Marissa bought 12.8 pounds of potatoes at $1.35 per pound. How much did Marissa spend for the potatoes? Explain
12.8 * 1.35 =17.28
Therefore Marissa spent $17.28 on potatoes.
How many congruent triangles do the midsegments of an equilateral triangle partition the triangle into? Explain.
Answer:
4
Step-by-step explanation:
Let us consider an equilateral triangle ABC. Now, we will define midsegments:
A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle (here triangle ABC). This segment has two special properties. It is always parallel to the third side, and the length of the midsegment is half the length of the third side.
Refer the attached image:
Now, from the definition of midsegment we can see that:
[tex]PQ=\frac{1}{2}BC[/tex]
[tex]\therefore PQ=BR[/tex]
and PQ is also parallel to BR.
Now, again from the definition of midsegment we can see that:
[tex]QR=\frac{1}{2}AB[/tex]
[tex]\therefore QR=PB[/tex]
and QR is parallel to PB.
therefore, PQBR forms a parallelogram
And a diagonal of a parallelogram divides it into two congruent triangles.
Hence, triangle 2 (triangle PBR) is congruent to triangle 4(triangle PQR).
Similarly, triangle 3 (triangle QRC) and triangle 1 (triangle APQ) are congruent to triangle 4 (triangle PQR), Therefore, there are 4 congruent triangles formed when midsegments of an equilateral triangle partition the triangle.
The midsegments of an equilateral triangle partition it into four smaller congruent triangles, due to the Triangle Midsegment Theorem and the Third theorem of congruence for triangles.
When the midsegments of an equilateral triangle are drawn, they connect the midpoints of the sides of the triangle. These segments will each be parallel to one side of the triangle and half its length, according to the Triangle Midsegment Theorem. Drawing all three midsegments partitions the equilateral triangle into four congruent smaller triangles. Each smaller triangle will be similar to the original equilateral triangle.
By the Third theorem of congruence for triangles (which is often referred to as SSS or side-side-side), if three sides of one triangle are congruent respectively to the corresponding sides of another triangle, the two triangles are congruent. In this case, each smaller triangle formed by the midsegments shares a side with the original triangle and has the other two sides equal in length to the midsegments, which are congruent to each other by construction.
Therefore, all four smaller triangles are congruent to each other.
[tex] \frac{3}{4} q - 7 = 8[/tex]
Please help me out by answering this and please show your work...
[tex]\frac{3}{4}q[/tex] - 7 = 8
+7 +7
[tex]\frac{3}{4}q[/tex] = 15
[tex]4(\frac{3}{4}q)[/tex] = 4(15)
3q = 60
[tex]\frac{3q}{3} = \frac{60}{3}[/tex]
q = 20
Answer: q = 20
What is the density of a material that has a mass of 2,500 grams and volume of 500 cubic centimeter, in grams per cubic centimeter
Answer:
Density of the material is 5 grams per cubic centimeter.
Step-by-step explanation:
The answer is required to be given in grams per cubic centimeter.
So we should first convert the values to match the units.
Mass is given as 2500 grams so we don't need to change the units.
Volume is given in cubic centimeters. So we don't need to change the units.
Density = [ Mass of the material / Volume of the Solvent]
=2500 grams / 500 cubic centimeters
=5 grams per cubic centimeter
Evaluate the expression –0.4(3x – 2) + for x = 4
The expression evaluates to -4 when x equals 4.
To evaluate the expression –0.4(3x – 2) + for [tex]\( x = 4 \)[/tex], follow these steps:
1. Substitute the value of [tex]\( x \)[/tex] into the expression.
2. Perform the arithmetic operations according to the order of operations (PEMDAS/BODMAS).
Here's the step-by-step calculation:
Given expression: [tex]\(-0.4(3x - 2) +\)[/tex]
Substitute [tex]\( x = 4 \)[/tex]:
[tex]\(-0.4(3(4) - 2) +\)[/tex]
Now, simplify inside the parentheses first:
[tex]\(-0.4(12 - 2) +\)[/tex]
[tex]\(-0.4(10) +\)[/tex]
Next, multiply [tex]\(-0.4\)[/tex] by [tex]\( 10 \)[/tex]:
[tex]\(-4 +\)[/tex]
Finally, there's no more to compute since there's no other term. So the result is:
[tex]\(-4\)[/tex]
Therefore, the value of the expression [tex]\(-0.4(3x - 2)\)[/tex] when [tex]\( x = 4 \)[/tex] is [tex]\( -4 \)[/tex].
Andrew deposited $500 in a savings account that offers an interest rate of 6.5%, compounded continuously. Andrew's initial deposit will grow to $543 in ___ months.
Answer:
The answer is 15 months.
Step-by-step explanation:
p = $500
r = 6.5% or 0.065
A = $543
t = ?
