The coordinates of W'X'Y'Z' are W'(5, 25), X'(30, 25), Y'(30, 60) and Z'(5, 10) respectively.
Given that, polygon WXYZ has vertices W( 1, 5 ), X( 6, 5), Y( 6, 10), and Z(1, 10).
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
We know that, scale factor = Dimension of the new shape ÷ Dimension of the original shape
Dimension of the original shape W'= 5(1, 5) = (5, 25)
X' =5(6, 5) = (30, 25)
Y' =5(6, 10) = (30, 60)
Z' =5(1, 10) = (5, 10)
Therefore, the coordinates of W'X'Y'Z' are W'(5, 25), X'(30, 25), Y'(30, 60) and Z'(5, 10) respectively.
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5 ptsIn Ms. Johnson's class a student will get 3 points forhaving their name on their paper and 4 points for eachquestion that is correct. In Mr. Gallegos class, a studentwill get 7 points for having their name on their paper and2 points for each question correct. Which inequalitycould be used to determine x, the number of questionsthat would give you a higher grade in Ms. Johnson'sclass?
In Ms. Johnson's class a student will get 3 points for
having their name on their paper and 4 points for each
question that is correct. In Mr. Gallegos class, a student
will get 7 points for having their name on their paper and
2 points for each question correct. Which inequality
could be used to determine x, the number of questions
that would give you a higher grade in Ms. Johnson's
class?
we have
Ms. Johnson's class
3+4x
Mr. Gallegos class
7+2x
so
the inequality is given by
3+4x > 7+2x
solve for x
4x-2x > 7-3
2x>4
x> 2
the number of question must be greater than 2
Find the surface area of the triangular prism. 13 in. 5 in. 4 in. 12 in.
The first face is a triangle with height 5in and base 12in
Traingular face area = 1/2 x bh
=1/2 x 12 x 5
= 30 in^2
The area of the other triangular base = 30 in^2
Area of left side face = Length x breadth
= 5 x 4 = 20in^2
Area of the slant face = Length x breadth
= 13 x 4 = 52in^2
Area of the bottom face = Length x breadth
= 12 x 4 = 48in^2
Total surface area = 30 in^2 + 30 in^2 + 20in^2 + 52in^2 + 48in^2
=180in^2
A rectangle with an area of 20 square units is dilated by the scale factor of 3.5. find the area of the new rectangle
We are given the area of a rectangle. The area of a rectangle is the product of the length and the height. Therefore, we have:
[tex]A=lh[/tex]If we scale the rectangle by a factor of 3.5 this means that we multiply the length and the height by 3.5, like this:
[tex]A^{\prime}=(3.5l)(3.5h)[/tex]Solving the product:
[tex]A^{\prime}=12.25lh[/tex]Since "lh" is the original area we have:
[tex]A^{\prime}=12.25A[/tex]Now, we substitute the value of the original area:
[tex]A^{\prime}=12.25(20)[/tex]Solving the operations:
[tex]A^{\prime}=245[/tex]Therefore, the new area is 245 square units.
How many different amounts of money can be made
with six pennies, two nickels, and one quarter?
Based on the number of pennies, nickels, and quarters, the number of different amounts of money that can be made are 42.
How to find the different amounts that can be made?First, find out the number of ways to select the different amounts.
There are six pennies so there are 7 ways to collect them including:
(0 times, 1 time, 2, 3, 4, 5, 6)
There are 3 ways to collect nickels and there are two ways to collect quarters.
The number of different amounts of money that can be made are:
= 7 x 3 x 2
= 42 different amounts of money
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4(x - 3) - (x - 5) = 0
4(x - 3) - (x - 5) = 0
Solving for x:
4(x - 3) - (x - 5) = 0
4x - 12 - x + 5 = 0
4x - x = 12 - 5
3x = 7
x = 7/3
Answer:
x = 7/3 = 2.33
A new statue in a local park has a length (L), width (W), and height (H) (all in feet) that can be expressed by a system of equations. L+W=28L+H=26W+H=22What is the width of the statue?
