Final answer:
To graph the scenario where the number of loaves of bread on hand (L) minus the number of reservations (R) must be greater than 5, one would represent this inequality on a two-dimensional graph with L on the horizontal axis and R on the vertical axis, shading the region above the line L - R = 5.
Explanation:
The subject of the question is Mathematics, with a focus on inequalities and graphical representation of constraints. The scenario describes the requirement that the number of loaves of bread on hand minus the number of reservations must be greater than 5. To represent this mathematically, let's define the variable L as the number of loaves of bread on hand and R as the number of reservations. The inequality can, therefore, be expressed as L - R > 5.
This inequality needs to be represented on a graph. To do this, one typically uses a two-dimensional coordinate system where the horizontal axis, often labeled as x, could represent the number of loaves of bread (L), and the vertical axis, often labeled as y, could represent the number of reservations (R). The region that satisfies the inequality L - R > 5, would be shaded above the line L - R = 5 (since we are looking for L being greater than R by more than 5 units). This line will have a slope of 1 and a y-intercept at R = -5.
Spaceship Earth, a spherical attraction at Walt Disney worlds epcot center, has a diameter of 50 meters. Find the surface area of the structure. (JUSTIFY)
Answer:
The surface area of the structure is [tex]SA=2,500\pi\ m^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of a sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
In this problem we have
[tex]r=50/2=25\ m[/tex] -----The radius is half the diameter
substitute
[tex]SA=4\pi (25)^{2}[/tex]
[tex]SA=2,500\pi\ m^{2}[/tex]
How many numbers are there between 199sq and 200sq
Answer: 398
Step-by-step explanation:
200^2 - 199^2 = 399
Answer:
397
Step-by-step explanation:
200^2 - 1 = 40000 - 1 = 39999
199^2 + 1 = 39601+ 1 = 39602
Difference = 397
A couple of things you should keep in mind.
Between means that the end points are not included. That means you do not subtract 39601 from 40000 to get the answer.The minus 1 from 40000 makes sure that you exclude 40000The plus 1 added to 39601 makes sure that you exclude 49601Find the volume of the following solid figure. A rectangular solid has sides of 10.5 cm, 6.5 cm, and 8.5 cm. What is its volume? Volume (to the nearest tenth) = cm3
For this case we have that by definition, the volume of a rectangular solid is given by the product of its length (l), its width (w) and its height (h).
Then, according to the data, it is not specified to which side each measurement corresponds. So, we multiply:
[tex]V = 10.5 * 6.5 * 8.5\\V = 580.125[/tex]
Rounding:
[tex]V = 580.1cm ^ 3[/tex]
Answer:[tex]V = 580.1cm ^ 3[/tex]
Two mechanics Worked on a car The first mechanic charge $55 per hour The second mechanic charge $80 per hour the mechanics work for a combined total of 15 hours and together they charged a total of $950 how long did the mechanic work?
a = hours worked by the first mechanic
b = hours worked by the second mechanic.
since the first mechanic charges $55 per hour, then for "a" hours that'd be a total of 55*a or 55a, likewise, for the second mechanic that'd be a total charge of 80*b or 80b.
we know all hours combined are 15, so then a + b = 15.
we also know that all charges combined are $950, so 55a + 80b = 950.
[tex]\bf \begin{cases} a+b=15\\ \boxed{b}=15-a\\ \cline{1-1} 55a+80b=950 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{55a+80\left( \boxed{15-a} \right)=950} \\\\\\ 55a+1200-80a=950\implies -25a+1200=950\implies -25a=-250 \\\\\\ a=\cfrac{-250}{-25}\implies \blacktriangleright a = 10\blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{b=15-a\implies }b=15-10\implies \blacktriangleright b=5 \blacktriangleleft[/tex]
Do you guys know the answer for number 5
Answer:
60 inches squared
Step-by-step explanation:
The formula for the area of a triangle is as follows:
[tex]A=\frac{1}{2} bh[/tex]
Where A=area, b=base, and h=height.
Plug in 15 for your base and 8 for your height and solve.
