Answer:
[tex]x=-1;\ y=8\\x=5;\ y=2[/tex]
Step-by-step explanation:
You can make both equations equal and solve for the variable x, as you can see below:
[tex]-x+7=0.5(x-3)^2[/tex]
Keep on mind that:
[tex](a-b)^2=a^2-2ab+b^2[/tex]
Then:
[tex]-x+7=0.5(x-3)^2\\-x+7=0.5(x^2-2(x)(3)+3^2)\\-x+7=0.5x^{2}-3x+4.5\\0=0.5x^2-2x-2.5[/tex]
Apply the quadratic formula:
[tex]x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-2)+/-\sqrt{(-2)^2-4(0.5)(-2.5)}}{2(0.5)}\\x=-1\\x=5[/tex]
Substitute each value into one of the originl equations to find y, then:
[tex]y=-(-1)+7=8\\y=-5+7=2[/tex]
Answer:
The solutions are (-1,8) and (5,2).
Step-by-step explanation:
At one school half of the students live within 1 mile, 78% live within 2 miles, and 0.1 of the students live between 2 and 3 miles from the school.
The question deals with the distribution of students' residences relative to their school. Calculations suggest 22% live between 1 and 2 miles away, 10% live between 2 to 3 miles away, and the remaining students live more than 3 miles away from the school.
Explanation:The question relates to the distribution of students' residences in relation to the school. Given that, at one school, half of the students live within 1 mile, 78% live within 2 miles, and 0.1 of the students live between 2 and 3 miles from the school. This implies that 22% of students live between 1 and 2 miles of the school (the difference between 78% and the half who live within 1 mile), and 0.1 of the students live further than 2 miles but less than 3 miles from the school. So, the remaining students, which is 100% minus (half + 22% + 0.1*100%), live more than 3 miles away from the school.
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To find the probability that a randomly chosen student at the local community college lives within five miles of the campus or receives some kind of financial aid, the formula for the union of two events can be used. Substituting the given probabilities, the probability is found to be 0.35.
Explanation:To find the probability that a randomly chosen student at the local community college lives within five miles of the campus or receives some kind of financial aid, we need to understand the given information.
We know that 20% of the students live within five miles of the campus and 30% receive financial aid. Of those who live within five miles, 75% receive financial aid.
To find the probability, we can use the formula for the union of two events:
P(A or B) = P(A) + P(B) - P(A and B)
In this case, A represents living within five miles of the campus and B represents receiving financial aid. Substituting the given probabilities, we have:
P(lives within five miles or receives financial aid) = 0.20 + 0.30 - (0.20 * 0.75)
P(lives within five miles or receives financial aid) = 0.20 + 0.30 - 0.15
P(lives within five miles or receives financial aid) = 0.35
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What is the value of d? Assume that the line is tangent to the circle.
Answer:
121°
Step-by-step explanation:
We have been given a chord and tangent to a circle, and also a minor arc measure that is equal to 118°We know that; An angle formed by a secant and tangent of circle is half of the measure of intercepted arc.Therefore; ∠ x = 1/2 mABC
We can find intercepted arc by subtracting minor arc measure from 360 degrees because minor and major arcs add up to 360 degrees.Thus; 360° - 118° = 242°
Using the formula; ∠ x = 1/2 mABC
Then; d = 242/2
= 121°
59 =7r+3 what is the answer
Answer:
r=8
Step-by-step explanation:
59 =7r+3
Subtract 3 from each side
59 -3 = 7r+3-3
56 = 7r
Divide each side by 7
56/7 = 7r/7
8 =r
Answer:
[tex]\boxed{\bold{r=8}}[/tex]
Step-by-step explanation:
Switch sides
[tex]\bold{7r+3=59}[/tex]
Subtract 3 from both sides
[tex]\bold{7r+3-3=59-3}[/tex]
Simplify
[tex]\bold{7r=56}[/tex]
Divide both sides by 7
[tex]\bold{\frac{7r}{7}=\frac{56}{7}}[/tex]
Simplify
[tex]\bold{r=8}[/tex]
Plz help me !!!!!!!!!!!
