3x+3 + 10x-4 +90 (because complementary angle add up to 90)
13x-1+90 (add 1)
13x/13=91 (divide 13 on both sides)
x=7
now you fill in 7 for x
m<K=24 and m<L=66
hope i helped
The measures of both angles are 24° and 66°.
Given:
m<K = 3x + 3
m<L = 10x-4
Note:
Complementary angles are angles whose sum equals 90 degrees.
Therefore:
[tex]m \angle K + m \angle L = 90^{o}[/tex]
Substitute
[tex](3x+3) + (10x-4) = 90[/tex]
Solve for x
[tex]3x+3 + 10x-4 = 90\\[/tex]
Add like terms
[tex]13x-1 = 90\\[/tex]
Add 1 to both sides
[tex]13x = 90 + 1\\13x = 91[/tex]
Divide both sides by 13
[tex]x= 7[/tex]
Substitute the value of x in each of the expressions of the two given complementary angles.
[tex]m\angle K = 3(7) + 3 = 21 + 3\\m\angle K = 24^{o}[/tex]
[tex]m\angle L = 10(7) - 4 = 70 - 4 \\m\angle L = 66^{o}[/tex]
Therefore, the measures of both complementary angles are: 24° and 66°.
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the 26-oz jar of chocolate fudge costs $3.12. The 16-oz jar costs $2.40. How much can you save on each ounce by choosing the better buy?
Answer:
¢8.3 per ounce with the 26 ounce jar
¢6.6 per ounce with the 16 ounce jar
Step-by-step explanation:
divide 26 and 3.12
divide 16 and 2.40
Answer: $0.03
To solve this problem, you must find the unit rate that each jar of chocolate fudge is offering:
For the 26oz jar, you must divide 3.12 by 26 (3.12/26), which will give you an answer of $0.12 per ounce
For the 16oz jar, you must divide 2.40 by 16 (2.40/16), which will give you an answer of $0.15 per ounce
Doing the math, you will find that the 26oz jar has a better deal (less money per ounce), by 0.15-0.12 = $0.03 per ounce (saved on the better deal)
Write a rule to describe each transformation
To write a rule describing a transformation, you need to identify the specific transformation being applied and use the correct rule for that type of transformation. Examples of rules are given for translation, reflection, rotation, and dilation.
Explanation:To write a rule describing a transformation, you need to identify the specific transformation being applied to a shape. Here are examples of rules for different transformations:
Translation: If you move a shape (x units, y units) to the right and up, the rule would be (x, y). Reflection: If you reflect a shape across the x-axis, the rule would be (x, -y). If you reflect a shape across the y-axis, the rule would be (-x, y). Rotation: If you rotate a shape 90 degrees clockwise, the rule would be (y, -x). If you rotate a shape 90 degrees counterclockwise, the rule would be (-y, x). Dilation: If you enlarge a shape by a scale factor of k, the rule would be (kx, ky). Learn more about Transformations here:
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Lines are L and M are parallel. Find m<1
why shouldn't you let a doctor put one of those sticks in your mouth
just because they are scary
if you have a strong gag reflex. You also might get splinters from the stick so you should avoid it.
HELP PLEASE
Drag a reason to each box to complete the proof.
Given: AC=BD
Line segment A D with points A B C D on order from left to rightLine segment A D with points A B C D on order from left to right
Prove: AB=CD
Statements Reason
1. AC=BD
2. AC=AB+BC
3. BD=BC+CD Segment Addition Postulate
4. AB+BC=BC+CD
5. AB=CD Subtraction Property of Equality
Answer:
1. AC+BD given.
2. AC=AB+BC; Segment addition postulate.
4. AB+BC=BC+CD; Substitution property of equality.
Step-by-step explanation:
We have been given a line segment AD with points A B C and D sitting on AD from left to right and we are asked to find the reasons for given statements.
1. AC=BD is given. Therefore, we will add 'given' in first reason box.
2. We know If two points (A and C) lies on a line segment and third point (B) lies between these points then by segment addition postulate the distance between AC will be equal to sum of distances between AB and BC.
4. Since we know that substitution property of equality states that if x=y than we can substitute x in place of y in any equation and y in place of x as well in any equation. Since we know that [tex]AC=AB+BC[/tex] and [tex]BD=BC+CD[/tex]
Therefore, by substitution property of equality [tex]AB+BC=BC+CD[/tex].
5 smoothies in each batch.hom many smoothie did she make today
Is there any more info?
What are the coordinates of the orthocenter of △JKL with vertices at J(−4, −1) , K(−4, 8) , and L(2, 8) ?
ANSWER
The orthocenter is [tex](-4,8)[/tex]
EXPLANATION
The orthocenter is the point of intersection of all the altitudes of a triangle.
If it is a right angle triangle then the orthocenter is the point at which the right angle is made.
If it is not a right angle triangle, then you have to find the equations of any two of the altitudes and solve simultaneously.
So you must first check to see if it is a right angle triangle that way you do not have to do bunch work.
The given triangle has vertices [tex]J(-4,-1)[/tex], [tex](-4,8)[/tex], and [tex]L(2,8)[/tex].
[tex]Slope_{JK}=\frac{8--1}{-4--4}[/tex]
[tex]Slope_{JK}=\frac{8+1}{-4+4}[/tex]
[tex]Slope_{JK}=\frac{9}{0}[/tex]
Since the denominator is zero, the slope is undefined.
If the slope of a straight line is undefined, then that line is parallel to the y-axis. In other words, it is a vertical line.
[tex]Slope_{JL}=\frac{8--1}{2--4}[/tex]
[tex]Slope_{JL}=\frac{8+1}{2+4}[/tex]
[tex]Slope_{JL}=\frac{9}{6}[/tex]
[tex]Slope_{JL}=\frac{3}{2}[/tex]
[tex]Slope_{KL}=\frac{8-8}{2--4}[/tex]
[tex]Slope_{KL}=\frac{0}{2+4}[/tex]
[tex]Slope_{KL}=\frac{0}{6}[/tex]
[tex]Slope_{KL}=0[/tex]
if a straight line has a slope of zero, that line is parallel to the x-axis or it is horizontal.
From the slopes we can see that side KL of the triangle is horizontal and side JK is vertical. This two sides will meet at right angles at K.
See graph.
Therefore the coordinates of K, [tex](-4,8)[/tex] is the orthocenter of the given triangle.
David wants to fill his backyard swimming pool. His garden hose delivers 40 gallons in 5 minutes. How many gallons of water will be in the pool after 20 minutes? After 1 hour?
Eva sees a dolphin 3.2 meters below sea level and a bird 47/10 meters above sea level. Which of the following expressions represents the vertical distance between the dolphin and the bird?
Answer:
Vertical distance between dolphin and the bird is 7.9 meters.
Step-by-step explanation:
Eva sees a Dolphin at the distance 3.2 meters below the sea level.
At the same time she sees a bird [tex]\frac{47}{10}[/tex] meters above the sea level.
Therefore, vertical distance between the dolphin and the bird = Distance of dolphin below the sea level + Distance of the bird above the sea level
= 3.2 + [tex]\frac{47}{10}[/tex]
= 3.2 + 4.7
= 7.9 meters
Answer is 7.9 meters.
Determine the equation of the parabola whose graph is given below
The trajectory of a projectile is proven to be parabolic by eliminating time from the horizontal and vertical motion equations to receive the form y = ax + bx², thus describing the projectile's path.
Explanation:To prove the trajectory of a projectile is parabolic, we start with the motion equations given for horizontal and vertical positions, which are x = V0x t and y = V0y t - (1/2)gt2, respectively.
First, we solve the horizontal motion equation for t to find t = x/V0x.
We then substitute this expression for t into the vertical position equation to eliminate t.
After substitution, we get an equation of the form y = ax + bx2, where a is V0y/V0x and b is -g/(2V0x2).
These constants a and b represent the initial velocity components and the acceleration due to gravity, which together describe the parabolic path of a projectile motion.
The equation of the parabola is: y = 0(x - (-2.5))^2 + 2
To determine the equation of the parabola, we can use the general form of the equation for a parabola:
y = a(x-h)^2 + k
where (h, k) represents the vertex of the parabola.
Given two points on the graph, (-2,2) and (-3,4), we can use these points to find the values of h and k.
Let's start by finding the x-coordinate of the vertex, h. Since the parabola is symmetric, the x-coordinate of the vertex is the average of the x-values of the two given points:
h = (-2 - 3)/2 = -5/2 = -2.5
Next, let's find the y-coordinate of the vertex, k. We substitute the x-coordinate of the vertex into the equation and solve for y:
2 = a(-2.5 - (-2.5))^2 + k
Simplifying:
2 = a(0)^2 + k
2 = k
Therefore, the vertex of the parabola is (-2.5, 2).
Now that we have the values of h and k, we can substitute them into the equation to find the value of a. Using one of the given points, (-2,2), we have:
2 = a(-2 - (-2.5))^2 + 2
2 = a(-2 + 2.5)^2 + 2
2 = a(0.5)^2 + 2
2 = 0.25a + 2
0.25a = 0
a = 0
Therefore, the equation of the parabola is:
y = 0(x - (-2.5))^2 + 2
Simplifying:
y = 2
In this case, the parabola is a horizontal line passing through the vertex at y = 2.
The pool at "Splash Around" is open for 14 weeks during the summer. You can swim for $6 a session, or you can buy a membership for $100 and pay only $4 a session. Which equation would you use to determine how many sessions you must use the pool to justify buying the membership? A) 4x = 100 + 6x B) 6x + 4x = 100 C) 6x = 100 + 4x D) 100 - 4x = 6x
Answer:
C) [tex]6x=100+4x[/tex]
Step-by-step explanation:
Let the number of sessions be x
Let the total payment be y
Without membership, the equation becomes:
[tex]y=6x[/tex]
With membership, the equation becomes:
[tex]y=100+4x[/tex]
Now to justify, $100, we will equal both to get the number of sessions.
[tex]6x=100+4x[/tex]
[tex]=> 2x=100[/tex]
Dividing both sides by 2;
x = 50
Hence, the right equation is : [tex]6x=100+4x[/tex]
simplify the expression x^-4×y^3×x^4×y^2.
For simplifying an expression like this where the same bases with different exponents are to be multiplied, remember the Product rule. It says that when multiplying two or more powers having the same base (x and y in this case), you must add the exponents. For example, here in this expression there are two x's and two y's with different powers so you can simple add the powers of x and for y like shown below:
x^-4×y^3×x^4×y^2
= x^(-4+4) × y^(3+2)
=x^1 × y^5
since x^1 = x so we can omit the power 1 and write x instead.
xy^5 (here the power 5 only raises y and not x since it is not applied to whole)
The sum of 4 and three times a number is 19
Let the number be x
According to question
4 + 3 x = 19
3x = 19 - 4
3x = 15
x = 15 /3
x = 5
y=3x−7
Complete the missing value in the solution to the equation.
(1,___)
I beleive the answer = (1, -4)
Answer:
Step-by-step explanation:
y= 3x-7= -4x
A snail moves 1 50th of a mile in 5 6ths of an hour if the snail continurs at this pace how far in miles does it move in 1 hour
It Moves [tex]\frac{1}{60}[/tex]
Or In Decimal Form 0.016
Hope It Helps Mark Me The Brainlyest Please
A function is described by the equation y = 6x - 15. If the domain of the function is {-2, 0, 2, 4}, find the range.
range is {- 27, - 15, - 3, 9 }
substitute each of the values from the domain into the equation for x and solve for y
These values are the range
x = - 2 : y = - 12 - 15 = - 27
x = 0 : y = 0 - 15 = - 15
x = 2 : y = 12 - 15 = - 3
x = 4 : y = 24 - 15 = 9
Which point is a solution to the inequality shown in this graph
Answer:
D: (1,5) Apex
Step-by-step explanation:
Answer:
Option D. (1, 5)
Step-by-step explanation:
An inequality has been graphed in the given question.
The shaded part upwards the dotted line shows that the solution of the inequality lies in this region.
Now we will consider those points of the options as a solution which lie in the shaded region.
Option A.(3, -1)
Since line is in dotted form therefore points lying on the line are not the solution.
Option B. (5, -5)
Since this point lie below the shaded region so it's not the solution.
Option C. (-3, -3)
This point is again on the dotted line so it's not the solution.
Option D. (1, 5)
This is the correct option because this point lies in the shaded region above the dotted line.
a square had the dimensions of 45x67x36 what is the are of the square show your work and label
To find the area of a square with given dimensions, square one of its sides to get the area. In this case, using a side length of 45, the area is calculated as 2025 square units.
Explanation:The area of a square with dimensions 45 x 67 x 36 is calculated by finding the square of one of its sides. Since a square has all four sides equal, you can use any of the given dimensions to find the area. In this case, let's use 45 as the side length:
Side length of the square (s) = 45Area of the square = s²Area = 45² = 2025 square unitsI need help with 8x+3-10=-2 (x-2)+3
0 ≠ 4. The equation is wrong, and has no true solution.
8x + 3 - 10x = -2(x - 2) + 3
Distributive property.
8x + 3 - 10x = -2x + 4 + 3
Combine like terms.
-2x + 3 = -2x + 7
Cancel like terms.
Subtract 3 from both sides.
0 ≠ 4
How do you factor by finding the common monomial factor?
To find the greatest common factor of two monomials, first find the prime factorization of each monomial, including all the variables (and a – factor if necessary). Then take the product of all common factors. First, find the prime factorization of each monomial. So, the GCF is 3 p 2 r 3 .
Mark and his friends are out at Applebee’s. Their bill totaled 52.35. If they left the server a 20% tip, how much would each person pay splitting the bill evenly?
52.35 * 20% = 10.47
52.35+10.47 =62.82 total bill plus tip
62.82/ by number of people (this piece is missing)
a farmer bought a pig weighing 30 pounds. He expects it to gain 13 pounds a month and he plans on selling tge pig when it weighs approximately 212 pounds. How many months will it be before he can sell the animal
It will take exactly 14 months for the pig to be 212.
Factoriss fully. Brainliest answer will be awarded. 100 points up! please help quickly!
[tex]20 {x}^{2} - 5[/tex]
Answer: 5 (2x+1 ) ( 2x - 1)
Step-by-step explanation:
Factor commum term 5 :
Rewrite 20 as 5*4
5 * 4x² - 5
Factor common term 5 :
= 5 ( 4x²-1 )
Factor 4x²-1 :
(2x+ 1) (2x-1 )
Therefore:
= 5 (2x+1 ) ( 2x - 1)
Hope that helps!
The rectangle below has a total perimeter of 143 m:
Which of the following equations can be used to determine the length of the longer side of the rectangle?
(a) x + 11 = 143
(b) 11x = 143
(c) 121x = 143
(d) 2x + 22 = 143
We are given a side of the rectangle = 11 m.
Let us assume other side of the rectangle = x meter.
We know, formula for Perimeter of the rectangle :
Periemter = 2×one side + 2× other side .
We are given perimeter = 143 m.
Therefore,
2 × 11 + 2 × x = 143
22 +2x =143.
Therefore, (d) 2x + 22 = 143 equation can be used to determine the length of the longer side of the rectangle.
Convert 36 cm/min= m/h
To convert cm/min to m/h, multiply by 0.6, resulting in 21.6 m/h as the answer.
To convert 36 cm/min to m/h, you need to multiply by the conversion factor which is 60 min/h. Here's the step-by-step calculation:
36 cm/min = 36/100 m/min= 0.36 m/min= 0.36 x 60 m/h= 21.6 m/hA motel clerk counts his $1 and $10 bills at the end of the day. He finds that he has a total of 53 bills having a combined monetary value of $ 182. Find the number of bills of each denomination that he has.
The clerk has___ ones and ___ Tens.
A motel clerk counts his $1 and $10 bills at the end of the day. He finds that he has a total of 53 bills having a combined monetary value of $ 182.
let x be the number of $1 bills
y be the number of $10 bills
There are total of 53 bills so the equation becomes
x+y=53 ---> first equation
Bills having a combined monetary value of $ 182
x + 10 y = 182 ----> second equation
Now we solve for x and y
x+y=53
y = 53 - x
Now plug in 53 - x in second equation
[tex]x + 10 (53 - x) = 182[/tex]
[tex]x + 530 - 10x = 182[/tex]
[tex] -9x + 530 = 182[/tex] (subtract 530 on both sides)
-9x= -348
[tex]x=\frac{116}{3}[/tex]
Recheck the numbers given in the question. because we got answer in fraction form.
We know y = 53 - x
[tex]y = 53 - \frac{116}{3} = \frac{43}{3}[/tex]
What is the range of the given function?
The range would be [9, 0, -7, -1]
The range of any function is simply the values of y that are possible. In this case, there are only these three numbers.
Answer:
y= -7,-1,0,9
the answer is B
The Yu family and the Sainz family went on vacation together and each family leased a car. The leasing company charged a flat rental fee for the week, plus a charge for each mile driven. The Yu's drove 222 miles; their car cost $110.30 for the week. The Sainz's drove 147 miles; their car cost $99.05. What is the linear equation that represents the cost of a rental car? Round to the nearest hundredth
Answer:
y = 0.15x+77 is the equation linear connecting total cost y and miles driven x
Step-by-step explanation:
Given that the leasing company charged a flat rental fee for the week, plus a charge for each mile driven.
Let flat rental fee be c and cost per mile driven = m and miles driven = x
Total cost =y
Then y = mx+C is the linear equation.
to find m and c, we use the fact that y =110.30 when x = 222
i.e. 110.30 = c+222x
and similarly 99.05 = c+147x
Subtract to eliminate c
11.25 = 75 x
0.15 =x
Substitute in I equation
110.30 = c+222(0.15)
c = 77
Hence y = 0.15x+77 is the equation linear connecting total cost y and miles driven x
Answer:
y = 0.15x+77
Step-by-step explanation:
Draw a model, and write an equation to represent "4 times as many as 3 is 12." Explain your work.
The equation [tex]4 * 3 = 12[/tex] is an accurate mathematical representation of the statement. First, create a model using objects, such as circles or blocks, to represent the numbers involved:-
Now,
Draw three circles to represent the number 3.
Then, draw four groups of three circles each, representing "4 times as many as 3."
In total, you will have 12 circles.
Now, write an equation to describe this model:-
[tex]4 * 3 = 12[/tex]
In this equation:-
The number 4 represents the "4 times as many as" part of the statement.
The number 3 represents the initial quantity, which is multiplied.
The result, 12, represents the total or the final amount.
The equation [tex]4 * 3 = 12[/tex] is an accurate mathematical representation of the statement. It shows that when you multiply 3 by 4, you indeed get 12, which aligns with the given statement that "4 times as many as 3 is 12." This visual and algebraic representation helps to understand and demonstrate the concept of multiplication.
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If 3 · N = 1, then N is the _____.
additive inverse
additive identity
multiplicative inverse
multiplicative identity
ANSWER
Multiplicative Inverse
EXPLANATION
If we multiply any number by its multiplicative inverse, the result is 1.
So for the given equation
[tex]3\times N=1[/tex]
[tex]N[/tex] is the multiplicative inverse of [tex]3[/tex]. That is why the result is [tex]1[/tex]
Answer:
C. Multiplicative inverse.
Step-by-step explanation:
We have been given an equation [tex]3\cdot N=1[/tex]. We are asked to find the name of N.
We can see that N is multiplied by 3 and the result is 1.
We know that a number is known as multiplicative inverse of another number, when the product of both numbers equal to 1.
Since product of 3 and N is 1, therefore, N is multiplicative inverse for our given equation.