To prove that △RST ≅ △UVW by ASA (Angle-Side-Angle) congruence, we need to show that angle S is congruent to angle U, side ST is congruent to side VW, and angle R is congruent to angle V.
To prove that △RST ≅ △UVW by ASA (Angle-Side-Angle) congruence, we need to show that angle S is congruent to angle U, side ST is congruent to side VW, and angle R is congruent to angle V.
1. Given that ∠R ≅ ∠U, we have the first angle in both triangles congruent.
2. Given that ST ≅ VW, we have the side opposite to the congruent angles congruent in both triangles.
3. Given that ∠S ≅ ∠V, we have the second angle in both triangles congruent.
Using ASA congruence, we can conclude that △RST ≅ △UVW.
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Final answer:
Triangles △RST and △UVW are congruent by ASA postulate, which states if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Explanation:
To prove that triangles △RST and △UVW are congruent by the Angle-Side-Angle (ASA) postulate, we first observe the given congruent parts: ∠R ≅ ∠U, ST ≅ VW, and ∠S ≅ ∠V. Now, by the ASA postulate, if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. We have two pairs of congruent angles: ∠R ≅ ∠U and ∠S ≅ ∠V, and one pair of congruent sides: ST ≅ VW (△RST's side ST is included between ∠R and ∠S, and △UVW's side VW is included between ∠U and ∠V). This satisfies the requirements for the ASA postulate, so we can conclude the triangles are congruent: △RST ≅ △UVW.
HELP PLEASE WILL GIVE 30 POINTS !!!!!! Determine the amount you need to invest to have $22,000 dollars in 4 years if you invest at 5% annual interest, compounded quarterly. ADD WORK PLEASE
Answer:
$18 034.42
Step-by-step explanation:
The formula for the future value of an account paying 5 % annual interest compounded quarterly for four years is
[tex]A = P(1 +\frac{r }{n })^{nt}[/tex]
A = $22 000
r = 0.05
n = 4 times per year
t = 4 years
[tex]22 000 = P(1 +\frac{0.05 }{4 })^{4\times4}[/tex]
[tex]22 000 = P(1 + 0.0125)^{16}[/tex]
[tex]22 000 = P(1.0125)^{16}[/tex]
22 000 = P x 1.220
P = 2 000/1.220
P = $18 034.42
You must invest $18 034.42.
Find the equation that represents a line that passes through the point (7,-5) and has slope -4/7
Answer:
The equation would be y = -4/7x - 1
Step-by-step explanation:
Given that we have the slope and the point, we can solve for the equation using point-slope form.
y - y1 = m(x - x1)
y + 5 = -4/7(x - 7)
y + 5 = -4/7x + 4
y = -4/7x - 1
The equation that represents a line that passes through the point (7,-5) and has a slope of -4/7 is,
⇒ 7y = - 4x - 7
The equation of a line in point-slope form passing through the point
(x₁ , y₁) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Given that,
The equation of line passes through the point (7,-5) and has a slope of -4/7.
Here we have,
[tex](x_1 , y_1) = (7, - 5)[/tex]
And, [tex]m = \frac{- 4}{7}[/tex]
Substitute the given values in the above equation,
[tex]y - y_1 = m (x - x_1)[/tex]
[tex]y - (- 5) = \frac{-4}{7} (x - 7)[/tex]
[tex]y + 5 = \frac{-4}{7} (x - 7)[/tex]
Multiply by 7 on both sides,
[tex]7 (y + 5) = - 4 (x - 7)\\7y + 35 = - 4x + 28\\ 7y =- 4x 28 - 35\\ 7y = - 4x- 7\\[/tex]
So, the equation of a line is,
7y = - 4x - 7
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Please help please help
Answer:
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Step-by-step explanation:
How much of a spice that is 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5% salt?
Please Helpppp!!
Answer:
Let y represents the ounces of first spice.
From the given statements, we draw a table as shown below:
ounces of spice Percentage ounces of salt
First spice y 3% 0.03x
Second spice 175 6% 175(0.06)
Final mixture y + 175 5% (x+15)(0.05)
Now, to solve for y
we have;
Final spice = First spice + second spice
[tex]0.03y + 175(0.06) = (y+175)(0.05)[/tex]
[tex]0.03y+ 10.5= 0.05y+ 8.75[/tex]
Subtract 10.5 on both sides we have;
[tex]0.03y+ 10.5 -10.5= 0.05y+ 8.75 -10.5[/tex]
Simplify:
[tex]0.03y = 0.05y -1.75[/tex]
Subtract 0.05y on both sides
[tex]0.03y -0.05y= 0.05y -1.75-0.05y[/tex]
Simplify:
[tex]-0.02y = -1.75[/tex]
Divide both sides by -0.02, we get;
[tex]y = \frac{-1.75}{-0.02} = 87.5[/tex]
Therefore, 87.5 ounces of spices that is 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5% salt
It needs 87.5 ounces of spice that is 3% salt.
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem !
[tex]\texttt{ }[/tex]
Given:
175 ounces of a spice that is 6% salt
[tex]\texttt{mass of salt from this spice} = s_1 = 6\% \times 175 = 10,5 \texttt{ ounces}[/tex]
[tex]\texttt{ }[/tex]
x ounces of a spice that is 3% salt
[tex]\texttt{mass of salt from this spice} = s_2 = 3\% \times x = 0.03x \texttt{ ounces}[/tex]
[tex]\texttt{ }[/tex]
(175 + x) ounces of a spice that is 5% salt
[tex]\texttt{total mass of salt} = s_1 + s_2[/tex]
[tex]5\% \times ( 175 + x ) = 10.5 + 0.03x[/tex]
[tex]8.75 + 0.05x = 10.5 + 0.03x[/tex]
[tex]0.05x - 0.03x = 10.5 - 8.75[/tex]
[tex]0.02x = 1.75[/tex]
[tex]x = 1.75 \div 0.02[/tex]
[tex]x = 175 \div 2[/tex]
[tex]x = 87.5 \texttt{ ounces}[/tex]
[tex]\texttt{ }[/tex]
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Student's Shirt : https://brainly.com/question/909783Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces , Number , 51 , 33 , 1/3
if you have 10 cookies and you want to give 1/2 of them to a friend. How many do you give to your friend
Answer: You would give your friend 5 cookies
Step-by-step explanation:
One half of the cookies, is basically saying divided by two. 10 divided by 2 is 5. To check that answer, multiply 5 by 2, and you will get 10
3 X 1,000 + 3 X 10 + 3 X 1/100 + 3 in X 1/1000i in decimal form
Answer:
3030.033
Step-by-step explanation:
Multiply each piece out and add them together
3 X 1,000 + 3 X 10 + 3 X 1/100 + 3 in X 1/1000
3000 + 30+.03 + .003
3030.033
a-5/a divided by 4/a
Answer:
[tex]\frac{a-5}{4}[/tex]
Step-by-step explanation:
the given equation is
[tex]\frac{a-5}{a} /\frac{4}{a}[/tex]
from the multiplication rules we know that
[tex]\frac{a}{b}/\frac{c}{d}=\frac{a}{b}*\frac{d}{c}[/tex]
so for the given equation changing the sidn of division to multiplication
the equation becomes
[tex]\frac{a-5}{a} * \frac{a}{4}[/tex]
a cancels out from both numerator and denominator
so it becomes
[tex]\frac{a-5}{4}[/tex]
which is the answer
What is the equation of the line?? Please help!!
The point-slope form of a line:
[tex]y-y_1=m(x-x_1)[/tex]
We have the slope m = -4 and the point (8, -7). Substitute:
[tex]y-(-7)=-4(x-8)[/tex] use distributive property
[tex]y+7=-4x+32[/tex] subtract 7 from both sides
[tex]y=-4x+25[/tex] add 4x to both sides
[tex]\boxed{4x+y=25}[/tex]
What is 575 written as a mixed number
The 575 written as a mixed number is A. 5 3/4 . Therefore , A. 5 3/4 is correct .
You have correctly outlined the steps to convert 575% to a mixed number. Let me summarize the process:
Convert the Percentage to a Decimal:
Divide the percentage by 100 to convert it to a decimal:
[tex]\frac{575}{100}[/tex]% = 5.75.
Separate the Whole Number and Decimal Part:
Separate the whole number part from the decimal part:
5.75=5+0.75.
Convert the Decimal to a Fraction:
Convert the decimal part to a fraction with a denominator of 100:
0.75× [tex]\frac{100}{100}[/tex] = [tex]\frac{75}{100}[/tex] .
Combine the Whole Number and Fraction:
Combine the whole number and the fraction into a mixed number:
5 + [tex]\frac{75}{100}[/tex] =5 [tex]\frac{3}{4}[/tex] .
Therefore, 575% written as a mixed number is 5 [tex]\frac{3}{4}[/tex] .
This means there are 5 whole units and [tex]\frac{3}{4}[/tex]of an additional unit in the given percentage.
It's a clear and accurate way to represent a percentage as a mixed number.
Write the expression (4x-6) x 6(2x+7)
Answer:
48x² + 96x - 252
Step-by-step explanation:
(4x - 6) × 6(2x + 7) Reorder the factors
= 6(4x – 6)(2x+ 7) Multiply the binomials
= 6(8x² + 16x - 42) Remove parentheses
= 48x² + 96x - 252
javier opens a savings account with a starting balance of $200 and plans to deposit $75 each week after opening the account and savings over time is represented by the graph below how would the graph change if javier open his account with a starting balance of $300 instead
If Javier starts with a higher initial balance of $300, the initial point on his savings graph would be higher by $100, and all subsequent points would reflect this initial increase, though the slope of the graph would remain unchanged.
If Javier opens a savings account with a starting balance of $300 instead of $200 and then deposits $75 each week, the graph representing his savings over time would change in the following way:
The initial point on the graph, representing the starting balance, would be higher.
This is because the starting balance would be $300 instead of $200.
After this initial change, the slope of the graph, representing the weekly deposits of $75, would remain the same.
However, every point on the graph after the initial deposit would be $100 higher than it was before because each point on the savings graph accumulates the effects of the higher starting balance.
The ordered pairs model an exponential decay function.
{(−1,30), (0,21), (1,14.7), (2,10.29)}
What is the function equation?
Enter your answer in the box.
f(x)=
Answer to your question:
f(x)= 12x
Answer:
f(x)=12 Hope this helps you!
I don't get this problem from maths.
Answer:
100/3 or 33.33
Step-by-step explanation: If the perimeter of the whole figure is 220, we can use that number to solve the equations on the trapezoid.
2(2x-3) + 2(4) + 2(4x+1)
4x - 6 + 8 + 8x + 2
12x + 2
Now we have to set the equation equal to the perimeter to find the value of x
12x + 2 = 220
12x = 218
x = 109/6
Since we are only finding the length of PS, we will plug x into its equation (2x - 3).
2(109/6) - 3
109/3 - 3
109/3 - 9/3
100/3
check the picture below.
[tex]\bf \stackrel{\textit{perimeter of the trapezoid}}{(4x+1)+(4x+1)+(4)+(4)+(2x-3)+(2x-3)} \implies 12x+4[/tex]
Which sign makes the statement true 17/20 ? -11.95
To make the statement '17/20 ? -11.95' true, the correct symbol to use is '>'. We find this by comparing the result of 17 divided by 20 (which is 0.85) with -11.95.
Explanation:The question is asking us to find the correct sign (either less than '<', equal '=', or greater than '>') to make the mathematical statement '17/20 ? -11.95' true.
To solve this, we first need to divide 17 by 20 to get 0.85. Then, we compare this result with -11.95.
Since 0.85 is greater than -11.95, we use the '>' symbol. Thus, the statement '17/20 > -11.95' is true.
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Reagan surveyed a number of her classmates about what time they usually go to bed. Of the fifteen classmates she asked, three said 9 p.m. What percent of the students is this?
Answer:
20%
Step-by-step explanation:
We can say that 3/15 students usually go to bed at 9 P.M. We can set up a proportion to solve this problem.
3/15=x/100
We cross multiply to find x
15x=300
Divide both sides by 15
x=20
So 20% of the classmates usually sleep at 9 P.M.
Answer:
20% of the students
Step-by-step explanation:
You are working as a locksmith. Of the 50 customers you had today, 15 of them needed a new key for their car. What percentage of today’s customers needed a new key for their car?
How do i figure this out ??
A.0.030%
B.0.3%
C.3%
D.30%
E.300%
PLEASE HELP I HAVE 49 POINTS!
show work
Answer:
1. y = 2x-4
2 y = -1/2x+3
Step-by-step explanation:
Slope intercept form of the equation is y= mx+b
where m is the slope and b is the y intercept
1. y- 2x = -4
We need to solve for y
Add 2x to each side
y -2x+2x = 2x-4
y = 2x-4
2 y-3 = -1/2 x
We need to add 3 to each side
y-3+3 = -1/2x +3
y = -1/2x+3
Answer:
1. y = 2x - 4
y = -1/2x + 3
Step-by-step explanation: You have to isolate or get y by itself.
1:
y - 2x = -4
+ 2x + 2x
y = 2x - 4
2:
y - 3 = -1/2x
+ 3 + 3
y = -1/2x + 3
what is the slope of the line shown
(4, 2) (-4, -2)
m=?
(4, 2) (-4, -2)
Slope is the change in Y over the change in X
From the two points given:
Slope =( -2 - 2 ) / ( -4 -4)
Slope = -4 / -8
Slope = 1/2
m = 1/2
estimate 782 divided by 50
Answer: about 15.72
Step-by-step explanation: i used a calculator
What number comes between 2 and 4
Answer:
3
Step-by-step explanation:
Count 1 to 5 (1,2,3,4,5). You can see 3 is between 2 and 4.
A number that comes between 2 and 4 would be 3.
Used the concept of a number system that states,
A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols.
Given that,
Two numbers are 2 and 4.
Let us assume that the number that comes between 2 and 4 is, x
Then,
[tex]x = \dfrac{(2 + 4)}{2}[/tex]
[tex]x = \dfrac{(6)}{2}[/tex]
[tex]x = 3[/tex]
Therefore, the number would be 3 which comes between 2 and 4.
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Evaluate − a + ( − b ) −a+(−b) where a = 6 . 0 5 a=6.05 and b = 3 . 6 1 1 b=3.611.
Answer:
-19.322
Step-by-step explanation:
− a + ( − b ) −a+(−b)
First step is to combine like terms
-a -a + -b + -b
-2a -2b
We know a = 6.05 and b = 3.611
-2 (6.05) -2(3.611)
-12.1 - 7.222
-19.322
Answer:
Step-by-step explanation:-9.661
What is the cheapest way to go to a ball game if the admissions options are as shown? A) $10 for a single B) $15 for a couple C) $20 for a triple D) $35 for a group of four E) $50 for a group of five
Answer: C
Step-by-step explanation: A = 10 for one person. B = 7.5 for one person. C = 6.67 for one person. D = 8.75 for one person. E = 10 for one person.
Out of all of these, C is the cheapest.
Find the Nonpermissible replacement for y in this expression y-9/y+3
Answer:
y = - 3
Step-by-step explanation:
Providing you mean (y - 9)/(y + 3) then it is always the variable in the denominator that is going to cause trouble. If it equals zero at any point, it's game over.
It's a little better if you get a result like 0/0. That problem has a "depends" as an answer, but by and large, you don't want to monkey around with 0 in the bottom of a fraction.
y + 3 = 0 Subtract 3 from both sides.
y + 3 - 3 = 0 - 3 Combine
y = - 3
Ellentown college has appoximately 3 times 10 to the 3 power students and pengrove university approximate 30,000 students. how many times as much is the number of students at pengrove university as the number of students at Ellwntown college
Answer:
Given: Ellentown college has approximately 3 times 10 to the 3 power students and pengrove university approximate 30,000 students.
⇒ number of students approximately in Ellentown college = [tex]3 \times 10^3[/tex]
also,
the number of students approximately in Pengrove university = 30,000 or [tex]3 \times 10^4[/tex]
We have to find how many times as much is the number of students at pengrove university as the number of students at Ellentown college.
[tex]\frac{number of students in Pengrove University}{number of students in Ellentown college}[/tex] = [tex]\frac{3 \times 10^4}{3 \times 10^3} = 1 \times 10^1 = 10[/tex]
therefore, 10 times as much is the number of students at pengrove university as the number of students at Ellentown college.
Jake wants to estimate 15.92+0.85 . How can he use rounding to estimate the sum? What is the estimate?
Answer:
17
Step-by-step explanation:
15.92 is close to 16
0.85 is close to 1
15.92 + 0.85 is close to 16 + 1
16 + 1 = 17
15.92 + 0.85 is approximately 17
Colin and Rosie had the same number of cashews at first. Each day, Colin ate 5 cashews and Rosie ate 8 cashews. When Rosie had 4 cashews left, Colin had 10 times as many cashews left as Rosie. How many cashews did each child have at first?
Using the given scale factor and center dilate the following figures and state the new coordinates
Answer:
B' = (-8,-1) , C' = (4, 5)
Step-by-step explanation:
The coordinates of A are (-5,-7)
The coordinates of C are 3 units to the right and 4 up from A.
So for a dilation factor 3 C' will be 9 to the right and 12 up from A.
C' = (-5 + 9) , (-7 + 12)
= (4, 5).
The point B is 1 unit to left and 2 up from A.
So B' is (-5 -3) , (-7+ 6)
= (-8, -1).
After a dilation scale factor of 3 centered at A, B'(- 18, - 15), and C'(- 6, - 9).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, A triangle ABC.
The coordinate of B is (- 6, - 5), and the coordinate of C is (- 2, - 3).
After a dilation scale factor of 3 centered at A coordinates of B' would be
(- 6×3, - 5×3) = (- 18, - 15) and C'(- 2×3, - 3×3) = (- 6, - 9).
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to the nearest whole degree what angle measure has a tangent of 5.6922
Answer:
80° has a tangent of 5.6922..Step-by-step explanation:
We are given value of tangent trigonometric ratio = 5.6922.
We need to find the angle in degrees whose measure has a tangent of 5.6922..
So, we need to find the value of [tex]tan^{-1}(5.6922)[/tex].
On plugging [tex]tan^{-1}(5.6922)[/tex]in calculator, we get
80.03°.
Now, we need to round it to the nearest whole degree.
Therefore, 80.03°≈ 80°.
Therefore, 80° has a tangent of 5.6922..What is Perimeter of triangle ABC?
ΔABC and ΔFEG are congruent. Therefore we have the equation:
7x - 19 = 2x + 11 add 19 to both sides
7x = 2x + 30 subtract 2x from both sides
5x = 30 divide both sides by 5
x = 6
AB = 24
AC = 2x + 11 → AC = 2(6) + 11 = 12 + 11 = 23
BC = 6x - 8 → BC = 6(6) - 8 = 36 - 8 = 28
The perimeter of ΔABC = 24 + 23 + 28 = 75
Answer: 75 feetThe ratio of blueberry bagels to all bagels is 1:4. Does this ratio represent a part to part or part to whole ratio
Answer:
Part to whole ratio
Step-by-step explanation:
The 1 represents the blueberry bagels. This is just a part of the entire variety that is offered, so this is a part.
The 4 represents all of the bagels. It is the whole amount, which makes this the whole.
This means it is a part to whole ratio.