Answer:
AC=96 units
Step-by-step explanation:
x^2 - 16 = 6x
x^2 - 6x - 16 = 0
(x - 8)(x + 2) = 0
x - 8 + 8 = 0 + 8
x = 8 WORKS
x + 2 - 2 = 0 - 2
x = -2 CANT WORK BECAUSE IS NEG
CE = 6(8)
48
AC = AE + CE
AC = 48 + 48
AC = 96
Answer: AC = 96
Football party favors come in packages like the one shown. How much would it cost to buy 56 party favors? Think about how you can model with math to help solve the problem. It's $4 per package
Answer:
$224.
Step-by-step explanation:
If the packages cost $4 each then 56 packages will cost 56 * 4 dollars.
56 * 4 = $224.
In 1929, Farmer Giles took his animals to market. He had some cows, sheep and chickens to sell. Cows sold for ten pounds each. Sheep sold for one pound each. Chickens were sold for one pound for a brood of eight (they were only sold in whole broods). Farmer Giles had a good day and sold 100 animals for exactly £100. The day did have its down side; he had to sell Daisy, his favourite cow. How many sheep did Farmer Giles sell?
Answer:
90 sheep?
Step-by-step explanation:
1 sheep= 1 pound
1 cow= 10 pounds
total amount made= 100 pounds
100 ÷ 1 (the cost for sheep) = 100 sheep
100 - 90 (the cost of cows) = 10
10 sheep
Answer:
21 sheep
Step-by-step explanation:
100 = x + y + 8z
10x + y + z = 100
x = 1
y + 8z = 99
y + z = 90
x = 2
y + 8z = 98
y + z = 80
x = 3
y + 8z = 97
y + z = 70
x = 4
y + 8z = 96
y + z = 60
x = 5
y + 8z = 95
y + z = 50
x = 6
y + 8z = 94
y + z = 40
x = 7
y + 8z = 93
y + z = 30
7z = 63
z = 9
y = 30 - 9 = 21
x = 7 (7 cows)
y = 21 (21 sheep)
z = 9 (9×8 = 72 chicken)
Of regular movie goers, 40% watch romantic movies, 60% watch action movies, and 24% watch both types. Are watching romantic movies independent or dependent of watching action movies?
Answer:
depend on watching action movies
Step-by-step explanation:
because most watch action
Based on the given data, watching romantic movies and watching action movies are independent events, as the probability of both occurring matches the product of their individual probabilities.
Explanation:We need to determine if the events of watching romantic movies and watching action movies are independent or dependent. The definition of independent events in probability is that the outcome of one event does not change the probability of the outcome of another event.
If watching romantic and action movies were independent events, we would expect the percentage of people who watch both to be the product of the individual probabilities. That would be 0.40 (the probability of watching romantic movies) times 0.60 (the probability of watching action movies), which equals 0.24 or 24%.
However, we are told that 24% of people watch both romantic and action movies. This matches our calculation exactly, so we can infer that the event of watching romantic movies is independent from the event of watching action movies. This means that watching a romantic movie does not affect the likelihood of watching an action movie, and vice versa.
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What is the area? (Will mark if correct)
Answer:
81
Step-by-step explanation:
All you have to do is times 9*9=81
Answer:
A=40.5
Step-by-step explanation:
A=pq /2
A= 9x9/2
A=81/2
A=40.5
6) What is 100 percent of 14 ?
Answer: 14
Step-by-step explanation:
100% of 14
= 100/100 × 14/1
14
Answer:14
Step-by-step explanation:
Percent= 100%
From= 14
Value= [tex]\frac{100}{100}[/tex] x 14= 1x 14 =14
If you multiple me by 7 add 1 then divide by 4 you get 9, what number am I.
Answer:
The number is 5
Step-by-step explanation:
I like to do the equation backwards, so x*7+1/4=9 becomes:
9*4=36
36-1=35
35/7=5
And there is your answer!!!
Convert the following. (You may use a calculator.)
24 centimeters to inches (to the nearest hundredth)
Answer:
9.45 (rounded)
Step-by-step explanation:
- The formula is to divide the centimeters by 2.54, and this will give you the amount of inches.
Answer:
9.45 inches
Step-by-step explanation:
2.54cm in 1 inch
Find the mean of this set of numbers:
10, 10, 7, 12, 11
Answer:
u just take the sum of all numbers divide by the number of numbers (5)
In below diagram, line AB is parallel to CB.
i.e. AB∥CD
∠AGF = 68°
Find ∠EGB.
