Answer:
200 children and 300 adults
Step-by-step explanation:
No. of children = c
No. of adults = a
EQUATION 1: a + c = 500
EQUATION 2 : 23c + 47a = 18700
a = 500 - c
23c + 47(500 - c) = 18700
23c + 23500 - 47c = 18700
-24c = 18700 - 23500
-24c = -4800
-4800/-24 = c
c = 200
a = 500 - 200
a = 300
1.5 x 10^9 and 1.1 x 10^8 as scientific notation
Answer:
4.875 × 105^5
Step-by-step explanation:
find the equation of the line passing through the point (-6,4)(−6,4) that is perpendicular to the line 5x 3y
The required equation of line is: [tex](y - 4)= \frac{3}{5}(x+6)[/tex]
What is the equation of a line to the curve?A line's equation has the standard form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c. It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.Given:
Equation of line: 5x + 3y = 5New line passes through the point (-6,4)New line perpendicular to given line.To find: Equation of new line
Finding:
Given equation of line: 3y = 5 - 5x=> y = [tex]\frac{5}{3} (1-x) = \frac{-5}{3}(x-1)[/tex]
On comparison with a standard equation of line: [tex](y-y_0) = m(x-x_0)[/tex], where, m = slope of the line[tex](x_0,y_0)[/tex] = coordinates of point through which the line passes.We get: m = -5/3 and [tex](x_0,y_0)[/tex] = (1,0) for the given line.
Now, since the given line is perpendicular to the new line,Slope of the new line = m' = [tex]\frac{-1}{m} = \frac{3}{5}[/tex]
Hence, On substituting the values for [tex](x_0,y_0)[/tex] and m', we get the equation of the new line as:
[tex](y - 4)= \frac{3}{5}(x+6)[/tex]
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Why might two students have different calculated areas when measuring the same rectangle?
Because of differences in the given dimensions, two students have different calculated areas when measuring the same rectangle.
What is a rectangle?In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.Because all of its angles are equal, it is also known as an equiangular quadrilateral or a parallelogram with a right angle.A square is a rectangle with four equal-length sides.So,
1st students measurement:
Length = 20.70, width = 10.442nd students measurement:
Length = 20.74, width = 10.46The formula of area:
Area = length × width1st students measurement:
Area = 20.70 × 10.44Area = 216.108 cm²2nd students measurement:
Area = 20.74 × 10.46Area = 216.940 cm²Therefore, because of differences in the given dimensions, two students have different calculated areas when measuring the same rectangle.
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The complete question is given below:
Calculating the area of a rectangle
Your measurements Another student's measurements
Length (cm) 20.70 20.74
Width (cm) 10.44 10.46
Area (cm2)
Required:
Why might two students have different calculated areas when measuring the same rectangle?
Triangle HOP has coordinates H (2, 1), O (-3, 4), and P (5, 7). Determine the coordinates of the
image of AHOP after each rotation.
a A rotation 90° clockwise about the origin
b) A rotation 90° counterclockwise about the origin
A rotation 180° about the origin
The image of ΔHOP with coordinates H(2,1), O(-3,4), and P(5,7).
(a) after 90° clockwise rotation is H'(1,-2,),O'(4,3),P'(7,-5) ,
(b) after 90° counterclockwise rotation is H''(-1,2),O''(-4,-3),P''(-7,5) ,
(c) after 180° rotation is H'''(-2,-1),O'''(3,-4),P'''(-5,-7) .
When a point (x,y) is rotated 90° in clockwise about the origin then the image after rotation becomes (y,-x) .
When a point (x,y) is rotated 90° in counterclockwise about the origin then the image after rotation becomes (-y,x) .
When a point (x,y) is rotated 180° about the origin then the image after rotation becomes (-x,-y) .
Part(a)
The ΔHOP with coordinates H(2, 1), O(-3, 4), and P(5, 7) is rotated 90° in clockwise direction ,
we know the points (x,y) becomes (y,-x),
So the image of ΔHOP after rotation becomes H' , O' , P' .
H(2, 1) → H'(1,-2)
O(-3, 4) → O'(4,3)
P(5,7) → P'(7,-5)
Part(b)
The ΔHOP with coordinates H(2, 1), O(-3, 4), and P(5, 7) is rotated 90° in counterclockwise direction ,
we know the points (x,y) becomes (-y,x),
So the image of ΔHOP after rotation becomes H'' , O'' , P'' .
H(2, 1) → H''(-1,2)
O(-3, 4) → O''(-4,-3)
P(5,7) → P''(-7,5)
Part(c)
The ΔHOP with coordinates H(2, 1), O(-3, 4), and P(5, 7) is rotated 180°,
we know the points (x,y) becomes (-x,-y),
So the image of ΔHOP after rotation becomes H''' , O''' , P''' .
H(2, 1) → H'''(-2,-1)
O(-3, 4) → O'''(3,-4)
P(5,7) → P'''(-5,-7)
Therefore , The image of ΔHOP
(a) after 90° clockwise rotation is H'(1,-2,),O'(4,3),P'(7,-5) ,
(b) after 90° counterclockwise rotation is H''(-1,2),O''(-4,-3),P''(-7,5) ,
(c) after 180° rotation is H'''(-2,-1),O'''(3,-4),P'''(-5,-7) .
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Answer:
D
Step-by-step explanation:
the picture
-15-3w = 4w-2w
H is it a infinite solution or no solution
The solution is an infinite solution.
What is an infinite solution?An infinite solution can be defined as a solution with both sides equal to each other
Given the expression;
-15 - 3w = 4w - 2w
Let's simply the expression
Collect like terms
- 3w - 4w + 2w = 15
Add or subtract like terms
-5w = 15
Make 'w' the subject
w = 15/ -5
w = -3
Thus, the solution is an infinite solution.
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Complete the sentence.
3mi ≈ ____ km
The complete sentence is 3 mi ≈ 4.827 km
How to complete the sentence?The open sentence is given as:
3mi ≈ ____ km
In the standard unit of conversion, we have
1 mi ≈ 1.609 km
Multiply both sides by 3
3 * 1 mi ≈ 1.609 km * 3
Evaluate the product
3 mi ≈ 4.827 km
Hence, the complete sentence is 3 mi ≈ 4.827 km
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Use the Law of Syllogism to draw a valid conclusion from each set of statements, if possible. If no valid conclusion can be drawn, write no valid conclusion and explain your reasoning.If the measure of an angle is between 90-180 , then it is obtuse,
If an angle is obtuse, then it is not acute.
Given that statements 1 and 2 are true statements, the conclusion agrees with the laws of syllogism.
What is syllogism?In syllogism, we have a pattern of reasoning in which the flow is that the premise must lead to the conclusion. This implies that reasoning must be logically sound and unbiased.
Now let us look at the statements that we have here;
Statement 1 - .If the measure of an angle is between 90-180 , then it is obtuse
Statement 2 - If an angle is obtuse, then it is not acute.
We know that these are true syllogisms because mathematically, we define the obtuse angle as an angle that is greater than 90 degrees but less than 180 degrees.
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Pls help me I know absolutely nothing abt geometry
Answer:
choice 2,5,6
Step-by-step explanation:
Answer:
i took it like 2 years ago. i think its MNP, N, 1, and PNM?
Rewrite the following expression.
The following expression i.e.[tex]x^{\frac{10}{3} }[/tex] is rewritten as [tex](x^{3} )\sqrt[3]{x}[/tex]
Expression:
An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)
You can think of expression as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a whole sentence.
⇒ [tex]x^{\frac{10}{3} }[/tex] { given a exponential expression }
⇒ [tex]x^{\frac{9+1}{3} }[/tex] { spliting the power into parts }
⇒[tex]x^{3+\frac{1}{3} }[/tex]
⇒ [tex]x^{3}[/tex]×[tex]\sqrt[3]{x}[/tex] { spliting the terms by using properties of exponent }
⇒ [tex](x^{3} )\sqrt[3]{x}[/tex]
Hence, [tex](x^{3} )\sqrt[3]{x}[/tex] is rewritten form of the given expression i.e.[tex]x^{\frac{10}{3} }[/tex]
Therefore,The following expression i.e.[tex]x^{\frac{10}{3} }[/tex] is rewritten as [tex](x^{3} )\sqrt[3]{x}[/tex]
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Two angles of a triangle have measures 45⁰ and 92⁰ . What type of triangle is it?
a. obtuse scalene
b. obtuse isosceles
c. acute scalene
d. acute isosceles
A triangle with two angles measuring 45⁰ and 92⁰ is an obtuse scalene triangle. The answer is A.
A triangle is a two-dimensional shape that has three sides and three angles. The sum of its interior angles is 180⁰.
If two angles of a triangle have measures 45⁰ and 92⁰, solving for the third angle
180⁰ = 45⁰ + 92⁰ + third angle
third angle = 43⁰
If a triangle has an angle greater than 90⁰, then it is an obtuse triangle.
If a triangle has angles less than 90⁰, then it is an acute triangle.
If a triangle has an angle equal to 90⁰, then it is a right triangle.
An isosceles triangle is a triangle with two congruent sides and congruent base angles (2 angles are equal).
An equilateral triangle is a triangle with all three sides equal and all three angles are of equal measures.
A scalene triangle is a triangle with no sides are equal and no angle are equal also.
Since our triangle has 3 unique angles: 43⁰, 45⁰, and 92⁰, with one angle greater than 90⁰, then it is an obtuse scalene triangle.
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Roman Derleth
Write Single Inequality from Context
Sep 21, 7:53:35 PM
?
Jonathan and his children went into a restaurant and will buy hamburgers and tacos.
Each hamburger costs $5 and each taco costs $2.50. Jonathan has a total of $60 to
spend on hamburgers and tacos. Write an inequality that would represent the
possible values for the number of hamburgers purchased, h, and the number of tacos
purchased, t.
Answer:
Submit Answer
The inequalities that represent the problem is 5h + 2.50t ≤ 60
How to find the inequality that represent the problem?Each hamburger costs $5 and each taco costs $2.50.
He has a total of $60 to spend on hamburgers and tacos.
The inequalities that would be used to represent the possible values for the number of hamburgers purchased, h, and the number of tacos purchased, t is as follows:
Therefore,
h = number of hamburgers purchased
t = the number of tacos purchased
Hence,
5h + 2.50t ≤ 60
Therefore, the inequalities that represent the problem is 5h + 2.50t ≤ 60
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gabriela is building a brick wall. each row of bricks is 6.5\,\text{cm}6.5cm6, point, 5, start text, c, m, end text tall except that the top row is 1\,\text{cm}1cm1, start text, c, m, end text shorter because it has no mortar. she wants the wall to be 259\,\text{cm}259cm259, start text, c, m, end text tall.
The equation is 6.5 (r-1) + 5.5 = 259 or 6.5 r - 1 = 259.
In this case, r stands for the overall number of rows.
The answer indicates that each row is 6.5 cm tall.
What is an equation?A formula known as an equation uses the equals sign (=) to express how two expressions are equal. The word "equation" and its cognates in other languages may have slightly different meanings. For instance, in French, an equation is defined as having one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. The task of solving an equation with variables entails figuring out which values of the variables cause the equality to hold true. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions. Identity equations and conditional equations are the two types of equations.
The height of the top row is 6.5 - 1 = 5.5 cm.
Except for this row, there are total rows of = (r-1)
So, 6.5 is the total length of these rows (r-1)
The overall length of the wall is therefore equal to the sum of the (r-1) row and the top row.
However, once more in line with the inquiry,
Exactly 259 centimeters must be on the wall.
⇒ 259 = 6.5(r-1) + 5.5
⇒ 6.5(r-1) + 5.5 = 259
⇒ 6.5 r - 6.5 + 5.5 = 259
⇒ 6.5 r - 1 = 259
Which is the required equation for finding the number of rows (r).
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Carrie collected canned food for a homeless shelter in her area each day for one week. On day one, she collected 7 cans of food. On day two, she collected 8 cans. On day three, she collected 10 cans. On day four, she collected 13 cans. If Carrie wanted to give at least 100 cans of food to the shelter and this pattern of can collecting continued, did she meet her goal?
The number of can collected by Carrie after one week if the pattern continued will be; 105 cans and hence, she met her goal.
How many cans were collected by Carrie and dis she meet her goal?It follows from the task content that Carrie's target for can collection was 100 units of can collected over 1 week.
Since, one week contains seven, 7 days, it follows that she has 7 days to meet her target.
Following from observation, she increased the number of cans collected each day following a pattern; 7, 8, 10, 13.... where the difference between two successive days increases by 1 each time.
Hence, the number of cans collected for the rest of the days are as follows;
Day 5 = 13 + 4 = 17Day 6 = 17 + 5 = 22Day 7 = 22 + 6 = 28Therefore, the total number of cans collected is; 7 + 8 + 10 +13 + 17 + 22 + 28 = 105 cans and hence, she meets her goal.
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Analysis of data reveals a correlation coefficient of r = 0.77. this is a ______ relationship.
Analysis of data that reveals a correlation coefficient of 0.77 shows a strong relationship between variables.
What is correlation?Correlation can be defined as any statistical relationship, whether causal or not, between two random variables or bivariate data. The type of correlation that we have include;
Positive correlationnegative correlationzero correlationA calculated number greater than 1.0 or less than -1.0 means that there was an error in the correlation measurement while a correlation that is between 0.6 and 0.9 are classified as a strong relationship.
Hence we can conclude that analysis of data that reveals a correlation coefficient of 0.77 shows a strong relationship between variables.
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The area of a rhombus is 400msq.If its height is 20m, what is its base
By using area formula, we get base is [tex]20 m[/tex]
What do you mean by area?
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. For instance, On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Given that:
Area of a rhombus is [tex]400 m^{2}[/tex]
Height of a rhombus is [tex]20 m[/tex]
We know that,
Area of rhombus = base × height
Substituting area and height in above formula
[tex]400[/tex] = base × [tex]20[/tex]
∴ Base = [tex]\frac{400}{20}[/tex]
=[tex]20[/tex]
Therefore, by using area formula, we get base of a rhombus is [tex]20 m[/tex]
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4 - 5/3x - 7 = 4 please help solve
Step-by-step explanation:
multiply through by the LCM=3x-7
4(3x-7)-5=4(3x-7)
12x-28-5=12x-28
The integer coefficient of x on both sides of the equation=+12 so there's no integer solution for the equation
Questions 18-30 pls help due tomorrow
Answer:
Step-by-step explanation:
30
Step-by-step explanation:
以下の情報を添えて、このチラシを当社の登録従業員の 1 人に渡してください。 より多くのチラシを提出した先生がピザ パーティーを勝ち取ります。
Suppose that the height of the slide is 2 feet,
when x = 20. What is the average rate of change
over the entire slide?
(answer is -3.9 on edge 2022 but all the other top brainly answers were incorrect)
The average rate of change over the entire slide if the height of the slide is 2 feet is; -3.9
What is the average rate of change?
Average rate of change is defined as a measure of how much the function changed per unit, on average, over that interval.
First, we will calculate the average rate from x = 0 to x = 15:
We have:
R = ((80 - 10)/(0 - 15))
R = -4.667
Let us now calculate average rate of change for the entire interval supposing that the height of the slide is 2 feet,:
From x = 0 to x = 20, we have;
R = ((80 - 2)/(0 - 20))
R = -3.9
Thus, we can conclude that the average rate of change over the entire slide is; -3.9
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Answer:
slower than & -3.9
Step-by-step explanation:
Cual es la Respuesta de 5a+7a
Answer:
12a
Step-by-step explanation:
HELP ME PLEASE!!!!! I WILL NAME YOU BRAINLIEST
please solve question 2 part b :)
The equivalent of the given expression ( (4 1/2)x - 3 ) + ( -2 + (1 3/4)x ) is (6 1/4)x - 5.
What is the equivalent of the given expression?Given the expression in the question;
( (4 1/2)x - 3 ) + ( -2 + (1 3/4)x )
First, convert the mixed fractions into an improper fractions.
( (4 1/2)x - 3 ) + ( -2 + (1 3/4)x )
( (4×2 + 1/2)x - 3 ) + ( -2 + (1×4 + 3/4)x )
( (8 + 1/2)x - 3 ) + ( -2 + (4 + 3/4)x )
( (9/2)x - 3 ) + ( -2 + (7/4)x )
Now, remove the parenthesis and collect like terms
(9/2)x - 3 + -2 + (7/4)x
(9/2)x + (7/4)x - 3 - 2
9x/2 + 7x/4 - 5
Now, add the two fractions containing x
(9x × 4)+(7x × 2)/8 - 5
( 36x + 14x )/8 - 5
50x/8 - 5
(50/8)x - 5
(25/4)x - 5
Convert 25/4 into an improper fraction
(6 1/4)x - 5
Therefore, the equivalent of the given expression ( (4 1/2)x - 3 ) + ( -2 + (1 3/4)x ) is (6 1/4)x - 5.
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10-8(2x-7)
please help!!!!!!!!
What’s is the answer
Answer:
C
Step-by-step explanation:
Taking a square root of a number that doesn't have a square root like [tex]\sqrt{17}[/tex] will result in an infinite number of random digits which is an irrational number. Hence, C is the answer.
D isn't the answer because even though [tex]\sqrt{5}[/tex] is irrational, you're adding [tex]\sqrt{5}[/tex] and then subtracting [tex]\sqrt{5}[/tex] from the total sum. Hence the total sum would be 5+14.
5+[tex]\sqrt{5}[/tex]+14-[tex]\sqrt{5}[/tex] =5+14+[tex]\sqrt{5}[/tex]-[tex]\sqrt{5}[/tex]= 5+14 ==> 19 is a rational number
A solid cylinder has a volume of 454 cm³.
The cylinder has a height of 10 cm.
A similar cylinder has a height of 30 cm.
What is the volume of the larger cylinder?
30 10×3=30 that how you get it
Which of the following can be used to correctly solve the equation `-\frac{1}{3}x=18`?
Answer:
x = -54
Step-by-step explanation:
Let's solve your equation step-by-step.
[tex] \sf \: `-\frac{1}{3}x=18`[/tex]
Step 1: Multiply both sides by 3/(-1).
[tex] \sf( \frac{3}{ - 1} ) \times ( \frac{ - 1}{3} x) = ( \frac{3}{ - 1} ) \times (18)[/tex]
[tex] \sf \: x = - 54[/tex]
The farmer’s market opens for 2 ⅕ hours in the morning and 3 ⅔ hours in the afternoon. How long is the farmer’s market open in a day?
pls help me out with this
Step-by-step explanation:
"complimentary" means together they have 90°.
"supplementary" means together they have 180°.
which can be easily and quickly found on any internet search.
7.
A = 70°
A + B = 90°
70 + B = 90
B = 90 - 70 = 20°
B + C = 180°
20 + C = 180
C = 180 - 20 = 160°
8.
A + B = 90°
B + C = 180°
C = 100°
B + 100 = 180°
B = 180 - 100 = 80°
A + 80 = 90
A = 90 - 80 = 10°
What is an expression for the sale price of a bracelet that has been discounted 35% from its
sticker price? Evaluate the expression for a sticker price of $60. Use the variable s for the sale
price and p for the sticker price.
The expression which represents the sales price of the bracelet in terms of the sticker price is; s = 0.65p and the evaluation for a sticker price of $60 is; $39.
Which expression represents the sales price of the bracelet in terms of the sticker price?It follows from the task content that the bracelet has been discounted 35% from its sticker price.
Hence, the sales price of the bracelet is therefore; (100 - 35)% of sticker price, p.
Therefore, we have;
s = (65/100) × p
s = 0.65p.
Ultimately, the evaluation for a sticker price of $60 is; s = 0.65(60).
s = $39.
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Please help! (Also show work)
Tutorials :D
The five-number summary is:
Minimum: 9
First Quartile: 16.5
Median: 25.5
Third Quartile: 39
Maximum: 51
3. Range = 42
4. Interquartile range = 22.5
How to Find the Five-number Summary of a Data?Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:
1. The numbers in ordered from the smallest to the largest would be:
9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51
2. The five-number summary for the lengths in minutes would be:
Minimum value: this is the smallest lengths, which is 9First Quartile (Q1): this is the middle of the first half of the data set of the lengths in minutes, which is 16.5.Median: the median is the center of the data distribution which is 25.5.Third Quartile: this is the middle of the second half of the data set of the lengths in minutes, which is 39.Maximum: this is the largest length in minutes, which is, 51.3. Range of the data = max - min = 51 - 9 = 42
4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5
Interquartile range for the data set = 22.5
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Find the perimeter of ∠A B C to the nearest hundredth, given the coordinates of its vertices. A(-3,2), B(2,-9), C(0,-10)
The perimeter of the triangle ABC is approximately equal to 35.633 units.
How to determine the perimeter of a triangle
In this problem we find the locations of the three vertices of the triangle and from which we have to calculate the length of each of the three sides. The perimeter is the sum of the three lengths. First, determine the vectors of each side:
AB = (2, - 9) - (- 3, 2)
AB = (5, - 11)
BC = (0, - 10) - (2, - 9)
BC = (- 2, - 1)
AC = (0, - 10) - (- 3, 2)
AC = (3, - 12)
Second, calculate the magnitudes of the three sides:
AB = √[5² + (- 11)²]
AB = √146
BC = √[(- 2)² + (- 11)²]
BC = 5√5
AC = √[3² + (- 12)²]
AC = 3√17
Third, add the three lengths to find the perimeter:
p = √146 + 5√5 + 3√17
p ≈ 35.633
Remark
The statement reports a typing mistake that it would take a triangle for an angle, which is absurd since angles only have one vertex. Correct statement is shown below:
Find the perimeter of Δ ABC to the nearest hundred, given the coordinates of its vertices A(x, y) = (- 3, 2), B(x, y) = (2, - 9) and C(x, y) = (0, - 10).
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PLEASE
Solve for X
4(5x+6)=12
-3(2x-4)=18
26=2(3x-2)
Answer:
Below in bold.
Step-by-step explanation:
4(5x + 6) = 12
20x + 24 = 12
20x = -12
x = -12/20 = -3/5
-3(2x - 4) = 18
-6x + 12 = 18
-6x = 6
x = -1.
26 = 2(3x - 2)
26 = 6x -4
30 = 6x
x = 30/6 = 5.