in this problem we have that
Triangle JTN is an isosceels triangle, because the triangle has two equal sides and two equal interior angles
segment TE is the altitude of triangle JTN, its a perpendicular bisector segment JN
that means
JE=NE
we have
JT=NT
mso
triangle TJE and triangle TNE are congruent by SAS
triangles TJE and trTNE are acute triangles
Jenny’s rectangular bedroom has one wall that is 5 feet long. The distance from one corner of the bedroom to the other corner is 13 feet. How long is the other wall?
The other wall is 12 feet long can be evaluated using Pythagoras theorem.
What is Pythagoras theorem?
The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.
Here given in the question that one side of the wall 5 feet
So as it is a rectangular bedroom it can be split into 2 right-angled triangles.
So the hypotenuse of the triangle is 13 feet
Now using the Pythagoras theorem we can find out the length of the other wall
b²=h²-p²
b²=13²-5²
b²=169-25=144
b=√144
b=12 feet
Hence the other wall is 12 feet long.
Learn more about Pythagoras theorem, by the following link
https://brainly.com/question/231802
#SPJ1
here is the 5th one to do.
Answer:
a is not equivalent to b and c.
Step-by-step explanation:
a.
[tex]50( {2}^{x + 2} ) = 25 \times 2( {2}^{x + 2} ) = 25( {2}^{x + 3} )[/tex]
b.
[tex]25( {2}^{2x + 1} ) [/tex]
c.
[tex]50( {4}^{x} ) = 50( { {2}^{x} )}^{2} = 50( {2}^{2x} ) = 25 \times 2( {2}^{2x} ) = 25( {2}^{2x + 1} )[/tex]
Nobody is answering mathematics anymore so it doesn't matter just pls answer
Answer:
7/20 of the laundry still needs to be washedStep-by-step explanation:
Laundry washed:
2/5 and 1/4 of totalWho washed more?
Compare the fractions by bringing them to common denominator:
2/5 = (2*4)/(5*4) = 8/20,1/4 = (1*5)/(4*5) = 5/20.Compare the numerators:
8 > 5,It means Mrs. Stem washed more than laundry her son.
Total portion of laundry washed:
8/20 + 5/20 = 13/20Laundry left to wash is the difference of full and the fraction of washed laundry:
1 - 13/20 = 20/20 - 13/20 =(20 - 13)/20 = 7/20Answer:
7/20 of laundry is still pending.
Step-by-step explanation:
Now the both washed is,
→ (2/5) + (1/4)
→ ((2 × 4)/(5 × 4)) + ((1 × 5)/(4 × 5))
→ (8/20) + (5/20)
→ 13/20
Forming the equation,
→ (13/20) + x = 1
Then required value of x will be,
→ (13/20) + x = 1
→ x = 1 - (13/20)
→ x = (20/20) - (13/20)
→ x = (20 - 13)/20
→ [ x = 7/20 ]
Hence, 7/20 of laundry is pending.
D
If the conditional statement "If I use my cell phone too much, my bill will be expensive," is true, which other statement must also be true?
If I do not use my cell phone too much, my bill will not be expensive.
O None must be true.
Of my bill is expensive, I used iny cell phone too much.
If my bill is not expensive. I did not use my cell phone too much
4
Answer: "If my bill is not expensive. I did not use my cell phone too much"
Reason:
The original statement is of the form "If P, then Q"
P = "I use my cell phone too much"
Q = "my bill will be expensive"
An equivalent form to the original condition is known as the contrapositive of the form "If not Q, then not P". We swap the positions of P and Q. We also negate each part. You can use a logical truth table to verify that the conditional and contrapositive have equivalent truth values, which means they are effectively equivalent statements.
Answer:
If my bill is not expensive. I did not use my cell phone too much
Step-by-step explanation:
Angles abc and bcj are alternate interior angles. use a transformation that takes angle abc to angle bcj to prove that alternate interior angles are congruent
Angle two and angle six line up with one another. Angle three would consequently be consistent with angle six. Angles two and three are congruent because they both have vertical angles.
What are the alternate interior angles?Alternate internal angles are the pair of angles formed on the inner side of the parallel lines and on the opposing sides of the transversal when two parallel lines are intersected by a transversal. These angles are all equal. There is an alternative perspective on this. The parallelism or non-parallelism of the provided lines can be determined by the alternative inner angles. If these angles are equivalent, the given lines that a transversal crosses are said to as being parallel.