[tex]A=\frac{1}{2} (15)(8)\\A=7.5(8)\\A=60[/tex]
Answer:
B) 60 squared inches
Step-by-step explanation:
To find the area of a triangle you have to use this equation:
A = 1/2 b*h
Now plug in the numbers,
A = 1/2 15*8
15*8 = 120
1/2 of 120 = 60
A = 60
The area of this triangle is 60 squared inches.
The equations X-2Y=1, 3x-y=-1, x+2y=-1, and 3x+y=1 are shown on the graph below.
Which system of equations has a solution of approximately (0.6, –0.8)?
A. x+2y=-1 and 3x+y=1
B. x-2y=1 and 3x+y=1
C. x-2y=1 and 3x-y=-1
D. x+2y=-1 and 3x-y=-1
Answer:
When you graph all the equations into a graphing calculator, you find the answer is:
C. x-2y=1 and 3x-y=-1
The system of equations has a solution of approximately (0.6, –0.8) are;
x + 2 y = - 1 and 3 x + y = 1
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
From this information, it is clear that the green line and the Purple line intersect each other at an approximate point (0.6, -0.8).
Since, the green line passes through the x-intercept (-1,0) and y-intercept (0,-0.5).
Therefore, the equation of the green line will be;
⇒ x + 2y = - 1
Again, the purple line passes through the point (0,1) and has a negative slope thus, the equation of purple line will be;
3x + y = 1 {Since it has negative slope}
Therefore, the first option will be the answer.
Learn more about equations here;
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Janelle and her best friend Carmen go shopping. The function p(t) = 5x4 − 3x3 + 2x2 + 24 represents how much money each girl spent based on the number of hours they were shopping. If Janelle and Carmen each go shopping for 2 hours, how much money did they spend together?
Answer:
$176
Step-by-step explanation:
The function[tex]p(x) = 5x^4-3x^3 + 2x^2 + 24[/tex] represents how much money each girl spent based on the number of hours they were shopping.
Janelle goes shopping for 2 hours, then x=2 and
[tex]p(x)=5\cdot 2^4-3\cdot 2^3+2\cdot 2^2+24=5\cdot 16-3\cdot 8+2\cdot 4+24=80-24+8+24=88[/tex]
Thus, Janelle spent $88.
Carmen goes shopping for 2 hours, then x=2 and
[tex]p(x)=5\cdot 2^4-3\cdot 2^3+2\cdot 2^2+24=5\cdot 16-3\cdot 8+2\cdot 4+24=80-24+8+24=88[/tex]
Thus, Carmen spent $88 too.
Together they spent
$88+$88=$176
Answer:
176
Step-by-step explanation:
when planning for a party one caterer recommends the amount or meat be at least 2 pounds less than 1/3 the total number of guests. which graph represents this scenario?
Answer:
Let x be the number of guest and y be the quantity of meat,
According to the question,
[tex]y\geq \frac{x}{3}-2[/tex]
Since, the related equation of the above inequality,
[tex]y=\frac{x}{3}-2[/tex]
Having x-intercept = (6,0),
y-intercept = (0,-2)
Also,'≥' shows the solid line,
Now, 0 ≥ 0/3 - 2 ( true )
Hence, the shaded region of above inequality will contain the origin,
Therefore, by the above information we can plot the graph of the inequality ( shown below ).
Answer:
Its the 4th graph.
Step-by-step explanation:
Which of these situations can be represented by the opposite of 10?
You climb up 10 flights of stairs
You walk down 10 flights of stairs
The temperature rises 10°F
A plant grows 10 inches taller
Choose the correct answer below
O A. You climb up 10 flights of stairs.
OB. You walk down 10 flights of stairs.
OC. The temperature rises 10°F.
OD. A plant grows 10 inches taller.
B. You walk down 10 flights of stairs
The situation that can be represented by the opposite of 10 is B. You walk down 10 flights of stairs. The concept of 'opposite' here refers to the negative version of a number, which, in this case, would be -10. When you climb up 10 flights of stairs, that's a positive movement upward, analogous to a positive 10. However, walking down 10 flights is the opposite direction, corresponding to -10. Similarly, a temperature rise or a plant growing represents an increase, not the opposite of 10.
