2y-z=0\ldots(i) \\ 4y-z=1\ldots(ii) \\ -x-2y+z=2\ldots(iii) \end{gathered}[/tex]Multipliy (iii) by 2 to get:
[tex]-2x-4y+2z=4\ldots.(iv)[/tex]Add (i) and (iv)
[tex]\begin{gathered} 2x+2y-z=0 \\ + \\ -2x-4y+2z=4 \\ -2y+z=4\ldots(v) \end{gathered}[/tex]Add (ii) and (v) to get:
[tex]\begin{gathered} 4y-z=1 \\ + \\ -2y+z=4 \\ 2y=5 \\ y=\frac{5}{2} \end{gathered}[/tex]Put y=5/2 in (ii) to get:
[tex]\begin{gathered} 4(\frac{5}{2})-z=1 \\ 10-z=1 \\ -z=-9 \\ z=9 \end{gathered}[/tex]Put y=5/2 and z=9 in (i) to get:
[tex]\begin{gathered} 2x+2(\frac{5}{2})-9=0 \\ 2x+5-9=0 \\ 2x=4 \\ x=2 \end{gathered}[/tex]Hence x=2, y=5/2 and z=9.
Hannah bought 3.8 pounds of tomatoes at a farmer's market for $1.45 per pound. How much did Hannah pay for the tomatoes?
Answer:
Hanna would pay $5.51 for the tomatoes.
Step-by-step explanation:
You can multiply 3.8 by 1.45 and that will get you 5.51.
Making 5.51 your total cost.
The amount for 3.8 pounds of tomato is given by the equation A = $ 5.51
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount for the tomatoes be represented as A
Now , the equation will be
The cost of 1 pound of tomatoes = $ 1.45
Now , Hannah bought 3.8 pounds of tomatoes
So , the amount for 3.8 pounds of tomatoes A = 3.8 x cost of 1 pound of tomatoes
Substituting the values in the equation , we get
The amount for 3.8 pounds of tomatoes A = 3.8 x 1.45
On simplifying the equation , we get
The amount for 3.8 pounds of tomatoes A = $ 5.51
Therefore , the value of A is $ 5.51
Hence , the amount is $ 5.51
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А
B
The scale factor that takes A onto B is
The scale factor that takes B onto A is
Let,
x₁, y₁ = 2, 2
x₂, y₂ = 6, 10
a.) The slope of the line.
[tex]\text{ Slope = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{\text{ 10 - 2}}{\text{ 6 - 2}}\text{ = }\frac{\text{ 8}}{\text{ 4}}[/tex][tex]\text{ Slope = 2}[/tex]Therefore, the slope of the line is 2.
b.) The y-intercept of the line.
Substitute slope = m = 2 and x, y = 2, 2 in y = mx + b
[tex]\text{ y = mx + b}[/tex][tex]\text{ 2 = 2(2) + b}[/tex][tex]\text{ 2 = 4 + b }\rightarrow\text{ b = 2 - 4}[/tex][tex]\text{ b = y-intercept = -2}[/tex]Therefore, the y-intercept is -2.
For us to answer the other 2 questions, let's first complete the equation of the graph.
Substitute slope = 2 and y-intercept = -2 in the y = mx + b
y = mx + b
y = (2)x + (-2)
y = 2x - 2
The equation of the line is y = 2x - 2
c.) Finding the value of a.
x = a
y = 8
We get,
[tex]\text{ y = 2x - 2}[/tex][tex]\text{8 = 2a - 2}[/tex][tex]\text{ 2a = 8 + 2 = 10}[/tex][tex]\text{ }\frac{\text{2a}}{\text{ 2}}\text{ = }\frac{\text{10}}{\text{ 2}}[/tex][tex]\text{ a = 5}[/tex]Therefore a = 5
d.) Finding the value of b.
x = 4
y = b
[tex]\text{ y = 2x - 2}[/tex][tex]\text{ b = 2(4) - 2}[/tex][tex]\text{ b = 8 - 2 = 6}[/tex]Therefore, b = 6
change the quadratic equation from standard from to vertex form
Answer:
[tex]y=\left[x-\left(-2\right)\right]^2+\left(-9\right)[/tex]Explanation:
Given the quadratic equation in standard form:
[tex]y=x^2+4x-5[/tex]1. Transpose the c-value to the left side of the equation.
[tex]y+5=x^2+4x[/tex]2. Complete the square of the expression on the right side of the equation to get a perfect square trinomial. Add the resulting term to both sides.
[tex]\begin{gathered} y+5+(\frac{4}{2})^2=x^2+4x+(\frac{4}{2})^2 \\ \implies y+5+(2)^2=x^2+4x+(2)^2 \end{gathered}[/tex]3. Add the numbers on the left and factor the trinomial on the right.
[tex]$ y+9=(x+2)^2 $[/tex]4. Transpose the number across to the right side to get the equation into the vertex form, y=a(x-h)²+k.
[tex]y=(x+2)^2-9[/tex]5. Make sure the addition and subtraction signs are correct to give the proper vertex form.
[tex]y=\left[x-\left(-2\right)\right]^2+\left(-9\right)[/tex]The vertex form of the given quadratic equation is:
[tex]y=\left[x-\left(-2\right)\right]^2+\left(-9\right)[/tex]
MathTaAngel LoweA coin is tossed. What is the theoretical probability of the coin NOT showing tails?P(Not tails) =
Since is a theoretical probability, the probability of a coin showing heads (no tails) should be somewhere around 50%.
A coin toss has two possible results.
50% tails
50% heads
1. Nasir had 2.45 inches of tape thatwill be divided into 3 pieces. What is the length of each piece round-ed to the nearest hundredth?a. .81b. .82c. 7.35d. 7.36
Answer:
b. 0.82
Explanation:
Nasir had 2.45 inches of tape
The tape will be divided into 3 pieces.
Therefore:
[tex]\text{Length of each piece}=2.45\div3[/tex]Now, we know that:
[tex]\begin{gathered} \frac{245}{3}=81\frac{2}{3} \\ \frac{2}{3}=0.667 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 2.45\div3=0.81667 \\ \approx0.82\text{ }(to\text{ the nearest 100th}) \end{gathered}[/tex]The correct choice is B.
Helpppppppppppppppppp
Answer: The restaurant requires some additional forks in supply, there are currently 287 forks in the restaurant, and there should be at least 732.
The new forks come in sets of 10, the inequality which represents the number of sets that Peyton needs to buy is:
[tex]\begin{gathered} 10x+287\ge732\rightarrow(1) \\ \\ x\rightarrow\text{ Number of fork sets which contain 10 forks} \end{gathered}[/tex]Therefore the inequality (1) represents the number of sets of forks that Peyton needs to buy, the solution for this inequality is as follows:
[tex]\begin{gathered} 10x+287\geqslant732 \\ \\ \\ 10x\ge732-287 \\ \\ \\ 10x\ge445 \\ \\ \\ x\ge\frac{445}{10} \\ \\ \\ x\ge44.5 \end{gathered}[/tex]which is the graph of f(x)=2(3)^2
You have the folowing function:
f(x) = 2(3)ˣ
In order to determine which of the given graph belongs to f(x), you verufy if the given points of the graphs correspond to f(x). You proceed as follow:
For first graph:
x = 1
f(x) = 2(3)¹ = 2(3) = 6
The point is (1,6)
The previous point is the same that the graph has, hence, the first graph belongs to f(x) = 2(3)ˣ
Then, it is not necessary to check the other points becasue they are not agree with f(x)
Claire has 11/12pound of butter. She will use 5 /12 pound of butter to make cookies She estimates she will have 1 /2 pound of butter when she is finished. Is Claire correct?
Explanation:
We have to substract 5/12 from 11/12:
[tex]\frac{11}{12}-\frac{5}{12}=\frac{11-5}{12}=\frac{6}{12}[/tex]And simplify the fraction:
[tex]\frac{6}{12}=\frac{1}{2}[/tex]Answer:
Claire is correct, she'll have 1/2 pound of butter.
D In the diagram, ABDE, ZA ZD, andCAFD What theorem can be used to prove the triangles are congruent? E HL SSA AAS SAS
there are two triangles and
it is given that two sides of both the triangle is equal or congruent
and there is also given that so by side - angle - side the given triangles are congruent
so the answer is SAS.
write the equation of the line that is perpendicular to the graph of y=3/4x-3, and whose y-intercept is -8
write the equation of the line that is perpendicular to the graph of y=3/4x-3, and whose y-intercept is -8
step 1
Find the slope of the given line
y=(3/4)x-3
the slope is m=3/4
step 2
Find the slope of the perpendicular line
REmember that
If two lines are perpendicular, then the product of their slopes is equal to -1 (inverse reciprocal)
so
the slope of the perpendicular line is
m=-4/3
step 3
Find the equation of the line
we have
m=-4/3
y-intercept is -8
so
b=-8
y=mx+b
substitute
y=-(4/3)x-8Part 2
write an equation of the line that is parallel to the graph of y=-4x-9, and whose y-intercept is 3
step 1
Find the slope of the given line
y=-4x-9
the lope is m=-4
step 2
Find the slope of the parallel line
Remember that
If two lines are parallel, then their slopes are the same
so
the slope of the parallel line is m=-4
step 3
Find the equation of the line in slope intercept form
y=mx+b
we ahve
m=-4
b=3
substitute
y=-4x+3Instructions: Find the missing angle. Round your answer to the nearesttenth.
