The distance between pair of parallel lines with the given equation
y=-6 y=1 is 7 units
Definition of parallel linesParallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.
The fundamental characteristics listed below make it simple to recognize parallel lines.
Straight lines which are always the same distance apart from one another are known as parallel lines.No matter how far apart they are from one another, the parallel lines can never intersect.The two lines have the coefficient of x, zero. So, the slopes are 0.
Therefore, the lines are horizontal lines passing through y = −6 and y = 1.
The perpendicular distance between the these horizontal lines is
1 - (-6) = 7 units.
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simplify this algebraic expression
y - 3/3 + 12
A.y - 11
B.y + 13
C.y + 11
D.y - 5
two cars travel down the highway at the same speed. if the first car travels 10 kilometers per hour faster than its current speed and the second car travels 10 kilometers per hour slower than its current speed than the first car would travel in two hours the same distance the second car would travel in thee hours. what is the original speed of the cars?
Answer:
The original speed of the cars is 50 km/hStep-by-step explanation:
Let the original speed of the cars be x.
The first carWhen speed is x + 10 the distance in two hours is:
2(x + 10)The second carWhen speed = x - 10 the distance in three hours is:
3(x - 10)Since the distance is same in both cases, set them equal and solve for x:
2x + 20 = 3x - 303x - 2x = 20 + 30x = 50The original speed of the cars is 50 km/h
Answer:
Original speed = 50 km/h
Step-by-step explanation:
Given that,
→ first car travels 10 km faster than its current speed. It would travel in two hours the same distance.
→ second car travels 10 km per hour slower than its current speed. It would travel in 3 hours the same distance.
Then the equation will be,
→ 2(x + 10) => 1st car
→ 3(x - 10) => 2nd car
→ 2(x + 10) = 3(x - 10)
Now the original speed of the cars is,
→ 2(x + 10) = 3(x - 10)
→ 2x + 20 = 3x - 30
→ 2x - 3x = -30 - 20
→ -x = -50
→ [ x = 50 km/h ]
Hence, the original speed is 50 km/h.
Zach found four consecutive odd integers such that 5 times the sum of the first and the third was 22 greater than the product of 8 and the sum of the second and the fourth. What were the integers?
Answer:
3, 5, 7, 9
Step-by-step explanation:
Give Brainliest if I helped!
The four consecutive odd integers that Zach found are x, x + 2, x + 4, and x + 6 are -11, -9, -7, and -5.
To solve this problem, set up equations based on the given information.
"5 times the sum of the first and the third":
[tex]5(x + x + 4)[/tex]
"the product of 8 and the sum of the second and the fourth":
[tex]8((x + 2) + (x + 6))[/tex]
According to the problem, the first equation should be 22 greater than the second equation:
[tex]5(x + x + 4) = 8((x + 2) + (x + 6)) + 22[/tex]
Next, simplify and solve the equation:
[tex]5(2x + 4) = 8(2x + 8) + 22[/tex]
Remove the bracket by multiplying the terms:
[tex]10x + 20 = 16x + 64 + 22[/tex]
Take the variables to LHS and constants to other side and solve it:
[tex]6x = -66[/tex]
On dividing by 6 on both sides:
x = -11
Now that the value of x, and find the four consecutive odd integers:
x = -11
On substituting x value in the following terms:
[tex]x + 2 = -11 + 2 \\= -9\\x + 4 = -11 + 4\\ = -7\\x + 6 = -11 + 6 \\= -5[/tex]
Therefore, the four consecutive odd integers are -11, -9, -7, and -5.
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Find the quotient.
2³. 12 / 6
Answer: It is 32
Step-by-step explanation:
The length of an animal's stride is the distance between two consecutive tracks. The average stride length of a turkey is about 11 inches. Write a glide reflection that can be used to predict the location of the next track for the following animal tracks.
turkey
The glide reflection ( x + 5.5 , y ) is that is reflected in the line that separates the left prints from the right prints.
A glide translation is what?
A glide reflection is made up of a translation and a reflection in which the translation and the reflection are parallel to each other or the direction of the translation. A gliding reflection has opposite isometry and is -commutative.Now, let's assume that the initial position is (x , y) .
Since, the average stride length of a turkey is about 11 inches; also since the turkey has two legs, therefore, the average stride length between the two legs is as shown below:
average = 11/2 = 5.5
Thus, the glide reflection is ( x + 5.5 , y )
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Twelve is greater than the sum of 6 and a number.
012>6+n
O 12<6n
012<6+n
12 >6n
Answer:
12<6+n
this is the answer
Suppose you make a 4-minute local call using a calling card and are charged 7.6 cents. The cost of a local call varies directly with the length of the call. How much more will it cost to make a 30 -minute local call?
a. Which quantity is the dependent quantity?
For the linear equation C = kl, where c, cost is the local variable and it takes 49.4 cents more for a 30 min local call. The dependent variable is the price of a local call.