In the diagram below AQRS is an equilateral triangle and RT
OS
Which statement must be true?
A. RT2.07 B. QR RT
C. AQRT is a 45-45-90 triangle
D. AQRT is a 30-60-90 triangle.
Answer:
The answer is D.
Step-by-step explanation:
AQRT is a 30-60-90 triangle.
Answer:
The answer id D. AQRT is a 30-60-90 triangle.
Hope this Helps!
If f(x) = 4 - x? and g(x) = 6x, which expression is equivalent to (g- 1)(3)?
Answer:
17Step-by-step explanation:
[tex](g-f)(x)=g(x)-f(x)\\\\f(x)=4-x,\ g(x)=6x\\\\(g-f)(x)=6x-(4-x)=6x-4-(-x)=6x-4+x=7x-4\\\\(g-f)(3)-\text{put}\ x=3\ \text{to the expression}\\\\(g-f)(3)=7(3)-4=21-4=17[/tex]
if x^2 +x-12 is a factor of x^3+ax^2-10x-b then find the values of a and b
Answer:
a=3
b=24
Step-by-step explanation:
If [tex]x^2+x-12[/tex] is a factor of [tex]x^3+ax^2-10x-b[/tex], then the factors of [tex]x^2+x-12[/tex] must also be factors of [tex]x^3+ax^2-10x-b[/tex].
So what are the factors of [tex]x^2+x-12[/tex]? Well the cool thing here is the coefficient of [tex]x^2[tex] is 1 so all we have to look for are two numbers that multiply to be -12 and add to be positive 1 which in this case is 4 and -3.
-12=4(-3) while 1=4+(-3).
So the factored form of [tex]x^2+x-12[/tex] is [tex](x+4)(x-3)[/tex].
The zeros of [tex]x^2+x-12[/tex] are therefore x=-4 and x=3. We know those are zeros of [tex]x^2+x-12[/tex] by the factor theorem.
So x=-4 and x=3 are also zeros of [tex]x^3+ax^2-10x-b[/tex] because we were told that [tex]x^2+x-12[/tex] was a factor of it.
This means that when we plug in -4, the result will be 0. It also means when we plug in 3, the result will be 0.
Let's do that.
[tex](-4)^3+a(-4)^2-10(-4)-b=0[/tex] Equation 1.
[tex](3)^3+a(3)^2-10(3)-b=0[/tex] Equation 2.
Let's simplify Equation 1 a little bit:
[tex](-4)^3+a(-4)^2-10(-4)-b=0[/tex]
[tex]-64+16a+40-b=0[/tex]
[tex]-24+16a-b=0[/tex]
[tex]16a-b=24[/tex]
Let's simplify Equation 2 a little bit:
[tex](3)^3+a(3)^2-10(3)-b=0[/tex]
[tex]27+9a-30-b=0[/tex]
[tex]-3+9a-b=0[/tex]
[tex]9a-b=3[/tex]
So we have a system of equations to solve:
16a-b=24
9a-b=3
---------- This is setup for elimination because the b's are the same. Let's subtract the equations.
16a-b=24
9a-b= 3
------------------Subtracting now!
7a =21
Divide both sides by 7:
a =3
Now use one the equations with a=3 to find b.
How about 9a-b=3 with a=3.
So plug in 3 for a.
9a-b=3
9(3)-b=3
27-b=3
Subtract 27 on both sides:
-b=-24
Multiply both sides by -1:
b=24
So a=3 and b=24
The cost function for Judy’s new clothing store where she sells t-shirts is c=$11.50n + 925. What will Judy’s total cost for this month be if she sells 32 t-shirts this month?
A. $925
B. $1293
C. $368
D. $1475
(Apex)
Answer:
The correct option is Option B. $1293
Step-by-step explanation:
It is given that,the cost function for Judy’s new clothing store where she sells t-shirts is c=$11.50n + 925. She sells 32 t-shirts this month
To find the total cost for this month
cost for n shirt , c=$11.50n + 925
Cost for 32 shirts = 11.50 * 32 + 925
= 368 + 925
= 1293
Therefore the total cost = $1293
The correct answer is option B. $1293
Assume y varies directly as x. If y = 30 when x = -3, find y when x = -9.