To see the many internal angles, look at the following diagram. Here, a transversal divides AB and CD, two parallel lines.
Alternate Interior Angles Theorem's opposite, then?The two lines are said to be parallel if a transversal intersects them such that their alternate interior angles are equal, according to the converse of the alternate interior angles theorem.
Let's examine the following diagram to better comprehend this: 1 = 5 (matching angles), 3 = 5 (vertically opposite angles). Thus, ∠1 = ∠3. The same goes for the demonstration of 2 = 4. This demonstrates that the two supplied lines are parallel to one another since their alternate inner angles are equal.
Example: Two lines are parallel to one another if the alternate interior angles created by the transversal line on two coplanar are congruent. As a result, we can write that 2 and 5 are corresponding angles.
Transformations would show that the accompanying exterior angles EBI and BCJ are congruent, proving that an is parallel to a pair of alternate exterior angles with measurements of 130° and 50°.
To know more about alternate interior , visit:
https://brainly.com/question/15685431
#SPJ4
Can someone answer these please?
Answer:
Step-by-step explanation:
1. -17x+1
2. -5/6a-1/2
3.-2/3x+2/5
4.-6(2x+3y+0.6)
5.2/3(x+6)
PLSsSsSsSsSssSsSSSsSS HeEeEeEeeEeLPpPpPPp!!!!!!!
Answer:
Function 1 is increasing bcz the slope is positive since it is observed that the values of the abscissa (X) increase as well as the values of the ordinate (Y), while function 2 is decreasing, bcz it has a negative slope since it is observed that as the values of the abscissa (X) increase, the values of the ordinate (Y) decrease
A 6 inch personal pizza has 620 calories, with 240 of those fromfat. A 16 inch pizza is cut into 8 slices. Estimate the number ofcalories in one slice of a 16 inch pizza.calories
Given:
A 6-inch personal pizza has 620 calories, with 240 of those from fat.
A 16-inch pizza is cut into 8 slices.
So, the total number of calories in a 16-inch pizza will be calculated using the ratio and the proportions:
A 6-inch pizza : A 16-inch pizza
6 : 16
620 : x
Using the cross product:
[tex]x=\frac{16\cdot620}{6}=1653.33[/tex]A 16-inch pizza is cut into 8 slices.
So, the number of calories in one slice =
[tex]\frac{1653.33}{8}\approx206.67[/tex]So, the answer will be:
The number of calories in one slice = 206.67 calories
Match the Parallel line of y=-1/2x-2
The family of all linear equations that are parallel to y=-1/2x-2 is defined as:
y = (-1/2)*x + b
Such that b ≠ -2.
Which lines are parallel to the given one?We know that a general linear equation is written in the slope-intercept form as:
y = m*x + b
Where m is the slope and b is the y-intercept.
We know that two linear equations are parallel if and only if the lines have the same slope and a different y-intercept.
So the family of lines parallel to:
y = (-1/2)*x - 2
Are of the form:
y = (-1/2)*x + b
Where b ≠ -2.
All these lines are parallel to the given ones.
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
write 10x10x10x10x10 with an exponet explain how you decided what exponet to write
Answer:
10^5
Step-by-step explanation:
10 is multiplied by itself 5 times so you use 5 as the exponent
10 is the number you're multiplying so it the bottom number
10^5
Based on the diagram below, we can say that the two triangles ___.
Solution
Step1
The AA criterion for triangle similarity states that if two triangles have two pairs of congruent angles, then the triangles are similar.
Step2
Two pairs angles are equal, hence they are similar
Answer
Are similar by AA
Question 1-1
The Jansen family has an SUV that gets 25 miles per gallon and a sedan that gets 32 miles per gallon. They plan to go on a 125-
mile car trip and know that gas costs $4 per gallon. The relationship between miles and gallons is proportional, as is the
relationship between gas price and gallons.
How much money will they save if they take the sedan instead of the SUV? Round to the nearest cent if needed.
