Answer:
Ages are as follows:
Father: 40
Mother: 37
Son: 11
Each twin daughter: 6
Step-by-step explanation:
Interesting puzzle!
Let
F denote the age of the father
M the age of the mother
S the age of the son
D the age of each of the twin daughters
Total of all ages is
F + M + S + 2D = 100 [1]
We also have
F + S = 51 ==> S = 51- F [2]
F - M = 3 ==> M = F - 3 [3]
S - D = 5 ==> D = S -5 [4]
==> D = (51-F) -5
==> D = 46 - F [5]
Substitute this in equation [1] to get
We now have everyone's age in terms of the father's age F
Substituting each of equations [2], [3] and [5] into [1] we get one equation in terms of F
F + (F-3) + (51-F) + 2(46-F) = 100
(F + F - F -2F ) + (-3 + 51 + 92) = 100
-F + 140 = 100
- F = 100 - 140
-F = -40
or
F = 40
From [3]
M = F - 3 = 40 - 3 = 37
From [2]
S = 51 - F = 51 - 40 = 11
From [4]
D = S - 5 = 11 - 5 = 6
Verify:
F + M + S + 2D = 40 + 37 + 11 + 2 x6 = 100
Step-by-step explanation:
a = father age
b = mother age
c = son age
d = daughters age
1. a + b + c + 2d = 100 (don't forget : twin-daughters)
2. a + c = 51
3. a = b + 3
4. d = c - 5
we need to transform the equations 2-4 to express 3 variables by the 4th, and then put that into the first equation and solve for that one variable.
once we have that, we can use again the equations 2-4 to solve for the other variables.
2. tells us that
c = 51 - a
3. tells us that
b = a - 3
4. and 2. tells us that
d = c - 5 = (51 - a) - 5 = 46 - a
with that we get in 1.
a + (a - 3) + (51 - a) + 2(46 - a) = 100
a + a - 3 + 51 - a + 92 - 2a = 100
2a - 3a + 48 + 92 = 100
-a + 140 = 100
-a = -40
a = 40
b = a - 3 = 40 - 3 = 37
c = 51 - a = 51 - 40 = 11
d = c - 5 = 11 - 5 = 6
so, the father is 40 years old
the mother is 37 years old
the son is 11 years old
both of the twin daughters are 6 years old.
PLEASE HELP NOW!!! THX :))
You are baking doughnuts for your class. There are 8 total students in your class and you have baked 11 doughnuts. Write and solve an equation to find the additional number x of doughnuts you need to bake in order to have 4 doughnuts for each student. Write your equation so that the units on each side of the equation are doughnuts per student.
Answer: 4x + 11 = 4(8)
Step-by-step explanation:
The function -2x^2-8x+42 represents the approximate height of an object (x seconds) after it is thrown off the top of a building. How many seconds does it take for the object to hit the ground?
The function is given to be:
[tex]-2x^2-8x+42[/tex]The object hits the ground when the function is equal to zero:
[tex]-2x^2-8x+42=0[/tex]Solving the equation by factorization, we have:
[tex]\begin{gathered} 2(-x^2-4x+21)=0 \\ -x^2-4x+21=0 \\ -x^2-7x+3x+21=0 \\ -x(x+7)+3(x+7)=0 \\ \therefore \\ (-x+3)(x+7)=0 \\ Hence \\ x=3,x=-7 \end{gathered}[/tex]Since the time cannot be negative, then the time will be 3 seconds.
Therefore, it will take 3 seconds for the object to hit the ground.
b/c=a solve for c b nb
Answer:
b = ca
c = ba
Step-by-step explanation:
PLEASE HELP ME ! due tonight , Will make you a brainlist if you give me the correct answer .
Answer:
y=3/2x+3
Step-by-step explanation:
gradient is dy/dx
so up 3 and across 2
3/2
crosses at 3
Answer:
y=-3/2x+3
Step-by-step explanation:touches y axis at 3 and negative 3/2 slope
five hundred feet of fencing is available for a rectangular pasture alongside a river, the river serving as one side of the rectangle (so only three sides require fencing). find the dimensions yielding the greatest area
The dimensions yielding the greatest area (125*250).
What is a dimensions?
The minimal number of coordinates required to specify any point within a dimensional vector space (or object) is known as the dimension in physics and mathematics. Because only one coordinate is required to specify a point on a line, such as the point at 5 on the a number line, a line is said to have one dimension (1D). Because two coordinates are required to specify a point on a surface, such as the perimeter of a sphere or cylinder, it is referred to as having a dimension of two (2D). For instance, a point on the a sphere's surface requires both a latitude and a longitude to be located. A two-dimensional space just on plane is referred to as a Euclidean space.
