a rectangle has a perimeter of 182 in and length of 52 in. What is the width?
Answers
Related Questions
In the triangle below, determine the value of a.
Answers
a=14tan42°
a≈12.61 (to the nearest hundredth of a unit)
Use tangent to find the opposite to the adjacent side (14) from the angle (in this case a).
a = 14*tan(42°) = 14*0,9 = 12,6 (approssimatively)
Which of the following equations describes the graph shown?
A.) y = x+2
B.) y = -x - 2
C.) y = x - 2
D.) y = -x + 2
Answers
Answer: The correct option is (D) y = -x + 2.
Step-by-step explanation: We are to select the correct equation that describes the given graph.
We can see that the graph is a straight line passing through the points (0, 2) and (1, 1).
So, the slope of the line will be
[tex]m=\dfrac{2-1}{0-1}=-1.[/tex]
Therefore, the equation of the line with slope m = -1 and passing through the point (0, 2) is given by
[tex]y-2=m(x-0)\\\\\Rightarrow y-2=-1\times x\\\\\Rightarrow y-2=-x\\\\\Rightarrow y=-x+2.[/tex]
Hence, the equation that describes the graph is y = -x + 2.
Thus, (D) is the correct option.
what is the degree of 12x^4-8x+4x^2-3
Answers
4th degree
Answer:
The degree of [tex]12x^4-8x+4x^2-3[/tex] is 4.
Step-by-step explanation:
The given polynomial is [tex]12x^4-8x+4x^2-3[/tex]
This polynomial is of one variable which is x. Hence, the degree of the polynomial is the highest exponent.
For the given polynomial, the highest exponent is 4.
Therefore, the degree of [tex]12x^4-8x+4x^2-3[/tex] is 4.
At the middle school graduation dance, the DJ played 12 slow dances, which was equal to the quotient of the number of fast dances and two.
Answers
quotient means divide
so 12 = x/2
x = 12*2 = 24
x =24 fast songs
I have 3 questions here , one of them I just need my answer checked on and the other two I really need help with. Thank you!!
Answers
The narrowest graph happens when the leading coefficient is furthest from 0. In this case, that happens to be 4 which is the coefficient in choice B.
See the attached image "figure1" for the graph. The functions are color coded
y = -x^2 is in red
y = 4x^2 is in blue
y = (1/4)x^2 is in green (note: 1/4 = 0.25; so y = (1/4)x^2 is the same as y = 0.25x^2)
y = (1/9)x^2 is in purple (note: 1/9 = 0.11 approximately; so y = (1/9)x^2 is roughly the same as y = 0.11x^2)
As you can see in figure1, the blue graph corresponding to y = 4x^2 is the most narrowest.
----------------------------------------------------------------------------------------------
Problem 2)
See figure2 for the graph. The image is also attached along with figure1.
Figure2 shows a parabola that opens upward and the lowest point is at (0,2) which is the vertex. This point is shown in red as point A.
y = x^2+2 is the same as y = 1(x-0)^2 + 2. That second equation is in the form y = a(x-h)^2 + k where a = 1, h = 0, k = 2
So the vertex is (h,k) = (0,2). The fact that 'a' is positive (a = 1) indicates that the parabola opens upward and this implies the vertex is the lowest point.
Therefore the vertex (0,2) is the minimum
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Problem 3)
You have the correct answer here. Nice work.
Match the pairs of values of f(x) and g(x) with the corresponding values of h(x) if h(x) = f(x) ÷ g(x).
Screenshot of the tiles below
(Please help)
Answers
2)f(x)/g(x)=x^2-4x+3/x-3=x+1
3)f(x)/g(x)=x^2+4x-5/x-1=x+5
4)f(x)/g(x)=x^2-16/x-4=x+4
The We have given that the pairs of values of f(x) and g(x) with the corresponding values of h(x) s given below.
(x^2-9)/(x-3)
x^2-4x+3/x-3
x^2+4x-5/x-1
x^2-16/x-4
We have to match the pairs of values of f(x) and g(x) with the corresponding values of h(x) if h(x) = f(x) ÷ g(x).
What is the function?A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.
