The compound inequality that describes the elevation x of Ted's house with respect to Sakura's house is: D. 113 < x - 15 < 120.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).Based on the information provided, the minimum and maximum heights for Sakura's house can be represented by this compound inequality:
113 < x < 120
Since Ted lives about 15 meters below her, compound inequality would be rewritten as follows:
113 < x - 15 < 120.
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if it takes 6 men 25 hours to dig 5 holes, how many hours does it take to dig 5 holes with 10 men
Answer: Answer is 15 hours
Step-by-step explanation:Given 6 men dig 5 holes in 25 hours
Therefore 10 men will take to dig 5 holes is
workers(1) × time(1) = workers(2)×time(2)
(This formula is used when Total work is same)
where workers(1)= 6 men
Time (1) = 25 hours
workers (2) = 10 men
We have find out Time(2)=T(2)
by applying above formula
6×25=10×T2
after simplify
T2= 15 hours
An oatmeal cookie recipe calls for 1/3 cup of butter to make 12 cookies. Hilda needs to make 36 cookies for the bake sale. How many cups of butter will she need?
Answer:3/3 cup or 1 full cup
Step-by-step explanation:1/3 cup=12
2/3 cup=24
3/3 or 1 whole cup=36
A silversmith combined pure silver that cost $34.48 per ounce with 51 oz of a silver alloy that cost $25.35 per ounce. How many ounces of pure silver were used to make an alloy of silver costing
$28.87.per.ounce?
32 ounces of pure silver were used to make the silver alloy.
Here, we are given that a silversmith combines pure silver that costs $34.48 per ounce with 51 oz of a silver alloy that cost $25.35 per ounce.
Let the amount of pure silver = x oz
Cost of pure silver = $34.48 per ounce
Thus, total cost of pure silver = $34.48x
Similarly, amount of silver alloy = 51 oz
Cost of silver alloy = $25.35 per ounce
Thus, total cost of silver alloy = 25.35 x 51 = $1292.85
Now, the total weight of the new silver allow formed = (x + 51) Oz
and the cost of this new allow = $28.87 per ounce
Thus, the total weight of the new alloy = $28.87 (x + 51)
Hence, we can form the following equation-
$34.48x + $1292.85 = $28.87 (x + 51)
34.48x + 1292.85 = 28.87x + 1472.37
34.48x - 28.87x = 1472.37- 1292.85
5.61x = 179.52
x = 179.52/ 5.61
x= 32
Hence, 32 ounces of pure silver were used to make the silver alloy.
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Two cyclists, 54 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as
the other. If they meet 3 hours later, what is the speed (in mi/h) of the faster cyclist?
a. Write an equation using the information as it is given above that can be solved to answer this problem.
Use the variable r to represent the speed of the slower cyclist.
b. What is the speed of the faster cyclist?
mi/hr
The equation that we need to solve is:
(S + 2*S)*3h = 54mi
The speed of the slower cyclist is 6 mi/h
The speed of the faster cyclist is 12 mi/h.
How to write an equation that models this situation?Let's define S as the speed of the slower cyclist, thus 2*S will be the speed of the other cyclist.
They travel in opposite directions, and after 3 hours the travel a combined distance of 54 miles, then we can write the equation:
(S + 2*S)*3h = 54mi
With that equation, we can determine the speeds of the cyclists.
Solving for S we get:
(S + 2*S)*3h = 54mi
3*S = 54mi/3h = 18 mi/h
S = (18 mi/h)/3 = 6 mi/h
Then the speed of the slower cyclist is 6 miles per hour, and the speed of the faster cyclist is twice that, so it is 2*6 mi/h = 12 miles per hour.
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A total of 491 tickets were sold for the school play. They were either adult tickets or student tickets. There
were 60 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
Adult tickets = 276
Step-by-step explanation:
a + s = 491 Eq. 1
a = s + 61 Eq. 2
a = adult tickets
s = student ticket
Replacing Eq. 2 in Eq. 1:
(s+61) + s = 491
2s + 61 = 491
2s = 491 - 61
2s = 430
s = 430/2
s = 215
from the Eq. 2
a = s + 61
a = 215 + 61
a = 276
Check:
from Eq. 1:
a + s = 491
276 + 215 = 491
Kadeem has $680 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
• He buys a new bicycle for $470.65.
• He buys 2 bicycle reflectors for $7.87 each and a pair of bike gloves for $15.18.
• He plans to spend some or all of the money he has left to buy new biking outfits for $50.98 each.
Write and solve an inequality which can be used to determine x, the number of outfits Kadeem can purchase while staying within his budget.
