Answers
Answer:
1. Their ages are:
Steve's age = 18
Anne's age = 8
2. Their ages are:
Max's age = 17
Bert's age = 11
3. Their ages are:
Sury's age = 19
Billy's age = 9
4. Their ages are:
The man's age = 30
His son's age = 10
Step-by-step explanation:
1. We make the assumption that:
S = Steve's age
A = Anne's age
In four years, we are going to have:
S + 4 = (A + 4)2 - 2 = 2A + 8 - 2
S + 4 = 2A + 6 .................. (1)
Three years ago, we had:
S - 3 = (A - 3)3
S - 3 = 3A - 9
S = 3A - 9 + 3
S = 3A – 6 …………. (2)
Substitute S from (2) into (1) and solve for A, we have:
3A – 6 + 4 = 2A + 6
3A – 2A = 6 + 6 – 4
A = 8
Substitute A = 8 into (3), we have:
S = (3 * 8) – 6 = 24 – 6
S = 18
Therefore, we have:
Steve's age = 18
Anne's age = 8.
2. We make the assumption that:
M = Max's age
B = Bert's age
Five years ago, we had:
M - 5 = (B - 5)2
M - 5 = 2B - 10 .......................... (3)
A year from now, it will be:
(M + 1) + (B + 1) = 30
M + 1 + B + 1 = 30
M + B + 2 = 30
M = 30 – 2 – B
M = 28 – B …………………… (4)
Substitute M from (4) into (3) and solve for B, we have:
28 – B – 5 = 2B – 10
28 – 5 + 10 = 2B + B
33 = 3B
B = 33 / 3
B = 11
If we substitute B = 11 into equation (4), we will have:
M = 28 – 11
M = 17
Therefore, their ages are:
Max's age = 17
Bert's age = 11.
3. We make the assumption that:
S = Sury's age
B = Billy's age
Now, we have:
S = B + 10 ................................ (5)
Next year, it will be:
S + 1 = (B + 1)2
S + 1 = 2B + 2 .......................... (6)
Substituting S from equation (5) into equation (6) and solve for B, we will have:
B + 10 + 1 = 2B + 2
10 + 1 – 2 = 2B – B
B = 9
Substituting B = 9 into equation (5), we have:
S = 9 + 10
S = 19
Therefore, their ages are:
Sury's age = 19
Billy's age = 9.
4. We make the assumption that:
M = The man's age
S = His son's age
Therefore, now, we have:
M = 3S ................................... (7)
Five years ago, we had:
M - 5 = (S - 5)5
M - 5 = 5S - 25 ................ (8)
Substituting M = 3S from (7) into (8) and solve for S, we have:
3S - 5 = 5S – 25
3S – 5S = - 25 + 5
-2S = - 20
S = -20 / -2
S = 10
Substituting S = 10 into equation (7), we have:
M = 3 * 10 = 30
Therefore, their ages are:
The man's age = 30
His son's age = 10
Related Questions
An evergreen tree is supported by a wire extending from 1.5 feet below the top of the tree to a stake in the ground. The wire is 24 feet long and forms a 58° angle with the ground. how tall is the tree?
Answers
Answer:
Approximately [tex]21.9\; \rm ft[/tex] (assumption: this tree is perpendicular to the ground.)
Step-by-step explanation:
Refer to the diagram attached (not drawn to scale.)
Label the following points:
[tex]\rm S[/tex]: stake in the ground.[tex]\rm A[/tex]: top of the tree.[tex]\rm B[/tex]: point where the wire is connected to the tree. [tex]\rm C[/tex]: point where the tree meets the ground.Segment [tex]\rm SB[/tex] would then denote the wire between the tree and the stake. The question states that the length of this segment would be [tex]24\; \rm ft[/tex]. Segment [tex]\rm AB[/tex] would represent the [tex]1.5\; \rm ft[/tex] between the top of this tree and the point where the wire was connected to the tree.
The question is asking for the height of this tree. That would correspond to the length of segment [tex]\rm AC[/tex].
If this tree is perpendicular to the ground, then [tex]\rm \angle A\hat{C}S =90^\circ[/tex]. Triangle [tex]\rm \triangle BCS[/tex] would be a right triangle with segment [tex]\rm SB[/tex] as the hypotenuse.
The question states that the angle between the wire (segment [tex]\rm SB[/tex]) and the ground (line [tex]\rm SC[/tex]) is [tex]58^\circ[/tex]. Therefore, [tex]\rm \angle A\hat{S}C = 58^\circ[/tex].
