Describe all numbers x that are at a distance of 4 from the number 7.Express this using absolute value notation.
SOLUTION:
Step 1:
In this question, we are given the following:
Describe all numbers x that are at a distance of 4 from the number 7.
Express this using absolute value notation.
Step 2:
The details of the solution are as follows:
Given:
Number x at a distance of 4 from the number 7.
Calculation:
The given statement is the numbers x are at a distance of 4 from the
number 7;
The number x at a distance of 4 is:
[tex]y\text{ = }\lvert{x}\rvert\text{ + 4}[/tex]x at a distance of 4 from the number 7;
[tex]y\text{ = }\lvert x-7\text{ }\rvert\text{ + 4}[/tex]CONCLUSION:
Thus, the absolue value equation is:
[tex]y\text{ = }\lvert{x-7}\rvert\text{ + 4}[/tex]What is the function g(x) that results when translating the function f(x) = |x| to the left 12 units and reflecting it over the x-axis?
Answer: Translation up 5 units means g(x)=f(x)+5g(x)=f(x)+5. Reflecting this across the x-axis means g(x)=-(f(x)+5)g(x)=−(f(x)+5).
-(4x+5)=-4x-5
−(4x+5)=−4x−5
Step-by-step explanation:
Answer:
g(x) = -|x + 12|
Step-by-step explanation:
Translation to left ≡ f(x + 12)
f(x + 12) = | x + 12 |
Reflection of a function f(x) about the x - axis is keeping the x value same but negating the y values
Reflected f'(x) = -y = -f(x)
Taken together
g(x) = -(|x + 12|)
A worker assembles 5.4 products per hour. At this rate how many products will she assemble in a year if she works 40 hours per week and gets two weeks of vacation each year? (Assume no holidays.) A) 432 products B) 2,700 products C) 5,400 products O D) 10,800 products
we have:
5.4 products per hour
1 year = 52 weeks
40 hours -----> 1 week
x hours -------> 50 weeks
[tex]\begin{gathered} x\times1=40\times52 \\ x=2000 \end{gathered}[/tex]she works 2080 hours per year
then,
5.4 products ----> 1 hour
y products -------> 2000 hours
[tex]\begin{gathered} y\times1=5.4\times2000 \\ y=10800 \end{gathered}[/tex]answer: D. 10,800 products
Raven goes to the salon to get a $50 haircut and has a coupon for 15% off. What will be the cost of her hair cut after the discount from her coupon?
Cost of hair = $50 - discount
discount = 15% of $50
[tex]\begin{gathered} =\text{ }\frac{15}{100}\text{ x 50} \\ =\text{ }\frac{750}{100} \\ \text{Discount = \$7,5} \end{gathered}[/tex]Therefore,
Cost of haircut = $50 - $7.5
= $42.5
In the news, you heard tuition is expected to increase from the current per cost $950 to $2,350 over the next ten years. This represents a __% increase from the current Tuition
ANSWER
[tex]147.37\%[/tex]EXPLANATION
To find the percentage increase in the tuition, we have to find the difference between the new tuition and the old tuition and divide it by the old tuition.
Therefore, we have that:
[tex]\%_{inc}=\frac{N-O}{O}\cdot100[/tex]Therefore, the percentage increase is:
[tex]\begin{gathered} \%_{inc}=\frac{2350-950}{950}\cdot100 \\ \%_{inc}=147.37\% \end{gathered}[/tex]That is the answer.
Select the correct answer from each drop menu Short answers only and this time also not a test
The parent function f(x) has a horizontal asymptote located at:
[tex]y=0[/tex]Since g(x) has the horizontal asymptote located at:
[tex]y=3[/tex]We can conclude that g(x) is the result of translate f(x) 3 units up, therefore:
[tex]g(x)=\frac{1}{x}+3[/tex]Answer:
k = 3
Ma Baker's Pies charges $12 for a pumpkin pie and $14 for an apple pie. Last week, they sold athird as many pumpkin pies as apple pies, for a total of $5,400. How many pumpkin pies were soldlast week ?
the third part can be expressed as x / 3 of pumpkins with a value of 5,400
[tex]undefined[/tex]The graph below shows Carlos’s speed on his trip to school. Which segment on the graph shows Carlos’s speed decreasing most rapidly? A. Segment CB. Segment EC. Segment FD. Segment I
Explanation
In the graph we can see different speeds Carlos used on his way to school, subdivided into different segments.
The segment on the graph that depicts Carlos's speed decreasing the most rapidly is given by the segment with the steepest look. By steepest look, this implies that the segment rises of falls sharply, in a form that is almost perpendicular.