Answer: [tex]\large{x^{\frac{1}{4}}y^{\frac{1}{2}}}[/tex]
Step-by-step explanation:
[tex]\sqrt[8]{x^2y^4}=x^{\frac{2}{8}}y^{\frac{4}{8}}=\huge\boxed{x^{\frac{1}{4}}y^{\frac{1}{2}}}[/tex]
the question applies to #41
There are many ways to write a transformation.
This shows the translation as a function.
f(x) = y = | x |
f(x-11)
This shows the translation as a column vector.
[tex]\left[\begin{array}{ccc}-11\\0\end{array}\right][/tex]
The vertices of a triangle are A(7,5) B(4,2) and C(9,2) what is mABC
Answer:
A(7,5)
Step-by-step explanation:
This is correct because the area of a triangle is b × h = a.
Answer:
The measure of ∠ABC is 45°.
Step-by-step explanation:
Given : The vertices of a triangle are A(7,5) B(4,2) and C(9,2).
To find : What is ∠ABC ?
Solution :
First we side the length of the sides,
Using Distance formula,
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Length of side AB, A(7,5) and B(4,2)
[tex]c= \sqrt{(7-4)^2 + (5-2)^2} \\c= \sqrt{(3)^2 + (3)^2} \\c= \sqrt{9+9} \\c= \sqrt{18}[/tex]
Length of side BC, B(4,2) and C(9,2)
[tex]a= \sqrt{(4-9)^2 +(2-2)^2} \\a= \sqrt{(-5)^2 + 0} \\a= \sqrt{25} \\a= 5[/tex]
Length of the side AC, A(7,5) and C(9,2)
[tex]b = \sqrt{(7-9)^2 +(5-2)^2}\\ b= \sqrt{(-2)^2 + (3)^2} \\b= \sqrt{4+ 9}\\b=\sqrt{13}[/tex]
By the Law of Cosines,
[tex]\cos B=\frac{a^2 + c^2 -b^2}{2ac}[/tex]
Substitute the values,
[tex]\cos B=\frac{(5)^2 + (\sqrt{18})^2 - (\sqrt{13})^2}{2\times 5\times \sqrt{18}}[/tex]
[tex]\cos B =\frac{25+18-13}{10\sqrt{18}}[/tex]
[tex]\cos B=\frac{30}{10\sqrt{18}}[/tex]
[tex]\cos B =\frac{3}{\sqrt{18}}[/tex]
[tex]\cos B= \frac{3}{3\sqrt{2}}[/tex]
[tex]\cos B= \frac{1}{\sqrt{2}}[/tex]
Taking Inverse Cosine function,
[tex]B= \cos^{-1}( \frac{1}{\sqrt{2}})[/tex]
[tex]B=45^\circ[/tex]
Therefore, The measure of ∠ABC is 45°.
Write the equation of the line that passes through (–1, 5) and has a slope of 3 in point-slope form.
Answer:
y - 5 = 3 (x + 1)
Step-by-step explanation:
Start with the pertinent equation of a straight line: the point-slope form:
y-k = m(x-h), where (h,k) is the given point and m is the given slope.
Then y - 5 = 3(x-(-1) ), or y - 5 = 3 (x + 1).
Answer: [tex]y-5=3(x+1)[/tex]
Step-by-step explanation:
By definition the equation of the line written in point-slope form is the following:
[tex]y-y_1=m(x-x_1)[/tex]
Where ([tex]x_1,y_1[/tex]) is a point of the line and m is the slope.
You know that the slope is 3 and the ine that passes through (-1, 5).
Then, when you substitute these values into the equation, you obtain:
[tex]y-5=3(x-(-1))[/tex]
[tex]y-5=3(x+1)[/tex]
Julie wants to save $162 for a trip to an amusement park. She sets aside $12 of her allowance at the end of each week. How many weeks will it take her to save enough money for the whole trip?
It will take her 14 weeks to save up $162 dollars.
You need to do 162÷12 to do this. Although 162÷12 is 13.5, you have to round up, getting you the 14 weeks.
