The answer of the problem is -48.
The evaluation:
given that m = -32, n = 2, p= -8, and r = 4
∴ we have to find the value of pr/n + m
⇒ pr/n + m
⇒ -8×4/2 + (-32)
⇒ -8×2 - 32
⇒ -16 - 32
⇒ -48
So the value of the figure is -48.
In the high chool band there are 2 percuionit on the ideline to every 13 marching intrument. If the high chool band ha 150 total member, then how many percuionit are on the ideline?
There are 23 percuionit are on the ideline.
Given that in the high school band there are 2 percuionit on the ideline to every 13 marching instrument.
We have to find the percuionit are on the ideline when the high school band has 150 total member.
Firstly, we will find the scale factor by dividing the number of percuionit on the ideline to the every marching instrument.
According to the given question, the scale factor = number of percuionit on the ideline / the every marching instrument
Scale factor=2/13
Now for 150 members number of percussionists is
(2/13)×150=23.07 or 23
Hence, the number of percussionists on the ideline is 23 when the high school band has 150 total member.
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Naomi is working two summer jobs, making $10 per hour washing cars and $12 per hour tutoring. Last week Naomi earned a total of $108 and worked 2 more hours washing cars than hours tutoring. Determine the number of hours Naomi worked washing cars last week and the number of hours she worked tutoring last week.
Answer: 6 hours washing cars and 4 hours tutoring
Step-by-step explanation:
# of hours washing cars can be represented as x
# of hours tutoring can be represented by y
10x + 12y = $108
y + 2 = x
10 (y +2) + 12y = 108
10y + 20 + 12y = 108
22y + 20 = 108
22y = 88
y = 4 hrs tutoring
4 + 2 = 6 hrs washing cars
Check:
10(6) + 4(12) = 108
108 = 108
The number of hours Naomi worked washing cars last week and the number of hours she worked tutoring last week will be 4 and 6 hours respectively.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, Naomi is earning $10 per hour washing cars and $12 per hour tutoring during the summer. Naomi worked 2 more hours washing cars last week than tutoring, earning a total of $108.
Suppose the number of hours invested in washing cars is x and tutoring be y.
It is given that, Naomi is earning $10 per hour washing cars and $12 per hour tutoring during the summer and earning a total of $108.The obtained equation is
10x + 12y = $108 -----(1)
If Naomi worked 2 more hours washing cars last week than tutoring. The obtained equation is
y + 2 = x -----(2)
Substitute the value of y in equation 1
10 (y +2) + 12y = 108
10y + 20 + 12y = 108
22y + 20 = 108
22y = 88
y = 4 hrs
The value of x is,
x=y+2
x=4+2
x=6
Thus, the number of hours Naomi worked washing cars last week and the number of hours she worked tutoring last week will be 4 and 6 hours respectively.
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Line SD is a line of symmetry for figure ASMHZDPX. Tyler says that ASDPX is congruent to SMHZD because side
Tyler's statement is incorrect , SMHZD and SAXPD are correct congruence for the given pentagons.
a.
Tyler's congruence is incorrect because line SD is a line of symmetry for ASMHZDPX so ASDPX and SMHZD are about SD symmetry therefore the figure division must be start from S or D.
b.
SMHZD And SAXPD are correct congruence for the given pentagons because they both start with the letter S which is in the line of symmetry SD.
Therefore Tyler's statement is incorrect , SMHZD and SAXPD are correct congruence for the given pentagons.
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Rebecca is x years old.
Mary is 8 years older than Rebecca. Jill is three times older than Mary. The sum of their ages is 67.
(a) Form an equation in terms of x
(b) Solve the equation and work out Rebecca’s, Mary’s and Jill’s ages.