Therefore, the right segment will be
Answer: Segment E
A metallurgist has one alloy containing 43% aluminum and another containing 63% aluminum. How many pounds of each alloy must he use to make 43 pounds of a third alloy containing 49% aluminum? (Round to two decimal places if necessary.)
We will need a weight of 30.1 pounds of alloy having 43% aluminium and 12.9 pounds of alloy with 63% aluminium to make a 43 pounds of alloy containing 49% aluminium.
Let The weight(in pounds ) of first alloy be x.
So, The weight(in pounds ) of second alloy will be 43-x.
Now, we can generate the typical mixture in a linear equation as
0.43(x) + 0.63 (43-x) = 0.49(43)
0.43(x) + 0.63 (43) - 0.63(x) = 0.49(43)
0.63(43) - 0.49 (43) = 0.63(x)-0.43(x)
0.43(63-49)= (0.63-0.43)x
0.43(14)=0.2x
x = 30.1 pounds
So, We can say that we will need a weight of 30.1 pounds of the alloy with 43% aluminium and 12.9 pounds of alloy with 63% aluminium.
Learn more about linear equation here
https://brainly.com/question/18751934
#SPJ1
formula de la rotacion?
Answer:
Índice de rotación de personal= (A+D)/PE
Siendo A, el número de personas contratadas durante el período considerado. D, las personas desvinculadas durante el mismo período. PE, es el » promedio efectivo» del período considerado
Step-by-step explanation:
hope it helps have a nice day
Solve for y.Simplify your answer as much as possible 6y+34+3y=7
To solve the given equation for y, first, we add like terms:
[tex]\begin{gathered} 6y+34+3y=7, \\ 9y+34=7. \end{gathered}[/tex]Subtracting 34 from the equation, we get:
[tex]\begin{gathered} 9y+34-34=7-34, \\ 9y=-27. \end{gathered}[/tex]Finally, dividing by 9, we get:
[tex]\begin{gathered} \frac{9y}{9}=-\frac{27}{9}, \\ y=-3. \end{gathered}[/tex]Answer: [tex]y=-3.[/tex]A. 110 degreesB. 180 degrees C. The measure of the angle can not be determined D. 70 degrees
Given:
[tex]\angle4=70[/tex]To find
[tex]\angle5[/tex]Since the vertically opposite angles are equal.
So,
[tex]\angle4=\angle7=70[/tex]Then, the corresponding angles are equal.
Therefore,
[tex]\angle7=\angle5=70^{\circ}[/tex]Thus, the measure of angle 5 is 70 degrees.
Elmer is checking the distance between two landmarks on a map. The map uses a scale in which 2 inches equals 100 feet. If the actual distance between the landmarks is 7300 feet, how far is it between the landmarks on the map, in inches? Your answer can be exact or rounded to two decimal places. label optional
Desmond bets his buddy Calvin that he can calculate the height of the Cullison Monumentwithout googling it to find out. At 1:30 PM, Desmond measures the monument's shadow(22.5 feet) and Calvin's shadow (3.5 feet). If Calvin is 6.25 feet tall, use similar triangles toestimate the height of the monument.
Step 1
At 1:30 pm
Monument's shadow= 22.5 feet
Calvin's shadow =3.5 feet
Calvin is 6.25 feet tall
a) for the monument
shadow= adjacent side=22.5 ft
hypotenuse= unknow=h1
height of the monument = opposite side= y1
b) for Calvin
shadow= adjacent side=3.5 ft
hypotenuse= unknow=h2
height of the Calvin = opposite side= 6.25
Step 2
those triangles are similar, so the ratio between the shadow and the height must be constant, so
[tex]undefined[/tex]The
Sugar Sweet Company is going to transport its sugar to market. It will cost $3500 to rent trucks plus $175 for each ton of sugar transported. The total cost C (in dollars), for transporting tons is given by the following.
C=3500+175n
Answer the following questions.
(a) If the total cost is $7350, how many tons is the company transporting?
____ tons
(b) What is the total cost of transporting 13 tons?
$___
Answer: A. 22 tons B. $5775
Step-by-step explanation:
Substitute the values in for C.
Let's start with part a
7350 = 3500+175n
-3500 -3500- Subtract 3500 from both sides to isolate the 175n
----------------------------------------
3,850=175n
divide 175n from both sides to simplify it using the division property of equality
And you get 22=n!
