Answers
Answer:
[tex]{ \tt{volume = base \: area \times height \times length}} \\ \\ { \tt{v = \frac{1}{2} (a + b) \times h \times l }} \\ \\ { \tt{v = \frac{1}{2} (1.7 + 2.3) \times 1.3 \times 1.5}} \\ \\ { \tt{v = 2 \times 1.3 \times 1.5}} \\ \\{ \tt{v = 3.9 \: {m}^{3} }}[/tex]
Answer:
3.9 m³
Step-by-step explanation:
To find the volume of a right prism, multiply its base area by its height.
For the given shape:
Base = trapezoid ABCDHeight = 1.5 mArea of a trapezoid
[tex]\boxed{A = \dfrac{1}{2}(a+b)h}[/tex]
Where a and b are the bases and h is the height.
From inspection of the given diagram:
a = BC = 1.7 mb = AD = 2.3 mh = CD = 1.3 mSubstitute the given values into the formula to find the area of the trapezoid base (ABCD):
[tex]\begin{aligned}A & = \dfrac{1}{2}(a+b)h\\\implies ABCD & = \dfrac{1}{2}(BC+AD)CD\\ &=\dfrac{1}{2}(1.7+2.3)(1.3)\\&=\dfrac{1}{2}(4)(1.3)\\&=(2)(1.3)\\&=2.6\; \sf m^2\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\textsf{Volume of prism} & = \textsf{Area of base} \times \sf height\\\implies V & = ABCD \times 1.5\\V & = 2.6 \times 1.5\\V & = 3.9\;\sf m^3\end{aligned}[/tex]
Related Questions
Please help I will give you 30 points
Answers
Step-by-step explanation:
520÷13=40..............
Answer:
The answer is C 40
Step-by-step explanation:
520/ 13 = 40
:) have a nice day
Find the area of this shape.
6
13
Diagram NOT to scale
The units of the dimensions are m.
Give your answer in m².
m²
Answers
Answer:
78m
Step-by-step explanation:
6×13
78
not too sure tho
Match the sequence to its equation
2, -4,-10, -16
Answers
Answer: 2, -4, -10. -16, ..., -6n+8 n=1, 2, 3, ...
Step-by-step explanation:
2, -4, -10, -16
a₁=2
a₂=-4
a₃=-10
a₄=-16
a₂-a₁=-4-2=-6
a₃-a₂=-10-(-4)=-6
a₄-a₃=-16-(-10)=-6
Hence, this is an arithmetic progression: a₁=2 d=-6
[tex]a_n=a₁+(n-1)d\\a_n=2+(n-1)(-6)\\a_n=2-6n+6\\a_n=-6n+8[/tex]
choose the definition for the function
Answers
Answer: C
Step-by-step explanation:
Since the inequalities for all 4 options are different, all you need to look at are the inequality signs.
For the line with a positive slope (bottom left to top right), the point it ends at is not filled in, so that point is not included meaning it is x > 1.
For the line with a negative slope (top left to bottom right), the point it ends at is filled in, so that point is included meaning it is x [tex]\leq[/tex] 1.
C. is the only one that has these inequalities.
Find the area of the polygon.
The area of the polygon is what?
Answers
Answer:
Area = 792 m
Step-by-step explanation:
You can cut the polygon into 2 rectangles.
Subtracting 18 from 60 can give you the length of rectangle A, so 42 will be the new length for rectangle A.
Multiply 6 and 42 to get 252 for the area of rectangle A.
Multiply 18 and 30 to get 540 for the area of rectangle B.
(You multiply to find the area.)
Lastly you add both areas, 252 + 540, and the final result is:
Area = 792 m
Suppose you write and solve an equation to determine the amount of money m you have in your bank account after several weeks. You find that m=-36 . What does this solution mean?
Answers
Answer:
From the Soldier's point of view, the American Civil War was not a continuous battle. Instead, it was long monotonous marches and long residency in camps punctuated by the terror and chaos of combat. When winter set in and the campaigning season came to a close, most Soldiers counted on a long, cold stay in a winter camp. The four log cabins at the center of the Army Heritage Trail represent the types of buildings which Soldiers in both the Union and the Confederate Armies spent the long dreary months of winter. The cabins are modeled after images from the USAHEC collection, including the Army of the Potomac's winter camp at Brandy Station and the Confederate camp at Centerville
Z is a standard normal random variable. what is the value of z if the areato the right of z is 0.0122?
