Answer:
[tex]D E F = 196[/tex]
Step-by-step explanation:
Given
[tex]ABC = 56, 64\ and\ 72[/tex]
[tex]Largest\ of\ D E F = 252[/tex]
Required
Determine the smallest side of DEF
Since both sides are similar, then the sides of DEF can be calculated using:
[tex]D E F = k * ABC[/tex]
First, we need to solve for k
From the given parameters
[tex]D E F = 252[/tex] when [tex]ABC = 72[/tex]
This is so because these are the largest sides of both triangles respectively
[tex]D E F = k * ABC[/tex]
[tex]252 = k * 72[/tex]
Divide through by 72
[tex]252/72 = k * 72/72[/tex]
[tex]k=252/72[/tex]
[tex]k=3.5[/tex]
We make use of the same formula to determine the length of the smallest side.
The smallest of ABC is 56, so we have:
[tex]D E F = k * ABC[/tex]
[tex]D E F = 3.5 * 56[/tex]
[tex]D E F = 196[/tex]
Hence, the smallest side of DEF is 196
Last year, Keith opened an investment account with $8200. At the end of the year, the amount in the account had decreased by 7.5%. How much is this decrease in dollars? How much money was in his account at the end of last year?
Answer:
You would multiply $8200 by .075, giving you 615. Then to find the decrease. Take the starting value (8200) by the end value (615). and you would get 7,585.
Round 831,638 to the nearest thousand
Answer:
832,000
Step-by-step explanation:
If △EFG ≅ △HJK, complete each part.
Answer:
[tex] \overline{EG} \cong \overline{HK} [/tex]
[tex] \overline{HJ} \cong \overline{EF} [/tex]
[tex] \angle F \cong \angle J [/tex]
[tex] \angle H \cong \angle E [/tex]
∆FGE ≅ ∆JKH
Step-by-step explanation:
Since ∆EFG ≅ ∆HJK, therefore, the corresponding sides and angles of both ∆s are congruent.
Thus:
[tex] \overline{EG} \cong \overline{HK} [/tex]
[tex] \overline{HJ} \cong \overline{EF} [/tex]
[tex] \angle F \cong \angle J [/tex]
[tex] \angle H \cong \angle E [/tex]
∆FGE ≅ ∆JKH (take note of the arrangement of the letters or naming of each vertex of both triangles. Each vertex of in one ∆ must correspond to the vertex of the other for the ∆s to be congruent)
△EFG ≅ △HJK,
From the figure attached we can conclude that
[tex]\rm \bar {EG}[/tex] ≅ [tex]\rm \bar {HK}[/tex]
[tex]\rm \bar HJ[/tex] ≅ [tex]\rm \bar FE[/tex]
∠[tex]\rm F[/tex] ≅∠[tex]\rm J[/tex]
∠[tex]\rm H[/tex] ≅∠[tex]\rm E[/tex]
△FGE ≅ △JKH
Given that
△EFG ≅ △HJK,
Since △EFG ≅ △HJK is given hence we can conclude that corresponding sides and corresponding angles of both the triangles will be equal.
Two triangles are said to be congruent when they are of similar shape and size means all the angles of one triangle are equal to the corresponding angles of other triangle and all the sides of one triangle are equal to corresponding sides of other triangle.
From the figure attached we can conclude that
[tex]\rm \bar {EG}[/tex] ≅ [tex]\rm \bar {HK}[/tex]
[tex]\rm \bar HJ[/tex] ≅ [tex]\rm \bar FE[/tex]
∠[tex]\rm F[/tex] ≅∠[tex]\rm J[/tex]
∠[tex]\rm H[/tex] ≅∠[tex]\rm E[/tex]
△FGE ≅ △JKH
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(4x + 8) + (7x + 3) =
plsss help me and tell me the answerrrr
Answer:
11x+11
Step-by-step explanation:
4x+8+7x-3=11x+11
Hope this helps :D
Answer:
11x + 11
Step-by-step explanation:
( 4x + 8 ) + ( 7x + 3 )
Remove parenthesis;
Note: Remember, the associate property states that if an equation is either all multiplication or addition, then it can be done in any order, hence the parenthesis holds no weight in this case.
4x + 8 + 7x + 3
Combine like terms;
11x + 11
Round 3/18 to the nearest half
Explanation: 1 / 2 = 9 / 18 Halfway that and 0 would be 4.5 / 18 Since 3 / 18 is below that, we would round to 0
Below are two inequalities and the graphs of their lines without the shading. By imagining where the shading should be, identify which point would satisfy BOTH inequalities
We want to imagine where the shading should be, and with that determine which point is a solution for both inequalities. We will see that the solution is the point (7, -8)
Interpreting inequalities:
In this case, the inqualities are:
y < -x + 1y < (-1/2)*x - 1You can see that in both cases, y is smaller than the line, thus, for both inequalities, we must shade the part that is below the lines.
With that in mind, the region of solution will be the region that is below both lines at the same time, and that region will be the "triangle" that you can see at the middle below the horizontal axis.
Now that we know the region of solutions, we only need to see which point belongs there, from the given options the only that belongs to that region is the point (7, -8), which means that this point is a solution for both inequalities.
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Sophia earns 40 points every time she shops at a grocery store. She needs a total of 2,680 points to receive a free prize. So far, she has earned 1,280 points. How many more times will Sophia have to shop at the grocery store in order to earn the additional points she needs for a free prize? Let t represent the number of times Sophia visits the store. Which of the following equations best represents the solution to the above question? 100 points !!! quick PLEASE HELP I GUURL OUT
The equation that best represents this solution is:
40t + 1,280 = 2,680
What is the algebraic equations?
An algebraic expression is when we use numbers and words in solving a particular mathematical question.
Each time Sophia shops at the grocery store, she earns 40 points. If she needs a total of 2,680 points to receive a free prize and she has already earned 1,280 points, then she needs to earn an additional 2,680 - 1,280 = 1,400 points. Let t represent the number of times Sophia visits the store.
Since Sophia earns 40 points every time she shops at the grocery store, the total number of points she will earn after t visits is 40t. Therefore, we can set up the following equation:
40t = 1,400
Solving for t, we can divide both sides of the equation by 40:
t = 1,400/40
t = 35
Hence, Sophia will need to shop at the grocery store 35 more times in order to earn the additional points she needs for a free prize.
The equation that best represents this solution is:
40t + 1,280 = 2,680
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Fine the values of x and y
Answer:
x=5 and y=1
Step-by-step explanation:
HELP ASAP PLS I HAVE A MATH EXAM AND IM DESPRATE T-T
4/15 rounded to the nearest thousandth
Answer:
0.26 possibly
Step-by-step explanation:
PLEASE HELP I WILL GIVE BRAINLIEST IF 2 PEOPLE ANSWER! Find the area of a square with side length x when x is equal to the given value. Are the area of a square and the length of its side directly proportional? Justify Your Answer.
x = 15 inches.
The area of the square is __ square inches.
Answer:
The area of the square is 15²
the area of a square and the length of its side are directly proportional because The area of the square is x²=> when its edge decreases, the area of the figure decreases
Step-by-step explanation:
Nate has 5 green marbles and 3 red marbles. Select the ratios that compares the number of red marbles to the total number of marbles. Mark all that apply.
3 to 8
5 to 8
3:8
5:3
5/8
3/8
Answer:
5 to 8 & 5/8
Step-by-step explanation:
what does x equal?
Answer:
16 = x
Step-by-step explanation:
Since angle B and E are congruent to each other (because triangle ABC is congruent to triangle DEC), We can set up an equation to find x.
x + 15 = 6x - 65
Add 65 and subtract x to and from both sides.
80 = 5x
Divide by x.
16 = x.
Use the table and graph that relates dog ages to human ages to
following question.
question: would there ever be one year assigned to two different quantities? explain.
please help ill mark brainlest and like and rate your answer.
Answer:
No
Step-by-step explanation:
True or False: (x + 4)(x - 4) = x2 - 8x + 16
3(5 +6) =
can someone please help?
Answer:
33
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
3(11)=33
hope this help
plzzzzzz help me Find the slope when given the following points. 2) (2, 1) and (5, 3)
Answer:
2/3
Step-by-step explanation:
3-1/5-2=
2/3
plz help
Solve the system by Substitution
y=2x+15
7x+2y=−14
A(-6, 3)
B(4, -7)
C(6, -7)
D(-4, 7)
Answer
D
Step-by-step explanation:
y=2x+15
7=2(-4)+15
7=15-8
7=7
7x+2y=-14
7(-4)+2(7)=-14
-28+14=-14
-14=-14
How do I find the slope of the line from the graph?
Answer:
The slope is most easily defined as rise over run.
First, find a point you like because it is directly on the line and is where for example starting from the origin which you know should be always (0, 0).
Then find another point that is on the line and is perfectly aligned where on the graph is like (1, 2).
Then, as I said earlier, rise over run. So you climb up from for example the origin which is in the graph and climb up to the (1, 2) point. It should go up two units because it is increasing in intervals of 2 but has the notches in the half mark of 1.
So the rise is 2 because it climbed from 0 to 2.
The run is running from the 0 in the origin on the x-axis and running to the 1 because it is (1, 2) where it is in the form (x,y).
Since it is rise over run, the rise is 2 and the run is 1 so 2 over 1 is 2.
Hence the slope is 2.
Step-by-step explanation:
no clue what to do lol
Answer:
Thanks for the free points
Answer:
So, the answer for b is 20.
The way to figure this out is:
angle N is congruent to angle S
angle M is congruent to angle M
side NM is 10
because of the three things above, triangle NHM is congruent to triangle SML because of SAS(side angle side postulate)
Hope that helps! Let me know if it does! ;P
5 and (-5) are a zero pair.
True
or
False
Answer:
true!
Step-by-step explanation:
I need help with the problem
Eight poles are 30m apart. What is the distance in meters from the first to the last pole?
A 3-column table with 2 rows. Column 1 is labeled Scale factor with entries 1, 1.25. Column 2 is labeled Width with entries 8 inches, A. Column 3 is labeled Length with entries 28 inches, B.
The value of A is ____?
The value of B is____?
Answer:
The Value of "A" is 10.0 Inches
The Value of "B" is 35 Inches
Step-by-step explanation:
Got it right on
E D G E N U I T Y 2021
The value of A is 10.
The value of B is 35.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A 3-column table with 2 rows. Column 1 is labeled Scale factor with entries 1, 1.25. Column 2 is labeled Width with entries 8 inches, A. Column 3 is labeled Length with entries 28 inches, B.
Hence, We can formulate;
The value of A = 1.25 × 8
= 10
And, The value of B is,
⇒ 1.25 × 28
⇒ 35
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Simplify.
312+18
358
3210
368
334
The sum of 312+18 is 330.
To simplify the sum of 312 + 18, we add the two numbers together:
When three hundred twelve is added with eighteen we get three hundred thirty.
312
+18
________
330
Hence, the value of 312+18 is 330.
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Anna invested $28,000 in an account paying an interest rate of 6.5% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $39,500?
Answer:
It will take 5.3 years to reach $39,500
Step-by-step explanation:
Compound Interest
It occurs when the interest is reinvested rather than paying it out.
Interest in the next compound period is then earned on the principal sum plus the previously accumulated interest.
The formula is:
[tex]\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
We are required to find the time needed to convert the principal P into a given final amount.
Solving the above equation for t, we get:
[tex]\displaystyle t=\frac{log(A/P)}{n\cdot log\left(1+r/n\right)}[/tex]
Anne invested P=$28,000 in an account at r=6.5%=0.065 compounded daily. There are 360 days in a year, so n=360. The final amount A=$39,500.
Substituting into the formula:
[tex]\displaystyle t=\frac{log(39,500/28,000)}{360\cdot log\left(1+0.065/360\right)}[/tex]
t=5.3 years
It will take 5.3 years to reach $39,500
Answer:5.3
Step-by-step explanation:
i need help with problem 16
Answer:
she decorated two cookies per minute
Step-by-step explanation:
72 cookies divided by 36 minutes
When a rational number is written as a fraction, which statement is always true about the numerator and the denominator of the fraction?
A.
They are both integers.
B.
They are both prime numbers.
C.
They are both natural numbers.
D.
They are both composite numbers.
A number written in the form p/q such that q ≠ 0 will be rational if and only if p and q both are integers so option (A) will be correct.
What is an irrational number?Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is referred to as an irrational number.
Let's suppose a decimal number,
2.256
By removing decimal
2.256 → 2256/1000 here 2256 and 1000 both are integers which means they will be a rational numbers.
Now take another example,
√2 → √2/1 here √2 is not an integer and if we expand √2 then it will be non-repeating and non-terminating so we cannot write in form of p/q.
Hence "A number written in the form p/q such that q ≠ 0 will be rational if and only if p and q both are integers".
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Use an integer strategy to find each answer.
(-4) + (-8) + 11 – (-2)
Answer:
1
Step-by-step explanation:
(-4) + (-8) + 11 - (-2)
~Simplify
-4 - 8 + 11 + 2
~Subtract
-12 + 11 + 2
~Add
-1 + 2
~Add
1
Best of Luck!
What are the like terms you must combine first? 4(x + 3) – 2x + 8 = 28
Answer:
the answer is x = 4
Step-by-step explanation:
first you wanna subtract 8 from both sides
then it should look like this... [tex]4\left(x+3\right)-2x=20[/tex]
then this... 2x+12=20
next you need to subtract 12 from both sides
then it'll look like this 2x=8
then this... [tex]\frac{2x}{2}=\frac{8}{2}[/tex]
lastly your gonna simplify it and and your answer will be...
x = 4
hope this helps :)
0.6x -5 = 0.1x + 7
please help me with the answer for math so i can pass her class
Answer: x
=
24
Step-by-step explanation:
hope you pass
Answer:
x=24
Step-by-step explanation:
Personally I like fractions better so lets turn the decimals to FRACTIONS!
6/10 x - 5 = 1/10 x +7
+5 +5
________________-
6/10x = 1/10x + 12
-1/10 -1/10
__________________-
5/10x=12
÷5/10 ÷5/10
__________________
x= 12 ×10/5
x=120/5
x=24
Hope this helps :D