Johann uses 42 +7 to represent the number of players who are on teams.
Explain what 42÷7 means.
_______________________________
42 +7 = the number of players who are on teams
42 = he number of players who are on teams minus 7
42 players
________________________
Dividing by 7 (the number of player per group)
Each team has 7 players
_____________
231 students of the Brooklyn Public Library went on a field trip. Some students rode in vans that hold 7 students each, and some students rode in buses that hold 25 students each. How many of each type of vehicle did the students ride in if there were 15 total vehicles? *
We have the next information
In total, we have 231 students
van--- 7 students
bus - 25 students
in total, we have 15 vehicles
So our first equation is
x+y=15
where
x is the number of vans
y is the number of buses
The second equation is
7x+25y=231
so we will isolate the x of the first equation
x=15-y
then we substitute this equation in the second equation
7(15-y)+25y=231
105-7y+25y=231
then we sum like terms
18y=126
then we isolate the y
y=126/18
y=7
Then for the value of x we use the equation with the x isolate and we substitute the value of y
x=15-7=8
Therefore the answer is 8 vans and 7 buses
2 angles are Supplementary. One angle has a measure that is 5 times the other Angle. Type in the measure of the bigger angle.
Step 1: Let's recall that Supplementary angles are two angles with a sum of 180∘
Step 2: Let's write the equation to solve the problem.
• Let x to represent the smaller angle,
,• Let 5x to represent the bigger angle
Therefore, we have:
x + 5x = 180
6x = 180
Dividing by 6 at both sides:
6x/6 = 180/6
• x = You can calculate the value of x dividing 180 by 6 and that is the measure of the smaller angle.
,• 5x = You multiply the value of x by 5 and that's the measure of the bigger angle.
Don't forget that the sum of both angles should be 180.
Every month Pablo earns $40 for walking his neighbors dog after school how much does he earn from his job in one year?
We know that Pablo earns $40 every month.
Then, to calculate how much he makes in a year, we use the fact that a year has 12 months.
Then, we can write:
[tex]40\frac{\$}{\text{month}}\cdot12\text{ }\frac{months}{year}=480\frac{\$}{\text{year}}[/tex]Answer: he earns $480 per year.
Does the coordinate (-2,5) land on the linear equation y = 2x + 9 ?yesnomaybe
Answer:
Yes
Explanation:
The coordinate (-2,5) corresponds to the point (x, y).
This means that:
x= -2 and y=5
To check if the coordinate land on the equation y=2x+9, calculate the value of y when x= -2
[tex]\begin{gathered} \text{When x=-2} \\ y=2(-2)+9 \\ =-4+9 \\ =5 \end{gathered}[/tex]Therefore, the coordinate (-2,5) land on the linear equation y = 2x + 9.
I need to find the exact area of the sector.
Select the correct choice below and, if necessary, fill in the answer box to complete your choiceO A. The function is continuous on(Type your answer in interval notation.)0 B. The function is not continuous
From the given image, we can affirm that the function is continuous in all its domain. That's the interval:
[tex]\lbrack4,\infty)[/tex]f(x) = -4x – 7 find the equation for the inverse function
Answer:
[tex]f^{-1}(x)=-\frac{1}{4}(x+7)[/tex]
Step-by-step explanation:
[tex]f(x)=-4x-7 \implies x=-4f^{-1}(x)-7 \\ \\ x+7=-4f^{-1}(x) \\ \\ f^{-1}(x)=-\frac{1}{4}(x+7)[/tex]
The function f(x) = log2 x is transformed 3 units to the right and vertically compressed by a factor of 0.6 to become g(x).Which function represents the transformation g(x)?
Translation h units to the right and compressed by a factor A:
[tex]f(x)=A\log_2(x-h)[/tex]Then, if g(x) is f(x) after the given transformations, it has the next equation:
[tex]\begin{gathered} g(x)=0.6\log_2(x-3) \\ \\ g(x)=\frac{3}{5}\log_2(x-3) \end{gathered}[/tex]Answer: last option21 pointUse the given information to complete the proof of the following theorem.If a quadrilateral is a parallelogram, then its opposite sides are congruent.By definition, a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.Use this definition in your proof.angle-side-angleCorresponding parts of congruent triangles are congruent.side-angle-sideOpposite sides of a parallelogram are congruent.
The Solution:
Required:
To prove that opposite sides are congruent in a parallelogram.
Step 1:
Draw a parallelogram.
Step 2:
[tex]DB\cong DB\text{ \lparen Reason: Reflexive property\rparen}[/tex]Step 3:
[tex]AB\parallel CD\text{ and BC }\parallel AD\text{ \lparen Reason: Definition of a parallelogram\rparen}[/tex]Step 4:
[tex]\angle1\cong\angle4\text{ and }\angle2\cong\angle3\text{ \lparen Reason: Alternative angles are equal.\rparen}[/tex]Step 5:
[tex]\angle ABD\cong\angle CDB\text{ \lparen Reason: Angle-Side-Angle \lparen ASA\rparen Theorem\rparen}[/tex]Step 6:
[tex]undefined[/tex]help me with this question please
Part a
the given polygon has 8 sides
so
Is a octagon
Part b
The given polygon is not a regular polygon, because all their sides don't have equal lengths and their interior angles are not equals
Joanie believes that you cannot use cross products to solve the proportion 50 / 3 equals 75 over x 4x she says that if you multiply both sides of the equation by X you get 50 x / 3 equals 75 then if you multiply both sides of the equation by 3 you get 50 x equals 75 which is a different equation then you would get if you cross multiply what mistake did Yuri make in her reasoning?
The proportion is shown below and we cross multiply, do algebra, to solve it.
[tex]\begin{gathered} \frac{50}{3}=\frac{75}{x} \\ 50x=3\cdot75 \\ 50x=225 \\ x=\frac{225}{50} \\ x=\frac{9}{2} \end{gathered}[/tex]If you read the question, so will see this part:
if you multiply both sides of the equation by 3 you get 50 x equals 75
This is the part where there is a problem. You did say to multiply by 3 (both sides). But don't multiply the right hand side of "75" mistakenly.
The last part of this line should be "equals 75 times 3"
This is the mistake.
a circle has a diameter of 10 feet what is the circumference in square feet 28.2 31.4 36.8 40.5
Given a circle has a diameter = 10 feet
The circumference of the
A garden that is 10/3 of an acre is to be divided into 5 equal-size areas. What is the size of each area?
Answer:
2/3 of an acre
Explanation:
To find the size of each area, we divide the area of the garden by 5. This gives
[tex]\frac{10}{3}\div5[/tex]Now at this point we remind ourselves that if we are dividing a fraction by a number, then we can turn the division into multiplication by taking the reciprocal of the number.
The number we are dividing our fraction by in this case is 5. Now, the reciprocal of 5 is 1/5 and so we can write the above as
[tex]\frac{10}{3}\div5\Rightarrow\frac{10}{3}\times\frac{1}{5}[/tex]Multiplying the denominators together gives
[tex]\frac{10}{3}\times\frac{1}{5}=\frac{10}{3\times5}=\frac{10}{15}[/tex]Now dividing both the numerator and the denominator by 5 gives
[tex]\frac{10\div5}{15\div5}=\frac{2}{3}[/tex]Hence,
[tex]\frac{10}{3}\div5=\frac{2}{3}[/tex]Therefore, the size of each area is 2/3 of an acre.
the life expectancy of a circulating coin is 30 years. the life expectancy of a circulating dollar bill is only 1/20 as long. find the life expectancy of circulating paper money. Life expectancy= how many years ( type a whole number or a mixed number simplify your answer)
Given
the life expectancy of a circulating coin is 30 years
the life expectancy of a circulating dollar bill is only 1/20 as long.
Procedure
c=life expectancy of a circulating coin
p= life expectancy of circulating paper money
[tex]p=\frac{1}{20}\cdot c[/tex][tex]\begin{gathered} p=\frac{1}{20}\cdot30 \\ p=\frac{30}{20} \\ p=1.5 \end{gathered}[/tex]The answer is: life expectancy of a dollar bill = 1.5 years
What is the value of x? R 2x+880 Q 78° 8x-940 X+790 s T
We have here that all of these angles must sum 360 degrees since we have here a circle. Then, we have that:
[tex]2x+88+8x-94+x+79+78=360[/tex]Now, to solve this equation, we need to group and sum the like terms:
[tex]2x+8x+x+88-94+79+78=360_{}[/tex][tex]11x-6+157=360\Rightarrow11x+151=360[/tex]To isolate 11x, we need now to subtract 151 to both sides of the equation:
[tex]11x+151-151=360-151\Rightarrow11x=209[/tex]Divide both sides of the equation by 11:
[tex]\frac{11x}{11}=\frac{209}{11}\Rightarrow x=19[/tex]We can check this solution if we substitute the value x = 19 in the original equation (after the simplification process):
[tex]11x+151=360\Rightarrow11\cdot(19)+151=360\Rightarrow209+151=360\Rightarrow360=360[/tex]Since the last result is TRUE, then the value for x = 19 is the correct solution.
In summary, the value for x = 19.
Solve Equation: 12(x-2.3)= 15.6 Help
To solve for x you can first divide by 12 into both sides of the equation, like this
[tex]\begin{gathered} \frac{12\mleft(x-2.3\mright)}{12}=\frac{15.6}{12} \\ x-2.3=1.3 \end{gathered}[/tex]Now, you can add 2.3 from both sides of the equation
[tex]\begin{gathered} x-2.3+2.3=1.3+2.3 \\ x=3.6 \end{gathered}[/tex]Therefore, the value of x that satisfies the equation is
[tex]x=3.6[/tex]Finally, to check that this value satisfies the given equation, just plug x = 3.6 into the equation and see that a true proposition is reached. So, you have
[tex]\begin{gathered} 12\mleft(x-2.3\mright)=15.6 \\ \text{ Replace x = 3.6} \\ 12(3.6-2.3)=15.6 \\ 12(1.3)=15.6 \\ 15.6=15.6 \\ \text{ True proposition} \end{gathered}[/tex]Question 5 Find the area of the parallelogram shown belo 44
please help I will give a good review.... can you help me with these two questions
When a system of equations has infinite solutions, you'll end up with a statements that's true no matter what. For example, 6=6. Or when the graphs of the equations are the same exact line.
Then:
3x+4y=12 and
6x+8y=24 divided by 2: 3x+4y=12. That means they are the same exact line, so it has infinite solutions.
[tex]\begin{gathered} 3(2x+y)=24 \\ 6x+3y=24 \\ y=-6x+24\text{ dividing by 3} \\ y=-2x+8 \end{gathered}[/tex]The answer would be the first one and the third one.
The function of a circle is ysquared +x?=r? where r is the radius (any number). Make a circle with a radius of 16. Where does the circle intersect the X and Y axis? What is the relationship between where the circle intersects the axes and the radius (16)? IThe function of a circle is y?+x?=r? where r is the radius (any number). Make a circle with a radius of 16. Where does the circle intersect the X and Y axis? What is the relationship between where the circle intersects the axes and the radius (16)?
112 the circle of the radius
Step-by-step explanation:
3122
subtract the following polynomials2x−6 and 7 x ^2 + 6 x + 4as well as7 x ^2 + 6 x + 4 and 2x-6
We are given the following polynomials:
[tex]\begin{gathered} 2x-6 \\ 7x^2+6x+4 \end{gathered}[/tex]Now, we subtract the second polynomial from the first:
[tex]2x-6-(7x^2+6x+4)[/tex]Now, apply the distributive property on the parenthesis. To do that we change the sign of each of the terms inside:
[tex]2x-6-7x^2-6x-4[/tex]Now, we associate like terms.:
[tex](2x-6x)+(-6-4)-7x^2[/tex]Now, we solve the operations of the like terms:
[tex]-4x-10-7x^2[/tex]Since we can't simplify any further this is the final answer.
Hello I’ve been trying to solve this but have no luck :(
1. Domain, x ∈ [-9 , 8]
2. Range, y ∈ [-10 , 10]
3. f(x) is not an increasing function, its a decreasing function.
4. f(x) is decreasing for interval, x ∈ [-9,2] ∪ [7,8]
5. f(x) is constant function for the interval, x ∈ [2,7]
Domain:- The value of x for which function f(x) is defined
Range : the value of y or f(x)
Increasing function: while increasing the value of x, f(x) is increasing and vice versa, called increasing function.
Decreasing function: while increasing the value of x, f(x) is decreasing and vice versa, called increasing function.
From graph,
It seems very clear that,
1. Domain :-
x ∈ [-9 , 8]
or -9 ≤ x ≤ 8
2. Range :-
y ∈ [-10 , 10]
or -10 ≤ x ≤ 10
3. Interval for which f(x) is increasing :-
f(x) is not an increasing function, its a decreasing function.
4. Interval for which f(x) is decreasing:-
f(x) is decreasing for interval,
x ∈ [-9,2] ∪ [7,8]
5. Interval for which f(x) is constant function
f(x) is constant function for the interval,
x ∈ [2,7]
To learn more about Domain visit:https://brainly.com/question/28135761
#SPJ9
Solve the inequality and graph the solution on the line provided. -2 + 6x > 34 Л ^ < OT Inequality Notation: Number Line: 8 12 6 2 10 -8 -2 0 4 -6 -12 -10 -4 Click and drag to plot line. Submit Answer at
The inequality to solve is:
[tex]-2+6x>34[/tex]We can take the numbers to one side and variables to one and solve for x. Shown below:
[tex]\begin{gathered} -2+6x>34 \\ 6x>34+2 \\ 6x>36 \\ x>\frac{36}{6} \\ x>6 \end{gathered}[/tex]This is the solution
x > 6Graphing this on a number line would look something like this:Note: the open circle in '6' means the number six isn't included.
Determine the perimeter of kite NITE below where EB = 40 feet and BI = BN= 9. Round your answer to the nearest hundredth necessary.BE
From the basic knowledge of pythagoras thorem,
EH
X ^2 = 40^2 + 9^2 = 1`600 + 81 = 1681
X = square root of 1681
= ET = EH = X = 41 feet
NI
y ^ 2 = 9 ^2 + 9^2 = 81 + 81 = 162
y = square root of 162
NI = T I = y = 12.72 feet
The perimeter of the Kite = EN + ET + NI + TI = 41 + 41 + 12. 72 + 12. 72 = 107.44 feet
3.5% of 300 is what number
To find 3.5% of 300, we have to multiply 0.035 by 300.
[tex]0.035\times300=10.5[/tex]Hence, the answer is 10.5.Answer:10.5
Step-by-step
Elaine is starting at point A, she wants to get to point B. She is only allowed to move along the arrows, how many different paths could she take?
if we count the paths we have:
1. A to B the top part
2. Ato B the bottom part
3. we look after that A first top arrow, down one arrow and a straight line
and so on
i counted 12 different ways
A shipping container will be used to transport several 40-kilogram crated across the country by rail. The greatest weight that can be loaded into the container is 24500 kg.other shipments waiting 11300 kilograms have already been loaded into the container. right and solved an inequality which can be used to determine x, the number of 40 kg crates that can be loaded into the shipping container.
The greatest load that fits in the container is 24500kg
There are already 11300Kg loaded
Let x indicate the number of 40Kg crates, then 40x symbolized the total weight of the crates loaded.
You can express the inequality as
[tex]11300+40x\leq24500[/tex]From this expression we can calculate the number of crates that can be loaded as follows:
[tex]\begin{gathered} 11300+40x\leq24500 \\ 40x\leq24500-11300 \\ 40x\leq=13200 \\ \frac{40x}{40}\leq\frac{13200}{40} \\ x\leq330 \end{gathered}[/tex]You can load up to 330 crates into the container.
If ∆RST ~ ∆YSZ, find the value of x.
Answer:
x = 48
Step-by-step explanation:
Function A is represented by the equation y=-2x + 1.Function B is a linear function that goes through the points shown inthe table.x 1346y 19 13 21Which statement correctly compares the rates of change of the twofunctions?O A. The rate of change of function A is-2The rate of change of function B is 4.O B. The rate of change of function A is 1.The rate of change of function B is 8.C. The rate of change of function A is 1.The rate of change of function B is 4.D. The rate of change of function A is-2The rate of change of function B is 8.
In linear functions, the rate of change is equivalent to the slope of the line. In function A we already now the slope intercept equation, which means that we already now the slope of the function.
In this case, the slope of function A is -2 so is the rate of change.
To find the rate of change of function B, we need to use 2 of the ordered pairs in the formula to find the slope of a line:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Let's choose two of the given ordered pairs and replace for them in the formula. We are going to use (1,1) and (3,9):
[tex]m=\frac{9-1}{3-1}=\frac{8}{2}=4[/tex]The slope of function B is 4 so is the rate of change.
In conclusion, the correct choice is A. The rate of change of function A is -2. The rate of change of function B is 4.
4 pointsTriangle BAC is shown on the coordinate grid. The coordinates of eachvertex of the triangle are integers. Numerical answers as decimal or wholenumber only (do not write as a fraction).6AB5321с012What is the slope of BC?Your answerThis is a required question
The Solution.
The slope of line BC is given below:
[tex]\begin{gathered} \text{slope = }\frac{y_2-y_1}{x_2-x_1} \\ B(1,6)\rightarrow(x_1=1,y_1=6) \\ C(4,0)\rightarrow(x_2=4,y_2=0) \end{gathered}[/tex]Substituting the values above into the formula, we get
[tex]\text{Slope = }\frac{0-6}{4-1}=-\frac{6}{3}=-2[/tex]Thus, the correct answer is -2.
Angela has 3 gallons of milk. How many quarts of milk does she have?- word problem
Angela has 12 quartz of milk
Explanations:Note:
1 gallon = 4 quartz
3 gallons of milk = (3 x 4) quartz
3 gallons of milk = 12 quartz of milk
Therefore, Angela has 12 quarz of milk