We have a point A=(7,-3) that is reflected over point C=(6,-5). This means that is refected in an axis that is perpendicular to the segment AC.
The image is point B, and we need to calculate its coordinates.
We can relocate the center of coordinates to point C, do the reflection and then relocate the original center of coordinates.
If now C became the center of coordinates A becomes:
[tex]A^{\prime}=A-C=(7-6,-3-(-5))=(1,2)[/tex]Now, we can reflect it as normal:
[tex]\begin{gathered} (x,y)\longrightarrow(-x,-y) \\ A^{\prime}=(1,2)\longrightarrow B^{\prime}=(-1,-2) \end{gathered}[/tex]Now, we convert this to the original coordinates as:
[tex]B^{\prime}=B-C\longrightarrow B=B^{\prime}+C=(-1+6,-2-5)=(5,-7)[/tex]The point B is (5,-7).
The half life of Pb-210 is 22 years. A decayed animal shows 48% of the original Pb-210 remains; how long has the animal been deceased to the nearest tenth of a year?A .0.01 yearsB. 23.3 yearsC. 0.04 yearsD. 23.29 years
SOLUTION:
Step 1:
In this question, we are given the following:
The half-life of Pb-210 is 22 years.
A decayed animal shows 48% of the original Pb-210 remains;
how long has the animal been deceased to the nearest tenth of a year?
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} From\text{ the question, we can see that:} \\ 0.\text{ 5 = e}^{22k} \\ Making\text{ k the subject of the formulae, we have that:} \\ k\text{ = \lparen}\frac{ln\text{ 0. 5}}{22})\text{ --- equation 1} \end{gathered}[/tex][tex]\begin{gathered} \text{0. 48 = e}^{(\frac{I\text{n 0. 5}}{22})t} \\ Taki\text{ng In of both sides, we have that:} \\ ln\text{ \lparen0. 48 \rparen= \lparen}\frac{ln\text{ 0. 5}}{22}\text{ \rparen t} \end{gathered}[/tex][tex]Multiply\text{ both sides by \lparen}\frac{22}{ln\text{ 0. 5 }})\text{ , we have that:}[/tex][tex]\begin{gathered} \text{t = \lparen ln 0.48 \rparen }\times\text{ \lparen}\frac{22}{ln\text{ 0. 5 }}) \\ t=\text{ 23.29566} \\ t\approx\text{ 23.29 years \lparen OPTION D \rparen} \end{gathered}[/tex]
CONCLUSION:
The final answer is:
[tex]\text{t }\approx\text{ 23. 29 years \lparen OPTION D \rparen}[/tex]at a local gym you can either pay $90 for money pass then pay for dollars each time you go to the gym or you can pay $13 each time you go with no monthly pass fee what is the cost where the two options are the same?
Option A
$90 + $4 each time
Option B
$13 each time
Procedure
Equations
[tex]\begin{gathered} (1)\to C=90+4t \\ (2)\to C=13t_{} \\ \\ 90+4t=13t \\ 13t-4t=90 \\ 9t=90 \\ t=\frac{90}{9} \\ t=10 \end{gathered}[/tex]The cost would be
[tex]\begin{gathered} C=90+4\cdot10 \\ C=90+40 \\ C=130 \end{gathered}[/tex]The answer would be $130
Find the range of the function Find the x and y intercepts
For the function f(x) to be greater than 0 (f(x) > 0), we need to identify those regions strictly above the x-axis.
From the graph, these regions are (in interval notation):
[tex]\begin{gathered} R_1=(-6,-1) \\ \\ R_2=(4,6\rbrack \end{gathered}[/tex]For each region there is an inequality:
[tex]\begin{gathered} R_1:-6\lt x\lt-1 \\ \\ R_2:4\lt x\leqslant6 \end{gathered}[/tex]The domain is the set of x-values the function takes. Then, from the graph, we can see that the function is defined from x = -7 to x = 6. The domain of f(x) is:
[tex]Dom_f={}\lbrace x|-7\leqslant x\leqslant6\rbrace[/tex]The range is the set of y-values the function takes. From the graph, we see that the function has a minimum of -8 and a maximum of 12. Then, the range is:
[tex]Ran_f={}\lbrace y|-8\leqslant y\leqslant12\rbrace[/tex]For the x-intercepts (points with y = 0), we have:
[tex]-6,-1,4[/tex]For the y-intercept (the point with x = 0):
[tex]-4[/tex]Factor the polynomial completely.
