Hey there! :)
Answer:
SA = 144 cm².
Step-by-step explanation:
Find the surface area by calculating the areas of each of the lateral sides and bases:
In this instance, the bases are triangles, so the formula A = 1/2(bh) will be used:
Bases:
A = 1/2(bh)
A = 1/2(4·3)
A = 1/2(12)
A = 6 cm².
There are two bases, so:
6 × 2 = 12 cm²
Find the areas of the lateral sides using A = l × w:
5 × 11 = 55 cm²
4 × 11 = 44 cm²
3 × 11 = 33 cm²
Add up all of the areas:
12 + 55 + 44 + 33 = 144 cm².
Answer:
144 cm^2
Step-by-step explanation:
So, first find the area of the triangle. To find that you need to use the formula A = bh ÷ 2 (Area = base x height ÷ 2)
A = (4)(3) ÷ 2
A of triangle = 6
Since there are 2 triangles, you need to multiply the area by 2, which equals 12.
To find the area of the rectangles, you need to use the formula A = lw (Area = length x width)
For the first rectangle,
A = 11 x 5
A = 55
For the second rectangle,
A = 4 x 11
A = 44
For the third rectangle,
A = 3 x 11
A = 33
Now, you need to add the areas of the triangles and rectangles together to get your surface area.
12 + 55 + 44 + 33 = 144cm^2
So, the surface area of the triangular prism is 144 cm^2.
find the difference between the endpoints of the interval on the y-axis. (1) [y-value at x=p] - (2) [y-value at x=p+k]
I know you don't need this anymore but for the ones who do this is the answer.........Look at the graph and trust it. Yes, I know it says to substitute and you can following the last page on part a) Doing what they do in the tables and it will get you the same answer as if you'd just look at the graph.
The answer for the y- value at x=p IS 8. and the answer for the y-value at x=p+k IS 5. So go ahead and write that down if you haven't already!
For step2 Find the difference between the endpoints of the interval on the y-axis. The answer to your question, Is and always will be 3! The difference is 3 because you subtract 3 from 8 and you get 5.
If you didn't read clearer, I'll write it for you again, The length interval is K, it is the length between p and p+k.
For the following questions, does your answer to step 2 depend on p, well I suppose. This is why....The answer does depend on p because we are dealing with a slope. if you move up or down the slope it will not be the same.
For the question..... Is the difference between the y-values the same regardless of where the interval starts? The answer is yes!!! And No!!! But WRITE YES! Why? Because if the interval moves as a whole the difference between the y-values is the same! Try it for yourself. Move K back two x-values and the difference for the y-values will be the same, IT WILL STILL BE THREE.
Hope you understood!
And for part one the answer on part c (-2). It depends on K.
Helppp!!!! please!!!
Answer: B. rectangular pyramid
The sum of digits in two-digit number is 13. If the place values of the digits are reversed, the new number is 27 more than the original number. Find the original number.
Answer: 58
Step-by-step explanation:
The sum of the two digit number is 13. On reversing its digits the new number is 27 more than the original number find the number?
Let's set up a system with two variables: x = tens place of our answer, y = units place of our answer.
Digit sum of a two digit number is 6:
x+y=13
Reverse the digits and you get 27 more than the original value:
10y+x=10x+y+27
Now let's solve:
y=13-x
10(13-x)+x=10x+(13-x)+27
130-10x+x=130x-10x + 27
130-9x=9x+40
-90=18x
x=5
y=13-5
y=8
So our original number was 58. Sum of digits is 13. Swap the order of the digits to make 85, and you have a number 27 more than the original number.
The value of original number is, 58.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The sum of digits in two-digit number is 13.
And, If the place values of the digits are reversed, the new number is 27 more than the original number.
Now, Let the one's place digit is y and the ten's place is x of the original number.
Then, We get;
⇒ x + y = 13 .. (i)
And, If the place values of the digits are reversed, the new number is 27 more than the original number.