Answer:
∠EGB= 68°
Step-by-step explanation:
∠EGB= ∠AGF ( vert. opp. ∠s)
∠EGB= 68°
If 2 straight lines intersect, then the angles facing opposite each other are equal. In this case, the 2 lines are AB and EF.
You roll a six-sided die. How likely is it that you roll a 3?
A) certain
B) likely
C) unlikely
D) impossible
Answer:
The answer is C) Unlikely.
Step-by-step explanation: This is because the likelihood of you rolling a 3 on a six-sided die is approximately 3/36.
It is unlikely to roll a 3.
Option C is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Possible outcomes of rolling a six-sided die.
= {1, 2, 3, 4, 5, 6}
We can say that,
If the probability of an event is 50% or above it is likely.
If the probability of an event is less than 50% it is unlikely.
If the probability of an event is 100% it is certain.
If the probability of an event is less than 0% it is impossible.
Now,
Probability of rolling a 3.
= 1/6 x 100
= 16.67%
This means,
Unlikely.
Thus,
It is unlikely to roll a 3.
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Two positive integers have a product of 50. One
integer is twice the other. What are the
integers?
Separate the answers with a comma.
Enter the correct answer.
which postulate proves these two triangles are congruent
Answer: nonenot congruent
Step-by-step explanation:
there are 250 toothpicks in a regular size box. a jumbo size box is made by tripling the length,width, and height of the regular box. how many toothpicks will the jumbo box hold
Answer:6750
Step-by-step explanation:
Final answer:
The jumbo-sized box, created by tripling each dimension of a regular-sized box that holds 250 toothpicks, will have a volume 27 times greater. Therefore, it will hold 250 × 27 = 6,750 toothpicks.
Explanation:
The question is asking how many toothpicks a jumbo-sized box can hold if it is created by tripling the length, width, and height of a regular-sized box that holds 250 toothpicks. To find the answer, we need to consider the volume of the boxes because the toothpicks are arranged in three-dimensional space.
The volume of a box is calculated by multiplying its length by its width by its height. If we triple each of these dimensions for the jumbo box, the new volume will be 27 times the volume of the original box (since 3 × 3 × 3 = 27). Therefore, if the original box holds 250 toothpicks, the jumbo box will hold 250 × 27 toothpicks.
To find the total number of toothpicks:
Multiply the number of toothpicks in the original box (250) by 27.
Calculate 250 × 27 to get 6,750 toothpicks.
Thus, the jumbo-sized box would be able to hold 6,750 toothpicks.
how to solve and graph this inequality 8-u>4
Answer:
u < 4
Step-by-step explanation:
Step 1: Subtract 8 from both sides
8 - u - 8 > 4 - 8
-u > -4
Step 2: Divide both sides by -1
-u / -1 > -4 / -1
Since you divide by a negative, you flip the sign.
u < 4
Answer: u < 4
what’s the vertex of f(x)= (x-4)^2+7
Answer:
vertex is 4
Step-by-step explanation:
y = (x-4)^2 + 7
(x-4) (x-4)
x * x = x^2
x * -4 = -4x
-4 * x = -4x
-4 * -4 =16
x^2 - 8x + 16
y = x^2 -8x + 16 + 7
y = x^2 -8x + 23
a b c
formula to find vertex: -b / 2a
= -b / 2a
= - (-8) / 2 (1)
= 8 / 2
= 4
vertex = 4
(what i did was work out the exponent outsite the parentesis then i got the equation i wanted, and from that equation i used the formula to find the vertex and i just plugged the numbers of the equation into the formula and work it out)
Answer:
(4,7)
Step-by-step explanation:
The equation for a parabola can be written as
y = a(x-h)^2 +k where (h,k) is the vertex
given f(x) = (x-4)^2+7
The vertex is (4,7)
Javier moves backward so that his horizontal distance from the tree is
greater. Will the distance from his eyes to the top of the tree also be
greater? Explain.