Total money with Kadeem = $680
Money spent by him on a new bicycle = $470.65
Money left with him after buying a new bicycle = 680 - 470.65 = 209.35
Money spent by him on 2 bicycle reflectors = 7.87*2 = $15.74
Money left with him after buying reflectors = 209.35 - 15.74 = $193.61
Money spent by him on bike gloves = $15.18
Money left with him after buying biking outfits: 193.61 - 15.18 = $178.43
Cost of each outfit = $50.98
Let the number of outfits Kadeem can buy be x, therefore formulating the equation we get:
50.98x< = 178.43
x< = 3.5
So, Kadeem can buy 3 outfits while staying within budget
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15% of the students in the 6th grade wear glasses. If 12 students wear glasses, how can you determine the number of students in the 6th grade? Explain your reasoning.
Answer: There are 80 people in the 6th grade
Step-by-step explanation:
A particular shade of paint is made by mixing five parts of red paint with seven parts of blue paint. To make the correct shade, Shannon makes 12 quarts of blue paint with 8 quarts of red paint. Did Shannon mix the correct shade? Explain.
We get that Shannon did not mix the correct shade as the ratios are not equal.
We are given that a particular shade of paint is made by mixing five parts of red paint with seven parts of blue paint.
This means that the ratio of the paints in that shade is
Red : Blue = 5 : 7.
Now, we are also given that to make the correct shade, Shannon makes 12 quarts of blue paint with 8 quarts of red paint.
Here the ratio becomes:
Red : Blue = 8 : 12
= 4 : 6
= 2 : 3
Now, since both the ratios are not equal, he did not mix the correct shade.
Therefore, we get that Shannon did not mix the correct shade as the ratios are not equal.
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Find the next three terms in each sequence
Nina can swim 4 laps in 2 1/3 minutes. At this rate, how many laps can she swim in one minute
lap(s) in one minute
nina can swim 8/7 laps in one minute
given that
nina can swim 4 laps in 7/2 minutes
we have to calculate that how many laps can nina swim in 1 minute
then 4 laps= 7/2 minutes
then 4*2 /7 =1 minute
8/7=1 minute
thus nina can swim 8/7 laps in one minute
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Convert 40 miles per hour to feet per second.
Translate this phrase into an algebraic expression.
67 decreased by twice a number
Use the variable n to represent the unknown number.
Answer:
2n-67
Step-by-step explanation:
Twice a number means 'multiply by 2' so we can write 2 x n. We can also write this in a simpler form- 2n
'67 decreased' means minus 67 off your answer so therefore the answer must be:
2n-67
Love answering your questions by the way :)
HELP ME! AND PLSSSS EXPLAIN!
Ariel received so many flowers for her birthday that they wouldn't all fit on her desk. By
lunch, her office was decorated with 7 flower bouquets, 5 of which were rose bouquets.
If Ariel randomly selected 4 bouquets to take home, what is the probability that all of them
are rose bouquets?
Write your answer as a decimal rounded to four decimal places.
The probability that all of them are rose bouquets is 0.143.
How to calculate the probability?It should be noted that this question is about probability without replacement.
The probability of picking a rise bouquet is 5/7. It should be noted that each value decreases since Ariel is selecting 4 bouquets.
The probability that all of them are rose bouquets will be:
= 5/7 × 4/6 × 3/5 × 2/4
= 5/7 × 2/3 × 3/5 × 1/2
= 30/210
= 1/7
= 0.143
The probability is 0.143.
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please help
maths geometry
Step-by-step explanation:
since both shapes are totally symmetric, a few answers are obvious :
(1) F2 = F1 = 50°
(3) B1 = D1 = 20°
last but not least, D2 = B2.
using the fact that the sum of all angles in a triangle is always 180°.
and that the sum of all angles sind a single point on one side of a line is also always 180° :
in the triangle CDF the inner angle C is
C = 180 - 20 - 50 = 110°.
therefore, C1 = 180 - 110 = 70°
E1 = 90° (a major rule for the diagonals of a kite).
D2 = 180 - 90 - 70 = 20°
and so, B2 = 20°
(2) D2 = 20°
(4) B2 = D2 = 20°
en que se parece el Palacio Versalles y el Palacio el escorial
Answer:
Las primeras y quizá más sobresaliente características del monasterio y palacio real San Lorenzo de el Escorial son la composición geométrica y simétrica del edificio, el uso de los espacios cuadrados, y la preferencia por lo poco ornamentado, esto resulta bastante contrastante con la arquitectura regular de Europa, en la cual, sobre todo en Italia había predilección por las líneas curvas, los espacios ovalados, circulares, asimétricos y la predominación de un estilo muy ornamanetado con la intención de mover intensamente al espectador ante la unión del poder terrenal y espiritual. Existen rasgos en común con la arquitetura barroca foránea, como el uso de lo clásico como modelo riguroso y la necesidad de representar la grandiosidad e imponencia de la nobleza en la magnitud del palacio. Juan de Herrera fue el arquitecto del rey Felipe II, y quien impuso como estilo español arquitectónico barroco lo poco ornamentado, el recuerdo de lo clásico y los edificios de líneas rectas y grandes magnitudes.