So since n is each ton of sugar transporting, it's 22 tons being transported
FOR PART B
Substitute 13 tons for n since they're asking how many tons
Multiply 175 and 13 to get 2275
Add 2,275 and 3,500 to get 5775
Since they're asking for the amount in dollars, just say $5775
Hope I helped!! Have a wonderful day :))
Suppose your friend is trying to answer the following question:"How many centimeters are in 4.7 meters?"Your friend knows there are 100 cm in 1 m, exactly. Yet, when they solve the problem, they got an incorrect answer of "0.047 cm." Explain what they may have done wrong and how you could help them fix their mistake.
we know that
1 m=100 cm
so
to convert 4.7 meters to cm
Multiply 4.7 by 100
4.7*100=470 cm
Your friend instead of multiplying 4.7 by 100, divide 4.7 by 100
Cindy and Cora are going to a movie. Cindy forgot her money and is going to pay Cora back later. The cost of the two tickets is $16.50 and a bucket of popcorn is $3.66. What is the total cost that Cora will pay for two tickets and one bucket of popcorn?
Answer: I think 10.08
$16.50 and a bucket of popcorn is $3.66
$16.50 + $3.66 = 20.16
20.16/2= 10.08
I need help please. I can’t do this I’m so lost!
To solve for the angles in a parallel line:
For a pair of parallel lines:
Corresponding Angles are equal m<1 = m<5 = 143°
Alternate Interior Angles are equal m<4 = m<6
Alternate Exterior Angles are equal m<2 = m<8
Consecutive Interior Angles add up to 180° m<3 + m<6 = 180
... then the lines are Parallel
[tex]\begin{gathered} m<5+m<6=180 \\ 143+m<6=180 \\ m<6=180-143 \\ m<6=37^0 \end{gathered}[/tex]Therefore the consecutive interior angles add up to 180
[tex]\begin{gathered} m<3+m<6=180 \\ m<3+37=180 \\ m<3=180-37 \\ m<3=143^0 \end{gathered}[/tex]Therefore the consecutive interior angles add up to 180
[tex]\begin{gathered} m<3+m<2=180 \\ 143+m<2=180 \\ m<2=180-143 \\ m<2=37^0 \end{gathered}[/tex]Hence the corresponding angle for m<3 = 143° and m<2 = 37°
Berto's age is x years. Rico's age is four times Berto's age.
In 10 years' time Rico's age will be twice Berto's age.
Use this information to write an equation in x.
Solve your equation to find Berto's present age.
The equation is 4x+10 = 2x+20 and value of x is 5.
What is equation?
Equation, a statement of equality between two expressions made up of variables and/or numbers. In essence, equations are questions, and the development of mathematics has been driven by attempts to find systematic answers to those questions. Equations range in complexity from simple algebraic equations (involving only addition or multiplication) to differential equations, exponential equations (involving exponential expressions), and integral equations.
Here Berto's age is x years. then
Rico's age = 4 times of Berto's age
=> Rico's age = 4x.
In 10 years then Berto's age = x+10, then ,
Rico's age +10 = 2(x+10)
now put Rico's age = 4x then,
=> 4x+10 = 2x+20
=>4x-2x=20-10
=>2x=10
=> x= 5
Hence the equation is 4x+10 = 2x+20 and value of x is 5.
To learn more about equation refer the below link
https://brainly.com/question/27572890
#SPJ1
The value of a truck bought new for $32,000 decreases 16.5%each year. Write an exponential function, and graph the function.Use the graph to predict when the value will fall to $3000.
The exponential decay function can be written as :
[tex]f(t)=P(1-r)^t[/tex]where P = initial amount
r = rate of decay (decreasing value)
t = time in years
From the problem, we have :
P = $32,000
r = 16.5% or 0.165
The function will be :
[tex]\begin{gathered} f(t)=32000(1-0.165)^t \\ f(t)=32000(0.835)^t \end{gathered}[/tex]Using desmos, the graph of the function will be :
Then use the graph to predict when the value will fall to $3000
That will be :
in about 13 years, the value will fall to $3000
ANSWER :
The function is :
[tex]f(t)=32000(0.835)^t[/tex]The value will fall to $3000 in about 13 years.
What is the domain of the function y = 2 StartRoot x minus 5 EndRoot?
x greater-than-or-equal-to negative 5
x greater-than-or-equal-to 2
x greater-than-or-equal-to 5
The domain of the function given; y = 2 StartRoot x minus 5 EndRoot is; x greater-than-or-equal-to 5.
What is the domain of the function given; y = 2√(x -5)?It follows from the task content that the domain of the square root function is to be determined.
Recall, that the domain of a function involving square roots includes all values of x except those which render the expression in the square root less than 0.