$4 is what percent of $8
Answer:
50%
Step-by-step explanation:
Is means equals and of means multiply
4 = P * 8
Divide each side by 8
4/8 = P 8/8
.5 = P
Multiply each side by 100 to change from decimal form to percent form
50% = P
4 is 50% of 8
Answer:
$4 is 50% of $8.Step-by-step explanation:
[tex]\begin{array}{ccc}\$8&-&100\%\\\\\$4&-&p\%\end{array}\qquad\text{cross multiply}\\\\\\8p=(4)(100)\\8p=400\qquad\text{divide both sides by 8}\\p=50\ (\%)[/tex]
What is the surface area of a sphere with a radius of 12 units
Answer:The surface area would be 1809.56units
Step-by-step explanation:
Answer:
576 pi units^2
Step-by-step explanation
I got it wrong and I'm giving you all the answer :)
what is the experimental probability of rolling a sum of 7 or 11?
I NEED HELP IT WILL MEAN THE WORLD
Answer:
Step-by-step explanation:
1 + 6 = 7
2 + 5 = 7
3 + 4 = 7
4 + 3 = 7
2 + 5 = 7
1 + 6 = 7
6 + 5 = 11
5 + 6 = 11
8 / 36 = 4 / 18 = 2 / 9
Eliminate the parameter.
x = 4 cos t, y = 4 sin
Select from the drop-down menu to correctly compare the numbers. 85‾‾‾√ 8.9860...
Answer:
Answer is. >
√85 > 8.9860
Step-by-step explanation:
√85 > 8.9860
This means that √85 is greater than 8.9860
This is because;
√85 = 9.2195...
9.2195.. is greater than 8.9860..
Answer:
>
Step-by-step explanation:
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with the number a. For example b = 2 when a = –2. Which equation represents this direct variation between a and b?
Answer:
a=-b? That might be wrong, sorry. But that's what it sounds like.
Step-by-step explanation:
The equation that represents the direct variation between the numbers a and b is b = -a.
Explanation:The equation that represents the direct variation between the numbers a and b is given by b = -a. In direct variation, when one variable increases, the other variable also increases, but in this case, they increase in opposite directions. For example, when a = -2, b = 2, and when a = 2, b = -2. Therefore, b varies directly with a, but in the opposite direction.
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What is the fifth term of the geometric sequence 5,15,45,...
Answer:
405
Step-by-step explanation:
This is a geometric sequence, so we need the common ratio and the first term
To find the common ratio, we take the second term and divide by the first term
15/5 =3
The common ratio is 3
We are multiplying by 3 each time
The first term is 5
The formula is
an = a1 * (r) ^ (n-1) where n is the term number
We want the 5th term
a5 = 5 * (3) ^ (5-1)
a5 = 5 *3^4
= 5 *81
= 405
The fifth term is 405.
[tex]a_{n}[/tex] = [tex]a_{1}[/tex]* [tex]r^{n-1}[/tex]
In this formula,[tex]a_{1}[/tex] is the first term,
r is the common ratio, and
n is the term number.
From the given sequence 5, 15, 45,..., we can identify the following:
[tex]a_{1}[/tex] = 5
r = 15 / 5 = 3 (common ratio)
Now, we need to find the fifth term (n = 5):
[tex]a_{5}[/tex] = 5 * [tex]3^{5-1}[/tex]
= 5 * [tex]3^{4}[/tex]
= 5 * 81
= 405
So, the fifth term of the geometric sequence is 405.
3x10-2 in standard notation
Answer: 0.032
Step-by-step explanation: poof
What would be the answer to this question
Answer:
The third one is the one I would choose
Hope this helped :)
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
([tex]\frac{f}{g}[/tex])(x)
= [tex]\frac{3x+5}{3x^2-x-10}[/tex] ← factor denominator
= [tex]\frac{3x+5}{(x-2)(3x+5)}[/tex] ← cancel (3x + 5), leaving
= [tex]\frac{1}{x-2}[/tex]
The denominator cannot be zero as this would make the fraction undefined. Equating the denominator to zero and solving gives the value that x cannot be.
solve x - 2 = 0 ⇒ x = 2 ← excluded value
domain is the set of all real numbers except 2
The expression (x^3 )(x^(-17) ) is equivalent to (x^n). What is the value of n?
