Answer:
Step-by-step explanation:
We are given that the perpendicular bisector of side AB of ∆ABC intersects side BC at point D.
this means that side AE=BE.
Also, we could clear; ly observe that
ΔBED≅ΔAED
( since AE=BE, side ED common, ∠BED=∠AED
so by SAS congruency, the two triangles are congruent)
Now we are given that:
the perimeter of ∆ABC is 12 cm larger than the perimeter of ∆ACD.
i.e. AB+AC+BC=AC+AD+CD+12
AB+BC=AD+CD+12
as AD=BD
this means that AD+CD=BD+CD=BC
AB+BC=BC+12
AB=12
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The perimeter of 40 cm. and lengths of two sides of ∆ABC where side AC is 10 cm gives;
The perimeter of ∆AEC is 25 centimeters How can the perimeter of the formed ∆AEC be found?Given:
AB = BC
AC = 10 cm.
The perimeter of ∆ABC = 40 cm.
Therefore;
∆ABC is an isosceles triangle
AB + BC + AC = 40
AB + AB + 10 = 40 by substitution property of equality
2 × AB = 40 - 10 = 30
AB = 30 ÷ 2 = 15AB = BC = 15 cm.
Using the rule of cosines, we have;
10² = 15² + 15² - 2×15×15 × cos(A)cos(A) = (15² + 15² - 10²) ÷ (2×15×15)
A = arccos (350 ÷ 450) ≈ 51.06°<BED ≈ 180° - (90° + 51.06°) = 38.94°
DB = AB ÷ 2
Therefore;
DB = 15 ÷ 2 = 7.5From the rule of sines, we have;
DE/sin(51.06°) = 7.5/sin(38.94°)DE = 7.5/sin(38.94°) × sin(51.06°) ≈ 9.28
According to Pythagorean theorem, we have;
BE ≈ √(7.5² + 9.28²) ≈ 11.93Similarly, we have;
AE ≈ √(7.5² + 9.28²) ≈ 11.93EC ≈ 15 - 11.93 = 3.068
Perimeter of ∆AEC = AE + EC + AC
Which gives;
The perimeter of ∆AEC = 11.93 + 3.068 + 10 ≈ 25
The perimeter of ∆AEC = 25 cmLearn more about the rule of sines and cosines here:
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move the dot -(-D) on the number line
Answer:
the answer is 1/2
Step-by-step explanation:
-(-D) = -(-1/2)
2 negatives make a positive so it would be 1/2 or in other cases, 0.5
Compare these three ratios using fractions.
3 to 2 5:6 8 to 12
Think about the steps you could take to compare the ratios using fractions.
The first step is to write the ratios as fractions.
The next step is to use a
to rewrite the fractions.
Finally, compare the
to help you order the ratios.
Answer:
i think it would be greatest common factor
Step-by-step explanation:
Susan needs material for her school project. She buys 3.75 yards of material at $5.72 a yard. What is the total cost of the material? Round to the nearest cent.
Answer: $21.45
Step-by-step explanation:
FACTS:
1 yard costs $5.72.
She bought 3.75 yards
Total cost= cost per yard x number of yards
Total: t
t= 5.72x3.75
t= $21.45
She spent $21.45 for 3.75 yards of material
Find the sale price using the following numbers.
Original price: $180; Rate of discount: 15%
Please help me to answer this question!
TYSM!!!!!
Answer:
$180 - (15% * $180) = $153
Step-by-step explanation:
Answer:
$153
Step-by-step explanation:
Hello!
Original Price: $180
Original Percentage: 100% (multiplier = 1)
Discount: 15% (multiplier = 0.15)
Given that the Original Percentage is 100% and the Discount is 15%, we are trying to find 85% of the Original Price.
Sale Price: 85% of Original Price (multiplier = 0.85)
SP = 85% of OPSP = 0.85(180)SP = 153The sale price is $153.
two numbers are the ratio of 2:7. their sum is 63. what is the larger number?