Answer:
Yes it will be greater, he is moving back 3 feet so what you are doing is taking the leg (a2) and multiplying it by 3. Once you do, you see triangle 1 has double and so did triangle 2. Triangle 1 was originally 5.6 (rounded to 6) than went up to 26.1. Triangle 2 was originally 24 and went up to 74.7 (or 75)
Step-by-step explanation:
Triangle 1 (when multiply by 3)
a2+b2=c2
7(square to 2)+b2=27(square to 2)
49+b2=729
-49 -49
--------------------
b2=680
(square root it)
b=26.1 Rounded to nearest tenth
Triangle 2:
a2+b2=c2
7(square to 2)+b2=75(square to 2)
49+b2=5625
-49 -49
-------------------
b2=5576
(square root it)
b=74.7 (or 75 rounded to nearest tenth)
Hope this helps anyone who needs it :)
Yes, the distance from his eyes to the top of the tree will also be greater.
What is function?A function is a relation between a dependent and independent variable.
Mathematically, we can write → y = f(x) = ax + b.
Given is that Javier moves backward so that his horizontal distance from the tree is greater.
Before moving backward, the distance from Javier's eyes to the top of the tree can be written as -
cosФ = b/h
h = b/cosФ
Now, we can see that -
h [tex]\alpha[/tex] b
As base increases, the hypotenuse length or the distance from Javier's eyes to the top of the tree will increase.
Therefore, yes, the distance from his eyes to the top of the tree will also be greater.
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I need help. Can someone pls answer with working thx
Question 1:
The given formula is
[tex]I=\frac{PTR}{100}[/tex]
To make T, the subject we multiply both sides by 100:
[tex]100I=\frac{PTR}{100} \times 100[/tex]
This becomes
[tex]100I=PTR[/tex]
Divide both sides by PR
[tex]T=\frac{100I}{PR}[/tex]
b) Amanda's principal is , P=€2565
The interest rate is 3.5% p.a. that is R=3.5
We want to find how many years, her money will gain an interest of I=€718.20
We substitute into the formula for T,
[tex]T=\frac{100 \times 718.20}{2565 \times 3.5}[/tex]
This simplifies to:
T=8
Therefore it will take 8 years
2) Percentage profit
[tex] = \frac{profit}{cost \: price} \times 100\%[/tex]
The cost price of the 80 articles €200
The selling price is 3.5×80=€280
The profit =€280-€200=€80
The percentage profit is now
[tex] = \frac{80}{200} \times 100\%[/tex]
[tex] = 0.4 \times 100\%[/tex]
[tex]40\%[/tex]
The percentage profit is 40%
Question 3)
Let the original price of the calculator be x.
Then 85% of this price will be:
[tex] \frac{85}{100} \times x[/tex]
This is the same as€32.89
We equate and solve for x.
[tex] \frac{85}{100} x= 32.89[/tex]
[tex]0.85x = 32.89[/tex]
[tex]x = \frac{32.89}{0.85} [/tex]
[tex]x = 38.69[/tex]
The original price is €38.69
What is the answer to 2(-2-4p)+2(-2p-1)
Answer:
4p-6
Step-by-step explanation:
distribute within parenthesis:
-4+8p-4p-2
Combine like terms
4p-6
i hope this helps u
please give thx and a brainliest to level up
Answer:
2(-2-4p)+2(-2p-1)
-4-8p -4p-2
-12p-6
Step-by-step explanation:
the sum of (-9) and a number (n) is multiplied by 1/2. the result is 20. what is the number?
Answer:
Step-by-step explanation:
1/2(-9+n)=20
n=40+9
n=49
Answer:
49
Step-by-step explanation:
Sum means add
-9+n
Multiply this by 1/2
1/2(-9+n)
This is equal to 20
1/2(-9+n) = 20
Solve
Multiply each side by 2 to get rid of the fraction
2*1/2(-9+n) = 20*2
-9+n = 40
Add 9 to each side
-9+9 +n = 40+9
n = 49
Is -2/9 rational,irrational,integer, or etc?
Answer:
rational
Step-by-step explanation:
hope this helps!
