Answer:
Option C is correct.
Step-by-step explanation:
The equation given is y = 0.5x +5
where x is the number of miles and y is the total cost.
We need to find total cost y if the car has traveled 30 miles
so, x=30
Putting value of x in the given equation:
y = 0.5x +5
y = 0.5(30) + 5
y = 15 + 5
y = 20
So, the total cost is $20
Option C is correct.
Answer:
the answer is $20 i just did that one :))
Step-by-step explanation:
good luck!
A toy plush weighed one- sixth of a pound. A flimsy box can hold 4 pounds. How many toy plushes could the box hold?
Answer:
24 plushies
Step-by-step explanation:
1 pound = 6 toy plushies
6(4)=24
Identify an equation in point-slope form for the line perpendicular to
y=-4x – 1 that passes through (-2,7).
Answer:
[tex]\large\boxed{y=\dfrac{1}{4}x+\dfrac{15}{2}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\==================================[/tex]
[tex]\text{We have}\ y=-4x-1\to m_1=-4\\\\\text{Therefore}\ m_2=-\dfrac{1}{-4}=\dfrac{1}{4}.\\\\\text{The equation of a line perpendicular to}\ y=-4x-1:\\\\y=\dfrac{1}{4}x+b\\\\\text{Put the coordinates of the point (-2, 7) to the equation:}\\\\7=\dfrac{1}{4}(-2)+b\\\\7=-\dfrac{1}{2}+b\qquad\text{add}\ \dfrac{1}{2}\ \text{to both sides}\\\\7\dfrac{1}{2}=b\to b=7\dfrac{1}{2}=\dfrac{7\cdot2+1}{2}=\dfrac{15}{2}\\\\\text{Finally:}\\\\y=\dfrac{1}{4}x+\dfrac{15}{2}[/tex]
helppppppppppppppppppppping
Answer:
B
Step-by-step explanation:
First we simplify the equation:
3y − 2x = k (5x − 4) + 6
3y − 2x = 5k x − 4k + 6
3y = (5k + 2) x − 4k + 6
y = (5k + 2)/3 x + (6 − 4k)/3
The line has a positive slope and negative y-intercept. So:
(5k + 2)/3 > 0
(6 − 4k)/3 < 0
Solving for k in each:
k > -2/5
k > 3/2
k must be greater than -2/5 and 3/2. Since 3/2 is already greater than -2/5, then k must be greater than 3/2.
If k > 3/2, then it's also true that k > 0. So the answer is B.
simplify the following fraction (9/16/1/4)-1/5
Answer: [tex]\frac{41}{20}[/tex]
Step-by-step explanation:
The first step is to make the division of the fractions [tex]\frac{9}{16}[/tex] and
[tex]\frac{1}{4}[/tex]. To do this, you can flip the fraction [tex]\frac{1}{4}[/tex] over and multiply the numerators and the denominators of the fractions. Then:
[tex](\frac{\frac{9}{16}}{\frac{1}{4}})-\frac{1}{5}=(\frac{9}{16}*4)-\frac{1}{5}=\frac{36}{16}-\frac{1}{5}[/tex]
Reduce the fraction [tex]\frac{36}{16}[/tex]:
[tex]=\frac{9}{4}-\frac{1}{5}[/tex]
Now you can make the subtraction: in this case the Least Common Denominator (LCD) will be the multiplication of the denominators. Divide each denominator by the LCD and multiply this quotient by the corresponding numerator and then subtract the products. Therefore you get:
[tex]=\frac{45-4}{20}=\frac{41}{20}[/tex]
Derive the equation of the parabola with a focus at (−5, −5) and a directrix of y = 7.
f(x) = −one twenty fourth(x − 1)2 − 5
f(x) = one twenty fourth(x − 1)2 − 5
f(x) = −one twenty fourth(x + 5)2 + 1
f(x) = one twenty fourth(x + 5)2 + 1
Answer:
[tex]y = - \frac{1}{24} (x + 5) + 1[/tex]
Explanation
The directrix y=7, is above the y-value of the focus. The parabola must will open downwards.
Such parabola has equation of the form,
[tex] {(x - h)}^{2} = - 4p(y - k)[/tex]
where (h,k) is the vertex.