1)f(x)/g(x)=(x^2-9)/(x-3)=x+3
2)f(x)/g(x)=x^2-4x+3/x-3=x+1
3)f(x)/g(x)=x^2+4x-5/x-1=x+5
4)f(x)/g(x)=x^2-16/x-4=x+4
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Find the missing factor x(y+6)-5(y+6)( ) (y+6)
Answers
We are given the equation:
x (y + 6) – 5 (y + 6) ---> 1
We are to look for the missing factor in the equation: (_) (y + 6) from the given values.
Knowing the rules of the polynomial multiplicity, we can have an idea that the given equation can also be written in the form of:
(x – 5) (y + 6) ---> 2
wherein the whole factor (y + 6) was simply distributed to the values in the factor (x – 5). To prove that equations 1 and 2 are equal:
x (y + 6) – 5 (y + 6) = (x – 5) (y + 6)
Expanding:
x y + 6 x - 5 y – 30 = x y + 6 x – 5 y – 30 (EQUAL!)
Therefore our missing factor is:
(x – 5)
Determine the distance between a(-1, 2,3) and b(4,-5, 6) to the nearest tenth
Answers
the distance between A(-1, 2,3) and B(4,-5, 6)
AB= √((4-(-1)²+(-5-2)² + (6 - 3 ) ²) =√(25 +49 +9) = √83 ≅ 9.11
In 45-45-90 right triangle, what is the ratio of the length of one leg to the length of the other leg
Answers
Answer: it’s 1:1
Step-by-step explanation:
The figure shows secant GC and tangent GB intersecting to form an angle. Find x and y If necessary, round to the tenths place.
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Let`s look at the triangle: Δ GBC. GB is a tangent.
29° + 90° + y = 180°
y = 180° - 90° - 29° = 61°
Then ∠ B = 30° : 2 = 15°
In a triangle ΔADC : ∠ A = 180° - ( 29° + 15° ) = 180° - 44° = 136°
x = 180° - 136° = 44°
Answer: x = 44°, y = 61°
The value of y, calculated using the difference between the intercepted arcs, is 69.5° when rounded to the tenths place.
The figure provided depicts a circle with a secant (line GC) and a tangent (line GB) intersecting at point G, forming an angle. There are several angle measures given in the figure: angle ECA is 30°, angle ADB is 58°, and angle EAB is 161°. The angles x° and y° are what we need to find.
Here's how to find x and y:
1. To find x:
- The angle formed by a tangent and a chord (GB and BA in this case) is equal to the angle in the alternate segment of the circle. Therefore, x is equal to the angle in the alternate segment, which is angle ADB (58°). So, x = 58°.
2. To find y:
- The angle formed by a tangent and a secant (GB and GC in this case) from the external point G is equal to the difference between the measure of the intercepted arc (the large arc EAC) and the measure of the adjacent arc (the small arc EC). This can be calculated by the formula [tex]\( y = \frac{1}{2}(\text{large arc} - \text{small arc}) \).[/tex]
- The large arc EAC is the full circle (360°) minus the small arc EBC (161°), so the measure of arc EAC is 360° - 161° = 199°.
- The small arc EC is twice the angle ECA (which is an inscribed angle) because the measure of an arc is twice the measure of an inscribed angle that subtends it. So, the measure of arc EC is 2 * 30° = 60°.
- Now we can calculate y using the formula: [tex]\( y = \frac{1}{2}(199 - 60) \).[/tex]
Let's calculate the exact values for x and y.
The value of x is equal to the angle ADB, which is 58°.
The value of y, calculated using the difference between the intercepted arcs, is 69.5° when rounded to the tenths place.
Therefore, [tex]\( x = 58 \) and \( y = 69.5 \).[/tex]
If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?
m∠A = 15° and m∠C = 35°
m∠A + m∠B = 155°
m∠A + m∠C = 60°
m∠A = 20° and m∠C = 30°.
Answers
all angles in a triangle add to 180
so
if the angles are m∠A, m∠B, m∠C, then
either m∠A=m∠B or m∠B=m∠C or m∠A=m∠C
anyway
so if we assume that vertex B is the one that has a twin then
130+130+?=180
260+?=180
?=-80
false, we can't have a negative angle measure
so 130 must be the odd one
?+?+130=180
2?+130=180
2?=50
?=25
so
m∠A=m∠C=25°
let's test the 2nd answer choice
m∠A+m∠B=25+130=155, yep
test 3rd
m∠A+m∠C=25+25=50≠60, nope
not 3rd one
so answer is 2nd statement
m∠A + m∠B = 155°
the square has a radius of 3 square root 2 what is the apothem?
