The volume of this prism is 3150 cm³.
How to find the volume of the prism?step1:
given 11cm, 19cm, 14cm, 11cm
To find: volume of given prism
the given prism is combination two prism
Triangular prism
cuboidal prism
volume of cuboidal prism =l*b*h
=(15*14*11) cm^3
=2310cm^3
step2:
volume of triangular prism=1/2*l*b*h
=1/2*15*8*14
=840cm^3
step3:
volume of given prism=volume of cuboid + volume of triangular prism
=(2310+840)cm^3
=3150cm^3
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What is the length of Line segment B C?
Answer:
(c) 15 units
Step-by-step explanation:
Given a right triangle with hypotenuse 17 and one leg 8, you want the measure of the other leg.
Pythagorean theoremThe Pythagorean theorem tells you the relationship between the sides of a right triangle:
a² +b² = c² . . . . . . where c is the hypotenuse
Applicationa² +8² = 17² . . . . . . using given values of b, c
a² = 289 -64 = 225 . . . . subtract 8²
a = √225 = 15
The length of segment BC is 15 units.
__
Additional comment
These side lengths {8, 15, 17} can be considered to be a "Pythagorean triple." It is one of a few that often appear in algebra and geometry problems. Others include {3, 4, 5}, {5, 12, 13}, {7, 24, 25}. Multiples of these are also commonly seen, such as 2×{3, 4, 5} = {6, 8, 10}.
What is the derivative of ln ln 4x ))?
what type of variable is the number of gallons of gasoline pumped by a filling station during a day? qualitative continuous attribute discrete
The number of gallons of gasoline pumped by a filling station during a day represents a B: "quantitative " type of variable.
Quantitative variables are data about numeric values such as how much; how often; or how many. In other words, quantitative variables are referred to as any variables that represent amounts, such as age, height, or weight.
In the given case, it is talked about the number of gallons of gasoline filled during a day; since it represents the quantity or number of gallons so it is a type of quantitative variable, representing the number of gallons of gasoline to be pumped.
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What is the slope of the line?
m
Answer:
Step-by-step explanation:
using the rise over run method:
1 up and three to the right
the slope is 1/3
m = 1/3
Find the length of the third side. If necessary, write in simplest radical form.
Answer:
3
Step-by-step explanation:
x = the third side
x² + ([tex]\sqrt{55}[/tex])²= 8²
x² = 64 - 55 = 9
x = [tex]\sqrt{9}[/tex] = 3
Use the discriminant to describe the roots of each equation. Then select the best description. 2x2 + 7x + 6 = 0 real and irrational roots real and rational roots double root non-real roots
Answer:
roots are real and rational
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 ) , then the discriminant is
b² - 4ac
the discriminant informs on the nature of the roots
• if b² - 4ac > 0 then roots are real and irrational
• if b² - 4ac > 0 and a perfect square, then roots are real and rational
• if b² - 4ac = 0 , then roots are real and equal
• if b² - 4ac < 0 , then the roots are not real
for 2x² + 7x + 6 = 0 , in standard form
with a= 2, b = 7 , c = 6 , then
b² - 4ac = 7² - (4 × 2 × 6) = 49 - 48 = 1
since b² - 4ac > 0 and a perfect square, then the roots are real and rational
At Nation Office Supply, pens are $1.69 per dozen and notepads are $4.59 per dozen. If Marley purchases 9 dozen pens, how many notepads can she purchase if her total is $56.52?
At Nation Office Supply, Marley purchased 9 dozen notepads.
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.
We have to given that;
At Nation Office Supply, pens are $1.69 per dozen and notepads are $4.59 per dozen.
Here, Marley purchases 9 dozen pens, and spend total $56.52.
Let number of notepads can she purchase = x
So, We can formulate;
⇒ 9 × $1.69 + $4.59x = $56.52
⇒ 15.21 + 4.59x = 56.52
⇒ 4.59x = 56.52 - 15.21
⇒ 4.59x = 41.31
⇒ x = 41.31 / 4.59
⇒ x = 9
Thus, Marley purchased 9 dozen notepads.
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On each coordinate plane, the parent function f(x) = |x] is represented by a dashed line and a translation is
represented by a solid line. Which graph represents the translation g(x) = |x|- 4 as a solid line?
4.
3-
24
1+
14
2
1(x)-x
b
-q
-4
3-
O
10x)=x
234
fox) -
2-
--2-1
-2-
-3-
4
M
45
100-4
We have a translation of 4 units downwards, so the correct graph is the first one (the one you answered).
Which graph represents the translated function?Here we start with the parent function:
f(x) = |x|
And the translated function is:
g(x) = |x| - 4
Remember that a general vertical translation of N units of a function f(x) can be written as:
g(x) = f(x) + N
if N > 0 the translation is upwards.
if N < 0 the translation is downwards.
Here N = -4, so the translation is 4 units downwards.
Then the correct graph is exactly the one that you marked.
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How do you find the y-intercept with code?
Formula used to calculate the y-intercept when coordinates of two points are given is as follow: y = mx + c where 'm' represents the slope and 'c' represents the y-intercept.
As given in the question,
Let us consider points of two coordinates be equal to
( x₁ , y₁ ) = ( 2, 3 )
( x₂ , y₂ ) = ( 4, 7 )
Equation of the line is equal to :
( y - y₁ ) / ( x - x₁ ) = ( y₂ - y₁ ) / ( x₂ - x₁ )
⇒ ( y - 3 ) / ( x - 2 ) = ( 7 - 3 ) / ( 4 - 2 )
⇒ ( y - 3 ) / ( x - 2 ) = 2
⇒ y - 3 = 2x - 4
⇒ y = 2x - 1
Same as y = mx + c
Here c = -1
Here y-intercept is equal to -1 by substituting x = 0 we can get y - intercept.
Therefore, the value of y-intercept can be calculated with the coordinates of the given points using formula given by :
y = mx + c where 'c' represent y-intercept.
The given question is incomplete, I answer the question in general according to my knowledge:
If you're given coordinates of 2 points, how do you find the y-intercept?
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solving exponential equations by rewriting the base
Exponential equation is an equation whose exponent or part of the exponent is a variable.
If 8^y = 16^y+2, what is the value of y?
The value of y after solving the given equation is -8.
We can calculate the value of y through the following method,
We have been provided with an exponential equation [tex]8^{y} = 16^{y+2}[/tex]
As we know, an exponential equation is an equation whose exponent or part of the exponent is a variable.
For solving an exponential equation, we need to use logarithms and their properties.
We can write [tex]8^{y}[/tex] also as [tex]2^{3y}[/tex] since we know that 2³ = 8
Similarly, we can write [tex]16^{y+2}[/tex] also as [tex]2^{4(y+2)}[/tex] since we know that [tex]2^{4}[/tex] = 16
Therefore we get the new equation as,
[tex]2^{3y}[/tex] = [tex]2^{4(y+2)}[/tex]
Now we will add log with base 10 on both the sides
Therefore the equation will become,
log₁₀ [tex]2^{3y}[/tex] = log₁₀ [tex]2^{4(y+2)}[/tex]
Since, according to the property of logarithm,
log₁₀ aᵇ = b log₁₀ a
Therefore,
3y log₁₀ 2 = 4(y + 2) log₁₀ 2
We can cancel out log₁₀ 2 on both sides
We get the equation as,
3y = 4(y + 2)
3y = 4y + 8
y = -8
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For 2x2— 5x —3 = 0, determine which of the following are solutions?(i) x = 3 (ii) x= –2
(iii) x=-1/2 (iv) x=-1/3
The given options (i), (ii) and (iv) are all solutions of the equation. Option (iii) is not a solution of the equation since x=-1/2 does not equal 3 or -2.
The given equation is 2x2 - 5x - 3 = 0. The solutions of a quadratic equation are found by setting the equation equal to zero and solving for x. The solutions of this equation can be found by using the Quadratic Formula:
x = [-b ± (√b2 – 4ac)] / 2a
Using this formula:
x = [-(-5) ± (√(-5)2 – 4(2)(-3))] / 2(2)
x = [5 ± (√25 + 24)] / 4
x = [5 ± (√49)] / 4
x = [5 ± 7] / 4
Therefore, the solutions are x = 3 and x = -2.
The given options (i), (ii) and (iv) are all solutions of the equation. Option (iii) is not a solution of the equation since x=-1/2 does not equal 3 or -2.
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Find the ratio in which the point P(4, 3) divide the line joining the points A(8,-1) and B(2, 5)? points (4 12)
Use the section formula to get the coordinates of a point that separates a line segment outside or internally in a specific ratio.
What is meant by section formula?By building two right triangles and applying AA similarity, the section formula can be obtained. After determining the ratio of the triangle's side lengths in terms of the supplied ratios, we may solve for x and y to determine the coordinates of the point that divides the line segment.
To determine the coordinates of a point that splits a line segment externally or internally in a certain ratio, apply the section formula. A line segment's midpoint can be determined using this technique as well.
By section formula, we have, if (x, y) divides the line segments joining [tex]$\left(x_1, y_1\right)$[/tex] and [tex]$\left(x_2, y_2\right)$[/tex] internally in the ratio m: n then,
[tex]$x=\frac{m x_2+n x_1}{m+n}$[/tex] and [tex]$y=\frac{m y_2+n y_1}{m+n}$[/tex]
Here,
[tex]\left(x_1, y_1\right)=(8,-1) \\\\ \left(x_2, y_2\right)=(2,5) \\\\ (x, y)=(4, 3) \\[/tex]
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Which of the following describes a perpendicular bisector of a triangle?
answer choices
A segment that is perpendicular to the side of a triangle at its midpoint.
A segment with endpoints at the vertex and midpoint of the opposite side.
A segment that connects two midpoints of two sides.
A segment that connects the vertex and the opposite side at 90 degrees.
A perpendicular bisector of a triangle is a segment that is perpendicular to the side of a triangle at its midpoint. So option A is the correct answer.
Specifically, it is a line which passes through the midpoint of a side of the triangle, and is perpendicular to that side. It crosses the side at a 90 degree angle, and divides the side into two equal parts.
It can also be thought of as a line which connects the vertex and the opposite side at 90 degrees. In order for a triangle to be equilateral, the three perpendicular bisectors must all intersect at the same point, which is the center of the triangle.
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Karen adds up 4 consecutive odd integers find the sum if the smallest one is 2m-1
Karen adds up 4 consecutive odd integers ,the sum if the smallest one is 2m-1 is 8m + 8.
What is consecutive odd integers?Odd integers that follow one another and differ by 2 are referred to as consecutive odd integers. If x is an odd number, then x + 2, x + 4, and x + 6 are also odd numbers that follow each other. The sum of any sequence of odd numbers, starting with 1, is always equal to the square of the total number of digits. If the numbers 1,3,5,7,9,11,..., and (2n-1) are odd numbers, then the first odd number's sum equals 1. Sum of the first two odd numbers is (1 + 3 = 4; 4 = 2 x 2)
Since they are odd numbers, each time it must be +2 (since +1 goes odd, even, odd, even, etc.), therefore the result will be:
(2m - 1) + (2m + 1) + (2m + 3) + (2m +5) = 8m + 8
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The data set shows the ages of people riding a bus.
What is the mode for this data set?
18 16 11 45 33 11 33 14 18 11
21
17
11, 18, and 33
11
By the definition of the mode, we can say the mode of this data is 33.
What is the mode?
The mode in statistics refers to a number in a set of numbers that appears the most often. For example, if a set of numbers contained the following digits, 1, 1, 3, 5, 6, 6, 7, 7, 7, 8, the mode would be 7, as it appears the most out of all the numbers in the set.
We have given,
Data set 18 16 11 45 33 16 33 14 18 33.
To find what is the mode for this data set.
Solution: We have given
Data set 18 16 11 45 33 16 33 14 18 33.
Mode: The mode of a set of data values is the value that appears most often.
So,
We can see the most repeated number is 33. ( 3 times)
Hence, by the definition of the mode, we can say the mode of this data is 33.
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What is a inverse example?
A inverse example is when two variables are inversely related, meaning that as one increases, the other decreases. For example, as the temperature outside rises, the amount of ice cream sold decreases.
Inverse relationship means that the two variables are directly proportional to each other; if one increases, the other decreases. An example of an inverse relationship is the relationship between the temperature outside and the amount of ice cream sold. As the temperature outside rises, the amount of ice cream sold decreases. This is because people are less likely to buy ice cream when it is hot outside.
A inverse example is when two variables are inversely related, meaning that as one increases, the other decreases. For example, as the temperature outside rises, the amount of ice cream sold decreases.
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What is (-2x+6) - (x-3) subtracted?
Answer: i believe its -3x+9
Step-by-step explanation:
it is important to recognize that the minus sign in front of −(x−3) applies to both x and −3.
remove the parentheses by distributing the minus sign to the terms inside them: −2x+6−(x−3)
⇒−2x+6−x−(−3)
⇒−2x+6−x+3
combine similar terms: ⇒(−2x−x)+(6+3)
⇒−3x+9
Althea volunteers in the school library for 2 1/4 hours on Mondays, Wednesdays, and Fridays. On Tuesdays and Thursdays, she volunteers for 1 3/4 hours. Althea thinks she volunteers more than 10 hours a week. How many hours does she volunteer?
Althea volunteers 10.25 hours a week.
Given that Althea volunteers in the school library for 2 1/4 hours on Mondays, Wednesdays, and Fridays.
She volunteers 2 1/4 hours a day.
First we convert the improper fraction 2 1/4 to a proper fraction.
2 1/4 = 9/4
So by unitary method for three days the number of hours she volunteer:
3 × 9/4 = 27/4
Also, she volunteers for 1 3/4 hours on Tuesday and Thursday.
She volunteers 1 3/4 hours a day.
First we convert the improper fraction 1 3/4 to a proper fraction.
1 3/4 = 7/4
So by unitary method for two days the number of hours she volunteer:
2 × 7/4 = 14/4
So, the total number of hours Althea volunteers for a week,
27/4 + 14/4
= 41/4
= 10.25 hours
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in the space provided below, simplify the expression (shown below) Show all work and write your responses in the space provided below.
Simplifying 1/(1/4x -1/x+5) gives 4x²+20x)/5-3x
What is simplifying expression?Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.
1/(1/4x -1/x+5) = 1 ÷ 1/4x -1/x+5
= 1÷ (x+5 -4x)/4x²+20x
= 1× 4x²+20x/5-3x
= (4x²+20x)/5-3x
therefore the simplification of 1/(1/4x -1/x+5) is (4x²+20x)/5-3x
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Part d - finding the relationship between θ and ϕ find the relationship between angles θ and ϕ using the equations of equilibrium and solve for θ. Suppose that the angles are expressed in radians
The equation of equilibrium states that the sum of the forces in the x-direction must be zero.
Equation of equilibrium:
F_x = 0 = mgsinθ - mgsinϕ
mgsinθ = mgsinϕ
sinθ = sinϕ
θ = ϕ
The equation of equilibrium states that the sum of the forces in the x-direction must be zero. This means that the force due to gravity in the x-direction, mgsinθ, must be equal to the force due to gravity in the x-direction, mgsinϕ. This can be rearranged to sinθ = sinϕ, which means that the angles θ and ϕ must be equal. Thus, the relationship between angles θ and ϕ is that they are equal.
The equation of equilibrium states that the sum of the forces in the x-direction must be zero.
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Heather will spend more than $26 on gifts. So far, she has spent $15. What are the possible additional amounts she will spend?
Use c for the additional amount (in dollars) Heather will spend.
Write your answer as an inequality solved for c.
Answer: c is greater than 11
Step-by-step explanation:
Since Heather needs to spend more than $26 and she already spent $15, we can write this out as
c + 15 is greater than 26
subtracting 15 from both sides;
c is greater than 11
Find the equation of a line that passes through the point (0,3) and has a gradient of 2. Leave your answer in the form y = m x + c.
The equation of a line that passes through the point (0,3) and has a gradient of 2 is: y = 2x + 3
We know that the point-slope form of equation of line is:
(y - y₁) = m(x - x₁)
where m is the slope (also called as gradient)
Here, we have been given a point (0, 3) and the slope of the line is 2.
Let us assume that (x₁, y₁) = (0, 3)
and slope (m) = 2
Using point-slope form of equation of line,
(y - y₁) = m(x - x₁)
(y - 3) = 2(x - 0)
y - 3 = 2x
y - 3 + 3 = 2x + 3
y = 2x + 3
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How do you draw a parallel line in Class 7?
No matter how far they reach, parallel lines are those that do not have a shared meeting point in the same plane.
If two lines cannot collide when extended in both directions to infinity, they are said to be parallel in a plane. Throughout the entire length, there remains a constant gap between two lines.
|| is the symbol used to represent the parallel lines. Assuming that lines "a" and "b" are parallel to one another, we may indicate this using the symbol "a||b," which means "a is parallel to b."
We need a ruler and a compass to create a line parallel to the other line starting from an outside point. The diagram of parallel line is given below:
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How do you find the perimeter of a 30 60 90 right triangle?
The 30, 60, and 90 are special right triangles. the perimeter of the triangle is = [tex]a+b+c[/tex] =[tex]x+2x+x\sqrt{3}[/tex]
30,60,90 special right triangles because there is a relation between height, base, and the hypotenuse.
Point to be noted
the opposite side of [tex]30^o[/tex] is height, the opposite side of [tex]60^o[/tex] is base, and the opposite side of [tex]90^o[/tex] is the hypotenuse.
Assume the height of the triangle = [tex]x[/tex]
In this type of triangle, the hypotenuse is double of height,
so, hypotenuse = [tex]2x[/tex]
and the base of the triangle is [tex]\sqrt{3}[/tex] of the height.
Therefore, base = [tex]x\sqrt{3}[/tex]
so that, The perimeter of the triangle = [tex]x+2x+x\sqrt{3}[/tex]
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Lmno is a parallelogram. If nm = x + 5 and ol = 2x + 3, find the value of x and then find nm and ol.
The value of x is 2 and NM = OL = 7
Now, According to the question:
What is a parallelogram?
A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
Given that, LMNO is a parallelogram and NM = x + 5 and OL = 2x + 3,
Since, we know that, opposite sides of a parallelogram are equal,
Therefore,
NM = OL
x+5 = 2x+3
x = 2
Therefore, NM = OL = 7
Hence, the value of x is 2 and NM = OL = 7
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A vertical number line is given.
A vertical number line starting at negative 5 with tick marks every one fourth unit up to positive 5. The point negative 1.25 is labeled.
What is the absolute value of the number plotted on the number line?
−1.5
−1.25
1.25
1.5
The absolute value of the number plotted on the number line is 1.25
A body of mass 5 kg initially at rest is subjected to a force of 20 N find kinetic energy acquired by the body in 10 sec
Kinetic energy acquired by the body in 10 sec is 4000 J.
What is kinetic energy?
The energy that an object has as a result of motion is known as kinetic energy. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its acceleration until its speed changes.
Here. we ave
Given: A body of mass 5 kg initially at rest is subjected to a force of 20 N
Force = mass × acceleration
A= F/m
a= 4 m/s ².
We know that,
K.e = 1/2 mv²
To find v:-
V= u+at
V= 0+40
V= 40 m/s.
K.E = 1/2 ×5×40×40
K.E = 4000 J.
Hence, kinetic energy acquired by the body in 10 sec is 4000 J.
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What is the example of inverse in math?
The inverse meaning in math is a function or operation which reverses the order or operation of another function or operation.
Let us take an inverse math example, The inverse operation of addition is subtraction, and the inverse operation of multiplication is division.
For example, The multiplication of two numbers 3 and 6 is 3 × 6 = 18. The inverse operation of this is a division which is as follows: 18/6 = 3.
The Inverse of a Number
Consider a number y where y is not equal to zero. Then the inverse of a number y is the reciprocal of the number that is 1/y.
For example, The inverse of the number 200 is 1/200, and the inverse of the number 32 is 1/32.
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7. Why is it not possible solve the equation 7^x=28 by changing the base of both sides?
In the given expression, 7^x=28, as there is variable in one side while in other side there is constant, also there is no logarithmic value, so it is not possible to solve the equation by changing the base of both sides
The basic formula has been changed to logb b a = [logc c a] / [logc c b]. It simply implies that to alter the base of a logarithm logb b a, we divide [log a] / [log b], where these logarithms might have any (same) positive number as a basis.
The change of base formula gives you the answer of a log with a different base by utilizing only log computations with a base of 10. The formula instructs you to divide the log of the number in parentheses by the log of your base.
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George is 21 years of age and a full-time student living with his parents who are paying more than 50% of his support. He had wages of $1,375 ($140 of income tax withholding) for 2018. Can George’s parents claim him on their tax return even though he will file a tax return to claim his refund of $140?
Yes, George can be claimed as a dependent by his parents.
A dependent is a person who qualifies for a dependency exemption but is not the taxpayer or the taxpayer's spouse. Every exemption for a dependent reduces the amount of taxable income by the exemption amount.
If a full-time student, your child must be younger than 24 or younger than 19 years old. If your child is totally and permanently incapacitated, there is no upper age restriction. Are these your roommates? There are a few situations where your child does not need to live with you for more than half the year.
Your child must be younger than you and either be a "student" younger than 24 years of age as of the end of the calendar year, or be younger than 19 years old.
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