Answer:
AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of each triangle
Kristina invests a total of $28,500 in two accounts. The first account earned a rate of return of 10% (after a year). However, the second account suffered a 4% loss in the same time period. At the end of one year, the total amount of money gained was $1,310.00. How much was invested into each account?
$_______was invested in the account that gained 10% and
$_______ was invested in the account that lost 4%.
Answer:
$17,500 was invested in the account that gained 10% and
$11,000 was invested in the account that lost 4%
Step-by-step explanation:
Define the variables:
Let x be the money invested in the account that gained 10%.Let y be the money invested in the account that lost 4%.Given information:
$28,500 = total amount invested between the two accounts$1,310.00 = total amount gainedPercentages in decimal form:
10% = 0.14% = 0.04Create a system of equations using the given information and defined variables:
[tex]\begin{cases}x + y = 28500\\0.1x - 0.04y = 1310 \end{cases}[/tex]
Rewrite Equation 1 to make y the subject:
[tex]\implies y=28500-x[/tex]
Substitute into Equation 2 and solve for x:
[tex]\implies 0.1x-0.04(28500-x)=1310[/tex]
[tex]\implies 0.1x-1140+0.04x=1310[/tex]
[tex]\implies 0.14x=2450[/tex]
[tex]\implies x=17500[/tex]
Substitute the found value of x into Equation 1 and solve for y:
[tex]\implies 17500+y=28500[/tex]
[tex]\implies y=11000[/tex]
Conclusion
$17,500 was invested in the account that gained 10% and
$11,000 was invested in the account that lost 4%
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Kamar Spends of wis salary on School fees and 1/2 of the rematader on rent He spends 3/8 of the remainder on food and saves the rest . He he saves 25,000 shillings, what is his salary.
Answer:
37.170
Step-by-step explanation:
is hard to explain uwuBrandon wants to ride his bicycle 21 miles this week. He has already ridden 6 miles. If he rides for 5 more days, write and solve an equation which can be used to determine xx, the average number of miles he would have to ride each day to meet his goal.
Answer:
Step-by-step explanation:
6 + 5X = 21
5X = 21-6 = 15
X = 15/5 = 3 miles per day on an average
Keep the Old Car or Buy a Used Car
Manny is an online student who currently owns an older car that is fully paid for. He drives, on average, 140 miles per week to commute to work. With gas prices currently at $2.87 per gallon, he is considering buying a used, fuel-efficient car, and wants to know if it would be a good financial decision.
The old car Manny owns currently gets 20 miles per gallon for average fuel efficiency. It has been a great vehicle, but with its age, it needs repairs and maintenance that average $740 per year (as long as nothing serious goes wrong).
He is considering buying a newer used car that will cost a total of $5,500 over a three-year loan process. The used car gets 33 miles per gallon and would only require an average of $10 per month for general maintenance. To help make a decision Manny wants to calculate the total costs for each scenario over three years. He decides to use the Quantitative Reasoning Process to do this.
Find the total costs for the newer used car (gas, maintenance/repairs, purchase price) for each scenario over the three years.
Round your answers to the nearest dollar.
Answer:
buy a new car because cars depreciates
This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Answer:
(2^3t•2^t)/16 isn't a not equivalent
If 2x/7 divided by 1=0 then what will be value of x is
The value of x = -3/2 .
What is an Equation ?An equation is a mathematical statement that relates unknown variable to constants to determine their value.
The equation given is
(2x+3 ) / 7 Divided by 1 = 0
2x +3 = 0
2x = -3
x = -3/2
Therefore the value of x = -3/2 .
The complete equation is
(2x+3)/7
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If a container is ¾ full of water which is equivalent to 30litres. What will be the full capacity of the container?
What is the surface area of this complex figure?
Enter your answer in the box.
The surface area of the complex figure is: 582 ft².
What is the Surface Area of the Complex Figure?Surface area of the complex figure = surface area of the triangular prism + surface area of the rectangular prism - 2(area of the face of the triangular prism that joins with the rectangular prism).
Surface area of the triangular prism = (s1 + s2 + s3)L + bh = (11 + 9 + 9)5 + (11)(7)
Area of the triangular prism = 222 ft²
Surface area of the rectangular prism = 2(wl+hl+hw) = 2·(5·15+8·15+8·5) = 470 ft².
2(area of the face of the triangular prism that joins with the rectangular prism) = 2(lw) = 2(11)(5) = 110 ft²
Surface area of the complex figure = 222 + 470 - 110
Surface area of the complex figure = 582 ft².
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Find RS.
A. 10
B. 9
C. 12
D. 5
Answer:
D. 5
Step-by-step explanation:
2x - 6 + 1 + x - 4 = 18
3x - 9 = 18
3x = 27
x = 9
RS = x - 4 = 9 - 4 = 5
Answer: D. 5
Choose the graph of y = |x – 5| by translating the parent function.
Answer:
x y
3 2
4 1
5 0
6 1
7 2 (There is a line between the x and y that goes all the way down the numbers so they are seperated)
Step-by-step explanation
Answer:
esa respuesta está difícil pero si calculamos la creta de tu mamá con la semilla mía xrei que puede dar tu maldita madre
HELP! ASAP!
F is a right angle, and segment (a)(f), BG, and CH are all parallel. Use this information to explain why ∆AFD ~ ∆BGD ~∆CHD. Support your answer using a postulate or theorem.
Use the diagram to answer each part of the question
By the corresponding angles theorem,
∠AFG, ∠BGD, and ∠CHD are congruent∠BAF, ∠CBG, and ∠DCH are congruentThus, triangles AFD, BGD, and CHD are similar by AA.
Given the figure, triangles AFD, BGD, CGD are similar by Angle-Angle-Angle (AAA) criterion for the similarity.
The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that “If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar”.
In the given question,
∠F = ∠G = ∠H = 90°
Let ∠D = x°
In triangle CHD,
∠H = 90°
∠D = x°
∠C = 180 - 90 - x = (90-x)°
In triangle BGD,
∠G = 90°
∠D = x°
∠B = 180 - 90 - x = (90-x)°
In triangle AFD,
∠F = 90°
∠D = x°
∠A = 180 - 90 - x = (90-x)°
In triangle AFD and BGD and CHD,
∠A = ∠B = ∠C
∠F = ∠G = ∠H
∠D = ∠D =∠D
triangle AFD and BGD and CHD are similar.
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On Monday, Chris and Rachel went to the gym. Chris plans to return every second day. Rachel plans to return every fourth day. If they follow their plans, what is the next day of the week they will both be at the gym on the same day?
A. Wenesday B. thursday C. friday D. saturday
14 MINS LEFT HELP ME PLS Lakesha gave three tenths of her cookies to Bailey and five tenths of her cookies to Helen. What fraction of her cookies did Lakesha give away?
eight tenths of her cookies,
five tenths of her cookies,
three tenths of her cookies,
or two tenths of her cookies.
Lakesha gave away 8/10 of her cookies.
What fraction of her cookies did Lakesha give away?
We know that she gave away 3/10 of her cookies to Bailey and 5/10 of her cookies to Helen.
Then the fraction that she gave away is:
3/10 + 5/10
Notice that both fractions have the same denominator, then we can directly add the numerators:
3/10 + 5/10 = 8/10
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solve by substitution method 2x+y=-2 5x-2y=-23
Step-by-step explanation:
SOLVED BY SUBSTITUTION !Answer:
x= -3
Step-by-step explanation:
2x + y = -2 ---> y = -2 - 2x
instead: 5x-2y = -23 ---> 5x - 2(-2 -2x) = -23 ----> 5x+4+4x= -23 ---> 9x= -27
---> x = -3
solve equation -4m +5=3m-9
pls workings
Answer:
2
Step-by-step explanation:
- 4m + 5 = 3m - 9
3m - 9 = 5 - 4m
3m + 4m = 5 + 9
7m = 14
m = 14 / 7
m = 2
Jorge earns $8.50 per hour at his job. Last month, Jorge earned $544. Which equation can be used to find the number of hours, h, Jorge worked last month?
Answer:544/8.50=h
Step-by-step explanation:
544 divided by 8.50 = the number of hours
Find the value of y. y=[?]
HELP NEEDED PLEASE
Answer:
[tex]\sf y=\sqrt{21}[/tex]
Step-by-step explanation:
Altitude: A line segment drawn from a vertex that is perpendicular to the side opposite that vertex.
Therefore, the altitude on the given diagram is y.
The two internal triangles formed by drawing the altitude are similar to the original triangle. If two triangles are similar, their sides are proportional in length.
[tex]\implies \sf \dfrac{segment}{altitude}=\dfrac{altitude}{segment}[/tex]
[tex]\implies \sf \dfrac{3}{y}=\dfrac{y}{7}[/tex]
[tex]\implies \sf 3 \cdot 7=y \cdot y[/tex]
[tex]\implies \sf y^2=21[/tex]
[tex]\implies \sf y=\sqrt{21}[/tex]
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This table shows equivalent ratios.
A 2-column table has 4 rows. Column 1 is labeled A with entries 12, 24, 32, 48. Column 2 is labeled B with entries 2, 4, 6, 8.
Which ratio is not equivalent to the other ratios shown in this table?
12 to 2
24 to 4
32 to 6
48 to 8
Using proportions, the ratio that is not equivalent to the ones shown in the table is given by:
32 to 6.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In the table, the ratios is given as follows:
r1 = 12/2 = 24/6 = 48/8 = 6.r2 = 32/6 = 5.3.Hence the different ratio is:
32 to 6.
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the physical orders 1500 flu injection and use 300 shots in september and 450 shots given in october and 665 given in november what percentage of flu vaccine remains
Answer:
7%
Step-by-step explanation:
1500 is 100%. We divide 300, 450, and 665 shots by 1500 to get their percentages, 20%, 30%, and 43.333333333333333333333333333%, rounded to 43%. We subtract all the percentages from 100 and we get 7 percent left! (If this is wrong, I am only 10 so don't judge me)
Which graph represents y > 2x^2 – 8x + 4?
Answer:
C ON EDGE
Step-by-step explanation:
What is the solution to the system of equations?
y= 2/3x + 3
X=-2
Answer:
(x, y) = (-2, 5/3)
Step-by-step explanation:
The system of equations is easily solved by substitution.
SolutionUsing the given value of x, substitute for x in the first equation to find y.
y = 2/3(-2) +3
y = -4/3 +9/3 = 5/3
The solution is (x, y) = (-2, 5/3).
Jane evaluates x2-3x+5 for x=-2 below.
Step 1: (-2)²-3(-2)+5
Step 2: -4+6+5
=
Step 3: = 7
What, if any, was Jane's mistake?
Jane made no mistakes.
O Jane incorrectly evaluated (-2)² in step 2.
Jane incorrectly added the terms in step 3.
O Jane incorrectly substituted in x=-2 in step 1.
K
Answer: Jane incorrectly evaluated (-2)² in step 2.
Step-by-step explanation:
[tex](-2)^{2}=4[/tex], not -4.
regular number after 167, 118, 82, 57, 41, ?
Answer...
32!!
Step-by-step explanation:
Subtract the numbers to see a pattern of decreasing odd numbers
167-118 = 49
118-82 = 36
82-57 = 25
57-41 = 16
The difference between is 13 then 11 then 9 so the next number should be x-7
Given that the Earth orbits the Sun with an orbital velocity of about 29.8 km/s and a radius of 1 AU, use the equation above to estimate the total mass in the solar system inside the orbit of the Earth. Is this similar to the mass of the Sun? Remember to convert units to S.I. units of meters, kilograms, and seconds before proceeding so that your answer is in kg.
Answer:
I would like to use lb if that's ok
What type of number is √5? Choose all answers that apply:
A:Whole number
B:Integer
C:Rational
D:Irrational
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What type of number is [tex]\bf{\sqrt 5}?[/tex] Select all that apply
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
Let's start by taking a look at all the four sets of numbers.
A: Whole number{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22...∞}The set is shown above. To be honest, this is an infinitely small part of the number set; the whole number set would take FOREVER to type ;)
B: Integers{∞...-2,-1,0,1,2,3,4,5,6,7,8,9...∞}Wow, this set starts at negative infinity and ends at positive infinity!
C: RationalThis set consists of all integers, decimals, and fractions.
D: IrrationalThat's where the desired number [tex]\bf{\sqrt{5}}[/tex] belongs!
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=The\;fourth\;option}[/tex]
[tex]\LARGE\boxed{\bf{aesthetics \not1\theta l}}[/tex]
∞
6) The circumference of a circle is
approximately 37.68 centimeters. What is the radius of the circle to the nearest centimeter?
A. 6 cm
C. 12 cm
B. 8 cm
D. 16 cm
Answer: A, 6 cm
Step-by-step explanation:
Circumference is 2(radius) * pi.
A. 12pi C. 24pi B. 16pi D. 32pi
Assuming pi is roughly 3,
A = 36
C = 72
B = 48
D = 96
A is the closest and if you actually used pi, it would be about 3.14159265 which would make the circumference slightly over 36, which 37.68 is.
Hope this helped.
4.22 next decimal in number
Answer:
4.23
Step-by-step explanation:
add 0.01
I need help with this question please!! :)
Problem 34
Answer: [tex]\boldsymbol{n(B) = 3}[/tex]
Reason:
We count the number of items inside set B. In this case there are 3 values, so that is why n(B) = 3
===========================================================
Problem 36
Answer: [tex]\boldsymbol{n(A \cap C) = 1}[/tex]
Reason:
To be able to count the number of items inside set [tex]A \cap C[/tex], we first need to determine what this set looks like. In other words, we need to know the number(s) inside this set.
The upside down U symbol is the intersection symbol. It indicates we want to find what the sets A and C have in common. In this case, it's the value "4" and nothing else. This number is in both set A and set C at the same time. It might help to draw a venn diagram as you see below. I'm ignoring set B entirely since your teacher is not asking about the set in this problem.
We can then say [tex]A \cap C = \{4\}[/tex]
There's only one item inside this set, which is why [tex]n(A \cap C) = 1[/tex]
what is the next # in this sequence 3, 5, 12, 55, 648
Answer:
35 585
Step-by-step explanation:
Each term is the product of the previous two terms minus the term that is two before
3*5 - 3 = 12
5 x12 - 5 = 55
12 x 55 - 12 = 648
55 * 648 - 55 = 35 585
or each term is term that is two before x (term before -1)
3 (5-1) = 12
5 x (12-1) = 55
12 * (55-1) = 648
55 * ( 648-1) = 35 585
The required next term in the sequence is 35,185.
What is inductive reasoning?Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.
here,
Given sequence 3, 5, 12, 55, 648
The given sequence has the following pattern,
3 × 5 - 3 = 12
5 × 12 - 5 = 55
12 × 55 - 12 = 648
55 × 648 - 55 = 35,185
Thus, the required next term in the sequence is 35,185.
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13. Find the perimeter.