The formula to be used here is :
[tex]A=pe^rt[/tex]
[tex]t=(log(A/p)/log(e))/r[/tex]
Putting the values in formula we get:
[tex]t=(log(543/500)/log(e))/0.065[/tex]
[tex]t=(log(1.086)/log(e))/0.065[/tex]
This gives t = 1.3 years
In months it will be 1 year(12 months) + 3 months = 15 months.
Hence, the answer is 15 months.
Answer:
15 months
Step-by-step explanation:
Use the graph to determine the solution of the inequality |x + 1| + 2 > 5.
Use the graph to determine the solution of the inequality |x + 1| + 2 > 5.
To graph this , first we make the absolute function alone
|x + 1| + 2 > 5
to make absolute function alone we subtract 2 from both sides
|x + 1| > 3
x+1 inside the absolute function . so x=-1
From -1, move 3 units to the right and 3 units to the left.
For x>2 , shade the graph to the right
For x< -4, shade the graph to the left
The graph is attached below
The solution to the inequality is x<-4 and x>2
Answer:
Its A on E2020
Step-by-step explanation:
plz answer 17 16 and 18 show work
Graph the slow intercept equation: y=2/3x-2
Remark
The slope intercept graph needs a table like the one provided by the graph shown below.
A sample calculation would look like this
y = (2/3)x - 2 Let x = 6 (which is not plotted on the graph).
y = 2/3 * 6 - 2 The 3 will divide into the 6 two times
y = 4 - 2
y = 2
So you would plot this as (6,2)
i need help please i dont know how to do this?
if you know two points on a line, how can you find the right the rate of change of the variables being graphed?
You divide the difference in y-coordinates by the diffrence in x-coordinates. Or whatever the variables are.
Lets say the coordinates of the two points are (a,b) and (c,d). Then:
Rate of change is "rise/run" = (b - d)/(c - a) = (d - b)/(a - c)
Which sequence of transformations creates a similar, but not congruent, triangle?
A Rotation and translation
B Dilation and rotation
C Reflection and rotation
D Translation and reflection
Answer:
It would be B.
Step-by-step explanation:
Dilation is the only transformation that is NOT congruent. It is similar.
find three consecutive integers with a sum of 24
The three consecutive numbers that can be equal to 24 are 7,8,9
7+8+9=24
Which of the following is not example of a type of savings vehicle?Certificate of deposit (CD)
Money Market Account
Checking Account
Savings Account
Checking Account
it should be that
The account which is not the example of the type of savings vehicle is Checking Account. Thus option 3rd is correct.
What are the 3 types of savings?The three kinds of the saving account are regular deposit, money market, and Certificate of Deposits. There is a difference in all the three types in terms of the accessibility and amount of interest.
The Checking account is the account which carries the day to day transactions of the money. It ensures the easy access to the money. Many of the people generally uses the debit card or the checks to make the purchases. Thus option 3rd is correct.
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Ruben has 6 new books for his collection. This increases his collection by 12%? How many books does he have now?
Ruben has 6 new books for his collection. This increases his collection by 12%
Let x be the number of books Ruben has before 6 new books added
x + 12% of x = x+6
x + 0.12x = x+6
1.12 x = x+6
Subtract x on both sides
0.12x = 6
Divide by 0.12
x = 50
6 new books are added for his collection
So 50 + 6 = 56
He have 56 books now.
solve inequality -12 < 3x- 15 < 9
[tex] - 12 \leqslant 3x - 15 \leqslant 9[/tex]
[tex]-12\leq3x-15\leq9\qquad|+15\\\\3\leq3x\leq24\qquad|:3\\\\1\leq x\leq8[/tex]
Jim decided to go for a drive in his car. He started out at 0 miles per hour(mph). He then accelerated 20 mph down his street. Then, to get on the highway he accelerated another 35 miles per hour. A car was going slow in front of him so he slowed down 11 mph. He then go off the highway, so he slowed down another 7 mph. At what speed was he driving?
Answer:
37 mph
Step-by-step explanation:
if he starts at 0 then goes to 20 then add another 35 which gives you 55mph then he slows down you decrease 11 which is 44 then decrease again 7 gives you 37mph
Answer:
37 mph
Step-by-step explanation:
if he starts at 0 then goes to 20 then add another 35 which gives you 55mph then he slows down you decrease 11 which is 44 then decrease again 7 gives you 37mph
at a chess tournament the number of competitors in each round is 50% of the number of competitors in the previous round. What type of relationship most appropriately models this situation?
exponential growth
linear increase
linear decrease
exponential decay
This type of relationship is exponential decay
Becky gets $5.00 a week for chores, and helps with chores for 4 weeks. If Becky wants to spend only half of her money, how much will she have left to save?
$5.00 x 4 = $20.00.
$20.00 divided by 2 = $10.00
She will have $10.00 to save.
Hope I helped!
Good Luck!
What is the slope of the perpendicular line x-2y=12
Hey there!!
Slope-intercept form :
y = mx + b
m is the slope and b is the y-intercept.
Given equation :
x - 2y = 12
We will have to isolate the y.
... x - 2y = 12
... -2y = x - 12
... y = ( x - 12 ) / -2
... y = x / - 2 + 6
Hence, the slope is -1/2
Hope my answer helps!
the length of rectangle is 17cm more than double the width. the perimeter is 76cm
7 x 4 x ?? =2,800 and 7 x 4 x ?? =28,000
NEED ANSWERS NOW
Which equation correctly applies the distributive property?
A. −1.2⋅0.57⋅0.5=−1.2⋅0.5⋅0.57
B. −2.5⋅(4⋅1.045)=(−2.5⋅4)⋅1.045
C. (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2)
D. 50+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005)
The answer is choice C
On the left side we have something in the form a*b+a*c+a*d
On the right side we have something in the form a*(b+c+d)
All together, we have a*b+a*c+a*d = a*(b+c+d), where the letters a,b,c,d are to be replaced with the proper values (0.5, 0.5, 0.3, and 0.2 in that exact order).
The idea of distribution is to multiply the outer value 0.5 by each of the values inside the parenthesis (0.5, 0.3, and 0.2) and add up the products.
Equation C and D that is (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2) and 0+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005) applies the distributive property correctly as defined "multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together".
What is distributive property?The distributive law, which states that in elementary algebra, equality is always true, is generalized by the distributive property of binary operations. For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication. In order to quickly solve expressions, a number is distributed among the numbers in the brackets. When using the distributive property of multiplication, for instance, to resolve the expression 4(2 + 4), we would do so as follows: 4(2 + 4) = (4 × 2) + (4 × 4) = 8 + 16 = 24.
The distributive property states,
A × (B + C) = AB + AC
for equation C
(0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2)
for equation D,
50+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005)
According to the definition of the distributive property, which states that "multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together," Equations C and D, which are correctly applied that is (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2) and 50+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005).
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Pls help I’ll put in 25
given -2(x + 1) = 5x + 4 - x ( distribute left side )
-2x - 2 = 4x + 4 ( simplifying both sides )
subtract 4x from both sides
- 6x - 2 = 4 ( add 2 to both sides )
- 6x = 6 ( variable by itself on left side )
divide both sides by - 6
x = [tex]\frac{6}{-6}[/tex] = - 1
as a check, substitute x = - 1 into the equation and if both sides are equal then it is the solution.
left side = - 2(-1 + 1 ) = - 2 × 0 = 0
right side = (5 × - 1) + 4 - (- 1) - 5 + 4 + 1 = 0
hence x = - 1 is the solution
A subway in New York is located at 25 feet below sea level. In Chicago a train is 27 feet above sea level. How much higher is the train than the subway?
All you have to do is add 25+ 27= 52
Give me a short answer only plz
-2x^6 That is pertty short :)
what is 22 + 5d = -8(7d-4)
22+5d=-8x7d=56d+ -8x-4=32
22+5d=-56d+32
22+32=54 and -56d+5d=-51d
The answer would be 51d+54
Remark
The steps are the same usually. Remove the brackets and collect like terms on each side of the equal sign.
Solution
22+5d = -8(7d - 4) Remove the brackets.
22+5d = -56d + 32 Notice the sign change on 32. 2 minus quantities = a plus when multiplied. Add 56d to both sides.
22 + 5d + 56d = - 56d + 56d + 32
22 + 61d = 32 Subtract 22 from both sides.
61d = 32 - 22
61d = 10 Divide by 51
d = 10/61
d = 0.1639 Answer
Check
LHS
22 + 5*0.1639 = 22.8197
RHS
-8(7*0.1639 - 4)
-8(1.1473 - 4)
-8(-2.8527)
22.8216
The difference is a rounding error.
About how much farther away from the Sun is Earth than Mercury? Write your answer in standard form and scientific notation.
The approximate distance from each planet to the Sun is given below.
Mercury: 35,983,610
Earth: 92,957,100
Neptune: 2,798,842,000
Move the decimal until its below 10 and greater than 1:
Mercury: 3.5 x 10^7
Earth: 9.2 x 10^7
Neptune: 2.7 x 10^9
hope this helps :)
Three fourths ÷ one fourth
The way I did this was made everything decimals so .75/.25 and it equals 3
Rewrite the fractions 2/5 and 4/15 as fractions with a least common denominator
The two fractions with the common denominator will be 6/ 15 and 4 / 15.
What is a fraction?The fraction is defined as the division of the whole part into an equal number of parts.
The two fractions are 2 / 5 and 4 / 15 will be converted into the same common denominator as;-
For fraction 2 / 5 multiply it by 3 in both the numerator and the denominator.
= ( 2 x 3 ) / ( 5 x 3 )
= ( 6 / 15 )
Therefore two fractions with the common denominator will be 6/ 15 and 4 / 15.
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