Answer:
see explanation
Step-by-step explanation:
1
Given
y - 4 = 5(x + 2) ← distribute parenthesis
y - 4 = 5x + 10 ( add 4 to both sides )
y = 5x + 14 → B
Subtract y from both sides
0 = 5x - y + 14 ( subtract 14 from both sides )
- 14 = 5x - y → C
--------------------------------------------------
2
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 5 and c = 1, thus
y = 5x + 1 → A
P(A)= .50 P(B)=.80 P(A and B)=.20 what is P(B/A)
Answer:
Final answer is [tex]P(B|A)=0.40[/tex].
Step-by-step explanation:
Given that P(A)= .50, P(B)=.80 , and P(A and B)=.20.
Now we need to find about what is the value of P(B/A).
So apply the formula of compound probability :
P(A and B) = P(A)*P(B/A)
Plug the given values into above formula
0.20 = 0.50*P(B/A)
0.50*P(B/A) = 0.20
[tex]P(B|A)=\frac{0.20}{0.50}[/tex]
[tex]P(B|A)=0.40[/tex]
Hence final answer is [tex]P(B|A)=0.40[/tex].
A store is having a sale on walnuts and chocolate chips. For 3 pounds of walnuts and 2 pounds of chocolate chips, the total cost is $13. For 8 pounds of walnuts and 4 pounds of chocolate chips, the total cost is $33. Find the cost for each pound of walnuts and each pound of chocolate chips .
Final answer:
By setting up and solving a system of linear equations, we find that walnuts cost $3.50 per pound and chocolate chips cost $1.25 per pound.
Explanation:
The question involves using a system of two linear equations to find the cost per pound of walnuts and chocolate chips. We can define w to be the cost of one pound of walnuts and c to be the cost of one pound of chocolate chips. From the information given, we can set up the following two equations:
3w + 2c = 13
8w + 4c = 33
To solve these equations, we can use either substitution or elimination. Let's use elimination:
Multiply the first equation by 2 to align the coefficients of c. This gives us: 6w + 4c = 26.
Now, subtract the newly obtained equation from the second one: (8w + 4c) - (6w + 4c) = 33 - 26, which simplifies to 2w = 7.
Divide both sides by 2 to find w: w = 7/2, so w = $3.50 per pound for walnuts.
Substitute the value of w back into the first equation: 3(3.50) + 2c = 13. Therefore, 10.50 + 2c = 13.
Subtract 10.50 from both sides to find c: 2c = 2.50.
Divide both sides by 2 to get: c = 2.50 / 2, so c = $1.25 per pound for chocolate chips.
Therefore, walnuts cost $3.50 per pound and chocolate chips cost $1.25 per pound.
You are choosing sprinklers for an irrigation system. One sprinkler that covers a full circle specifies a watering radius of 14 ft at 25lbs per square inch of water pressure. What is the maximum area to the nearest sq. foot that this sprinkler will cover at this pressure?
Answer:
Area= 615 ft²
Step-by-step explanation:
Apply the formula for area of a circle to find the area watered when a sprinkler covers a full circle
Area of a circle= [tex]\pi r^{2}[/tex]
r= 14ft
Area= 3.14 × 14²
Area=615.44 ft²
Area= 615 ft²
9 with negative 3/2 exponent
Answer:
i believe it would be 1/27 or 0.037 depending on the form you need it in
Step-by-step explanation:
[tex] \bf \underline{Solution-} \\ [/tex]
[tex]\textsf{Given}\\[/tex]
[tex] \sf{ {9}^{ \frac{3}{2} } } \\ [/tex]
[tex] \longrightarrow{ \: ( {3}^{2} {)}^{ \frac{3}{2} } } \\ [/tex]
[tex] \longrightarrow{ \: {3}^ { \cancel2 \times \frac{3}{ \cancel2} } } \\ [/tex]
[tex] \longrightarrow{ {3}^{3} } \\ [/tex]
[tex] \longrightarrow{ \: 3 \times 3 \times 3} \\ [/tex]
[tex] \sf \longrightarrow{ \: 27 \: ans.} \\ [/tex]
[tex]\textsf{Hope this helps!!}\\[/tex]
a triangle has a base of 7m and a hypotenuse of 25m what is the area
Answer:
84 m²
Step-by-step explanation:
If you mention "hypotenuse," I automatically assume that this is a right triangle. We can find the length of the third side using the Pythagorean Theorem: 7² + x² = 25², or x² = 625 - 49 = 576.
Then the 3rd side (which is also the height of the triangle) is x = √576 = 24.
The base of this triangle is 7 m and the height is 24 m.
The area is thus:
A = (1/2)(base)(height) = (1/2)(7 m)(24 m) = 84 m²
Pete borrowed $400 for 1 year. He paid back a total of $440. What was the interest rate per year?
I=PRT/100
1. Make R (rate) subject
R/100= I/PT
2. Substitute and calculate
r/100= i/pt
r/100= 40/400 × 1
(40 is from 440-400.The interest)
r/100= 0.1
r/100×100= 0.1×100
r=10% (interest rate per year)
To confirm
I=PRT
I= 400×10/100×1
I= $40 (Interest)
Answer:
$40
Step-by-step explanation:
find Y
$400=x
$440=x+y
x+$40=x+y
$40=y
Quadrilateral ABCD is transformed according to the rule (x, y) → (y, –x). Which is another way to state the transformation?
Step-by-step explanation:
That means it is rotated 90° clockwise about the origin.
Answer:
90° clockwise rotation .
Step-by-step explanation:
Given : Quadrilateral ABCD is transformed according to the rule (x, y) → (y, –x).
To find : Which is another way to state the transformation.
Solution : We have given that Quadrilateral ABCD
(x, y) → (y, –x).
It can be stated as it is as 90° clockwise rotation .
Therefore, 90° clockwise rotation .
The length of the diagonal of a square is 6√2. What is the length of one side?
Answer:
6
Step-by-step explanation:
Given in the question that,
length of the diagonal of a square = 6√2
As we know that a square have all lengths equal in size and lengths are perpendicular to each other so to solve this question we will use pythagorus theorem
hypotenuse² = base² + height²
here,
hypotenuse is the diagonal of the square
base and height side length of the square
Plug value in the formula
6√2² = l² + l²
36(2) = 2l²
72 = 2l²
l² = 72/2
l² = 36
take square root on both sides of the equation
l = √36
l = 6Answer:
6
Step-by-step explanation:
The diagonal of the square represents the hypotenuse of a right triangle formed by the diagonal and 2 sides of the square.
Using Pythagoras' theorem
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
let x be the side of the square then
x² + x² = ( 6[tex]\sqrt{2}[/tex])²
2x² = 72 ( divide both sides by 2 )
x² = 36 ( take the square root of both sides )
x = [tex]\sqrt{36}[/tex] = 6
- 6x +15
Can anyone please show me the steps of solving this equation
Answer:
-6x + 15 = - 69 which x = 14
Step-by-step explanation:
You cannot solve this equation. There is no equal sign anywhere. Either you mean
-6x = 15 in which case the answer is
-6x/-6 = 15/-6
x = - 2 1/2 or x= - 2.5
or you mean that you use the distributive property
- 3(2x + 5)
You may have left something out of this.
-6x + 15 = - 69
You can do it now that you have the complete equation. But you need the entire equation before you can answer the question.
Subtract - 15 from both sides.
-6x + 15 - 15 = -69 - 15
-6x = - 84
Divide by - 6
-6x/-6 = - 84/-6
x = 14
But what you want is
-6x + 15
-6*14 + 15
-84 + 15
-69
-6x + 15 = - 69
when x = 14 which is usually what you are asked.
The constant of proportionality for the amount of electricity in kilowatt hours and the cost per kilowatt hour is $0.11. Which graph models this situation?
Answer:
The answer I beleive is actually A because if you divide the x value by the y-value it gives you 0.11 and no other graph gives you that exact amount dividing either y or x values
Step-by-step explanation:
Sorry for being so late lol
The answer is, electticity cost.
What is graph in math definition?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.What is graph explain with example?A graph is a common data structure that consists of a finite set of nodes (or vertices) and a set of edges connecting them. A pair (x,y) is referred to as an edge, which communicates that the x vertex connects to the y vertex. In the examples below, circles represent vertices, while lines represent edges.Why do we use graphs?Graphs and charts are effective visual tools because they present information quickly and easily. It is not surprising then, that graphs are commonly used by print and electronic media. Sometimes, data can be better understood when presented by a graph than by a table because the graph can reveal a trend or comparison.Learn more about graphs here:
https://brainly.com/question/19040584
#SPJ2
10. Which of the following is a linear equation?
a. 4x² +9y2 = 25
b. 2+ 6 = 15
C. 2x-3y=7
d. 4x+6 = 30
Answer:
C.
Step-by-step explanation:
It is linear because it have two variables (x and y) and the highest powers that they are raised to are 1
For this case we have that by definition, a linear equation is of the form:
[tex]ax + b = 0[/tex]
That is, the largest exponent of the variable is 1.
Then, according to the options given, we have that the correct option is option D, that is:
[tex]4x + 6 = 30[/tex]
Answer:
Option D
Find the mean and standard deviation of the
data. Round to the nearest tenth.
62, 37, 48, 67, 44, 58, 47, 47
Calculate the mean, standard deviation, and a value one standard deviation below the mean for a data set.
Mean: To find the mean, add all the numbers together and divide by the total count. (62 + 37 + 48 + 67 + 44 + 58 + 47) / 7 = 49.6
Standard Deviation: Calculate the standard deviation using a formula or a calculator. For the given data, the standard deviation is approximately 9.7 rounded to the nearest tenth.
One Standard Deviation Below Mean: To find this value, subtract the mean from one standard deviation: 49.6 - 9.7 = 39.9
Find the value of x
Α. 7
B. 9
c. 11
D. 12
Answer:
Final answer is [tex]x=9[/tex].
Step-by-step explanation:
we know that if BD is angle bisector of angle B in triangle ABC then
[tex]\frac{AB}{BC}=\frac{AD}{DC}[/tex]
[tex]\frac{36}{28}=\frac{x}{DC}[/tex]
[tex]\frac{36}{28}=\frac{x}{16-x}[/tex]
[tex]\frac{9}{7}=\frac{x}{16-x}[/tex]
cross multiply
[tex]7x=9(16-x)[/tex]
[tex]7x=144-9x[/tex]
[tex]7x+9x=144[/tex]
[tex]16x=144[/tex]
[tex]x=\frac{144}{9}[/tex]
[tex]x=9[/tex]
Hence final answer is [tex]x=9[/tex].
The height of a rectangular prism is found by dividing volume, V, by the base area, B.
If the volume of the rectangular prism is represented by 6x2 – 2x + 8 and the base area is 2x – 4, which expression represents the height?
Answer:
[tex]3x+5 + \frac{28}{2x-4}[/tex]
Step-by-step explanation:
If the volume of the rectangular prism is represented by [tex]6x^2 - 2x + 8[/tex] and the base area is [tex]2x - 4[/tex]
Volume of a prism = base area times height
we replace the volume and the base area
[tex]6x^2-2x+8 = (2x-4) \cdot height[/tex]
Divide both sides by 2x-4
[tex]height= \frac{6x^2-2x+8}{2x-4}[/tex]
we use long division.
3x+5
----------------------------------------------
[tex]2x-4[/tex] [tex]6x^2 - 2x + 8[/tex]
[tex]6x^2 - 12x[/tex]
-----------------------------------------------(subtract)
[tex]10x+8[/tex]
[tex]10x-20[/tex]
------------------------------------------------(subtract)
28
[tex]3x+5 + \frac{28}{2x-4}[/tex]
x=
- 100
- 120
- 140
THE ANSWER ABOVE/ BELOW IS WRONG!!!
The correct answer is actually:
140
Answer:
140
Step-by-step explanation:
Two cell phone companies have different rate plans. Runfast has monthly charges $8 plus $8 per gig of
data. B A &D’s monthly charge is $15 plus $4 per gig of data. Your task is to determine under what
circumstances each company has the better pricing. You will derive and solve a set of equations, graph
those equations, and evaluate the meanings for these events. Don’t worry; I have a series of questions
to guide you through the process. Good luck!
1. Determine the equation for the monthly charges for Runfast and BA&D. (2 points)
Runfast= ______________________
BA&D=________________________
2. Use your mathematical skill to solve this system of equations using the substitution method. (4
points)
Show your work here:
Answer:
Part 1) The equation for the monthly charges for Runfast is [tex]y=8x+8[/tex] and for BA&D is [tex]y=4x+15[/tex]
Part 2) The solution of the system of equations is the point (1.75.22)
Step-by-step explanation:
Let
x -----> the number of gig of data
y -----> the total monthly charges
we know that
Runfast Company
[tex]y=8x+8[/tex] -----> equation A
BA&D Company
[tex]y=4x+15[/tex] -----> equation B
Part 2) Use your mathematical skill to solve this system of equations using the substitution method
we have
[tex]y=8x+8[/tex] -----> equation A
[tex]y=4x+15[/tex] -----> equation B
Substitute equation B in equation A and solve for x
[tex]4x+15=8x+8[/tex]
[tex]8x-4x=15-8[/tex]
[tex]4x=7[/tex]
[tex]x=1.75\ Gb[/tex]
Find the value of y
[tex]y=8(1.75)+8=\$22[/tex]
so
The solution is the point (1.75.22)
That means
For the number of gig equal to 1.75 the monthly charge is equal to $22 in both company's
therefore
For a number of gigs less than 1.75 the company Runfast has the better pricing, while for a number of gigs greater than 1.75 the company BA&D has the better pricing
what is the value of the inequality?
n+7 <5
Hello there! n < -2.
Solve for n. To do this, you want to get all other terms on the other side of the equation. The only other term is 7 in this case, so subtract 7 from both sides of the equation.
n +7-7< 5-7
n < -2
This is your final answer! I hope this helps and have a great day!
Answer:
The solution is n<-2
Step-by-step explanation:
The given inequality is:
n+7 <5
We solve this inequality by adding -7 to both sides of the inequality:
n+7 +-7<5+-7
We simplify to get:
n+0<5-7
this finally gives us:
n<-2
The solution is n<-2
The price of a flight was increased by 3% to £720. What was the price before the increase?
Give your answer to the nearest penny.
To fond the price before the increase divide the new price by 1 plus the percent of increase:
720 / 1.03 = 699.029
Rounded to the nearest penny = 699.03
Solve the formula C = td for d.
Answer:
d = C /t
Step-by-step explanation:
C = td
We want to isolate d, so divide each side by t
C/t = td/t
C/t = d
d = C /t
Answer: c/d = t
Since d is being multiplied by t, to get d by itself we simply divide both sides of the equation by t and we have c/d = t which is our final answer.
The expression x2 – 25 is equivalent to which of the following expressions
The equivalent expression would be,
⇒ (x - 5) (x + 5)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ x² - 25
Now, We can simplify as;
⇒ x² - 25
⇒ x² - 5²
⇒ (x - 5) (x + 5)
Thus, The equivalent expression would be,
⇒ (x - 5) (x + 5)
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ3
Final answer:
The expression x²- 25 is a difference of squares and can be factored into (x - 5)(x + 5), which is the product of two binomials.
Explanation:
The expression x²² – 25 can be factored into a product of two binomials because it represents a difference of squares. A difference of squares is a specific type of polynomial that takes the form a²– b², which can be factored into (a – b)(a + b). In the case of x² – 25, we can identify a as x and b as 5 since 52 equals 25.
Therefore, we can factor the expression x² – 25 into:
(x – 5)(x + 5)
This utilizes the factoring technique, which is a crucial algebraic skill for simplifying expressions and solving equations.
Drag the correct steps into order to evaluate 27 – t • 3 for t = 6.
Answer:
the answer is 9
Answer:
27 - t · 3
27 - 6 · 3
27 - 18
9
Step-by-step explanation:
You and 3 friends went out for dinner. The bill is $85.36. How much does each person owe?
Answer:
$21.34
Step-by-step explanation:
You and 3 friends went out for dinner, total 4 people
The bill is $85.36
So
Each person owes = $85.36 / 4 = $21.34
Answer:28.45
Step-by-step explanation:divide 3 by 85.36
Every month, $65 is withdrawn from Tom's savings account to pay for his gym membership. He has enough savings to withdraw no more than $585. For how many months can Tom pay for his gym membership?
Answer:
hey can pay for 9 months
Step-by-step explanation:
585/65
Just simply divide 585 with 65 and you get number of months.
[tex]585\div65=\boxed{9}[/tex]
Tom can pay for 9 months for his gym membership.
Hope this helps.
r3t40
what is the solution set for 3x+1≥8 and 10x≤15
A. { x : 1 1/2 ≤ x ≤ 2 1/2 }
B. no solution
C. { x : 5 < x < 7 }
D. { x : x < 5 or x > 7 }
Answer:
the answer is D
Step-by-step explanation:
To solve the inequalities 3x + 1 ≥ 8 and 10x ≤ 15, we find that no x can satisfy both inequalities simultaneously. Thus, the solution set is empty and the correct answer is B. No solution.
Solving the System of Inequalities
We need to find the solution set for the system: 3x + 1 ≥ 8 and 10x ≤ 15.
Solve the first inequality:3x + 1 ≥ 8
Subtract 1 from both sides: 3x ≥ 7
Divide by 3: x ≥ 7/3 x ≥ 2.33
Solve the second inequality:10x ≤ 15
Divide by 10: x ≤ 1.5
Combine the two results:For the two conditions x ≥ 2.33 and x ≤ 1.5 to both be true, there is no number x that satisfies both.
Therefore, the solution set is empty.
The correct answer is B. No solution.
the first ferris wheel was built in 1893 in chicago. It’s diameter was 250 feet. How many feet did the ferris wheel rotate with one complete turn?
Answer:
about 785.4
Step-by-step explanation:
The circumference of a circle is pi times the diameter:
C = πd
C = π·(250 ft) ≈ 785.4 ft
_____
Most scientific or graphing calculators have the value of π built in. If yours doesn't, a value good for at least 6 significant figures is the ratio 355/113.
The ferris wheel rotates approximately 785 feet in one complete turn. This was calculated using the circumference formula, 2πr, with the radius derived from the given diameter of 250 feet.
Explanation:To solve this problem, we need to determine the circumference of the Ferris wheel as that would be equivalent to the distance the ferris wheel rotated in one complete turn. The formula to calculate the circumference of a circle (or ferris wheel in this case) is 2πr (2 times pi times the radius), where 'r' is the radius of the circle. However, since we're given the diameter of the Ferris wheel as 250 feet, we know that the radius 'r' would be half of the diameter. That would imply that the radius in this case is 250/2 = 125 feet. So, using the aforementioned formula, the circumference would therefore be 2 × π × 125, or approximately 785 feet. Therefore, with each complete turn, the Ferris wheel would rotate by about 785 feet.
Learn more about Circumference Calculation here:https://brainly.com/question/30656333
#SPJ3
Please help!
Solve the equation for x.
Answer:
c. 10
Step-by-step explanation:
First of all, the sum can be simplified.
[tex]\sum\limits^6_{n=1} {(x-3n)}=\sum\limits^6_{n=1} {x}-3\sum\limits^6_{n=1} {n}\\\\=6x-3\cdot\dfrac{6\cdot 7}{2} =6x-63[/tex]
This result can be used in the equation ...
6x -63 = -3
6x = 60 . . . . . add 63
x = 10 . . . . . . . divide by 6
_____
Comment on the ∑n
The sum of numbers 1 to n is n(n+1)/2. We have used that fact here. For this problem, the sum is short enough you can simply add it up: 1+2+3+4+5+6 = 21.
[tex]\bf \displaystyle\sum\limits_{n=1}^{6}~(x-3n)=-3\implies \sum\limits_{n=1}^{6}~x-\sum\limits_{n=1}^{6}~3n=-3\implies \sum\limits_{n=1}^{6}~x-3\sum\limits_{n=1}^{6}~n=-3 \\\\\\ 6(x)~~-~~3\left[ \cfrac{6(6+1)}{2} \right]=-3\implies 6x~~-~~3[3(7)]=-3\implies 6x - 63 = -3 \\\\\\ 6x=60\implies x=\cfrac{60}{6}\implies x=10[/tex]
A bag contains six red marbles three blue marbles and five green marble the three marbles are drawn out of the bag what is the probability to the nearest one hundredth that all three marbles will be drawn red?
Answer:
Step-by-step explanation:
Red = 6
Blue = 3
Green = 5
Total = 14
First marble = 6/14 = 3/7 You now have 5 reds and 13 total
Second Marble = 5 * 13 which brings you down to 4 red and 12 total.
Third Marble = 4/12 = 1/3
Result
P(3 Red) = 3/7 * 5/13 * 1/3 cancel the 3s
P(3 Red) = 1/7 * 5/13
P(3 Red) = 5/91
P(3 Red) = 0.0549 . Rounding to the nearest 1/100 depends on what you have been told about rounding. I would say the answer is 0.05 but your teacher may say something different.
Math problem!!! Help needed 10 points !!!
ANSWER
Option D
EXPLANATION
The parent radical function is
[tex]f(x) = \sqrt{x} [/tex]
The transformed function is
[tex]g(x) = 2 \sqrt{x - 3} [/tex]
This is a transformation of the form.
[tex]y = a \sqrt{x - k} [/tex]
which shifts the parent function horizontally by k units to the right and stretches the parent function vertically by a factor of 'a'.
In this case a=2 and k=3,
there is a horizontal shift of 3 units to the right and a vertical stretch by a factor of 2.
The last choice is correct.
Solve the matrix equation for X.
See the attached picture:
Answer:
[tex]\large\boxed{\left[\begin{array}{ccc}-2&11\\-1&10\end{array}\right]}[/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}8&-7\\1&-5\end{array}\right] +X=\left[\begin{array}{ccc}6&4\\0&5\end{array}\right]\\\\\left[\begin{array}{ccc}8&-7\\1&-5\end{array}\right] -\left[\begin{array}{ccc}8&-7\\1&-5\end{array}\right]+X=\left[\begin{array}{ccc}6&4\\0&5\end{array}\right] -\left[\begin{array}{ccc}8&-7\\1&-5\end{array}\right]\\\\X=\left[\begin{array}{ccc}6-8&4-(-7)\\0-1&5-(-5)\end{array}\right]\\\\X=\left[\begin{array}{ccc}-2&11\\-1&10\end{array}\right][/tex]
Find the tenth term in the sequence
that is defined as follows:
an = 4 + (-1)^n
Answer: 4 + (-1)^10 = 4+ 1 = 5
The tenth term of the sequence is 5.
Given to us,
Sequence, [tex]\bold{a_n=4+(-1)^n}[/tex]
For tenth term,
n = 10,
Subsituting the value of n we get,
[tex]{a_n=4+(-1)^n}\\a_{10}=4+(-1)^{10}\\a_{10} = 4 + 1\\a_{10} = 5[/tex]
Hence, the tenth term of the sequence is 5.
To know more visit:
https://brainly.com/question/21961097