Justify the congruence between each of the following pairs of triangle.
Answer:
[tex]\sf\blue{triangle \: \: is \: \: congruent \: \: } \\
\sf\huge{by \: \: S.A.S \: axiom \: \: }[/tex]
Answer:
Refer to the attachment for the labelling of the triangles.
In △ABD & △ACD,
AD = AD (common side)
∠A = ∠A (common angle)
AB = AC (equal pair of sides)
•°• △ABD ≅ △ACD (Single-Angle-Side congruence rule → SAS congruence rule)
Hope it helps ⚜
C
Jane got a prepaid debit card with $25 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon
was 21 cents per yard. If after that purchase there was $16.39 left on the card, how many yards of ribbon did Jane buy?
yards
?
Step-by-step explanation:
so, she spent 25-16.39 = $8.61 on the ribbon.
1 yard of the ribbon costs $0.21.
how many yards did she buy with that amount of money ?
well, as many times as 0.21 fits into 8.61 :
8.61 / 0.21 = 41
so, she bought 41 yards of ribbon.
I'm happy to help you today!
Answer:
41 yards is correct
Step-by-step explanation:
Step 1. The information we have is:
Originally Jane had $25 on her debit card.
She made a purchase of bulk ribbon for 21 cents per yard.
And after that she ended up with $16.39 on the card.
Step 2. Make an equation to describe the situation.
The equation that describes this situation is:
[tex]\tt 25-0.21y=16.39[/tex]
Where 25 is the initial amount and to that, we subtract 0.21y, where y is the number of yards that she bought of ribbon. And all of this has to be equal to the final amount of 16.39.
Step 3. Solve the equation for y:
To solve for y, we subtract 25 to both sides of the equation:
⇒ [tex]\tt-0.21y=16.39-25[/tex]
⇒ [tex]\tt -0.21y=-8.61[/tex]
Then, divide both sides of the equation by -0.21:
[tex]\tt y=\frac{-8.61}{-0.21}[/tex]
The result is:
[tex]\tt y=41[/tex]
The answer is 41 yards of ribbon.
Hope this helps you!Have an awesome day! :)[tex]-Nature-[/tex]
Pete's Pasteris sells cupcakes in packs of 4. A caterer needs between 42 and 50 cupcakes for dessert. Name two possible number between 42 and 50 that are multiple of 4. Explain
Answer:
44 48
Step-by-step explanation:
A group of friends go ice skating. They purchase one group ticket to get in and then each person rents skates and buys a hot chocolate.
It costs
$
10
to purchase a group ticket to get into the skating rink.
It costs
$
4
per person to rent skates.
It costs
$
1.75
per person for hot chocolate.
How many friends go ice skating if they spend a total of
$
38.75
?
The number of friends that can go ice skating is 5.
What is the total number of friends that can go ice-skating?The total amount spent = cost of the group ticket + total cost of the hot chocolate + total cost of renting the skates
$38.75 = $10 + $4x + $1.75x
Where x represents the total number of friends.
In order to determine the total number of friends, take the following steps:
Combine similar terms
$38.75 - $10 = $4x + $1.75x
Add similar terms
$28.75 = $5.75x
Divide both sides of the equation by 3.75
x = 5
To learn more about division, please check: https://brainly.com/question/13281206
11) Tickets to a concert cost either $15 or
$20. A total of 300 tickets were sold and
the total receipts were $5300. How many
of each kind of ticket were sold.
Answer:
There were 140 tickets sold that cost $15 and 160 tickets sold that cost $20.
Step-by-step explanation:
To solve this problem, we should create a system of equations. Let's let the variable x represent the number of $15 tickets sold and let the variable y represent the number of $20 tickets sold. Using these variables, we can make the following equations:
x + y = 300
15x + 20y = 5300
To solve this equation, we can use substitution. Our first step in this case is solving the first equation for one variable; let's choose x.
x = 300 - y
Now, we can substitute this value for x into the second equation.
15(300-y) + 20y = 5300
Next we can distribute through the parentheses on the left side of the equation.
4500 - 15y + 20y = 5300
We can combine like terms on the left side of the equation to simplify.
4500 + 5y = 5300
We should then subtract 4500 from both sides of the equation.
5y = 800
Finally, we can divide both sides of the equation by 5.
y = 160
To solve for x, we can substitute this value for y into either of our original equations, but we should probably choose the first one for simplicity.
x + y = 300
x + 160 = 300
x = 140
Therefore, x = 140 and y = 160; this means that 140 $15 tickets were sold and 160 $20 tickets were sold.
Hope this helps!
(Algebra 2)
f(x) = |2x - 6| + 8
g(x) = -10x + 5
What is (f + g)(x)?
A. (f + g)(x) = |2x - 6| + 10x +3
B. (f + g)(x) = |2x - 6| - 10x + 13
C. (f + g)(x) = |-8x| + 7
D. (f + g)(x) = |-8x - 1| + 8
Determine the slope and y-intercept given the equation below, explain your answer.
x + y = -1
Answer:
slope is -1, y-intercept is -1
Step-by-step explanation:
x+y=-1
convert to slope-intercept form
y=-x-1
y=-1x-1
slope is -1, y-intercept is -1
Solution:
Let's convert the equation into slope-intercept form.
x + y = -1y = -x - 1In this equation, the slope is the coefficient of x.
The following points can be made:
Since there is a "-" in front of the x variable, the coefficient of x is -1.Since the coefficient is -1, the slope of the line is -1.The y-intercept of the equation will be a constant.
The following points can be made:
Since there is a constant on the RHS, that constant will be the y-intercept.Since the constant on the RHS is -1, the y-intercept of the line is -1.In conclusion...
Slope of line: -1y-intercept of line: -1Your father is planning to cook for 35 people using a recipe that specifies two and a half cups of sugar for each six people,
For the larger group, your father will require
cups of sugar
Your father will require 14.6 cups of sugar for the larger group
Ratio and proportionsFrom the question, we have that 2.5 cups of sugar can be used to make recipes for 6 people that is;
6 people = 2.5 cups of sugar
In order to calculate for 35 people, we will have;
35 people = x
Taking the ratio of the expressions
6/35 = 2.5/x
6x = 87.5
x = 87.5/6
x = 14.6
Hence your father will require 14.6 cups of sugar for the larger group
Learn more on ratio and proportions here: https://brainly.com/question/19994681
The hypotenuse of a 30°-60°-90° triangle measures 8√3 inches. What is the length of the shorter leg?
Answer: 8 inches
Step-by-step explanation:
In a 30-60-90 triangle, the ratio of the short side to the long side is 1/sqrt(3).
Therefore the short side is the long side divided by sqrt(3).
So the short side = 8 sqrt(3)/sqrt(3) = 8 inches
Which TWO systems of equations have exactly one solution ?
6x−3y=3
2x−y=4
y=−2x−8
y=x+1
6x−3y=12
2x−y=4
x−4y=8
3x+2y=10
y=2x+1
y=2x−2
Answer: 2nd and 4th set
Step-by-step explanation:
1st set has no solution because the left side of the second equation is that of the first equation divided by 3, but the right side is not.
2nd set has 1 solution because it is the set of 2 lines with different slopes and y-intercepts.
3rd set has infinitely many solutions because multiplying the top equation by 1/3 gives you the bottom equation.
4th set has only solution for the same reason as 2nd set.
5th set has no solution because the two lines are parallel, but have different y intercepts, meaning they never intersect.
Please give question for the answer.
Answer:
[tex]f(x)=\sqrt[3]{x} \\a=5[/tex]
Step-by-step explanation:
[tex]f(x)=\sqrt[3]{x} \\a=5[/tex]
Verify the identity.
Answer:
first blank box:
cos^2(a)
second blank box:
sin^2(a)
see image.
Step-by-step explanation:
Usually, to "verify" you work on the equation using algebra and identities...BUT ONLY CHANGING ONE SIDE. Keep the other side the same and try to make them look the same.
The step to get what's in the first blank box is multiplying
(1-cos a)(1+cos a)
which will make a difference of two squares.
The second blank is using a pythagorean identity that
cos^2 + sin^2 = 1
so
1 - cos^2 = sin^2
see image.
Help please I don't know how to do this and it is due soon!!
Answer:
its an isosceles triangle not a right angle triangle.part A:
[tex]\sf AB^2 = (-2-1)^2 + (1+3)^2[/tex]
[tex]\sf AB^2 =25[/tex]
[tex]\sf AB =5[/tex]
[tex]\sf AC^2 = (2-1)^2 + (4+3)^2[/tex]
[tex]\sf AC^2 = 50[/tex]
[tex]\sf AC = \sqrt{50}[/tex]
[tex]\sf AC = 5\sqrt{2}[/tex]
[tex]\sf BC^2 = (2--2)^2 + (4-1)^2[/tex]
[tex]\sf BC^2 = 25[/tex]
[tex]\sf BC = 5[/tex]
use the formula:
short side² + short side² = long side²
( 5√2 )² + 5² = ( 5√2 )²
75 = 50
It's isosceles
A(-3,1)B(1,-2)C(4,2)[tex]\\ \rm\hookrightarrow AB=\sqrt{(-2-1)^2+(1+3)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]
[tex]\\ \rm\hookrightarrow BC=\sqrt{(2+2)^2+(4-1)^2}=\sqrt{16+9}=5[/tex]
[tex]\\ \rm\hookrightarrow AC=\sqrt{(4+3)^2+(2-1)^2}=\sqrt{50}[/tex]
AB=BCIts isosceles
Need help please! Will give brainliest
Answer:
The answer is 1920 cm
Step-by-step explanation:
First we need to break up to two separate shapes. These shapes are both rectangles, one on the right and one on the left.
To find the volume of a Prism, the equation is V=lwh (length x width x height).
So by splitting up the shape we have two different equation
V= (10)(8)(14) =1120
V= (10)(8)(10)=800
Now we add 1120+800 to get the volume of the entire shape, which is 1920 cm.
Write the following numbers in words:
a. 48 973
b. 153 862
c. 903 036
d. 444 333
e. 16
Solve the system of equations.
y = -5x - 8
y = 4x + 1
a.
( 1, -3)
c.
( 3, 1)
b.
( -1, -3)
d.
No solution
Please select the best answer from the choices provided
A
B
C
D
Answer: B
Step-by-step explanation:
Setting the equations equal to each other,
-5x-8 = 4x+1
-8 = 9x + 1
-9 = 9x
x = -1, meaning y=-5(-1)-8 = -3.
I would really appreciate it if someone could help me out with this problem
Answer:
2018, 2004
Step-by-step explanation:
substitute C(t) for 1274 because it's the cost
1274=6(t-11)^2+980
6(t-11)^2=294
(t-11)^2=49
x-11=7 x-11=-7
x=18, x=4
Answer:
2018, and 2004.
Step-by-step explanation:
do the math "using Your heads".
If the area of triangle is 360 cm2 and the height is 18cm, find its base
Formula for area of a triangle is 1/2 x base x height.
musing the information given you have:
360 = 1/2 x base x 18
First multiply both sides by 2:
720 = base x 18
Now divide both sides by 18:
Base = 720/18
Base = 40 cm
Solution:
Note that:
Area of triangle = 1/2 x Base x HeightArea of triangle = 360 cm²Height = 18 cmUsing the formula to find the area:
1/2 x Base x Height = Area of triangle=> 1/2 x Base x 18 = 360 cm²=> Base x 9 = 360 cm²=> (Base x 9)/9 = 360/9 cm²=> Base = 40 cmA 141 inch pipe is cut into two pieces. One piece is two times the length of the other. Find the lengths of the two pieces
Find the product. (-3x - 7)(5x + 8)
Step-by-step explanation:
= -15x²-24x-35x-56
= -15x²-59x-56
GIVING BRAINILEST! Find the perimeter of the figure!
Stephanie scored 18 points fewer than her friend Jenna.
If Stephanie scored 12 points, how many points did Jenna
score? HELP PLEASEEE
Answer:
30 points
Step-by-step explanation:
Points by Jenna = J
=> J - 18 = 12
=> J = 30 points
Help will give brainlest!
Answer:
1; 4; 3;
Step-by-step explanation:
i think this involves ratios>> if not, sorry-
someone help, please
Answer:
13/28
Step-by-step explanation:
26/(26 + 30) = 26/56 = 13/28
10(-0.4x + 3y) = ?x + ?y
10(? + ?) = ? + ?
?=?
Answer:
2x(57x74)94
Step-by-step explanation:
Original price:
Discount:
30%
Sale price:
$206.50
HELP ASAP PLSPLSPLS Question 8 (Fun-The-Blank Worth 6 points)
(05.03 LCJA polygon is shown
4 units
M
N
2 ore
3 urits
1.
R
7 units
square units input whole numbers only, such as 8.)
The area of polygon INOPOR S Area of a rectangle that is 12 square units Area of a rectange that is
Numerical Answers Expected!
Answer for Blank 1
Answer:
3
Step-by-step explanation:
(7 - 4) * (3 - 2) = 3
The formula E= MHz, where E = gravitational potential energy , mass, g = gravity, and h= Height, is used to calculate gravitational potential energy. Solve this formula for h.
Select the correct answer.
What is the solution of 5/2x-7=3/4x+14?
А.x=-6
В.x=6
C.x=8
D. r= 12
Answer:
D) x = 12
Step-by-step explanation:
we can change 5/2 to 10/4 and now have:
10/4x-7 = 3/4x + 14
we can subtract 3/4x from each side:
7/4x-7 = 14
add 7 to each side:
7/4x = 21
multiply each side by 4/7:
x = 84/7
x = 12
A room measure 9.68 metres long and 6.2 m wide Find its area Also find how many tiles will be needed to pave if the size of a tile 22cm × 10cm .
Answer:
Area is easy, just do 9.68*6.2 which = 60.02 (Rounded to the nearest hundreth)
Step-by-step explanation:
For how many tiles we need
60.02 m is the area of the room, each tile would be 22cmx10cm
There are 100 cm in 1 m
What we can do is find the area of the tiles
22x10 which is 220 CM
220CM is 2.2M
Now that we know the area of the tile is 2.2M we can do 60.02/2.2
Which would be 27.28 tiles (Rounding to the nearest hundreth)