The perimeter is 2a+b = 500
b= 500-2a
Max are is A = ab
A= a(500-2a)
= 500a - 2[tex]a^{2}[/tex]
for max value
a = -y/2x
= -500/2(-2)
= 125 feet
and b = 250 feet
Greatest area (125*250) = 31250 feet²
Hence dimensions yielding the greatest area (125*250).
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Connor left his house for work and was gone 4 hours. He spent a total of
hour driving to and from work and didn't go anywhere else. How long was he
at work?
A. 4 hours
B. 3 hours
c. 4 hours
D. 3 hours
HELP FAST GIVING HIGHEST AMOUNT OF POINT
Answer:
4 hours
Step-by-step explanation:
he was gone for 5 hours, he spent an hour driving.
5 - = 4 hours at work.
Answer:
4 hours
Step-by-step explanation:
says he was gone 4 hours, he was at work
Two planes left the same airport traveling in opposite directions. The
lirections. The first plane left at 9:00 a.m. and 2.25 hours later, the two planes
were 1825 miles apart. The second plane left at 10:00 a.m. and its average
average rate. Let x represent the first plane's average rate.
rate was 108 miles per hour slower than the first plane's
What was the first plane's average rate?
Enter an equation that can be used to solve this problem in the first box.
Solve for x and enter the first plane's average rate in the second box.
Answer: x=560 miles per hour
Step-by-step explanation:
[tex]\displaystyle\\2.25=\\\\2\frac{1}{4}= \\\\\frac{2*4+1}{4}=\\\\\frac{8+1}{4}=\\\\\frac{9}{4}\ hours[/tex]
The second plane left at 10:00 a.m. so, him fly was 1.25 hours:
[tex]\displaystyle\\1.25=\\\\1\frac{1}{4}=\\\\\frac{1*4+1}{4}=\\\\\frac{4+1}{4} =\\\\\frac{5}{4} \ hours[/tex]
Let x represent the first plane's average rate
Hence, (x-108) represent the second plane's average rate
So,
[tex]\displaystyle\\\frac{9}{4}x+\frac{5}{4} (x-108)=1825\ \ \ \ (1)\\[/tex]
Multiply both parts of the equation by 4:
[tex]9x+5(x-108)=7300\\\\9x+5x-540=7300\\\\14x-540+540=7300+540\\\\14x=7840[/tex]
Divide both parts of the equation by 14:
[tex]x=560\ miles/hour[/tex]
Penny is going to make a donation to our local animal shelter. The price of each item she will donate is shown.
so far she has 30 cans of cat food 34 cans of dog food and 18 bags of cat she wants the value of her donation to be more than $380 how many bags of dog food does Penny need to donate to meet her goal?
Answer:
Second Choice: 8.73b + 171.48 > 381
Step-by-step explanation:
This is a tricky question because the first two choices both represent an inequality that satisfy the conditions
First, let's eliminate obvious wrong choices.
If b represents the number of bags of dog food and one bag costs $8.73, there should be term 8.73b somewhere in the inequality since 8.73b represents the total $ cost of b bags of dog food.
This means we can eliminate the last two choices
Let's deal with the knowns and compute the dollar amounts of each of the products being donated
30 cans of cat food at $0.57 per can = 0.57 x 30 = $17.10
34 cans of dog food at $0.84 per can = 0.84 x 34 = $28.56
18 bags of cat food at $$6.99 per bag = 6.99 x 18 = $125.82
The sum of these is $171.48
She is also donating b bags of dog food at $8.73 per bag = 8.73 x b = $8.73b
So the total cost of the donation =
8,73b + 171.48 which has to exceed 381
So the inequality is
8.73b + 171.48 > 381
Which is the choice you have selected and I believe it is correct
Now, the tricky part comes because if you subtract 171.84 from both sides of the inequality we get
8.73b > 318 - 171.48
Both inequalities are equivalent but we would not write an inequality of the type where the RHS is a mathematical expression. We would instead simplify the right hand side and write it as
8.73b > 209.52 (381-171.48 = 209.52)
I believe the way the question is worded is the LHS should be the $sum of all the donations and the RHS the minimum value.
So the best choice is choice 2: 8.73b + 171.48 > 381
i hope that helps.