Notice, that in right triangle [tex]\rm \triangle BCS[/tex], segment [tex]\rm BC[/tex] is the side opposite to the angle [tex]\rm \angle B\hat{S}C = 58^\circ[/tex]. Therefore, the length of segment [tex]\rm BC\![/tex] could be found from the length of the hypotenuse (segment [tex]\rm SB[/tex]) and the cosine of angle [tex]\rm \angle B\hat{S}C = 58^\circ\![/tex].
[tex]\displaystyle \cos\left(\rm \angle B\hat{S}C\right) = \frac{\text{length of $\mathrm{BC}$}}{\text{length of $\mathrm{SB}$}} \quad \genfrac{}{}{0em}{}{\leftarrow\text{opposite}}{\leftarrow \text{hypotenuse}}[/tex].
Rearrange to obtain:
[tex]\begin{aligned}& \text{length of $\mathrm{BC}$} \\ &= (\text{length of $\mathrm{SB}$}) \cdot \cos\left(\angle \mathrm{B\hat{S}C}\right)\\ &= \left(24\; \rm ft\right) \cdot \cos\left(58^\circ\right) \approx 20.35\; \rm ft\end{aligned}[/tex].
In other words, the wire is connected to the tree at approximately [tex]20.3\; \rm ft[/tex] above the ground.
Combine that with the length of segment [tex]\rm AB[/tex] to find the height of the entire tree:
[tex]\begin{aligned}&\text{height of the tree} \\ &= \text{length of $\mathrm{AC}$} \\ &= \text{length of $\mathrm{AB}$} + \text{length of $\mathrm{BC}$}\\ &\approx 20.35\; \rm ft + 1.5\; \rm ft \\ &\approx 21.9\; \rm ft\end{aligned}[/tex].
Which of the following situations results in a sum of 1 1/2 ? Select all that apply .
1. I painted 5/8 of one room and 7/8 of another .
2. I gained 6 1/2 pounds and my wife lost 8 pounds .
3. I had 4 1/4 bottles of juice and drank 1 3/4 of them .
4. I cut 3 1/3 inches from my grass. The grass grew 1 5/6 inches over the next week .
5.I used up 1/4 of a pound of coffee and bought 1 1/4 of a Pound of coffee from the store .
6. I used 3/4 of a pound of ground beef to make burgers and purchased 2 1/4 of a pound of ground beef .
Answers ASAP!!!!
Answers
Answer:
A, E, And D
Step-by-step explanation:
i did the quiz :)
A survey of U.S. adults found that 67% oppose raising the Medicare eligibility age from 65 to 67. You randomly select 80 U.S. adults S and ask them how they feel about raising the Medicare eligibility age from 65 to 67. Find the probability that the number who oppose raising the age is (a) at least 65, (b) exactly 50, and (c) more than 60, and (d) identify any unusual events. Explain.
Answers
Answer:
0.477%
6.55%
5.05%
Event in question (a)
Step-by-step explanation:
Given that:
p = 0.67 ; n = 80
Using Normal approximation :
Mean (m) = np = 80 * 0.67 = 53.6
Standard deviation (s) = sqrt(np(1-p)) = sqrt(80*0.67*0.33) = 4.2057
probability that the number who oppose raising the age is
(a) at least 65
65 - 0.5 = 64.5 = x
Z = (x - m) / s
Z = (64.5 - 53.6) / 4.2057 = 2.592
P(Z ≥ 2. 592) = 0.004771 (Z probability calculator)
(b) exactly 50
x = 50 + 0.5 = 50.5 ; x = 50 - 0.5 = 49.5
Z = (50.5 - 53.6) / 4.2057 = - 0.737
Z = (49.5 - 53.6) / 4.2057 = - 0.974
P(Z < - 0.737) - p(Z < 0.974) (Z probability calculator)
0.23056 - 0.16503 = 0.06553
(c) more than 60, and (d) identify any unusual events
x = 60 + 0.5 = 60.5
Z = (60.5 - 53.6) / 4.2057 = 1.64
P(Z > 1.64) = 0.0505
D.) Event with probability of less than 5%, which is event in (a) with probability of 0.477%
-2 (x + 4) – (3x – 8)
What it equals
Answers
Answer:
-2x+-8-3x-8
Step-by-step explanation:
-2 times x =-2x
-2 times 4=-8
Answer:
x
Step-by-step explanation:
-2 (x + 4) – (3x – 8)
-2x-8-3x+8
x+0
x
Place each pair of angles in the correct column.
Answers
Answer:
congruent: 1 & 8,
congruent & corresponding: , 4&8
supplementary: 2&5, 3&5, 3&4
i don’t see how anything can be congruent AND supplementary unless the angles are both 90.... hope this helped
? QUESTION
Laura is saving money to buy a bike that costs $125. She has $60 and will save an additional $5 each week. In how many weeks will she have enough money
to buy the bike?
