According to the given statement;
The difference of 9 and the quotient of a number f and 6 is 5.
the value of f is = -24
What is Variable?A variable is an alphabet or term that stands in for an unknowable quantity, value, or number. Particularly in the case of algebraic expressions or algebra, the variables are used. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.
The variable is a quantity that can change or is not fixed. Typically, in algebra, we use the terms "x" and "y" to express an unknown number. However, this is not unique, and we are free to use any alphabet.
According to the given value;
9 - (f÷ 6) = 5
Subtract 9 from both sides.
9 - 9 - (f ÷ 6) = 5 - 9
Simplify.
- (f ÷ 6) = -4
Distribute -1 throughout the parenthesis.
-f ÷ -6 = -4
Multiply both sides by -6.
-f ÷ -6 × -6 = -4 × -6
Simplify.
-f = 24
Divide both sides by -1.
-f ÷ -1 = 24 ÷ -1
Simplify.
f = -24
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The sum of the measures of the angles in △ABC is 180°. The sum of the measures of angle B and angle C is twice the measure of angle A. The measure of angle B is 32° less than the measure of angle C.
Answer:
< A = 60 degrees.
< B = 44 degrees
<C = 76 degrees.
Step-by-step explanation:
A + B + C = 180 --------(1)
2A = B + C -------(2)
B = C - 32 -------(3)
We see from equation 2 that B + C = 2A so we
replace The A + B in equation (1) by 2A:
A + 2A = 180
3A = 180
A = 60.
Substitute A = 60 in equation (2):
120 = B + C
Rearranging equation (3):
32 = -B + C
Adding theses last 2 equations:
152 = 2C
C = 152/2 = 76.
Substituting for A and C in equation (1):
60 + 76 + B = 180
B = 180 - 60 - 76 = 44 degrees.
Use the net to calculate the surface area of
the polyhedron.
The total area of given polyhedron is 68.75 sq. units
The given polyhedron is made up of 1 square, 2 triangles, and 2 rectangles.
Firstly. the dimensions of triangle are -
base = 2.5 units,
height = 3.5 units
area of the triangle = 1/2 × B × H
= 1/2 × 2.5 × 3.5
= 4.375 sq. units
The area of 2 triangles will be - 2 (area of 1 triangle)
⇒ 2× 4.375
= 8.75 sq. units
Area of Rectangle 1 = L × B
Length = 5 units
Breadth = 3 units
Area = 5×3 = 15 sq. units
Area of Rectangle 2 = L × B
Length = 5 units
Breadth = 4 units
Area = 20 sq. units
Area of square = Side²
⇒ 5 × 5
= 25 sq. units
Total area of polyhedron = Area of 2 triangles + Area of 2 Rectangles + Area of square
⇒ 8.75 + 15 + 20 + 25
= 68.75 sq. units
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Translation of (x-1)²+(y+3)²=36,2 units left and 4 units down
Identify the centers and radii of the two circles. To find the transformation rule, we need to find how many units horizontally and vertically to move the center of one circle to the center of the other circle.
The equation for the shifted circle is
(x+2) ^2+(y+4) ^2=36.
Description: The standard shape of a circle is
(x−h)2+(y−k)2=r2,
where r is the circle's radius and (h,k) is the circle's center.x2+y2=36 centered at (0,0). If the circle is shifted two units to the left, it means that the new center is h = -2. If we move the circle down four units, the new center is k = −4. So, the shifted circle has the equation (x+2)2+(y+4)2=36.
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Every item in the Just a Dollar store is priced
$
1.00
. When Jack opens the store, there is
$
125.00
in the cash register. When he counts the money in the cash register at the end of the day, the total is
$
935.00
. If the sales tax rate is
8
%
, how many items were sold that day?
750 items were sold that day
How to calculate the number of items sold ?The first step is to calculate the total revenue
Total revenue= 935 - 125
= 810
Therefore the number of items sold can be calculated as follows
810= 1x + 8/100
810= 1x + 0.08x
810= 1.08x
x= 810/1.08
x= 750
Hence 750 items were sold that day
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in the figure below, G is between E and H, and F is the midpoint of EG. if EH = 14 and FG = 3, find GH
The length of GH is 8 units.
The image is not given. Attached a sample image below.
Given,
We can assume that the figure may be a line.
G is between points E and H
F is the midpoint of EG
The length of EH = 14 units
The length of FG = 3 units
We have to find the length of GH.