determina la distancia recorrida por un automóvil si primero viajo 2 horas a 80 Km/h ,después 3 horas a 110 km/h y por ultimo 30 minutos a 40 km/h
Answer: Total distance travelled is 510 km
Step-by-step explanation:
it is given that an automobile travels for
2 hours at 80km/h
3 hours at 110km/h
30 min at 40km/h
to find distance=x(let)
since
distance = speed * time
so
x= 80*2 +110*3 +40*(1/2) [since 1 hour =60 min so 30 min =1/2 hour]
x=160+330+20
x=510
hence total distance travelled is 510 km
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where RS=8y+5, ST=3y+4, and RT=97.
a. What is the value of y?
b. Find RS and ST
The answer of part a is y = 8
The answer of part b is RS = 69, ST = 28
Step-by-step explanation:
a. Since RT = RS + RT, subsitute values of RS and RT in the equation
97 = (8y + 5) + (3y + 4)
97 = 11y + 9
97 - 9 = 11y
88 = 11y
y = 8
b. Subsitute the value of y in RS and ST just like done in part a
Kendra is making a large salad for a party. She buys lettuce for $2.25 per pound and tomatoes for $2.65 per pound. She spends at
least $8.
Let x represent the number of pounds of lettuce that Kendra buys. Let y represent the number of pounds of tomatoes that Kendra
buys.
Which inequality represents this situation?
Answer:
(D)
Step-by-step explanation:
Given that Kendra is making a large salad for a party. She buys lettuce for $2.25 per pound and tomatoes for $2.65 per pound. She spends at least $8.
x represent the number of pounds of lettuce that Kendra buys and y represent the number of pounds of tomatoes that Kendra buys.
We are to select the inequality that represents the situation.
We have
total amount of money that Kendra spends on lettuce is given by
and the total amount of money that she spends on tomatoes is
Therefore, the inequality can be written as
Thus, option (D) is CORRECT.
A projectile is fired straight up from ground level. After t seconds, its height above the ground is s feet, where s= - 16t² + 128t
For what time period is the projectile at least 192 feet above the ground?
Select the correct choice below and fill in the answer boxes to complete your choice.
OA. For the time period between (and inclusive of)
(Simplify your answers.)
OB. For the time period between (and not inclusive of)
(Simplify your answers.)
seconds and
seconds and
seconds the projectile will be at least 192 ft above the ground.
seconds the projectile will be at least 192 ft above the ground.
For the time period of the projectile at least 192 feet above the ground is between 2 second and 6 second
Since s=128t-16t2, we want to know the 2 times where 128t-16t2=192, as those two values will be the begin and end times of the interval in question. We can rewrite that equation in standard quadratic equation form:
16t2-128t+192=0 or, simplified, 8t2-64t+96=0
or t2-8t+12=0
since it is now in quadratic form, we can solve using the quadratic formula:
t = 2 and 6
So the time period from approximately 2 second and 6 second has the projectile above 192 feet.
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Consider the following sequence. -5,5,15,25,35. Write an explicit formula for the sequence.
This sequence's explicit formula is [tex]a_n=-5+(n-1)*10[/tex]
What is a sequence?
A sequence is indeed an acknowledged group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has individuals. The length of the series is the number of components (potentially infinite).The convergence features of sequences can be used to analyze functions, spaces, as well as other mathematical structures in a variety of mathematical fields. In particular, sequences serve as the foundation for series, which are crucial to analysis and differential equations.The common distinction is equal to:
10
The sequence's total is equal to:
40
This sequence's explicit formula is:
[tex]a_n=-5+(n-1)*10[/tex]
This sequence's recursive formula is:
[tex]a_n=a_((n-1))+10[/tex]
Next terms:
-5,5,15,25,35,45,55,65,75,85,95...
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A store has clearance items that have been marked down by 60% they are having a sale advertising an additional 30% off clearance items. What percent of the original price do you end up paying?
What is 1/3 of 1/4 what is 1/3 1/4
Answer:
%8.3 or 8.3/100
Step-by-step explanation:
o the answer is 7/12 because 1/3 plus 1/4 is 4/12 + 3/12 is 7/12
What is the approximate value for
813 divided by 13
A. 30
B. 35
C. 40
D. 45
None of the options is correct. 813 divided by 13 equals 62.538461, whose approximate value is 62
13 times 813 equals 62.538461.
813/13 produces a non-terminating, repeating decimal as a consequence.
The repeating pattern seen above, 538461, is referred to as repetend and is shown with an overline and vinculum.