Answer:
21
Step-by-step explanation:
Answer:
[tex]n=-14[/tex]
Step-by-step explanation:
The given expression is
[tex](x^3)(x^{-17})=x^n[/tex]
Recall that; [tex]a^m\times a^n=a^{m+n}[/tex]
We apply this property to the left hand side to obtain;
[tex]x^{3+-17}=x^n[/tex]
This simplifies to;
[tex]x^{3-17}=x^n[/tex]
[tex]x^{-14}=x^n[/tex]
Since the bases are the same; the exponents are also the same.
[tex]\therefore n=-14[/tex]
Save You More offers a buy one/get one free item each week. Customers who purchase only one of the items must pay the regular price. The limit is one deal per customer. Is the relation (# sale items purchased, price) a function? Why or why not? A) It is a function because the input can be either 1 or 2 items, but the output will always be the same price. B) It is not a function because the input can be either 1 or 2 items, but the output will always be the same price. C) It is a function because the input will always be the same price, but the output can be either one or two items. D) It is not a function because the input will always be the same price, but the output can be either one or two items.
Answer:
B
Step-by-step explanation:
Since a function would mean that a customer is able to purchase 1.1 of an item or 1.5 of an item, which is false. It also means that the customers pay the same price for a different amount of items.
Answer: The answer is A
It is a function because the input can be either 1 or 2 items, but the output will always be the same price.
According to the stated relation, (# sale items purchased, price), the input is the number of sale items purchased and the output is the price. The input values of a function can be different and have the same output value. However, a function cannot have different outputs for the same input.
Solve and graph the absolute value inequality: |2x + 1| ≤ 5.
Answer:
–7/2 ≤ x ≤ 5/2
Step-by-step explanation:
Given in the question an inequality
| 2x + 1 | ≤ 5
–5 ≤ 2x + 1 ≤ 5
–6 – 1 ≤ 2x + 1 -1 ≤ 6 – 1
–7 ≤ 2x ≤ 5
–7/2 ≤ x ≤ 5/2
Then the solution to | 2x + 1 | ≤ 5 is the interval –7/2 ≤ x ≤ 5/2
Graph is attach below
The solution to the absolute value inequality |2x + 1| ≤ 5 is the interval -3 ≤ x ≤ 2. To find this, two separate inequalities are solved based on the non-negative and negative cases within the absolute value. The graphical representation is a closed interval from -3 to 2 on the number line.
Explanation:To solve and graph the absolute value inequality |2x + 1| ≤ 5, we need to consider two cases based on the definition of absolute value.
If the expression inside the absolute value is non-negative (2x + 1 ≥ 0), then the inequality becomes 2x + 1 ≤ 5.If the expression inside the absolute value is negative (2x + 1 < 0), then the inequality becomes -(2x + 1) ≤ 5 which simplifies to 2x + 1 ≥ -5.We then solve these two inequalities:
2x + 1 ≤ 5 → 2x ≤ 4 → x ≤ 22x + 1 ≥ -5 → 2x ≥ -6 → x ≥ -3The solution set is the intersection of these two sets of numbers, which is -3 ≤ x ≤ 2. Graphically, this is represented on the number line as a closed interval from -3 to 2.
Find the length of ''C '' to the nearest tenth using the Pythagorean theorem.
Answer:
c = 10.63 unitsStep-by-step explanation:
a² + b² = c²
8² + 7² = c²
64 + 49 = c²
113 = c²
c = √113 = 10.63 units
The length of C for the triangle is 10.63 units
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.
The value of C is calculated by using the Pythagorean theorem.
a² + b² = c²
8² + 7² = c²
64 + 49 = c²
113 = c²
c = √113 = 10.63 units
Therefore, the length of C for the triangle is 10.63 units
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What values of c and d make the equation true? Assume x>0 and y >=0.
square root of 50x^6y^3/9x^8 = 5y^c square root of 2y/dx.
