M
9. If LK = MK, LK = 7x-10, KN = x + 3, MN = 9x - 11. and KJ = 28, find L.
LK: 7-10 kn +3 INOX
LJ = LK + KJ
LJ= 7x 28
LJ = 78+ 38
The exact value of [tex]\( L \) is \(-\frac{44}{3}\).[/tex]
To find [tex]\( x \)[/tex], we need to use the fact that [tex]\( LK = MK \)[/tex] and apply the given values and equations.
1. Set up the equation for [tex]\( LK \)[/tex] and [tex]\( MK \):[/tex]
Since [tex]\( LK = MK \),[/tex] we can write:[tex]\[LK = MK\][/tex]Given:
[tex]\[LK = 7x - 10\][/tex][tex]\[MK = KN + MN\][/tex]2. Substitute the given expressions:
[tex]\[MK = KN + MN\][/tex][tex]\[MK = (x + 3) + (9x - 11)\][/tex][tex]\[MK = x + 3 + 9x - 11\][/tex][tex]\[MK = 10x - 8\][/tex]3. Set up the equation [tex]\( LK = MK \)[/tex]
[tex]\[7x - 10 = 10x - 8\][/tex]4. Solve for [tex]\( x \):[/tex]
[tex]\[7x - 10 = 10x - 8\][/tex][tex]\[-10 + 8 = 10x - 7x\][/tex][tex]\[-2 = 3x\][/tex][tex]\[x = -\frac{2}{3}\][/tex]5. Find [tex]\( L \):[/tex]
With [tex]\( x = -\frac{2}{3} \), substitute \( x \) into the expression for \( LK \):[/tex][tex]\[LK = 7x - 10\][/tex][tex]\[LK = 7 \left(-\frac{2}{3}\right) - 10\][/tex][tex]\[LK = -\frac{14}{3} - 10\][/tex]Convert 10 to a fraction:
[tex]\[LK = -\frac{14}{3} - \frac{30}{3}\][/tex][tex]\[LK = -\frac{44}{3}\][/tex]Thus, [tex]\( L \)[/tex] would be [tex]\(-\frac{44}{3}\)[/tex], assuming [tex]\( L \)[/tex] represents the value of [tex]\( LK \).[/tex]
The complete question is:
If LK = MK, LK = 7x-10, KN = x + 3, MN = 9x - 11. and KJ = 28, find L.
(2x - 3) + [4x(3x + 2)] what is the answer
Answer:
22x-3
Step-by-step explanation:
(2x-3)+[4x(3x+2)]
(2x-3)+12x+8x
2x-3+20x
12x^2
Complete each of the statements.
Answer:
Complete each of the statements below.
When work is done on a system by its surroundings, the sign of w is [ Select ] ["positive", "negative"] .
When work is done by a system on its surroundings, the sign of w is [ Select ] ["negative", "positive"] .
When q has a negative sign, we can say that heat is transferred [ Select ] ["from", "into"] the system [ Select ] ["from", "into"] its surroundings.
If ∆U for a system is 0 and w is negative, then q must be [ Select ] ["positive", "negative"] .
Step-by-step explanation:
1. Expression 1: [tex]\((3x^2 - 6x + 11) \cdot (10x^2 - 4x + 6)\)[/tex]:[tex]\[30x^4 - 72x^3 + 34x^2 - 44x + 66\][/tex]
2. Expression 2: [tex]\((-3x^2 - 5x + 3) \cdot (-10x^2 - 7x + c)\)[/tex]:[tex]\(30x^4 + 71x^3 + 5x^2 - 21x + 3c\).[/tex]
3. Expression 3: [tex]\((12x^2 + 6x - 5) \cdot (5x^2 + 8x - 12)\)[/tex]: [tex]\(60x^4 + 126x^3 + 53x^2 + 40x - 60\).[/tex]
the expressions step by step:
1. Expression 1: [tex]\((3x^2 - 6x + 11) \cdot (10x^2 - 4x + 6)\)[/tex]
To multiply these two expressions, we'll use the distributive property (also known as the FOIL method). Multiply each term in the first expression by each term in the second expression and then combine like terms.
- Multiply the first terms: [tex]\(3x^2 \cdot 10x^2 = 30x^4\)[/tex]
- Multiply the outer terms: [tex]\(3x^2 \cdot (-4x) = -12x^3\)[/tex]
- Multiply the inner terms: [tex]\((-6x) \cdot 10x^2 = -60x^3\)[/tex]
- Multiply the last terms: [tex]\((-6x) \cdot (-4x) = 24x^[/tex]2\)
Now add up all the results:
[tex]\[30x^4 - 12x^3 - 60x^3 + 24x^2 + 11 \cdot 10x^2 - 11 \cdot 4x + 11 \cdot 6\][/tex]
Combine like terms:
[tex]\[30x^4 - 72x^3 + 34x^2 - 44x + 66\][/tex]
So, the equivalent expression is:[tex]\(30x^4 - 72x^3 + 34x^2 - 44x + 66\)[/tex].
2. Expression 2: [tex]\((-3x^2 - 5x + 3) \cdot (-10x^2 - 7x + c)\)[/tex]
Follow the same steps as above to multiply the expressions:
- Multiply the first terms: [tex]\((-3x^2) \cdot (-10x^2) = 30x^4\)[/tex]
- Multiply the outer terms: [tex]\((-3x^2) \cdot (-7x) = 21x^3\)[/tex]
- Multiply the inner terms: [tex]\((-5x) \cdot (-10x^2) = 50x^3\)[/tex]
- Multiply the last terms: [tex]\((-5x) \cdot (-7x) = 35x^2\)[/tex]
Combine the results:
[tex]\[30x^4 + 21x^3 + 50x^3 + 35x^2 + 3 \cdot (-10x^2) + 3 \cdot (-7x) + 3c\][/tex]
Combine like terms:
[tex]\[30x^4 + 71x^3 + 35x^2 - 30x^2 - 21x + 3c\][/tex]
Simplify further:
[tex]\[30x^4 + 71x^3 + 5x^2 - 21x + 3c\][/tex]
So, the equivalent expression is: [tex]\(30x^4 + 71x^3 + 5x^2 - 21x + 3c\).[/tex]
3. Expression 3: [tex]\((12x^2 + 6x - 5) \cdot (5x^2 + 8x - 12)\)[/tex]
Apply the same process:
- Multiply the first terms:[tex]\(12x^2 \cdot 5x^2 = 60x^4\)[/tex]
- Multiply the outer terms: [tex]\(12x^2 \cdot 8x = 96x^3\)[/tex]
- Multiply the inner terms:[tex]\(6x \cdot 5x^2 = 30x^3\)[/tex]
- Multiply the last terms:[tex]\(6x \cdot 8x = 48x^2\)[/tex]
Combine the results:
[tex]\[60x^4 + 96x^3 + 30x^3 + 48x^2 + 5 \cdot 5x^2 + 5 \cdot 8x - 5 \cdot 12\][/tex]
Combine like terms:
[tex]\[60x^4 + 126x^3 + 53x^2 + 40x - 60\][/tex]
The equivalent expression is: [tex]\(60x^4 + 126x^3 + 53x^2 + 40x - 60\).[/tex]
Lucy earns money babysitting. Her earnings and hours worked represent a direct variation. She worked for 4 hours and earned $25.
Determine the constant of proportionality for dollars earned per hour worked
Determine the constant of proportionality for hours worked per dollar earned.
Final answer:
The constant of proportionality for dollars earned per hour worked is 6.25, and the constant of proportionality for hours worked per dollar earned is 0.16.
Explanation:
To find the constant of proportionality for dollars earned per hour worked, we can use the formula y = kx, where y is the amount earned and x is the number of hours worked. Given that Lucy earned $25 for 4 hours of work, we can substitute these values into the equation:
25 = k * 4
Solving for k, we divide 25 by 4:
k = 25 / 4 = 6.25
Therefore, the constant of proportionality for dollars earned per hour worked is 6.25.
To find the constant of proportionality for hours worked per dollar earned, we can rearrange the equation to x = my, where x is the number of hours worked and y is the amount earned. Substituting the values, we get:
4 = m * 25
Solving for m, we divide 4 by 25:
m = 4 / 25 = 0.16
Therefore, the constant of proportionality for hours worked per dollar earned is 0.16.
Which statement is true? A. 13/14 > 25/28 B. 21/45 < 4/9 C. 5/6 > 11/12 D. 4/5 < 8/25
Rewrite the fractions with common denominators and then answer:
A:
13/14 > 25/28
26/28 > 25/28
This is True
B) 21/45 < 20/45 False
C) 10/12 > 11/12
False
D) 20/25 < 8/25
False
The true statement is A.
At Santa Maria High School the juniors an
are selling raffle tickets. So far, the juniors
solved 580 tickets and are averaging 29 tickets
day. The seniors have sold 490 tickets but vow to
win the contest by selling an average of 35 tickets
per day. If both grades continue collecting at these
rates, after how many days will the number of
tickets sold be equal?
Answer: 580+29x = 490 + 35x
90 = 6x
15 = x
15 days is your answer
Step-by-step explanation:
Convert 0.00049 to scientific notation.
Answer:
4.9 x 10^-4 is the scientific notation
Move the decimal 4 places from left to right
Answer:
[tex]\displaystyle 4,9 \times 10^{-4}[/tex]
Step-by-step explanation:
[tex]\displaystyle 0,00049 = 4,9 \times 10^{-4}[/tex]
You move the decimal mark four times to the left.
I am joyous to assist you anytime.
Suppose that y is directly proportional to x, and y = 6 when x = 54. What is the constant of proportionality?
A) 1/9
B) 1/6
C) 6
D) 9
Answer:
C
Step-by-step explanation:
Answer: The correct option is
(A) [tex]\dfrac{1}{9}.[/tex]
Step-by-step explanation: Given that y is directly proportional to x, and y = 6 when x = 54.
We are to find the constant of proportionality.
According to the given information, we can write that
[tex]y\propto x\\\\\Rightarrow y=kx~~~~~~~~~~~[\textup{where k is the constant of proportionality}]\\\\\Rightarrow k=\dfrac{y}{x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
When y = 6 and x = 54, then from equation (i), we get
[tex]\dfrac{6}{54}=k\\\\\Rightarrow k=\dfrac{1}{9}.[/tex]
Thus, the required value of the constant of proportionality is [tex]\dfrac{1}{9}.[/tex]
Option (A) is CORRECT.
Gustavo wants to buy more than two sandwiches at the city fair. There are three sandwich stands, and each is offering a different deal.
Benny's Sandwiches 4 sandwiches for $5.00
ABC Sandwiches, Inc. 4 sandwiches for $6.00
Sandwich Hut 1 sandwich for $2.00 *Buy 1, get 1 Free*
Answer:
sandwich hut is the best deal (what's the question????)
Step-by-step explanation:
because sandwich hut is buy one get one free, one sandwich costs $1.00 ($2 divided by 2 sandwiches)
Benny's costs $1.25 per sandwich ($5 divided by 4 sandwiches)
ABC costs $1.50 per sandwich ($6 divided by 4 sandwiches)
Answer:
Sandwich hut is the best deal.
Step-by-step explanation:
Find the unit rate of each stand, and you find which one is the best deal.
Use the number line to determine the absolute value. Enter the value, as a mixed number in simplest form, in the box. ∣∣−223∣∣ =
Answer:
[tex]2\frac{2}{3}[/tex]
Step-by-step explanation:
we know that
Absolute value is a term which is used to indicate the distance of a point or number from the origin of a number line or coordinate system.
In this problem
we have to find the absolute value of the given number
[tex]\left \| -2\frac{2}{3} \right \|[/tex]
that means we have to find the distance of [tex]\left \| -2\frac{2}{3} \right \|[/tex] from the origin of a number line.
Distance of [tex]-2\frac{2}{3}[/tex] from the origin is [tex]2\frac{2}{3}[/tex] .
Remember that the distance cannot be a negative number.
Therefore, the absolute value of [tex]\left \| -2\frac{2}{3} \right \|[/tex] is [tex]2\frac{2}{3}[/tex]
see the attached figure to better understand the problem
Answer:
2_2/3
Step-by-step explanation:
Draw a model. Then, write the numerical expressions.
a. The difference between 8 forty-sevens and 7 forty-sevens
b. 6 times the sum of 12 and 8
Answer with Step-by-step explanation:
a. The difference between 8 forty-sevens and 7 forty-sevens
Let ⊕ repesents forty- sevens.
So, Model can be represented by
8⊕ - 7⊕
=⊕⊕⊕⊕⊕⊕⊕⊕-⊕⊕⊕⊕⊕⊕⊕
=⊕
Mathematically,
let x represents forty-sevens.
So, it becomes
[tex]8x-7x=x[/tex]
b. 6 times the sum of 12 and 8.
Mathematically, it is expressed as
[tex]6\times (12+8)\\\\=6\times 20\\\\=120[/tex]
Let 12 be written as 4×3
and 8 be written as 4×2
Let ⊕ represents 4 i.e. fours.
so, there are sum of 2 fours and 3 fours.
So, it becomes,
6×(⊕⊕+⊕⊕⊕)
=6×(⊕⊕⊕⊕⊕)
=⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕
=4×30
=120
Answer:
thanks
Step-by-step explanation:
Rosa has 412 punds of pizza dough. She uses 34
of a pound for one pizza. How many pizzas could be made from Rosa's dough?
a furniture store sells 48 tables for every 60 chairs in a given week. what is the unit rate of tables to chairs? reduce the unit rate.
Answer:
4:5
Step-by-step explanation:
You can divide both numbers by 12, therefore simplifying the numbers to the lowest they can be
Answer:
Ratio of table to chair : [tex]\frac{4}{5}[/tex].
Step-by-step explanation:
Given : furniture store sells 48 tables for every 60 chairs in a given week.
To find : what is the unit rate of tables to chairs.
Solution: We have given
Table = 48 .
Chair = 60 .
Ratio of table to chair : [tex]\frac{48}{60}[/tex].
On dividing both number by 4
Ratio of table to chair : [tex]\frac{12}{15}[/tex].
On dividing both number by 3
Ratio of table to chair : [tex]\frac{4}{5}[/tex].
Therefore, Ratio of table to chair : [tex]\frac{4}{5}[/tex].
Giving 15 points help
Image:
Answer: To find out the unlabeled one on the inside subtract 180- 123, then you Get 57. Now do 180 = 57 + x +
92. Add up the whole numbers to get 180 = 149 + x now subtract 149 from 180, to get 31 and it equals x TADA
Step-by-step explanation:
-2x + 5 = -12x -15 solve and check
Answer:
10/7
Step-by-step explanation:
Step 1: Subtract 12x from both sides.
−2x+5−12x=12x−15−12x
−14x+5=−15
Step 2: Subtract 5 from both sides.
−14x+5−5=−15−5
−14x=−20
Step 3: Divide both sides by -14.
−14x/14=−20/14
x=10/7
You get 10 over 7 because you simplify 20 over 14 by dividing them by 2 which would give you 10/7.
Dr. Mann mixed 10.357 g of chemical a 12.062 g of chemical B and 7.506 g of chemical see to make five doses of medicine
Answer:
Part a) The estimate amount of medicine is 30.0 grams
Part b) The actual amount of medicine is 29.925 g. The difference between the estimate and the actual amount, is 0.075 g
Part c) 5.985 grams
Part d) 6 grams
Step-by-step explanation:
The complete question is
Dr. Mann mixed 10.357 g of chemical A, 12.062 g of chemical B, and 7.506 g of chemical C to make 5 doses of medicine.
a. About how much medicine did he make in grams? Estimate the amount of each chemical by rounding to the nearest tenth of a gram before finding the sum. Show all your thinking.
b. Find the actual amount of medicine mixed by Dr. Mann. What is the difference between your estimate and the actual amount?
c. How many grams are in one dose of medicine? Explain your strategy for solving this problem.
d. Round the weight of one dose to the nearest gram
Part a) round to the nearest tenth of a gram first
Chemical A
10.357 g -----> 10.4 g
Chemical B
12.062 g -----> 12.1 g
Chemical C
7.506 g -----> 7.5 g
To find out the estimate amount of medicine sum the three values
10.4+12.1+7.1=30.0 g
therefore
The estimate amount of medicine is 30.0 grams
Part b)
The actual amount of medicine is
10.357+12.052+7.506=29.925 g
To find out the difference between your estimate and the actual amount, subtract the actual amount from the estimate
30.0-29.925=0.075 g
Part c) To find out how many grams are in one dose of medicine, divide the actual amount of medicine by five
29.925 g/5=5.985 g
Part d) Round the weight of one dose to the nearest gram
we have
5.985 g ------> 6 g
a has a coordinate (-2,4). B has a coordinate (9,11). find the coordinate of point p has a p that partion AB into a ratio 3:4
Answer:
see explanation
Step-by-step explanation:
Using the Section formula, then
[tex]x_{P}[/tex] = [tex]\frac{3(9)+4(-2)}{3+4}[/tex] = [tex]\frac{27-8}{7}[/tex] = [tex]\frac{19}{7}[/tex]
and
[tex]y_{P}[/tex] = [tex]\frac{3(11)+4(4)}{3+4}[/tex] = [tex]\frac{33+16}{7}[/tex] = [tex]\frac{49}{7}[/tex] = 7
Hence
P = ( [tex]\frac{19}{7}[/tex], 7 )
Brice had $73 and then he earned d more dollars. Write an expression that shows how much money he has now.
Answer:
73+d
We don’t know what d equals so leave the variable, then just add the 73 he already had.
Step-by-step explanation:
I need help with number 5
Answer:
-14 *F
Step-by-step explanation:
-3 minus 11 is -14
hope this helps
Hey!
-------------------------------------------------
[tex]\large\boxed{A) -14~degrees~fahrenheit}[/tex]
-------------------------------------------------
Steps To Solve:
~Create an equation
-3 - 11
~Subtract
-14
-------------------------------------------------
Hope This Helped! Good Luck!
1 pound is now many grams
The answer is "453.592 grams." One pound does indeed equal 453.592 in grams.
Hope this helps.
What is the value of (x) = -3.25x + 22.41 at x = -4.2?
Two similar triangles are shown.
AMNO was dilated, then
to create AYHO.
rotated
reflected
translated
dilated
Triangle MNO was dilated (increased) and then rotated to create triangle YHO.
TransformationTransformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure to create an image.
Triangle MNO was dilated (increased) and then rotated to create triangle YHO.
Find out more on transformation at: https://brainly.com/question/1548871
Is this statement true or false?
To find the mode of a list of numbers, arrange the numbers from smallest to largest
Select the correct answer.
false
true
Homeowners are building a square closet in a rectangular room that is 24 feet long and 18 feet wide. They want the remaining floor area to be at least 400 square feet. Because they don’t want to cut any of the 1 foot by 1 foot square floor tiles, the side length of the closet floor should be a whole number of feet. Make a table showing possible side lengths of the closet floor and the remaining area for each side length.
Answer: i can't speak english
Step-by-step explanation:
a certain fish can swim 6 1/3 times faster than a person. if a person swims 5 7/8 miles per hour, how fast can the fish swim?
Answer: 37.2204mph
Step-by-step explanation: First, I converted 5 7/8 into 5.88 then I converted 6 1/3 into 6.33 and then multiplied the two then I got my answer.
Answer:
37 5/24 mph
Step-by-step explanation:
You need to multiply the numbers. First, convert them into fractions.
6 1/3 * 5 7/8 =
= (6 + 1/3) * (5 + 7/8)
= (6/1 + 1/3) * (5/1 + 7/8)
= (18/3 + 1/3) * (40/8 + 7/8)
= (19/3) * (47/8)
= 893/24
= 37 5/24
Solve the inequality -5(3x+4)<6-3x
Answer:
x>-13/6
Step-by-step explanation:
First you multiply inside the bracket by -5 on left side. You get
-15x-20<6-3x
Then you place the like terms on same sides for which you add 3x to both side to get rid of 3x from right side and you add 20 to both sides to get ride of 20 from left side
-15x+3x<20+6
then you solve for x
-12x<26
x<-26/12
x> -13/6 (the inequality sign changes due to multiplication by a negative number)
A horse began running due east and covered 25 km in 4.0 hr. What is the average
velocity of the horse?
Answer:
6.25 km an hour
please mark brainliest
Step-by-step explanation:
Answer:
Average velocity = 6.25 km/h
Step-by-step explanation:
Given : A horse began running due east and covered 25 km in 4.0 hr.
To find : What is the average velocity of the horse.
Solution : We have given
Displacement = 25 km
Time = 4 hr.
Velocity = [tex]\frac{Total\ displacement}{time}[/tex].
Velocity = [tex]\frac{25}{4}[/tex].
Average velocity = 6.25 km/h
Therefore, Average velocity = 6.25 km/h
7. Below are the points that Jesse scored in each game during the basketball season.
12, 15, 14, 12, 4, 8
Which of the following values would increase his mean number of points scored? Choose all that apply.
13
10
08
12
Answer:
13, 12, and 11. Im on connexus and when i submitted it said those are the correct answers. Hope it helps! :)
Step-by-step explanation:
through(-3,0)and (0,3)
Answer:
Step-by-step explanation:
the equation line passes through(-3,0)and (0,3) is : y=ax+b
a is the slope a = (3-0)/(0+3) = 1
so : y= x +b calculate b line passes through(-3,0)and (0,3)
x=0 y=3 : 3 = 0+b so b= 3
this equation is : y= x+3
Which inequality is represented by the graph?
A) y≥−12x+2.5
B) y>−2x+2.5
C) y≥−2x+2.5
D) y≤−2x+2.5
Answer: The answers C
Step-by-step explanation: Use Desmos to find it
Answer:
Option C.
Step-by-step explanation:
If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
From the given graph it is clear that the related line passes thorough the points (0,2.5) and (2,-1.5).
The equation of related line is
[tex]y-2.5=\frac{-1.5-2.5}{2-0}(x-0)[/tex]
[tex]y-2.5=\frac{-4}{2}(x)[/tex]
[tex]y-2.5=-2x[/tex]
Add 2.5 on both sides.
[tex]y-2.5+2.5=-2x+2.5[/tex]
[tex]y=-2x+2.5[/tex]
Th sign of inequality is either ≤ or ≥ because the related line is a solid line. It means the points on the line are included in the solution set.
Let the required inequality is
[tex]y\geq -2x+2.5[/tex]
(1,1) is included in the shaded region. So, the above inequality is true for (1,1).
[tex]1\geq -2(1)+2.5[/tex]
[tex]1\geq 0.5[/tex]
The assumed inequality is true for (1,1). So, the required inequality isn [tex]y\geq -2x+2.5[/tex].
Therefore, the correct option is C.