5x2 + 3x - 14
Group of answer choices
(x - 7)(5x + 2)
(x - 2)(5x + 7)
prime polynomial
(x + 2)(5x - 7)
[tex]5 {x}^{2} + 10x - 7x - 14 \\ = (5 {x}^{2} + 10x) - (7x + 14) \\ = 5x(x + 2) - 7(x + 2) \\ = (x + 2)(5x - 7)[/tex]
LAST OPTION IS THE ANSWER.
Please just answer part B And please explain every step and how its simplified so I can understand better.
Given that
We have to find the inverse of a function and the function is
[tex]g(x)=2^{x-1}[/tex]Explanation -
The steps to find the solution are -
(1). First, we will consider the function equal to y as
[tex]\begin{gathered} g(x)=y \\ x=g^{-1}(y)----------(i) \\ y=2^{x-1} \end{gathered}[/tex](2). Now from this, we will find the value of x in terms of y.
And we will take the base of the log as 2 because the x is in the power of 2. As an exponential function.
As
[tex]\begin{gathered} y=\frac{2^x}{2} \\ Taking\text{ the }\log_2\text{ on both sides we have} \\ \log_2y=\log_2(\frac{2^x}{2}) \\ \log_2y=\log_22^x-\log_22 \\ \\ Using\text{ the formulae of log,} \\ \begin{equation*} \log_a(\frac{b}{c})=\log_ab-\log_ac \end{equation*} \\ \log_aa^p=p\times\log_aa \\ and\text{ }\log_aa=1 \\ \\ Now,\text{ } \\ \log_2y=\log_22^x-1 \\ \log_2y=x\log_22-1 \\ \log_2y=x-1 \\ x=\log_2y+1 \end{gathered}[/tex](3). Now from eq (i) we have
[tex]g^{-1}(y)=\log_2y+1[/tex](4). At last, we will replace y with x. Then,
[tex]g^{-1}(x)=\log_2x+1[/tex]Final answer -
The final answer is [tex]g^{-1}(x)=\log_2x+1[/tex]What is the range for the distance between A and C
The range of distance from A to C is greater than 12.3 feet and less than 32.1 feet.
What is the Triangle inequality Theorem?To precisely state the dimensions of a triangle's sides, the triangle inequality theorem is a crucial component of geometry.
According to this rule, a triangle's third side must be longer than the sum of its other two sides.
Say, AB, BC, and CA make up three of the sides of the triangle ABC.
The length of (AB + BC) must therefore be longer than CA according to the triangle inequality theorem.
As a result, CA > (AB + BC).
The sum of the lengths of BC and CA must exceed the length of AB.
As a result, AB > (BC + CA).
The sum of the lengths of AB and CA must exceed the length of BC.
Consequently, (AB + CA) > BC.
As per the question:AB = 22.2 feet
BC = 9.9 feet
Taking AB as the longest side of the triangle.
The measure of AB must be less than the sum of AC and BC.
⇒ AC < AB + BC
⇒ AC < 22.2 + 9.9
⇒AC < 32.1 feet
Therefore, the range of distance from A to C is greater than 12.3 feet and less than 32.1 feet.
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The PTA sold 460 t-shirts on Friday
and 310 on Saturday. How many t-shirts did
they sell in all?
What is the area of a square with a side length of 12 units? What is the area of a square with a side length of 2.5 units?
what number 14 is 70 percent of
Answer:
20
Step-by-step explanation:
70% of x = 14
0.7x = 14
x = 14/0.7
x = 20
In a sock drawer there are 8 black socks, 4 red socks and 6 orange socks, none of which are kept in a pair.
What is the probability that you will pull one red sock and one orange sock from the drawer with your first two random selections from the drawer?
Show your answer as decimal number, to two decimal places.
The probability that you will pull one red sock and one orange sock from the drawer will be 0.074, then the decimal number is 0.074.
Its fundamental tenet is that something almost probably will occur. the proportion of positive occurrences to all occurrences. The probability is then stated as,
What is a Probability :Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. Probability measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.