Answers
Answer:
13
Step-by-step explanation:
125 - 60= 65
65/5= 13
itll take her 13 weeks
Is 9.78778777... a rational or irrational number?
Answers
Answer:
rational
Step-by-step explanation:
A decking company estimates how many gallons of stain each deck requires before starting construction. Apart from knowing the total area of each deck, which additional quantity will allow the decking company to make an accurate estimation
Answers
Answer:
Concept: Engineering Statistics
To make accurate estimations they need the total volume of the area.Hence they need the area coverage by the selected stain.Solution: Are covered by each gallon of stain This provides an accurate representation to a significant figure.help me pls ill mark brainly
Answers
Answer:
First step: 8% as a decimal is 0.08 if you move the decimal of 8 twice to the left.
Second step: I think it would be 0.08 x 25.
Third step: 2. I'm pretty sure there are 2 people that wear glasses in his class because 0.08 times 25 is 2.
Fourth step: Friendly percent is 10%. It is always even.
Hope this helps!
can u pls help me with this question
and the equations to choose from are
y=k+x
y=k
y=kx
Answers
y=kx
Step-by-step explanation:
That's the formula for direct variation relationships!
The other two answers are nonsense and don't mean anything.
2 - 20
16) Solve the problem.
Use the Associative Property of Addition to find the equivalent expression. Replace the
variable with the given number to prove the expression is equivalent.
* + (4 + 6) = ---
I = 5
Answers
Answer:
The answer is 15=15
Step-by-step explanation:
go to math
way, which is a website
and put your question in and the answer waill come to you!
Which statement is true? 7.11≤−7.1 7.11>−7.1 7.11<−7.1 7.11=−7.1
Answers
Answer:
7.11 > -7.1
Step-by-step explanation:
Please help! I need help on this ! I will give brainliest!
Find the equation of a line that is parallel to the line x = 12 and contains the point (-6,4).
The equation of the parallel line is . (Type an equation.)
Answers
Answer:
x = -6 and x = 12 are parallel
Step-by-step explanation:
they are both vertical lines, one crosses the x-axis at -6, the other at 12
A machine fills boxes at a constant rate. At the end of 35 minutes, it has filled 5 boxes. Which table represents the relationship between the number of minutes the machine fills boxes and the number of boxes it has filled?
Answers
Hope that helps u:)
In 7 minutes machine can fill 1 box.
Given that, a machine fills boxes at a constant rate. At the end of 35 minutes, it filled 5 boxes.
What is the constant rate?A rate of change is constant when the ratio of the output to the input stays the same at any given point in the function. The constant rate of change is also known as the slope. Linear functions will have a constant rate of change.
Now, in 35 minutes machine has filled 5 boxes.
So, 1 box is filled in 35/5=7 minutes.
Therefore, in 7 minutes machine can fill 1 box.
To learn more about the constant rate visit:
https://brainly.com/question/13659182.
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(Will mark brainlest Help please)out of 800 students at icenhower intermediate 208 live inside the city of mansfield
Answers
Answer:
Doesn't this mean that 592 students live outside the city of mansfield?
Step-by-step explanation:
800 - 208
I GIVE BRANLILSET
Maddie prepared 24 kilograms of dough after working 6 hours. How many hours did Maddie work if she prepared 40 kilograms of dough? Assume the relationship is directly proportional.
Answers
Answer:
10 hours
Step-by-step explanation:
24kg dough/6 hours = 4kg dough/hour
4kg dough / 1 hour
*10 *10 (multiply both sides by 10)
---------------------------
40kg dough/10hrs
Write a function formula for g using the function f.
g(x)=
Write a function formula for f using the function g.
f(x)=
Answers
Answer:
g(x) = -f(x+3)
f(x) = -g(x-3)
Step-by-step explanation:
Transformations
Function f can be obtained by knowing function g and vice-versa.
Suppose we know the expression of function f. If we reflect f across the x-axis, we get function g but displaced 3 units to the right.
Thus, we only have to translate the reflected f 3 units to the left:
g(x) = -f(x+3)
Similarly, if g(x) is reflected across the x-axis and translated by 3 units to the right, we get f(x), thus:
f(x) = -g(x-3)
Round 48.47 to the ones place
Answers
Answer:
48.7 I think
Step-by-step explanation:
hears the sender buddy
Answer:
48.5 the 7 is close to 10 so it rounds the 4 to 5
3. Two cars are parked, 150m apart, and on opposite sides of a building. A camera on the top of the building rotates and can view both cars. One car can be viewed at an angle of depression of 370, and the other car can be viewed at an angle of depression of 420. How tall is the building?