The vertex is the midway from the focus to the directrix
The x-value of the vertex is x=-5 because it is on a vertical line that goes through (-5,-5).
The y-value of the vertex is
[tex]y = \frac{ 7 + - 5}{2} [/tex]
[tex]y = \frac{ 2}{2} = 1[/tex]
The equation of the parabola now becomes
[tex]{(x + 5)}^{2} = - 4p(y - 1)[/tex]
p is the distance from the focus to the vertex which is p=|7-1|=6
Substitute the value of p to get:
[tex]{(x + 5)}^{2} = - 4 \times 6(y - 1)[/tex]
[tex]{(x + 5)}^{2} = - 24(y - 1)[/tex]
We solve for y to get:
[tex]y = - \frac{1}{24} (x + 5) + 1[/tex]
Answer:
f(x) = −one twentyfourth (x + 5)2 + 1
Step-by-step explanation:
Which expression is equivalent to -3 - 3x – 1 + x?
A. 2x - 4
B. -2x+4
C. -2x-4?
D. 4-2x
Answer:
C. -2x-4
Step-by-step explanation:
-3 - 3x – 1 + x
Combine like terms
-3 -1 -3x +x
-4 -2x
Rearrange the order to put the x term first
-2x-4
c
just got it right on edge
55. If 3x = 4y, the value of (x + y)^2 : (x - y)^2 is:
Answer:
[tex]\large\boxed{(x+y)^2:(x-y)^2=49}[/tex]
Step-by-step explanation:
[tex]3x=4y\qquad\text{subtract}\ 3y\ \text{from both sides}\\\\3x-3y=y\qquad\text{distributive}\\\\3(x-y)=y\qquad\text{divide both sides by 3}\\\\x-y=\dfrac{y}{3}\qquad(*)\\------------------\\3x=4y\qquad\text{add}\ 3y\ \text{to both sides}\\\\3x+3y=7y\qquad\text{distributive}\\\\3(x+y)=7y\qquad\text{divide both sides by 3}\\\\x+y=\dfrac{7y}{3}\qquad(**)\\------------------[/tex]
[tex](x+y)^2:(x-y)^2=\dfrac{(x+y)^2}{(x-y)^2}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\=\left(\dfrac{x+y}{x-y}\right)^2\qquad\text{substitute}\ (*)\ \text{and}\ (**)\\\\=\left(\dfrac{\frac{7y}{3}}{\frac{y}{3}}\right)^2=\left(\dfrac{7y}{3}\cdot\dfrac{3}{y}\right)^2\qquad\text{cancel}\ 3\ \text{and}\ y\\\\=(7)^2=49[/tex]
If ELF is congruent to GJH, EF=12 and LF=7.8 find IJ. Round answer to the hundredths place. A. 4.78 B 5.62 C 4.98 D 5.07
EF = 12
KF = 6
LF = 7.8
LK = sqrt(7.8^2-6^2) = 4.98
IJ = LK
Answer with explanation:
→ΔELF ≅ Δ GHJ-------[Given]
→EF=GH----------[CPCT]
→GJ=FL-------[CPCT]
Let , O be the center of the circle.
→ EK=KF--------[Perpendicular from the center to the chord bisects the chord.]
→GI=IH------[Reason same as Above]
→→EK=GI, KF=HI
→→OJ=OL
→OK=KI
→OJ-OK=OL-KI
→LK=IJ
⇒→Δ LKF ≅ Δ JIG-------[SAS]
Now, In Δ LKF, By Pythagorean Theorem
→(LF)²=(LK)²+(KF)²
→(7.8)²=(LK)²+(6)²
→60.84-36=(LK)²
→24.84=(LK)²
LK=4.98
→→LK=IJ=4.98
Option C:→4.98
Alex and his father took a taxi cab that charges $2.60 per mile plus $1.50 for each passenger, and they paid a total of $18.60. Alex wrote the equation 18.60=2.60b+3 for this situation and found b=6. Which statement is true about the solution b=6?
Answer:
The solution b=6 tells us that Alex and his father traveled 6 miles on the taxi
Step-by-step explanation:
Given
18.60=2.60b+3
Here 18.60 is the total amount paid, 2.60 is the rate per mile and 3 is the charges for two passengers.
The solution b=6 tells us that Alex and his father traveled 6 miles on the taxi i.e. b represents miles ..
the answer is: the solution b = 6 gives the number of miles the taxi traveled.
i just did the workbook :)
how do I solve this: 9b less than 40
Answer:
b < 4.44
Step-by-step explanation:
This is an inequality.
The sign for 'less than' is '< '
Write 9b less than 40 in inequality form.
9b < 40 (Take 9 on the other side of the inequality and divide it by 40)
b < 40/9
b < 4.44
!!
Is 24/40= 4/8 true proportion?
Answer:
No, that is not the true proportion.
Step-by-step explanation:
40 divided by 8 is 5. 5 multiplied by 4 is 20. Therefore, the true proportion would be 20/40 = 4/8.
What is the solution to the equation 9-3x = 7?
Answer:
x = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Given
9 - 3x = 7 ( subtract 9 from both sides )
- 3x = - 2 (divide both sides by - 3 )
x = [tex]\frac{-2}{-3}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]\huge{\boxed{x=\frac{2}{3}}}[/tex]
Add [tex]3x[/tex] on both sides. [tex]9=7+3x[/tex]
Subtract 7 from both sides. [tex]2=3x[/tex]
Divide both sides by 3. [tex]\boxed{\frac{2}{3}}=x[/tex]
Petro was given this system of equations.
-14x-2y = 24
14x+8y = -12
Petro’s work is shown in the table. Where, if anywhere, did Petro first make a mistake?
-
A) step 1
B) step 2
C) step 3
D) no mistake
Answer:
Option C step 3
Step-by-step explanation:
we have
-14x-2y=24 ------> equation A
14x+8y=-12 -----> equation B
step 1
Solve the system by elimination
Adds equation A and equation B
-14x-2y=24
14x+8y=-12
---------------------
-2y+8y=24-12
6y=12
The step 1 is correct
step 2
Solve for y
Divide by 6 both sides
6y/6=12/6
y=2
The step 2 is correct
step 3
Find the value of x
substitute the value of y in the equation A
-14x-2(2)=24
-14x-4=24
14x=-4-24
14x=-28
x=-2
The step 3 is not correct
therefore
Petro first make a mistake in Step 3
Answer:
Step 3 in the correct answer. Thx. Just to verify with everyone it is step 3.
Step-by-step explanation:
On Edge 2020 got it correct.
Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]
A. 26.47 units²
B. 28.53 units²
C. 33.08 units²
D. 27.28 units²
Answer:
Option B [tex]28.53\ units^{2}[/tex]
Step-by-step explanation:
The area of quadrilateral ABCD is equal to the area of triangle ABD plus the area of triangle ADC
we know that
Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.
Let
a,b,c be the lengths of the sides of a triangle.
The area is given by:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]
where
p is half the perimeter
[tex]p=\frac{a+b+c}{2}[/tex]
step 1
Find the area of triangle ABD
we have
[tex]a=AB=2.89\ units[/tex]
[tex]b=BD=8.59\ units[/tex]
[tex]c=DA=8.6\ units[/tex]
Find the half perimeter p
[tex]p=\frac{2.89+8.59+8.6}{2}=10.04\ units[/tex]
Find the area
[tex]A=\sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)}[/tex]
[tex]A=\sqrt{10.04(7.15)(1.45)(1.44)}[/tex]
[tex]A=\sqrt{149.89}[/tex]
[tex]A=12.24\ units^{2}[/tex]
step 2
Find the area of triangle ADC
we have
[tex]a=AC=4.3\ units[/tex]
[tex]b=AD=8.6\ units[/tex]
[tex]c=DC=7.58\ units[/tex]
Find the half perimeter p
[tex]p=\frac{4.3+8.6+7.58}{2}=10.24\ units[/tex]
Find the area
[tex]A=\sqrt{10.24(10.24-4.3)(10.24-8.6)(10.24-7.58)}[/tex]
[tex]A=\sqrt{10.24(5.94)(1.64)(2.66)}[/tex]
[tex]A=\sqrt{265.35}[/tex]
[tex]A=16.29\ units^{2}[/tex]
step 3
Find the total area
[tex]A=12.24+16.29=28.53\ units^{2}[/tex]
Answer:
B.) 28.53 units²
Step-by-step explanation:
I got it correct on founders edtell
1.
1400
Simplify: -
Show your work.
Answer:
1400
Step-by-step explanation:
Nothing can be done further. If I saw the rest of the question, I would be capable of assisting you.
I am joyous to assist you.
QUIZ
ALU
0 2 O) A 5 OU
Which shows the four-term polynomial and factored form of x2 + 6x-27?
O x2 + 3x – 9x - 27 = (x + 3)(x -9)
O x2 + 6x – 3x-27 = (x + 6)(x – 3)
O x2 + 9x -3x – 27 = (x + 9)(x – 3)
O x2 + 3x – 6x-27 = (x + 3)(x-6)
Answer:
C
Step-by-step explanation:
O x² + 9x -3x – 27 = (x + 9)(x – 3)
x² + 6x - 27 = (x + 9)(x - 3)
A high school coach needs to buy new athletic shorts for the 15 members of the basketball team. The coach must spend less than $200 and needs to determine how much he can spend per pair of shorts. Write and solve an inequality to determine the maximum price for each pair of shorts. What does the solution represent?
Answer:
15x < 200; x < 13.33; the maximum price for a pair of shorts
Step-by-step explanation:
1. Set up the inequality
Let x = price of a pair of shorts. Then
15x = price of shorts for the team
You have one condition:
15x < 200
2. Solve the inequality
[tex]\begin{array}{rcl}15x & < & 200\\\\x & < & \dfrac{200}{15}\\\\x & < & \mathbf{13.333}\\\end{array}[/tex]
3. Meaning of solution
The solution represents the maximum price the coach can pay for a pair of shorts.
If the coach pays $13.33 per pair, the total cost for the team will be $199.95, and the condition is satisfied.
Answer: The coach may spend up to $13.33 per pair of shorts.
Step-by-step explanation:
Hi, to answer this question we have to write an inequality with the information given:
Number of shorts: 15 (for 15 members) Budget: $200So, we have to multiply the number of shorts by the price of each one, we will represent the price with the variable "x".(15x)
That cost must be equal or less to 200.
Mathematically speaking
15 x ≤ 200
Solving for x
x ≤200/15
x ≤ 13.33
This solution represents that the coach may spend up to $13.33 per pair of shorts.
Feel free to ask for more if needed or if you did not understand something.
On a quiz worth 5 points, eight students earned a 5, two students earned a 4, five students earned a 3, six students earned a 2, five students earned a 1, and zero students earned a zero. Find the class average on this quiz.
Express your answer rounded to the tenths place.
Answer:
Step-by-step explanation:
[tex]\frac{8(5)+2(4)+5(3)+6(2)+5(1)}{26}[/tex]
Now we simplify:
[tex]\frac{80}{26}[/tex]
[tex]\frac{40}{13}[/tex]
Now we divide:
[tex]3.1[/tex]
A cierta hora del dia los rayos solares forman un angulo de 60° con el suelo. ¿Que sombra dara el arbol de 7 m de altura? Auxilioooooo por favorecer help!!
Answer:
4.04 m
Step-by-step explanation:
El arbol y el suelo forman un angulo de 90°. Son los catetos de un triangulo rectangulo.
Los rayos solares forman un angulo de 60° con el suelo y forman la hipotenusa del triangulo.
Se tiene un triangulo rectangulo de angulos de 30°-60°-90°.
En este genero de triangulo, el cateto mayor mide [tex] \sqrt{3} [/tex] veces el cateto menor.
cateto menor = [tex] \dfrac{7}{\sqrt{3}} [/tex]
[tex] = \dfrac{7\sqrt{3}}{3} [/tex]
[tex] = 4.04 ~m [/tex]
The length of the shadow of the tree would be -
s = {7/√3}.
What is a mathematical function, equation and expression?function : In mathematics, 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.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that at a certain time of day the sun's rays make an angle of 60° with the ground.
Assume that the length of the shadow is [x] meters. Using the trigonometric ratios, we can write -
tan (60) = (height of tree {h})/(length of shadow {s})
sin(60)/cos(60) = (height of tree)/(length of shadow)
(√3/2)/(1/2) = {7/s}
√3/2 x 2 = 7/s
√3 = 7/s
s = {7/√3}
Therefore, the length of the shadow of the tree would be -
s = {7/√3}.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
{The question in english is -
At a certain time of day the sun's rays make an angle of 60° with the ground. What shade will the 7 m tall tree cast?}
Keri and his friends are on their way to visit some family friends who lives 1050 miles away from them.based on the route they shoes they expect to complete their trip in three days. The distance and average speeds for the first two days driven are shown below:
First day : 5 hours at an average speed of 70 miles per hour
Second day: 7 hours at an average an average speed of 65 miles per hour
If the average speed on the third day is 70 miles per hour how many more hours will it take for them to reach their friends home
Answer:
3.5 hours
Step-by-step explanation:
5 x 70 = 350
7 x 65 = 455
350 + 455 = 805
1050 - 805 = 245
245/ 70 = 3.5
They will take an additional 3.5 hours on the third day to reach their destination.
Explanation of the distance covered in the first two days and how much more time it will take on the third day to reach their destination.
The distance covered in the first two days can be calculated using the formula:
Distance = Speed x Time
First day: 5 hours x 70 mph = 350 milesSecond day: 7 hours x 65 mph = 455 milesTherefore, after the first two days, they have covered a total distance of 350 + 455 = 805 miles. They have 1050 - 805 = 245 miles left to travel.
On the third day, at an average speed of 70 mph, they will cover the remaining 245 miles. Therefore, the time it will take for them to reach their friends' home on the third day is:
Time = Distance / Speed = 245 miles / 70 mph = 3.5 hours
They will take an additional 3.5 hours on the third day to reach their destination.
Jorie leaves work 30 minutes late. She decides to make up time by taking the toll road instead of side streets. She can travel four times faster by taking the toll road. Create an equation to represent her total travel time, including wait time, where x is the number of minutes the drive was expected to take.
A. y = \frac{1}{4}x -30
B. y = 4x - 30
C. y = \frac{1}{4}x + 30
D. y = 4x + 30
Answer:
OPTION C
Step-by-step explanation:
We know that the toll road is 4 times faster than the side streets.
If 'x' represents the number of minutes she usually spend taking the side streets. The [tex]\frac{1}{4} x[/tex] represents the time she takes taking the toll road.
Also we need to create an equation to represent her total travel time, including wait time. Therefore, the equation is:
[tex]y = \frac{1}{4}x + 30[/tex]
Therefore, the correct solution is the OPTION C.
Answer:
c
Step-by-step explanation:
took the test but give the other guy brainliest he deserves it
Solve the system of equations and choose the correct answer from the list of options. (4 points)
x − y = 7
y = 3x + 12
2 over 19 comma 2 over 33
negative 2 over 19 comma negative 33 over 2
negative 19 over 2 comma negative 33 over 2
19 over 2 comma 33 over 2
Answer:
x=-19/2 y=-33/2
Step-by-step explanation:
x − y = 7
y = 3x + 12
Substituting the second equation into the first
x − (3x+12) = 7
Distribute the minus sign
x-3x-12 = 7
Combine like terms
-2x-12 =7
Add 12 to each sid
-2x-12+12 =7+12
-2x=19
Divide each side by -2
-2x/-2 = 19/-2
x = -19/2
Now we need to find y
y = 3x+12
y = 3(-19/2) +12
y = -57/2 +24/2
y = -33/2
Answer:
(-19/2, -33/2)
Step-by-step explanation:
Lucy Furr must supply 2 different bags of chips for a party. She finds 10 varieties at her local grocer. How many different selections can she make?
Answer:
she can make 50 different selections!
Step-by-step explanation:
To find the different selections that can be made, we use the formula:
nCr = n! / r! * (n - r)!. Where 'n' represents the number of items available and 'r' represents the nuber of items being chosen
In this case:
'n' equals 10 and 'r' equals 2. Therefore:
[tex]10C_{2} = \frac{10!}{2!(10-2)!} = \frac{10!}{2!8!} = \frac{90}{2} =50[/tex]
So she can make 50 different selections!
Answer: 45
Step-by-step explanation:
The combination of n things taking r at a time is given by :-
[tex]C(n;r)=\dfrac{n!}{(n-r)!}[/tex]
Given : Lucy Furr must supply 2 different bags of chips for a party.
She finds 10 varieties at her local grocer.
Then the number of different selections she can make is given by :-
[tex]C(10;2)=\dfrac{10!}{2!(10-2)!}\\\\=\dfrac{10\times9\times8!}{2\times8!}=\dfrac{90}{2}=45[/tex]
Hence, the number of different selections she can make= 45
What is the ratio of 102 steps walked in 1 minute?
Answer:
102 steps/1minute
In seconds it would be 102/60 which can be reduced to 17/10, or 1.7
Help please and fast
Answer:
b. 7/16
Step-by-step explanation:
We can see in the figure that the total dimension parallel to C is 15/16.
The other half dimension with c is 1/2
We will get the dimension C by subtracting 1/2 from 15/16
So,
C = 15/16 - 1/2
= (15-8)/16
=7/16
So the dimension C is 7/16.
Hence option b is correct ..
Select the correct answer from each drop-down menu. The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same. The volume of pyramid A is the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is the volume of pyramid A.
Step-by-step explanation:
The formula of a volume of a pyramid:
[tex]V=\dfrac{1}{3}BH[/tex]
B - base area
H - height
H - height of pyramids
Pyramid A:
[tex]B=(10)(2)=200\ m^2[/tex]
[tex]V_A=\dfrac{1}{3}(200)H=\dfrac{200}{3}H\ m^3[/tex]
Pyramid B:
[tex]B=10^2=100\ m^2[/tex]
[tex]V_B=\dfraC{1}{3}(100)H=\dfrac{100}{3}H\ m^3[/tex]
[tex]V_A>V_B\\\\V_A=2V_B[/tex]
The volume of the pyramid A is twice as large as the volume of the pyramid B.
The new height of pyramid B: 2H
The new volume:
[tex]V_{B'}=\dfrac{1}{3}(100)(2H)=\dfrac{200}{3}H\ m^3[/tex]
The volume of the pyramid A is equal to the volume of the pyramid B.
To compare the volumes of the two pyramids, we first need to calculate the volume of each pyramid using the formula for the volume of a pyramid:
\[ V = \frac{1}{3}Bh \]
where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height.
First, let's calculate the volume of pyramid A:
\[ \text{Area of base of pyramid A} = \text{length} \times \text{width} = 10 \, \text{meters} \times 20 \, \text{meters} = 200 \, \text{square meters} \]
Now, let's call the height of pyramid A (and originally pyramid B) \( h \). Then, the volume of pyramid A is:
\[ V_{\text{A}} = \frac{1}{3} \times 200 \, \text{m}^2 \times h = \frac{200h}{3} \, \text{cubic meters} \]
Next, let's calculate the volume of pyramid B with its original height \( h \):
\[ \text{Area of base of pyramid B} = \text{side} \times \text{side} = 10 \, \text{meters} \times 10 \, \text{meters} = 100 \, \text{square meters} \]
So the original volume of pyramid B is:
\[ V_{\text{B}} = \frac{1}{3} \times 100 \, \text{m}^2 \times h = \frac{100h}{3} \, \text{cubic meters} \]
Now we can compare the volumes of pyramid A and the original volume of pyramid B:
\[ \frac{V_{\text{A}}}{V_{\text{B}}} = \frac{\frac{200h}{3}}{\frac{100h}{3}} = \frac{200}{100} = 2 \]
So, pyramid A has twice the volume of pyramid B.
Now, if the height of pyramid B increases to twice that of pyramid A, its new height is \( 2h \). Therefore, the new volume of pyramid B is:
\[ V_{\text{B new}} = \frac{1}{3} \times 100 \, \text{m}^2 \times 2h = \frac{200h}{3} \, \text{cubic meters} \]
Comparing this new volume of pyramid B to the volume of pyramid A:
\[ \frac{V_{\text{B new}}}{V_{\text{A}}} = \frac{\frac{200h}{3}}{\frac{200h}{3}} = 1 \]
So, the new volume of pyramid B is equal to the volume of pyramid A.
In summary, the volume of pyramid A is twice the volume of pyramid B when their heights are the same. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is equal to the volume of pyramid A.
PLEASE, I NEED HELP NOW!!!!!!
Find the approximate area of a circle that has a radius of 14 feet. Round your answer to the nearest hundredth.
A = ___ ft2
Don't forget to round!
Answer:
1934.2
Step-by-step explanation:
3.14*14=43.98 squared=1934.2
Answer:
615.75
Step-by-step explanation:
Use A = πr², letting r = 14, so that:
A = π(14)²
≈ 615.75 ft²
Rounding to the nearest hundredth would make the answer 618
Check each set that includes the number shown 5/9 a. natural numbers b.whole numbers c.integers d. rational numbers e.irrational numbers f.real numbers
Answer:
5/9 from these categories can only be classified as rational and real.
Step-by-step explanation:
Natural numbers are counting numbers. People don't ever say the number 5/9 when counting people. So 5/9 is not natural.
Whole numbers are counting numbers plus also including 0. So we already said 5/9 is not natural and it is definitely not 0 so 5/9 is not whole.
Integers are whole numbers plus the opposite of the whole numbers. 5/9 is not whole and it is certainly not negative so we don't need to even consider if is the opposite of a whole number.
Rational numbers are numbers that can be expressed as a fraction where the top and bottom are integers. 5/9 is a rational number because 5 and 9 are whole numbers which are integers.
Irrational numbers are numbers that aren't rational. Our number 5/9 is rational so it isn't irrational.
Real numbers are any number that isn't imaginary. Doesn't include the imaginary unit. Our number doesn't include the imaginary unit so it is real.
Answer:
d. Rational Numbers
f. Real Numbers
Step-by-step explanation:
The number shown is 5/9
Let us see the options one by one
a. Natural numbers
Natural numbers consists of counting from 1 to infinity. The fractions are not included in the natural numbers hence it will not be the correct answer.
b. Whole numbers
Whole numbers is the set of natural numbers along with zero so it is also not the right answer.
c. Integers
Integers are combination of negative and positive whole numbers hence it is also not correct.
d. Rational numbers
Rational numbers are numbers which can be written in the form of p/q where p and belong to integers and q is not equal to zero. It is correct as the number is 5/9 where 5 is also an integer and 9 is also an integer. Also 9 ≠ 0 so 5/9 is a rational number.
e. As the number is rational, it cannot be irrational
f. Real numbers
As real numbers is the set of all rational and irrational numbers, 5/9 will also be a part of the set .. Hence it is also correct ..
f(x) = -x^3 + 3x^2 + x - 3 Using the end behavior of f(x), determine the graph of the function
Answer:
Here, the given function,
[tex]f(x) = -x^3 + 3x^2 + x - 3[/tex]
Since, the leading coefficient is negative, and degree is odd,
Thus, the end behaviour of the function is,
[tex]f(x)\rightarrow \infty\text{ as }x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow \infty[/tex]
Therefore, the graph rises to the left and falls to the right.
Now, when f(x) = 0
[tex]-x^3+3x^2+x-3=0[/tex]
[tex]\implies -(x-3)(x-1)(x+1)=0[/tex]
[tex]\implies x=3, 1, -1[/tex]
That is, graph intercepts the x-axis at (3, 0), (1, 0) and (-1, 0).
When x = 0,
[tex]f(x) = - 3[/tex]
That is, graph intersects the y-axis at ( 0, -3),
Also, for 0 > x > -1 , f(x) is decreasing,
For 2.55 > x > 0, f(x) is increasing,
For 3 > x > 2.55, f(x) is decreasing,
Hence, by the above explanation we can plot the graph of the function ( shown below )
Answer:w
Step-by-step explanation: it should be w i got it on plato
Find the value of y .
(Either leave your answer as a fraction, or round to the nearest hundredth.)
Answer:
y=5/3 or y=1.67
Step-by-step explanation:
In this problem we have that
(5x+8)=21x ----> given problem
21x-5x=8
16x=8
x=0.5
In the same way
Remember that the slope of a line is a constant
so
20y-2=17y+3
Solve for y
20y-17y=3+2
3y=5
y=5/3 or y=1.67