Probability = (Favorable event) / (Total event)
There are 8 black socks,
4 red socks, and
6 orange socks, every one of which is kept individually in a sock basket.
The total number of events will be,
Total number of events = 8 black socks + 4 red socks + 6 orange socks
Total number of events = 18 socks
The probability that you will pull one red sock and one orange sock from the drawer will be given as,
P = (4/18) x (6/18)
P = (2/9) x (6/18)
We can divide the numbers,
P = (2/9) x (1/3)
We can multiply the numbers,
P = 2/27
P = 0.074
Therefore,
The probability that you will pull one red sock and one orange sock from the drawer will be 0.074, then the decimal number is 0.074.
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solve for x5(x-2)^2+4=9
the square root of 1 has 2 solutions: 1 and -1, then:
[tex]\begin{gathered} x_1-2=1 \\ x_1=1+2 \\ x_1=3 \\ or \\ x_2-2=-1 \\ x_2=-1+2 \\ x_2=1 \end{gathered}[/tex]Select all the equations that have the same solution as 2x – 5 = 15. A: 2x = 10 B: 2x = 20 C: 2(x – 5) = 15 D: 2x – 20 = 0 E: 4x – 10 = 30 F: 15 = 5 – 2x
The equation that has same solution as that of equation 2x - 5 = 15 is 2x = 10.
What is an equation?
An equation in mathematics is used to equate two expressions using a equals sign. For example -
x = 4y
3x = 7y
Given is the following equation -
2x - 5 = 15
The solution of the equation will be the value of [x] for which the LHS equals to RHS. On solving -
2x - 5 = 15
2x = 10
x = 5
Only equation [A] has the same solution as that of equation -
2x - 5 = 15
Equation [A] is -
2x = 10
x = 5
Therefore, the equation that has same solution as that of equation 2x - 5 = 15 is 2x = 10.
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You want to build a deck in your back yard. The deck will be 14 feet long and 12 feet wide. If you will put railing along all four sides of the deck, how many feet of railing are needed?A) 26 feetB) 38 feetC) 52 feetD) 104 feet
C) 52 feet
Explanation:
Since the deck will be 14 feet by 12 feet and it has four sides, we can deduce that it's a rectangle.
Therefore all you need to do is sum up all the sides together
14 + 14 + 12 + 12 => 14 * 2 + 12 * 2 = 52 feet
marilee plants a vegetable patch measuring 12 m x 8 m .she plants carrots on half of the patch ,and potatoes on a quarter of the patch each .Calculate the area covered by each type of vegetable?
The area covered by each type of vegetables is 48 meter square and 24 meter square.
What is Area of rectangle?
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.
Area of rectangle = length × breadth
Total Area of rectangle = 12(8) = 96
Half area covered by carrots,
area of carrots patch = 96/2 = 48
area covered by potatoes = 96/4 = 24
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Jaime opens an account with a $400 deposit that earns 7% simple interest annually. She makes no other deposits or withdrawls. This situation can be modeled by {blank} function that grows {blank} each year After 4 years, she earned {blank}. Fill in the blanks.
This situation can be modeled by a linear function that grows at a constant rate each year After 4 years, she earned $112.
What is the interest after four years?Simple interest is the amount of interest that is earned on amount that is deposited or invested. The simple interest earned is a function of the amount invested, interest rate and the duration of the investment.
An amount that earns a simple interest grows linearly and can be modelled using a linear function. A linear function is a function that increases at a constant rate and when it is drawn on graph, it is a straight line.
Simple interest = amount deposited x time x interest rate
$400 x 0.07 x 4 = $112
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do jalapenos come from northeast region
Answer: Jalapeño peppers are a top crop of Mexico and the Southwestern United States, but our Northeast region can produce some of the best jalapeños out there
Step-by-step explanation:
The majority of the U.S. commercial jalapeño supply is grown in New Mexico, Texas, and California
Answer:
No, but they can come from there.
Step-by-step explanation:
help me please
thank you
Answer:
Domain: A, [tex][1, \infty)[/tex]
Range: [tex][-4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Write the following comparison as a ratio reduced to lowest terms.223 inches to 19 feet
Given:
223 inches to 19 feet.
Required:
To write the given comparison as a ratio reduced to lowest terms.
Explanation:
1 feet = 12 inches
19 feet = 228 inches.
