A bookcase is to have 4 shelves including the top as pictured below.
The width is to be 14 feet less than 3 times the height. Find the width and the height if the carpenter expects
to use 28 feet of lumber to make it.
Width:
feet
Height:
feet
Question Help: Video
Answer:
w= 3 feet
h= 5 feet
Step-by-step explanation:
H=height; W=width=2H-7ft
W=2H-7ft
2H+4W=22ft Substitute for W
2H+4(2H-7ft)=22ft
2H+8H-28ft=22ft Add 28 ft to each side.
10H=50ft
H=5 ft ANSWER 1: The bookshelf is 5 feet high.
W=2H-7ft=2(5ft)-7ft=10ft-7ft=3ft
ANSWER 2: the bookshelf is 3 feet wide.
CHECK:
2H+4W=22ft
2(5ft)+4(3ft)=22ft
10ft+12ft=22ft
22ft=22ft
Hope this helps!
What is the range of f?
O -15≤x≤35
Oy > 15
Oy> 35
O all real numbers
The possible values for the range of f(x) are given by:
y > 15.y > 35.all real numbers.What is the range of a function f(x)?The range of a function f(x) is the set that contains all possible output values for the function. Looking at the graph of the function, the range is composed by the values of y.
In this problem, the function is not given, so I can't give you an exact answer, but since the range is composed by the values of y, the first option is not possible, and the possible values for the range of f(x) are given by:
y > 15.y > 35.all real numbers.More can be learned about the range of a function at https://brainly.com/question/28015028
#SPJ1
Which is the value of this expression when m-3 and n=-5
Answer:
1/8
Step-by-step explanation:
(6m^-1n^0)^-3 =
= (6 × 1/3 × (-5)^0)^-3
= (6/3)^-3
= 2^-3
= 1/2^3
= 1/8
Which did you include in your response?
The relation is a function if there is only one point of
intersection for any vertical line on the graph.
The relation is not a function if any vertical line has
more than one point of intersection on the graph.
The vertical line test is used to determine if one
input has exactly one output.
Use the vertical line test to determine whether a graph represents a function or not .
If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is a relation but not a function.
A function can only have one output, y, for each unique input, x. If a vertical line intersects a curve on an xy-plane more than once then for one value of x the curve has more than one value of y, and so, the curve does not represent a function.
what is function?
function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Therefore, a relation which maps a given input to more than one output is not a function, as such, given that the line intercepts the vertical line twice, then for a given value of x, which is the input, there are more than one value of y, which is the output, as such the relation is not a function.
To learn more about Functions
visit : brainly.com/question/11624077
#SPJ9
Ashton is hosting a banquet. He plans to spend $400, plus or minus $50, at a cost of $25 per guest. Solve |25x-400|= 50 to find the maximum and minimum number of guests. If there can be up to 7 guests at each table, what is the minimum number of tables Ashton should reserve so that every guest has a seat?
Answer: The maximum is 18 and the minimum is 14. He should rent at least 3 tables.
Step-by-step explanation:
When there can be up to 7 guests at each table, the minimum number of tables that Ashton should reserve so that every guest has a seat will be 3 tables.
How to calculate the value?It should be noted that the expression given is illustrated as:
|25x-400|= 50
25x = 50 + 400
25x + 450
Divide
x = 450/25
x = 18
The maximum number of guests will be 18.
The minimum number will be:
25x = 400 - 50
25x = 350
Divide
x = 350/25
x = 14
The minimum number is 14.
Therefore, when there can be up to 7 guests at each table, the minimum number of tables that Ashton should reserve so that every guest has a seat will be:
= 18 / 7
= 3 tables approximately.
Learn more about expressions on:
brainly.com/question/25968875
#SPJ1
find the perimeter and area of the figure? G( -4,1), H(4,1),I(0,-2)
Perimeter = 18 units; Area = 9 sq. units
GH = √(-4-4)²+(1-1)² = 8 units
HI = √(4-0)²+(1+2)² = 5 units
IG = √(0+4)²+(-2-1)² = 5 units
Perimeter of the given triangle = 8+5+5=18 units
Semi-perimeter of triangle = 18÷2=9 units
Using Heron's formula; √[s(s-a)(s-b)(s-c)]=Area of triangle;
A= √(9)(9-8)(9-5)(9-5)
= √(9)(3)(3)
= 9 sq. units
To learn more about this; visit: https://brainly.com/question/24701453
#SPJ9
Which figure below represents a rotation of 90° clockwise of the trapezoid shown?