Answer:
y is 90
Step-by-step explanation:
The y/x is proportional per point (x,y) since this is a direct variation.
That is ,
[tex]\frac{30}{-3}=\frac{y}{-9}[/tex].
Cross multiply:
[tex]30(-9)=y(-3)[/tex]
Simplify:
[tex]-270=-3y[/tex]
Divide both sides by -3
[tex]\frac{-270}{-3}=y[/tex]
[tex]90=y[/tex]
Consider the relationship 3r+2t=18
A. write the relationship as a function r=f(t)
B. Evaluate f(-3)
C. solve f(t)= 2
Answer and Explanation:
Given : Consider the relationship [tex]3r+2t=18[/tex]
To find :
A. Write the relationship as a function r=f(t)
B. Evaluate f(-3)
C. Solve f(t)= 2
Solution :
A) To write the relationship as function r=f(t) we separate the r,
[tex]3r+2t=18[/tex]
Subtract 2t both side,
[tex]3r=18-2t[/tex]
Divide by 3 both side,
[tex]r=\frac{18-2t}{3}[/tex]
The function is [tex]f(t)=\frac{18-2t}{3}[/tex]
B) To evaluate f(-3) put t=-3
[tex]f(-3)=\frac{18-2(-3)}{3}[/tex]
[tex]f(-3)=\frac{18+6}{3}[/tex]
[tex]f(-3)=\frac{24}{3}[/tex]
[tex]f(-3)=8[/tex]
C) Solve for f(t)=2
[tex]\frac{18-2t}{3}=2[/tex]
[tex]18-2t=6[/tex]
[tex]2t=12[/tex]
[tex]t=\frac{12}{2}[/tex]
[tex]t=6[/tex]
The value of f(-3), to write the relationship as a function (r = f(t)) and to solve the (f(t) = 2) expression, arithmetic operations can be use. Refer the below calculation for better understanding.
Given :
3r + 2t = 18
A) 3r = 18 - 2t
[tex]r = 6-\dfrac{2t}{3}[/tex] ---- (1)
where, [tex]\rm f(t)=6-\dfrac{2t}{3}[/tex] ----- (2)
B) [tex]r = 6-\dfrac{2t}{3}[/tex]
Given that f(-3) imply that t = -3. So from equation (2) we get
f(-3) = 8
C) Given that f(t) = 2. So from equation (2) we get,
[tex]2 = 6 -\dfrac{2t}{3}[/tex]
2t = 12
t = 6
The value of f(-3), to write the relationship as a function (r = f(t)) and to solve the (f(t) = 2) expression, arithmetic operations can be use.
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Suppose you make a conjecture that your dog only eats dog food A. A valid counterexample is that last night he ate dog food.
True or False
Answer:
False
Step-by-step explanation:
A counterexample goes against what you said in the conjecture. An example of a counterexample in this case would be that your dog ate a burger, which is not dog food, last night.
it is reported that the grizzly bear population has increased by 140% since 1975.
there are now 600 grizzly bears living in the wild.
how many grizzly bears were there living in 1975?
Answer:
250
Step-by-step explanation:
If we let p represent the 1975 population, we have ...
p + 140%×p = 600
p(1 +1.40) = 600
p = 600/2.4 = 250
There were 250 grizzly bears living in the wild in 1975.
Circle X with a radius of 6 units and circle Y with a radius of 2 units are shown.

Which steps would prove the circles similar?
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 4.
Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 4.
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 3.