Hence, the domain of.the function given is;
x - 5 ≥ 0.
x ≥ 5.
Ultimately, the domain of the function is all values of x greater than or equal to; 5.
Read more on domain of the function;
https://brainly.com/question/1369616
#SPJ1
1. There were 330 people at a play. the admission price was $3 for adults and $1 for children. the admission receipts were $650. how many adults and how many children attended? A) Children: 170, Adults: 60B) Children: 30, Adults: 300C) Children: 160, Adults: 170D) Children: 170, Adults: 160
Explanation
Step 1
Set the equations
let x represents the number of adults attended
let y represents the number of children attended
so
There were 330 people at a play:
it means the sum of adults and children is 330
[tex]x+y=330\Rightarrow equation(1)[/tex]and
if the admission price for $3 for adults, the money from the adult tickets is
[tex]3x[/tex]and $1 for children
[tex]1y[/tex]admission receipts were $650,hence
[tex]\begin{gathered} 3x+y=650\Rightarrow equation(2) \\ \end{gathered}[/tex]Step 2
solve the equations
[tex]\begin{gathered} x+y=330\Rightarrow equation(1) \\ 3x+y=650\Rightarrow equation(2) \\ \end{gathered}[/tex]a) isolate y in equation (1) and replace in equation (2)
[tex]\begin{gathered} x+y=330\Rightarrow equation(1) \\ \text{subtract y in both sides} \\ x+y-y=330-y \\ x=330-y \\ \text{Now , replace in equation (2)} \\ 3x+y=650\Rightarrow equation(2) \\ 3(330-y)+y=650 \\ 990-3y+y=650 \\ 990-2y=650 \\ \text{subtract 990 in both sides} \\ 990-2y-990=650-990 \\ -2y=-340 \\ divide\text{ both sides by -2} \\ \frac{-2y}{-2}=\frac{-340}{-2} \\ y=170 \end{gathered}[/tex]therefore
170 childrend attended
b) now, to find x, replace the y value in equation (1)
[tex]\begin{gathered} x+y=330\Rightarrow equation(1) \\ x+170=330 \\ \text{subtract 170 in both sides} \\ x+170-170=330-170 \\ x=160 \end{gathered}[/tex]Therefore,
160 adults attended
so, the answer is
[tex]D)\text{Children:}170\text{ , Adults :160}[/tex]I hope this helps you
Find the standard form of the equation of the circle having the following properties:Center at the originContaining the point (-5,4)Type the standard form of the equation of this circle.
Equation of a circle in standard form:
[tex](x-h)^2+(y-k)^2=r^2[/tex](h,k) is the center of the circle
r is the radius
For the given circle:
Use the center and the given point to find the radius: the radius is the distance from the center to any point in the circumference.
Distance between two points:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\begin{gathered} (0,0) \\ (-5,4) \\ \\ r=\sqrt[]{(-5-0)^2+(4-0)^2} \\ r=\sqrt[]{(-5)^2+4^2} \\ r=\sqrt[]{25+16} \\ r=\sqrt[]{41} \end{gathered}[/tex]Use the center (0,0) (the origin) and the rafius to write the equation of the circle:
[tex]\begin{gathered} (x-0)^2+(y-0)^2=(\sqrt[]{41})^2 \\ \\ x^2+y^2=41 \end{gathered}[/tex]Then, the equation of the given circle in standard form is:[tex]x^2+y^2=41[/tex]3) cos X 2 37 12 35 35 B) ما را با را 35 12 C 35 D) 12
We get that
[tex]\cos x=\frac{35}{37}[/tex]The number N of cars produced at a certain factory in 1 day after t hours of operation is given by N(V) = 900t- 58 O st$ 10. If the cost C (in dollars) of producing N cars is C(N) = 45,000 + 5000N, find the cost C as a function of the time of the operation of the factory
The cost written as a function of time of operation is C(t) = 4500000t - 245,000
How to express the cost as a function of time?Given N(V) = 900t- 58 and C(N) = 45,000 + 5000N
To find cost C as a function of the time of the operation of the factory, we will substitute the values of N(V) into C(N). Thus:
Since N(V) = 900t- 58, we have:
C(t) = 45,000 + 5000(900t- 58)
= 45,000 + 4500000t - 290,000
= 4500000t - 245,000
Therefore, the cost as a function of the time of operation is C(t) = 4500000t - 245,000
Learn more about modeling function on:
https://brainly.com/question/24853174
#SPJ1
0) is Po= 9, and the population after 7 weeks is P7 = 51. Find an explicit formula for the beetle population after n weeks. Pn how many weeks will it take to reach beetle population 129
The time it will take to reach population of 129 is 20 weeks
What is Arithmetic progression?