Given that Rebecca is x years old and Mary is 8 yrs older than her , so the age of Mary will be;
[tex]\longrightarrow Age_{Mary}= x+8 [/tex]
Again Jim is 3 times older than Mary, so the age of Jim will be,
[tex]\longrightarrow Age_{Jim}= 3(x+8) [/tex]
Now we are given that the sum of their ages is 67. So that ;
Equation in terms of x :-
[tex]\longrightarrow x + (x+8) +3(x+8)=67 [/tex]
Solving the equation,
[tex]\longrightarrow x + x +8+3x+24=67\\ [/tex]
[tex]\longrightarrow 5x + 32 =67\\ [/tex]
[tex]\longrightarrow 5x = 67-32 \\ [/tex]
[tex]\longrightarrow 5x = 35\\ [/tex]
[tex]\longrightarrow x = 7 [/tex]
So ,
Age of Rebecca= x = 7 yrs Age of Mary = x+8 = 15yrsAge of Jim =3(x+8) = 45 yrs .And we are done!
What is the sum
of the solutions to
x² - 7 = 6x?
Step-by-step explanation:
x² - 7 = 6x
x² - 6x - 7 = 0
the generation solution to such a quadratic ratatouille
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a) =
= (6 ± sqrt((-6)² - 4×1×-7))/(2×1) =
= (6 ± sqrt(36 + 28))/2 = (6 ± sqrt(64))/2 =
= (6 ± 8)/2 = (3 ± 4)
x1 = 3 + 4 = 7
x2 = 3 - 4 = -1
the sum of both solutions is : 7 + -1 = 7 - 1 = 6
(X^2+6x-27)/3x^2+27/(x+5)
Answer:
x^2 (x^2 + 6x - 27)(x+5) + 81/3(x+5)
Step-by-step explanation:
1) Use this rule: a/b x c = ac/b.
(x^2 + 6x - 27)/3 + 27/x + 5
2) Regroup terms.
x^2 (x^2 + 6x - 27)/3 + 27/x+5
3) Rewrite the expression with a common denominator.
x^2 (x^2 + 6x - 27) (x + 5) 27 x 3/ 3(x + 5)
4) Simplify 27 x 3 to 81.
x^2 (x^2 + 6x - 27)(x+5) + 81/3(x+5)
Thanks
Write the following expression in simplest form. the expression quantity negative three fifths times x minus 7 end quantity minus quantity negative 12 plus three tenths times x end quantity
Answer:
[tex]-\frac{9}{10} x+5[/tex]
Step-by-step explanation:
[tex](-\frac{3}{5} x-7)-(-12+\frac{3}{10} x)\\\\-\frac{3}{5} x-7+12-\frac{3}{10} x\\\\-\frac{3}{5} x+5-\frac{3}{10} x\\\\-\frac{6}{10} -\frac{3}{10}x+5\\\\-\frac{9}{10} x+5[/tex]
Hair alon increaed it price for a hair cut from $25 to $50, what might happen to demand for that ervice? What hould happen if the oppoite occurred - if the price wa reduced from $50 to $25? What other factor could influence conumer demand in thee ituation? EXPLAIN
If the price is increased from $25 to $50 the demand will fall whereas when the price is decreased from $50 to $25 the demand for haircut will increase.
The price has the greatest influence on a product's demand. The cost of a thing and the demand for it generally go hand in hand. Demand of a product is inversely proportional to its price.
Lower prices increase demand, while higher prices decrease it. This is a result of consumer satisfaction levels.
The other factors influencing consumer demand are:-
Tastes and preferences.Consumer's income.Availability of substitutes.Number of consumers in the market.Consumer's expectations.Elasticity vs. inelasticityTo study the demand in detail visit;
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What fraction can we use to rename 5 2 as tenths?
25/10 is used as tenths.
From the question, we have
5/2 = 5*5/2*5 = 25/10
25/10 is used as tenths.
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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The average class size at Lexington Middle School is 21 students, which is 5% larger than it was a decade ago. What was the average class size then?
Proportionately, the average class size at Lexington Middle School a decade ago was 20.
What is the proportion?Proportion is the ratio or relative numerical relationship of two or more values equated to one another.
