The area of the parallelogram is 42 cm².
The perimeter of the parallelogram is 48 cm.
Given a parallelogram ABCD.
We have to find the area and perimeter of the parallelogram.
Given,
AB = 14 cm and BC = 10 cm.
DE = 8 cm
Using Pythagoras theorem, height is,
CE = √(10² - 8²) = 6
Area of the parallelogram = 1/2 × 14 × 6
= 42 cm²
Perimeter of the parallelogram = 2(14 + 10)
= 48 cm
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40 POINTS! In ΔTUV, t = 22 inches, u = 79 inches and ∠V=51°. Find ∠U, to the nearest degree.
The value of the angle that has been marked as U is 77 degrees.
Cosine ruleThe cosine rule, also known as the law of cosines, is a trigonometric relationship that relates the lengths of the sides of a triangle to the cosine of one of its angles.
If we know the lengths of the other two sides and the measurement of the included angle, we can use the cosine rule to determine the length of one side of a triangle.
We know that
[tex]v^2 = t^2 + u^2 - 2(ut) Cos 51\\v^2 = (22)^2 + (79)^2 - 2(22 * 79) Cos 51\\v^2 = 6725 - 2188[/tex]
v = 63
Using the sine rule;
v/Sin V = u /Sin U
U = Sin-1 (uSin V/v)
U = Sin1-1(79 * Sin 51/63)
U = 77 degrees
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Illustrate the following numbers using base 10 blocks ,345
Answer:
3 hundred blocks
----------------
| | |
| 100 | 100 |
|______|_______|
| | |
| 100 | 100 |
|______|_______|
| | |
| 100 | 100 |
|______|_______|
4 tens blocks
-------------
| | |
| 10 | 10 |
|_____|_____|
| | |
| 10 | 10 |
|_____|_____|
5 one's blocks
-------------
| | |
| 1 | 1 |
|___|___|
| | |
| 1 | 1 |
|___|___|
| | |
| 1 | 1 |
|___|___|
| | |
| 1 | 1 |
|___|___|
| | |
| 1 | 1 |
|___|___|
To earn extra spending money, Tim does yard work for his neighbors. In the summer, he mows lawns. In the winter, he shovels snow. Last year, he kept track of how much money he earned each month doing these jobs. These box plots show the results. Money earned ($) Mowing Shoveling 0 40 80 120 160 200 Which job had more variation in earnings?
Mowing lawns had more variation in earnings compared to shoveling snow.
To determine which job had more variation in earnings based on the given box plots, we need to compare the spread or interquartile range (IQR) of each job.
The interquartile range represents the range of the middle 50% of the data, which provides a measure of the variation in earnings.
Looking at the box plots, we can compare the lengths of the boxes or the distances between the first quartile (Q1) and the third quartile (Q3) for each job.
From the given information, it appears that the box plot for mowing has a larger spread than the box plot for shoveling. This can be observed by comparing the lengths of the boxes or the distances between Q1 and Q3.
Therefore, based on the given box plots, mowing lawns had more variation in earnings compared to shoveling snow.
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A father's age is three times the sum of the ages of his two children. After 5 years his age will be two times the sum of their ages. Find the present age of the father. EXPLAIN WITH FULL STEPS BY ELIMINATION METHOD
The present age of the father is 10 years.
What is the present age of the father?Let
Age of the father = x
Age of each child = y
Number of children = 2
Current age:
x = 2y
After 5 years:
(x + 5) = 2(2y)
x + 5 = 4y
Substitute x = 2y into
x + 5 = 4y
2y + 5 = 4y
5 = 4y - 2y
5 = 2y
divide both sides by 2
y = 5/2
y = 2.5
So,
x = 2y
x = 2(2.5)
x = 5
Therefore, present age of the father;
x + 5
= 5 + 5
= 10
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If a =⟨ – 7,2⟩ and b =⟨7,2⟩, find the difference a – b . How do u solve it and what's the answer
Answer:
Step-by-step explanation:
To find the difference between vectors a and b, we subtract the corresponding components of the vectors.
Given that a = ⟨ -7, 2 ⟩ and b = ⟨ 7, 2 ⟩, we can calculate the difference a - b as follows:
a - b = ⟨ -7, 2 ⟩ - ⟨ 7, 2 ⟩
Subtracting the corresponding components:
a - b = ⟨ -7 - 7, 2 - 2 ⟩
Simplifying:
a - b = ⟨ -14, 0 ⟩
Therefore, the difference a - b is ⟨ -14, 0 ⟩.
formula for density
formula for density
Answer:
The formula for density (ρ) is:
Density (ρ) = Mass (m) / Volume (V)
Step-by-step explanation:
Where:
Density is measured in units such as kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³).Mass is the amount of matter in an object and is typically measured in kilograms (kg) or grams (g).Volume is the amount of space occupied by an object and is typically measured in cubic meters (m³) or cubic centimeters (cm³).Determine if true or false
Answer:
1.) true 2.) false
Step-by-step explanation:
How much more money will a person spend who buys three orders
of nachos than a person who buys three bags of popcorn?
The extra amount that a person spends who buys three orders of nachos than a person who buys three bags of popcorn is: $2.25.
What extra amount will be spent?The distributive property is a concept in math that says that when we multiply the sum of two numbers by a number, this is equal to multiplying those same numbers individually by the same number.
The extra amount that the person who buys three orders of nachos will spend compared to the person who buys three bags of popcorn will be obtained by multiplying 3 by the price of nachos and 3 by the price of a unit of popcorn. This gives us:
3($6) - 3($5.25)
= 18 - 15.75
= $2.25
So, the extra amount that will be spent by the individual who buys three orders of nachos than a person who buys three bags of popcorn is $2.25.
Complete Question:
c. How much more money will a person spend who buys three orders of
nachos than a person who buys three bags of popcorn?
Item Price
Ticket $8.50
Popcorn $5.25
Soda $4.00
Candy $3.75
Nachos $6.
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What is the rate of increase for the function f(x)
The rate of increase for the function f(x) = 1/3(∛24)²ˣ is 2∛3
How to calculate the rate of increase for the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 1/3(∛24)²ˣ
When the exponent is evaluated, we have
f(x) = 1/3(2∛3)ˣ
An exponential function is represented as
f(x) = abˣ
Where
a = initial valueb = growth or decay factorUsing the above as a guide, we have the following:
b = 2∛3
Hence, the rate of increase for the function is 2∛3
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Which of the following are ways the hexagon can be decomposed into triangles and quadrilaterals? Select all that apply.
A.
Four right triangles
B.Two trapezoids
C. Three rhombi
D.
One rectangle and two triangles
E. Six equilateral triangles
The ways the hexagon can be decomposed into triangles and quadrilaterals is
one rectangle and two triangles.What is a hexagon?In mathematics, a hexagon can be described as the six-sided polygon. and in this there are 720° of internal angles in a standard hexagon. however hexagon is a closed, six-sided, two-dimensional polygon in mathematics.
It should be noted that the hexagon has six sides and six angles however Every side and angle of a regular polygon are the same. In geometry, a hexagon is been regarded as the figure that posses six which is six-sided .
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complete options;
a. One rectangle and two triangles
b. Six equilateral triangles
c. Four right triangles
d. Two trapezoids
e. Three rhombi
I need help with Pre-Calc Trig
Note that the graph of the above function g(x) = -4sin(πx - π/6) + 2 is described as follows.
What are the features of the above graph?The graph of the function g(x) = -4sin(πx - π/6) + 2 exhibits periodic behavior with oscillations above and below the x-axis.
Note that it is a sinusoidal wave that has an amplitude of 4, a period of 2, and a phase shift of π/6 to the right.
The waveform reaches its maximum value of 2 and its minimum value of - 6. It represents a damped oscillation or a decaying sinusoidal function.
See the attached graph.
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What is the amount that shareholders contribute in exchange for a company’s shares known as, and where is it located on the balance sheet?
The amount that shareholder’s contribute in exchange for a company’s shares is known as
, and this amount is listed in the balance sheet as a part of
.
On the balance sheet, share capital is listed under the "Shareholders' Equity" or "Owner's Equity" section is typically located towards the bottom of the balance sheet.
The amount that shareholders contribute in exchange for a company's shares is known as "share capital" or "shareholders' equity."
Share capital represents the initial investment made by shareholders in the company and is typically recorded in the equity section of the balance sheet.
It is categorized as a component of the company's equity, along with other items such as retained earnings additional paid-in capital and accumulated other comprehensive income.
The specific presentation of share capital may vary depending on the accounting standards and reporting requirements applicable to the company.
It may be further broken down into different classes of shares, such as common shares and preferred shares, each with its own corresponding value.
The amount that shareholders contribute in exchange for a company's shares is a crucial aspect of the company's financial structure and is an important component of its balance sheet, reflecting the ownership interest and investment made by the shareholders.
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To find the distance AB across a river, a distance BC=290 is laid off on one side of the river. It is found that B=117degrees and C=24degrees. Find AB.
The value of distance AB is 187.5 units
What is sine rule?Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other.
sine rule can be expressed as;
a/sinA = b/sinB = c/sinC
The opposite side to angle A is BC
the opposite side to angle C is AB
therefore;
A = 180-( 117 +24)
A = 180- 141
A = 39°
290/sin 39 = x/ sin24
xsin39 = 290 × sin24
0.629x = 117.95
x = 117.95/0.629
x = 187.5
therefore the distance AB is 187.5
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pls help me for brainleist
Answer: 110 degrees
Step-by-step explanation: If we have a triangle with an exterior line sticking out, we can determine the measure of the exterior angle by applying the Exterior Angle Theorem. According to the theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
In this case, the two known interior angles are 65 degrees and 45 degrees. To find the measure of the exterior angle, x, we add these two angles:
x = 65 degrees + 45 degrees
x = 110 degrees
[tex]\large \maltese \:{ \underline { \underline{ \pmb{ \sf{SolutioN }}}}} : -[/tex]
we have given ,
∠ A = 65°∠ B = 45°∠ C = ?? ( to be calculated)★ According to Angle sum property of triangle, the sum of interior angles of a triangle is 180°.
➝ ∠ A + ∠ B + ∠ C = 180°
➝ 65° + 45° + ∠ C = 180°
➝ 110° + ∠ C = 180°
➝ ∠ C = 180° - 110°
➝ ∠ C = 70°
Now,
★ Calculating for x :-
↝ ∠ C + x = 180°
↝ 70° + x = 180°
↝ x = 180° - 70°
↝ x = 110°
Hence, The value of x will be 110°.
At a graduation dinner, an equal number of guests were seated at each of the 4 large tables, and 8 late-arriving guests were seated at a smaller table. There were 48 guests in all
Answer:
4n + 8 = 48
Step-by-step explanation:
In the situation you described, there are 4 large tables with an equal number of guests seated at each table. Let’s represent the number of guests at each large table with the variable n. There are also 8 late-arriving guests seated at a smaller table. The total number of guests at the dinner is 48. So we can write an equation to represent this situation: 4n + 8 = 48, where 4n represents the total number of guests seated at the 4 large tables and 8 represents the number of late-arriving guests seated at the smaller table.
An employee started a new job and must enroll in a new family health insurance plan. One of the plans involves prescription drug coverage. The employee estimates that the entire family will fill 10 prescriptions per month, totaling $1,250. The employee has two options to choose from:
Option A: $94 monthly premium; 80% coverage for all prescription costs
Option B: $42 monthly premium; 75% coverage for first $500 in prescription costs, then 85% coverage for all prescription costs over $500
Which option would result in the highest overall cost for the employee, and by how much?
Option A has the highest overall cost by $64.50.
Option B has the highest overall cost by $64.50.
Option A has the highest overall cost by $106.50.
Option B has the highest overall cost by $106.50
Where the above is given, Option B has the highest overall cost by $685.50.
How is this so ?To find the option would result in the highest overall cost for the employee, we need to calculate the total cost under each option.
Option A
Monthly premium: $94
Prescription coverage: 80%
Total cost under Option A
Monthly premium: $94
Prescription costs covered: 80% of $1,250
= $1,000 (since the employee estimates filling 10 prescriptions totaling $1,250)
Employee's portion of prescription costs: 20% of $1,250 = $250
Overall cost = $94 + $250 = $344
Option B
Monthly premium $42
Prescription coverage 75% for first $500, then 85% for costs over $500
Total cost under Option B
Monthly premium: $42
Prescription costs covered up to $500: 75% of $500 = $375
Prescription costs covered over $500is
85% x ($1,250 - $500)
= 85% of $750
= $637.50
Employee's portion of prescription cost is
($1,250 - $375) + ($750 - $637.50)
= $875 + $112.50
= $987.50
Overall cost: $42 + $987.50 = $1,029.50
Hence Option B has the highest overall cost by $1,029.50 - $344 = $685.50.
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What is the meaning of "[tex]\exists p_{1},...,\exists p_{n} (p=p_{1},...,p_{n})[/tex]"?
The notation ∃p1,............... ∃pn indicates the existence of such values for p1, p2, ..., pn that satisfy the given condition.
The statement "∃p1,............... ∃pn (p= (P1,..., Pn))" means that there exists a tuple of variables p1, p2, ..., pn, which represents a set of values P1, P2, ..., Pn. The notation (p1, ..., pn) denotes a tuple, where each pi corresponds to a specific value.
In this context, the statement asserts the existence of a tuple (p1, ..., pn) that satisfies the condition p = (P1, ..., Pn), where p is a shorthand representation of the tuple (P1, ..., Pn). It implies that there are values P1, P2, ..., Pn that can be assigned to p1, p2, ..., pn, respectively.
The notation ∃p1,............... ∃pn indicates the existence of such values for p1, p2, ..., pn that satisfy the given condition. It is a way of expressing that there are values within the domain that make the statement true.
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Which of the following shows the simplified function of cosine squared x over the quantity 1 plus sine x end quantity question mark
1 + cos x
1 − cos x
1 + sin x
1 − sin x
The one which shows the simplified function is:
1 − sin x
How to determine which one shows the simplified function?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
We have:
cos²x/(1 + sin x)
Recall that in trigonometry function:
cos²x = 1 - sin²x
= 1² - sin²x (difference of two squares)
= (1 + sin x)(1 - sin x)
Thus, we can say:
cos²x/(1 + sin x) = [(1 + sin x)(1 - sin x)] / [(1 + sin x)]
= 1 - sin x
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square
triangle
trapezoid
circle
non-square rectangle
2
Mark this and return
3
A cross section is made by the intersection of a plane and a square pyramid at an angle either parallel or
perpendicular to the base.
The cross section can be which of these shapes? Select three options.
4 5 6
Save and Exit
7
Next
8 9
Submit
10
]The cross-section could be of these shapes square and triangle.
We know that a cross-segment is a plane segment that is a segment of a three-dimensional item that is parallel to one among its planes of symmetry or perpendicular to considered one of its traces of symmetry.
An instance of a segment would be a circle.
However, cross-phase is seen whilst a 3-dimensional figure is reduced through a plane. within the case of the cone, a circular go-segment emerges while the cone is cut parallel to its base
The go-sectional region is the location of a 3-dim figure that is acquired whilst a three-dimensional object - inclusive of a cylinder - is sliced perpendicular to some designated axis at a point.
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Triangle PQR is rotated 90 degrees counterclockwise about the origin to form the image triangle P'Q'R'. What are the vertices of triangle PQR
Answer:
Hope this helps!
Step-by-step explanation:
Triangle PQR has vertices P (3, 3), Q (5, -1), and R (1, -3). When triangle PQR is rotated 90 degrees counterclockwise about the origin to form the image triangle P’Q’R’, the vertices of the new triangle are P’(-3, 3), Q’ (1, 5), and R’ (3, 1)
May I please have some help
Answer:
D
Step-by-step explanation:
please say thank you and please verify this answer and name me brainliest
Find all real zeros h(x)=5(x-5)(x+5)^2(x^2-1)
Answer:
[tex]x=-5,-1,1,5[/tex]
Step-by-step explanation:
Use the Zero Product Property and set each factor equal to 0
[tex]h(x)=5(x-5)(x+5)^2(x^2-1)[/tex]
[tex]0=x-5\\x=5[/tex]
[tex]0=(x+5)^2\\0=x+5\\x=-5[/tex]<-- Multiplicity of 2
[tex]0=x^2-1\\0=(x-1)(x+1)\\x=-1,1[/tex]
Therefore, all real zeroes of the function are [tex]x=-5,-1,1,5[/tex]
2. What is the equation of a circle with center (0, 4) and point (-1, 8) on the circle?
A x2 + ( - 4)2 = 17
B x2 - ( + 4)2 = 17
C X2+ (y - 4)2 = 117
D (x 4)2 + 2 = 17
The equation of the circle with the center (0, 4) and a point (-1, 8) on the circle is x² + (y - 4)² = 17.
What is the equation of the circle?The standard form equation of a circle with center (h, k) and radius r is:
(x - h)² + (y - k)² = r²
Given that the center is (0, 4) and a point (-1, 8) is on the circle, we can calculate the radius using the distance formula:
[tex]r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\r = \sqrt{(-1 - 0)^2+(8-4)^2} \\\\r = \sqrt{(-1 )^2+(4)^2} \\\\r = \sqrt{1+16} \\\\r = \sqrt{17}[/tex]
Now, let's plug the values of the center (0,4) and the radius √17 into the standard form of the equation of a circle:
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 4)² = (√17)²
Simplify
x² + (y - 4)² = 17
Therefore, the equation of the circle is x² + (y - 4)² = 17.
Option C) x² + (y - 4)² = 17 is the correct answer.
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The compound shape below is formed from rectangle ABDE and right-angled triangle BCD. What is the area of this shape? Give your answer in cm² and give any decimal answers to 1 d.p. 8 cm 3 cm 8 E 3 cm D 17 cm Not drawn accurately
The area of the compound shape is 84 cm squared.
How to find the area of a compound shape?A compound shape is a shape that has two or more shapes in it. Therefore, the sum of the individual area is the area of the compound shape.
Therefore,
area of the compound shape = area of the rectangle + area of the triangle
area of the rectangle = 3 × 8
area of the rectangle = 24 cm²
Let's find the base of the triangle using Pythagoras's theorem.
Hence,
17² - 8² = b²
b = √289 - 64
b = √225
b = 15 cm
Therefore,
area of the triangle = 1 / 2 × 15 × 8
area of the triangle = 60 cm²
Finally,
area of the compound shape = 60 + 24
area of the compound shape = 84 cm²
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Select the correct answer.
Which statement is true?
O A. A sample statistic can never be equal to the population parameter.
OB.
Point estimates are defined for both samples and populations.
O C.
To calculate a sample proportion, we need to know the population size.
O D. To calculate a point estimate, we need to know the sample size.
The solution is :
Option C is true. To calculate a sample proportion, we need to know the population size.
Here, we have,
To calculate a sample proportion, we need to know the population size. - This is the true statement.
A sample statistic can never be equal to the population parameter. This is false. A statistic is a feature of sample and a parameter is a feature of population. Every sample of the selected size has an equal chance of being used.
Point estimates are defined for both samples and populations. This is false. A point estimate is used to estimate the population parameter.
To calculate a point estimate, we need to know the sample size. This is false. Population is needed.
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+ Simplify the following Loga + 3Logax -2 Log al4x
The simplified expression of the logarithmic expression is Log(a³ˣ ⁺ ¹ ⁻ ¹⁶ˣ²)
How to simplify the logarithmic expressionFrom the question, we have the following parameters that can be used in our computation:
Loga + 3Logaˣ - 2 Log a⁴ˣ
Express properly
So, we have
Log(a) + 3Log(aˣ) - 2 Log(a⁴ˣ)
So, we have
Log(a) + Log(a³ˣ) - Log(a¹⁶ˣ²)
The logarithmic expression can be simplified using the product and the quotient rule
This gives
Log(a * a³ˣ/a¹⁶ˣ²)
So, we have
Log(a³ˣ ⁺ ¹ ⁻ ¹⁶ˣ²)
Hence, the simplified expression is Log(a³ˣ ⁺ ¹ ⁻ ¹⁶ˣ²)
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Question on graphs , quite easy i think :')
1) Note that the grid needs to be 8 squares wide to accommodate the data.
2) a scale of 0.2 km per square on the vertical axis would provide a clear representation of the data while utilizing the available space effectively.
What is the explanation for this ?1) To find the width of the grid, we need to find the total number of data points on the x- axis.
Here , the time since the start is given at intervals of 5 minutes. From 0 - 35 minutes, there are a total of 8 data points.
Thus, we are right to state that the grid needs to be 8 squares wide to accommodate the data.
2)
We must decide the optimal scale for visualizing data on the vertical axis because the grid is 20 squares tall. Looking at the distance from the starting point, we can see that the figures range from 0 to 1.9 kilometers.
To make the best use of the grid area, we may select an appropriate scale that includes the data range.
In this scenario, a vertical scale of 0.2 km per square would offer a clear depiction of the data while properly utilizing the available space.
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Hii please help i would really appreciate it
(multiple choice)
x= [select]
-140
-120
-160
-100
y= [select]
-50
-60
-80
-70
Answer:
x = 120 , y = 50
Step-by-step explanation:
1 and 140° are a linear pair and sum to 180° , that is
1 + 140 = 180 ( subtract 140 from both sides )
1 = 40
the sum of the 3 angles in Δ ABE = 180° , so
∠ BAE = 180° - ( 80 + 40)° = 180° - 120° = 60°
∠ BAE and ∠ CDE are same- side interior angles and sum to 180° , that is
x + 60 = 180 ( subtract 60 from both sides )
x = 120
the sum of the 3 angles in Δ CDE = 180° , that is
10 + x + 2 = 180
10 + 120 + 2 = 180
130 + 2 = 180 ( subtract 130 from both sides )
2 = 50
AED is a straight line , then
y + 80 + 2 = 180
y + 80 + 50 = 180
y + 130 = 180 ( subtract 130 from both sides )
y = 50
David found a vintage watch his father lost 38 years ago. The watch’s date showed that it had worked for over two years after his father lost it. When David found the watch, it was 3 times as old as when his father lost it. How old was the watch when David’s father lost it?
Answer:
Step-by-step explanation:
Hey there,
Here's my reasoning regarding the problem:
Let's assume that the watch at the time it was lost was x years old.
When it was picked it was 3 times as old as it was when it was lost therefore it's currently 3x. The time between when it was lost and when it was found is 38 years. We can break this down into a simple algebraic formula:
3x - x = 38
2x = 38
x = 19
What is the equation of a circle with center (10, -10) and radius length of 20 units?