To determine the width of the statue:
[tex]\begin{gathered} L+W=28\ldots\ldots..(1) \\ L+H=26\ldots\ldots\ldots(11) \\ W+H=22\ldots\ldots..(111) \end{gathered}[/tex]A local park has a length (L), width (W), and height (H) (all in feet)
Solve equation 1 and 2 simultaneously,
[tex]\begin{gathered} L+W=28 \\ L+H=26 \\ \text{Subtract equation (1) - (11)} \\ W-H=2\ldots\ldots\ldots(IV) \end{gathered}[/tex]Solve equation 3 & 4 simultaneously, make W the subject of formular
[tex]\begin{gathered} W+H=22 \\ W-H=2 \\ \text{Add the two equation} \\ 2W=24 \\ \text{divide both side by 2} \\ \frac{2W}{2}=\frac{24}{2} \\ W=12 \end{gathered}[/tex]Therefore the value of width of the statue = 12 feet
If Triangle ABC is dilated by a scale factor of 3 and the length of side AB is 15 inches, what is the length of side A'B'? Complete the statement: The length of side A'B' would be inches. Your answer
If Triangle ABC is dilated by a scale factor of 3 and the length of side AB is 15 inches, what is the length of side A'B'? Complete the statement: The length of side A'B' would be inches.
To find out the length side of A'B' multiply the length side AB by the scale factor
so
A'B'=3*(15)=45 inches
Compute the sums below. (Assume that the terms in the first sum are consecutive terms of an arithmetic sequence.) 9 + 4 + (-1) + ... + (-536)
SOLUTION
The terms below make an A.P. Now we are told to find the sum of the AP.
Sum of an AP is given by
[tex]S\text{ = }\frac{n}{2}\lbrack2a\text{ + (n-1)d\rbrack}[/tex]Where S = sum of the AP, a = first term = 9, d = -5, n= ?
So we have to find n first before we can find the sum. The nth term which is the last term = -536. So we will use it to find the number of terms "n"
[tex]\begin{gathered} \text{From T}_{n\text{ }}=\text{ a +(n-1)d where T}_{n\text{ }}=\text{ -536} \\ -536\text{ = 9+(n-1)-5} \\ -536\text{ = 9-5n+5} \\ -536\text{ = 14-5n} \\ -5n\text{ = -536-14} \\ -5n\text{ = -550} \\ n\text{ = 110} \end{gathered}[/tex]Now let's find the sum
[tex]\begin{gathered} S\text{ = }\frac{n}{2}\lbrack2a\text{ + (n-1)d\rbrack} \\ S\text{ = }\frac{110}{2}\lbrack2\times9\text{ + (110-1)-5\rbrack} \\ S\text{ = 55\lbrack{}18+(119)-5\rbrack} \\ S\text{ = 55\lbrack{}18 - 595\rbrack} \\ S\text{ = 55}\times-577 \\ S\text{ = -31735} \end{gathered}[/tex]Therefore, the sum = -31735
Answer this, please
Zachariah and Khai collect stamps. Zachariah has 7 American stamps out of 12 stamps. Khai has 15 American stamps out of 24 stamps. Which statement is correct?
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is greater than 15 over 24.
Khai has a higher ratio of American stamps than Zachariah because 7 over 12 is less than 15 over 24.
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is less than 15 over 24.
Zachariah and Khai have the same ratio of American stamps.
The last statement would be true, because you would convert 7/12 into a fraction and 15/24 into a fraction. From their fraction eyes to State you would turn them into decimals and then percentiles.
Answer:
D: They are both the same
Step-by-step explanation:
I took the test
L is the midpoint of JM. K is the midpoint of JL. JL = 15. What is thelength of KM?
We can draw the situation as:
So, if L is the midpoint of JM, JL is equal to LM and JM is equal to 2 times JL
JL = LM
JL + LM = JM
JL + JL = JM
2JL = JM
We can calculate JM using JL as:
2JL = JM
2*15 = JM
30 = JM
Then, if K is the midpoint of JL, JK is equal to KL and JL is 2 times JK
JL = 2JK
Replacing JL by 15, we get:
15 = 2JK
15/2 = JK
7.5 = JK
Finally, KM can be calculated as:
KM = JM - JK
KM = 30 - 7.5
KM = 22.5
Answer: 22.5
Solve for z. 24z - 48 = 16z + 112
Answer: z = 20
Explanation:
The given equation is
24z - 48 = 16z + 112
Subtracting 16z from both sides of the equation, we have
24z - 16z - 48 = 16z - 16z + 112
8z - 48 = 112
Adding 48 to both sides, we have
8z - 48 + 48 = 112 + 48
8z = 160
Dividing both sides by 8,
8z/8 = 160/8
z = 20
Consider the line y= 3/5x-3Find the equation of the line that is parallel to this line and passes through the point (3, 4).Find the equation of the line that is perpendicular to this line and passes through the point (3, 4).
a) y = 3/5x + 11/5
b) y = -5/3x + 9
Explanation:[tex]\begin{gathered} a)\text{ }y\text{ = }\frac{3}{5}x\text{ - 3} \\ \text{compare with equation of line:} \\ y\text{ = mx + b} \\ m\text{ =slope, b = y-intercept} \\ m\text{ =slope = 3/5} \\ b\text{ = -3} \end{gathered}[/tex]For a line to be parallel to another line. the slope of the 1st line will be equalt to the slope of the 2nd line:
slope of 1st line = 3/5
So, the slope of the 2nd line = 3/5
Given point: (3, 4) = (x, y)
To get the y-intercept of the second line, we would insert the slope and the point into the equation of line
[tex]\begin{gathered} y\text{ = mx + b} \\ 4\text{ = }\frac{3}{5}(3)\text{ + b} \\ 4\text{ = 9/5 + b} \\ 4\text{ - }\frac{\text{9}}{5}\text{ = b} \\ \frac{20-9}{5}\text{ = b} \\ b\text{ = 11/5} \end{gathered}[/tex]The equation of line parallel to y = 3/5x - 3:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = }\frac{3}{5}x\text{ + }\frac{11}{5} \end{gathered}[/tex][tex]b)\text{ line perpendicular to y = 3/5x - 3}[/tex]For a line to be perpendicular to another line, the slope of one will be the negative reciprocal of the second line
Slope of the 1st line = 3/5
reciprocal of 3/5 = 5/3
negative reciprocal = -5/3
slope of the 2nd line (perpendicular) = -5/3
We need to get the y-intercept of the perpendicular line:
[tex]\begin{gathered} \text{given point: (3,4) = (x, y)} \\ y\text{ = mx + b} \\ m\text{ of the perpendicular = -5/3} \\ 4\text{ = }\frac{-5}{3}(3)\text{ + b} \\ 4\text{ = -5 + b} \\ 4\text{ + 5 = b} \\ b\text{ = 9} \end{gathered}[/tex]The equation of line perpendicular to y = 3/5x - 3:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = }\frac{-5}{3}x\text{ + 9} \end{gathered}[/tex]Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a = 3.0, b = 4.0, C = 58°
Answer
A = 46.3°
B = 75.7°
c = 3.5
Explanation
We will be using both Cosine and Sine rule to solve this.
For Cosine rule,
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the Cosine rule is given as
c² = a² + b² - 2ab Cos C
a = 3.0
b = 4.0
C = 58°
c² = 3² + 4² - 2(3)(4)(Cos 58°)
c² = 9 + 16 - (24)(0.5299)
c² = 25 - 12.72 = 12.28
c = √12.28 = 3.50
To find the other angles, we will now use Sine Rule
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is given as
[tex]\frac{\text{ Sin A}}{a}=\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]So, we can use the latter parts to solve this
[tex]\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]B = ?
b = 4.0
C = 58°
c = 3.5
[tex]\begin{gathered} \frac{\text{ Sin B}}{4}=\frac{\text{ Sin 58}\degree}{3.5} \\ \text{ Sin B = }\frac{4\times\text{ Sin 58}\degree}{3.5}=0.9692 \\ B=Sin^{-1}(0.9692)=75.7\degree \end{gathered}[/tex]We can then solve for Angle A
The sum of angles in a triangle is 180°
A + B + C = 180°
A + 75.7° + 58° = 180°
A = 180° - 133.7° = 46.3°
Hope this Helps!!!
The current in a simple electrical circuit is inversely proportional to the resistance. If thecurrent is 30 amperes (an ampere is a unit for measuring current) when the resistance is 5ohms, find the current when the resistance is 7.8 ohms.
Hello there. To solve this question, we'll have to remember some properties about inversely proportional terms.
Let's start labeling the terms:
Say Current is given by I, Resistance is given by R and voltage is given by V.
By Ohm's Law, we know that:
[tex]V=R\cdot I[/tex]In fact, this is the definition we need to find the answer.
But, to understand why the question mention the fact that they are inversely proportional, note:
We say two numbers x and y are inversely proportional when:
[tex]x\cdot y=k[/tex]Their product is equal to a constant. k is the constant (of proportionality).
Now, using the given values in the question, we can solve this question.
If the current is 30 ampère when the resistance is 5 ohms, we have to find the current when the resistance is 7.8 ohms.
First scenery:
[tex]V=30\cdot5[/tex]Multiply the numbers
[tex]V=150[/tex]Second scenery:
[tex]V=7.8\cdot I[/tex]Plugging V = 150, we get:
[tex]150=7.8\cdot I[/tex]Divide both sides of the equation by a factor of 7.8
[tex]I=\frac{150}{7.8}[/tex]Simplify the fraction by a factor of 2
[tex]I=\frac{75}{3.9}[/tex]Using a calculator, we get the following approximation
[tex]I\approx19.2\text{ A}[/tex]A is for Ampère.
Find the median and mean of the data set below: 3, 8, 44, 50, 12, 44, 14 Median Mean =
the median is 25, because:
[tex]=\frac{3+8+44+50+12+44+14}{7}=\frac{175}{7}=25[/tex]the mean value is :
[tex]14[/tex]There is sales tax of $9.00 on an item t that costs $ 120.00 before tax. The sales tax on a different item is $ 19.05. How much does the second item cost before tax?
SOLUTION:
Step 1:
In this question, we are given that:
There is sales tax of $9.00 on an item that costs $ 120.00 before tax.
The sales tax on a different item is $ 19.05.
We are meant to find how much the second item cost before tax.
Step 2:
Assuming that there is an equal percentage of tax,
and let the second item cost before tax be y,
then we have that:
[tex]\frac{9}{120}\text{ = }\frac{19.05}{y}[/tex]Cross-multiply, we have that:
[tex]\begin{gathered} 9\text{ x y = 19.05 x 120} \\ 9y\text{ = 2286} \\ \end{gathered}[/tex]Divide both sides by 9, we have that:
[tex]\begin{gathered} y\text{ = }\frac{2286}{9} \\ y\text{ = 254} \end{gathered}[/tex]CONCLUSION:
The cost of the second item before tax = $ 254
Please help, algebra 1, i dont know how to begin to solve it :/ thank you thank you.Simplify:
Given the expression:
[tex](x^2-4x^3)+(5x^3+3x^2)[/tex]You can simplify it as follows:
1. Distribute the positive sign. Since the sign between the parentheses is positive, it does not change the signs of the second parentheses:
[tex]=x^2-4x^3+5x^3+3x^2[/tex]2. Add the like terms.
By definition, like terms have the same variables with the same exponent.
In this case, you need to add the terms with exponent 3 and add the terms with exponent 2. Notice that:
[tex]\begin{gathered} -4x^3+5x^3=x^3 \\ \\ x^2+3x^2=4x^2 \end{gathered}[/tex]Then, you get:
[tex]=x^3+4x^2[/tex]Hence, the answer is:
[tex]=x^3+4x^2[/tex]Mary Bought her car for $20,000. After 5 years she decided to sell her car for a 25% increase invalue. What is the price that Mary decided to sell her car for?
Original Car price = $20,000
Price increase after 5 years = 25%
To calculate the price after 5 years, first multiply the original price (20,000) by the percentage increase in decimal form ( divided by 100) to obtain the increase amount:
20,000 x (25/100) = 20,000 x 0.25 = $5000
Finally, add the increase amount to the original price:
20,000+5,000 = $25,000
How much would you need to deposit in an account now in order to have $20,000 in the account in 4 years? Assume the account earns 5% interest.I want answer and explanation.
The rule of the simple interest is
[tex]\begin{gathered} I=PRT \\ A=P+I \end{gathered}[/tex]I is the amount of interest
P is the initial amount
R is the interest rate in decimal
T is the time
We need to find the initial amount if the new amount is $20,000, the interest rate is 5% for 4 years, then
A = 20000
R = 5/100 = 0.05
T = 4
Substitute them in the rules above
[tex]\begin{gathered} I=P(0.05)(4) \\ I=0.2P \\ 20000=P+0.2P \\ 20000=1.2P \\ \frac{20000}{1.2}=\frac{1.2P}{1.2} \\ 16666.67=P \end{gathered}[/tex]You need to deposit $16,666.67
The rule of the compounded interest
[tex]A=P(1+r)^t[/tex]A is the new amount
P is the initial amount
r is the interest rate in decimal
t is the time
A = 20000
r = 0.05
t = 4
Substitute them in the rule above
[tex]\begin{gathered} 20000=P(1+0.05)^4 \\ 20000=P(1.05)^4 \\ \frac{20000}{(1.05)^4}=\frac{P(1.05)^4}{(1.05)^4} \\ 16454.05=P \end{gathered}[/tex]You need to deposit $16,454.05
i need help solving this and also what does the 2 that's on the top of some letters mean
given the expression :
[tex]a-bc^2[/tex]We need to evaluate the expression when :
[tex]\begin{gathered} a=3 \\ b=2 \\ c=-1 \end{gathered}[/tex]So, substitute with a , b and c at the expression
The result will be :
[tex]\begin{gathered} a-bc^2 \\ =3-2\cdot(-1)^2 \\ =3-2\cdot1 \\ =3-2 \\ \\ =1 \end{gathered}[/tex]There is another expression :
[tex]c^2+a^2b[/tex]By substitute with the values of a, b and c
so, the result will be :
[tex]\begin{gathered} c^2=(-1)^2=1 \\ a^2=3^2=9 \\ \\ c^2+a^2b=1+9\cdot2=1+18=19 \end{gathered}[/tex]IF P(A)=0.2 P(B)=0.1 and P(AnB)=0.07 what is P(AuB) ?A.0.13 B. 0.23 C. 0.3 D.0.4
ANSWER
P(AuB) = 0.23
STEP-BY-STEP EXPLANATION:
Given information
P(A) = 0.2
P(B) = 0.1
P(AnB) = 0.07
What is P(AUB)
[tex]P(\text{AuB) = P(A) + P(B) }-\text{ P(AnB)}[/tex]The next step is to substitute the above data into the formula
[tex]\begin{gathered} P(\text{AuB) = 0.2 + 0.1 - 0.07} \\ P(\text{AuB) = 0.3 - 0.07} \\ P(\text{AuB) = 0.23} \end{gathered}[/tex]In order for the parallelogram to be a rhombus, x equals?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
parallelogram diagram
Step 02:
geometry:
solve for x:
(5x + 25)° = (12x + 11)°
5x + 25 = 12x + 11
25 - 11 = 12x - 5x
14 = 7x
14 / 7 = x
2 = x
The answer is:
x = 2
23.What is the missing piece of information required to provethese triangles congruent?a) QYQYb) NYPYC) ZN 2 Pd) QY is the perpendicular bisector
In this case, the information that is explicitly seen in the graph is that we have 2 pairs of equal sides.
The missing information, that can also be seen in the picture, is that we have a shared side that is QY.
If we applied the reflexive property, we know that:
[tex]QY\cong QY[/tex]and then we know that we have 3 pairs of equal sides, what proves that the triangles are congruent.
Answer: QY = QY (Option A).
What is the output value for the following function if the input value is 5?y = 4x - 34223172
Answer:
17
Explanation:
Given the function:
[tex]y=4x-3[/tex]When the input value, x = 5
[tex]\begin{gathered} y=4x-3 \\ =4(5)-3 \\ =20-3 \\ =17 \end{gathered}[/tex]The output value if the input value is 5 is 17.
Which ordered pair is a solution tothe system of inequalities shown?
We want to know which ordered pair is a solution of the system of inequalities shown:
[tex]\begin{cases}x-4y\ge0 \\ x-y<-1\end{cases}[/tex]For doing so, we will try to solve both inequalities for one variable, in this case, we will use y.
On the first equation:
[tex]\begin{gathered} x-4y\ge0 \\ x\ge4y \\ y\le\frac{x}{4} \end{gathered}[/tex]On the second equation:
[tex]\begin{gathered} x-y<-1 \\ x+1-y<0 \\ x+1And joining those two results we get:[tex]x+1Now we check each of the ordered pairs, if they hold the condition above:For (0, 2)
We have that x=0, and y=2. Thus,
[tex]\begin{gathered} x+1=1 \\ \frac{x}{4}=0 \\ \text{And as }2>0,\text{ (0, 2) is NOT a solution of the system.} \end{gathered}[/tex]For (-3, 8)
In this case, x=-3 and y=8.
[tex]\begin{gathered} x+1=-2 \\ \frac{x}{4}=-\frac{3}{4} \\ \text{As }8>-\frac{3}{4},\text{ this means that (-3, 8) is NOT a solution of the system.} \end{gathered}[/tex]For (2,5)
In this case, x=2 and y=5.
[tex]\begin{gathered} x+1=3 \\ \frac{x}{4}=\frac{2}{4}=\frac{1}{2} \\ \text{As }5>\frac{1}{2}\text{ this means that (2, 5) is NOT a solution of the system.} \end{gathered}[/tex]For (-7, -4)
In this case, x=-7 and y=-4.
[tex]\begin{gathered} x+1=-6 \\ \frac{x}{4}=-\frac{7}{4} \\ \text{As }-6<-4\le-\frac{7}{4},\text{ (-7, -4) is a SOLUTION of the system.} \end{gathered}[/tex]For (6, -1)
We have that x=6 and y=-1.
[tex]\begin{gathered} x+1=7 \\ \frac{x}{4}=\frac{6}{4}=\frac{3}{2} \\ \text{As }7>-1,\text{ (6, -1) is NOT a solution of the system. } \end{gathered}[/tex]Thus, the ordered pair which is a solution of the system is (-7, -4).I need to know how to 53 evaluate the inverse trigonometric function give answers in both radians and degrees
GIVEN:
We are given the following trigonometric expression;
[tex]Tan^{-1}(-1)[/tex]Required;
We are required to evaluate and answer both in radians and in degrees.
Step-by-step solution;
We shall begin by using the trig property;
[tex]tan^{-1}(-x)=-tan^{-1}(x)[/tex]Therefore, we now have;
[tex]tan^{-1}(-1)=-tan^{-1}(1)[/tex]We now use the table of common values and we'll have;
[tex]tan^{-1}(1)=\frac{\pi}{4}[/tex]Therefore;
[tex]-tan^{-1}(1)=-\frac{\pi}{4}[/tex]We can now convert this to degrees;
[tex]\begin{gathered} Convert\text{ }radians\text{ }to\text{ }degrees: \\ \frac{r}{\pi}=\frac{d}{180} \end{gathered}[/tex]Substitute for r (radian measure):
[tex]\begin{gathered} \frac{-\frac{\pi}{4}}{\pi}=\frac{d}{180} \\ \\ -\frac{\pi}{4}\div\frac{\pi}{1}=\frac{d}{180} \\ \\ -\frac{\pi}{4}\times\frac{1}{\pi}=\frac{d}{180} \\ \\ -\frac{1}{4}=\frac{d}{180} \end{gathered}[/tex]Now we can cross multiply;
[tex]\begin{gathered} -\frac{180}{4}=d \\ \\ -45=d \end{gathered}[/tex]Therefore,
ANSWER:
[tex]\begin{gathered} radians=-\frac{\pi}{4} \\ \\ degrees=-45\degree \end{gathered}[/tex]Determine the value of b for which x = 1 is a solution of the equation shown.
2x + 14 = 10x + b
b=
Answer
Step-by-step explanation:
solve for b.
2x+14=10x+b
Step 1: Flip the equation.
b+10x=2x+14
Step 2: subtract 10x from both sides.
b+10x+−10x=2x+14+−10x
b=−8x+14
Answer:
b=−8x+14
3, -10, 16, -36, 68, ___-3, 12, -33, 102, -303, ___Identify a pattern in each list of numbers. Then use this pattern to find the next number.
As for the sequence 3,-10,16,-36,68,..., notice that
[tex]\begin{gathered} 3-13=-10 \\ -10+26=-10+2(13)=-10+2^1(13)=16 \\ 16-52=16-4(13)=16-2^2(13)=-36 \\ -36+104=-36+8(13)=-36+2^3(13)=68 \end{gathered}[/tex]Therefore, the next term is
[tex]68-2^4(13)=68-16(13)=-140[/tex]The answer is -140.
Regarding the second pattern, notice that
[tex]\begin{gathered} -3+15=12 \\ 12-45=12-3(15)=12-3^1(15)=-33 \\ -33+135=-33+9(15)=-33+3^2(15)=102 \\ 102-405=102-27(15)=102-3^3(15)=-303 \end{gathered}[/tex]Then, the next term of the sequence is
[tex]-303+3^4(15)=912[/tex]The answer is 912
What is the value of 9 − (−4)?
Answer:13
Step-by-step explanation:
Step-by-step explanation:
remember, when 2 signs and/operations come together, for addition/subtraction and multiplication/division it always applies :
+ + = +
- + = -
+ - = -
- - = +
and therefore,
9 - (-4) = 9 + 4 = 13
a minus meeting a minus always results in a plus.
Given that figure ABCD is a dilation of figure KLMN, find the missing values:(note that values are slightly different because of a round-off error)
• Given the dimensions of ABCD:
m∠A = 71.68 degrees
m∠C = 47.68 degrees
m∠D = 141.87 degrees
CD = 4
AD = 6
BC = 8
• Dimensions of KLMN:
m∠K = 71.52 degrees
m∠L = 98.87 degrees
m∠M = 47.53 degrees
KL = 10
KN = 15
MN = 10
Let's find the missing values.
Given that figure ABCD is a dilation of KLMN, both figures are similar.
• Similar figures have proportional corresponding sides.
,• Similar figures have equal corresponding angles.
Therefore, we have the corresponding sides:
AB ⇔ KL
BC ⇔ LM
CD ⇔ MN
AD ⇔ KN
The corresponding angles are:
m∠A = m∠K
m∠B = m∠L
m∠C = m∠M
m∠D = m∠N
Thus, to find the missing values, we have:
• X = m∠B = m∠L = 98.87 degrees
X = 98.87 degrees.
• Y = m∠N = m∠D = 141.87 degrees.
Y = 141.87 degrees
• To find the value of ,a,, apply the proportionality equation:
[tex]\frac{AB}{AD}=\frac{KL}{KN}[/tex]Plug in values and solve for a:
[tex]\begin{gathered} \frac{a}{6}=\frac{10}{15} \\ \\ \text{Cross multiply:} \\ 15a=10\times6 \\ \\ 15a=60 \\ \\ a=\frac{60}{15} \\ \\ a=4 \end{gathered}[/tex]• To find the value of ,b,, apply the proportionality equation:
[tex]\begin{gathered} \frac{DC}{BC}=\frac{NM}{LM} \\ \\ \frac{4}{8}=\frac{10}{b} \\ \\ \text{Cross multiply:} \\ 4b=10\times8 \\ \\ 4b=80 \\ \\ b=\frac{80}{4} \\ \\ b=20 \end{gathered}[/tex]ANSWER:
• X = 98.87°
,• Y = 141.87°
,• a = 4
,• b = 20