Proportions are fractional values, showing how much of a number is contained in another or the whole.
Proportions are depicted as decimals, fractions, or percentages.
The current average class size at Lexington Middle School = 21 students
The percentage increase in class size = 5%
Let the current average class size = 105% (100 + 5)
The previous decade's average class size = 21/105% = 20
Thus, a decade ago, the average class size was 20, proportionately increasing by 5%.
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Tanya walked for 17 minutes from her home to a friend that lives 1.5 kilometers away.
d(t) models Tanya's remaining distance to walk (in kilometers), t minutes since she left home.
What's the appropriate domain?
Celine i etimating the number of tile in a moaic. There are 7 different color, and 472 tile of each color. There are alo 96 blank tile. What hould Celine’ etimate be?
Celine should estimate 3400 tiles in a mosaic.
The total number of tiles in mosaic will be sum of coloured tiles and blank tiles. So, there is a variety in coloured tiles. To calculate this we will perform multiplication.
Number of coloured tiles = Number of different coloured tiles × Number of each different coloured tile
Number of coloured tiles = 7 × 472
Performing multiplication on Right Hand Side of the equation
Number of coloured tiles = 3304
Total number of tiles = 3304 + 96
Performing addition on Right Hand Side of the equation
Total number of tiles = 3400 tiles
The estimate will be 3400 tiles.
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Identify the slope and y-intercept of the function y = -2x + 3.
OA. The slope is 2.
The y-intercept is (0, 3).
OB. The slope is 3.
The y-intercept is (0, -2).
OC. The slope is 3.
The y-intercept is (0, 2).
OD. The slope is -2.
The y-intercept is (0, 3).
The slope and the y-intercept of the function y = -2x+3 is -2 and (0,3).
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount. The slope is constant (the same) anywhere on the line.
Slope is calculated as (change in y divided by change in x). i.e.
slope=dy/dx
What is y-intercept?The y- intercept of a graph is the point where the graph intersects the y-axis.
The x-coordinate of any point on the y-axis is 0. So the x-coordinate of a y-intercept is 0.
So the y-intercept of the function y = -2x+3 is y= 3 i.e. (0,3).
slope = dy/dx = d/dx(-2x) + d/dx(3) = -2
⇒slope = -2.
Therefore slope of y = -2x+3 is -2 and y-intercept is (0,3).
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HURRY!!! Points G (-5,-8) and H (3,7) are plotted on a coordinate grid. Point J is plotted so that is the hypotenuse of the right triangle formed by joining the three points. What are the coordinates of point J? Select all that are possible.
(-3,-8)
(5,-7)
(-3,8)
(-5,7)
(3,8)
(5,7)
(-5,-7)
(3,-8)
To make GH the hypotenuse of the right triangle formed by combining the three points, we need to know the coordinates of point J. (3,-8).
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
Given is a coordinate grid with the points G (-5, -8) and H (3, 7) plotted on it. In order for GH to be the hypotenuse of the right triangle created by joining the three points, point J is plotted.
Thus, to make GH the hypotenuse of the right triangle formed by combining the three points, we need to know the coordinates of point J. (3,-8).
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Alec buys a frying pan priced at $13. If the sales tax is 10%,how much tax will Alec pay?
w/5=3
can someone please help me on this asap
Reason:
Multiply both sides by 5 to undo the division.
w/5 = 3
5*(w/5) = 5*3
w = 15
As a way to check, plug in w = 15
w/5 = 3
15/5 = 3
3 = 3
We get a true statement at the end to confirm w = 15 is indeed the answer.
△KIX can be mapped onto \triangle REM△REM by a rotation. If \text{m}\angle X = 117^{\circ}m∠X=117
∘
and \text{m}\angle I = 2^{\circ}m∠I=2
∘
, find \text{m}\angle Rm∠R.