Figure in option A is the figure that represents a rotation of 90° clockwise of the trapezoid
What is rotation?
The term rotation refers to the circular movement of an object or something about a point. The point mentioned is also called axis. The movement is circular because it involves turning round.
Rotation may be clockwise or anticlockwise. clockwise is the reverse of anticlockwise, and clockwise involves moving in same direction as the clock is turning,
As regards the trapezium, rotating it clockwise will result to the image depicted by option A
Read more rotation here: https://brainly.com/question/26249005
#SPJ1
simplify:39÷(5+(4×5÷2) )
Answer:
this question is wrong .................
Answer:
39÷(5+(4×5÷2) )
39÷(5+(20÷2) )
39÷(5+10)
39÷15
2.6
From this year to ten years, the number of people employed as physician assistants in the country is expected to increase by 39%. The number of people employed as physician assistants today is 56,000. Find the predicted number of physician assistants after ten years.
Answer:
the predicted number of physician assistants after ten years is 77840.
Step-by-step explanation:
The number of people employed as physician assistants today is 56,000.
increment in employment =39%
after 10 years
total physicians= 56000*(1+0.39)
[ total =initial + profit]
[profit =profit*initial]
=77840
the predicted number of physician assistants after ten years is 77840.
Learn more here
https://brainly.com/question/28497209
#SPJ9
Can you solve this
5 is multiplied by the cube of a number
Step-by-step explanation:
We will assume “a number” is “a”. When it is cubed it will be represented by
= “a³”.
When we multiply the number with 5 then the new cube will be
= (5a)³
Now distribute the exponent to the factors inside the parentheses.
= 125a³
What happens in the parentheses is 5*5*5 = 125
a*a*a = a³
So by multiplying your number with 5 it gets increased by 125 times.
X,Y, and Z are collinear points on the same segment, and Y is between X and Z. If XY = 11 and XZ = 13, use the
Segment Addition Postulate to find YZ.
Answer: X, Y, Z are collinear points on the same segment, Then YZ=2.
Step-by-step explanation:
Collinear points are the points that lie on the same straight line or in a single line. If two or more than two points lie on a line close to or far from each other, then they are said to be collinear, in Euclidean geometry.
X, Y, Z are collinear points on the same segment, and Y is between X and Z.
As given Y is between X and Z
We can write,: YZ+XY=XZ
If, XY=11
XZ=13
Replace XY and XZ values in above equation
So, YZ+XY=XZ
YZ+11=13
Solve to get, YZ=13-11
YZ=2
So, X, Y, Z are collinear points on the same segment, and Y is between X and Z, use the segment addition postulate, then YZ=2.
Learn more about area here https://brainly.com/question/5191341
#SPJ9
What is the solution to this inequality?
X-8>-3
OA. x < -11
OB. x>-11
OC. x<5
OD. x>5
Answer:
OD
Step-by-step explanation:
move the -8 to the right, and change its sign
x > 5
In a study conducted by a human resource management organization, human resource professionals were surveyed. Of those surveyed, % said that their companies conduct criminal background checks on all job applicants. Complete parts (a) through (d).
What is the exact value that is 41% of 379 survey subjects?
(Type an integer or a decimal. Do not round.)
The exact value is ____
Using proportions, it is found that the exact value of 41% of 379 is of 155.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The proportion of 41% of 379 is given as follows:
0.41 x 379 = 155.39.
Since 0.39 < 0.5, the exact value is rounded to 155.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
The equation 3x2+2x−4=0 has two solutions. What are they?
Answer:
x =(2-√52)/6=(1-√ 13 )/3= -0.869
x =(2+√52)/6=(1+√ 13 )/3= 1.535
it has either 0.868 or -1,85
How can you recognize when two integers are opposite numbers? Opposite numbers are always to the right of zero on the number line. Opposite numbers are always to the right of zero on the number line. Opposite numbers are the same distance from zero on both sides of the number line. Opposite numbers are the same distance from zero on both sides of the number line. Opposite numbers have one even number and one odd number. Opposite numbers have one even number and one odd number. Opposite numbers are always negative.
One can recognize when two integers are opposite numbers as C. Opposite numbers are the same distance from zero on both sides of the number line.
How to illustrate the information?It should be noted that opposite numbers are given as being 0 when added.