solve each system by elimination
-x-5y-5z=2
4x-5y+4z=19
x+5y-z=-20
Answer:
x = -2 , y = -3 , z = 3
Step-by-step explanation:
Solve the following system:
{-x - 5 y - 5 z = 2 | (equation 1)
4 x - 5 y + 4 z = 19 | (equation 2)
x + 5 y - z = -20 | (equation 3)
Swap equation 1 with equation 2:
{4 x - 5 y + 4 z = 19 | (equation 1)
-x - 5 y - 5 z = 2 | (equation 2)
x + 5 y - z = -20 | (equation 3)
Add 1/4 × (equation 1) to equation 2:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x - (25 y)/4 - 4 z = 27/4 | (equation 2)
x + 5 y - z = -20 | (equation 3)
Multiply equation 2 by 4:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x - 25 y - 16 z = 27 | (equation 2)
x + 5 y - z = -20 | (equation 3)
Subtract 1/4 × (equation 1) from equation 3:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x - 25 y - 16 z = 27 | (equation 2)
0 x+(25 y)/4 - 2 z = -99/4 | (equation 3)
Multiply equation 3 by 4:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x - 25 y - 16 z = 27 | (equation 2)
0 x+25 y - 8 z = -99 | (equation 3)
Add equation 2 to equation 3:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x - 25 y - 16 z = 27 | (equation 2)
0 x+0 y - 24 z = -72 | (equation 3)
Divide equation 3 by -24:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x - 25 y - 16 z = 27 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Add 16 × (equation 3) to equation 2:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x - 25 y+0 z = 75 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Divide equation 2 by -25:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x+y+0 z = -3 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Add 5 × (equation 2) to equation 1:
{4 x + 0 y+4 z = 4 | (equation 1)
0 x+y+0 z = -3 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Subtract 4 × (equation 3) from equation 1:
{4 x+0 y+0 z = -8 | (equation 1)
0 x+y+0 z = -3 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Divide equation 1 by 4:
{x+0 y+0 z = -2 | (equation 1)
0 x+y+0 z = -3 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Collect results:
Answer: {x = -2 , y = -3 , z = 3
simplify to create an equivalent expression
-r + 8(-5r -2).
Multiply 8 by -5r - 2
- r - 40r - 16.
Combine -r and -40r
-41r - 16 is a simplified equivalent expression of -r + 8(-5r - 2)
Answer:
-41r - 16
Step-by-step explanation:
-r + 8 (-5r - 2)
-r - 8*5 r -8*2
-r - 40r - 16
-41r - 16
the roots of the equation x²-kx+28=0 are alpha (a) and alpha (a) + 3.find the values of k.
Solution:
Given that equation is:
[tex]x^2 - kx + 28 = 0[/tex]
Roots are:
[tex]\alpha\\\\\alpha + 3[/tex]
To find: value of x
The general quadratic equation is:
[tex]ax^2 + bx + c = 0[/tex]
[tex]\text{ Product of roots } = \frac{c}{a}\\\\\text{ Sum of roots } = \frac{-b}{a}[/tex]
From given,
[tex]x^2 - kx + 28 = 0[/tex]
a = 1
b = -k
c = 28
Therefore,
[tex]Product\ of\ roots = \frac{28}{1} = 28[/tex]
[tex]Sum\ of\ roots = \frac{-k}{1} = -k[/tex]
Given roots are:
[tex]\alpha\\\\\alpha + 3[/tex]
Therefore,
The two roots are two numbers whose difference is 3 and whose product is 28
Those two roots are 4 and 7 or -4 and -7
Then, sum of roots are:
4 + 7 = 11
-4 - 7 = -11
Therefore, the possible values of k are -11 and 11
siw is a fourth as old as mother, and Mona is a fifth as old as mother. Mother is 22 years older than the two girls together. How old are they?
Answer:
Siw's age is 10 years old
Mona's age is 8 yers old
Mother's age is 40 years old
Step-by-step explanation:
Let
x ----> Siw's age
y ---> Mona's age
z ---> Mother's age
we know that
Siw is a fourth as old as mother
so
[tex]x=\frac{1}{4}z[/tex] ----> equation A
Mona is a fifth as old as mother
so
[tex]y=\frac{1}{5}z[/tex] ----> equation B
Mother is 22 years older than the two girls together.
so
[tex]z=x+y+22[/tex] ----> equation C
substitute equation A and equation B in equation C
[tex]z=\frac{1}{4}z+\frac{1}{5}z+22[/tex]
solve for z
Multiply by 20 both sides to remove the fraction
[tex]20z=5z+4z+440[/tex]
[tex]20z-9z=440\\11z=440\\z=40\ years[/tex]
Find the value of x
[tex]x=\frac{1}{4}(40)=10\ years[/tex]
Find the value of y
[tex]y=\frac{1}{5}(40)=8\ years[/tex]
therefore
Siw's age is 10 years old
Mona's age is 8 yers old
Mother's age is 40 years old
To rent a beach chair and umbrella, there is a rental fee of $10. Then it costs $2 per day. Use the equation c = 2d + 10 to complete the table.