Answer:
49
Step-by-step explanation:
step 1: Add the ratios 2:7 which is 2+7=9
step 2: divide the bigger ratio (7) by the total calculated in step 1 (9) and multiply by the total number given (63)....
step 3: we have 7/9×63 which is 49
therefore the bigger number is 49
Determine whether it’s a change in increase or decrease then find the person, make sure to ROUND to nearest whole percent:
ALSO THE ANSWER IS NOT 182%
1994 cost: $171.33 and 1995 cost: $201.59
Answer:
it is 82%
Step-by-step explanation:
Which of the coordinate pairs below are separated by a vertical distance of greater than 5 units? Select all that apply.
A)(-1, −52) and (-1, −32)
B) (1.8, -3.4) and (1.8, 2.2)
C) (-3.5, -4.2) and (-3.5, 1.3)
D) (4, 5) and (4, 1)
Answer: A
Step-by-step explanation:
A. yes because -52 and -32 are separated by a distance of 20 units
B. no because -3.4 and 2.2 are not separated by more than 5 units
C. no because -4.2 and 1.3 are not separated by more than 5 units
D. no becasue 5 and 1 are not separated by more than 5 units
Answer:
A, B, C
Step-by-step explanation:
A coordinate is written as (x, y) where:
x is the horizontal distance of the point from the origin.y is the vertical distance of the point from the origin.For a pair of coordinates to be separated by a vertical distance of greater than 5 units, the difference in their y-values should be greater than 5. To find the difference between two values, subtract the smaller value from the larger value.
A. (-1, -52) and (-1, -32)
Difference in y-values: (-32) - (-52) = 20
B. (1.8, -3.4) and (1.8, 2.2)
Difference in y-values: (2.2) - (-3.4) = 5.6
C. (-3.5, -4.2) and (-3.5, 1.3)
Difference in y-values: (1.3) - (-4.2) = 5.5
D. (4, 5) and (4, 1)
Difference in y-values: 5 - 1 = 4
Therefore, coordinate pairs A, B and C are all separated by a vertical distance of greater than 5 units.
15. The total mass of 6 similar bags of salt is 4.5 kg. What is the mass of each bag of salt rounded to 1 decimal place? Give the answer in kilograms.
Answer:
0.7kgStep-by-step explanation:
Total mass of the bags of salt = 4.5kgnumber of bags of salt = 6To find the mass of each bag of salt, we divide the total mass by the number of salt bags we have which is 6Therefore 4.5 ÷ 6 = 0.75 KgMass of each bag of salt = 0.75 Kg0.75Kg rounded to ONE decimal place = 0.7 KgHope this helps.Good luck ✅.8.45 At some point in the season, the Unicorns had won 60% of their basketball games. After that point, they won 8 more games and lost 2 , to finish the season having won 65% of their games. How many games did the Unicorns play during the season?
Hint: Assign a variable.
Answer:
The total number of games won by Unicorn is 40.
Step-by-step explanation:
We are given with a word problemWe are asked to find the number of unicorns played during the seasonWe can do this in two stepsStep 1: Finding the win percentage
Step 2: Finding the number of unicorns played during the season
Step 1 of 2
Let the number of games played by unicorn be x.The unicorn won 60% of the first x-10 games That is [tex]$\frac{60}{100} \times(x-10)$[/tex]
Combining the 8 games we get,
[tex]$$\begin{gathered}\frac{60}{100}(x-10)+8=\frac{60}{100} \times x-\frac{60}{100} \times 10+8 \\0.6 x-6+8=0.6 x+2\end{gathered}$$[/tex]
Step 2 of 2
The unicorn totally won 65% of the games played.
That is [tex]$\frac{65}{100} \times x=0.65 x$[/tex]
Equating both the equation gives
[tex]$$\begin{gathered}0.6 x+2=0.65 x \\2=0.65 x-0.6 x \\2=0.05 x \\\frac{2}{0.05}=x \\40=x\end{gathered}$$[/tex]
Write the following in algabraic expression: the sum of the number a and three times the square of the number b
Answer:
a+3b^2
Step-by-step explanation:
Write each ratio as a fraction in lowest terms:
Q1 - 24.8 to 13.4
Q2 - 1.5 to 4.5
Answer:
124/67 and 1/3
Step-by-step explanation:
The second ratio is 1.5/4.5, which readily reduces to 1/3.