For example, the addition of 3 and -3 will be equal to 0.
Therefore, one can recognize when two integers are opposite numbers as Opposite numbers are the same distance from zero on both sides of the number line.
Learn more about integers on:
brainly.com/question/17695139
#SPJ1
Pupils Per Teacher The frequency distribution shows the average number of pupils per teacher in some states of the United States. Find the variance and standard deviation for the data. Use a TI-83 Plus/TI-84 Plus calculator. Round your answers to at least one decimal place.
The variance and standard deviation for the frequency of pupils per teacher in some states of US is; Variance= 4.62 = 4.6 and Standard Deviation = 2.14 = 2.1
What is variance?Variance(σ²) is a measure of dispersion. A measure of dispersion is a quantity that is used to check the variability of data about an average value. Data can be of two types - grouped and ungrouped. When data is expressed in the form of class intervals it is known as grouped data.
The standard deviation(σ) of a random variable, is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation.
That means;
Standard Deviation = √variance.
For the given data the sum of frequencies = 1+16+11+7+1+2= 38.
Midpoint is 12,15,18,21,24,27.
ni x mi = 12,240,198,147,24,54.
Sum of ni + mi = 675.
Mean (u) = 17.76
mi - u is -5.76,-2.76,0.24,3.24,6.24,9.24.
(mi - u)² is 33.17,7.61,0.057,10.49,38.93,85.37.
Sum of (mi - u)² = 175.62.
Variance = Sum of (mi - u)² / sum of frequencies
= 175.62/38
= 4.62 = 4.6.
Standard deviation = √variance.
= √4.62
= 2.14 = 2.1.
To learn more about standard deviation visit:
brainly.com/question/13074796
#SPJ1
refer to the image please
A formula for the normal systolic blood pressure for a man age A , measured in mmHg, is given as P=0.006A2−0.02A+120 . Find the age of a man whose normal blood pressure measures 124 mmHg.
Answer:
27.5 years old
Step-by-step explanation:
We are given the formula: [tex]P=0.006A^{2} -0.02A+120[/tex] relating a patient's pressure to age.
We are also given the value for pressure (P) as 124 mmHg and need to find age (A). In order to do this, we can substitute the value 124 for P in the equation and solve the quadratic equation to obtain A:
[tex]124=0.006A^{2} -0.02A+120[/tex]
1. Set equation to 0 by subtracting 124 from both sides:
[tex]124-124=0.006A^{2} -0.02A+120-124\\= > 0.006A^{2} -0.02A-4=0[/tex]
2. Solve equation using a calculator:
It should give the solutions: [tex]A= 27.54, -24.2[/tex]
It doesn't really make sense for someone's age to be negative, therefore we can accept the positive solution as our answer.
The man whose normal blood pressure measures 124 mmHg is 27.5 years old.
Hope this helped!
Use the method of completing the square to solve the quadratic equation
t2+5t−1=0.
The solution to the given quadratic equation using the completing the square method is t = -5/2 ±√29/4
Completing the square methodGiven the quadratic equation expressed as;
t^2+5t−1=0
Add 1 to both sides
t^2+5t−1 + 1 = 0+1
t^2 + 5t = 1
Take the square of half of the coefficient of t to have:
t^2 + 5t + (5/2)^2 = 1 + (5/2)^2
(t+5/2)^2 = 1+25/4
(t+5/2)^2 = 29/4
t + 5/2 = ±√29/4
t = -5/2 ±√29/4
Hence the solution to the given quadratic equation using the completing the square method is t = -5/2 ±√29/4
Learn more on completing the square method here: https://brainly.com/question/26107616
#SPJ1
is it true that perpendicular lines meet one another at 100°
Answer:
No, it is not true.
Perpendicular lines meet one another at 90°.
Answer:
It is false
Step-by-step explanation:
It is false because perpendicula line meet in 90 degree
HELP ASAP!!!
Identify the zeros of the function f(x) = x² – 3x.
A.0, -3
B.0,3
C.3,3
D.-3, -3
Answer:
B. 0,3
Step-by-step explanation:
[tex]\texttt{Identify the zeros of the function}:f(x)=x^2-3x[/tex]
The roots are the x values in which where the graph intersects the x-axis. In order to solve, we will need to find the roots by replacing y with 0. In the end, we will solve for x.
= 0,3
| y - 4 | = | y + 10|
Show how to solve too !!