Here,
EH = EG + GH
Length of EG = FG + EF
F is the mid point of E and G. So, EF = FG ⇒ 3 units
Now,
EG = FG + EF
EG = 3 + 3
EG = 6 units
Now, we can find GH.
GH = EH - EG
EG = 6 units
EH = 14 units
Therefore,
GH = 14 - 6
GH = 8 units.
The length of GH is 8 units.
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Determine whether each sequence is arithmetic, geometric, or neither. Then find the tenth term. -5,15,-45,135,-405,. . . .
The sequence -5,15,-45,135,-405,. . . . is a geometric sequence and its 10th term is a(10) = 98,415
To determine whether a sequence is an arithmetic or geometric one, we need to check the relation between two consecutive terms.
In an arithmetic sequence, the nth term is obtained by adding the (n-1)th term with a constant, called a common difference (d).The given sequence is:
-5,15,-45,135,-405,....
In this sequence:
a(1) = -5
a(2) = 15
a(3) = -45
and so on.
Notice that:
15 = -5 . (-3) ⇒ a(2) = a(1) . (-3)
-45 = 15 . (-3) ⇒ a(3) = a(2) . (-3)
Since the n-th term is obtained by multiplying the (n-1)-th term by a constant, r = -3, hence, the given sequence is a geometric sequence.
The formula for the nth term in a geometric sequence is given by:
a(n) = a(1) . rⁿ⁻¹
Substitute n = 10, r = -3, and a(1) = -5
a(10) = (-5) . (-3)¹⁰⁻¹
a(10) = (-5) . (-3)⁹
= 98,415
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kinetic equation problem
Use the kinematic formula
[tex]{v_2}^2 - {v_1}^2 = 2a\Delta x[/tex]
where [tex]v_1,v_2[/tex] are initial/final velocities, [tex]a[/tex] is acceleration, and [tex]\Delta x[/tex] is displacement. We're given [tex]a=-5.00\frac{\rm m}{\rm s^2}[/tex] and [tex]\Delta x=15.0\,\rm m[/tex], and the car comes to a stop so [tex]v_2=0[/tex]. Solve for [tex]v_1[/tex].
[tex]-{v_1}^2 = 2\left(-5.00\dfrac{\rm m}{\rm s^2}\right) (15.0\,\mathrm m) \\\\ ~~~~ \implies {v_1}^2 = 150.\dfrac{\rm m^2}{\rm s^2} \\\\ ~~~~ \implies v_1 = \sqrt{150.\dfrac{\rm m^2}{\rm s^2}} \approx \boxed{12.2 \dfrac{\rm m}{\rm s}}[/tex]
6. Savannah is making pots and plates to sell at a local art fair. Each pot weighs 2 pounds and each plate weighs 1 pound. Savannah cannot carry more than 50 pounds to the fair. She only has enough clay to make 40 plates. In addition, she only has enough clay to make 24 pots. She will make $12 profit on every plate and $25 for every pot that she sells. How many pots and how many plates should Savannah make to maximize her profit?
Answer
She should make 24 pots and 2 plates
PLEASE HELP! The value of x is 6 numbers away from –1 on a number line. Which numbers could be the value of x?
On a number line, the value of x is six places away from zero. Any of the following numbers, from 1 to 5, could serve as the x.
When X is 6 numbers away from -1, it has a value of 5.
The values from -1 after 6 is -1,0,1,2,3,4,5 so 5 is the 6th number from -1
A number line is a straight line with numbers spaced at equal segments or intervals in mathematics.
A number line is often shown horizontally and can be extended indefinitely in any direction.
Moving from left to right causes the numbers on the number line to climb, whilst moving from right to left causes them to fall.
On a number line, both positive and negative integers can be shown.
Comparing numbers is made simpler by writing them on a number line. The number line's leftmost numerals are smaller than its right most digits.
A number line can be used to do addition, subtraction, and multiplication. We always move to the right, to the left, or by skipping a count while adding, subtracting, or multiplying.
Hence, x could be any one of the following Numbers: 5, 4, 3, 2, or 1.
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Which of the following are reasonable answers for the product of two negative numbers and a positive number? Select all that apply. A. 20 B. 10 C. negative 20 D. negative 15
Add or Subtract.