Answers
Answer:
The building is 61.5 m tall
Step-by-step explanation:
The image below is a diagram where all the given distances and angles are shown. We have additionally added some variables:
h = height of the building
a, b = internal angles of each triangle
x = base of each triangle
The angles a and b can be easily found by subtracting the given angles from 90° since they are complementary angles, thus:
a = 90° - 37° = 53°
b = 90° - 42° = 48°
Now we apply the tangent ratio on both triangles separately:
[tex]\displaystyle \tan a=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
[tex]\displaystyle \tan 53^\circ=\frac{150-x}{h}[/tex]
[tex]\displaystyle \tan 48^\circ=\frac{x}{h}[/tex]
From the last equation:
[tex]x=h.\tan 48^\circ[/tex]
Substituting into the first equation:
[tex]\displaystyle \tan 53^\circ=\frac{150-h.\tan 48^\circ}{h}[/tex]
Operating on the right side:
[tex]\displaystyle \tan 53^\circ=\frac{150}{h}-\tan 48^\circ[/tex]
Rearranging:
[tex]\displaystyle \tan 53^\circ+\tan 48^\circ=\frac{150}{h}[/tex]
Solving for h:
[tex]\displaystyle h=\frac{150}{\tan 53^\circ+\tan 48^\circ}[/tex]
Calculating:
h = 61.5 m
The building is 61.5 m tall
Molly shared a spool of ribbon with 12 people. Each person received 3 feet of ribbon. Which equation can she use to find
r, the number of feet of ribbon that her spool originally had?
Answers
Answer: R/12=3
Step-by-step explanation: This is because / = divide so since we need to divide then multiply its better you go with /
Answer:D
Step-by-step explanation:
Please help me!!! I’ll mark Brainlyest!
Answers
Answer:
12/6 2 is the best answer
This gives you 12/3(2).
3 x 2 = 6
12/6 can be simplified as 2.
B is the answer :)
Sharon uses 1 1/2 cups of sugar to make 2 batches of cookies. How much sugar will she use to make 6 batches of Cooke’s?
Answers
Answer:
8 Batches
Step-by-step explanation:
Simple. Since it takes 2/3 of a cup for one batch, we divide 5 1/3 by 2/3, wich equals 8.
I really need help with this
"Simplify this equation."
Answers
Answer:
2nd one
Step-by-step explanation:
show the steps on how to use the distributive property to evalute 9·67
Answers
Answer:
6.oz I will ply to get a
Step-by-step explanation:
ok is the only
Answer:
Step-by-step explanation:
9(67)=9(70-3)=
There are 32 desks in a room,
If x represents the number of rows of desks, which expression would equal the number of desks in each row?
32 x
32-x.
32 +x
32/x
Answers
32/x
Explanation
I think this is correct, the others wouldn’t make sense
The expression would equal the number of desks in each row is 32/x. Therefore, option D is the correct answer.
Given that, there are 32 desks in a room.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Now, x represents the number of rows of desks.
The number of desks in each row = Total number of desks in a room / The number of rows of desks
= 32/x
The expression would equal the number of desks in each row is 32/x. Therefore, option D is the correct answer.
To learn more about an expression visit:
https://brainly.com/question/13947055.
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The volume of a rectangular prism is represented by the function x
representing the width of the box.
Ox- 4
OX-1
Ox+1
Ox+4
Answers
Answer:
x = 4
Step-by-step explanation:
Hope this helps! Consider Brainiest! <3
ewkrfmwekosdfgseargfaerfgaerfmwoegm :
Answers
Answer:
Ok thats really cool thanks :)
Find the value of the variable.
Answers
The slope of a line is 2 the y-intercept of the line is - 6 which statement accurately describes how to grab the function
Answers
Answer:
Step-by-step explanation:
The slope of the line is 2 and the y-intercept is -6. y-intercept is the point where x is zero. Hence, the point is (0,-6) When we graph a linear function by slope-intercept method, first of all we plot the y-intercept. Hence, first of all we plot the point (0,-6) Now, slope is given by if rise is positive then we move up from the y -intercept and if negative then move down. We keep run always positive and hence we move right from the rise point. rise = 2 run = 1 Rise is positive hence, we move 2 units up from the point (0,-6) and then move 1 unit right to get the next point. Then we draw a line passing through these points. A is the correct option.
help pls my math teacher is rude
Answers
Answer:
2.25 or 2 1/4 pounds
Step-by-step explanation:
if you add them all up (I converted them to decimals when adding) you get 13.5 or 13 1/2 if your using fractions, then you divide that by 6 because thats how many jars there are and you get 2.25 or 2 1/4