Answer:
y = -3
Step-by-step explanation:
You want the solution to the absolute value equation | y-4 | = | y+10 |.
Absolute valueThe absolute value function ...
f(x) = | x |
is piece-wise defined as ...
[tex]f(x)=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x\ge 0\end{cases}[/tex]
That is, the function is defined differently for argument values less than 0.
Given relationThe above observation regarding the absolute value function means the nature of the given equation changes where the absolute value arguments are zero. Those values are ...
y -4 = 0 ⇒ y = 4
y +10 = 0 ⇒ y = -10
In other words, the points y = -10 and y = 4 divide the domain of the equation into three parts. The behavior will be different in each of those parts.
To solve the equation, we must examine each region of the domain for possible solutions.
y < -10When y < -10, both of the absolute value functions change the sign of their argument. Then the equation is ...
-(y -4) = -(y +10)
Adding y to both sides of this equation gives ...
4 = -10 . . . . . false
This means there is no solution to the equation in the region y < -10.
-10 ≤ y < 4When -10 ≤ y < 4, the absolute value function |y -4| changes the sign of its argument, but the other function does not. In this region, the equation becomes ...
-(y -4) = (y +10)
-6 = 2y . . . . . . . . . add y-10 to both sides
-3 = y . . . . . . . . divide by 2. This value is in the region -10 ≤ y < 4.
The solution to the equation is y = -3.
4 ≤ yWhen 4 ≤ y, neither absolute value function changes the sign of its argument. In this region the equation becomes ...
y -4 = y +10
Subtracting y from both sides of this equation gives ...
-4 = 10 . . . . . false
This means there is no solution to the equation in the region 4 ≤ y.
__
Additional comment
The first attached graph shows the given equation rewritten as two functions. The solution is where those functions have equal values: the point(s) where the graphs intersect.
We often find it more convenient to rewrite equations like this to the form f(x) = 0. Here, that might mean we define ...
f(x) = |y -4| -|y +10|
Then the solution is found on the graph at the x-intercepts. The graph in the second attachment shows this solution, and clearly shows the changes in behavior at x = -10 and x = 4.
Arianys wants to ride her bicycle 55.5 miles this week. She has already ridden 19 miles. If she rides for 5 more days, which equation could be used to determine, m, the average number of miles she would have to ride to meet her goal?
A: 19m=55.5−519 m is equal to 55 point 5 minus 5
B: 5m=19−55.55 m is equal to 19 minus 55 point 5
C: m=55.5−195m is equal to the fraction with numerator 55 point 5 minus 19 and denominator 5
D: 55.5=19m+555 point 5 is equal to 19 m plus 5
Answer:
b
Step-by-step explanation:
Trust me
The equation that could be used to determine, m, is 5m = 55.5 - 19. The correct option is C. m = (55.5 - 19)/5
Writing equationFrom the question, we are to determine the equation that could be used to determine, m, the average number of miles she would have to ride to meet her goal
From the given information,
"Arianys wants to ride her bicycle 55.5 miles"
and
"She has already ridden 19 miles"
Thus,
The number of miles she needs to ride more is
55.5 miles - 19 miles
= 36.5 miles
If m is the average number of miles she would have to ride for 5 more days to complete her goal,
Then, we can write that
m = 36.5/5
OR
m = (55.5 - 19)/5
Hence, the equation that could be used to determine, m, is 5m = 55.5 - 19. The correct option is C. m = (55.5 - 19)/5
Learn more on Writing equation here: https://brainly.com/question/28351087
#SPJ1
Triangle ABC has coordinates A(0, 6), B(3, 0), and C(4, 3). Triangle ABC is reflected across the x-axis. What are the coordinates of C’?
Answer:
Step-by-step explanation:
create the cartesian system, sign the points, because the new triangle is reflected, so we need to use the straight lines which points on its ends, perpendicular to the x-axis, then we get A(0,-6), B(3,0), C(4,-3)
pleaseee help! Will mark brainliest!!! And 100 points!! Sorry for so many questions but please I need answers!