O $1.75
O $7.00
O $1.09
O $4.38
Type here to search
Ħ
Pause Test
DELL
PRAISE
5
Next >
4-
2:17 PM
11/3/2022
Answer: 4.38
Step-by-step explanation:
Firstly to answer this question we need to take a look at both of the mpg for each of them. We already know that the SUV has 25 mpg and the Sedan has 32 mpg, to figure this out we need to get the answer to $4 x 25 and $4 x 32.
The answer to that is $100 for the SUV and $128 for the Sedan. Next, we need to figure out the mile difference between to 2 vehicles.
100 x 2 = 200
128 x 2 = 256
knowing those numbers overall we can conclude that the sedan will cost $4.38 less than the Suv
When spinning a wheel with 1 red, 2 blue, and 3 green spaces, what
is the probability that you will not spin a red?
Step-by-step explanation:
so, we have 1 + 2 + 3 = 6 total spaces.
a probability is always the ratio
desired cases / totally possible cases
the probability to spin red is therefore
1 desired case
6 total possible cases
1/6 = 0.166666666...
a probability of 1 means a sure result = anyone of the totally possible cases.
so, 6/6 = 1 in our case.
if the desired cases are everything but red, we need to eliminate the possible red results (1) from the amount of our desired cases : 6 - 1 = 5
so the probability of not spinning a red is
5/6 = 0.833333333...
formally we can also say this is the sure thing minus the opposite of what we want to have. the opposite of not spinning a red is spinning a red (1/6) :
1 - 1/6 = 5/6 = 0.833333333...
Objective function Z=3x+6yFind the value at each corner of the graph
Given: An objective function
[tex]z=3x+6y[/tex]with constraints-
[tex]\begin{gathered} \\ \begin{cases}{x\ge0,y\ge0} \\ {2x+y\leq12} \\ {x+y\ge6}\end{cases} \end{gathered}[/tex]Required: To graph the linear inequalities representing the constraints and determine the objective function's value at each corner.
Explanation: The inequalities can be graphed by considering them as equations and then determining the shaded region by less than or greater than symbol.
The equation for the first inequality is-
[tex]2x+y=12[/tex]This represents a straight line passing through points (6,0) and (0,12).
The shaded region will be below this line as the inequality is-
[tex]2x+y\leq12[/tex]Similarly, the inequality-
[tex]x+y\ge6[/tex]Represents a shaded region above the line x+y=6.
The inequalities-
[tex]x\ge0,y\ge0[/tex]Represents the positive values of x and y. Hence we need to determine the graph in the first quadrant.
The graph of the inequalities is-
The graph in blue represents the inequality-
[tex]2x+y\leq12[/tex]While the graph in green represents the inequality-
[tex]x+y\ge6[/tex]The corner points of the common shaded area are A(0,6), B(0,12), and C(6,0).
Now the value of the objective function at these points is-
a) At A(0,6)
[tex]\begin{gathered} z=3(0)+6(6) \\ =36 \end{gathered}[/tex]b) At B(0,12)
[tex]\begin{gathered} z=3(0)+6(12) \\ =72 \end{gathered}[/tex]c) At C(6,0)
[tex]\begin{gathered} z=3(6)+6(0) \\ =18 \end{gathered}[/tex]Final Answer: a) The graph is drawn.
b) 36,72,18
The Triple L investment club is considering purchasing a certain stock. After considerable research, the club members determine that there is a 50% chance of making $12,000, a 20% chance of breaking even, and a 30% chance of losing$6,600. Find the expectation of this purchase.
We would apply the formula for calculating the expectation of the mean or expected value which is expressed as
Ex = ΣxP(x)
In this scenario, from the information given,
12000 is profit at 50%
Breakeven mean = 0 because there is no profit or loss' at 20%
loss = - 6600 at 30 %
Thus,
Expectation = 50/100 * 12000 + 20/100 * 0 + 30/100 * 6600
Expectation = 6000 + 0 + 1980
Expectation = 7980
the expectation of this purchase is $7980
what is y+2=-6(x-3) in standard form?
Answer: 6x + y = 16
Step-by-step explanation:
I need help to Find the missing percentages and what is the independent and dependent variable.
Solution:
From the given table;
Where, the November values is used as 100 percent;
To find the missing percentages of Elm leaves
For the month of May
[tex]\begin{gathered} For\text{ the month of November: 3481} \\ For\text{ the month of May;} \\ =\frac{1739}{3481}\times100\%=49.95690\approx50.0\%\text{ \lparen1 decimal place\rparen} \\ For\text{ the month of August} \\ =\frac{35}{3481}\times100\%=1.00545\approx1.0\%\text{ \lparen1 decimal place\rparen} \end{gathered}[/tex]To find the missing percentages of Hazel leaves
[tex]\begin{gathered} For\text{ the month of November:}1723 \\ For\text{ the month of May;} \\ =\frac{501}{1723}\times100=\:29.07719\approx29.1\%\text{ \lparen1 decimal place\rparen} \\ For\text{ the month of August;} \\ =\frac{62}{1723}\times100\%=3.59837\approx3.6\%\text{ \lparen1 decimal place\rparen} \end{gathered}[/tex]What is the independent and dependent variable?
An independent variable is a variable that does not depend on any other variable.
For example,
[tex]3y=4x+1[/tex]x is an independent variable because for every value of x, there is a different value of y
A dependent variable is a variable whose value depends upon an independent variable.
For example;
[tex]y=5x[/tex]From the expression above, the value of y depends on the value of x
Solve - 8x = 56 for x.
How many ways can the letters in the word PARALLEL be arranged?
Answer:
3,360 ways.
Explanation:
In the word PARALLEL
• Number of letters = 8
,• Number of Ls = 3
,• Number of As = 2
Since no other restriction is given, the number of ways in which the letters can be arranged is:
[tex]\frac{8!}{3!\times2!}[/tex]We solve to obtain our result.
[tex]\begin{gathered} \frac{8!}{3!\times2!}=\frac{8\times7\times6\times5\times4\times3!}{3!\times2!} \\ =\frac{8\times7\times6\times5\times4}{2!} \\ =8\times7\times6\times5\times2 \\ =3360\text{ ways} \end{gathered}[/tex]The word can be arranged in 3,360 ways.
Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the unknowns.6 divided by the sum of 4 and a number
Let:
x = Unknown number
[tex]\frac{6}{x+4}\equiv6_{\text{ }}divided_{\text{ }}by_{\text{ }}the_{\text{ }}sum_{\text{ }}of_{\text{ }}4_{\text{ }}and_{\text{ }}a_{\text{ }}number[/tex]what do we do with 3 1/3 in the problem and also i need the answer to all of it
The answer after solving the expression 12x - 3y / 4x - z with x = 3,y=1/3 and z = 5 is 5.
Given:
x = 3 , y = 1/3 and z = 5 and expression 12x - 3y / 4x - z.
substitute the x,y,z values in expression.
= 12(3)-3(1/3) / 4(3)-5
= 36 - 3/3 / 12 - 5
= 36 - 1 / 7
= 35/7
= 5.
Therefore the answer after solving the expression 12x - 3y / 4x - z with x = 3,y=1/3 and z = 5 is 5.
Learn more about the expression here:
https://brainly.com/question/14083225
#SPJ1
What is the cube root of 3 and 512
Answer:
1.4422
Step-by-step explanation:
Depends what they are asking for in some cases they will want you to simplify it to 1.4 or
[tex]\sqrt[n]{x}[/tex] It might also look like this with a 3 on top and bottom
sry if this is confusing
If you have any questions just ask : )
Please help me with this and make it quick because it due 6:00
• x(5-2)=4x-x
distributive property:
5x -2x = 4x -x
3x =3x
Infinite solutions
• 14x - 17 -8x + 2 = 12x +3 -x - 10
Combine like terms:
14x -8x -12x +x = 3 - 10 + 17 - 2
-5x= 8
x = -8/5
Unique solution
• 6(x-2)=6x-12
Apply distributive property:
6(x) + 6(-2) = 6x-12
6x - 12 = 6x - 12
Since both sides are equal:
Infinite solutions
• 2/3x - 7/4 = 4/3x - 2/3 (x+5)
Apply distributive property:
2/3x-7/4 = 4/3x - 2/3(x) - 2/3(5)
2/3x-7/4= 4/3x-2/3x - 10/3
Combine like terms
2/3x + 2/3x - 4/3x = -10/3 + 7/4
0 = -19/12
Since 0 is not equal to -19/12
No solution
Select the correct answer.
Consider the graph of function g.
A parabola labeled lowercase g declines through the points (negative 4, 4), (negative 3, 2 point 2), (negative 2, 1), (0, 0), (2, 1) and (3 point 5, 3) on the x y coordinate plane.
If f(x) = x2, which equation represents function g?
A. g(x) = f(2x)
B. g(x) = f(4x)
C. g(x) = 2 f(x)
D. g(x) = f(1/2x)
The correct option is B that is g(x)=f(4x) as the condition says, "A parabola labeled lowercase g declines through the points (negative 4, 4), (negative 3, 2 point 2), (negative 2, 1), (0, 0), (2, 1) and (3 point 5, 3) on the x y coordinate plane".
What is parabola?A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side intersect. Ideally, a projectile traveling under the pull of gravity will travel along a curve similar to this one. A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
To know more about parabola,
https://brainly.com/question/21685473?referrer=searchResults
#SPJ1
Solve the following inequality and select all possible solutions.
A box of fruit has four times as many oranges as grapefruit. Together there are
60 pieces of fruit. How many pieces of each type of fruit are there?
The number of mangoes = 48
The number of grapefruit = 12
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A box of fruit has four times as many oranges as grapefruit.
And, Total number of fruit = 60 pieces
Now,
Let number of grapefruit = x
Then, Number of Mangoes = 4x
So, We can formulate;
⇒ x + 4x = 60
Solve for x as;
⇒ 5x = 60
⇒ x = 12
Thus, Number of grapefruit = x
= 12
Then, Number of Mangoes = 4x
= 4 × 12
= 48
Therefore, The number of mangoes = 48
The number of grapefruit = 12
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Literal equation
6 = 2(m-b)/m+b
for b.
Answer:
b= −1/2m
Step-by-step explanation:
Step 1: Multiply both sides by b+m.
6b+6m=−2b+2m
Step 2: Add 2b to both sides.
6b+6m+2b=−2b+2m+2b
8b+6m=2m
Step 3: Add -6m to both sides.
8b+6m+−6m=2m+−6m
8b=−4m
Step 4: Divide both sides by 8.
For t(x) = 3x - 5, find the value of x
for which /(x) = 4.
Answer:7
Step-by-step explanation:
3x-5
replace x for 4
3(4)-5
=12-5
=7
If a_1=6a
1
=6 and a_n=a_{n-1}+3a
n
=a
n−1
+3 then find the value of a_4a
4
.
The fourth term a₄ of the sequence is 15
How to determine the value of a₄?The definition of the function is given as
a₁= 6
aₙ = aₙ₋₁ + 3
The above definitions imply that we simply add 3 to the previous term to get the current term
using the above as a guide,
so, we have the following representation
a₂ = 6 + 3
a₂ = 9
Also, we have
a₃ = 9 + 3
a₃ = 12
Lastly, we have
a₄ = 12 + 3
Evaluate the equation
a₄ = 15
Hence, the value of a₄ is 15
Read more about sequence at
https://brainly.com/question/7882626
#SPJ1
Which function is best represented by this graph?
Responses
A
y = - 2 x + 2
5y = - 2 x + 2 5
B
y = - 5 x + 5
2y = - 5 x + 5 2
C
y = - 5 x + 2
2y = - 5 x + 2 2
D
y = 2 x + 2
5
The function best represented by the graph is y = - 5 x + 5 2y = - 5 x + 5². Option B.
Use the vertical line test to determine if a graph represents a function. A graph is a function if a vertical line moves across it and touches it only at one point at a time. If a vertical line touches a graph at multiple points, the graph is not a function.
Calculation:-
X intercept = 2
y intercept = 5
slopt = y/x
= 5/2
= 2.5
For the line to be perpendicular to each other angle must be 90⁰.
Hence option B.
B.y = - 5 x + 5
2y = - 5 x + 5 2
slope m = 5/2
2.5.
A function is defined as a relation between a set of inputs each with an output. Simply put, a function is a relationship between inputs, each associated with exactly one output. Each function has a domain and a codomain or scope. The graph of a quadratic function is called a parabola and has a curved shape. One of the main points of the parabola is the vertex.
Learn more about A function here:-https://brainly.com/question/25638609
#SPJ1