[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$700\\ r=rate\to 15\%\to \frac{15}{100}\dotfill &0.15\\ t=years\dotfill &3 \end{cases} \\\\\\ I=(700)(0.15)(3)\implies I=315[/tex]
there are 21 marbles in a blue jar. the blue jars has 3 times as many marbles as a red jar. let m be the number of marbles in the red jar
Answer:
m=7
Step-by-step explanation:
1 blue jar = 21 marbles
1 blue jar = 3 red jars
Therefor
21 marbles= 3 red jars
(Now let m=1 red jar)
21= 3m
(Then sine we have 3m dived both sides by 3 to isolate the m)
21/3= 3m/3
7=m
There are 7 marbles in a red jar if there are 21 marbles in a blue jar. The blue jars have 3 times as many marbles as a red jar.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
There are 21 marbles in a blue jar. The blue jars have 3 times as many marbles as a red jar.
Let m be the number of marbles in the red jar
From the problem, we can make a linear equation in one variable:
3m = 21
m = 7
Thus, there are 7 marbles in a red jar if there are 21 marbles in a blue jar. The blue jars have 3 times as many marbles as a red jar.
Learn more about the linear equation here:
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solve the proportional equation below 6/2=(v-8)/(v-3)
½ = v; multiply the divisor to remove the variable from the denominator.
Given that EH is a median of EFG what can you say about HF and HG
Answer:
Option C.
Step-by-step explanation:
we know that
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side
therefore
In this problem
HF=HG
Lyle is camping at a campground. Lyle's cabin is represented by the point (-27,23). The dining hall is located 21 meters east and 20 meters south of Lyle's cabin and is represented by the point (-6,3).
The shortest distance from Lyle's cabin to the dining hall is_____meters.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{\textit{Lyle's cabin}}{(\stackrel{x_1}{-27}~,~\stackrel{y_1}{23})}\qquad \stackrel{\textit{dining hall}}{(\stackrel{x_2}{-6}~,~\stackrel{y_2}{3})}\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-6-(-27)]^2+[3-23]^2}\implies d=\sqrt{(-6+27)^2+(3-23)^2} \\\\\\ d=\sqrt{21^2+(-20)^2}\implies d=\sqrt{841}\implies d=29[/tex]
The shortest distance from Lyle's cabin to the dining hall is 29 meters.
To calculate the shortest distance between Lyle's cabin and the dining hall, we can use the distance formula for two points in a coordinate plane. The distance formula is:
d = √[(x2 - x1)² + (y2 - y1)²]
Given:
Lyle's cabin coordinates: (-27, 23)
Dining hall coordinates: (-6, 3)
We use the following steps:
Calculate the difference in the x-coordinates: -6 - (-27) = -6 + 27 = 21
Calculate the difference in the y-coordinates: 3 - 23 = -20
Square these differences: 21² = 441 and (-20)² = 400
Add the squares: 441 + 400 = 841
Take the square root of the sum: √841 = 29
Thus, the shortest distance from Lyle's cabin to the dining hall is 29 meters.
Quadrilateral JKLM has vertices J(8,4)K(4,10)L(12,12) and M (14,10) . Match each quadrilateral,described by its vertices ,to sequence of transformation that will show it is congruent to quadrilateral JKLM
- A translation to 3 units left and 2 units up = E
- A translation to 2 units right and 3 units down = O
- A sequence of reflections across the x- and y-axes, in any order = A
- A translation to 3 units down and 3 units left = W
- Ouma
Translating 3 units left and 2 units right gives E(5,6), F(1, 12), G(9, 14) and H (11, 8)
Translating 2 units right and 3 units down gives O(10, 1), P(6, 7), Q(14, 9) and R(16, 7)
Reflecting across the x and y axis gives A(-8, -4), B(-4, -10), C(-12, -12) and D(-14, -10)
Translating 3 units down and 3 units left gives W(5, 1), X(1, 7), Y(9, 9) and Z(11, 7)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.
Quadrilateral JKLM has vertices J(8,4), K(4,10), L(12,12) and M (14,10) .