\text{m}\angle Rm∠R
can
be determined. \text{m}\angle R =m∠R=
The measure of angle R, found through the angle sum property of a triangle and corresponding angles in ΔKIX and ΔREM is m∠R = 61°
What are corresponding angles?Corresponding angles are angles in two congruent or similar triangles, located between a pair of segments in one triangle that are congruent to a pair of segment in the other triangle
The details of the question are;
The transformation that maps triangle ΔKIX unto triangle ΔREM is a rotation.
Please see attached the example drawing of ΔKIX and ΔREM created with MS Excel.
A rotation transformation is a rigid transformation, therefore, the side lengths and shape of triangle ΔKIX is preserved in the image of the triangle, ΔREM
The measure of angle ∠X in triangle ΔKIX is ∠X = 117°
The measure of angle ∠I in ΔKIX is ∠I = 2°
∠K + ∠I + ∠X = 180° (angle sum property of a triangle)
The measure of angle ∠K = 180° - (∠X + ∠I)
Therefore;
m∠K = 180° - (117° + 2°) = 61°
m∠K = 61°
Based on the naming of the triangles ΔKIX and ΔREM, we have;
∠K corresponds to ∠R, ∠I corresponds to ∠E, and ∠X corresponds to angle ∠R, therefore;
∠K ≅ ∠R, ∠I ≅ ∠E, ∠X ≅ ∠R, which by the definition of congruency indicates;
∠K = ∠R, ∠I = ∠E, ∠X = ∠R
m∠R = m∠K = 61°
m∠R = 61°
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question help u guys what is -3/14 + 5/14
[tex]=\frac{-3+5}{14} \\=\frac{2}{14}[/tex]
This can be simplified to give [tex]\frac{1}{7}[/tex]
3/7 of a number is 69. What is the number?
The number is 161.
Given,
In the question:
3/7 of a number is 69.
To find the what is the number?
Now, According to the question:
Based on the given condition :
Formulate:
3/7 of a number is 69.
=> 3/7 = 69
=> 3 = 69 x 7
Calculate the product or quotient.
=> 3 = 483
Divide by 3 on both sides:
=> 483/3
= 161
Hence, The number is 161.
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HELLPPPPPP I DONT UNDER
Answer:
y=16
Step-by-step explanation:
Notice that the first equation was multiplied by 4, so you have to multiply the result by 4 to keep it as a true equation
PLEASE HELP ME!!
Amelia needs to buy some cat food. At the nearest store, 2 bags of cat food cost $9.50 . How much would amelia spend on 3 bags of cat food?
Answer:
$14.25
Step-by-step explanation:
2 bags of cat food costs $9.50. To calculate the price of one, divide $9.50 in half.
$9.50/2 = $4.75
Now, to calculate how much she'd have to spend on 3 bags, you need to multiply $4.75 by 3
$4.75 x 3 = $14.25
by using division, we can find what 1 bag of cat food is worth. Then, we can use multiplication to find what 3 bags of cat food are worth
Process:Worth of One Bag
where w is the worth of one bag
Set up equation w = 9.50/2
Solve w = $4.75
Worth of Three Bags
where w is the worth of 3 bags
Set up equation w = 4.75(3)
Solve w = $14.25
Answer: $14.25Write the Parabola in standard form
Y=-x² + 4x-1
For the function, the vertex of the function's graph is given. Find the unknown coefficients.
y=[tex]x^{2}[/tex]+bx+c; (3,-5)
The unknown coefficients will be b = -2/3 and c = -12
Vertex of a graph is a point where two lines meet in a parabola.
It is represented as ( h , k ) = ( -2a / b , f( -2a / b) )
Vertex is given to us in the question as (3 , -5)
Also coefficient of [tex]x^{2}[/tex] is given to us as 1
Now by putting values of 'a' and vertex in the vertex formula we get
3 = -2a / b
b = -2/3
Now put value of b in y = [tex]x^{2}[/tex] + bx + c
b = -2/3
As we know that vertex (3 , -5) are points on parabola for the given function we will replace it with x and y respectively
x = 3
y = -5
-5 = [tex]3^{2}[/tex] + ( -2/3 ) * 3 + c
-5 = 9 - 2 + c
c = -12
Therefore b = -2/3 and c = -12.
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Manny and Ada pool their money from a fundraiser. Manny raised 7 dollars less than twice what Ada raised.
Manny made $45 more than Ada. If the amount that Ada raised is represented by a then which of the following equations correctly models the information given?
(1) 2a-7-a=45
(2) 7-2a + a = 45
(3) 2a -7+ a = 45
(4) 2a-7+45=a
What proportional segment
lengths verify that QS || MN?
Fill the boxes to correctly
complete the proportion.
Answer:
9/1.5 = 12/2
Step-by-step explanation:
If QS || MN, the two triangles are similar, so the ratio between their corresponding side lengths will be equal.
What is the sum of three consecutive numbers as an expression?
(*Consecutive means in a row. Example: 1, 2, 3)
The sum of three consecutive numbers as an expression is 3x + 3.
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Let the consecutive numbers be x, x + 1 and x + 2.
The sum of three consecutive numbers as an expression will be:
= x + x + 1 + x + 2
= 3x + 3.
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math pls help!!!!! rewarding points
Answer:
x=90. 3x=270
Step-by-step explanation:
120•6=45•2+135•2+4x
X=90
3X=270
2b - 15 = 33
What is the answer?
Answer:
Step-by-step explanation:
2b - 15 = 33
+15 +15
2b = 48
b = 24
Fouteen le than two fifth of the area of a rectangle i the ame a one eighth the rectangle perimeter. If the area of the rectangle i 100, find the perimeter. Define variable, write an equation, and olve
The perimeter of the rectangle is 208
Given that,
Fourteen less than two fifth of the area of a rectangle is the same as one eighth the rectangle perimeter which can be written into equation as :
2/5a - 14 = 1/8(p) here,
a is area of rectangle
p is perimeter of rectangle
a is l*b and p is l+b
l is length of rectangle
b is breadth of rectangle
now,
2/5(lb) - 14 = 1/8(l+b)
2lb/5 - 14 = l+b/8
(2lb-70)/5 = l+b/8
16lb-560 = 5l+5b
5l+5b-16lb = -560
5l+5b-16(100) = -560
5l+5b-1600 = -560
5l+5b = -560 +1600
5l+5b = 1040
l+b =208
which is nothing but perimeter of rectangle.
Therefore, the perimeter of rectangle is 208 respectively.
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select all that apply. in a population of 250 students, 60% are whites, 20% are latinos, 15% are blacks, and 5% others. in a proportionate stratified random sample of 120, group of answer choices the number of whites selected is 72. the number of blacks selected is 50. the number of latinos selected is 37. the number of other racial and ethnicity background selected is 6.
In proportionate stratified random sample of 120, 72 are Whites, 24 are latinos, 18 are blacks, and 6 are others.
From the question, we have
In a population of 250 students, 60% are whites, 20% are latinos, 15% are blacks, and 5% others.
sample = 120
Number of whites = 60% of 120
= 0.6 × 120
=72
Number of latinos = 20% of 120
= 0.2 × 120
=24
Number of blacks = 15 % of 120
= 0.15 × 120
= 18
Number of others = 5% of 120
= 0.05 × 120
= 6
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. We frequently do one of the fundamental mathematical procedures. Using multiplication tables is the most obvious application. To represent the repetitive addition of one number to another, mathematicians multiply two numbers. Natural numbers, fractions, integers, whole numbers, and other types of numbers can be included. When M is multiplied by n, M is either added to itself 'n' times or subtracted from itself.
Complete question:
select all that apply. In a population of 250 students, 60% are Whites, 20% are Latinos, 15% are Blacks, and 5% others. In a proportionate stratified random sample of 120, ______.
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