Answers
The apothem of the square is equal to half the length of a side of the square, which can be calculated by doubling the radius. In this case, the apothem is 3√2.
Explanation:The apothem of a square is a line segment drawn from the center of the square to any side of the square, perpendicular to that side. The apothem is equal to half the length of a side of the square.
Given that the square has a radius of 3√2, we can determine the length of a side of the square by doubling the radius. So, the length of a side is 2 * 3√2 = 6√2.
Therefore, the apothem of the square is half the length of a side, which is (6√2)/2 = 3√2.
The perimeter of a rectangle is 276 centimeters. It's length is five times its width. What are the dimensions?
Answers
length = 5x
width = x
perimeter = 276
Its always easier to write down your givens in an equation
5x + x + x + 5x = 276
12x = 276
x = 23
The width is 23 cm
The length is 115 cm
if a radius of a circle is perpendicular to a chord, then it _____ that chord.
a. is equal in length to
b. bisects
c. is congruent to
d. parallels
Answers
If a radius of a circle is perpendicular to a chord, then it _bisects____ that chord.
What is radius of circle?
In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin radius, meaning ray but also the spoke of a chariot wheel.
What is chord?
A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. The infinite line extension of a chord is a secant line, or just secant. More generally, a chord is a line segment joining two points on any curve, for instance, an ellipse.
According to question, we have to fill in the blank.
The property of the circle is that if a radius of a circle is perpendicular to a chord, then it bisects that chord.
Hence we can conclude that Option(B) is correct.
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Final answer:
A radius of a circle that is perpendicular to a chord bisects the chord, dividing it into two equal segments.(Option b)
Explanation:
If a radius of a circle is perpendicular to a chord, then it bisects that chord. This statement is supported by a theorem in geometry which states that, in a circle, the radius bisecting an angle at the centre is perpendicular to the chord which subtends the angle and also bisects this chord. Therefore, by drawing a radius from the center of a circle to the midpoint of a chord, you create two equal segments, effectively bisecting the chord.
Thus, a perpendicular radius drawn from the center of a circle to a chord's midpoint ensures that the chord is bisected into two equal segments. This geometric principle facilitates chord division and enhances the understanding of circle properties.
Which algebraic expression represents “the difference of 54 and a number”?
Answers
For this case, the first thing we should do is define a variable.
We have then:
x: unknown number
Then, we write the algebraic expression that models the following problem:
the difference of 54 and a number.
We have then:
[tex]54-x[/tex]
Answer:
An algebraic expression that represents "the difference of 54 and a number" is:
[tex]54-x[/tex]
Answer:
A
Step-by-step explanation:
Bryce is testing whether school is more enjoyable when students are making high grades. He asked 100 students if they enjoyed school and whether their GPA was above or below 3.0. He found that 33 of the 40 students with a GPA above 3.0 reported that they enjoyed school, and 5 of the 60 students with a GPA below 3.0 reported that they enjoyed school. What is the probability that a student with a GPA below 3.0 does not enjoy school?
85%
92%
65%
75%
Answers
55/60 which is 0.916666666666
This is rounded to 92%! :)
Answer:
The answer is 92%.
Step-by-step explanation:
5 of the 60 students reported that they like school. This means that the other 55 don't like school. You then divide 55/60 and you get 92%. So, therefore, your answer is 52%.
The cells of a certain culture of bacteria triple every 2 minutes. If there are 40 cells in the beginning, in how many minutes will there be more than 9500 cells?
A) 4 min
B) 5 min
C) 11 min
D) 10 min
Answers
Answer: 10 min
Step-by-step explanation:
Final answer:
The bacterial culture that triples every 2 minutes will surpass 9500 cells just after 10 minutes. Since we cannot have a fraction of a minute in this context, the answer is 11 minutes (Option C).
Explanation:
The student is asking about exponential growth, specifically in a bacterial culture that triples every 2 minutes. To find out how many minutes it will take for the initial 40 cells to grow to more than 9500, we can use the formula for exponential growth:
N = N0 × 3t/2
Where N is the final number of cells, N0 is the initial number of cells (40 in this case), and t is the time in minutes.
We want N to be greater than 9500, so we solve the inequality:
9500 < 40 × 3t/2
Dividing both sides by 40 gives:
237.5 < 3t/2
Next, we find the smallest t for which the inequality holds by applying logarithms and solving:
t > 2 × (log3(237.5))
Calculating the right side, we get:
t > 10.096
So, the culture will have more than 9500 cells just after 10 minutes. The smallest whole number of minutes greater than 10.096 is 11, hence the answer is: C) 11 min
Solve 152x = 36. Round to the nearest ten-thousandth.
A. 0.6616
B. 2.6466
C. 1.7509
D. 1.9091
Answers
Since no one was getting the the answer that is on the assignment I plugged the problem into an algebra calculator, and got A 0.6616
Help Please!!!!!!
f(x)=5x^2+9x−4
g(x)=−8x^2−3x−4
Find (f+g)(x)
My Options Are...:
a. 3x^2+6x−8
b. −3x^3+6x^2−8x
c. −3x^4+6x^2−8
d. −3x^2+6x−8
Answers
Combine like terms
f+g(x)=-3x^2+6x-8
Final answer: D
PLEASE HELP ASAP 20 POINTS PLUS BRAINIEST!
Find the greatest possible error for each measurement.
3 ft
a.
1 ft
b.
1/2 ft
c.
1/4 c
d.
1/6 c
Answers
the greatest possible error when measuring in feet is 1/2 foot
answer is B
I NEEED HELPOPOP!!!!
PLEASE ASSIT ME FOR TWO MATH QUESTIONS
Answers
The only function in B has an inverse which is also a function (one x must have only 0 or 1 image (y)) for the first picture
Answer D for the second picture.
Answer B
What is the equation of the line that is parallel to the line y = x + 4 and passes through the point (6, 5)?
Answers
y-5=x-6
y=x-1 is parallel to y=x+4
A baseball team has won 13 out of 18 games they played this session. How many additional games must the team win in a row to raise its winning percentage to 80%?
A) 7
B) 14
C) 5
D) 24
Answers
Write cos 53 degrees in terms of sine.
Answers
cos(53) = sin(90 - 53)
cos(53) = sin(37)
The value of cos 53 degrees in terms of sine is,
⇒ sin 37 degree
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
We have to given that;
⇒ cos 53 degree
Hence, We can change it into sine as;
⇒ cos 53 degree
⇒ sin (90 - 53)
⇒ sin 37 degree
Thus, The value of cos 53 degrees in terms of sine is,
⇒ sin 37 degree
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what level of measurement is qualitative? Nominal? Ordinal? Interval? Or ration?
Answers
It is the only level of measurement which is only qualitative, whereas ordinal can be either qualitative or quantitative (depending on data), and interval and ratio can only be quantitative.
The term qualitative refers to the fact that non-numerical entries are used, meaning there are no numbers, and the word nominal refers to the Latin word for nouns, or words, which is why that is the correct answer. The rest of the options use numbers, but nominal doesn't.
If 35% of a natural area is to be developed, leaving 500 acres untouched, how many acres are to be developed?
Answers
Answer:
Area to be developed = 269.23 acres
Step-by-step explanation:
Let there is A acres natural area to be developed.
If 35% of A acres is developed then untouched area will be (100 - 35 = 65%)
Now it has been given in the question that 65% of A (untouched area) = 500 acres
[tex]A.\frac{65}{100}=500[/tex]
[tex]A=\frac{500}{0.65}=769.23[/tex]
So area of the natural field = 769.23 acres
Now 35% of the natural area which is to be developed = A×35%
[tex]=769.23.\frac{35}{100}=(769.23)(.35)=269.23[/tex]
Area of the natural area to be developed is 269.23 acres
The number of acres that are to be developed is 269 acres.
Number of acresUsing this formula
Number of acres=(Number of acres untouched/(100%-Percentage of natural area)×Percentage of natural area
Let plug in the formula
Number of acres=500 acres/(100%-35%)×35%
Number of acres=(500 acres/65%)×35%
Number of acres=769.23×35%
Number of acres=269 acres
Inconclusion the number of acres that are to be developed is 269 acres.
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A hyperbola centered at the origin has a vertex at (3, 0) and a focus of the hyperbola is located at (9, 0). What are the equations of the directrices?
x = ±
Answers
To find the equations of the directrices for a hyperbola centered at the origin with a vertex at (3, 0) and a focus at (9, 0), we use the formula x = ±a/e. The hyperbola's directrices are x = ± 1.
Explanation:The student asked about the equations of the directrices for a hyperbola that is centered at the origin, with a vertex at (3, 0) and a focus at (9, 0). A hyperbola has two directrices, and each is a line that is perpendicular to the transverse axis and equidistant from the center as the foci are, but on the opposite side. The equation of a directrix can be found using the formula x = ±a/e, where 'a' is the distance from the center to the vertex and 'e' is the eccentricity, which is the ratio of the distance from the center to a focus (c) over 'a'.
In this case, the hyperbola is aligned along the x-axis. Given a vertex at (3, 0), it implies that 'a' is equal to 3. Since the focus is at (9, 0), it suggests 'c' is equal to 9. The eccentricity 'e' can be found by e = c/a, which is 9/3 = 3. Using the directrix formula x = ±a/e, the two directrices of the hyperbola would be x = ±(3/3), which simplifies to x = ± 1.
what are the roots of the polynomial equation x3-7x=6x-12? Use a graphing calculator and a system of equations.
Answers
x3-7x-6x+12=0
x3-13x+12=0
(x-1)(x2+x-12)=0
Calculate delta of the second bracket:
delta = 1+4*12=49
sqrt(delta)=sqrt(49)=7
x_1=(-1-7)/2=-4
x_2=(-1+7)/2=3
(x-1)(x+4)(x-3)=0
Answear:
Roots: x=1, x=-4, x=3.
The roots of the polynomial equation x³ - 7x = 6x - 12 is x = 1, 3, -4 and graph is shown in the picture.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a polynomial equation:
x³ - 7x = 6x - 12
[tex]\rm x^3-7x+12=6x[/tex]
x³ - 13x + 2 = 0
(x - 1)(x -3)(x + 4) = 0
x = 1, 3, -4
Thus, the roots of the polynomial equation x³ - 7x = 6x - 12 is x = 1, 3, -4 and graph is shown in the picture.
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(05.05)What is the rate of change of the linear relationship modeled in the table?
x y
1 2
3 5
5 8
7 11
negative three over two
two over three
one
1 three over two
Answers
slope (rate of change) = (5 - 2) / (3 - 1) = 3/2 <==
Answer: three over two
Step-by-step explanation:
We know that the rate of change of a function [tex]y=f(x)[/tex] is given by :-
[tex]k=\dfrac{\text{change in y}}{\text{change in x}}[/tex]
From the consecutive values in the table, the change in x = [tex]3-1=2[/tex]
Change in y = [tex]5-2=3[/tex]
Now, the rate of change of the linear relationship modeled in the table will be ;-
[tex]k=\dfrac{3}{\text{2}}[/tex]
PLEASE HELP!!! Evaluate Show your work.
Answers
sqrt (7x)(sqrt (x) - 7sqrt (7)) =
sqrt (7x) * sqrt (x) - sqrt (7x) * 7sqrt (7)
now if you have two things multiplied by each other and they are both under the sqrt sign then we can multiply them by each other But we have to leave them under the sqrt sign. so this becomes:
sqrt (7x * x) - 7sqrt (7x *7) =
sqrt (7x^2) - 7sqrt (7^2 *x)
in the first sqrt we have x^2 And in the second we have 7^2. The sqrt of anything squared is the same number without the square. So sqrt (x^2) becomes x and sqrt(7^2) becomes 7. So now we have:
x * sqrt (7) - 7 * 7sqrt (x) =
xsqrt (7) - 49sqrt (x)
Answer:
[tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]
Step-by-step explanation:
Given: [tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})[/tex]
Simplify the expression.
[tex]\Rightarrow \sqrt{7x}(\sqrt{x}-7\sqrt{7})[/tex]
Distribute [tex]\sqrt{7x}[/tex] over parentheses
[tex]\Rightarrow \sqrt{7x}\cdot\sqrt{x}-\sqrt{7x}\cdot7\sqrt{7}[/tex]
[tex]\Rightarrow \sqrt{7x^2}-7\sqrt{7^2x}[/tex]
square term take out from square root
[tex]\Rightarrow x\sqrt{7}-7\cdot 7\sqrt{x}[/tex]
[tex]\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]
[tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]