A sum of money is divided among three girls, Rheanna, Kerisha and Anne, in the ratio 2:3:7, respectively. If Anne gets $15
more than Kerisha, what is the value of the total sum that was shared?
Using proportions, it is found that the value of the total sum that was shared was of $45.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the rates, Anne's and Kerisha's proportions, out of the total value N, are given by:
[tex]A = \frac{7}{2 + 3 + 7}N = \frac{7N}{12}[/tex][tex]K = \frac{3}{2 + 3 + 7}N = \frac{3N}{12}[/tex]The difference is of $15, hence:
[tex]A - K = 15[/tex]
[tex]\frac{7N}{12} - \frac{3N}{12} = 15[/tex]
[tex]\frac{4N}{12} = 15[/tex]
[tex]\frac{N}{3} = 15[/tex]
N = 15 x 3 = 45
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
in an enlargement PQ P1Q1|PQ|=3cm and|P1Q1|=15cm.Calculate the scale of the enlargement.
Answer:
374795-57770
Step-by-step explanation:
Abby uses
Given the system of inequalities: 4x – 5y < 1 one-halfy – x < 3 which shows the given inequalities in slope-intercept form? y < four-fifthsx – one-fifth y < 2x 6 y > four-fifthsx – one-fifths y < 2x 6 y > negative four-fifthsx one-fifth y > 2x 6
The slope- intercept is y> (1-4x) / 5 and y< 2x + 6
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
4x – 5y < 1 and 1/2y – x < 3
Solving
4x – 5y < 1
-5y < 1- 4x
-y < (1-4x) / 5
y> (1-4x) / 5
Now, the second inequality,
1/2y – x < 3
1/2y< 3+x
y< 2x + 6
Learn more about this concept here:
https://brainly.com/question/13762480
#SPJ1
hich of the following descriptions matches the tree diagram below?
Answer:
B
Step-by-step explanation:
There is 2 options, win and lose, no tie so 3 and 4 get cancelled. there are only 2 roots so 1 gets cancelled leaving 2 (B)
In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply.
m∠R > 90°
m∠S + m∠T < 90°
m∠S = m∠T
m∠R > m∠T
m∠R > m∠S
m∠S > m∠T
Answer:
1. m∠R > 90°
2. m∠S + m∠T < 90°
4. m∠R > m∠T
5. m∠R > m∠S
Step-by-step explanation:
General strategyprove the statement starting from known facts, ordisprove the statement by finding a counterexampleHelpful fact: Recall that the Triangle Sum Theorem states that m∠R + m∠S + m∠T = 180°.
Option 1. m∠R > 90°
Start with m∠R > m∠S + m∠T.
Adding m∠R to both sides of the inequality...
m∠R + m∠R > m∠R + m∠S + m∠T
There are two things to note here:
The left side of this inequality is 2*m∠RThe right side of the inequality is exactly equal to the Triangle Sum Theorem expression2* m∠R > 180°
Dividing both sides of the inequality by 2...
m∠R > 90°
So, the first option must be true.
Option 2. m∠S + m∠T < 90°
Start with m∠R > m∠S + m∠T.
Adding (m∠S + m∠T) to both sides of the inequality...
m∠R + (m∠S + m∠T) > m∠S + m∠T + (m∠S + m∠T)
There are two things to note here:
The left side of this inequality is exactly equal to the Triangle Sum Theorem expressionThe right side of the inequality is 2*(m∠S+m∠T)Substituting
180° > 2* (m∠S+m∠T)
Dividing both sides of the inequality by 2...
90° > m∠S+m∠T
So, the second option must be true.
Option 3. m∠S = m∠T
Not necessarily. While m∠S could equal m∠T, it doesn't have to.
Example 1: m∠S = m∠T = 10°; By the triangle sum Theorem, m∠R = 160°, and the angles satisfy the original inequality.
Example 2: m∠S = 15°, and m∠T = 10°; By the triangle sum Theorem, m∠R = 155°, and the angles still satisfy the original inequality.
So, option 3 does NOT have to be true.
Option 4. m∠R > m∠T
Start with the fact that ∠S is an angle of a triangle, so m∠S cannot be zero or negative, and thus m∠S > 0.
Add m∠T to both sides.
(m∠S) + m∠T > (0) + m∠T
m∠S + m∠T > m∠T
Recall that m∠R > m∠S + m∠T.
By the transitive property of inequalities, m∠R > m∠T.
So, option 4 must be true.
Option 5. m∠R > m∠S
Start with the fact that ∠T is an angle of a triangle, so m∠T cannot be zero or negative, and thus m∠T > 0.
Add m∠S to both sides.
m∠S + (m∠T) > m∠S + (0)
m∠S + m∠T > m∠S
Recall that m∠R > m∠S + m∠T.
By the transitive property of inequalities, m∠R > m∠S.
So, option 5 must be true.
Option 6. m∠S > m∠T
Not necessarily. While m∠S could be greater than m∠T, it doesn't have to be. (See examples 1 and 2 from option 3.)
So, option 6 does NOT have to be true.
Answer: Option 1, 2, 4, & 5 or
A. m∠R > 90°; B. m∠S + m∠T < 90°; D. m∠R > m∠T; & E. m∠R > m∠S
Step-by-step explanation: Trust Me!
m∠R > 90°m∠S + m∠T < 90°m∠R > m∠Tm∠R > m∠S
If you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful.
If you found any of my answers helpful please like and subscribe. I mean choose my answer as Brainliest. I would appreciate it!
Good luck everyone! :)
Please help very urgent I’m on a time limit and I need the answer this is a test
An isosceles triangle is one with two equal-length sides. The value of l is 8 ft.
What is an isosceles triangle?An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.
In the given image it can be observed except 140° angle, the other two angles are congruent to each other which means the triangle is an isosceles triangle.
As per the base angle theorem in an isosceles triangle the sides opposite to the congruent triangle are equal therefore, the length of side l will be 8 ft as well.
Hence, the value of l is 8 ft.
Learn more about Isosceles Triangle:
https://brainly.com/question/2456591
#SPJ1
Find the measure of angle 1.
5)
AB is a straight line.
A
152⁰
B
Let that angle be x
Linear pairs are supplementary
So
152+x=180x=180-152x=28°Which composition of similarity transformations maps ΔLMN to ΔL'M'N'?
Option A: a dilation with a scale factor less than 1 and then a reflection
Option B: a dilation with a scale factor less than 1 and then a translation
Option C: a dilation with a scale factor greater than 1 and then a reflection
Option D: a dilation with a scale factor greater than 1 and then a translation
Which model best represents the situation
Answer:
A
Step-by-step explanation:
she worked a total of 34 hours , then
x + y = 34
earnings are $10 per hour babysitting , that is 10x for x hours
$15 per hour for yardwork, that is 15y for y hours
she made a total of $410 , then
10x + 15y = 410
system of equations is
x + y = 34
10x + 15y = 410
-3(2x-5)<5(2-x)
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct option is an open circle at 5 and a bold line starts at 5 and is pointing to the right.
The given inequality is -3(2x-5)<5(2-x).
What is inequality?Inequality is a declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
At first simplify each side
LHS of inequality -3(2x - 5) = -3(2x) + -3(-5) [∵(-)(-) = (+)]
⇒ -3(2x - 5) = - 6x + 15
Now, RHS of the inequality 5(2 - x) = 5(2) + 5(-x) [∵(+)(-) = (-)]
⇒ 5(2 - x) = 10 - 5x
Now, - 6x + 15 < 10 - 5x
Subtract 15 from both sides
That is, - 6x < -5 - 5x
Add 5x to both sides
That is, - x < - 5
Remember the coefficient of x is negative, and then when you divide both sides by it you must reverse the sign of inequality.
Now, the coefficient of x is -1
So, divide both sides by -1
Then, x > 5.
Hence, the correct option is an open circle at 5 and a bold line starts at 5 and is pointing to the right.
To learn more about inequality visit:
https://brainly.com/question/20383699.
#SPJ1
PLEASE HELP
If 2 pounds is equal to 3 dollars, which of the following is incorrect?
A. 11 pounds is 16.50 dollars
B. 28 pounds is 44 dollars
C. 10 pounds is 15 dollars
D. 23 pounds is 34.50 dollars
Therefore, the incorrect statement is option B, which states that 28 pounds is equal to 44 dollars. The correct value should be 42 dollars.
To determine which statement is incorrect, we can use the given conversion rate of 2 pounds being equal to 3 dollars and evaluate each option accordingly:
A. 11 pounds is 16.50 dollars:
To check this, we can multiply 11 pounds by the conversion rate:
11 pounds * (3 dollars / 2 pounds) = 16.50 dollars
This statement is correct.
B. 28 pounds is 44 dollars:
Using the same calculation:
28 pounds * (3 dollars / 2 pounds) = 42 dollars
This statement is incorrect because 28 pounds would actually be equal to 42 dollars, not 44 dollars.
C. 10 pounds is 15 dollars:
Again, applying the conversion rate:
10 pounds * (3 dollars / 2 pounds) = 15 dollars
This statement is correct.
D. 23 pounds is 34.50 dollars:
Using the conversion rate:
23 pounds * (3 dollars / 2 pounds) = 34.50 dollars
This statement is correct.
For such more question on dollars
https://brainly.com/question/30057220
#SPJ8
What value of k makes the equation true? (5a^2n^3(6a^kb)=30a^6b^4
An equation is formed when two equal expressions. The value of k that makes the equation true is 4.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The value of k that will make the equation true is,
[tex]5a^2b^3(6a^kb)=30a^6b^4\\\\30\ a^{(2+k)}\ b^{(3+1)} = 30\ a^6\ b^4\\\\30\ a^{(2+k)} \ b^4 = 30\ a^6\ b^4\\\\a^{(2+k)} =a^6\\\\2+k = 6 \\\\ k = 4[/tex]
Hence, The value of k that makes the equation true is 4.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ1
answer?........................
Answer:
x- intercept = - 1 , y- intercept = 2
Step-by-step explanation:
the x- intercept is the value of the x- coordinate where the curve crosses the x- axis , that is
x- intercept = - 1
the y- intercept is the value of the y- coordinate where the curve crosses the y- axis , that is
y- intercept = 2
PLEASE PLEASE HELP ME WITH THSI MATH PROBLEM!!!
Answer:
23
Step-by-step explanation:
area of a trapezoid = 1/2 × (a + b) × h
so, we have
96 = 1/2 × ((4x - 1) + (x + 3)) × 6 = (5x + 2) × 3
32 = 5x + 2
30 = 5x
x = 6
a = 4x - 1 = 4×6 - 1 = 24 - 1 = 23
What is the effect on the graph of f(x) = x² when it is transformed to
h(x)=x²-16?
A. The graph of f(x) is vertically compressed by a factor of 7 and
shifted 16 units down.
B. The graph of f(x) is horizontally compressed by a factor of 7 and
shifted 16 units down.
C. The graph of f(x) is vertically compressed by a factor of 7 and
shifted 16 units to the right.
D. The graph of f(x) is horizontally stretched by a factor of 7 and
shifted 16 units to the right.
The correct answer is option A which is the graph of f(x) is vertically compressed by a factor of 7 and shifted 16 units down.
What is a graph?
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given functions are:-
f(x) = x²h(x)=x²-16When we plot the graph of the two functions given in the question we will see that the graph of the function F(x) = x²-16 is compressed by the factor 7 and the vertex of the graph shifted to the 16 points down.
Therefore the correct answer is option A which is the graph of f(x) is vertically compressed by a factor of 7 and shifted 16 units down.
To know more about graphs follow
https://brainly.com/question/25020119
#SPJ1
For her class, Mrs. Norman bought 31 student tickets and 32 adult tickets, which cost a total of $854. Mr. Horton spent $837, getting 31 student tickets and 31 adult tickets. What is the price for each type of ticket?
Answer:
Each student ticket costs $10, and each adult ticket costs $17.
Step-by-step explanation:
Let s represent the cost of a student ticket and a represent the cost of an adult ticket.
31s + 32a = 854
31s + 31a = 837
----------------------
a = 17
31s + 31(17) = 837
31s + 527 = 837
31s = 310, so s = 10
solve this question - one half x - 18 = 2
Answer:
x=10
Step-by-step explanation:
Combine like terms to create an equivalent expression.
Enter any coefficients as simplified proper or improper fractions or integers.
1/7 -3(3/7n-2/7)
The expression 1/7 – 3(3/7n – 2/7) is equivalent to the expression 1 – 9/7n.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The expression is given below.
⇒ 1/7 – 3(3/7n – 2/7)
On simplifying the expression, we have
⇒ 1/7 – 9/7n + 6/7)
⇒ 1 – 9/7n
More about the equivalent link is given below.
https://brainly.com/question/889935
#SPJ1
Answer:
-9/7 n + 1
Step-by-step explanation:
On khan
Es para hoy ayúdenme por favor
Answer:
Con qué necesitas ayuda?
Step-by-step explanation:
3. If there are 104 ounces in 2 quarts, how many quarts are there in 260 ounces?
A. 5
B. 2.5
C. 26
D. 1300
Which quadrilaterals have all of the properties of a parallelogram?
A)rhombus, kite, and trapezoid
B)rhombus, rectangle, and square
C)rhombus, kite, and square
D)rhombus, trapezoid, and rectangle
The first two terms of an arithmetic sequence are shown below. 1 2 x+2' x+3' ck to task your mistake. Find the third term of this sequence. Give your answer fully factorised. Watch video Answer > The first two terms of an arithmetic sequence are shown below . 1 2 x + 2 ' x + 3 ' ck to task your mistake . Find the third term of this sequence . Give your answer fully factorised . Watch video Answer >
Answer:
in picture
Step-by-step explanation:
added in the picture
What are the solutions to the system of equations?
Graph the system of equations to solve.
(−4,2) and (2,−1)
(0,0) and (−4,2)
(0,0) and (0,−2)
(2.9,0) and (−2.9,0)
Graphically, we will see that the solutions of the system are (−4,2) and (2,−1)
How to solve the system of equations?To solve the system of equations graphically, we need to graph both of the equations and see in which points the graphs intercept.
The graph of the system can be seen below, there you can see that the intercepts are at:
(-4, 2) and (2, -1)
So these are the two solutions of the system of equations.
if you want to learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
The difference of the product of 3 and 6 minus the quotant of 6 / 2
Answer:
Answer:
(3*6) - (6/2) = 15
Step-by-step explanation:
3 and 6 are being multiplied by them selves, and then subtracted by the answer of 6/2.
The answer of the equation is 15.
What is the image of (-9,3)(−9,3) after a reflection over the y-axis?
Answer:
(9, 3 )
Step-by-step explanation:
under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
(- 9, 3 ) → (9, 3 )
is the number there three? if you answer to me i will give you twenty Points.
Answer:
t = 2
Step-by-step explanation:
Look at the fraction on the left, 1/3.
Notice that the denominator is 3 times the numerator.
Since the fractions are equal, for the second fraction, you also need the denominator to be 3 times the numerator. Since the denominator is 6, the numerator must be 2 since 6 is 3 times 2.
Answer: t = 2
Of course, since you have two fractions that are equal, and fractions are also ratios, you have a proportion.
You can solve the problem as a proportion.
1/3 = t/6
Cross multiply:
3t = 1 × 6
3t = 6
t = 6/3
t = 2
Either way, you get t = 2.
the greatest common factor of 6x^2-8+22 is?
The greatest common factor for the numerical part will be 2.
How to find Greatest common factor?The greatest common factor, as the name implies, is the greatest among all common factors among the quantities given.
We can factorize the quantities in the smallest relative factors possible (one level of factors over which all quantities can form themselves), and collect as many common factors as we could.
Those will together compose GCF(The greatest common factor).
Given;
[tex]6x^2-8+22[/tex]
Since the expression contains both numbers and a variable part.
For numerical parts 6, -8, 22
The factors are
6 = -6, -3. -2, -1,1, 2, 3 , 6
8 = -8, -4, -2, -1,1, 2, 4, 8
22 = -22, -11, -2, -1,1, 2, 11, 22
The greatest common factor for the numerical part will be 2.
The number part does not contain any common variable factor.
Learn more about the greatest common factor here:
https://brainly.com/question/207329
#SPJ1
3.)3 * (2x - 6)
4.)2x * (5x + 11)
3) [tex]3(2x-6)=\boxed{6x-18}[/tex]
4) [tex]2x(5x+11)=10x^{2}+22x[/tex]
what are the x-intercept(s) of the function
To find the zeros of a rational function, we must identify values of x that make the numerator equal to 0. We can do this by factoring and by keeping in mind the zero-product property.
The zero-product property states that if the product of two terms is 0, then one of the terms must be equal to 0.
Solving the QuestionWe're given:
[tex]f(x)=\dfrac{4x^2-36x}{x-9}[/tex]
First, factor 4x out of the numerator:
[tex]f(x)=\dfrac{4x(x-9)}{x-9}[/tex]
Let f(x) = 0:
[tex]0=\dfrac{4x(x-9)}{x-9}[/tex]
In this case, either x or (x-9) is equal to zero, as they are the two terms being multiplied in the numerator to get 0 as a product.
This makes the x-intercepts of this function 0 and 9.
However, the denominator in this function is x - 9. If x = 9, then it would make the denominator 0, which is not allowed. Therefore, x cannot equal 9, and the only x-intercept is 0.
Answerx = 0
Explaintion needed.
Step-by-step explanation:
for straight Line AE:
110° + AČB = 180° ( angles on straight line )
A Č B = 70°
for triangle "A C B"
65° + 70° + x = 180° (sum of angles on triangle)
x = 45°
DO THE SAME THING FOR THE UPPER PART ( straight line A E and triangle A D C) PLEASE GIVE ME BRAINLIEST ANSWER