Answers
As per question, ‘Z’ is a standard normal random variable. And the value of ‘z’ is [tex]0.9878.[/tex]
According to the question, the area to left of ‘z’ and the equation can be written as:
[tex]P(Z > z) =0.01222[/tex]
Therefore,[tex]P(Z < z) =1-0.01222=0.9878[/tex]
Now the desired z-score corresponding to z-table graph = [tex]2.25[/tex]
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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work out y=8x+5 when x=-2 1/2
Answers
-20 + 5 = -15
Solve each equation. Check your answer.
2 x-5=17
Answers
Answer:
x = 11Step-by-step explanation:
Solve each equation. Check your answer.
2x - 5 = 17
2x = 12
x = 22 : 2
x = 11
------------------
check
2 * 11 - 5 = 17
22 - 5 = 17
17 = 17
the answer is good
Simplify (4.3)(4.3^2)^4.
(4.3)^6
(4.3)^7
(4.3)^9
(4.3)^8
Answers
The simplified form of the given expression is 4.3⁹. The correct option is the third option (4.3)^9
Simplifying an ExpressionFrom the question, we are to simplify the given expression
The given expression is
(4.3)(4.3^2)^4
This can be written as
(4.3)(4.3²)⁴
Applying the law of exponents, we get
(4.3)(4.3² ˣ ⁴)
(4.3)(4.3⁸)
Then,
4.3 × 4.3⁸
NOTE: 4.3 = 4.3¹
Thus,
4.3¹ × 4.3⁸
Applying the multiplication law of indices, we get
4.3¹ ⁺ ⁸
= 4.3⁹
Hence, the simplified form of the given expression is 4.3⁹. The correct option is the third option (4.3)^9
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PROOF Write a coordinate proof for each statement.The measure of the segment that joins the vertex of the right angle in a right triangle to the midpoint of the hypotenuse is one-half the measure of the hypotenuse.
Answers
We have proved that PA = 1/2 PB using the SAS rule or Side Angle Side rule.
A right angle triangle is given.
We have to prove that measure of the segment that joins the vertex of the right angle in a right triangle to the midpoint of the hypotenuse is one-half the measure of the hypotenuse.
What is a triangle ?
A triangle is a 3-sided shape. There are three sides and three angles in every triangle, some of which may be the same.
As per the question ;
Let's assume P is the midpoint of the hypotenuse of the right angle △ABC and it is right angled at B. Also , D is the midpoint of AB.
Now ;
Draw a line parallel to BC from P meeting B at O and join PB.
Here ;
In △PAD and △PBD
∠PDA =∠PDB = 90°
and
PD = PD common)
AD = DB (As D is mid point of AB)
So ;
△ PAD ≅ PBD
by SAS rule
and
PA = 1/2 PB
Thus , we have proved that PA = 1/2 PB using the SAS rule or Side Angle Side rule.
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Solve each equation. Check the solution. y/y+1 = 2/3
Answers
The solution of the given equation y/y+1 = 2/3 is calculated as (y = 2).
What is meant by cross multiplication?In cross-multiplication, the numerator of the first fraction is multiplied by the denominator of the second fraction, and the numerator of the second fraction is multiplied by the denominator of the first fraction.
Denominators are removed during cross multiplication. It's employed to make comparisons fraction sizes, solve proportional and percentage problems.A absent value or variable is common in proportion problems. After removing the denominators with cross multiplication, algebra skills are employed to solve again for missing variable. Percentage problems are solved in the same way that proportion problems are.Now, the given equation is as follows;
y/y+1 = 2/3
Cross-multiplying the values;
3y = 2(y + 1)
3 y = 2y + 2
Bring the variable on the single side and constants on the other.
3y - 2y = 2
y = 2
Therefore, the solution of the given equation y/y+1 = 2/3 is computed as (y = 2).
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|x-1| = |2x+3| ; solve for x
Answers
Answer: x=-2/3 x=-4
Step-by-step explanation:
[tex]|x-1|=|2x+3|\\[/tex]
Equate the submodular functions to zero:
x-1=0
x-1+1=0+1
x=1
2x+3=0
2x+3-3=0-3
2x=-3
Divide both parts of the equation by 2:
x=-1.5
Thus,
-∞____-1.5_____1____+∞
x∈[1,+∞)
x-1=2x+3
x-1-x-3=2x+3-x-3
-4=x∉[1,+∞)
x∈(-1.5,1)
-(x-1)=2x+3
-x+1=2x+3
-x+1+x-3=2x+3-x-3
-2=3x
Divide both parts of the equation by 3:
x=-2/3∈(-1.5,1)
x∈(-∞,-1.5]
-(x-1)=-(2x+3)
-x+1=-2x-3
-x+1+2x-1=-2x-3+2x-1
x=-4∈(-∞,-1.5]
guys please I had a zero on this
I just need help
Answers
Using conversion from fraction to decimal and rational numbers, we have that:
7. The fraction that has a corresponding decimal greater than 1 is 4/3.
8. One rational number between 7 and 8 is given by option a, which is 7.83838383...
How to convert a fraction to decimal?A fraction is converted to decimal dividing the numerator by the denominator.
In item 7, we consider fraction 4/3, for which:
The numerator is 4.The denominator is 3.Hence the corresponding decimal is given as follows:
4/3 = 1.333, which is the result of the division of 4 by 3, and is greater than 1.
What are rational numbers?The set of rational numbers is composed by all numbers that can be represented by fractions, such as integer, terminating decimals and repeating decimals.
In item 8, option a, we have the number 7.83, with the bar at 83. This means that 83 is the repeating decimal part, that is, the rational number is 7.83838383...
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Simplify by combining like terms. 5 v-3(2-v)
Answers
The simplification by combining like terms of 5v-3(2 -v) is 8v - 6.
According to the given question.
We have an expression5v - 3(2 - v).
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression
5v - 3(2 - v).
Here 5v, and 3v both are the like terms.
So, we add coeffcients of v to simplify the given expression.
Therefore, the simplification of 5v -3 (2 -v ) is given by
5v - 3(2 - v)
= 5v - 6 + 3v
= 8v - 6
Hence, the simplification by combining like terms of 5v - 3(2 - v) is 8v - 6.
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A dog breeder charges a certain amount of money for litter of puppies along with a per puppy share. A litter with 6 puppies costs $172 and a littered with 10 puppies costs $220. Write an equation that could be used to calculate the cost, y, of any number of puppies, x.
Hint: y = mx + b
Answers
Given the task content, the cost, y, of any number of puppies, x is modeled by the equation y = mx + b where cost of any number of puppies is $12
EquationThere are three major types of equation. Namely,
Linear equationQuadratic equationSimultaneous equationAn equation can be solved through the following methods:
FactorizationGraphical methodCompleting the square methodSubstitution methodElimination methodGiven:
6 puppies costs $172
10 puppies costs $220
y = mx + b
Where,
y = total costx = number of puppiesm = cost of each litterb = fixed cost172 = m(6) + b
220 = m(10) + b
172 = 6m + b
220 = 10m + b
substract the equation48 = 4m
m = 48/4
m = 12
Substitute m = 12 into172 = 6m + b
172 = 6(12) + b
172 = 72 + b
172 - 72 = b
100 = b
Therefore, the cost of any number of puppies is $12
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raise y to the 2nd power, add the result to z, then double what you have
Answers
Answer:
2y²+2z
Step-by-step explanation:
y² raise y to the second power
y²+z add result to z
(y²+z)(2) double it
2y²+2ź
The equation of a line is y + 5 = 6x + 13
What is the value of y at the point where the line crosses the y-axis?
Answers
Answer:
y=8
Step-by-step explanation:
The equation: y=mx+c
First you have to turn this equation into a proper equation (y=mx+c).
m = gradient
c = y-intercept (where the line goes through the y-axis).
To turn this into a proper equation, you have to isolate the y by subtracting 5 from both sides (because whatever you do to one side, you have to do the same to the other side).
So you subtract 5 by 5 and subtract 5 from 13. *You do not subtract 5 from 6x.
This will give you and answer of y=6x+8.
m = gradient = 6
c = y-intercept = 8
So the value of y is 8.
If Johnson & Johnson
sold $12,949,847 of hand
lotion in 2009 and $3,150,367
of that money was spent by
mothers of children who are
Hispanic, what percentage of
Johnson & Johnson's profits
were due to mothers who are
Hispanic? Round to the nearest
tenth
Answers
If Johnson & Johnson sold $12,949,847 of hand lotion in 2009 and $3,150,367 of the sales was spent by mothers of Hispanic children, the percentage of Johnson & Johnson's profits due to Hispanic mothers is 24.43%.
What is a percentage?A percentage is a ratio of one variable to the whole value or number.
Like ratios, probabilities, and proportions, percentages are expressed over 100.
Data and Calculations:The total sales revenue in 2009 = $12,949,847
The total sales revenue from Hispanic mothers = $3,150,367
The percentage of Hispanic sales over the total sales revenue = 24.43%($3,150,367/$12,949,847 x 100)
Thus, the percentage of Johnson & Johnson's profits due to Hispanic mothers is 24.43%.
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Evaluate the expression 3(x-1) to the 2 power + 2x-7 For x = 3
Answers
The value of the function is x = 3 is 11
Function and valuesFunctions are expressions that consists of dependent and independent variables. This variables are represented using letters. For instance, f(x) is a function of x.
Given the function below
f(x) = 3(x-1)² + 2x - 7
Given that the value of x is 3, hence;
f(x) = 3(3-1)² + 2(3) - 7
Expand to have:
f(3) = 3(2)² + 2(3) - 7
f(3) = 3(4) + 6 - 7
f(3) = 12 - 1
f(3) = 11
Hence the value of the function is x = 3 is 11
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A
2x
Find the value of x.
D
x+5
B
4
E
3
C
PLEASE HELP
Answers
Answer: x = -5
Step-by-step explanation:
Solve by substituton
Answers
Solve the first equation for [tex]x[/tex].
[tex]x+3y = -2 \implies x = -3y - 2[/tex]
Substitute this into the second equation and solve for [tex]y[/tex].
[tex]-3(-3y-2) + y = 6 \implies 9y + 6 + y = 6 \implies 10y = 0 \implies y=0[/tex]
Now solve for the value of [tex]x[/tex].
[tex]x = -3\cdot0 - 2 = -2[/tex]
So the solution to the system is the point [tex](x,y) = \boxed{(-2,0)}[/tex]
Answer:
[tex]\left( \: \boxed{-2}\:, \: \boxed{0} \: \right)[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}x+3y=-2\\-3x+y=6 \end{cases}[/tex]
To solve using the method of substitution, solve one equation for one of the variables.
Solving equation 2 for y:
[tex]\implies -3x+y=6[/tex]
[tex]\implies -3x+y+3x=3x+6[/tex]
[tex]\implies y=3x+6[/tex]
Substitute this expression into the other equation and solve for x:
[tex]\implies x+3y=-2[/tex]
[tex]\implies x+3(3x+6)=-2[/tex]
[tex]\implies x+9x+18=-2[/tex]
[tex]\implies 10x+18=-2[/tex]
[tex]\implies 10x+18-18=-2-18[/tex]
[tex]\implies 10x=-20[/tex]
[tex]\implies 10x \div 10=-20 \div 10[/tex]
[tex]\implies x=-2[/tex]
Substitute the found value of x into the expression for y, and solve for y:
[tex]\implies y=3x+6[/tex]
[tex]\implies y=3(-2)+6[/tex]
[tex]\implies y=-6+6[/tex]
[tex]\implies y=0[/tex]
Therefore, the solution to the given system of equations is:
[tex]\left( \: \boxed{-2}\:, \: \boxed{0} \: \right)[/tex]
Multiply Which it correct?
Answers
Answer:Your answer is the fourth one
Step-by-step explanation:Please give brainliest if right
Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. (Lesson 3-1)
∠5 and ∠7
Answers
Answer:
Step-by-step explanation:
Use the Alternate Exterior Angles Theorem. If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.
Circle J has a radius of 10 units, ®K has a radius of 8 units, and BC = 5.4 units. Find the measure.
CK
Answers
If circle J has a radius of 10 units and BC = 5.4 units then the measure of CK is 2.6 units.
What is meant by the radius of a circle?A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more modern usage, it is also their length. The name is derived from the Latin radius, which means both rays and spoke of a chariot wheel.
The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually represented by the letters 'R' or 'r'. This number is significant in almost all circle-related formulas. A circle's area and circumference are also measured in terms of radius.
Since the radius of K is 8 units, BK = 8.
CK + BC = BK
Where the value of BC = 5.4, we get
substitute the value of BC in the above equation, then we get
CK + 5.4 = 8
subtract 5.4 from both sides
CK + 5.4 - 5.4 = 8 - 5.4
simplifying the above equation,
CK = 2.6
Therefore, the measure of CK is 2.6 units.
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Express each fraction as a decimal to the nearest hundredth.
43/46
Answers
43/49= 0.93
To express each fraction into its decimal we need to bring 100 at the denominator.
Fraction = numerator\denominator
For example :
1> 4\5
= 4*20\ 5* 20
= 80\ 100
= 0.80
2> 1\4
= 1 *20\ 4 *20
= 20\ 100
= 0.20
3> 49/50
= 49*2/50*2
= 98/100
=0.98
There are some numbers where it is not possible to make the denominator 100
So by the process of division method, we can convert the fraction into decimal form
43/46
0.93
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Leah walks 13 miles in 6 hours .lee walks 5 miles in 3 hours .Hercules walks 36 miles in 8 hours which Person had the fastest pace
Answers
Answer: Hercules has the fastest pace
Step-by-step explanation:
L=Leah. l=lee. H=Hercules
**Since the speeds are in fractions, make the denominators the same.
L=13/6
l=5/3
l=(5*2)/(3*2)
l=10/6
H=36/8
H=(36*6/8)/(8*6/8)
H=(216/8)/(48/8)
H=27/6
27/6 > 13/6 > 10/6
H>L>l
Hercules has the fastest pace
Simplify each complex fraction.
2/x + y / 3
Answers
The simplification of the given complex fraction 2/(x +y/3) is
6/(3x + y).
Accoring to the given question.
We have a complex fraction.
2/(x +y/3)
As we know that, complex fraction is a rational expression that has a fraction in its numerator, denominator or both.
For example: (2/3)/(4/6)
So, the above complex fraction can be simplified by
(2/3) × (6/4)
= (2/3) × (3/2)
= 1
Thereofore, the siplification of the complex fraction 2/(x +y/3) is given by
[tex]\frac{2}{x + \frac{y}{3} }[/tex]
= [tex]\frac{2}{\frac{3x+y}{3} }[/tex]
= 2(3)/(3x + y)
= 6/(3x + y)
Hence, the simplification of the given complex fraction 2/(x +y/3) is
6/(3x + y).
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C
D₁
F
LL
A
DF EB and EF = AD
DF = 18
E
=
mZDEF = 61°
mZDCF = [? ]°
B
Answers
The angle of the parallelogram is mZDCF= 61°
DF= EB and EF = AD
DF =18, mZDEF =61°
□CDEF is parallelogram, so mZDEF =61°
With two sets of parallel sides, a parallelogram is a quadrilateral. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. The total internal angles add up to 360 degrees.
The term "parallelepiped" refers to a three-dimensional shape with parallelogram-shaped faces. The parallelogram's base (one of its parallel sides) and height (the distance between its top and bottom elevations) determine its area. The lengths of the four sides determine a parallelogram's perimeter.
A parallelogram's characteristics are shared by the shapes of a square and a rectangle. Rhombus: A parallelogram is a rhombus if all of its sides are congruent or equal to one another.
Hence, the angle of the parallelogram is mZDEF =61°
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What is an equation of the line passing through points (3,5) and (7,1) ?
Answers
The equation of the line passing through the points (3 , 5) and (7 , 1) is x + y = 8.
The equation of a line can be expressed in different forms: standard form, slope-intercept form, and point-slope form
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Given two points, (3 , 5) and (7 , 1), use the point-slope form to generate the equation of the line. But, first, get the slope of the line using the two points.
m = (y2 - y1)/(x2 - x1)
m = (1 - 5)/(7-3)
m = -4/4
m = -1
Substitute the value of the slope and one point to the point-slope form.
(y - y1) = m(x - x1)
y - 5 = -1(x - 3)
y - 5 = -x + 3
Combining the variable(s) in one side and the constant(s) in the other.
y - 5 = -x + 3
x + y = 3 + 5
x + y = 8
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