What is a linear equation?There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.
The equation representing the situation
C = kl
where c depicts the cost and l is the length of call.
The dependent variable is the price of a local call.
The term "mord more" denotes that we are searching for the price difference between a 4 minute call and a 30 minute call, or the price of a 26 minute call.
The cost for 26 minutes will be 49.4 cents.
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will give you EXTRA BRAINLIEST POINTS
i don't understand this and need to submit asap please help thanks :D
Denise is using a ladder to clean the outside of her second story windows. The ladder she is using is 24 feet long and she puts the base of the ladder 13 feet away from the house in order to avoid her flower gardens. How high up the side of her house does the ladder reach? Round to the nearest tenth, if necessary.
The ladder can reach 21.17 feet high up of Denise's house.
Given,
The length of ladder Denise used to clean the outside of her second story windows = 24 feet
The distance between the base of the ladder and house = 13 feet
We have to find the height of the house which the ladder can reach:
For that we can use Pythagorean Theorem.
That is,
Hypotenuse² = Altitude² + Base²
Here,
Hypotenuse is the length of the ladder = 24 feet
Altitude is the height of the house ladder can reach = x
Base is the distance between base of the ladder and house = 13 feet
Therefore,
24² = x² + 13²
576 = x² + 169
x² = 576 - 169
x² = 407
x = [tex]\sqrt{407}[/tex]
x = 21.17
That is, the ladder can reach 21.17 feet high up of Denise's house
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Latasha is baking cookies. The radius of each cookie is 9 centimeters.
What is the area of each cookie?
Use 3.14 for pi and round your answer to the nearest tenth.
PLEASE HELP!!!!
Answer:
The area of each cookie is 254.3
Find the circumference of circle described. Round to the nearest hundredth.
a. radius =2.5 centimeters
Answer:
15.71 cm
Step-by-step explanation:
circumference is [tex]\pi[/tex]d
diameter is 2r
radius = 2.5 cm so the diameter is 2.5*2 = 5 cm
circumference = [tex]\pi[/tex] (5) -> 15.707
rounded to the nearest hundredth is 15.71 cm
The company in Problem 2 has an alternative bonus plan. It pays a $ 5000 bonus if a new salesperson makes 10 sales in the first week and then improves by one sale per week each week thereafter. One salesperson qualified for this bonus with the minimum number of sales. How many sales did the salesperson make in week 50 ? In all 50 weeks?
The given situation shows an arithmetic sequence and the number of sales in the week 50 can be determined by using the nth term formula of arithmetic sequence. The sales in all 50 weeks can be determined by using the formula for sum of finite arithmetic sequence.
An arithmetic sequence is an ordered set of numbers that have a constant difference called a common difference between consecutive terms. Each term is obtained by adding the common difference to the previous term.
In the given situation, the first term (a) is the number of sales to be made in the first week. Hence, a = 10
The common difference (d) is the number added to get the number of sales in the next week. Hence,
d = 1
Hence, in the 2nd week the number of sales should be 11 and in 3rd week it should be 12.
Using the formula for nth term and n = 50,
an=a+(n-1)d
a50=10+(50-1)1
a50=10+(49)1
a50=10+49=59
The formula of finding the sum of the finite arithmetic sequence:
Sn=(n/2)(a1+an)
S50=(50/2)(10+59)
S50=25(69)=1725
Hence, the number of sales in the 50th week is 59 and the total number of sales made in the 50 weeks is 1725.
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y varies directly with x .
If y=5 when x=-3 , find x when y=-1 .
Using direct variation, the value of x for equation y = 5/-3 (x) is 3/5 when y = -1
What is direct and inverse variation?When x is not equal to zero, an equation of the form y = kx describes the linear function known as direct variation. When x is not equal to zero and k is a nonzero real number constant, the equation of the form xy = k describes the nonlinear function known as inverse variation.
Using direct variation,
y = kx
⇒ 5 = k(-3)
⇒ k = 5 / -3
for y = -1
y = 5/-3 (x)
⇒ -1 = 5/-3 × x
⇒ x = 3/5
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Carter wants to ride his bicycle 28.7 miles this week. He has already ridden 17 miles.
If he rides for 3 more days, write and solve an equation which can be used to determine m, the average number of miles he would have to ride each day to meet his goal.
Carter needs to ride 3.9 miles per day on an average to meet his target of riding 28.7 miles in a week.
We are given that:
The total number of miles that needs to be ridden by Carter = 28.7 miles
Now, he has already ridden 17 miles this week
So, the miles left to be ridden = 28.7 miles - 17 miles
Number of miles left = 11.7 miles.
Now, he has 3 more days to finish his target.
So, on an average, he should ride:
Average = 11.7 miles / 3 days = 3.8 miles per day
Therefore, Carter needs to ride 3.9 miles per day on an average to meet his target of riding 28.7 miles in a week.