Another typical parenthetical remark is this one: 813/13 = 62.(538461): However, it's likely that you may see the reptend marked with an ellipsis in daily use: 813 / 13 = 62.538461… .
Decimal 813 divided by 13 equals 62.538461.
In a fraction, 813 is equal to 813/13.
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Have this done correctly for brainliest!
Answer:
expression
Step-by-step explanation:
It's an expression. The expression happens to be a quadratic polynomial.
An equation must have an equal sign.
An equation is a statement that a number or expression equals a number or expression.
Here, there is no equal sign. There is only an expression.
Answer:
This is an expression
8x2+7x-15
00:00
Which equations show you how to find 13 - 6?
A. 7 + 3 = 10, 10+ 3 = 13
B. 6 + 4 = 10, 10+ 4 = 14
C. 6+4 = 10, 10+ 3 = 13
D. 8+2 = 10, 10+ 3 = 13
The number of students at Jefferson School is even.
The number has three digits.
The digit in the tens place is 4.
Write three numbers that could be how many students
there are at Jefferson School.
school
There are a total of 36 possible answers in digit .
What is digits in math?
A digit is a part of a set that, when taken as a whole, makes up a numeration system. A digit is a number in that particular circumstance. The members of the set 0 through 9 make up the digits of the decimal (base-10) Arabic numbering system.Let's assign three blanks for each digit of the unknown number. But let's fill in the tens digit because it is already specified.
_ 4 _
The last digit should be even to make it even. The possible digits for this are 2, 4, 6, and 8. The first digit could be any digit from 1 to 9. Therefore, the possible answers are
142 242 342 442 542 642 742 842 942
144 244 344 444 544 644 744 844 944
146 246 346 446 546 646 746 846 946
148 248 348 448 548 648 748 848 948
Therefore, there are a total of 36 possible answers.
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Lucy’s chocolate bar is 54% cocoa. If the weight of the chocolate bar is 54 grams, how many grams of cocoa does it contain? Round the answer to the nearest tenth
Answer:
29.16 grams
Step-by-step explanation:
To solve this, you have to use the weight of cocoa formula. So the weight of cocoa = 54% percent of chocolate bar's weight which is 54 gram. So weight of cocoa = 54/100*54. This will give you 29.16 grams.
The sum of 4 consecutive even integers is the same as the least of the integers find the integers
The four numbers are: -4, -2 ,0, 2 Answer.
How do you solve this: the sum of four consecutive even integers is equal to least of the integer
Solution: Let the numbers be n, n+2, n+4 and n+6.
Their sum = 4n+12 = n or
3n+12 = , or
3n = -12,
n= -4
therefore we get -4, -2, 0, 2
The four numbers are: -4, -2 ,0, 2 . Answer.
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A conjecture and the paragraph proof used to prove the conjecture are shown. Given: R S T U is a parallelogram. Angle 1 and angle 3 are complementary. Prove: angle 2 and angle 3 are complementary. Parallelogram J K L M. A diagonal segment U S is drawn across the parallelogram. Angle R U S is labeled 1. Angle U S T is labeled 2. A ray is extended diagonally up to the left of UT forming an interior angle labeled as 3. Drag an expression or phrase to each box to complete the proof.
It is given that RSTU is a parallelogram, so RU ∥ ST by the definition of parallelogram.
Therefore, ∠1 ≅ ∠2 by the alternate interior angles theorem, and m∠1 = m∠2 by the angle congruence postulate .
It is also given that ∠1 and ∠3 are complementary, so m∠1 + m∠3 = 90° by the definition of complementary .
By substitution, m∠2 + m∠3 = 90°, and so ∠2 and ∠3 are complementary by the definition of complementary.
How to prove the angles in a Parallelogram?
From the given image of the parallelogram, we are given that;
Angle 1 and angle 3 are complementary.
Now, complementary angles sum up to 90°. Thus;
∠1 + ∠3 = 90°
Now, according to definition of parallelogram, we know that alternate interior angles of a parallelogram are congruent(equal). Thus;
∠1 = ∠2
Since ∠1 = ∠2, then by substitution property into the first equation, we have; ∠2 + ∠3 = 90°
Since the sum of ∠2 and ∠3 is equal to 90°, then we can say that they are both complementary angles.
Thus, we conclude that;
It is given that RSTU is a parallelogram, so RU ∥ ST by the definition of parallelogram.
Therefore, ∠1 ≅ ∠2 by the alternate interior angles theorem, and m∠1 = m∠2 by the angle congruence postulate .
It is also given that ∠1 and ∠3 are complementary, so m∠1 + m∠3 = 90° by the definition of complementary .
By substitution, m∠2 + m∠3 = 90°, and so ∠2 and ∠3 are complementary by the definition of complementary.
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Pls Help me please!!