So, We get;
⇒ 10y + x = 27 + 10x + y
⇒ 10y - y + x - 10x = 27
⇒ 9y - 9x = 27
⇒ y - x = 3
⇒ y = x + 3 ... (ii)
Substitute the value of y from (ii) in (i), we get;
⇒ x + y = 13
⇒ x + x + 3 = 13
⇒ 2x = 13 - 3
⇒ 2x= 10
⇒ x = 5
And, From (ii);
⇒ y = x + 3
⇒ y = 5 + 3
⇒ y = 8
Thus, The original number is,
⇒ 10x + y = 10 × 5 + 8
= 50 + 8
= 58
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The numbers $1,$ $2,$ $\dots,$ $10$ are to be entered into the 10 boxes shown below, so that each number is used exactly once: \[P = (\square + \square + \square + \square + \square)(\square + \square + \square + \square + \square).\]What is the maximum value of $P$? What is the minimum value of $P$?
Answer:
Maximum = 756
Minimum = 600
Step-by-step explanation:
A square is a shape that has the large areas of a defined perimeter out of available rectangles. It implies they want the two parentheses to be as similar in value. as a result, to establish the maximum value of P.
And to establish the minimum value, to have the greatest difference for them. 1 + 2 + 3 ... +10=55, which wasn't even but which can be split as similarly as possible into 27 and 28 which have a product of 756. In this question it can be done in a variety of ways, one of which is:
(1 + 3 + 5 + 8 + 10) × (2 + 4 + 6 + 7 + 9) = 756
At the very least, the biggest difference can be created if one term is made of the smallest numbers, while the other full of the highest, or:
(1 + 2 + 3 + 4 + 5) × (6 + 7 + 8 + 9 + 10)=600
Which of the following functions is graphed below?
8
84
4.
24
-8
2
4
8
8
12
-2
4
-6+
-87
Answer:
Step-by-step explanation:-
-
-8239910.76
question 1: 5 1/8 is 2/3 of what number?
question 2: what fraction of 9 3/8 is 4 3/8?
Answer:
1) [tex]7 \frac{11}{16} [/tex]
2) [tex] \frac{7}{15} [/tex]
Step-by-step explanation:
1) Let's convert the mixed fraction into a improper fraction.
[tex]5\frac{1}{8} \\ = \frac{5(8) + 1}{8} \\ = \frac{41}{8} [/tex]
Let the number be x.
[tex] \frac{2}{3} x = \frac{41}{8} \\ x = \frac{41}{8} \div \frac{2}{3} \\ x = \frac{41}{8} \times \frac{3}{2} \\ x = \frac{123}{6} \\ x = 7 \frac{11}{16} [/tex]
2)[tex]4 \frac{3}{8} = \frac{35}{8} [/tex]
[tex]9 \frac{3}{8} = \frac{75}{8} [/tex]
[tex]4 \frac{3}{8} \div 9 \frac{3}{8} \\ = \frac{35}{8} \div \frac{75}{8} \\ = \frac{35}{8} \times \frac{8}{75} \\ = \frac{7}{15} [/tex]
Help please on linear math
Answer:
D
Step-by-step explanation:
[tex]y=\frac{-9x-5}{-8}[/tex]
factoring out a negative[tex]y=\frac{9x+5}{8}[/tex]
Answer:
[tex] \frac{5}{8} [/tex]Option D is the correct option.
Step-by-step explanation:
Given that
9x - 8y = 0
finding y-intercept
put x = 0 , we get
9(0) - 8y + 5 = 0
Calculate the product
-8y + 5 = 0
Move the constant to L.H.S and change its sign
-8y = 0 - 5
Calculate the difference
-8y = -5
divide both sides of the equation by -8
-8y/-8 = -5/-8
Calculate
y = 5/8
Hope this helps...
Good luck on your assignment...
which of the following shows the polynomial below written in descending order?
Answer:
A
Step-by-step explanation:
Descending order is where the monomials of a polynomial are arranged in decreasing exponent order so the answer is A.