So, we get 223 inches to 228 inches and now have to simplify
This is the same as
[tex]\begin{gathered} =\frac{223}{228} \\ \end{gathered}[/tex]Final Answer:
[tex]\frac{223}{228}[/tex]HARVEY HAS KEPT A RECORD OF ALL THE FISH HE CAUGHT IN WILLOW GROVE LAKE. HE HAS CAUGHT, 126 BASS 42 CATFISH 72 BLUE GILL WHAT IS THE EMPIRICAL PROBABILITY THAT THE NEXT FISH HE CATCHES WILL BE A CATFISH?
Given that Harvey caught:
• 126 bass.
,• 42 catfish.
,• 72 blue gill
You need to remember that, by definition, an Empirical Probability can be calculated by dividing the number of times the event occurs by the total number of trials.
In this case, you know that he caught 42 catfish. Therefore, you can identify that:
[tex]Number\text{ }of\text{ }times\text{ }the\text{ }event\text{ }occurs=42[/tex]You can also determine that:
[tex]Total\text{ }number\text{ }of\text{ }trials=126+42+72=240[/tex]Therefore, you can determine that the Empirical Probability that the next fish Harvey catches will be a catfish is:
[tex]P(E)=\frac{42}{240}=\frac{7}{40}=0.175[/tex]Hence, the answer is:
[tex]P(E)=0.175[/tex]Solve the equation for all real solutions. --d2 - 12d + 4 = -6d?
the real solutions for the equation d² - 12 d + 4 = 6 is d = 6 ± √38.
The equation given is:
d² - 12 d + 4 = 6
Subtract 6 from both the sides:
d² - 12 d + 4 - 6 = 6 - 6
d² - 12 d - 2 = 0
solve for the real solutions:
D = b² - 4ac
D = (-12)² - 4(-2)(1)
D = 144 + 8
D = 152
d = 12 ±√152 / 2 (1)
d = 6 ± √38
Therefore, we get that, the real solutions for the equation d² - 12 d + 4 = 6 is d = 6 ± √38.
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A trail mix recipe calls for the following ratios: 21.25 % raisins, 5/9 peanuts, 0.14 chocolate chips, and the rest is made up of chex mix. Approximately what percent is made up of chex mix?
Answer:
11.2%Step-by-step explanation:
Given ratios21.25% raisins,5/9 peanuts,0.14 chocolate chips,x - chex mixSolutionConvert every ratio into percentage and then find the missing value
Peanuts
5/9 = 5/9*100% = 55.55%Chocolate chips
0.12 = 0.12*100% = 12%Chec mix
x = 100% - (21.25% + 55.55% + 12%) = 100% - 88.8% = 11.2%4(x - 2)³6 = √x+4Which statement explains why the solution to the equation is= 4?OA. The x-value of 4 is a x-intercept for both f (x) = (x2)³6and g(x)O B.The x-value of 4 produces the same y-value in both f(x)OC.The x-value of 4 is undefined for both f(x)O D.The x-value of 4 is defined on the graphs of both f (x)===Reset(x-(2)³6and g(x)2)³ - 6and g(x)= √x+4.= √x+4.=Next(22)³6and g(x)=√x+4= √x+4.
Notice that:
[tex]\begin{gathered} (4-2)^3-6=(2)^3-6=8-6=2, \\ \sqrt[3]{4+4}=\sqrt[3]{8}=2. \end{gathered}[/tex]Therefore, the value x=4 is a solution because it produces the same value for both sides of the equation.
Answer: Option B.
If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?48O y - 3 (2)O y = 4g (2)(48)(B)O y--(48)(6)
The phrase y varies directly as x can be understood that y gets bigger when x gets bigger as well, this can be written as,
[tex]\frac{y_1}{x_1}=\frac{y_2}{x_2}[/tex]then, using the point (6,48) find the value when x is 2,
[tex]\frac{48}{6}=\frac{y_2}{2}[/tex]clear for y2,
[tex]y_2=\frac{48}{6}(2)[/tex]Answer:
[tex]y_=\frac{48}{6}(2)[/tex]Given m||n, find the value of x and y 35 need help please
Answer:
x = 35
Step-by-step explanation:
x and 35° are alternate angles and are congruent , then
x = 35
Triangle EFG is translated 3 units to the left. Then the image is dilated by a scale factor of 0.5 to form triangle E''F''G''. The center of dilation is the origin. Vertex E is located at (5, -6). What are the coordinates of vertex E''?