5/19 + 7/38
Answer:17/38
Step-by-step explanation:
5/19+7/38
\frac{5}{19}+\frac{7}{38}
Answer:
[tex]\frac{17}{38}[/tex]
Step-by-step explanation:
[tex]\frac{5 * 2}{19 * 2} +\frac{7}{38}[/tex]
[tex]\frac{10+ 7 }{38}[/tex] 10 +7 =17
[tex]\frac{17}{38}[/tex]
(3x^5+8x^3-10x^2)-(-12x^5+4x^3+14x^2)
Answer:x
2
(
15
x
3
+
4
x
−
24
)
Step-by-step explanation:
Expand each binomial. (x-y)³
The binomial expansion of the given expression is:
x³ - y³ - 3x²y + 3y²x
What is a polynomial?
A polynomial is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms.
Depending on the number of terms it can be :
monomialbinomialtrinomialWe solve first by perfect square trinomial, then we apply the distributive property.
(x- y)³ = (x - y)²(x - y)
(x - y)² = x² - 2xy + y²
(x - y)( x² - 2xy + y²)
x³ - 2x²y + y²x - x²y + 2y²x - y³
x³ - y³ - 3x²y + 3y²x
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How do i solve this?[tex]2(-15)-\sqrt[3]{18(-15)-1061}[/tex]
- 40.18 is the solution of this function .
What does a math cube root mean?
The factor we multiply by itself three times to obtain a number is its cube root. 3 cube root of, end cubic root is the symbol for the cube root. The opposite of cubing an integer is to get its cube root.Finding a number that, when multiplied twice by itself, equals the original number is necessary in order to compute the square root of any number. Similar to this, we must discover a number that, when multiplied three times by itself, equals the original number in order to find the cube root of any number.[tex]2( -15) - \sqrt[3]{18( -15 ) - 1061}[/tex]
= [tex]2 ( -15 ) - \sqrt[3]{3 - 1061}[/tex]
= [tex]-30 - \sqrt[3]{ - 1058}[/tex]
= - 30 - 10.18
= - 40.18
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PLEASE ANSWER FAST Estimate 4001 + 283 + 97 =
Answer:
4400
Step-by-step explanation:
4001→4000 (you need to round the number to the nearest thousand)
283→300 (you need to round the number to the nearest hundred)
97→100 (you need to round the number to the nearest ten, in this case 100)
4000+300+100= 4400
Hope this helps! :)
Write an equation of the line through each pair of points. Use point-slope form.
(3/2, -1/2) and (-2/3, 1/3)
The equation of the line in point-slope form, which passes through the pair of points located at (3/2 , -1/2) and (-2/3 , 1/3), is y + 1/2 = -5/13(x - 3/2).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (3/2 , -1/2) and (-2/3 , 1/3).
m = (y2 - y1)/(x2 - x1)
m = (1/3 - -1/2)/(-2/3 - 3/2)
m = (5/6)/(-13/6)
m = -5/13
Using the point slope form, plug in the values of the slope and one point to set up the equation.
(y - y1) = m(x - x1)
where m = -5/13 and (x1 , y1) = (3/2 , -1/2)
(y - -1/2) = -5/13(x - 3/2)
y + 1/2 = -5/13(x - 3/2)
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Find the geometric mean between pair of numbers.
1/5 and 60
The geometric mean of 1/5 and 60 is 2√3.
Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.
To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.
The formula for the geometric mean is given by:
GM = n√x1 x2 . . . xn
Solving for the geometric mean between 1/5 and 60 using the formula:
GM = n√x1 x2 . . . xn
where n = 2, x1 = 1/5, and x2 = 60
GM = √(1/5)(60)
GM = √12
GM = 2√3
Hence, the geometric mean of 1/5 and 60 is 2√3.
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The radius, diameter, or circumference of a circle is given. Find the missing measure to the nearest hundredth.
C = 35x cm, d=?, r=?
A circle is a curve sketched out by a point moving in a plane. The radius and the diameter of the circle are 5.57x cm and 11.14x cm, respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that circumference of the circle is 35x cm. Therefore, the radius and the diameter of the circle can be written as,
Circumference of circle = 2 × π × (Radius of the circle)
35x cm = 2 × π × (Radius of the circle)
(Radius of the circle) = 35x/ (2 × π)
The radius of the circle = 5.57x cm
Diameter of circle = 2 × (Radius of the circle)
= 2 × 5.57x cm
= 11.14x cm
Hence, the radius and the diameter of the circle are 5.57x cm and 11.14x cm, respectively.
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Elon works in New York City and makes $45 per hour. He works in an office and must get his suit dry cleaned everyday for $75. If he wants to make at least $260 a day, how many hours must he work?
Write the inequality that represent the situation above. (Use the variable h)
How many hours will the Elon need to work each day? (Round your answer to the nearest tenth)
If Elon earns $45 per hour, spend $75 on dry cleaning everyday and wants to make at least $260 a day then the inequality that shows the situation is 45x-75≥260 and he atleast work for 7 and half hour each day.
Given that Elon earns $45 per hour, spend $75 on dry cleaning everyday and wants to make at least $260 a day.
We are required to write the inequality that represent the situation of Elon.
Inequality is just like an equation that shows the relationship between two variables but in greater than, less than,greater than or equal to,less than or equal to signs.
Suppose the number of hours that Elon works be x hours each day.
The earning of Elon will be 45x.
Since the expenditure is $75,the saving will be 45x-75 and if he wants to make $260 a day, the inequality will be 45x-75≥260.
45x≥260+75
45x≥335
x≥335/45
x≥7.55
Hence if Elon earns $45 per hour, spend $75 on dry cleaning everyday and wants to make at least $260 a day then the inequality that shows the situation is 45x-75≥260 and he atleast work for 7 and half hour each day.
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Energy and mass are related by the formula, e=mc2, where m is the mass of the object and c is the speed of light. the equation that finds m, given e and c, is
Energy and mass are related by the formula, E = mc², where m is the mass of the object and c is the speed of light. The equation that finds m, given e and c, is: m = E/c²
The equation, E = mc² was coined from Albert Einstein's theory of relativity, which shows the relationship between mass and energy. It shows that energy and mass can be interchanged into each other. The equation tells us that if we multiply the mass of a body (m) with the square of the speed of light (c²), we will get the total amount of energy (E) contained in that body, which can potentially be converted to other forms of energy.
However, if are given the energy contained in a body and the speed of light, then told to find the mass of the body, we will divide the equation by the coefficient of m. The coefficient of m in the equation is c², thus:
E = mc²
E/c² = mc²/c²
c² divided by c² is 1, therefore, the new equation is:
m = E/c²
Thus, the equation that finds m, given e and c is m = E/c².
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Do the following side lengths form a right triangle?
95, 76, 57
Answer:
Yes
Step-by-step explanation:
A right triangle is a triangle that has one angle whose measure is 90°. A right triangle CANNOT have two 90º angles. This is because the angles of a triangle must add up to 180°. With one angle measuring 90°, the other two angles in the right triangle must add up to 90°
2. 8 × - 11 - 3× + 8
please solve this thankyou!!
Answer:
-54.8 ( in fraction -274/5)Step-by-step explanation:
2.8 × (-11) - 3 × 8 =
-30.8 - 24 =
-54.8 ( in fraction -274/5)
1. For the right triangle RST shown below, what is the tan R?
A. r/s
B. r/t
C. t/r
D. t/s
E.s/t
R
S
T
Reason:
Angle R is the reference angle since we're computing tan(R)
Side r is opposite angle R. This is the opposite side because it's furthest away from angle R.
Side t is opposite angle T. This is the adjacent side because it's nearest to reference angle R.
The tangent involves the ratio of opposite over adjacent
tan(angle) = opposite/adjacent
tan(R) = r/t
The system of equations below has no solution.
StartLayout enlarged left-brace 1st row two-thirds x + five-halves y = 15 2nd row 4 x + 15 y = 12
Which equation could represent a linear combination of the system?
Four-thirds x = 42
Fifteen-halves y = 33
0 = 0
I will give Brainliest to whomever answers this question quickly but CORRECTLY!!!!
An equation that could represent a linear combination of the system with no solution is: B) 0 = 26.
What is no solution?In Mathematics, no solution is sometimes referred to as zero solution. Additionally, an equation is considered as having no solution when the right hand side and left hand side of the equation are not the same or equal.
From the information provided above, we have this system of equations:
2x/3 + 5y/2 = 15 ........equation 1
4x + 15y = 12 ........equation 2
Multiplying equation 1 by 6, we have:
6 × (2x/3 + 5y/2 = 15)
4x + 15y = 90 ......equation 3
Subtracting the equation 3 from equation 2, we have:
(4x - 4x) + (15y - 15y) = (12 - 90)
0 + 0 = -78
0 = -78 ≡ 0 = 26.
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Complete question:
The system of equations below has no solution.
2x/3 + 5y/2 = 15
4x + 15y = 12
Which equation could represent a linear combination of the system?
A) 4/3x=42
B) 0 = 26
C) 15/2y=33
D) 0=0
Mr Tan gave $2000 to his wife and two children altogether. His wife received twice as much as his son. His daughter received $300 less than his wife. How much did Mr Tan's daughter receive?
Answer:
Mr Tan's daughter received $620
Step-by-step explanation:
the son received $460
$460 × 2 = $920
the wife received $920
$920 - $300 = $620
$460 + $920 + $620 = $2000
How can I solve this?
Answer:
Mean: 160
Median: 150
Mode: none
Range: 105
Standard deviation: 35.3
Step-by-step explanation:
Given:
Mean = 320Median = 300Mode = noneRange = 210Standard deviation = 70.6If each value in the data set is multiplied by a constant value, the mean, median, mode, range, and standard deviation will all be scaled by the same amount.
Therefore, if each value in the data set is multiplied by 0.5:
Mean: 320 × 0.5 = 160Median: 300 × 0.5 = 150Mode: none × 0.5 = noneRange: 210 × 0.5 = 105Standard deviation: 70.6 × 0.5 = 35.3Proof
Data set: {1, 2, 3, 4, 5}
[tex]\sf Mean\:\mu =\dfrac{\sum x_i}{n}= \dfrac{1+2+3+4+5}{5} = 3[/tex]
[tex]\sf Median = 3[/tex]
[tex]\sf Mode = none[/tex]
[tex]\sf Range = 5-1=4[/tex]
[tex]\sf Standard\:deviation\:\sigma=\sqrt{\dfrac{\sum (x_i-\mu)^2}{n}}=\sqrt{\dfrac{10}{5}}=\sqrt{2}[/tex]
If we multiply each value by 0.5, the new data set is:
{0.5, 1, 1.5, 2, 2.5}
[tex]\sf Mean\:\mu =\dfrac{\sum x_i}{n}= \dfrac{0.5+1+1.5+2+2.5}{5} = 1.5[/tex]
[tex]\sf Median = 1.5[/tex]
[tex]\sf Mode = none[/tex]
[tex]\sf Range = 2.5-0.5=2[/tex]
[tex]\sf Standard\:deviation\:\sigma=\sqrt{\dfrac{\sum (x_i-\mu)^2}{n}}=\sqrt{\dfrac{2.5}{5}}=\dfrac{\sqrt{2}}{2}[/tex]
Therefore, if each value in the data set is multiplied by 0.5, the mean, median, mode, range, and standard deviation are all scaled by the same amount.
Write these propositions using p and q and logical connectives (including negations). (a) you do not drive over 65 miles per hour. (b) you drive over 65 miles per hour, but you do not get a speeding ticket. (c) you will get a speeding ticket if you drive over 65 miles per hour
Writing the propositions using p and q with logical connectives, including negations, in each of the statement will give;
(a) you do not drive over 65 miles per hour-
¬ p
(b) you drive over 65 miles per hour, but you do not get a speeding ticket
p ∨ ¬ q
(c) you will get a speeding ticket if you drive over 65 miles per hour-
p → q
We are to represent each statement using letters; p and q
The letters p and q are then connected with the logical connectives symbols; example negation, conjunction, disjunction and implication symbols.
Thus, each statement given in the question is logically written as;
(a) ¬ p
(b) p ∨ ¬ q
(c) p → q
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2 (-8 - 7) ÷ 3(5)
explain please
Answer:
-50
Step-by-step explanation:
2(−8−7)
3
(5)
=
(2)(−15)
3
(5)
=
−30
3
(5)
=(−10)(5)
=−50
A line contains L(-4, -4) and M(2, 3). Line q is in the same coordinate plane but does not intersect IM. Line q contains point N. (Can someone please look at the picture and help me)
The line q passes through (2, 0) and (-7, -4)
How to find line LM?If line Q does not intersect the line LM, then these lines are parallel, thus, have the same slope.
The slope of line LM is given by:
s = (3 + 4)/(2 + 4) = 7/6
Now we know that the line Q contains point N (2, 0) ( i will assume is this because in the image the points don't have the correspondent names).
Then the line also passes through another point (a, b) such that:
s = (0 - b)/(2 - a) = 7/6
Then:
b = -7
a = -4
The line q passes through (2, 0) and (-7, -4)
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If a tourist paid Rs. 5610 for a carved window made of wood with a discount of 15% including 10% value added tax, how much does he get back while leaving Nepal? Find it.
Answer:
3/2
Step-by-step explanation:
15% × 10( use p%)
15/100 × 10 (simplify the expression)
15/10 (reduce the expression)
3/2(Solution)