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Arithmetic progression with the first term of 9.
The common difference is:
51-9/7 = 42/7 = 6.
6 beetles are added each week.
The general formula after n weeks is
Pn = 9 + 6n.
It will reach 129 when
Pn = 129,
129 = 9 + 6n
129 - 9 = 6n
120 = 6n
n = 120/6
n = 20
Hence, It will take 20weeks to reach beetle population 129
To learn more about Arithmetic progression click on the link
https://brainly.com/question/6561461
#SPJ9
Each event uses a standard deck of playing cards. The cards are chosen at random and put back after each draw. Match each event with itstheoretical probability.You choose a red card.You choose the queen of hearts.You choose a club.You choose a 5, 6, or 7.choices - 1/4, 1/52, 1/2, 3/13
Explanation:
There are 26 red cards in a pack of playing cards.
So,
Probability of picking a red card =Number of red cards/Total number of cards
We plug in what we know
[tex]\begin{gathered} =\text{ }\frac{26}{52} \\ =\frac{1}{2} \end{gathered}[/tex]Therefore, the probability of picking a red card is 1/2.
There is only one Queen of hearts in a deck of cards. So,
Probability of picking a Queen of hearts = Number of Queen of Hearts/ Total number of cards
[tex]=\frac{1}{52}[/tex]Therefore, the probability of picking a
Queen of hearts is 1/52.
There are 13 cards that are clubs. So,
Probability of picking a club = Number of Clubs/ Total number of cards
[tex]\begin{gathered} =\text{ }\frac{13}{52} \\ =\frac{1}{4} \end{gathered}[/tex]Therefore, the probability of picking a club is 1/4.
There are 4 cards that are 5, 6, and 7. This gives a total of 12 cards. So,
The probability of picking 5,6, or 7 = 12/52 = 3/13
Therefore, the probability of picking 5,6, or 7 is 3/13.
Use the above (rounded) slope and y-value to write the equation of the tangent line to the graph of f(x)at x=3. Write your answer in mx+b format.
In order to calculate the slope of f(x) at x = 3, we can use the formula below:
[tex]m=\frac{f(x+h)-f(x)}{h}[/tex]For x = 3 and h = 0.001, we have:
[tex]\begin{gathered} m=\frac{f(3.001)-f(3)}{0.001} \\ f(3.001)=4.8\cdot3.001^2-4.6\cdot3.001=43.2288048-13.8046=29.4242048 \\ f(3)=4.8\cdot3^2-4.6\cdot3=43.2-13.8=29.4 \\ m=\frac{29.4242048-29.4}{0.001}=\frac{0.0242048}{0.001}=24.2 \end{gathered}[/tex]The value of f(3), as calculated above, is 29.4.
The tangent line has a slope of m = 24.2 and it passes through the point (3, 29.4), so let's calculate the value of b:
[tex]\begin{gathered} y=mx+b \\ 29.4=24.2\cdot3+b \\ 29.4=72.6+b \\ b=29.4-72.6 \\ b=-43.2 \end{gathered}[/tex]Therefore the equation of the tangent line is y = 24.2x - 43.2.
are the two triagles similar?if yes, complete the similarity statment.select all that apply
Answer:
The triangles are similar.
[tex]\Delta BAC\text{ \textasciitilde }\Delta YXZ\text{ by SSS similarity}[/tex]Explanation:
Given the triangles in the attached image;
we want to confirm if they are similar.
Let us compare the ratio of corresponding sides of the triangles.
For them to be similar the ratio of the corresponding sides of the triangles must be equal.
[tex]\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}[/tex]substituting the values in the figure;
[tex]\frac{AB}{XY}=\frac{18}{24}=\frac{3}{4}[/tex][tex]\frac{BC}{YZ}=\frac{27}{36}=\frac{3}{4}[/tex][tex]\frac{AC}{XZ}=\frac{33}{44}=\frac{3}{4}[/tex]The ratio of the corresponding sides are equal.
Therefore, the triangles are similar.
[tex]\Delta BAC\text{ \textasciitilde }\Delta YXZ\text{ by SSS similarity}[/tex]According to historical records, the highest price for regular gas in Florida over the last ten years was just under $4.06 write an inequality to represent Florida's gas prices over the last ten years
We know that the regular gas over the last ten years was just under $4.06.
Also, it's important to keep in mind that the price must be more than zero.
Therefore, based on the given information, the inequality is
[tex]0