After a translate of 3 units to the left and dilation by a scale factor of 0.5, the coordinate of vertex E'' is (1, -3).
What is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure (object) in the same direction, as well as for the same distance.
Next, we would translate vertex E 3 units to the left by subtracting "3" from the x-coordinate as follows:
Vertex E = (5, -6) → Vertex E" = ((5 - 3), -6) = (2, -6).
Also, we would dilate the image E" by a scale factor of 0.5 as follows:
Vertex E" = (2 × 0.5, -6 × 0.5) → Vertex E" = (1, -3)
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Directions:Fill ih the missing measures.(parallelogram)Area:_Base: 7.4mHeight:9.3m
The formula for the area of parallelogram is,
[tex]A=bh[/tex]Here, b is base and h is height.
Determine the area of parallelogram for b = 7.4 and h = 9.3 m.
[tex]\begin{gathered} A=7.4\cdot9.3 \\ =68.82 \end{gathered}[/tex]So area is 68.82 meter square.
For the attached blue bird, find the quadratic equation written in vertex form
The vertex form of a quadratic equation is expressed as
y = a(x - h)^2 + k
where
h and k are the x and y x and y coordinates of the vertex of the parabola.
a is the leading coefficent
From the information on the graph,
h = 13
k = 13
By substituting these values into the formula,
y = a(x - 13)^2 + 13
On the graph, when x = 26, y = 0
Substituting these values into the equation, we have
0 = a(26 - 13)^2 + 13
0 = a * 13^2 + 13
0 = 169a + 13
169a = - 13
a = - 13/169
a = - 1/13
By substituting a = - 1/13, h = 13 and k = 13 into the verte form equation, the quadratic equation written in vertex form is
y = - 1/13(x - 13)^2 + 13
(a)Linda owns 28 shares of a certain stock. Yesterday the value of each share went up by 4 dollars. What was the total change in value of her shares?
The total change in the value of the shares is $112
Number of shares owned by Linda = 28 shares
The term "value change" describes the adjustment made to the share price to reflect the total number of issued and held by investors shares that are now outstanding. Investors' daily holdings of shares are influenced by changes in supply and demand, which can be periodically changed to keep up with the changes.
Increase in value of each share = $4
The total increase in value of shares = Number of shares*Increase in value of each share
= 28*4
So, the total increase in the shares = $112
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Brand A has a recognition value worth 43$ billion more than brand B. If the total value of these two brands is 107$ billion, find the value of each of the brands.
The value of Brand A is $75 billion and Brand B is $32 billion.
What is an expression?An expression is used to illustrate the relationship between the variables.
Let brand B value = x
Brand A has a recognition value worth 43$ billion more than brand B. This will be x + 45
The total value of these two brands is 107$ billion.
The expression to find the value is for each brand will be:
x + x + 43 = 107
2x + 43 = 107
Collect like terms
2x = 107 - 43
2x = 64
Divide
x = 64/2
x = 32
Brand B is $32 billion
Brand A = x + 43 = 32 + 43 = $75 billion.
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Forearm lengths of men, measured from the elbow to the middle fingertip, are normallydistributed with a mean 18.8 inches and a standard deviation 1.1 inches.If 1 man is randomly selected, what is the probability that his forearm length is below 17
Solution
Part A
What are the parameters?
The parameters are
[tex]\begin{gathered} \operatorname{mean}\text{ = }\mu=18.8 \\ \text{Standard Deviation = }\sigma=1.1 \end{gathered}[/tex]We want to find
[tex]p(\mu<17)[/tex]Part B
Find the z score
The formula to use is given by
[tex]z=\frac{\bar{X}-\mu}{\sigma}[/tex][tex]\begin{gathered} z=\frac{\bar{X}-\mu}{\sigma} \\ z=\frac{17-18.8}{1.1} \\ z=\frac{-1.8}{1.1} \\ z=-1.6363636363 \\ z=-1.64 \end{gathered}[/tex]The construction of the standard normal curve is shown below
Part C
We use the standard normal table (from statistical table)
Thus, From statistical table
[tex]p(z<-1.64)=0.05[/tex]