Answer:
Step-by-step explanation:
1 day -------------- $12
cost = 2(1 day) + 10
2 days ------------ $14
cost = 2(2 days) +10
3 days -------------$16
cost = 2(3)+10
and so on
Solve the following system,
x2 - y = 3
X-Y = -3
Answer:
[tex] x = 6 \\ y = 9[/tex]
Step-by-step explanation:
[tex]2x - y - (x - y) = 3 - ( - 3) \\ 2x - y - x + y = 6 \\ x = 6[/tex]
[tex]2x - y = 3 \\ 2 \times 6 - y = 3 \\ 12 - y = 3 \\ - y = 3 - 12 \\ - y = - 9 \\ y = 9[/tex]
[tex] x - y = - 3 \\ 6 - 9 = - 3 \\ - 3 = - 3[/tex]
hope this helps you,! have a nice day!!
The system of equations is solved by substituting the expression for y from the linear equation into the quadratic equation, factoring the resulting quadratic, and solving for the two values of x, which are then used to find the corresponding y values, yielding solutions (3, 6) and (-2, 1).
Explanation:To solve the system of equations given by
x2 - y = 3
x - y = -3
we observe that the second equation can immediately give us a value for y in terms of x. We can add 3 to both sides to isolate y:
y = x + 3
Next, we can substitute this expression for y into the first equation:
x2 - (x + 3) = 3
This simplifies to: x2 - x - 6 = 0
We can then solve this quadratic equation for x. A possible method is factoring, which, if the quadratic factors neatly, is often quicker than using the quadratic formula. The factored form is:
(x - 3)(x + 2) = 0
Setting each factor equal to zero gives us two solutions for x:
x = 3 or x = -2
Substituting these back into the equation y = x + 3 gives us the corresponding y values:
For x = 3: y = 3 + 3 = 6
For x = -2: y = -2 + 3 = 1
Thus, we have two solutions for the system: (3, 6) and (-2, 1).
simplify xz^3*4x^4z^5
To simplify the expression xz^3*4x^4z^5, the exponents of the like bases are added together resulting in 4x^5z^8. This application of exponent rules shows that the exponents on the same base are summed during multiplication.
Explanation:To simplify the expression xz^3*4x^4z^5, we need to apply the rules of exponents. Specifically, when multiplying two expressions with the same base, we add their exponents.
Beginning with the variable x, we have an implied exponent of 1 on the standalone x, so when combined with x^4, we get x^(1+4), which simplifies to x^5.
Next, we apply the same rule to the variable z.
The expression z^3 multiplied by z^5 becomes z^(3+5), which simplifies to z^8. Finally, we multiply these results by the constant 4 to get our simplified expression:
4x^5z^8.
As an example to clarify this process, imagine a simpler case like (5^3)^4.
This could be written out as multiple fives multiplied by each other, illustrating that the exponents are indeed added together when multiplying like bases, just as we did with x and z in our original expression.
Mary earned scores of 88, 91, 75, and 72 on four science tests. Determine her score on the
fifth test if her average for the five tests was 81.
о.
o
o
o
Answer:
Mary's score on the fifth test was 79.
Step-by-step explanation:
Mary's 1st score = 88Mary's 2nd score = 91Mary's 3rd score = 75Mary's 4th score = 72Mary's 5th score = xMary's average score for the five tests = 81Let's solve for x, this way:
Mary's average score for the five tests = (Mary's 1st score + Mary's 2nd score + Mary's 3rd score + Mary's 4th score + Mary's 5th score)/5
Replacing with the values given:
81 = (88 + 91 + 75 + 72 + x)/5
81 * 5 = 326 + x
405 = 326 + x
- x = 326 - 405
x = 79
Solve for x (round to the nearest tenth)
y/(5 + 3) = 5/y
y/8 = 5/y
y² = 40
y = 2√10
5/x = x/3
15 = x²
√15 = x
Answer:
3.9
Step-by-step explanation:
The right triangles are all similar, so the ratio of short side to long side is the same for all:
3/x = x/5
15 = x^2 . . . . . . . . multiply by 5x
x = √15 ≈ 3.9
Mrs. Green bought a cake mix with instructions to bake at 190 Celsius. Her American- made oven has only a Fahrenheit scale. At what degrees Fahrenheit should she bake the cake?
Answer:
374
Step-by-step explanation: