Final answer:
The modified surface area of a square pyramid, with the side length tripled and slant height divided by 5, is calculated as 9s^2 + 6sl/5, where 's' is the original side length and 'l' is the original slant height.
Explanation:
To find the modified surface area of the square pyramid when the side length is tripled and the slant height is divided by 5, we need to recall the formula for the surface area of a square pyramid. The original surface area formula for a square pyramid is given by the sum of the area of the base plus the area of the four triangular faces, which can be represented as:
Surface Area = base area + 4 × (1/2 × slant height × side length)
For the modified pyramid, if the original side length is 's' and the slant height is 'l', tripling the side length would make it '3s' and dividing the slant height by 5 would make it 'l/5'. Using these new values, the formula for the modified surface area becomes:
Modified Surface Area = (3s)^2 + 4 × (1/2 × (l/5) × 3s)
Simplifying, we get:
Modified Surface Area = 9s^2 + 6s(l/5)
This accounts for the nine-fold increase in the base area (since area is proportional to the side length squared) and the change in the area of the triangular faces.
Solve x2 + 12x + 6 = 0 using the completing-the-square method. (2 points)
Answer:
[tex]\large\boxed{x=-6\pm\sqrt{30}}[/tex]
Step-by-step explanation:
[tex](a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\x^2+12x+6=0\qquad\text{subtract 6 from both sides}\\\\x^2+2(x)(6)=-6\qquad\text{add}\ 6^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(6)+6^2}_{(*)}=-6+6^2\\\\(x+6)^2=-6+36\\\\(x+6)^2=30\Rightarrow x+6=\pm\sqrt{30}\qquad\text{subtract 6 from both sides}\\\\x=-6\pm\sqrt{30}[/tex]
5 -2x + 6y= -38
? 3x – 4y = 32
•(-4, - 5)
•(-5, 4)
•(1, – 6)
(4, - 5)
Answer:
Option D (4, -5)
Step-by-step explanation:
This question can be solved by various methods. I will be using the hit and trial method. I will plug in all the options in the both the given equations and see if they balance simultaneously.
Checking Option 1 by plugging (-4, -5) in the first equation:
-2(-4) + 6(-5) = -38 implies 8 - 30 = -38 (not true).
Checking Option 2 by plugging (-5, 4) in the first equation:
-2(-5) + 6(4) = -38 implies 10 + 24 = -38 (not true).
Checking Option 3 by plugging (1, -6) in the second equation:
3(1) - 4(-6) = 32 implies 3 + 24 = 32 (not true).
Since all the options except Option 4 have been ruled out, therefore, (4,-5) is the correct answer!!!
Find the measure of the numbered angle.
Select one:
A. 62.5
B. 105
C. 112.5
D. 115
C. 112.5
Step-by-step explanation:The Angles of Intersecting Chords Theorem states:
"If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle"
So, the arc intercepted by the angle ∠5 is:
360° - 50° - 115° - 85° = 110°
On the other hand, the arc intercepted by its vertical angle is:
115°
Therefore:
[tex]\angle 5 = \frac{1}{2}(110^{\circ}+115^{\circ}) \\ \\ \boxed{\angle 5 = 112.5^{\circ}}[/tex]
The circumference of a circle is 20 π.what is the radius of this circle
Answer:
The correct option is 10....
Step-by-step explanation:
The formula of circumference of the circle is:
C = 2πr
where C is the circumference of the circle
r = radius
In this question we have given the circumference and we have to find out the radius:
Thus substitute the values in the formula:
C = 2πr
20π= 2πr
Move 2π to the L.H.S.
20π/2π = r
Cancel out π by π and 20/2 by the table of 2
Therefore we have:
10=r
Thus the correct option is 10....
Answer is provided in the image attached.
Solve 14n+ 6p-8n= 18p for n.
Answer:
Step-by-step explanation:
14n+6p-8n=18p
6n=12p
n=2p
Answer:
n = 2pStep-by-step explanation:
[tex]14n+6p-8n=18p\qquad\text{combine like terms}\\\\(14n-8n)+6p=18p\qquad\text{subtract}\ 6p\ \text{from both sides}\\\\6n=12p\qquad\text{divide both sides by 6}\\\\n=2p[/tex]
A scale drawing of an office building is not labeled, but indicates 1/4 inch=5 feet. On the drawing, one wall measures 2 inches. How long is the actual wall?
Answer:
40 ft
Step-by-step explanation:
We can use ratios to solve this problem. Put the scale over the actual size
1/4 inch 2 inches
-------------- = ----------------
5 ft x ft
Using cross products
1/4 x = 2 *5
1/4 x = 10
Multiply each side by 4
4*1/4 x = 4 * 10
x = 40
The wall is 40 ft
The radius of a circular park is 107 m. To the nearest meter, what is the
circumference of the park?
Answer: D: 672
Step-by-step explanation:
use the equation C = 2πR, where C is circumference and R is radius
re-write the equation with 107 instead of R
C=2*π*107
then solve (use 3.14 for pi and round up)
3.14*2=6.28
6.28*107=671.96
then round up to get 672
I hope this helps!
The circumference of a circular park with a radius of 107 m, calculated with the formula Circumference = 2 * π * radius, is approximately 672 m.
Explanation:The circumference of a circle is calculated by using the formula: Circumference = 2 * π * radius. In this case, the radius of the circular park is given as 107 m. Substituting the radius into the formula, we obtain: Circumference = 2 * 3.14 * 107 which equals approximately 672 m. So, to the nearest meter, the circumference of the park is 672 m.
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An item is priced at $14.32. If the sales tax is 6%, what does the item cost including sales tax
Answer:
15.1792 or 15.18
Step-by-step explanation:
14.32 timex 6% or .06 is 0.8592. You add .8592 to 14.32 and get 15.1792 or 15.18 :)
Answer:
$15.18
Step-by-step explanation:
To find the sales tax, you would multiply $14.32 by 6%.
6% = 0.06
0.06*14.32 = 0.8592
Then add the sales tax to the original price to find how much the total costs.
0.8592 + $14.32 = $15.1792
Round $15.1792 to the nearest cent since its money.
So its $15.18
a profectile is shot upward, and it's distance above the ground, in feet after s t seconds is represented by the function below. s(t)-4t^2+24t. use the number line to represent the interval on which the projectile is desce ding
Answer:
Step-by-step explanation:
the curve is representing the projectile. at t=0, the projectile is on the ground. at t=6, the projectile has finished its journey and is back on the ground. In between t=0 and t=6 will be the projectile's peak altitude. the point between t=0 and t=6 is t=3. So plug in t=3 and solve for s(t), and you get 36ft. gg
find the missing factor in exponential form 33^9 = 11^9 * blank
Answer:
3^9 * 11^9
Step-by-step explanation:
33^9 =
We know that (ab)^c = a^c * b^c
(33)^9 = (3*11)^9 = 3^9 * 11^9
If two angles are complementary and one of them is 13º, what is the measure of the other angle?
A.73
B.77
C.63
D.13
Final answer:
The measure of the other angle that is complementary to a 13º angle is 77º.
Explanation:
If two angles are complementary, it means they add up to 90 degrees. In this case, one angle is given as 13º. To find the measure of the other angle, we subtract the given angle from 90º because complementary angles sum up to 90 degrees.
So, if we let x represent the measure of the other angle, the equation becomes:
13° + x = 90°
To find x, we subtract 13 from both sides:
The calculation would be:
90º - 13º = 77º.
Therefore, the measure of the other angle is 77º.
Hence, the correct answer is:
B. 77
The center of a circle is located at (6, −1) . The radius of the circle is 4.
What is the equation of the circle in general form?
x2+y2−12x+2y+21=0
x2+y2−12x+2y+33=0
x2+y2+12x−2y+21=0
x2+y2+12x−2y+33=0
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{6}{ h},\stackrel{-1}{ k})\qquad \qquad radius=\stackrel{4}{ r} \\\\[-0.35em] ~\dotfill\\[1em] [x-6]^2+[y-(-1)]^2=4^2\implies (x-6)^2+(y+1)^2=16 \\\\\\ \stackrel{\mathbb{F~O~I~L}}{(x^2-12x+36)}+\stackrel{\mathbb{F~O~I~L}}{(y^2+2y+1)}=16\implies x^2+y^2-12x+2y+37=16 \\\\\\ x^2+y^2-12x+2y+37-16=0\implies x^2+y^2-12x+2y+21=0[/tex]
ANSWER
Option A
EXPLANATION
When a circle has it's center at (h,k) and and radius r units, then its equation in standard form is
[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
The given circle has its center at (6,-1) and its radius is r=4 units.
We plug in these values to get
[tex]{(x - 6)}^{2} + {(y - - 1)}^{2} = {4}^{2} [/tex]
[tex]{(x - 6)}^{2} + {(y + 1)}^{2} =16[/tex]
We now expand to obtain
[tex] {x}^{2} - 12x + 36 + {y}^{2} + 2y + 1 = 16[/tex]
[tex] {x}^{2} + {y}^{2} - 12x +2 y + 36 + 1 - 16 = 0[/tex]
[tex]{x}^{2} + {y}^{2} - 12x +2 y + 21 = 0[/tex]
This is the equation in general form of the circle.
Explain how to model the division of –24 by –4 on a number line.
Answer:
Here's one way to do it.
Step-by-step explanation:
-24 ÷ (-4)
-24 is the final number on the number line
-4 means you count by 4s on the number line moving backwards.
Start at 0 facing forward. Move backwards in steps of four units from 0 to -24. Count the number of steps you took (six).Answer: +6 (The sign is + because you are still facing forward).
After modeling the division of [tex]-24[/tex] by [tex]-4[/tex] on the number line, we reach to zero after [tex]6[/tex] steps.
What is a number line?" Number line is defined as a straight line which represents the number at the equal interval on it on the both the side of zero."
According to the question,
Given division,
[tex](-24)[/tex] by [tex](-4)[/tex]
As shown on the model of number line the given division we have,
[tex](-24)[/tex] divided by [tex](-4)[/tex] is perfectly divisible.To reach zero moves [tex]6[/tex] steps to the right side of [tex](-24)[/tex] .Each step represents the movement of [tex](-4)[/tex].Hence, after modeling the division of [tex]-24[/tex] by [tex]-4[/tex] on the number line, we reach to zero after [tex]6[/tex] steps.
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What is the area of the hexagon? O 60 O 68 O 120 O 106
The hexagon is made up of two trapezoids, each having the following dimensions:
[tex]a=12\text{ m}\\b=5\text{ m}\\h=4\text{ m}[/tex]
So, its total area is the sum of the areas of those two trapezoids.
[tex]A_h=2A_t=2\cdot\dfrac{1}{2}(a+b)h=(a+b)h\\A_h=(12+5)\cdot 4=68\text{ m}^2[/tex]
Find the product.
(y-3)(y-4)=
Answer:
y^2+12-7y
Step-by-step explanation:
(y-3)(y-4)
I will split it up for us
y*y= y^2
-3*y= -3y. \
y*-4= -4y. / -7y
-3*-4= 12
y^2+12-7y
The product of (y-3)(y-4), is y^2 - 7y + 12.
To find the product of (y-3)(y-4), we will use the FOIL method, which stands for First, Outer, Inner, Last. This method is used to multiply two binomials.
First: Multiply the first terms of each binomial: y × y = y^2.
Outer: Multiply the outer terms: y × -4 = -4y.
Inner: Multiply the inner terms: -3 × y = -3y.
Last: Multiply the last terms of each binomial: -3 × -4 = 12.
Adding these products together, we get: y^2 - 4y - 3y + 12. Simplifying by combining like terms, the final product is: y^2 - 7y + 12.
Find the area of a trapezoid
Answer:
see below
Step-by-step explanation:
395.2
Step-by-step explanation:
Area of a trapezoid is:
A = ½ (a + b) h
where a and b are the top and bottom lengths and h is the height.
If 7.6 refers to the entire side length, then the area is:
A = ½ (2.6 + 7.6) (4)
A = 20.4
If 7.6 refers only to the length right of the right angle, we can use Pythagorean theorem to find the length on the left:
x² + 4² = 5²
x = 3
So the whole side length is 3 + 7.6 = 10.6. That means the area is:
A = ½ (2.6 + 10.6) (4)
A = 26.4
Need help asap less than 20
Answer:
D. 113°, Consecutive interior angles theorem.
Step-by-step explanation:
We use the interior angle theorem which states that when 2 lines are parallel and are intersected by a transversal, the interior angles on one side add up to 180°
67° and angle 2 are therefore supplementary angles.
67+ angle2=180°
angle2= 180-67 =113°
g(x) = 5x - 12. What is g(8)?
Answer:
28
Step-by-step explanation:
Substitute 8 for x in g(x) = 5x - 12:
g(8) = 5(8) - 12 = 28
By using PEDMAS rule, g(8) = 28
What is PEDMAS rule?PEDMAS rule states that the order of operation starts with the parentheses first or the calculation which is enclosed in brackets. Then the operation is performed on exponents(degree or square roots) and later we do operations on division & multiplication and at last addition and subtraction.
Given
g(x) = 5x - 12
Substitute x = 8
g(8) = [tex]5\times 8-12[/tex]
Calculate the product
g(8) = [tex]40-12[/tex]
Calculate the sum or difference
g(8) = 28
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El exceso de un número sobre 20 es igual a las tres cuartas partes del mismo número. ¿Cuál es el número?
Answer:
The number is 80
Step-by-step explanation:
The question in English is
The excess of one number over 20 equals three quarters of the same number. What is the number?
Let
x ------> the number
we know that
The linear equation that represent this situation is
[tex]x-20=\frac{3}{4}x[/tex]
Solve for x
[tex]x-\frac{3}{4}x=20[/tex]
[tex]\frac{1}{4}x=20[/tex]
[tex]x=80[/tex]
therefore
The number is 80
Write the equation of the line that passes through the points (7, –4) and (–1, 3), first in point-slope form, and then in slope-intercept form.
Final answer:
The equation of the line through (7, -4) and (-1, 3) has a slope of -7/8. It can be written in a point-slope form as y + 4 = -7/8(x - 7), and in slope-intercept form as y = -7/8x + 25/8.
Explanation:
To write the equation of the line that passes through the points (7, –4) and (–1, 3), the first step is to find the slope of the line. The slope (m) is given by the rise over run, which is the change in y divided by the change in x:
m = (3 - (-4)) / (-1 - 7) = 7 / -8 = -7/8Now that we have the slope, we can use the point-slope form which is given by the formula:
y - y1 = m(x - x1)We can choose one of the points for x1 and y1; let's use (7, -4):
y - (-4) = -7/8(x - 7)Therefore, the point-slope form of the line is:
y + 4 = -7/8(x - 7)Now, to convert this into the slope-intercept form (y = mx + b), we just solve for y:
y = -7/8x + 7/8 × 7 - 4After simplifying the constant term:
y = -7/8x + 25/8The slope-intercept form is y = -7/8x + 25/8, where -7/8 is the slope and 25/8 is the y-intercept.
What is the only even prime number?
Answer:
2 is the only even prime number.
Step-by-step explanation:
Two is the only even prime number. It's the only even number that can be divided by only itself (2) and one.
Hope this helped!
~Just a girl in love with Shawn Mendes
An online store sells two types of speaker docks for smartphones. The higher-priced speaker dock sells for $170 and the lower-priced speaker dock sells for $90. Last week the store sold three times as many lower-priced speaker docks as higher-priced speaker docks. Combined sales totaled $3,080. How many lower-priced speaker docks did it sell?
Answer:
7 high priced speakers
21 Low priced speakers
Step-by-step explanation:
170x7 =1190
90x21=1890
1890+1190=3080
90’s are the low speaker docks, and 170’s are the high speaker docks.
3 times 90 is 270, plus 170 is 440
3080 divided by 440 is 7, the number of 170’s they sold. 7 times 3 is 21, the number of 90’s they sold.
Use the recursive formula to answer the question.
a(1)=20 a(n)=a(n)-1-5
What is the 4th term in the sequence?
Answer:
5
Step-by-step explanation:
[tex]\tt a_n=a_{n-1}-5\\\\ a_1=20\\a_2=a_1-5=20-5=15\\a_3=a_2-5=15-5=10\\a_4=a_3-5=10-5=5[/tex]
Sound travels along a telephone cable at 1.91 * 10^8 ms^-1 .How long does it take Tetsuo's voice to travel from his office phone in Tokyo to his wife's phone 3740m away?
Answer:
1.958 * 10^-5 seconds or 0.00001958 seconds.
Step-by-step explanation:
3740 = 3.74 * 10^3 in scientific notation.
Time = distance / speed.
= 3. 74 * 10^3 / 1.91 * 10^8
= 1.958 * 10^-5 seconds.
It takes Tetsuo's voice approximately 1.96*10^-5 seconds to travel from his office phone in Tokyo to his wife's phone 3740m away using the speed of sound in telephone cables.
Explanation:SolutionTo find the time it takes for sound to travel a certain distance, we can use the formula time = distance / speed. In this case, the speed of sound along the telephone cable is 1.91 * 10^8 ms⁻¹ and the distance is 3740m.
So the time = 3740 / 1.91 * 10^8 = 1.96 * 10^-5 seconds.
Therefore, it takes Tetsuo's voice approximately 1.96*10^-5 seconds to travel from his office phone in Tokyo to his wife's phone 3740m away.
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simplify: (8 2/3^4)
Answer:
Simplify:
[tex](8\frac{2}{3} )^4[/tex]
Step-by-step explanation:
[tex](8\frac{2}{3})^4 =(\frac{26}{3} )^4=\frac{456976}{81}[/tex]
Answer:
The answer is
650/81
Step-by-step explanation:
I think this is a better representation
Of the given expression
(8 2/3^4)
To solve the problem let us perform a step by step operation
Step one
Let's us solve the bracket terms first
=(8 2/3^4)
3⁴= 3*3*3*3=81
=(8 2/81)
=Simplifying we have
=((81*8)+2)/81
=(648+2)/81
=650/81
what are all the possible rectangles with whole-number side
lengths that have a perimeter of 10 units.
Answer:
So (L,W) possibilities are:
(1,4),(4,1),(2,3),(3,2)
That makes 4 possibilities.
Step-by-step explanation:
The perimeter of a rectangle is P=2L+2W where L is the length and W is the width.
We have that P=10, so 10=2L+2W.
10=2L+2W
10=2(L+W) By factoring using the distributive property.
2(5)=2(L+W) I factored 10 as 2(5).
If 2(5)=2(L+W), then 5=L+W.
Whole numbers are {0,1,2,3,4,5,6,7,8,9,10,...}. They are your counting numbers and 0.
I think they want natural numbers {1,2,3,4,...}. This is also just called the counting numbers. The reason I think they want this because if one of the dimensions is 0, we won't actually have a rectangle.
So now looking for numbers from this set that satisfy: L+W=5.
L+W=5
1+4=5
4+1=5
2+3=5
3+2=5
So (L,W) possibilities are:
(1,4),(4,1),(2,3),(3,2)
That makes 4 possibilities.
The sum of the two digits of a number is 16. The number formed by reversing the digits is 18 more than the original
number. Determine the original number.
Let t = the tens digit, u = the units digit, and u + t = 16. Which of the following equations would complete the system?
Answer:
10u+t=18+10t+u
(If this doesn't match one of the equations, please post your options so I can put it in the form of one of your options.)
Step-by-step explanation:
Let there be a number [tu] where t is the tens and u is ones digit.
t+u=16.
Now we reverse the number [ut] is 8 more than [tu].
[ut]=18+[tu]
So [ut]=10u+t because u is the tens and t is the ones digit
and [tu]=10t+u because t is the tens and u is the ones digit.
The equation you are looking for is
10u+t=18+10t+u.
Let's solve it just for fun:
Subtract u on both sids:
9u+t=18+10t
Subtract 10t on both sides:
9u-9t=18
Divide both sides by 9:
u-t=2
The system is:
u-t=2
u+t=16
--------------add!
2u =18
u=9
If u=9 and u+t=16, then t=7.
To the original number is 79.
The new number is 97 (is this 18 more than the other; yep).
Answer:
97.
Step-by-step explanation:
SOLVE y = 3x – 2 x – y = 4 BY USING SUBSTITUTION!! SHOW ALL WORK! HELPPP!
The value of x = -1
The value of y = -5
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be A
The value of A is
y = 3x - 2 be equation (1)
Let the second equation be B
The value of B is
x - y = 4 be equation (2)
On simplifying equation (2) , we get
Adding y on both sides of the equation , we get
x = y + 4 be equation (3)
Substituting the value of x in equation (1) , we get
y = 3x - 2
y = 3 ( y + 4 ) - 2
y = 3y + 12 - 2
y = 3y + 10
Subtracting y on both sides of the equation , we get
2y + 10 = 0
Subtracting 10 on both sides of the equation , we get
2y = -10
Divide by 2 on both sides of the equation , we get
y = -5
Substitute the value of y in equation (3) , we get
x = y + 4
x = -5 + 4
x = -1
Therefore , the value of x is -1 and the value of y is -5
Hence , The value of x = -1
The value of y = -5
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Final answer:
To solve the equations using substitution, isolate y from the first equation, substitute it into the second, solve for x, and then use the value of x to find y. The solution to the system is x = -1 and y = -5.
Explanation:
To solve the system of equations by substitution, we will first isolate y in one of the equations and then substitute it into the other equation.
Step 1: Isolate y in the first equation.
We have y = 3x - 2. This equation is already solved for y, so we can use it as our substitution.
Step 2: Substitute y into the second equation.
Our second equation is x - y = 4. We substitute y with 3x - 2 to get x - (3x - 2) = 4.
Step 3: Solve for x.
Now, we simplify and solve for x:
x - 3x + 2 = 4
-2x + 2 = 4
-2x = 4 - 2
-2x = 2
x = -1
Step 4: Substitute x back into the first equation to solve for y.
Using x = -1 in the first equation y = 3x - 2, we get:
y = 3(-1) - 2
y = -3 - 2
y = -5
Therefore, the solution to the system of equations is x = -1 and y = -5.
Find the value of 1.85+38*4.1
Answer:
157.65
Step-by-step explanation:
38*4.1=155.8
155.8+1.85=157.65
For this case we must find the value of the following expression:
[tex]1.85 + 38 * 4.1 =[/tex]
According to the PEMDAS algebraic resolution method, multiplications must be made before the addition. So, we have:
[tex]1.85 + 155.8 =[/tex]
Adding we have:
157.65
Answer:
157.65
Which of the following appear in the diagram below?
Check all that apply
PLZZ HELP ME ASAP
In the given Angles and Rays question, Based on the given diagram descriptions, the correct answers are ray AB, ∠DCE, and ray CE. Therefore, the correct options are: B. ∠DCE, C. ray AB, D. ray CE.
The given question seems to be talking about geometric figures involving rays and angles. From the description, we know that there are two diagrams. The first diagram contains a ray namely AB and the second diagram contains two rays namely CD and CE forming angle DCE at common point C.
Based on the given information, Ray AB is correct because it's mentioned explicitly in first diagram. Angle DCE, represented as ∠DCE, is also correct as it has been stated to exist in the problem description within the second diagram. Lastly, ray CE is a legitimate answer as it is a fundamental part of the second figure forming an angle with ray CD at point C.
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