26 = -12u - 9 + 7u solve for u and simplify as much as possible
Answer:
u = -7
Step-by-step explanation:
26 = -12u - 9 + 7u
combine u terms on right side:
26 = -5u - 9
add 9 to both sides:
26 + 9 = -5u - 9 + 9
35 = -5u
divide both sides by -5:
35/-5 = -5u/-5
u = -7
The PTA prepared 10 gallons of punch to serve at their first meeting. If each serving is eight ounces, how many people can be served?
Based on mathematical operations, the number of people that 10 gallons of punch can serve is 192 persons.
How is the number determined?The number of people can be determined using mathematical operations of multiplication based on converting the gallons to ounces and division.
The number of gallons of punch to serve at the first meeting = 10 gallons
The quantity of punch per serving = 8 ounces
1 gallon = 153.722 ounces
10 gallons = 1537.22 ounces
The persons that can be served 8 ounces from the 10 gallons = 192 (1,537.22/8).
Thus, mathematically, from the 10 gallons of punch, the PTA can serve 192 persons.
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arcsin (-1)
compute the exact value
–π/2 is the exact value of arcsine (-1).
What is arcsine?The six main inverse trigonometric functions include arcsin. It is the sine function's inverse trigonometric function. The mathematical symbol for arcsin, commonly known as inverse sine, is arcsin x or sin-1x (read as sine inverse x). Sin-1x is not the same as (sin x)-1; that is, sin-1x is not the reciprocal function of sin x. This is an important distinction to make. We may use the six inverse trigonometric functions arccos, arcsin, arctan, arcsec, arccsc, and arccot to calculate angles. Arcsin x calculates the angle that corresponds to the right-angled triangle's perpendicular to hypotenuse ratio. We shall examine the idea of arcsin in this article and determine its formula. We'll also talk about the domain and range.
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Dominoes region seven manager projects a net income of $725,000 the net income typically represents 30% of total annual sales based on his projections what will be the annual sales
We were informed that the net income will be $725,000, since that value represents 30% of the total annual sales we can apply a rule of three to solve the problem. We do that by making 30% represent $725,000 in the same proportion that 100% represents the total anual sales, x. We have:
[tex]\frac{30}{100}\text{ }\frac{\text{ \%}}{\text{ \%}}=\frac{725000}{x}[/tex]We can cross multiply to find the value of "x".
[tex]\begin{gathered} 30\cdot x=100\cdot725000 \\ x=\frac{72500000}{30} \\ x=2416666.667 \end{gathered}[/tex]The total annual sale on this year will be approximately $2,416,666.667.
Find the average rate of change:
Input
1
2
3
4
5
Output
11
13
15
17
19
Average rate of change = 2
How to find the average rate of change?
Given:
Input(x) = 1, 2, 3, 4, 5
Output(y)= 11,13,15,17,19
We know,
Average rate of change = change in output/change in input
[tex]=\frac{y_1-y_2}{x_1-x_2}\\\\=\frac{11-13}{1-2} \\\\ =\frac{-2}{-1} \\\\=2[/tex]
What is average rate of change?
The average rate of change is a typical indicator of change over a period of time given in a function. It is equal to the difference between the function's input and output as a whole. It is a measurement of the average amount of change in the function per unit throughout that time. On the graph of the function, it is calculated from the slope of the straight line joining the interval's ends.To learn more about average rate of change, refer:
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given the quadratic equation below, evaluate f(-1):f(x)=(x-2)^2+3
The evaluation of f(-1) given the quadratic equation f(x)=(x-2)^2 + 3 gives 12
What will the value of the function be?Given the quadratic equation f(x)=(x-2)^2 + 3. To evaluate to f(-1), we will substitute x = -1 into the equation:
Since f(x)=(x-2)^2 + 3
Therefore f(-1) = (-1 - 2)^2 + 3
= (-3)^2 + 3
= 9 + 3 = 12
Therefore, the value of c is 12. This shows the concept of functions and equations.
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the product x squared and y increased by 4
[tex] x {6} \div x {15}[/tex]how to solve x to the 6th power divided by x to the 15th power
So, if we apply the power's rule, we notice that if the base is the same, the exponents can be substracted. Like this
So the answer is 1 / x to the 9th power
Read the following actions and decide if they are responsible (R) or irresponsible(IR).