Dividing both numerator and denominator of 24.8 / 13.4 by 2 yields the simpler 12.4 / 6.7 or 124/67. This latter result cannot be reduced.
2 ACTIVITY: Estimating a Percents
Work with a partner. Use a model to estimate the answer to each question. c. 18 is what percent of 40?
Answer: 45%
Step-by-step explanation:
Converting the word problem into words, we have:
18= x/100*40
Solving for it, we get that x=45.
You randomly choose one of the tiles above. Without replacing the first tile, you randomly choose a second tile. Find the probability of the compound event.
22. Choosing a red tile and then a vowel
Answer:
none
Step-by-step explanation:
8.42 Three bags of jelly beans contain 26,28 , and 30 beans. In each bag, the percent of the beans that are yellow is 50%, 25%, and 20%, respectively. All three bags of candy are dumped into one bowl. What percent of the beans in the bowl are yellow? Round your answer to the nearest integer.
Answer:
Step-by-step explanation:
Figure out the number of yellow beans in each bag:
Bag A: 0.5*26 = 13 beans
Bag B: 0.25*28 = 7 beans
Bag C: 0.2*30 = 6 beans
The total number of beans in the bowl: 26+28+30 = 84
Total number of yellow beans: 13+7+6 = 26
Percentage of yellow beans: 26/84 *100 = 30.9523
Rounded answer: 31%
Answer:
The percentage of yellow beans in the bowl of 84 is approximately 31%.
Step-by-step explanation:
We are given with a word problemWe are asked to find the total percentage of yellow jelly beans We can do this two stepsStep 1: Finding the number of yellows beans in each bags
Step 2: Finding the total percentage of yellow beans
Step 1 of 2
We are given that the three bags contain 26,28 and 30 beans totally in which the percent of yellow beans are 50%, 25% and 20% respectively.
We have to find the number of yellow beans in each bag.
[tex]$=\frac{50}{100} \times 26$$[/tex]
The number of yellow beans in first bag
[tex]$$\begin{aligned}&\frac{1}{2} \times 26=13 \\&=\frac{25}{100} \times 28\end{aligned}$$[/tex]
The number of yellow beans in second bag
[tex]$$\begin{aligned}&\frac{1}{4} \times 28=7 \\&=\frac{20}{100} \times 30 \\&\frac{1}{5} \times 30=6\end{aligned}$$[/tex]
The number of yellow beans in third bag
Step 2 of 2
From the first step we got the number of yellow beans in each bags.
The total number of yellow beans in the bowl =13+7+6
The total number of beans in the bowl
[tex]$$\begin{aligned}=26 &+28+30 \\=& 84 \\&=\frac{26}{84} \times 100\end{aligned}$$[/tex]
The percentage of yellow bean in the bowl
[tex]$$\begin{gathered}\approx 0.3095 \times 100 \\\approx 0.31 \times 100 \\\approx 31\end{gathered}$$[/tex]
Write A story that could represent This problem 2/6 x 3/4
Answer:
Bob at the store
Step-by-step explanation:
Bob is at a store and wants to buy a banana, last time he checked it costed 2/6 of a dollar. Now it costs 3/4 times more.
On a snowy day 85% of the students of Wilson high school were present. If 572 of the students were present, how many students were enrolled at the school?
Answer:
673
Step-by-step explanation:
okay so uh this is my way and the answer works so like yea teachers dont show like this but ii figured this works
okay so
85/100 = 572/?
so if you divide 85 by 85 its gonna equal 1 and 1 times 100 is gonna be 100
useing the same concept, it should be the same with 572 , but instead of divideing by 572, divide by 85.
basically 572/85
okay now thats gonna give you 6.72941176471 thats vasically 1% of the population.
so multiply 6.72941176471 * 100
so now you have
672.941176471 and you can round this to 673 kids.
and you know its right since 85% of 673 is 572.05 and you can sound to 572
Answer:
673 students
Step-by-step explanation:
Divide the number of students who applied and the decimal of the percentage they represent.
85% = 85/100 = 0.85
572/.85 = 673
Hope this helps
f(x)=(5x+3)(x−2)(3x+7)(x+5) has zeros at x = -5, x = -7/3, x = 2
What is the sign of f on the interval -7/3 < x < -3/5?
The sign of f on the interval -7/3 < x < -3/5 is always positive.
How to solve for the sign on the intervalWe have the equation
(5x+3)(x−2)(3x+7)(x+5) > 0
Now when f(x) > 0
Then -7/3 < x < -3/5
This would tell us that the sign would become positive when it changes from the less than to greater than sign
Complete Questionf(x)=(5x+3)(x-2)(3x+7)(x+5) has zeros at x=-5, x=-7/3, x=-3/5, and x=2
What is the sign of f on the interval -7/3<x<-3/5?
answer choices
f is always positive on the interval
f is always negative on the interval
f is sometimes positive and sometimes negative on the interval
f is never positive or negative on the interval
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7. Tyrone is thinking of a number. In his number:
- The digit 4 has a value of 0.04
- The digit 3 is in both the ones and tens places.
- The digit 5 is in the tenths place.
- The digit in the ones place is 2 more than the digit in the thousandths place.
What is Tyrone's number?
____ ____ . ____ ____ ____
Answer:
1. 72.33.24. none5.none6.97. 08. 4
Step-by-step explanation:
A camera usually sells for $68. Because it was slightly damaged, it sold for $59.90, what was the rate of the discount to the NEAREST PERCENT?
8.46 If 100 is decreased by a% and the result is decreased by b%, then what is the total percent decrease (in terms of a and b)? (You can assume that both a and b are between 0 and 100.)
Answer:
The total percent decrease is [tex]$a+b-\frac{a b}{100}$[/tex]
Step-by-step explanation:
We are given with a word problemWe are asked to find the total percentage decreaseWe can do this in two stepsStep 1: Finding the two percentage decrease
Step 2: Finding their difference
Step 1 of 2
Let the decrease by a% be 100-a
Then b% decrease is
[tex]$$\begin{aligned}\frac{b}{100} \times(100-a) &=\frac{100 b-a b}{100} \\\frac{100 b}{100}-\frac{a b}{100} &=b-\frac{a b}{100}\end{aligned}$$[/tex]
Step 2 of 2
The percentage difference between the two percentages is,
[tex]$$\begin{aligned}&(100-a)-\left(b-\frac{a b}{100}\right)=100-a-b+\frac{a b}{100} \\&100-a-b+\frac{a b}{100}=100-\left(a+b-\frac{a b}{100}\right)\end{aligned}$$[/tex]
Since 100 is the total percent [tex]$a+b-\frac{a b}{100}$[/tex] is the percentage decrease.
One of the angles in a right triangle is 20°. A median, an angle bisector, and a height are all drawn from the right angle.
a)Find the angle measure between the median and angle bisector.
b)Find the angle measure between the angle bisector and the height.
Answer: I would say A
Step-by-step explanation: The reason I say A is because One to find the angle you have to add( Okay I'm in 8th grade and My brain is slow so please don't judge) but maybe try adding and doing division? I'm not sure
7. 1 bag of beans weighs 0.7 lb. What is the weight in pounds of 2.5 bags of beans?
Write an equation showing the relationship between the number of baskets (b) made from outside the three-point line and the number of points scored (p).
Josh spent 8 hours in the gym last week.His goal was to spend 12 hours in the gym. What percent of the goal did he meet?
Answer:
2/3 or 66%
Step-by-step explanation:
If you divide 12 into 3 groups you get 4. 4 + 4 = 8 therefore 8/12 = 66%
find the solution B=√2+√3-√2-√3
Answer:
[tex]B=\sqrt{2}[/tex]
Step-by-step explanation:
Original equation:
[tex]B = \sqrt{2+\sqrt{3}} - \sqrt{2 - \sqrt{3}}\\[/tex]
Square both sides:
[tex]B^2=(\sqrt{2+\sqrt{3}})^2 + 2(\sqrt{2+\sqrt{3}} * (-\sqrt{2 - \sqrt{3}}) + (-\sqrt{2-\sqrt{3}})^2[/tex]
Cancel out the square roots and squares:
[tex]B^2=2+\sqrt{3}}+ 2(\sqrt{2+\sqrt{3}} * (-\sqrt{2 - \sqrt{3}}) + 2-\sqrt{3}[/tex]
Add the sqrt(3) and -sqrt(3) as well as 2 and 2
[tex]B^2=4 + 2(\sqrt{2+\sqrt{3}} * (-\sqrt{2 - \sqrt{3}})[/tex]
Use the identity: [tex]\sqrt{a} * \sqrt{b} = \sqrt{a * b}[/tex] to rewrite the two square roots being multiplied:
[tex]B^2=4 + 2(-\sqrt{(2+\sqrt{3}) * (2 - \sqrt{3}}))[/tex]
Use difference of squares: [tex](a-b)(a+b) = a^2-b^2[/tex]
[tex]B^2=4 + 2(-\sqrt{2^2-\sqrt{3}^2})[/tex]
Square both sides
[tex]B^2=4 + 2(-\sqrt{4-3})[/tex]
Subtract:
[tex]B^2=4 + 2(-\sqrt{1})[/tex]
Evaluate square root of 1:
[tex]B^2=4 + 2(-1)[/tex]
Multiply
[tex]B^2=4 -2[/tex]
Subtract
[tex]B^2=2[/tex]
Take square root of both sides:
[tex]B=\sqrt{2}[/tex]
7.6.3. A kangaroo chases a rabbit that starts 150 feet ahead of the kangaroo. For every 12 -foot leap of the kangaroo, the rabbit makes a 7 -foot leap. How many leaps will the kangaroo have to make to catch up to the rabbit if the two animals always leap at the same time?
Answer:
The number of leaps will the kangaroo have to make to catch up to the rabbit if the two animals always leap at the same time is 30 times.
Step-by-step explanation:
Given:
A kangaroo chases a rabbit that starts 150 feet ahead of the kangaroo.
For every 12 -foot leap of the kangaroo, the rabbit makes a 7 -foot leap.
Find:
the number of leaps will the kangaroo have to make to catch up to the rabbit if the two animals always leap at the same time
Step 1 of 1
The kangaroo gains 5 feet on every leap.
The kangaroo must gain 150 feet total,
so it must jump [tex]\frac{150}{5}=30$[/tex] times to catch the rabbit.
Kangaroo needs 30 leaps to make to catch up to the rabbit if the two animals always leap at the same time.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
A kangaroo chases a rabbit that starts 150 feet ahead of the kangaroo.
For every 12 -foot leap of the kangaroo,
the rabbit makes a 7 -foot leap.
Let n be the number of leaps.
According to the question:
We have the equation.
To solve for x;
12x = 7x + 150
12x - 7x = 150
5x = 150
x = 150/5
x = 30
Therefore, the Kangaroo needs 30 leaps to catch the rabbit.
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Write the percent as a decimal. 8. 55%
Answer:
0.0855
hope this is helpful!
Write the percent as a decimal.
15. 166%
Evaluate.
4 to the power of 3 + (-2) to the power of 4
Answer:
4
Step-by-step explanation:
3+(-2) is the same as 3-2 which is 1. and since with multiple exponents you work from the top you have 4 to the power of 1^4. 1^4 is 1, so it's 4^1, which is 4.
If data for the topics below were collected and displayed in a frequency table, which topic would most likely need to be shown in intervals?
(A) favorite food
(B) heights of trees
(C) eye color
(D) foot length of newborn babies