1) Translating 3 units left and 2 units right gives E(5,6), F(1, 12), G(9, 14) and H (11, 8)
2) Translating 2 units right and 3 units down gives O(10, 1), P(6, 7), Q(14, 9) and R(16, 7)
3) Reflecting across the x and y axis gives A(-8, -4), B(-4, -10), C(-12, -12) and D(-14, -10)
4) Translating 3 units down and 3 units left gives W(5, 1), X(1, 7), Y(9, 9) and Z(11, 7)
Find out more on transformation at: https://brainly.com/question/1620969
Ben wants to join a fitness club. The fitness club charges an initial membership fee of $49.50 and a monthly fee of $17.50. Question 1 Part A Ben has $172 to spend on a membership at the fitness club. How many months can Ben be a member of the fitness club?
Answer:
9 months
Step-by-step explanation:
Answer: 6 months
Step-by-step explanation: you take the initial membership fee of $49.50 and add it to the monthly for the first fee so it would be $67 and subtract that from the $172 he has. then divide the left over which is 105 and 17.50 you get 6
Rezolvati, in multimea numerelor intregi, inecuatiile
Exercitiul 8 va rog!
When solving integer inequalities, isolate the variable on one side just like an equation. If the inequality involves a negative number, remember to flip the sign.
Explanation:Since the exercise isn't specifically provided, I will walk you through a general process of solving integer inequalities.
First, treat the inequality similar to an equation. You'll need to isolate the variable (usually represented by 'x') on one side of the inequality.
Example 1: Let's say your inequality is x + 3 < 7. You can subtract 3 from both sides to isolate 'x', giving you x < 4.
Example 2: For an inequality like 5x > 30, you'd divide both sides by 5. This gives you x > 6. In both examples, the solution sets are all the integers less than 4 and greater than 6, respectively.
Remember that if you multiply or divide by a negative number, the inequality sign will flip.
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how many solutions exist for the givien equation 3(x+10)+6=3(x+12)
For this case we solve the following equation:
[tex]3 (x + 10) + 6 = 3 (x + 12)[/tex]
We apply distributive property to the terms within parentheses:
[tex]3x + 30 + 6 = 3x + 36[/tex]
We add similar terms:
[tex]3x + 36 = 3x + 36\\36 = 36[/tex]
Since 36 equals 36, then the equation will always be true for any value of x.
ANswer:
Infinite solutions
Solve the equation 8-6z=26
8-6z=26
8-8-6z=26-8
-6z=18
divide by -6 for -6z and 18
-6z/-6=18/-6
z=-3
Check answer by using substitution method
8-6(-3)=26
8+18= 26
26=26
Answer is z=-3
Answer:
answer - 3
Step-by-step explanation:
8 - 6z = 26 Subtract 8 from both sides.
8-8 - 6z = 26 - 8
- 6z = 18 Divide by - 6
-6z/-6 = 18/-6 Do the division. Note: you must leave the letter with 1 in front of it.
z = - 3
During the Winter, you charged people $ 15 for going to their house to shovel then $11 for every hour you bag groceries. If you make $48 one day how many hours did you spend bagging groceries?
Answer:
you spent 3 hours bagging groceries.
Step-by-step explanation:
you can use a calculator and do 11 times 3 plus 15.
Final answer:
To find out how many hours were spent bagging groceries when making $48 in total, solve the given equation with the respective earnings from shoveling and bagging.
Explanation:
The question: During the Winter, you charged people $15 for shoveling snow and $11 for every hour bagging groceries. If you made $48 one day, how many hours did you spend bagging groceries?
Step-by-step explanation:
Let's denote the hours spent bagging groceries as x.
Write the equation: $15 (for shoveling) + $11x (for bagging) = $48.
Solve the equation to find x: $15 + $11x = $48, $11x = $33, x = 3 hours.
What is the Greatest common factor of 18x^2 and 36x
For this case we have that by definition, the Greatest Common Factor or GFC of two or more numbers, is the largest number that divides them without leaving residue.
So:
We look for the factors of 18 and 36:
18: 1,2,3,6,9,18
36: 1, 2,3,4, 6,9,18 ...
Thus, the GFC of both numbers is 18.
Then, the GFC of[tex]18x ^ 2[/tex] and [tex]36x[/tex] is:
[tex]18x[/tex]
Answer:
[tex]18x[/tex]
Final answer:
The Greatest Common Factor of 18x² and 36x is 18x, which is the product of shared prime factors to the lowest powers and includes the variable x.