1. checking my credit score:
2. paying a credit card bill one day late:
3. listing expenses in a budget:
4.making decisions without all of the information:
5.purchasing something because it is on sale:
6.writing some goals:
7.researching what a mutual fund is:
8.making financial decisions without discussing it with your spouse:
9.finding a savings account with a great interest rate:
10. looking for the cheapest price for an item:
HELP ME PLEASE!!!!!!
Answer:
1. R
2. IR
3. R
4. IR
5. IR
6. R
7. R
8. IR
9. R
10. R
Step-by-step explanation:
Note on #5: purchasing something on sale that you were already going to buy would be responsible, but not simply BECAUSE the item is on sale and you were not already needing to purchase it.
ASAP!!
4/3x + 2/3x = 1/3x +5
Solve the equation for X and include all steps to get Branliest.
Answer: x=3
Step-by-step explanation: Multiply both sides of the equation by 3 to get 4x+2x=x+15. Combine like terms. (underlined) 6x=x+15. Move variable to left side and change its sign. 6x-x=15. Combine like terms again. 5x=15. Divide both sides of the equation by 5 to get x=3.
PLEASE HELP WHAT IS THE ANSWER
Triangle DAC is isosceles.
The correct option; Angle BAD is congruent to angle BCA, is requited to show ΔDBA ≅ ΔCBA by side-angle-side congruence theorem.
What is meant by congruence of triangles?If all 3 corresponding sides are equal as well as all 3 corresponding angles seem to be equal in measure, two triangles are said to be congruent.
These triangles could be moved, rotated, flipped, and turned to look exactly the same. They coincide if they are repositioned. ' is the symbol of congruence.side-angle-side congruence theorem: By SAS rule, two triangles are said to be congruent if any two sides and the angle would include between the sides with one triangle are equivalent to a corresponding two sides and also the angle would include here between sides of the second triangle.
For the given triangles;
ΔDBA and ΔCBA
Side AC = Side AD
Side AB = Side AB (common)
Thus, to make both triangles congruent the angles falling in between these two triangles must be equal.
Thus, Angle BAD is congruent to angle BCA,
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WILL MARK BRAINIEST Rewrite the radical expression as an expression with a rational exponent. 3 square root x 7
a x21
b x4
c x7/3
d x 3/7
WILL GIVE BRAINLY
PLS ANSWER QUICK
Use properties to evaluate [tex]-5x14 ÷ \frac{3}{4} x 15[/tex]
A. -350
B. -1400
C. 350
D. 1400
The expression has a value of -1400 when evaluated
How to evaluate the expression?From the question, the expression is represented as
-5 x 14 ÷ 3/4 x 15
Start by evaluating the product of -5 and 14
So, we have the following equation represented as
-5 x 14 ÷ 3/4 x 15 = -70 ÷ 3/4 x 15
Next, we rewrite the quotient as products
So, we have the following equation represented as
-5 x 14 ÷ 3/4 x 15 = -70 x 4/3 x 15
Divide 15 by 3
So, we have
-5 x 14 ÷ 3/4 x 15 = -70 x 4 x 5
Continue by evaluating the product of -70 and 4
So, we have the following equation
-5 x 14 ÷ 3/4 x 15 = -280 x 5
Lastly, we have
-5 x 14 ÷ 3/4 x 15 = -1400
Hence, the value of the expression is -1400
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i don't know non of this and i need help pls
By using the fact that ∠4 and ∠5 add up to 180° and ∠5 = ∠7, we conclude that the measures of the angles are:
∠5 = ∠7 = 56°.
How to find the measures of the angles?For angles formed by the interception between lines meet the following property.
If the angles are one next to the other, the measures add up to 180°.
If not, then the two angles have the same measure.
This means that:
∠5 = ∠7
∠8 = ∠6
And so on.
If the two horizontal lines are parallel, then:
∠5 = ∠1
And we know that:
∠4 + ∠1 = 180°
124° + ∠1 = 180°
∠1 = 180° - 124° = 56°
Then we get that:
∠5 = ∠7 = 56°.
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The larger of two numbers is 1 more than 3 times the smaller. Their sum is 65. Find the numbers.
The larger number is 49 and the smaller number is 16.
What are the numbers?The first step is to form a linear expression that represents the larger number.
Let the smaller number be represented with y
The larger number is represented with this linear expression : 1 + 3y
The sum of the two numbers : 1 + 3y + y = 65
Take the following steps to determine the value of the smaller number:
Combine similar terms: 65 - 1 = 3y + y
Add similar terms together: 64 = 4y
Divide both sides by 4: y = 64 / 4
y = 16
Larger number = 1 + 3(16)
1 + 48 = 49
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Express as a trinomial. (x-9)(x+6)
The expression of (x-9)(x+6) as a trinomial is x² -3x - 54
what is a trinomial?A trinomial is an algebraic expression that has three non-zero terms.