A.c = 1, d = 3
B.c = 1, d = 32
C.c = 2, d = 8
D.c = 2, d = 32
Answer:
A. c=1, d=3
Step-by-step explanation:
If x>0 and y>0, then
[tex]\sqrt{\dfrac{50x^6y^3}{9x^8}}=\sqrt{\dfrac{25\cdot 2y^2\cdot y}{9x^2}}=\dfrac{5y\sqrt{2y}}{3x}.[/tex]
If
[tex]\dfrac{5y\sqrt{2y}}{3x}[/tex]
is equal to
[tex]\dfrac{5y^c\sqrt{2y}}{dx},[/tex]
then
[tex]y=y^c\Rightarrow c=1,\\ \\3x=dx\Rightarrow d=3.[/tex]
Which shows the list of numbers in order from least to greatest?
Answer:
[tex]\textsf{A)}\;\;\; -2, \; \left|-\dfrac{4}{5}\right|, \; |-1|, \;|3.5|, \;|-4.2|[/tex]
[tex]\newline[/tex]
Step-by-step explanation:
[tex]\newline[/tex]
Given numbers:
[tex]\newline[/tex]
[tex]|-4.2|, \;\left|-\dfrac{4}{5}\right|, \; |-1|, \;-2, \; |3.5|[/tex]
[tex]\newline[/tex]
The absolute value of a number represents the distance of a number from zero on the number line, regardless of direction. This means that the absolute value of a number is always non-negative. For example, |-4.2| = 4.2, because the distance from -4.2 to 0 is 4.2 units.
[tex]\newline[/tex]
Evaluate each term:
[tex]\newline[/tex]
[tex]|-4.2|=4.2[/tex]
[tex]\left|-\dfrac{4}{5}\right|=\dfrac{4}{5}=0.8[/tex]
[tex]|-1|=1[/tex]
[tex]-2=-2[/tex]
[tex]|3.5|=3.5[/tex]
[tex]\newline[/tex]
Now, arrange them from least to greatest:
[tex]\newline[/tex]
[tex]-2, \;0.8, \;1, \;3.5, \;4.2[/tex]
[tex]\newline[/tex]
Therefore, the list of numbers in the correct order from least to greatest is:
[tex]\newline[/tex]
[tex]\large\boxed{-2, \; \left|-\dfrac{4}{5}\right|, \; |-1|, \;|3.5|, \;|-4.2|}[/tex]
25 + 13 points !!!!!!!
Ann has a net monthly income of $2,700.
Create a reasonable monthly budget for Ann. Be sure to include the following expenses:
Ann has a dog. Dog related expenses cost Ann about $150 every month.
Ann recently bought a new car. Her transportation expenses are $800 per month.
Answer:
ann would have $1700 left for bills or rent food etc
Step-by-step explanation:
Ann's proposed monthly budget takes into account her $2,700 net income and fixes expenses for her dog and new car. After allocating for these expenses, the budget proposes estimated allocations for rent, utilities, groceries, entertainment, and savings, with an emphasis on setting aside roughly 10% for savings as a good financial habit.
To create a reasonable monthly budget for Ann who has a net monthly income of $2,700, we need to allocate funds to her known expenses and then distribute the remaining amount to cover other typical living costs such as rent, utilities, groceries, and savings. Ann has two fixed expenses mentioned: dog-related expenses that cost about $150 every month, and her transportation expenses which are $800 for her new car. Once we subtract these amounts from her monthly income, we can allocate the rest to other necessary expenses.
Here is a proposed monthly budget for Ann:
Net Monthly Income: $2,700
Dog-Related Expenses: -$150
Transportation (Car Expenses): -$800
Rent: -$900 (estimate based on average rent costs)
Utilities: -$150 (estimate including electricity, water, and gas)
Groceries: -$300 (estimate for a single person)
Entertainment: -$100 (for dining out, movies, etc.)
Savings: -$200 (aiming for roughly 10% savings as good financial practice)
Find the real zeros of the function f(x)= x^4-15x^2+10x+24
Answer:
x=3,2,-1,-4
Step-by-step explanation:
The roots (zeros) are the x
values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x
Min's hose can pump 21 gallons of water every hour. How many gallons of water will he fill up if he runs the hose for 2/3 of an hour?
Final answer:
Min's hose will fill up 14 gallons of water if it runs for 2/3 of an hour, based on its rate of 21 gallons per hour.
Explanation:
The question asks us to calculate how many gallons of water Min's hose can pump if it runs for 2/3 of an hour, given that it pumps water at a rate of 21 gallons per hour.
First, we need to find out how much water the hose would pump in one hour and then calculate 2/3 of that amount:
Full capacity in one hour: 21 gallons
Capacity in 2/3 of an hour: (21 gallons) * (2/3) = 14 gallons
So, Min's hose will fill up 14 gallons of water if it runs for 2/3 of an hour.
Solve and explain the question below
Roman has a certain amount of money. If he spends $15, then he has 1/4 of the original amount left. How much money did Roman have originally?
The equation was solved step by step to find that Roman initially had $20.
Roman has a certain amount of money. If he spends $15, then he has 1/4 of the original amount left. To find out how much money Roman had originally, we can set up an equation. Let's call the original amount of money x. After spending $15, Roman has x - 15 dollars left, which we are told is 1/4 of the original amount, x.
So, the equation we can write is:
x - 15 = 1/4 x
To solve for x, we multiply each side of the equation by 4 to get rid of the fraction on the right side:
4(x - 15) = x
Which simplifies to:
4x - 60 = x
Then we subtract x from both sides to get x on one side:
3x - 60 = 0
Now, we add 60 to both sides to solve for x:
3x = 60
Finally, we divide both sides by 3 to find x:
x = 20
Therefore, Roman originally had $20.
Start at point A (-2,5). Translate it 3 units left and 4 units up on the coordinate plane. How will this affect the x- and y- coordinates of the point? Where will point A' be after the translation.
A. (1,9)
B.(-5,1)
C.(-5,1)
D.(-2,5)
Answer:
A.
Step-by-step explanation:
3 1/4 pt = _______ fl oz
Answer:
52
Step-by-step explanation:
3.25 pints = 52 fluid ounces since there are 16 fl oz in one pint.
David scored x marks for his mathematics test, Edwin scored 4/5 of what David scored. Frank scored 38 marks more than Edwin and Gabriel scored 5 fewer marks than Frank.
(a) Express Gabriel's marks in terms of x.
(b) if the average mark of the four boys is 64.5, find Gabriel's marks for the Mathematics test.
D=x
E=(4/5)•x
F=E+38
F=(4/5)•x+38
G=F-5
G=(4/5)x+38-5
G=(4/5)x+33. ⟨——answer for A
64.5=[d+e+f+g]/4
64.5=[5x/5+4x/5+4x/5+38+4x/5+33]/4
4•64.5=9x/5+8x/5+71
258=17x/5+71
258-17=17x/5
241=17x/5
5•241=17x
1205/17=x
70.88=x
G=(4/5)x+33
G=(4/5)(70.88)+33
G=89.7 ⟨——answer to part B
Gabriel's marks in terms of x is (G = 4x/5 + 38) and if the average mark of the four boys is 64.5 then Gabriel's marks for the Mathematics test is 89.7.
Given :
David scored x marks for his mathematics test, Edwin scored 4/5 of what David scored.Frank scored 38 marks more than Edwin and Gabriel scored 5 fewer marks than Frank.Score of David in the mathematics test is given by:
D = x
Score of Edwin in the mathematics test is given by:
[tex]\rm E = \dfrac{4}{5}x[/tex]
Score of Frank in the mathematics test is given by:
[tex]\rm F = \dfrac{4}{5}x + 38[/tex]
Score of Gabriel in the mathematics test is given by:
G = F - 5 ---- (1)
a) Now, substitute the value of F in the equation (1)
[tex]\rm G = \dfrac{4x}{5}+38-5[/tex]
[tex]\rm G = \dfrac{4x}{5}+33[/tex]
b) Given that the average mark of the four boys is 64.5 that is:
[tex]\rm \dfrac{G+F+E+D}{4}=64.5[/tex]
Now, substitute the values of G, F, E, and D in the above equation. After simplifying the expression:
[tex]258=\dfrac{17x}{5}+17[/tex]
Further, simplify the above expression it becomes:
x = 70.88
So, Gabriel's marks for the Mathematics test is:
[tex]\rm G = \dfrac{4\times 70.88}{5}+33[/tex]
G = 89.7
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