ANSWER :
scalene triangle
EXPLANATION :
From the problem, the vertices of a triangle are :
T(1, 1), V(4, 0) and S(3, 5)
A triangle is scalene if the three sides are different from each other.
A triangle is isosceles if two sides are congruent.
A triangle is equilateral if three sides are congruent.
So we need to get the distances between two points and determine the type of triangle accordingly.
Using the distance formula :
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)The distances are :
\(\begin{gathered} d_{TV}=\sqrt{(4-1)^2+(0-1)^2}=\sqrt{10} \\ \\ d_{TS}=\sqrt{(3-1)^2+(5-1)^2}=\sqrt{20} \\ \\ d_{VS}=\sqrt{(3-4)^2+(5-0)^2}=\sqrt{26} \end{gathered}\)Since the distances are different from each other, the triangle is scalene
This graph has a proportional relationship.
What is the constant of proportionality?
Answer:
k = \(\frac{9}{8}\)
Step-by-step explanation:
the equation for a proportional relationship is
y = kx ← k is the constant of proportionality
divide both sides by x
\(\frac{y}{x}\) = k
using the point ( \(\frac{2}{3}\), \(\frac{3}{4}\) ) with x = \(\frac{2}{3}\) and y = \(\frac{3}{4}\) , then
k = \(\frac{\frac{3}{4} }{\frac{2}{3} }\) = \(\frac{3}{4}\) × \(\frac{3}{2}\) = \(\frac{3(3)}{4(2)}\) = \(\frac{9}{8}\)
What is the Surface Area of the figure below?
A
60 units2
B
60 units3
C
104 units2
D
104 units3
Answer:
D
Step-by-step explanation:
I'm really sry if it's wrong!
A cookie recipe calls for 1/4 of a cup of sugar for one batch. How many complete batches can you make if you have 3 1/3 cups of sugar?
Answer:
Step-by-step explanation:
none
We can describe 3x- 2 as an expression. How can we describe the parts of the expression that the arrows point to? 3x- 2
Step-by-step explanation:
3x - 2 is formatted in the formula y = mx + c
To substitute for 3x - 2
y = 3x -2
find the value of x and y that make the quadrilateral
The quadrilateral have equal opposite sides, for example:
Then, (4x + 6) must be equal to (7x - 3), and (4y - 3) is equal to (3y + 1), therefore
\(4x+6=7x-3\)We can solve that equation for x
\(\begin{gathered} 4x+6=7x-3 \\ \\ 3x=9 \\ \\ x=\frac{9}{3}=3 \end{gathered}\)Hence, x = 3. Now let's solve the other equation
\(\begin{gathered} 4y-3=3y+1 \\ \\ y=4 \end{gathered}\)Then the value of y is 4.
Final answers:
x = 3
y = 4
Using technology we found the equation of the line to be y=-2x + 25. Using the given equation
predict the value of a car that is 3 and a half years old.
Answer:
A car that is 3 and a half years old would cost $18,000
Step-by-step explanation:
Using the given equation, \(y=-2x+25\), we replace 'x' with '3.5' and solve for 'y'.
\(y=-2(3.5)+25\)
\(y=-7+25\)
\(y=18\)
Dollar values on the graph are expressed in thousands. Thus, we multiply 18 by 1,000 to get $18,000
NEED HELP ASAP PLS AND THX PIC IS ATTACHED
The transformation composition displayed in the accompanying photograph is
1. 180-degree anticlockwise rotation of the starting point2. Refraction on the x-axisWhat does transformation mean?A transformation in mathematics is a modification of a geometric object or mathematical function's position, size, shape, or orientation. Shapes can undergo geometric modifications, such as rotations, reflections, dilatations, and translations.
The first transformation in the figure is a 90° clockwise rotation about the origin.
Reflection along the x-axis is the second transformation. This creates mirror image of the triangle below the line which is the axis of reflection
Learn more about transformation at:
https://brainly.com/question/1548871
#SPJ1
Jordan wants to bring his dog to the doggie day care while he is on vacation. The day care costs $120 per day. If Jordan leaves his dog at the daycare for 2 weeks, 3 days, and 5 hours, how much will it cost?