ANSWER
[tex]x=65.9^o[/tex]EXPLANATION
We are given a right-angled triangle.
We have that the hypotenuse is 46.
The side opposite the given angle is 42.
The angle given is x.
To solve this, we can use trigonometric ratios SOHCAHTOA.
We will use the SOH part of it:
[tex]\sin (x)\text{ = }\frac{opposite}{hypotenuse}[/tex]So, we have that:
[tex]\begin{gathered} \sin (x)\text{ = }\frac{42}{46} \\ \sin (x)\text{ = 0.9130 } \\ \text{ Find the sine inverse (sin}^{-1})\text{ of 0.9130 to get x:} \\ x=sin^{-1}(0.9130) \\ x=65.9^o \end{gathered}[/tex]That is the value of the missing angle x.
Solve the compound inequality.3x + 12 ≥ –9 and 9x – 3 ≤ 33 x ≥ –7 and x ≤ –4x ≥ 7 and x ≤ 4x ≥ 1 and x ≤ 4x ≥ –7 and x ≤ 4
To solve this problem, we will solve each inequality for x and the solution to the system will be the intersection of the solution sets.
1) Solving the first inequality for x we get:
[tex]\begin{gathered} 3x+12\ge-9, \\ 3x\ge-9-12, \\ 3x\ge-21, \\ x\ge-\frac{21}{3}, \\ x\ge-7. \end{gathered}[/tex]2) Solving the second inequality for x we get:
[tex]\begin{gathered} 9x-3\le33, \\ 9x\le33+3, \\ 9x\le36, \\ x\le\frac{36}{9}, \\ x\le4. \end{gathered}[/tex]Answer:
[tex]x\ge-7\text{ and x }\le4.[/tex]Find the distance between the points ( 3,1 ) and (9,9). Write answers as a whole number or a fully simplified radical expression. Do not round
The distance between two points (x1, y1) and (x2, y2) can be calculated as follows:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]The points are given: (3, 1) and (9, 9), thus:
[tex]d=\sqrt[]{(9-3)^2+(9-1)^2}[/tex]Operating:
[tex]\begin{gathered} d=\sqrt[]{6^2+8^2} \\ d=\sqrt[]{36+64} \\ d=\sqrt[]{100} \\ d=10 \end{gathered}[/tex]The distance is 10
The u.s system of weighs and measureenter the maximim number of whole feet and then the remaining inches. Simply your answer
One foot is 12 inches. So the maximum number of feet that fit into 78 inches is the quotient of the division of 78 by 12.
[tex]\frac{78}{12}[/tex]The above division gives us 6 whole feet and 6 inches.
Hence, the door is 6 feet and 6 inches high.
2.2Determine the value of n for which (3k - 2) = 70
The value of k is 24.
From the question, we have
(3k - 2) = 70
(3k) = 72
k=24
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
Complete question: Determine the value of k for which (3k - 2) = 70
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2b^2 (3a - 5b +8c)Multiply
Answer
2b² (3a - 5b + 8c)
= 6ab² - 10b³ + 16b²c
Explanation
We are told to multiply 2b² with (3a - 5b + 8c)
2b² (3a - 5b + 8c)
= 6ab² - 10b³ + 16b²c
Hope this Helps!!!
For each table below, describe whether the table represents a function that increasing or decreasing.
To determine the table that represents a function that is increasing, we check if the following holds.
• When x increases, f(x) increases.
In Options A, as x increases, f(x) increases.
In Options B, as x increases, g(x) decreases.
In Options C, as x increases, h(x) decreases.
In Options D, as x increases, z(x) increases.
Therefore, the table that
The 'range' of numbers is the greatest number minus the smallestnumber.OFalseTrue
If a set of numbers is given, then the range is largest number minus the smallest number in the given data set.
So, the given statement is true.