A. What is 0.54 rounded to the nearest tenth?
B. What is 2.65 rounded to the nearest tenth?
C. What is 28.17 rounded to the nearest tenth?
D. What is 3.09 rounded to the nearest tenth?
E. What is 2.41 rounded to the nearest tenth?
F. What is 9.86 rounded to the nearest tenth?
G. What is 15.234 rounded to the nearest tenth?
H. What is 1.37 rounded to the nearest tenth?
I. What is 0.76 rounded to the nearest tenth?
J. What is 39.18 rounded to the nearest tenth?
K. What is 2.48 rounded to the nearest tenth?
L. What is 0.84 rounded to the nearest tenth?
__________________________________________________________________
M. What is 4.112 rounded to the nearest whole number?
N. What is 3.89 rounded to the nearest whole number?
O. What is 23.14 rounded to the nearest whole number?
P. What is 7.6 rounded to the nearest whole number?
Q. What is 3.67 rounded to the nearest whole number?
R. What 53.2 rounded to the nearest whole number?
S. What is 3.08 rounded to the nearest whole number?
T. What is 27.51 rounded to the nearest whole number?
U. What is 11.08 rounded to the nearest whole number?
V. What is 17.28 rounded to the nearest whole number?
W. What is 92.6 rounded to the nearest whole number?
X. What is 24.8 rounded to the nearest whole number?
Y. What is 7.9 rounded to the nearest whole number?
Z. What is 3.06 rounded to the nearest whole number?
Answer:
A: 0.50
B: 2.70
C: 28.20
D: 3.10
E: 2.40
F: 9.90
G: 15.200
H: 1.40
I: 0.80
J: 39.20
K: 2.50
L: 0.80
Here are the first ones
M: 4
N: 4
O: 23
P: 8
Q: 4
R: 53
S: 3
T: 28
U: 11
V: 17
W: 92
X: 25
Y: 8
Z: 3
These are the last ones
Hope you found these helpful! <3
A rectangle the width of m-5 inches and height of 2m+1 inches. Find the simplified area of the rectangle
Answer:
6m - 8
Step-by-step explanation:
Add all of the sides
2m+1+2m+1+m-5+m-5
Then combine everything
6m - 8
Solve for F: C=5/9(F-32)
Answer:
F=9/5c+32
Step-by-step explanation:
Multiply both sides by 9/5 to cancel out the 5/9 on the right side of the equation. This gives you:
9/5C = F-32
C=F−32
Then add 32 to both sides, giving you:
9/5C + 32 = F
C+32=F
Thus, you have:
F= 9/5C + 32F=
5
9
C+32
Answer:
[tex]F= \frac{9}{5}C + 32[/tex]
Step-by-step explanation:
Multiply both sides by 9/5 to cancel out the 5/9 on the right side of the equation. This gives you:
[tex]\frac{9}{5}C = F-32[/tex]
Then add 32 to both sides, giving you:
[tex]\frac{9}{5}C + 32 = F[/tex]
Thus, you have:
[tex]F= \frac{9}{5}C + 32[/tex]
About how many pizzas does Mr. T's Pizzeria sell each week? Remember, there are 7 days in a week.
Mr. T's Pizzeria Daily Sales
Types of Pizza Number of Pizzas
Pepperoni 29
Sausage 35
Veggie 42
Cheese 28
A.
about 1,000 pizzas
B.
about 1,200 pizzas
C.
about 1,400 pizzas
D.
about 2,000 pizzas
Answer: a
Step-by-step explanation: hope it helps.
100 points Given f(x)=5(3−x), what is the value of f(−2)?
Given - F(x) = 5 × 3-x
F(-2) refers to x = -2
Therefore 5×3-(-2) = 5× (3+2) = 5×5 = 25
Hence 25 is the value of f(-2)
You have quarters, nickels,
and dimes that total $1.85. You have twice as many
nickels as dimes, and 2 more quarters than dimes.
How many of each coin do you have?
The number of dimes that we have are 3, the number of nickels are 6 and the number of quarters are 5.
Let the number of dimes be x.
So, we get that:
The number of quarters will be = x + 2
The number of nickels will be = 2 x
Now, 1 dime = $0.10.
1 nickel = $ 0.05
1 quarter = $ 0.25
Amount of dimes = 0.10 x
Amount of nickels = 0.10 x
Amount of quarters = 0.25 x + 0.5
Total amount of coins = $ 1.85
So, we get the equation as:
0.10 x + 0.10 x + 0.25 x + 0.5 = 1.85
0.45 x = 1.35
x = 135 / 45
x = 3
Dimes = 3
Nickels = 6
Quarters = 5
Therefore, we get that, the number of dimes that we have are 3, the number of nickels are 6 and the number of quarters are 5.
Learn more about equation here:
https://brainly.com/question/1214333
#SPJ9