Give the cost per day to be $120
Before we can get the cost of the dog at the day care for 2 weeks, 3 days, and 5 hours, we need tp first convert this to days
Since 1 week = 7days
2 weeeks = 14 days
Also if 24 hours = 1 day
5 hours = (5/24) day
Adding up in days:
2 weeks, 3 days, and 5 hours = 14days + 3 days + 5/24 days
2 weeks, 3 days, and 5 hours = 17 5/24days
Next is to calculate the cost
If 1 day = $120
17 5/24 days = x
cross multiply
x = 120 * 17 5/24
x = 120 * 413/24
x = 49560/24
x = 2,065
Hence the price of the dog when it is at the daycare for 2 weeks, 3 days, and 5 hours is $2,065
Find the additive inverse and multiplicative inverse of [14/15*(-25/28)]+[2/3*6/7]
The additive inverse of [14/15*(-25/28)]+[2/3*6/7] is 1
What is additive inverse?You should be aware that the additive inverse of a number is the number that, when added to a, yields zero and the multiplicative inverse is the reciprocal for a number
The given fractions are
[14/15*(-25/28)]+[2/3*6/7]
Let us solve it in parts
= 14/15*-15/28
=-392/420
The multiplicative inverse is
-392/420 *420/-392 =1
The second fraction is
[2/3*6/7]
The additive inverse is
12/21 -12/21 = 0
Therefore the additive inverse is 1+0 = 1
Learn more about additive inverse on https://brainly.com/question/13715269
#SPJ1
WILL GIVE 5 STARS
Angela plays soccer and golf for a total of 125 minutes every day. She plays soccer 45 minutes more than she plays golf.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Angela plays soccer (x) and the number of minutes she plays golf (y) every day. (5 points)
Part B: How much time does Angela spend playing golf every day? (3 points)
Part C: Is it possible for Angela to have spent 80 minutes playing soccer every day? Explain your reasoning.
A: The linear equations are x + y = 125 and x = y + 45.
B: Everyday Angela spends 40 minutes in playing golf.
C: No, it is not possible for Angela to spend 80 minutes playing soccer every day.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Part A:
Let x be the number of minutes Angela plays soccer every day
Let y be the number of minutes Angela plays golf every day
According to the problem statement the linear equations are -
x + y = 125 (total time playing both sports is 125 minutes)
x = y + 45 (Angela plays 45 more minutes of soccer than golf)
Part B:
Substitute x = y + 45 into the first equation -
(y + 45) + y = 125
Use the addition operation -
2y + 45 = 125
2y = 80
y = 40
Angela spends 40 minutes playing golf every day.
Part C:
If Angela spends 80 minutes playing soccer every day, then
x = 80
y + 45 = 80 (using the equation x = y + 45)
y = 35
But this would mean that she plays golf for 35 minutes and soccer for 80 minutes, which adds up to a total of 115 minutes.
This is not possible since the problem states that Angela plays both sports for a total of 125 minutes every day.
Therefore, it is not possible for Angela to have spent 80 minutes playing soccer every day.
To learn more about linear equation from the given link
https://brainly.com/question/2226590
#SPJ1
Pablo dice que descontar el 10% de un precio es lo mismo que $10 pero Andrés Dice que depende de lo que haya gastado quién tiene razón
Answer:
Andrés
Step-by-step explanation:
Andrés porque el 10% es .10 = 10 centavos
Does this table represent a function? Why or why not?
O
X
2
3
3
4
5
y
1
4
3
2
5
A. Yes, because there are different y-values.
B. Yes, because every x-value corresponds to exactly one y-value.
C.
No, because the y-values are positive.
D. No, because one x-value corresponds to two different y-values.
SUBMIT
The given table does not represent a function. The correct answer is D. No, because one x-value corresponds to two different y-values.
To determine if the table represents a function, we need to check if every x-value corresponds to exactly one y-value. Let's analyze the given table:
x | y
-------
O | 1
X | 4
2 | 3
3 | 2
3 | 5
4 |
5 |
From the table, we can see that the x-values are not unique. Both the values 3 and 4 appear twice in the x-column, but they have different corresponding y-values.
This violates the definition of a function, which states that each input (x-value) should have only one output (y-value).
Therefore, the given table does not represent a function.
The correct answer is D. No, because one x-value corresponds to two different y-values.
for such more question on function
https://brainly.com/question/13473114
#SPJ8
What is angle
Enter your answer in the box
Answer:
CAB is 37 degrees
Step-by-step explanation:
90 + 53 = 143
180 - 143 = 37
Please help me with this AP Calculus question!!
9514 1404 393
Answer:
B. 3
Step-by-step explanation:
If all you want is a numerical result, sometimes a graphing calculator can provide that easily. The attachment shows it calculates the slope at x=4 to be 3.
dy/dx = 3 at x = 4
__
The derivative of the expression can be found from the quotient formula:
d(u/v) = (du·v -u·dv)/v²
y' = ((x -2)(2x -7) -(x^2 -7x +2)(1))/(x -2)^2
= (2x^2 -11x +14 -x^2 +7x -2)/(x -2)^2
= (x^2 -4x +12)/(x -2)^2
= ((x -4)x +12)/(x -2)^2
Then for x=4, we have ...
y' = 12/4 = 3
dy/dx = 3 at x = 4
Answer:
The answer is B:3
Step-by-step explanation:
I saw this in class
help 128 ounces = ___ pounds
6
8
16
32
Answer:
8
Step-by-step explanation:
absolute value of x=5
what is x
Answer:
5
Step-by-step explanation:
5 = 5
The circumference of a circle is 15pi centimeters what is the area of the circle in terms of pi?
\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)
What is the length of the apothem of the regular pentagon shown below? Round to one decimal place
The length of the apothem of the regular pentagon shown is 5.2 meters
How to determine the length of the apothem?Represent the central angle of the regular pentagon using x
The value of the central angle of the regular pentagon is then calculated as:
x = 360/n
Where n represents the number of sides
i.e n = 5
So, we have:
x = 360/5
Evaluate the quotient
x = 72
Represents the apothem with y.
The apothem is then calculated as:
tan(x/2) = (Side length/2)/Apothem
This gives
tan(72/2) = (7.6/2)/y
Evaluate the quotient
tan(36) =3.8/y
Multiply both sides by y
y tan(36) = 3.8
Divide both sides by tan(36)
y = 3.8/tan(36)
Evaluate the quotient
y = 5.2
Hence, the length of the apothem of the regular pentagon shown is 5.2 meters
Read more about regular pentagon at:
https://brainly.com/question/14961220
#SPJ1
Convert 4feet to inches
Answer:
48
Step-by-step explanation:
multiply the length value by 12
the length is 4ft so you multiply it by 12
so
4×12=48
so the answer is 48
√2x² + 7x + 5√2 = 0
find the roots of the following quadratic equation by factorization method
PLS HELP ME FAST
Step-by-step explanation:
√2x² + 7x +√2=0
2x + 7x + √ 2 =0
√2=9x
x = o.15713484
expand and simplify
i’ll give u brainiest
√5(√10+√2)
Answer:
\( \sqrt{50} + \sqrt{10} \)
Step-by-step explanation:
\( \sqrt{5} ( \sqrt{10} + \sqrt{2} ) \\ (opening \: the \: bracket) = (\sqrt{10 \times 5} ) + ( \sqrt{5 \times 2} \\ = \sqrt{50} + \sqrt{10} \)
Answer:
√50 + √10 = 5√2 + √10
Please mark brainliest as answered correctly.
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 23.5 for a sample of size 775 and standard deviation 12.2. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level). Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:
\(22.6 < \mu < 24.4\)
How to obtain the confidence interval?The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:
\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)
Looking at the z-table, the critical value for a 95% confidence interval is given as follows:
z = 1.96.
The lower bound of the interval is then given as follows:
\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)
The upper bound of the interval is then given as follows:
\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
During the month, Fisher Company's Work in Process inventory account was credited for $120,500, which represented the Cost of Goods Manufactured for the month. Only one job remained in process on May 31; this job had been charged with $9,600 of applied overhead cost. The amount of direct materials cost in the unfinished job would be:
The amount of direct materials cost in the unfinished job would be $97600.
What is direct material cost?The price of direct materials is directly related to the unit of production and is immediately identifiable. For instance, the price of glass is a direct material expense in the production of light bulbs. The primary component needed for the production of commodities or products was material. Costs of raw materials or components used directly in the production of goods are referred to as direct material costs. For instance, if Company A manufactures toys, the cost of the plastic used to build the toys would be an example of a direct material cost.
Given Data
Work in Process inventory account was credited for $120,500.
charged with $9,600 of applied overhead cost.
Direct material cost = Work in progress - Overhead cost - Direct labor
Direct labor = 9600 ×\(\frac{100}{75}\)
Direct labor = 12800
Direct material cost = 120000 - 9600-12800
Direct material cost = 97600
The amount of direct materials cost in the unfinished job would be $97600.
To learn more about direct material cost, visit:
https://brainly.com/question/15012260
#SPJ9
Jack leaves from
school and goes 4 miles
north and 3 miles east to reach his home. How far is his home from school?
Answer:
It would be 7 miles away.
Step-by-step explanation:
I think.
Jack's home is 5 miles away from the school.
Important information:
Jack goes 4 miles north and 3 miles east to reach his home. Pythagoras Theorem:According to the Pythagoras Theorem:
\(\text{Hypotenuse}^2=\text{Perpendicular}^2+\text{Base}^2\)
Jack goes 4 miles north and 3 miles east. It forms a right triangle with legs 4 miles and 3 miles, and we have to find the hypotenuse to get the distance between his school and home.
Using the Pythagoras Theorem, we get
\(\text{Hypotenuse}^2=(3)^2+(4)^2\)
\(\text{Hypotenuse}^2=9+16\)
\(\text{Hypotenuse}=\sqrt{25}\)
\(\text{Hypotenuse}=5\)
Therefore, Jack's home is 5 miles away from the school.
Find out more about 'Pythagoras Theorem' here:
https://brainly.com/question/343682
A certain truck traveled 7,605 miles in 15 days. What is the average number of miles traveled per day?
If the certain truck traveled 7,605 miles in 15 days. The average number of miles traveled per day will be 507.
What is average?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
It is given that, a certain truck traveled 7,605 miles in 15 days.
The average number of miles traveled per day is obtained by dividing the total distance traveled by the total time taken as,
Suppose the average number of miles traveled per day is x,
x=76015 / 15
x=507 miles per day.
Thus, if the certain truck traveled 7,605 miles in 15 days. The average number of miles traveled per day will be 507.
Learn more about the average here:
brainly.com/question/24057012
#SPJ1
Solve each equation -3x + 2 = -1
Need help with the following question
NO LINKS!!! URGENT HELP PLEASE!!!
Solve ΔABC using the Law of Sines
1. A = 29°, C = 63°, c = 24
2. A = 72°, B= 35°, c = 21
Answer:
1) B = 88°, a = 13.1, b = 26.9
2) C = 73°, a = 20.9, b = 12.6
Step-by-step explanation:
To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:
\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)
Question 1Given values:
A = 29°C = 63°c = 24As the interior angles of a triangle sum to 180°:
\(\implies A+B+C=180^{\circ}\)
\(\implies B=180^{\circ}-A-C\)
\(\implies B=180^{\circ}-29^{\circ}-63^{\circ}\)
\(\implies B=88^{\circ}\)
Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:
\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)
\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)
Solve for a:
\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)
\(\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}\)
\(\implies a=13.0876493...\)
\(\implies a=13.1\)
Solve for b:
\(\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)
\(\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}\)
\(\implies b=26.9194211...\)
\(\implies b=26.9\)
\(\hrulefill\)
Question 2Given values:
A = 72°B = 35°c = 21As the interior angles of a triangle sum to 180°:
\(\implies A+B+C=180^{\circ}\)
\(\implies C=180^{\circ}-A-B\)
\(\implies C=180^{\circ}-72^{\circ}-35^{\circ}\)
\(\implies C=73^{\circ}\)
Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:
\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)
\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)
Solve for a:
\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)
\(\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}\)
\(\implies a=20.8847511...\)
\(\implies a=20.9\)
Solve for b:
\(\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)
\(\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}\)
\(\implies b=12.5954671...\)
\(\implies b=12.6\)
A rectangular piece of metal is 20 in longer than it is wide. Squares with sides 4 in long are cut from the four corners and the flaps are folded upwards to form an open box. If the volume of the box is 1716in ^3, what were the original dimensions of the piece of metal
The original dimension of the metal is width = 21 and length = 41 before cutting off the squares.
What is volume?The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry.
Let us suppose the width of the rectangular metal = w.
Then the length of the rectangular metal is = 20 + w
Given that squares of 4in are cut from the four corners, then the new width and length will be:
width = w - 8
length = 20 + w - 8
The height of the rectangular metal when the flaps are folded are 4 in.
The volume of the rectangular prism is:
V = (l)(w)(h)
Substituting the value of V = 1716, width = w - 8, length = 20 + w - 8, and h = 4 we have:
1716 = (w - 8)(20 + w - 8)(4)
1716 = 80w + 4w^2 - 32w - 640 - 32w + 256
1716 = 4w^2 + 16 w - 384
4w^2 + 16w -384 - 1716 = 0
4w^2 + 16w - 2100 = 0
w^2 + 4w - 525 = 0
w^2 + 25w - 21w - 525 = 0
w(w + 25) - 21 (w + 25) = 0
(w - 21) (w + 25) = 0
w = 21
w = -25
The dimensions of the box cannot be negative hence, the width is 21.
length = 20 + 21
length = 41
The original dimensions of the metal is width = 21 and length = 41 before cutting off the squares.
Learn more about volume here:
https://brainly.com/question/13338592
#SPJ1
I need the answers for the table below.
The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively
Given the function :
tan(πx)/7xSubstitute the given value of x to obtain the corresponding f(x) values :
x = -0.6
f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358
x = -0.51
f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350
x = -0.501
f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967
x = -0.5
f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959
x = -0.4999
f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958
x = 0.499
f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951
x = -0.49
f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188
x = -0.4
f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125
Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013
Learn more on functions : https://brainly.com/question/12634120
#SPJ1