L
For the function, f(x) = 38 • 0.24%, what is the decay factor? A) 38 B) 0.24 C) 0.14 D) 0.76
The decay factor is equal to 24%. In decimal form its equal to 0.24. Hence, the answer is B) 0.24
jared has 12 coin 4th 75 cents. 3 of the coins are worth twice as much as tge rest. construct a math argument to justify the conjecture thqt jared has 9 nickels and 3 dimes
To solve this question, we proceed as follows:
Step 1: Let x be the worth of one of the type of coins Jared has, and let y be the worth of the other type of coin
Thus:
Since 3 of the coins are of a different type, we have that:
[tex]\begin{gathered} 3x+(12-3)y=75 \\ \Rightarrow3x+9y=75 \end{gathered}[/tex]Also, since 3 of the coins are worth twice as much as the rest, we have that:
[tex]x=2y[/tex]Now, substitute for x in the first equation:
[tex]\begin{gathered} 3x+9y=75 \\ \Rightarrow3(2y)+9y=75 \\ \Rightarrow6y+9y=75 \\ \Rightarrow15y=75 \\ \Rightarrow y=\frac{75}{15} \\ \Rightarrow y=5cents \end{gathered}[/tex]Since y = 5 cents, we have that:
[tex]\begin{gathered} x=2y \\ \Rightarrow x=2(5) \\ \Rightarrow x=10cents \end{gathered}[/tex]Now, since x = 10 cents (the equivalent worth of a dime), and y = 5 cents (the equivalent worth of a nickel), we have from the first equation that:
[tex]3x+9y=75\text{cents}[/tex]From the above equation, therefore, we can conclude that Jared has nine 10 cents coins (dimes), and three 5 cents coins (nickels)
Alice traveled 30 miles in 3 hours. What graph shows the relationship between time traveled in hours and total miles traveled?The graph shows the relationship between the number of hours that Michelle has been driving and the distance that she has left to travel to get to her destination. Which statement is true? It took Michelle 6 hours to complete the trip. For each hour that Michelle drove, she traveled an additional 50 miles. In the first 6 hours, Michelle had traveled a total of 50 miles. In the first 3 hours, Michelle had traveled a total of 200 miles.
Given that Alice traveled 30 miles in 3 hours. Initially, the distance traveled is 0 miles.
Take distance on the x-axis and time on the y-axis.
From the given information, the two points on the graph are (0,0) and (30,3).
Mark the points on the graph.
The distance-time graph of a body is a straight line. Join the points by a straight line to get the required graph.
Area of a triangle = 16ft²B = 4ftH = ?
Given:
Area of a triangle, A = 16 ft²
Base of the triangle, b = 4 ft
Height of the triangle, h, is unknown.
To find the height of the triangle, h, apply the formula below:
[tex]A=\frac{1}{2}b\times h[/tex]Rewrite the formula for h.
Multiply both sides by 2:
[tex]\begin{gathered} 2A=\frac{1}{2}b\times h\times2 \\ \\ 2A=b\times h \end{gathered}[/tex]Divide both sides by b:
[tex]\begin{gathered} \frac{2A}{b}=\frac{b\times h}{b} \\ \\ \frac{2A}{b}=h \\ \\ h=\frac{2A}{b} \end{gathered}[/tex][tex]h=\frac{2A}{b}[/tex]Where,
A = 16 ft²
b = 4 ft
Substitute values into the formula and evaluate.
We have:
[tex]\begin{gathered} h=\frac{2A}{b} \\ \\ h=\frac{2(16)}{4} \\ \\ h=\frac{32}{4} \\ \\ h=8\text{ ft} \end{gathered}[/tex]Therefore, the value of h is 8 ft
ANSWER:
H = 8 ft
In the year 2010, Xavier's car had a value of $22,000. When he bought the car in 2006 he paid $28,000. If the value of the cardepreciated linearly, what was the annual rate of change of the car's value? Round your answer to the nearest hundredth if necessary.
The annual rate of change is given by:
[tex]A\mathrm{}R\mathrm{}C=\frac{f(b)-f(a)}{b-a}[/tex][tex]\begin{gathered} A\mathrm{}R\mathrm{}C=\frac{22000-28000}{2010-2006} \\ A\mathrm{}R\mathrm{}C=\frac{-6000}{4}=-1500 \end{gathered}[/tex]Hence, the annual rate of change is -1500 dollars/year, meaning the car depreciates/loses value by an amount of 1500 dollars
In the figure, segment RS bisects segment DE at S. Given that DS=4x+12 andSE=8x-8, find the value of x.
Step 1: Let's recall that a segment bisector is a ray or segment which cuts another line segment into two equal parts.
Step 2: Upon saying that, we have:
DS = SE
Step 3: Replacing with the equation we have to solve for x:
4x + 12 = 8x - 8
4x - 8x = - 8 - 12
-4x = -20
Dividing by - 4
-4x/-4 = -20/-4
x = 5
Step 4: If x = 5, let's find the length of DS and SE:
4 * 5 + 12 = 8 * 5 - 8
20 + 12 = 40 - 8
32 = 32
Step 5: x = 5 and DS/SE = 32