In a simpler terms, the definition of a trinomial is a math equation that has three terms which are connected by plus or minus notations.
Therefore, let's express (x-9)(x+6) as a trinomial.
Hence,
(x-9) (x+6) = x² + 6x - 9x - 54
Finally,
x² + 6x - 9x - 54 = x² -3x - 54
Therefore, the trinomial form of (x-9)(x+6) is x² -3x - 54
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A right pyramid has a surface area of 258 cm2. A right cone has a base radius of 4 cm. The cone and pyramid have equal surface areas. What is the height of the cone to the nearest tenth of a centimetre?
The height of the cone to the nearest tenth of a centimeter is 17.40 cm.
From the given information provided in the question, we can solve this problem by following a few steps.
The surface area of a right pyramid is 258 cm² according to the question.
The surface area of the cone is equal to the surface area of the right pyramid. Therefore the surface area of the cone is also 258 cm².
The surface area of a cone is denoted as ( πrh + πr² ).
Where h is denoted as the height and, r is denoted as the radius of the cone which is 4 cm.
Hence the surface area of the cone is,
SA = (π× 4× h+ π× 4² ) cm²
Now, we can generate an equation, as both represent the value of the surface area of the cone.
(π× 4× h+ π× 4² ) = 258
Or, (12.56h + 39.44) = 258 [ The value of π is 3.14 ]
Or, 12.56h = 258 - 39.44 [ subtracting 39.44 from both sides ]
Or, 12.56h = 218.56
Or, h = 218.56/12.56 [ dividing both sides by 12.56]
Or, h = 17.40
Now, we can conclude that the height of the cone is 17.40 cm.
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If you earn $7.50 per hour at your job how much will you earn if you work 25 hours?
Answer:
$187.5
Step-by-step explanation:
.
Answer:
187.50
Step-by-step explanation:
7.5(25)=187.50
hope this helped
have a good day^^
I need help with this can someone please help?
HG is the answer.
hope this helps
The first one is GH Segment.
Both shapes are similar. The figure on the right is a scaled version of the figure on the left. The VU edge in the left figure corresponds to the GH edge in the right figure.
The second one is %[tex]150[/tex].
As can be seen, the VU edge is [tex]2[/tex] units long while the GH edge is [tex]3[/tex] units long. By proportioning these edges and multiplying by [tex]100[/tex], we find the scaling factor. It is [tex]\frac{3}{2}[/tex].
Vistaprint offers the first 500 business cards for free. Then each additional set of 500 cards cost $9.99.
A. Write an equation that gives the total cosr (in dollars) of cards, C, in terms of the number (in groups of 500) of business cards, b, ordered.
B. Find the cost of buying 3500 business cards.
If the Vistaprint offers the first 500 business card for free and each additional set of 500 card cost $9.99
Part A
The equation that gives the total cost (in dollars) of card C, in terms of the number(in group of 500) of business cards b ordered is C = 9.99×b -9.99
Part B
The cost of buying 3500 business cards is $59.94
The Vistaprint offers the first 500 business cards for free
The cost of each additional set of 500 cards = $9.99
Part A
Consider the total cost of the card = C
Number of business card in group of 500 = b
Then the equation of the total cost of cards
C = 9.99×b -9.99
Part B
Total number of cards = 3500
Number of cards in group of 500 = 3500/500
= 7
The cost of buying 3500 business card = 9.99×7-9.99
= 69.93-9.99
= $59.94
Hence, If the Vistaprint offers the first 500 business card for free and each additional set of 500 card cost $9.99
Part A
The equation that gives the total cost (in dollars) of card C, in terms of the number(in group of 500) of business cards b ordered is C = 9.99×b -9.99
Part B
The cost of buying 3500 business cards is $59.94
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7.
In the given image, the measure of 2x is
Only enter the number.
P
N
142°
90°
X
* REQUIRED
M
U
Answer:
Angle LMN = 180 - 142
= 38° (sum of angles on a straight line=180)
x = 180 - 90 - 38
= 52° (sum of angles in triangle=180)
(5x²+23x+16) + (x+4)
÷
Answer:
5x2 + 24x + 20
Step-by-step explanation: