Answer:
Step-by-step explanation:
Formula
a = 9 / (f - 7)
Note
If you are going to try and isolate f, you must take the 7 with it, assuming that getting f to the left hand side will the your first step. It will be mine.
Solution
a = 9 / (f - 7) Multiply both sides by (f - 7) leave the brackets around (f - 7)
a(f - 7) = 9(f - 7)/(f - 7) Combine
a(f - 7) = 9 Remove the brackets
fa - 7a = 9 Add 63 to both sides
fa - 7a + 7a = 9 + 7a Combine
fa = 9 + 7a Divide by a
fa/a = (9 + 7a)/a Simplify
f = (9 + 7a)/a
Answer
f = (9 + 7a)/a
PQ = 15cm and QR = 17cm. Calculate the perimeter of PQR.
can u please tell if the figure is a right angled triangle??...cuz in order to find the perimeter, Pythagoras theorem must be applied but it's only for right angled triangle...so specify please
What is the area of this triangle?
1375 ft²
1500 ft²
3300 ft²
4500 ft²
Answer:
Area of a triangle = 1/2 * base * height
here ,
base = 120 ft
height = 25 ft
Area = 1/2* 120*25
= 60 * 25
= 1500 ft²
Answer 2
Answer:
1/2 * base * height
so 1/2 * 25 * 120
= 1500
B, C and D are points on the circumference of a circle, centre O.
AB and AD are tangents to the circle.
Angle DAB = 50 degrees
Work out the size of angle BCD.
Construct OD and BD. Then, in quadrilateral ABOD, angles ODA and OBA are right angles and thus angle DOB is 130 degrees (since angles in a quadrilateral add to 360 degrees).
So, this means arc DB also measures 130 degrees. Hence, by the inscribed angle theorem, angle BCD is 65 degrees.
The table shows some information about the lifetimes,
t
, in hours, of some lightbulbs.
Lifetime Frequency
25 <
t
≤ 50 70
50 <
t
≤ 100 76
100 <
t
≤ 150 29
150 <
t
≤ 200 91
200 <
t
≤ 250 0
250 <
t
≤ 300 15
300 <
t
≤ 350 23
Estimate the mean lifetime of a bulb.
Give your answer rounded to 2 DP.
Answer:
25 < t < 350
Step-by-step explanation:
The mean lifetime of a bulb ranges from 25 to 350 hrs but the question is unclear.
HELP NOW PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE PLEASE
Answer:
-3/2
Step-by-step explanation:
First, you divide by taking the reciprocal of -2/5 which is -5/2.
Second, you get the answer which is -5/4.
Add that with -1/4 and you will get -6/4.
Simplify to get the answer which is -3/2.
Answer:
[tex]-\dfrac{3}{2}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{\dfrac{1}{2}}{-\dfrac{2}{5}}+\left(-\dfrac{1}{4}\right)[/tex]
To divide fractions, flip the second fraction (make the numerator the denominator, and the denominator the numerator) then multiply it by the first fraction:
[tex]\implies \dfrac{1}{2} \times -\dfrac{5}{2}+\left(-\dfrac{1}{4}\right)[/tex]
To multiply the fractions, multiply the numerators and multiply the denominators:
[tex]\implies \dfrac{1 \times (-5)}{2 \times 2} +\left(-\dfrac{1}{4}\right)[/tex]
[tex]\implies -\dfrac{5}{4} +\left(-\dfrac{1}{4}\right)[/tex]
Apply the rule -a + (-b) = -a - b :
[tex]\implies -\dfrac{5}{4} -\dfrac{1}{4}[/tex]
As the denominators are the same, subtract the numerators and put the answer over the same denominator:
[tex]\implies \dfrac{-5-1}{4}[/tex]
[tex]\implies -\dfrac{6}{4}[/tex]
Simplify by dividing the numerator and denominator by the highest common factor:
[tex]\implies -\dfrac{6 \div 2}{4 \div 2}[/tex]
[tex]\implies -\dfrac{3}{2}[/tex]
Hi! So, I know I got this answer wrong, but I wasn't sure how to solve an equation with signs like: [brackets] in it, I've included my problem as an example, but can someone please teach me what those brackets mean, and how do I go about solving an equation (using this problem as an example) with brackets like these?
Step-by-step explanation:
Brackets is the bigger version of parentheses, you first solve the questions inside the parentheses, then move onto brackets.
For example, this question:
[tex]x=-1\\y=-2\\z=3[/tex]
[tex]5x-y[7-4(z-y)][/tex]
plug in x, y, and z.
[tex]5(-1)-(-2)[7-4(3-(-2))][/tex]
[tex]5(-1)-(-2)[7-4(5)][/tex]
[tex]5(-1)-(-2)[7-20][/tex]
[tex]5(-1)-(-2)[-13][/tex]
[tex]-5-(-2)[-13][/tex]
[tex]-5-26[/tex]
[tex]-31[/tex]
I hope you understand better now.
Which currency is it
Answer:
pounds (£)
Step-by-step explanation:
pounds are used in countries such as the UK and South Georgia
Desiree is given an aptitude test with 50 multiple-choice questions. For every correct answer, Desiree will get 3 points. For every wrong answer, 1 point will be deducted. For every question unanswered, 0.5 point is deducted. Desiree did not leave any question unanswered and gets 110 points on the test.
If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is
and the equation will have
.
Total number of multiple-choice questions that Desiree has to answer in Aptitude test = 50
Points given for every correct Answer = +3
Points deducted for every Incorrect Answer = -1
For every question unanswered ,
points Deducted = -0.5
Total Points Obtained by Desiree after Answering all the questions = 110
Number of Answers that Desiree answered correctly = x questions
Number of Incorrect Answers = (50 - x) questions
Then,the Equation representing above situation
→ 3 × x + ( -1 ) × ( 50 - x ) = 110
⇒3x - 50 + x = 110 ----------- equation that represents the given situation
⇒ 4x - 50 = 110
Adding 50, on both sides
→ 4x - 50 + 50 = 110 + 50
⇒ 4x = 160
Dividing both sides by, 4 we get
x = 40
Number of correct answers given by Desiree= 40 questions
Number of Incorrect Answers = 50 - 40
= 10 Questions .
Answer:
Desiree is given an aptitude test with 50 multiple-choice questions. For every correct answer, Desiree will get 3 points. For every wrong answer, 1 point will be deducted. For every question unanswered, 0.5 points is deducted. Desiree did not leave any questions unanswered and gets 110 points on the test.
If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is
3(50 - x) + x = 110
and the equation will have
no solution
.
Step-by-step explanation:
If 15 members vote to choose 4 group leaders, what is the probability that 4 candidates will be chosen for 4 positions
Answer:
[tex]\frac{4}{60}[/tex] = [tex]\frac{1}{15}[/tex]
Step-by-step explanation:
Missing angles/math please help guys
Answer:
Step-by-step explanation:
A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (0, 4) and (1, 1) The second line is labeled y - g(x) and is horizontal passing through (negative 2, 2), (0, 2), and (2, 2). The lines intersect at a point that is slightly to the right of (0.5, 2).
If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.
The value of x if both lines intersect is 2/3
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
Given the equation of a line that passed through the points (0, 4) and (1, 1) expressed as h(x) = -3x +4
The equation of the second line g(x) passing through the points (-2, 2) and (0, 2) is g(x) = 2
If the lines intersect, then h(x) = g(x)
Substituting the functions to get the value of "x"
-3x + 4 = 2
Subtract 4 from both sides
-3x + 4 - 4 = 2 - 4
-3x = - 2
Divide both sides by - 3
x = 2 / 3
Hence the value of x if both lines intersect is 2/3
To learn more about equations follow
brainly.com/question/13080629
#SPJ1
Answer:
2/3
Step-by-step explanation:
edge23
Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience. The path of the gymnasts is parabolic and modeled by the following equations, where y is the height of the flip and x is the time in seconds:
Answer:
4 secs
Step-by-step explanation:
Since they have to be synchronized, their parabolic equations must be equal to one another
3(t^2 + 9 - 6t) - (t^2 + 25 - 10t) - t + 2 = 0
2t^2 - 9t + 4
(2t - 1)(t - 4) = 0
t = 1/2, 4
From the options, the answer is 4
The gymnasts will be at the same height during their flips at two different times: 1/2 seconds and 4 seconds.
so, correct option is: C.
Here, we have,
To determine when the gymnasts will be at the same height during their flips, we need to find the time (x) at which the equations for y are equal.
The given equations are:
y = –(x – 5)² + 3
y = –3(x – 3)² + x + 1
Setting the two equations equal, we have:
–(x – 5)² + 3 = –3(x – 3)² + x + 1
Expanding the squared terms:
–(x² – 10x + 25) + 3 = –3(x² – 6x + 9) + x + 1
Simplifying the equation:
–x² + 10x – 25 + 3 = –3x² + 18x – 27 + x + 1
Combining like terms:
–x² + 10x – 22 = –3x² + 19x – 26
Rearranging the equation:
2x² - 9x + 4 = 0
To solve this quadratic equation, we can factor it:
(2x - 1)(x - 4) = 0
Setting each factor equal to zero:
2x - 1 = 0 or x - 4 = 0
Solving for x:
2x = 1 or x = 4
Dividing by 2:
x = 1/2 or x = 4
Therefore, the gymnasts will be at the same height during their flips at two different times: 1/2 seconds and 4 seconds.
To learn more on equation click:
https://brainly.com/question/14468218
#SPJ2
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form
Answer:
y = 3/4x + 2
Step-by-step explanation:
let me know if you want an explanation :))
How many square feet of outdoor carpet will we need for this hole.
Step-by-step explanation:
area of rectangle= 12×6
=72ft^2
A2=9ft^2 whereby the base of the hole is 3ft
height is 6ft
therefore the square is 18 ft
Abigail works as a salesperson at an electronics store and sells phone: accessories. Abigail earns a $12 commission for every phone she sells commission for every accessory she sells. On a given day, Abigail mad $258 in commission and sold 6 more accessories than phones. Write a equations that could be used to determine the number of phones sold a number of accessories sold Define the variables that you use to write thigail works as a salesperson at an electronics store and sells phones and phone cessories. Abigail earns a $12 commission for every phone she sells and a $3 mmission for every accessory she sells. On a given day, Abigail made a total of 258 in commission and sold 6 more accessories than phones. Write a system of quations that could be used to determine the number of phones sold and the umber of accessories sol Define the variables that you use to write the system.
The system of equations are:
$12p + $3a = $258
a - p = 6
Where:
a = phone accessories p = phoneWhat are the system of equations?Two linear equations would be derived from the question. The linear equations would be a function of the phones and accessories sold. These equations are known as simultaneous equations and they would have to be solved together in order to determine the required values.
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
#SPJ1
solve X-2=7 answer the question pls pls
Answer:
x = 9
Step-by-step explanation:
x-2 = 7
you solve by adding 2 to both sides to maintain equality. and you add by 2 to cancel out the -2 to isolate the x.
x = 9
Need help with this question (pic included)
Answer:
answer= 3
hope this helps if not I'll try to do it again
If m varies directly with n , and m = 8 when n = 24 . what is the value of n when m = 12
Answer:
the answer will be 36
Step-by-step explanation:
if you divide 24 by 8 it will be 3 so then you multiply 12 times 3 and it's 36
Alex, jas and stef each get a student loan to help with living expenses. they decide to allocate two fifths of their loans for food, and one-sixth for travel. what fraction of their student loan will be left to spend?
The fraction of their student loan will be left to spend is half of their loan.
A number expressed quotient, in which numerator is divided by denominator is called a fraction.
Let the loan amount be $100.
Expenses for food is given that two fifths of their loan
i.e.
= 2/5 × 100
= $40
Now,
Remaining part will be = $100- $40 = $60
So,
Expenses for travel are given that one sixth of their loan,
i.e.
= 1/6 × 60
= $10
So,
Remaining part will be = $60 - $10 = $50
Hence, the fraction of their student loan will be left to spend is half of their loan.
Learn more about fraction here:
https://brainly.com/question/415517
#SPJ10
what is the moop3fngonoi9w
1. A bus traveled for 4 hours and 30 minutes to travel 183 miles. What was it's average speed?
A. 42.56 mph
B. 40.67 mph
C. 32.09 mph
D. 30.67 mph
Answer:
B or 40.67mph
Step-by-step explanation:
To solve we will use formula distance over total time, so are distance is 183miles and are time is 4 hours and 30 minutes. If we put that in hours we get 4.5 hours. Now we simply divide 183/4.5 to get about 40.67 .
[20 Points]
Add the expressions 4- 2/3b+ 1/4a and 1/2a + 1/6b -7 . What is the simplified sum?
A: -1/6a + 5/12b - 3
B: 3/4a + 1/2b - 3
C: 3/4a + 5/6b - 3
D: 5/12a - 1/6b - 3
Answer:
B: 3/4a + 1/2b - 3
Step-by-step explanation:
A dilation maps (9, 12) to (3, 4). Find the coordinates of the point (8, 4) under the same dilation
Assuming the dilation is centered at the origin, the scale factor is 1/3.
This means the coordinates of the point (8,4) are [tex]\boxed{\left(\frac{8}{3}, \frac{4}{3} \right)}[/tex]
Using a standard deck of cards, find the probability of selecting a jack, replacing the card, and then selecting a king.
please explain
The probability of selecting a jack, replacing the card, and then selecting a king is 1/169
How to determine the probability?In a standard deck of cards, we have:
Total = 52
Jack = 4
King = 4
The probability of each is:
P(Jack) = 4/52
P(King) = 4/52
So, we have:
P = 4/52 * 4/52
Simplify
P = 1/13 * 1/13
Evaluate
P = 1/169
Hence, the probability is 1/169
Read more about probability at:
https://brainly.com/question/25870256
#SPJ1
Suppose you know the slope of a linear relationship and one of the points that it’s graph passes through how can you determine if the relationship is proportional or not?
Answer:
I exactly don't have or know the answer
(-4,3)
-5-4-3
24
5
432
-14
-2
-3-
A
(0,1)
1 2
(4,-1)
Which linear function is represented by the graph?
Of(x) = -2x + 1
Of(x)=x+1
O f(x) = x+1
Of(x)=2x+1
Answer: [tex]f(x)=-\frac{1}{2}x+1[/tex]
Step-by-step explanation:
The slope is [tex]\frac{-1-1}{4-0}=-\frac{1}{2}[/tex], which matches the second option.
Linear function that is represented by the graph is f(x)= -1/2 x+1.
Here, we have,
From the graph,
y - intercept of the linear function is 1 , i.e. c = 1
and there are two points on the line (-4, 3), (4, -1)
We can get the equation of line by applying slope-intercept formula,
Slope of the line,
m = y₂ -y₁ / x₂-x₁
so, we get,
m = -1 -3 / 4 + 4
= -4/8
= -1/2
Now applying slope-intercept formula,
y = mx+c
Putting the values,
=> y = -1/2 x + 1
=>f(x) = -1/2 x + 1.
Therefore, linear function that is represented by the graph is
f(x) = -1/2 x + 1.
To learn more on slope click:
brainly.com/question/3605446
#SPJ5
True or false: The factor by which a row operation changed the determinant is equal to the determinant of the elementary matrix corresponding to that row operation.
The given statement is false.
What is the effect of a row operation on a determinant?
The factor by which a row operation intends to change the determinant is not equal to the determinant of the elementary matrix corresponding to that row operation. Rather, when a row is scaled up by a factor in a matrix, the determinant of that matrix also scales up by that factor.
Similarly, the factor by which a row operation changes the determinant is equal to the factor times the determinant of the elementary matrix corresponding to that row operation.
Learn more about a matrix here:
https://brainly.com/question/9967572
#SPJ4
Deon has bought 18 pounds of dog food. He feeds his dog
Write your answer in simplest form.
2|3
pounds for each meal. For how many meals will the food last?
Answer:
6 to 9 meals
Step-by-step explanation:
9 If he feeds 2 pounds per meal. 18÷2 =9
6 if he feeds 3 pounds per meal. 18÷3=6
If salt (5.99 × 10–6 mol) is dissolved in 1.50 × 10–2 l of water, which expression can be used to find the molarity of the resulting solution? 2.50 × 10-8 m 2.50 × 103 m 3.99 × 10–4 m 3.99 × 104 m
The molarity of the resulting solution is 3.99 × 10⁻⁴ M. The correct option is the third option 3.99 × 10⁻⁴ M
Molarity of a solutionFrom the question, we are to determine the molarity of the resulting solution
From the given information,
Number of moles = 5.99 × 10⁻⁶ mol
Volume = 1.50 × 10⁻² L
Using the formula,
Molarity = Number moles / Volume
∴ Molarity = (5.99 × 10⁻⁶) / (1.50 × 10⁻²)
Molarity = 3.99 × 10⁻⁴ M
Hence, the molarity of the resulting solution is 3.99 × 10⁻⁴ M. The correct option is the third option 3.99 × 10⁻⁴ M
Learn more on Calculating molarity here: https://brainly.com/question/23051191
#SPJ1
Answer:
The answer is 3.99 × 10–4 M
Step-by-step explanation:
I just did the assignment on Edge :)
Solve for x using quadratic formula :
abx^2 + (b^2 - ac)x - bc = 0
[tex]\boxed{\sf x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}}[/tex]
Explanation:
Given expression: (ab)x^2 + (b^2 - ac)x + (-bc) = 0
Here given:
a = abb = b² - acc = -bcApply quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \ ax^2 + bx + c = 0[/tex]
Insert values:
[tex]\sf x = \dfrac{-(b^2 - ac) \pm \sqrt{(b^2 -ac)^2-4(ab)(-bc)} }{2(ab)}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2-ac\right)^2+4abbc} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{b^4+2b^2ac+a^2c^2} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2+ac\right)^2} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm( b^2+ac )}{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac +( b^2+ac )}{2ab} \quad or \quad \dfrac{-b^2 + ac -( b^2+ac )}{2ab}[/tex]
[tex]\sf x = \dfrac{2ac}{2ab} \quad or \quad \dfrac{-2b^2}{2ab}[/tex]
[tex]\sf x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}[/tex]
Apply quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-(b^2 - ac) \pm \sqrt{(b^2 -ac)^2-4(ab)(-bc)} }{2(ab)}[/tex]
[tex]\\ \sf\Rrightarrow x= \dfrac{-b^2 + ac \pm \sqrt{\left(b^2-ac\right)^2+4abbc} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm \sqrt{b^4+2b^2ac+a^2c^2} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2+ac\right)^2} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm( b^2+ac )}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac +( b^2+ac )}{2ab} \quad or \quad \dfrac{-b^2 + ac -( b^2+ac )}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{2ac}{2ab} \quad or \quad \dfrac{-2b^2}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}[/tex]