Answer:
the answer is option a because all the expression in option a is written descending power form.
Which number(s) below belong to the solution set of the inequality Check all that apply. x + 30 < 60 a.50 b.45 c.300 d.1 e.29 f.30
Answer:
e.29 d.1
Step-by-step explanation:
x+30<60 :we will replace with the values we have :
300 that's a big number . Obviously it isn't a solution 50 : 30+50 = 80>60 so no 45: 30+45= 75 >60 so no 30+30 = 60 we have < not ≤ so no 1 yes . it's obvious 29 +30 = 59<60 so yes !which shape is a parallelogram?
Answer:
A,C,and D are parralelograms
The parallelogram are shapes with figures having opposite sides which are parallel
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The sum of angles of a parallelogram is 360°
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the parallelogram be represented as ABCD
Now , from the figure 1
a)
The figure is having opposite sides are parallel
where AB = CD
And , BC = AD
So , it is a parallelogram
b)
The figure does not have any sides parallel
So , it is not a parallelogram
c)
The shape is having 2 sides as parallel
And , AB = CD
So , it is a parallelogram
d)
The shape is having 2 sides as parallel
And , AB = CD
So , it is a parallelogram
Hence , the parallelogram is solved
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find the value of a and b for which the system of equations has infinitely many solutions : 2x + 3y = 7 ; (a-b)x + (a+b)y = 3a + b - 2
Answer:
a= 5 and b=1
Step-by-step explanation:
To solve, we will follow the steps below:
2x + 3y = 7
(a-b)x + (a+b)y = 3a + b - 2
We should note that since it has infinitely many solutions then,
[tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }[/tex]
Hence
2/a-b = 3/a+b = 7/3a +b-2
2/a-b = 3/a+b
cross-multiply
3(a-b) = 2( a+b)
open the bracket
3a - 3b = 2a + 2b
collect like term
3a - 2a = 2b + 3b
a = 5b -------------------------------------------(1)
Similarly
3/a+b = 7/3a +b-2
cross-multiply
7(a+b) = 3(3a+b -2)
7a + 7b = 9a + 3b -6
take all the variables to the left-hand side of the equation
7a - 9a+ 7b-3b = -6
-2a + 4b = -6 ---------------------------------(2)
but a = 5b
substitute a= 5b in equation (2) and solve for b
-2(5) + 4b = -6
-10 + 4b = -6
add 10 to both-side of the equation
-10 + 10+ 4b = -6+10
4b = 4
divide both-side of the equation by 4
b = 1
substitute b= 1 in equation (1)
a = 5b
a =5(1)
a=5
Therefore, a= 5 and b=1
WILL GIVE BRAINLIEST THANKS AND 5 STARS... PLZ HELP
Answer:
507x223 is greater than 530 x 200
914x385 is less than 900 x 400
If (ax+b)(bx+a)=26x^2+ Box(x) +26, where a, b, and Box are distinct integers, what is the minimum possible value of Box, the coefficient of x?
Question in latex: If $(ax+b)(bx+a)=26x^2+\Box\cdot x+26$, where $a$, $b$, and $\Box$ are distinct integers, what is the minimum possible value of $\Box$, the coefficient of $x$?
Answer:
16.59
Step-by-step explanation:
Given:
[tex](ax+b)(bx+a)=26x^2+\Box\cdot x+26[/tex]
Expanding the left hand side, we have:
[tex](ax+b)(bx+a)=abx^2+a^2x+b^2x+ab\\=abx^2+(a^2+b^2)x+ab\\=26x^2+\Box\cdot x+26\\ab=26 \implies b=\frac{26}{a}[/tex]
Therefore:
[tex]a^2+b^2=a^2+\dfrac{26}{a} =\dfrac{a^3+26}{a}[/tex]
To find the minimum value, we take the derivative and solve for its critical point.
[tex]\frac{d}{da} (\frac{a^3+26}{a})=\frac{2a^3-26}{a^2}\\$Setting the derivative equal to zero, we have:\\2a^3-26=0\\2a^3=26\\a^3=13\\a=\sqrt[3]{13}[/tex]
Recall that:
[tex]\Box=a^2+b^2=\dfrac{(\sqrt[3]{13}) ^3+26}{\sqrt[3]{13}}\\=\dfrac{13+26}{\sqrt[3]{13}}\\\\\Box=16.59[/tex]
The minimum possible value of the coefficient of x is 16.59.
Answer:
173
Step-by-step explanation:
For sympliciy let the box equal y.
Expanding the left side we get (a*x+b)(b*x+a) = (a*b*(x)^2 + (a^2 + b^2)x + a*b). Hence we have that (a*b*(x)^2 + (a^2 + b^2)x + a*b) = 26*(x)^2 + x*y + 26. Scince the coefficients of like terms in our equation must be equal, ab=26. Hence (a,b) = (1,26),(26,1),(-1,-26),(-26,-1),(2,13),(13,2),(-2,-13),(-13,-2). Since a^2 + b^2 = y we can see that the only 2 values of y are 677 and 173 (by simply plug in the values of (a,b)), taking the smaller of the two our answer is [173].
Two pathways meet at 30° to each other. One pathway has lighting and the other does not.
The distance between successive lights on the lighted pathway is 5 metres. Each light has a
range of effective illumination of 6 metres.
What length of the pathway without lights is illuminated by the pathway with lights?
Answer:
12 meters
Step-by-step explanation:
Draw a picture of the two pathways 30° apart. Add a circle representing the illumination of the light on one of the pathways. Draw a line from the center of the circle to the last point where it intersects the pathway without lights.
This forms a triangle. One leg is x, the length of the pathway without lights. Another leg is 5n, where n is an integer. This represents how far the light is from where the pathways meet. The third and final leg is 6, the radius of the illumination.
Use law of cosine to solve:
6² = x² + (5n)² − 2x(5n) cos 30°
36 = x² + 25n² − 5√3 xn
0 = x² − 5√3 xn + 25n² − 36
In order to have a solution, the discriminant must be greater than or equal to 0.
b² − 4ac ≥ 0
(-5√3 n)² − 4(1)(25n² − 36) ≥ 0
75n² − 100n² + 144 ≥ 0
144 − 25n² ≥ 0
144 ≥ 25n²
144/25 ≥ n²
12/5 ≥ n
So n must be an integer less than 12/5, or 2.4. Therefore, the largest value of n is 2. Substituting:
0 = x² − 5√3 x(2) + 25(2)² − 36
0 = x² − 10√3 x + 64
Solve with quadratic formula:
x = [ 10√3 ± √(300 − 4(1)(64)) ] / 2(1)
x = (10√3 ± √44) / 2
x = 5√3 ± √11
x ≈ 5.34 or 11.98
We want the larger value of x. So approximately 12 meters of the pathway without lights is illuminated.
The planet mercury is approximately 6*10^7 miles from the sun. The distance between the sun and mars is approximately 2*10^8 miles. About how many times farther from the sun is mars than mercury.
Answer:
Around 10/3 or 3.33 times farther.
Step-by-step explanation:
We simply divide the larger distance by the smaller distance to find our ratio:
2(10⁸)/6(10⁷)
10/3
*Remember when you divide exponents, you subtract them
The following table shows the possible meal combinations when choosing an entrée and a side dish at Marty's Diner. Side Dish Entrée burger with salad burger with fries burger with fruit tacos with salad tacos with fries tacos with fruit pizza with salad pizza with fries pizza with fruit What is the probability of selecting a combination that includes a burger or a salad? Enter your answer as a reduced fraction, like this: 3/14
Answer:
5/9
Step-by-step explanation:
There are 9 total combinations and 3 of them include a burger, 2 of them that have salad but not a burger. If you add them together it equals 5/9
The probability of selecting a combination that includes a burger or a salad is 5/9
Since the total of 6 outcomes include fries or fruit as the side dish.
There is a total of 9 possible meal combinations. A person must choose an Entree and a side dish.
The Entrees consist of burgers, tacos, and pizzas.
The side dishes consist of salad, fries, and fruit.
To find the number of combinations consisting of fries or fruit, we calculate the individual combinations.
With fries as side dish, which can choose a burger, a pizza or a taco as your Entree.
There are 3 combinations each, there are a total of 6 combinations with fruit or fries as the side dish.
There are 9 total combinations and 3 include a burger, rest 2 that have salad but not a burger.
then probability = 5/9
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PLEASE HELP!
Evaluate the following using exact radian measure. Show all of your work.
[tex]cot { }^{ - 1} ( - \frac{1}{ \sqrt{3} } )[/tex]
Answer:
PEMDAS DAT
Step-by-step explanation:
New packaging for fruit snacks contains 10% less weight than the original packaging. If the new package costs 15% more than the original package, by what fraction did the unit price increase? Express your answer as a common fraction.
Answer:
5/18
Step-by-step explanation:
Let's say the original packaging was 1 lb of packaging for $1.
The cost was $1/lb.
Then the weight went down by 10% and the price went up by 15%.
Now 0.9 lb of packaging cost $1.15.
The new unit cost is $1.15/(0.9 lb)
The difference is
$1.15/(0.9 lb) - $1/lb =
= $1.15/(0.9 lb) - $0.9/(0.9 lb)
= $0.25/(0.9 lb)
=$25/(90 lb) = $5/(18 lb)
The price went up by 5/18.
please i know the awnser is 60 but i cant explain it
Answer:
a) 60 degrees
Step-by-step explanation:
b) The triangle shown is an equilateral triangle as all the sides are the same. This means that all the angles are the same as well.
Angles in a triangle add up to 180 degrees. There are 3 angles. Each angle is 60 degrees.
Angle x is an exterior corresponding angle and hence, that is why x = 60 degrees.
hope this helps : )Answer:
All of the measures of the interior angles of an equilateral triangle are 60°. Because x and 60° are alternate interior angles of parallel lines, this means that they are equal, therefore x = 60°.
2+2 what does it 1+!
Answer:
4 AND 2
Step-by-step explanation:
Answer:
Hello!
______________________
This question is very easy.
2 + 2 = 4
1 + 1 = 2
Step-by-step explanation: Add.
Hope this helped you!
What is the ratio of the Volume of the smaller pyramid to the larger pyramid
Can anyone help with this?
Answer:
115/5 23 so 20% =23 23x4 =92
Square all the integers from 1 to 10 inclusive. Then, round each number to the nearest hundred. Finally, sum the numbers. What do you get?
Answer:
22.467
Step-by-step explanation:
Hello,
You just have to do the computation in XL or using a calculator, and round each number to the nearest hundred
x sqrt(x)
1 1
2 1.414
3 1.732
4 2
5 2.236
6 2.449
7 2.646
8 2.828
9 3
10 3.162
and do the sum which is 22.467
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
300
Step-by-step explanation:
First let's square all the integers from 1 to 10 inclusive. We get:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100.
Rounding to the nearest hundred, we get that 1, 4, 9, 16, 36, and 49 all round to 0 and 64, 81, and 100 round to 100.
Therefore, we obtain
0+0+0+0+0+0+0+100+100+100,
or 300.
In circle C. r = 32 units.
What is the area of circle C?
A
32īt units?
c
641 units?
256TI units
1024Tt units?
Answer:
1024 pi
Step-by-step explanation:
r = 32 units.
Area = pi * r^2
Area = 3.14 * 32^2
Area = 1024 * pi
Tt = pi??
Find the total surface area of this triangular prism...
Answer:
144 cm^2
Step-by-step explanation:
8x6+4x10+4x8+4x6
48+40+32+24
80+40+24
120+24
144
HELPPP DO NOT LOOK IT UP PLS
At which root does the graph of f(x) = (x + 4) 6(x + 7)5 cross the x-axis?
-7
4
4
07
Answer:
-7 and -4
Step-by-step explanation:
The graph of the function f(x) = (x + 4)⁶ (x + 7)⁵ cross the X axis at x = -4 and x = -7.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given is a function,
f(x) = (x + 4)⁶ (x + 7)⁵
When the function cross the X axis, the value of the function will be 0.
Let f(x) = 0
(x + 4)⁶ (x + 7)⁵ = 0
This implies that, either x + 4 = 0 or x + 7 = 0
x + 4 = 0 ⇒ x = -4
x + 7 = 0 ⇒ x = -7
Hence the roots are -4 and -7 where the function crosses the X axis.
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Dos familias asisten a un sitio de comidas rápidas de la ciudad, una de ellas pide 4 perros calientes y 3 hamburguesas y pagan 43000 pesos, la otra familia, piden 5 perros calientes y 1 hamburguesa y pagan 34500 pesos, se desea saber ¿cuál es el valor de cada perro y de cada hamburguesa?.
Answer:
Cada perro caliente cuesta 5,500 pesos y cada hamburguesa cuesta 7,000 pesos.
Step-by-step explanation:
Sea x el precio de los perros calientes y y el precio de las hamburguesas.
Escribiendo los datos de la primera familia en forma de ecuación tenemos:
[tex]4x+3y=43,000[/tex] (4 perros calientes y 3 hamburguesas cuestan 43,000 pesos)
Escribiendo los datos de la segunda familia:
[tex]5x+y=34500[/tex] (5 perros calientes y 1 hamburguesa cuestan 34,500 pesos)
Vamos a resolver este sistema de ecuaciones por el método de suma y resta:
[tex]4x+3y=43,000\\5x+y= 34,500[/tex]
Multiplicando la segunda ecuación por -3 y sumando ambas tenemos:
[tex]4x+3y=43,000\\-15x-3y= -103,500\\\\-11x=-60,500\\x=-60,500/-11\\x= 5,500[/tex]
Por lo tanto, un perro caliente cuesta 5,500 pesos.
Ahora sustituimos este valor en nuestra segunda ecuación para encontrar el precio de las hamburguesas:
[tex]5x+y=34500\\5(5,500)+y=34,500\\27,500 +y=34,500\\y=34,500-27,500\\y=7,000[/tex]
Por lo tanto, las hamburguesas cuestan 7,000 pesos cada una
Consider the following 8 numbers, where one labelled x is unknown.
11, 1, 34, x, 41, 10, 47, 2
Given that the range of the numbers is 67,
work out 2 values of x.
Answer:
x=-20 or x=68
Step-by-step explanation:
you can either make it so 47 remains the largest number and so take 67 from 47 (=-20) or you can leave 1 as the smallest number and add 67 to 1 (=68)
Urgent ‼️50 POINTS NO BS OR I WILL REPORT YOU Why is partitioning a directed line segment into a ratio of 1:3 not the same as finding 1/3 the length of the directed line segment?
Answer:
3rd option
Step-by-step explanation:
The ratio of 1:3 mean that one part is 1 to the other part being 3.
That means the total is 1 + 3 = 4.
1 part to 3 parts is the same as 1 part to a whole of 4 and 3 parts to a whole of 4.
Answer: 3rd option
Answer:
The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.
Step-by-step explanation:
I like to call the numbers in the ratio 1 : 3 "ratio units".
That is, the short length is 1 ratio unit long, and the longer length is 3 ratio units long. The total (whole) length is 1+3 = 4 ratio units long. Then the short length (1 ratio unit) is 1/4 of the whole length (4 ratio units).
_____
Coment on the answer wording
I think you need to be careful with terminology. The word "part" has a different meaning in the first answer sentence "... part to part" than it does in the second answer sentence "... parts in the whole ...".
In the first sentence, it refers to "a piece of the line, no matter its length." In the second sentence, it refers to "that length of the line represented by 1 in the ratio."