Explanation:
Finding the Greatest Common Factor (GCF)
To find the Greatest Common Factor of 18x² and 36x, we need to break down each term into its prime factors and include the variable parts:
18x² can be factored into 2 × 3 × 3 × x × x (or 2 × 3² × x²)36x can be factored into 2 × 2 × 3 × 3 × x (or 2² × 3² × x)The GCF is the product of the lowest powers of common factors in both terms. Hence, the GCF of 18x² and 36x is 18x, which consists of 2 × 3 × 3 × x (or 2 × 3² × x).
In circle C, what is m?
I assume the 38º measurement refers to the measure of arc BE. Then
[tex]37^\circ=\dfrac{m\widehat{AJ}-38^\circ}2\implies m\widehat{AJ}=112^\circ[/tex]
and so
[tex]32^\circ=\dfrac{112^\circ-m\widehat{FH}}2\implies m\widehat{FH}=\boxed{48^\circ}[/tex]
(I think the theorem I used here is called "angle of intersecting secants")
which graph represents the piece wise- defined function f(x) =
Answer:
right-most fourth graph
Step-by-step explanation:
Given:
f(x)= -x+4 for 0≤x<3
i.e. from x=0 till x=3 the graph is linear line
then
f(x) = 5 for x≥3
i.e. at x=3 and onward graph is a straight line with y-axis point of 5 !
Answer:
The fourth graph, from left to right, is the correct answer.Step-by-step explanation:
The given piecewise function is
[tex]f(x)=\left \{ {{-x+4 \ ; \ 0\leq x<3} \atop {5 \ ; \ x\geq3 }} \right.[/tex]
Notice that the domain of the function specifies that, from zero to three, the function represents a decreasing (because the variable is negative) straight line. When the function is defined from 3 to infinite, the function is a constant of 5.
So, the right graph must shows first a decreasing line, where the initial point is solid and the final point is empty, as the fourth fraph (from left to right), then it must show a horizontal line with an initial point solid.
Therefore, the fourth graph, from left to right, is the correct answer.
PLEASE HELP!!!! The factored form of a quadratic expression is x (x – 4). The ordered pair (0, 0) represents one of the zeros of the associated quadratic function. Which ordered pair represents the other zero?
Answer:
The ordered pair that represent the other zero is [tex](4,0)[/tex]
Step-by-step explanation:
we know that
The zeros or x-intercepts of the quadratic function, represent the value of x when the value of y is equal to zero
In this problem to find the other zero equate (x-4) to zero and solve for x
[tex](x-4)=0[/tex]
[tex]x=4[/tex]
therefore
The ordered pair that represent the other zero is [tex](4,0)[/tex]
Which of the following is the solution to the quadratic equation -x2-5x-6=0 using the quadratic formula
Answer:
x = -2; x = -3
Step-by-step explanation:
(-x - 3)(x + 2) = 0
(-x - 3) = 0
x = -3
(x + 2) = 0
x = -2
How can you calculate the volume of a cylinder? Please help!
Step-by-step explanation:
Volume of a cylinder is the area of the circular cross section times the height:
V = πr²h
Answer:
V=(3.14)r^2×h
Step-by-step explanation:
(3.14)= pie
r^2= radius to the second power
h=height of cylinder
Monica runs on a treadmill at an average speed of 7.5 miles per hour for 15 minutes. If, the next day, she runs the same distance at a speed of 8 miles per hour, what is the average time taken?
Answer:
Option 2: 14.06 minutes
Step-by-step explanation:
For the first scenario, we will convert the minutes into hours first to get all the quantities in same unit
So,
15 minutes = 1/4 hours = 0.25 hours
Speed = 7.5 miles per hour
Now using the speed, distance and time formula
Speed = distance/time
[tex]Speed = \frac{distance}{time}[/tex]
[tex]7.5 = \frac{distance}{0.25}[/tex]
[tex]7.5 * 0.25 = Distance[/tex]
Distance = 1.875 miles
So the distance for 1st day is 1.875 miles.
For next day
Speed = 8 miles per hour
Distance = 1.875
So,
[tex]speed = \frac{distance}{time}[/tex]
[tex]8 = \frac{1.875}{time}[/tex]
[tex]time = \frac{1.875}{8}[/tex]
[tex]time = 0.234375 hours[/tex]
Converting the hours into minutes will give
0.234375 * 60 min = 14.0625 minutes
Rounding off to two decimals = 14.06 min
So 2nd option is correct..
Plz help with financial algebra !!
Answer: She will be there 8 years.
Step-by-step explanation:
What is the range of the function? f(x) = -2^x + 1
{y|1 > y}, (-∞, 1); you did not specifically mention what notation you needed, so I wrote both [Internal Notation and Set Notation].
Answer:
all real numbers less than or equal to 0
Step-by-step explanation:
EDGE 2020
Use the graph below to answer the question what is the slope of the weather is perpendicular to the line in the graph
Answer:
1
Step-by-step explanation:
Slopes of perpendicular lines are opposite reciprocal of one another i.e.
slope m1, of given line l1 = -1/slope m2, of its perpendicular line l2
slope m2, of its perpendicular line l2 = -1/slope m1, of given line l1
m2= -1/m1
Finding m1 from the given graph
m1= y2-y1/x2-x1
= -2-1/2+1
= -3/3
= -1
m2= -1/-1
= 1 !
Use the vertical line test to determine if the relation is a function!! HELP NEEDED!!
Below is an image of the vertical line test.
The vertical line test is passed only when a vertical line only intersects the graph once. As you can see this graph intersects the graph twice, and therefore is not a function.
The answer you selected was correct!
Hope this helped!
Paul is going to have the exterior of his home painted. Painting USA charges $75.00 to come out and evaluate the house plus $25.00 per hour of labor. Upscale Home Painting does not charge to evaluate the house. However, they charge $40.00 per hour.
If it takes 25 hours to paint Paul’s house, the most cost effective company will be
Answer:
Painting USA is the most cost effective company.
Step-by-step explanation:
Painting USA company charges:
$75.00 to evaluate the house
Plus, $25.00 per hour of labor.
Total number of hours taken to paint the house is 25 hrs
Total cost here = $75.00 + $25.00(25) = $700.00
Upscale Home Painting company charges:
$0.00 to evaluate the house
$40.00 per hour of labor.
Total number of hours taken to paint the house is 25 hrs
Total cost here = $0.00 + $40.00(25) = $1000.00
So Painting USA is the most cost effective company since it charges $700.00 which is less that Upscale Home Painting company's painting charges of $1000.00.
Answer:
Painting USA
Step-by-step explanation:
They will charge 700
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). A six-sided die of unknown bias is rolled 20 times, and the number 3 comes up 6 times. In the next three rounds (the die is rolled 20 times in each round), the number 3 comes up 6 times, 5 times, and 7 times. The experimental probability of rolling a 3 is %, which is approximately % more than its theoretical probability. (Round off your answers to the nearest integer.)
Answer:
The experimental probability of getting a 3 on a die is 30% which is approximately 13% more than its theoretical probability (17%).
Step-by-step explanation:
Theoretical probability of number 3 on a die:
Total no. of possibilities = 6
Probability of getting a 3 on a die each time it is rolled = 1/6
= 0.16667
= 17%
Experimental probability of number 3 on a die:
Total no. of rounds = 4
Rolls each round = 20
no. of 3s in round 1 = 6
no. of 3s in round 2 = 6
no. of 3s in round 3 = 5
no. of 3s in round 4 = 7
Total rolls = 20*4 = 80
no. of times 3 comes up = 6+6+5+7 = 24
Experimental probability of getting a 3 on a die
each time it is rolled = no. of 3s/total rolls
= 24/80
= 0.3
= 30%
Difference = 30% - 17% = 13%
Experimental probability of getting a 3 on a die is 30% which is approximately 13% more than its theoretical probability (17%).
Answer:
The experimental probability of rolling a 3 is 30 %, which is approximately 13 % more than its theoretical probability.
Step-by-step explanation:
PLATO
Kylie needs to pack her baton for a color-guard competition. The baton is 38 inches long. Will it fit in a rectangular box with a base of 13 inches by 35 inches and a height of 13 inches?
With the height of the rectangular box, the baton can fit diagonally in the box.
The length of the baton that Kylie needs to pack = 38 inches
The width of the rectangular box = 13 inches
The length of the rectangular box = 35 inches
The height of the rectangular box = 13 inches
Comparing the dimensions:
The baton is 38 inches long and longer than the length and width of the box.
The height of the box is 13 inches, making the box greater than the length of the baton diagonally.
Thus, the baton will fit in the box diagonally.
Sabina makes $2,000 per month. She spends $150 on store credit and $250 on an auto loan each month. Does she have excessive debt?
A.)Yes, because her debt-to-income ratio is higher than 36 percent.
B.)No, because her debt-to-income ratio is lower than 36 percent.
C.)No, because her debt-to-income ratio lower than 42 percent.
D.)Yes, because her debt-to-income ratio is 50 percent.
Answer:
A or B
Step-by-step explanation:
Answer:
Should be B, No because her debt-to-income ratio is lower than 36 percent.
Step-by-step explanation:
Cuales son las dimensiones de un rectángulo con un perímetro igual a 578 pulgadas, si su largo es 6 pulgadas menos que 4 veces su ancho
Answer:
The dimensions of rectangle are 230 in by 59 in
Step-by-step explanation:
The question in English is
What are the dimensions of a rectangle with a perimeter equal to 578 inches, if its length is 6 inches less than 4 times its width?
Let
x-----> the length of rectangle
y----> the width of rectangle
we know that
The perimeter of rectangle is equal to
P=2(x+y)
P=578 in
so
578=2(x+y)
289=x+y -----> equation A
x=4y-6 -----> equation B
substitute equation B in equation A
289=(4y-6)+y
5y=295
y=59 in
Find the value of x
x=4y-6 -----> x=4(59)-6=230 in
therefore
The dimensions of rectangle are
230 in by 59 in
if point c is between points a and b, then ac+cb=
Answer:
Step-by-step explanation:
ac + cb = ab
what is the volume of the cylinder below?
972pi mm^3 as height is 12 mm radius is half of 18 mm ie 9mm
therefore volume=pi(r^2)h
ie 972pi mm ^3
Answer: [tex]972\pi\text{ mm}^3[/tex]
Step-by-step explanation:
We know that the volume of a cylinder is given by :-
[tex]\text{Volume}=\pi r^2 h[/tex], where r is radius and h is height of the cylinder.
Given: Diameter of cylinder = 18 mm
Then , radius of cylinder = [tex]\dfrac{18}{2}=9\ mm[/tex]
Height of cylinder = 12 mm
Then the volume of cylinder will be :-
[tex]\text{Volume}=\pi (9)^2 (12)\\\\\Rightarrow\text{Volume}=972\pi\text{ mm}^3[/tex]
Hence, the volume of the given cylinder = [tex]972\pi\text{ mm}^3[/tex]
Is 1/4 of a circle a polygon? Explain.
A polygon is a plane figure with at least three straight sides and angles, and typically five or more. In other words, a polygon is a 2 dimensional shape with straight sides. No curves!
A quarter of a circle has a curve on one side, and is therefore not a polygon.
Find the measures of the interior angles.how do you find the measures of the interior angles
Answer:
'm guessing you mean with parallels and a transversal. If this is the case, then find he angle that is either
a; supplementary (creating a flat angle, 180 degrees) or
b; complimentary (creating a 90 degree angle)
Step-by-step explanation:
subtract the supplementary/complimentary angle from either 180 or 90 and the difference is your answer. Hope I helped!
* * * * *
More likely the question is concerned with the interior angles of a polygon. If the polygon is irregular then there is no simple answer. An interior angle can have any value.
However, if it is a regular polygon then the question can be answered. The sum of all the exterior angles is 360 degrees - irrespective of the number of sides (or vertices). Suppose the polygon has n sides/vertices.
Then, since it is regular, each exterior angle is 360/n. Therefore, each interior angle is 180-360/n degrees.
The sum of interior angles of a polygon can be found using the formula (n-2) x 180 degrees.
To find the measures of the interior angles of a polygon, you must first consider the type of polygon you're dealing with. For a triangle, the sum of the interior angles is always 180 degrees. If you're working with another type of polygon, such as a quadrilateral, the sum of the interior angles is greater, and there's a simple formula to follow: (n-2) imes 180 degrees, where n represents the number of sides of the polygon. This means that for a quadrilateral, with four sides, the sum of the interior angles would be (4-2) * 180 degrees, which equals 360 degrees.
When it comes to alternate interior angles, these are pairs of angles found on the inside of two lines that are cut by a transversal. If the lines are parallel, the alternate interior angles are equal in measure. For example, if you have two parallel lines cut by a transversal forming angle a and angle f, then a and f would be alternate interior angles and thus, would have the same measure.
The sum of the exterior angles in any polygon is 360 degrees, regardless of the number of sides. When finding the measure of an exterior angle, knowing the measure of its corresponding interior angle can be helpful because the interior and exterior angles form a linear pair (adding up to 180 degrees). Therefore, if the interior angle is 150 degrees, the exterior angle would be 180 degrees - 150 degrees, which equals 30 degrees.