Mark this and returnSave and Exit Next
Answer:
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3 ⇒ 3rd answer
Step-by-step explanation:
* Lets explain how to solve the problem
- To prove that all circles are similar, a translation and a scale factor
from a dilation will be found to map one circle onto another
- So we can translate the circles to share the same center and dilated
one of them by the scale factor of the dilation and the center of
dilation is the common center of the circles
* Lets solve the problem
∵ Circle X has a radius 6 units
∵ Circle Y has a radius 2 units
- At first we translate the circles to share the same center
∴ Use translation to put the centers of the circles at the same point
- Find the scale factor of the dilation from the radii of the two circles
∵ The radius of circle X is 6 units
∵ The radius of circle Y is 2 units
∴ The scale factor = 6/2 = 3
∴ Dilate circle y by scale factor 3
* The steps would prove the circles are similar are;
Translate the circles so they share a common center point, and
dilate circle Y by a scale factor of 3.
There are 4 different methods you could use to solve a quadratic equation that would depending upon the actual equation. They are: - factoring the equation - taking the square root of both sides - completing the square - using the quadratic formula In the two equations that are listed below, describe which method would be the most appropriate to determine a solution. Reference the parts of the equation to justify your response. (You do not have to solve the equation. Some words/phrases to consider using in your response would be:
- factor
- FOIL Method
- Zero-Product Property
- Standard Form
- quadratic expression
- quadratic equations
- coefficient
- perfect square
Part A: x^2 + 6x + 8 = 0
Part B: x^2 + 6x - 11 = 0
Answer:
Part A: x^2 + 6x + 8 = 0 use the factoring the equation method
Part A: x^2 + 6x + 8 = 0 use the quadratic formula
Step-by-step explanation:
Part A;
The equation is x^2 + 6x + 8 = 0 , looking at this quadratic expression, you notice it is written in a quadratic equation standard form of ax^2+bx+c=0. Additionally, you notice that can find what multiplied to get the quadratic equation,factor.You can identify two numbers that multiply to get ac and add to give b.In this question;
a=1,b=6,c=8
ac=8
The numbers are 4 and 2. Factoring the equation method will give;
x²+6x+8=0
x²+4x+2x+8=0
x(x+4)+2(x+4)=0
(x+2)+(x+4)=x²+6x+8
x+2=0, x=-2 and x+4=0, x=-4
Part B
The quadratic equation is ;
x²+6x-11=0
You notice that there are no factors that multiply direct to get the quadratic equation like in part 1. When you observe, a=1, b=6 and c=-11
ac=1×-11=-11 and b=6 .You notice there are no factors that multiply to give -11 and add to get 6, hence the factorizing the equation method can not be used.However, you can apply the quadratic formula that requires coefficients. You have a=1, b=c and c=-11 as the coefficients to use in the quadratic formula.
Answer:
Part A - use the factor method
Part B - use the quadratic equation
Step-by-step explanation:
Thinking process:
Let's look at the two parts in the problem:
Part A: x^2 + 6x + 8 = 0
This is a quadratic equation. Now, the product of the first and last term produces 8x². This product is a common multiple of 4 x and 2 x. These numbers can be added to get the middle term: 6x. Hence the equation can be solved by factorization.
Part B: x^2 + 6x - 11 = 0
Part B is also a quadratic equation. This equation can be analysed as follows:
The product of the first and last product gives -22x². Two factors are possibe: -11x and 2x or -2x and 11 x. These factors wjhen added or subtracted do not give the middle term (6x). Hence factorization will not work.
The best way to solve the equation is to use the quadratic formula:
[tex]x= \frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]
Find inverse of f(x)=x^3-9
Not sure of my answer!
as you may already know, to get the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".
[tex]\bf \stackrel{f(x)}{y}=x^3-9\implies \stackrel{\textit{quick switcheroo}}{\underline{x}=\underline{y}^3-9}\implies x+9=y^3\implies \sqrt[3]{x+9}=\stackrel{f^{-1}(x)}{y}[/tex]
The length of a diagonal of a square is 24 Square root two millimeters. Find the perimeter of the square.
Select one:
o a. 576 millimeters
O b.962 millimeters
C. 96 millimeters
d. 1152 millimeters
O
Answer:
96 mm
Step-by-step explanation:
A square has 4 equal lengths. If you cut through with a diagonal, then you have form a right isosceles triangle.
So we have the diagonal, the hypotenuse, is [tex]24\sqrt{2}[/tex] mm.
We need to find the side measurement of the square, one of the leg measurements of the right isosceles triangle.
Let's assume it's leg measurement is x.
So by Pythagorean Theorem we have:
[tex]x^2+x^2=(24\sqrt{2})^2[/tex]
Combine like terms and simplify:
[tex]2x^2=24^2(\sqrt{2})^2[/tex]
The square and square root cancel there.
[tex]2x^2=24^2(2)[/tex]
I'm going to stick 24^2 * 2 in my calculator:
[tex]2x^2=1152[/tex]
Divide both sides by 2:
[tex]x^2=576[/tex]
Take the square root of both sides:
[tex]x=24[/tex]
So each side of the square is 24 mm long.
To find the perimeter I add up add all the side measurements of the square or multiply 24 by 4 since all sides of square are congruent.
24(4)=96
Answer is 96 mm
Given the diagonal of a square is 24 Square root two millimeters, the perimeter is calculated by first finding the side length using the diagonal, which is 24mm, and then multiplying it by 4 to get the perimeter, resulting in 96 millimeters.
The question asks to find the perimeter of a square given that the length of a diagonal is 24 Square root two millimeters. To solve this, we use the property that the diagonal of a square is √2 times longer than its side (a). This stems from the Pythagorean theorem applied in a square, where the diagonal acts as the hypotenuse, leading to the equation a² + a² = d² (where a is the side length and d is the diagonal).
Therefore, a = d / √2. Substituting the given diagonal length, we get a = 24mm. Since the perimeter (P) of a square is 4 times the side length, P = 4a. Thus, the perimeter is 96 millimeters.
The system of equations y= 1/4x-1 and y= -1/2x-1/4 is shown on the graph below.
What is a reasonable estimate for the solution?
A. (1, -3/4)
B. (-3/4, 1)
C. (-1, 3/4)
D. (3/4, -1)
Answer:
A:(1,-3/4)
Step-by-step explanation:
Use substitution to solve the system
y= 1/4x-1
y= -1/2x-1/4
1/4x-1 = -1/2x-1/4, Solve for x
3/4x= 3/4, x = 1, Next solve for y by plugging the x-value into either equation.
y=1/4(1)-1
y=-3/4
Answer:
1,-3/4
Step-by-step explanation:
I need help with this problem. TIA
Answer:
The correct answer is B⊂A.
Step-by-step explanation:
The sets are:
A={x|x is a polygon}
B={x|x is a triangle}
According to the given sets Option 2 is correct:
The correct option is B⊂A.. We will read it as B is a subset of A.
The reason is that the Set A contains polygon and Set B contains triangle. A triangle is also a simplest form of polygon having 3 sides and 3 angles but a polygon has many other types also. Like hexagon, pentagon, quadrilateral etc. All the triangles are included in the set of polygon.
Thus the correct answer is B⊂A....
How much more snow fell in February 1889 than November 1888?
1)8.4 inches
2)11.4 inches
3)8.1 inches
4)5.4 inches
Answer:
Step-by-step explanation:
i believe it is 4.
assuming feburary it snowed about 8.5 inches and in november it is at about the 3 in line you would subtract to get about 5.5 inches
Answer:
4) 5.4 inches
Step-by-step explanation:
5.4 inches of snow fell in February 1889 than November 1888.
According to the graph:
Feb '89: 8.5 inches
Nov '88: 3 inches
8.5 - 3 = 5.5 or 5.4.
PLEASE! HELP!!!!!!!!!!!
Answer:
Look at the picture
Hope it helps ;)
Complete the equations of the line through (-8, - 2) and (-4, 6)
Answer:
y = 2x + 14
Step-by-step explanation:
As we move from (-8, - 2) to (-4, 6), x increases by 4 and y increases by 8.
Thus, the slope, m, equal to rise / run, is m = 8/4, or m = 2.
Use the slope-intercept form of the equatino of a straight line:
y = mx + b. This becomes 6 = 2(-4) + b, or 6 = -8 + b. Thus, b = 14, and the desired equation is y = 2x + 14.
8^3*8^-5*8^y=1/8^2, what is the value of y in the product of powers below?
For this case we have that by definition of multiplication of powers of the same base, the same base is placed and the exponents are added:
[tex]a ^ n * a ^ m = a ^ {n + m}[/tex]
So, we can rewrite the given expression as:
[tex]8 ^ {3-5 + y} = \frac {1} {8 ^ 2}\\8 ^ {- 2 + y} = \frac {1} {8 ^ 2}[/tex]
So, if [tex]y = 0[/tex]:
[tex]8 ^ {- 2} = \frac {1} {8 ^ 2}\\\frac {1} {8 ^ 2} = \frac {1} {8 ^ 2}[/tex]
Equality is met!
Answer:
[tex]y = 0[/tex]
Answer:
Value of y=0
Step-by-step explanation:
We need to solve
[tex]8^3*8^{-5}*8^y=1/8^2[/tex]
We know that 1/a^2 = a^-2
[tex]8^3*8^{-5}*8^y=8^{-2}[/tex]
[tex]8^y=\frac{8^{-2}}{8^3*8^{-5}}\\8^y=\frac{8^{-2}}{8^{3-5}}\\8^y=\frac{8^{-2}}{8^{-2}}\\8^y=1[/tex]
Taking ln on both sides
[tex]ln(8^y)=ln(1)\\yln(8)=ln(1)\\y= ln(1)/ln(8)\\We\,\,know\,that\,\,ln(1) =0\\y=0[/tex]
So, value of y=0
QUESTION - What information is true when calculating the surface area of a pyramid? Check all that apply.
A) A pyramid has only one base.
B) The base of a pyramid is a polygon.
C) If the altitude of a right pyramid and the apothem of the base are known, then the Pythagorean theorem can be used to find its slant height.
D) The slant height is always the same length as the base of the pyramid.
E) The lateral faces of a pyramid are rectangles.
F) The slant height is used to calculate the lateral area.
Step-by-step explanation:
Definition:
A pyramid is a polyhedron formed by connecting a one polygonal base and a point, called the apex. Each base edge and apex form a triangle.
A) A pyramid has only one base. TRUE (definition)
(look at any photo with the pyramid)
B) The base of a pyramid is a polygon. TRUE (definition)
(look at any photo with the pyramid)
C) If the altitude of a right pyramid and the apothem of the base are known, then the Pythagorean theorem can be used to find its slant height. TRUE
(look at the picture)
D) The slant height is always the same length as the base of the pyramid.
FALSE
E) The lateral faces of a pyramid are rectangles. FALSE (definition)
(the lateral faces of a pyramid always are triangles)
F) The slant height is used to calculate the lateral area. TRUE
(the lateral faces of a pyramid are triangles. The formula of an area of a triangle is A = (bh)/2. Where b - base of triangle, h - height of triangle)
Answer:
A: pyramid has only one base.
B: The base of a pyramid is a polygon.
C: If the altitude of a right pyramid and the apothem of the base are known, then the Pythagorean theorem can be used to find its slant height.
F: The slant height is used to calculate the lateral area.
a hose fills a hot tub at a rate of 4.39 gallons per minute. How many hours will it take to fill a 280-gallon hot tub?
[tex]\bf \begin{array}{ccll} gallons&minutes\\ \cline{1-2} 4.39&1\\ 280&x \end{array}\implies \cfrac{4.39}{280}=\cfrac{1}{x}\implies 4.39x=280\implies x=\cfrac{280}{4.39} \\\\\\ x\approx \stackrel{\textit{minutes}}{63.78}~\hspace{7em}63.78 ~~\begin{matrix} min \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \cdot \cfrac{hr}{60 ~~\begin{matrix} min \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ } \implies \boxed{1.063~hr}[/tex]
An investor puts $500 into an account that pays 3% interest compounded annually. The total amount A in the account after t years is given by which function below A = 500(1.03)t
A = 500(1.03)t
A = 500(103)t
A = 500 + (1.03)t
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years \end{cases} \\\\\\ A=500\left(1+\frac{0.03}{1}\right)^{1\cdot 5}\implies A=500(1.03)^t[/tex]
Answer:
b
Step-by-step explanation: