Answer:
1. Given.
2. Reflexive Property of Congruence.
3. Alternate Interior Angles Theorem.
4. SAS
5. <4 ~= <2
6. Converse of Alternate Interior Angles Theorem.
Let a and b be 3 by 3 matrices with det (a) = 3 and det (b) = 5. find the value of det(ab).
If the value of determinant a is 3, determinant b is 5 then the value of determinant ab is 15.
Given that the value of determinant a is 3, determinant b is 5.
We are required to find the value of determinant ab.
Determinant of a matrix is the scalar value computed for a given square matrix.It means the matrix which is not square does not have a determinant value. It is denoted by IAI.
We know that,
IaI*IbI=IabI
So we have to just put the values in the above formula to get the determinant of ab.
IabI=3*5
=15
Hence if the value of determinant a is 3, determinant b is 5 then the value of determinant ab is 15.
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pls help me solve these
The conversion of 9.204 to a mixed number will be 9 51/250.
How to illustrate the information?It should be noted that converting decimal to mixed numbers simply means changing them to whole numbers and fractions.
Therefore, 9.204 will be:
= 9 204/1000
= 9 51/250
The percentage equivalent of 3 7/8 will be:
= (3 × 100) + (7/8 × 100)
= 300 + 87.5
= 387.5%
Dividing 72 in the ratio 2:3:4 will be:
= 2/9 × 72 = 16
= 3/9 × 72 = 24
= 4/9 × 72 = 32
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Charlie began hiking from her campsite back to her car. Her campsite was located 9 miles from her car. She had walked for 1 hour and was 2 miles from her campsite when she realized she had forgotten her water bottle. She hurried back to her campsite in 0.5 hours, collected her water bottle, and rested for 0.5 hours. Then she began hiking back to her car at a quicker pace. She hiked for 3 more hours before she reached her car. Which graph represents Charlie's distance from her car at different times?
The graph which represents Charlies distance from her car at different times is indicated as attached. The schedule of her movement is also attached. This type of graph is called Distance Time Graph.
What is a distance-time graph?
A distance-time graph can show the distance traveled while an item moves in a straight line.
The gradient of the line in a distance-time graph is equal to the object's speed. The item is travelling more quickly the steeper the line and the larger the gradient.
See the attached for Charlies Distance - Time movements visualized in a graph.
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x - 2y = 3
5x + 3y = 2
The lines whose equations are shown intersect at which point?
The point of intersection of the two lines is at (1,-1)
System of equationThe given system of expression is shown below
x - 2y = 3
5x + 3y = 2
The solution to the system of equation is the point of intersection
From equation 1
x = 3 + 2y
Substitute into 2
5(3+2y) + 3y = 2
15 +10y + 3y = 2
13y = -13
y = -1
Substitute y = -1 into 3
x = 3 + 2y
x = 3+(-2)
x = 1
Hence the point of intersection of the two lines is at (1,-1)
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Which of the following is equivalent to 1/log3(m)
Answer: A
Step-by-step explanation:
We can rewrite the expression as
[tex]\frac{\log_{3} 3}{\log_{3} m}[/tex]
Using the change of base formula, we get [tex]\log_{m} 3\[/tex]
Please help I need an answer
The midpoint of the given line in coordinate form (x, y) is -0.5, 0)
Midpoint of a lineThe midpoint of a line is the middle of the given line. Given the coordinate points (x1, y1) and (x2, y2), the midpoint of the line is given as:
M(x, y) = {x1+x2/2, y1+y2/2}
Given the coordinate points on the line (-2, 1) and (1, -1)
Substitute the given coordinate points into the formula to have:
M(x, y) = {-2+ 1/2, 1-1/2}
M(x, y) = {-1/2, 0/2}
M(x, y) =(-0.5, 0)
Hence the midpoint of the given line in coordinate form (x, y) is (-0.5, 0)
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A soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more pairs of shorts, for a total of $62.
The system of equations that can be used to find x, the cost of each jersey, and y, the cost of each pair of shorts is shown.
12x + 12y = 156
4x + 6y = 62
What is the cost of each jersey?
The cost of each jersey is $8 dollar and that of shorts is $5
System of equationThis are expression that contain unknown equation and two or more equation.
According to the question, a soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more pairs of shorts, for a total of $62.
The system of equation that represent the expression is given as;
12x + 12y = 156
4x + 6y = 62
____________
6x + 6y = 78
4x + 6y = 62
Subtract
6x-4x = 78 - 62
2x = 16
x = 8
since 4x + 6y = 62
2x+3y = 31
2(8) + 3y = 31
3y = 31-16
3y = 15
y = 5
Therefore the cost of each jersey is $8 dollar and that of shorts is $5
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Question is in image below:
The sinusoidal equation will be Y=4.25 sin[(π/26)(t-11)]+12.25
How to compute the equation?The following can be deduced:
Function Y=Asin(wt-Φ)+β
Amplitude A=(16.5-8)/2=4.25 hours
Vertical shift β= (16.5+8)/2=12.25
Period is 52 weeks, thus 52=2π/ω→ω=2π/52=π/26
The phase shift Φ can be gotten if we divide the whole year in 4 sub-intervals each interval would be :
[0,13], [13,26],[26,39],[39,52]
The summer solstice occurs at the end of week 24.
The winter solstice occurs at the end of week 51.
The maximum of sine function happens at the end of the first sub-interval [0,13]
Here, Φ is 11, thus, the function would be
Y=4.25 sin[(π/26)(t-11)]+12.25.
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A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table shows the data:
Number of hours of sunlight
(x) 0 1 2 3 4 5 6 7 8 9
Height of plant in cm
(y) 4 7 10 13 16 19 22 25 28 31
Part A: Is there any correlation between the number of hours of sunlight that a plant receives and the height to which it grows? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indica
Answer: GET BRAINLY PLUS FOR VERIFIED ANSWERS NOW
Step-by-step explanation:
NOW
Michelle is purchasing fabric for two new sewing projects: a hat and a tote bag. The two projects each need red and black fabric. The hat requires 2 yards of red fabric and 1 yard of black fabric. The tote bag requires 2 yards of red fabric and 4 yards of black fabric. Michelle paid $14 for the hat’s fabric and $26 for the tote bag’s fabric. How much does one yard of each fabric cost?
The cost of one yard of black fabric is $4.
The cost of one yard of red fabric is $5.
What are the linear functions that represent the question?2r + b = 14 equation 1
2r + 4b = 26 equation 2
Where:
r = cost of one yard of red fabric
b = cost of one yard of black fabric
What is the cost of each type of fabric?
Subtract equation 1 from equation 2
3b = 12
b = 12 / 3
b = 4
Substitute for b in equation 1
2r + 4 = 14
2r = 14 - 4
2r = 10
r = 10 / 2
r = $5
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20 POINTS
Here are the scores of 18 students on a history test. 55, 57, 58, 61, 62, 66, 68, 68, 71, 75, 75, 78, 82, 83, 85, 86, 88, 89. Notice that the scores are ordered from least to greatest. Make a box-and-whisker plot for the data.
The median of this box and whisker plot is 73
A box and whisker plot is defined as a graphical method of displaying variation in a set of data. In most cases, a histogram analysis provides a sufficient display, but a box and whisker plot can provide additional detail while allowing multiple sets of data to be displayed in the same graph. Box and whisker plots are very effective and easy to read, as they can summarize data from multiple sources and display the results in a single graph. Box and whisker plots allow for comparison of data from different categories for easier, more effective decision-making.
From the given data, following can be inferred
Population size: 18Median: 73Minimum: 55Maximum: 89First quartile: 61.75Third quartile: 83.5Interquartile Range: 21.75which is demonstrated in the box and whisker plot below
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The projected worth (in millions of dollars) of a large company is modeled by the equation w = 241(1.06) t. the variable t represents the number of years since 2000. what is the projected annual percent of growth, and what should the company be worth in 2011?
Answer:
6%- 457 Million
Step-by-step explanation:
w=241(1.06)^11=457 million
Consider this function. f(x)=6log2x-3 over which interval is function f increasing at the greatest rate?
The function increased at the highest rate in the interval [1/8, 1/2], as can be seen from the function value and its interval values.
What is maxima and minima?A function's maxima and minima are its highest and lowest values, respectively, either on the entire domain or inside a certain range. They are referred to as the function's extrema collectively. The plural forms of maximum and minimum for a function are respectively known as maxima and minima.
Why do we use maxima and minima?The extreme values of a function—their maximum and minimum values—are referred to by the words maxima and minima. Maximum refers to the maximum value or amount that is feasible. A function's biggest value within its range is known as its absolute maximum.
According to the given information we have:f(x)=6log2x-3
For the interval x ∈[2, 6]
f(x) ∈ [-0.678, 3]
For the interval x ∈ [1/8, 1/2]
f(x) ∈ [ -9.96, -5.32]
For the interval x ∈ [1, 2]
f(x) ∈ [-3, -0.67]
For the interval x∈ [1/2, 1]
f(x) ∈ [-5.32, -3]
The function increased at the highest rate in the interval [1/8, 1/2], as can be seen from the function value and its interval values.
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Help help help help help help
Answer:
∠JKL = 98
Step-by-step explanation:
the two small vertical lines on JK & KL means that
JK & KL are the same length which means that
same length means same degrees
∠KJL & ∠KLJ are the same degrees
∠KJL & ∠KLJ are both 41 degrees
triangles are 180
41 + 41 = 82
180 - 82 = 98
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Cos C
C
21
B
35
28
A
Find the area of a kite with diagonal length of 10 and 25 meters.
The Area of the kite with the given diagonals is: 125 square meters.
What is a Kite?A kite can be described as a quadrilateral having four (4) sides, which can be categorized into two pairs of congruent sides, each of them is adjacent to the other. A kite has two diagonals that intersect, where by the longer diagonal divides the smaller diagonal into equal halves.
An example of a kite is shown in the image attached below, where:
JL and KM are the diagonals of the kite.
How to Find the Area of a Kite?The formula for finding the area of a kite is given as:
Area = 1/2 × (product of the lengths of the diagonals)
Given the following:
Length of diagonal 1 = 10 meters
length of diagonal 2 = 25 meters
Area = 1/2 × (product of the lengths of the diagonals) = 1/2 × (10 × 25)
Area of kite = 1/2 × (250)
Area of kite = 1/2 × (250)
Area of kite = 125 square meters.
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________ is the number of defects in a sample divided by the number of opportunities while ________ is the number of defects divided by the number of units tested within a sample.
DPU is the number of defects in a sample divided by the number of opportunities while DPMO is the number of defects divided by the number of units tested within a sample. Option B
What is DPU?Defects per unit (DPU) can be defined as the number of defects divided by the number of opportunities
It is also seen as the universal measure of quality.
For example, if there are 100 defects in 1,000 units produced, then the defects per unit will be 0.01.
Defects per million opportunities can be defined as a mathematical calculation of the estimated quality of a process
From this information, we can conclude that DPU and DPMO are measure of defects in a sample.
Thus, DPU is the number of defects in a sample divided by the number of opportunities while DPMO is the number of defects divided by the number of units tested within a sample. Option B
Complete question is;
________ is the number of defects in a sample divided by the number of opportunities while ________ is the number of defects divided by the number of units tested within a sample.
a. DPMO, DPU
b. DPU, DPMO
c. RTY, FTY
d. FTY, RTY
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Near the equator, the earth rotates approximately 34 kilometers every 32 seconds. what is the speed of earth's rotation near the equator? show your reasoning and include the unit of measure.
Answer:
Step-by-step explanation: The earth rotates 34 km every 32 seconds. We can simplify this by dividing both sides by 32. Now, we have 34/32 km every 32 seconds. Now, to further simplify this, we need to convert 34/32 to a mixed number 34/32 = 1 2/32 which then can be simplified to 1 1/16. So, near the equator, the speed of Earth's rotation is 1 1/16 km per second.
Please help me if you can
The time, t in seconds that it takes a car to travel a quarter-mile when starting from a full stop can be estimated by using the formula:
Where w = weight of the car
p = power delivered by the engine in horsepower (hp)
If the quarter-mile time for a 3,590-pound car is 13.4 s, how much power does its engine deliver? Round to the nearest pound.
Two students solved this problem. Natasha’s answer was 295 hp and Daniel’s was 679 hp. Why was Daniel wrong? Show each step that led Daniel to the wrong answer
Daniel’s answer was wrong because he used square root instead of the cubed root.
How can we calculate this?From the expression , which is [tex]t = 5.825 \sqrt[3]{3590/p}[/tex]
Then we can perform some operations to Solve for the value of p.
Then we can make division on the both sides of the equation using 5.825 , then we have
2.304 = [tex]} (3590/p)^{\frac{1}{3}[/tex]
We can cube the both side of the equation to will eliminate the radical and we will have
12.174 = 3590/p
then , p = 294.89 which implies that Natasha’s answer is correct.
Therefore , Daniel’s answer was wrong because he used square root instead of the cubed root.
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The Data
Decorative glass pebbles are often used in vases for their appearance, and to have their weight stabilize the vase. The table below gives the total weight of a vase full of uniform glass pebbles.
TABLE OF DATA ATTACHED BELOW*
The Analysis
1- Using the table of data above, determine if this relationship is linear or not. Explain how you know.
2-Write an equation that best represents this relationship:
Explain how you reach your answer and show your work below.
3- Graph the data on the grid to the right, label both axes, and label it Line 1.
4-
a) What is the meaning of the initial value in this scenario?
b) What is the meaning of the slope in this scenario?
5- How would the graph AND equation change if a Styrofoam cup is used to collect the data, instead of a glass vase? Explain your reasoning.
6- Based on your equation in question #2, how much will 112 pebbles weigh with the vase?
7- If the total weight is 504 g, how many pebbles are in the vase?
8- Your friend Wilma shares her analysis of similar data about pebbles and a vase, but her equation is W = 10p + 80.
a) Graph it on the same grid as question #3. Label it Line 2.
b)What are the coordinates of the point of intersection?
c)What does it mean in this scenario?
9- Write a SIMPLIFIED algebraic expression to represent the area of the following trapezoid. Show all your work.
(Hint: area of a trapezoid = [tex]\frac{h(a+b)}{2}[/tex])
TRAPEZOID ATTACHED BELOW*
10- Tanya is 12 years older than Leah. Three years ago, Tanya was five times as old as Leah. What is the age of Tanya and Leah now?
I NEED IT TODAY PLESE!
With the aid of the attached diagrams in the question, we have;
1- Linear relation
2- W = 8•P + 80
3- Please find attached the graph created using a graphing calculator.
4- a) The initial value is the mass of the vase
b) The slope is the mass of each pebble
5- The initial value is lesser than 80
6- 1.2 kilograms
7- 53 pebbles
8- a)
b) (0, 80)
c) The masses are the same
9- Trapezoid area, A = 14•x² - 4•x
10- Tanya and Leah are 18 and 6 years old respectively
How can the table and diagram be analyzed?1- The relationship between two variables (x and y) is linear if the difference between the terms of the x-values and the terms of the y-values are both constant.
From the table we have;
The difference between consecutive terms of the x-values is constant and equal to 10The difference between consecutive terms of the y-values is constant and equal to 80The relationship between the x and y-values in the table is therefore;
A linear relationship2. The slope, m, of the linear function is found as follows;
m = (360 - 280)/(30 - 20) = 8
The equation is therefore;
W - 360 = 8•(P - 30)
W = 8•P - 240 + 360 = 8•P + 80
The equation is; W = 8•P + 803. Please find attached the graph drawn with a graphing calculator.
4. The initial value is the output variable (W-value) when the input variable (P-value) is zero.
Therefore;
y = 8×0 + 80 = 80
a) The initial value indicates when the input, P-value is zero, which gives the mass of the vases
b) The slope indicates the number of times an additional pebble increases the weight of the vase and pebble, which is the mass of one pebble
5- A styrofoam cup is lighter than a glass cup, therefore, the initial value, which is the constant term, c, reduces.
The change is that, the initial value reduces and becomes less than 806- The weight, W, of 112 pebbles is therefore;
W = 10 × 112 + 80 = 1,200
The weight of 112 pebbles is 1,200 g, which is 1.2 kg.7- 504 = 8•P + 80
Which gives;
504 - 80 = 8•P
P = 424 ÷ 8 = 53
The number of pebbles in the vase when it weighs 504 g. is 53 pebbles8- Wilma's equation is; W = 10•P + 80
a) Please find the second graph showing the graphs of the two equations combined.
b) The point of intersection is given by the relation 10•P + 80 = 8•P + 80
2•P = 0
P = 0
Therefore, at the point of intersection, W = 80
The coordinates of the point of intersection is therefore;
(0, 80)c) The point of intersection means that the weight of Wilma's vase and the vase in question 1 are the same.
9. The area of the trapezoid, A, can be expressed as follows;
A = 4•x × ((2•x + 5)+(5•x - 7))/2
A = 2•x × (7•x - 2) = 14•x² - 4•x
Area of the trapezoid = 14•x² - 4•x10. Let T represent Tanya's age now and let L represent Leah's current age, we have;
T = L + 12
T - 3 = (L - 3) × 5
Solving gives;
L + 12 - 3 = (L - 3) × 5 (Substitution property)
L + 9 = 5•L - 15
4•L = 9 + 15 = 24
L = 24 ÷ 4 = 6
Leah's age now, L = 6 yearsT = L + 12
Therefore;
T = 6 + 12 = 18
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Part A: Write an algebraic expression for 6 more than 7 times a number. (5 points)
Part B: Write a verbal expression for 3(n + 8). (5 points)
The algebraic expression of the part A is 6+7x. And the verbal expression for 3*(n+8) is "the triple of the sum between the numbers n and 8".
Linear ExpressionA linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=2x+7.
Part AFirst, you should choose a variable for unknow number. Here, the variable will be x. Then, 7 times a number can be represented for 7x.
The word more will be represented for the add symbol (+). Thus,
the algebraic expression is 6+7x.
Part BThe expression 3*(n+8) can be represented for the sentence:
The triple of the sum between the numbers n and 8.
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2. A ribbon is 5 long. A piece of length 3 4/5 is cut from it. What is the length of the remaining piece?
Answer:
Given,The ribbon is 5m long.
The length of the piece = 3 ^ 4 / 5 m.
To find,The length of the remaining piece.
Solution,We can simply solve this mathematical problem by using the following mathematical process.
First of all, we have to convert the length of the cut piece into simple decimal value.
Length of cut piece =3^ 4 / 5 = (3 * 5 + 4) / 5 = 19/5 = 3.8m
Length of the remaining ribbon = Intital length cut length = 5 - 3.8 = 1.2m = 12/10 - m = 6/5 * m = 1 1/5 m
(The final value is also expressed in fractional form)Hence, the length of the remaining piece is 15m.Answer: 1 1/5
Step-by-step explanation:
5 - 3 = 2 - 4/5 = 1 1/5
For s=5 and t=8, 3st²-s²:
3st²-s² =
Step-by-step explanation:
Given,
s=5
t=8
solution,
= 3st² - s²
= 3*5*8² - 5²
= 3*5*64 - 25
= 960 - 25
= 935
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex] \sqrt{112x {}^{6}y {}^{3} {z}^{5} } \\ \sqrt{(2 {}^{4} \times 7 )x {}^{6}y {}^{2}yz {}^{4} z } \\ 2 {}^{2}x {}^{3} yz {}^{2} \sqrt{7yz} [/tex]
Last optionwhat is the general form of the equation for the given circle?
The general equation for a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex], where [tex](h,k)[/tex] is the centre of the circle and [tex]r[/tex] is the radius.
Solving the QuestionFirst, we can determine the centre of the circle.
( _ , _ )
The point directly on top is (4,7). Because it lies on the same vertical line as the centre, they have the same x-coordinate.
(4, _ )
The point directly to the right of it is (7,4). Because it lies on the same horizontal line as the centre, they have the same y-coordinate.
(4,4)
Therefore, the centre of the circle is (4,4). Plug this into the general equation:
[tex](x-h)^2+(y-k)^2=r^2\\(x-4)^2+(y-4)^2=r^2[/tex]
Now, we can determine the radius of the circle.
To do this, we can calculate the distance between the centre of the circle and one of the given points that lie on the circumference.
The centre is (4,4), and one of the points is (4,7). Because they only have a difference of 3 units in the y-direction (and none in the x-direction), this means that the radius is 3 units. Plug this into the general equation:
[tex](x-4)^2+(y-4)^2=r^2\\(x-4)^2+(y-4)^2=3^2\\(x-4)^2+(y-4)^2=9[/tex]
Answer[tex](x-4)^2+(y-4)^2=9[/tex]
please please please please please please please please please please please please please please please please please help mey,
Answer:
See below
Step-by-step explanation:
REMEMBER sec = 1/cos ...so the left side is
[1/cos -1] / [1/cos +1 ]
get common denominator for numerator and denominator
[ (1 -cos) /cos ] / [ (1+cos) / cos ]
now flip the bottom fraction and multiply to get
[(1-cos/cos) ] * [ cos / (1+cos) ] which simplifies to ( the 'cos' term cancels)
(1-cos) / (1+cos) done !
A vase in the shape of an oblique cylinder has the dimensions shown. What is the volume in the vase in liters?round nearest tenth
The volume of a vase with a radius of 1 m and height of 7 m is 22000 L
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Cylinder is solid geometrical figure with straight parallel sides and a circular or oval cross section
Let us assume that the vase has a base with radius of 1 m and height of 7 m, hence:
Volume of vase = π * radius² * height
Volume of vase = π * (1)² * 7 = 22 m³ = 22000 L
The volume of a vase with a radius of 1 m and height of 7 m is 22000 L
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3. What is the missing term in the sequence below?
3, 6, 11, ?, 27, 38, 51
Select the correct answer.
Which equation represents the vertical line passing through (14.-16)?
OA
OB. y=-16
OC
X= 14
OD.
y=14
X=-16
Check the picture below.
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 5 inches. The height of the cone is 15 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.
The volume of the cylinder and the cone is equal
Volume of a cylinder and a coneThe formula for calculating the volume of a cylinder is expressed as:
V = πr²h
where
r is the radius
h is the height
For the cylinder
r = 8/2 = 4 in
h = 5
Substitute
V = π(4)²*5
V = 80π cubic inches
For the cone
r = 4 in
h = 15in
Substitute
V = 1/3πr^2h
V = 1/3(π)(4)^2 * 15
V = 80π cubic inches
Hence the volume of the cylinder and the cone is equal
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