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Which equation represents a line with slope -2 and y -intercept 3 ?
f. 3 y=x-2
g. 3 y=-2 x+1
h. y=2 x-3
i. y=-2 x+3
Answer: Maybe f I'm not sure
Step-by-step explanation:
Find the measure. (Lesson 5-1)
TQ
If TQ = 2x - 6 and RQ = x + 3 then the measure of TQ = 12.
What is Perpendicular Bisector Theorem?The perpendicular bisector theorem states that if a point is on a segment's perpendicular bisector, it is equidistant from the segment's endpoints.
According to the perpendicular bisector theorem, any point on the perpendicular bisector is equidistant from both ends of the line segment on which it is drawn. If a pillar stands at an angle in the center of a bridge, all of its points will be equidistant from the bridge's end points.
Where, TQ = 2x - 6 and RQ = x + 3
By the Perpendicular Bisector Theorem, RQ = TQ.
2x - 6 = x + 3
x = 9
Substitute the value of x in TQ, we get
TQ = 2(9) - 6
= 18 - 6
= 12
Therefore, the value of TQ = 12.
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Two factory plants are making TV panels. Yesterday, Plant A produced 6000 fewer panels than Plant B did. Five percent of the panels from Plant A and 4% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 1410 defective panels?
Plant P produced 15333 numbers of panels when the two plants together produced 1410 defective panels using unitary method.
What is unitary method?It is a method for figuring out a single unit's value, then multiplying that value by itself to get the required value.
Given data
Plant produces defective panels = 1140
Plant A produce = 5%
Plant B produce = 4%
Assume,
Number panels Plant B produce = x
Number panels Plant A produce = x - 6000
[tex]\frac{5}{100}[/tex](x) + [tex]\frac{4}{100}[/tex](x-6000) = 1140
0.05x + 0.04x - 240 = 1140
0.09x = 1380
x = 15333
Plant P produced 15333 numbers of panels when the two plants together produced 1410 defective panels using unitary method.
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You invested money in a fund and each month you receive a payment for your investment. Over the first four months, you received $ 50, $ 52, $ 55 , and $ 59 . If this pattern continues, how much will you receive in the tenth month?
a. Write a formula to describe this sequence.
Money received in tenth month: $104.
A formula that describes this arithmetic sequence: [tex]a_n=a_{n-1}+n[/tex], n > 1., where n = number of month.
What is arithmetic progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
Money received in first four months: $50, $52, $55, %59.
To find: Money received in tenth month.
Finding:
As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.
That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.
Thus, for the tenth month, we can use the formula of recursion, given by: [tex]a_n=a_{n-1}+n[/tex], n ≥ 1.
For a₁ = 50, a₂ = a₁ + 2
=> a₂ = 50 + 2
This way, a₅ = a₄ + 5
=> a₅ = 59 + 5 = 64
a₆ = a₅ + 6
=> a₆ = 64 + 6 = 70
a₇ = a₆ + 7
=> a₇ = 70 + 7 = 77
a₈ = a₇ + 8
=> a₈ = 77 + 8 = 85
a₉ = a₈ + 9
=> a₉ = 85 + 9 = 94
a₁₀ = a₉ + 10
=> a₁₀ = 94 + 10 = 104
Thus, the payment received in tenth month will be $104.
A formula that describes this arithmetic sequence: [tex]a_n=a_{n-1}+n[/tex], n > 1., where n = number of month.
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What is the product of a number and 14 plus 10, written as an algebraic expression?
10(x + 14)
10x − 14
14 ÷ x − 10
14x + 10 please give me the answer i need help
Answer:
14x+10
Step-by-step explanation:
The product means multiplication
Answer:
D 14x+10
Step-by-step explanation:
A dance group of 17 teenagers had a mean mass of 44.5kg. to enter a competition there needs to be 18 people in the group with an average mass of 44.4kg or less. what is the maximum mass that the 18th person could be
Answer:
Step-by-step explanation:
so first it would be -0.1 but that means you need to remove the 17th person and get 2 really light people because one can not be negative hope this helps
Rosita runs every day in preparation for a marathon. If she runs 8.7 miles a day, how many
miles will she run in 26 days?
Answer:
226.2 miles
Step-by-step explanation:
8.7 x 26 = 226.2
Anne and Katherine are both saving money from their summer jobs to buy bicycles. If Anne had $150 less, she would have
exactly as much as Katherine. And if Katherine had twice as much, she would have exactly 3 times as much as Anne. How
much money have they saved together?
$300
$400
$450
$625
$750
Given that 32 √ 2 = 2ª, find the value of a.
The value of 'a' in the given expression is 11/2.
Elaborate about the square root.The square root formula can be used to calculate the square root of any number. The square root of any number is the value that, when multiplied by itself, yields the original number. Each number has two square roots, one positive and the other negative. For example, the number four has two square roots, -2 and 2.
Given [tex]$32 \sqrt{2}=2^a$[/tex]
We can write 32 as:
32 = 2 × 2 × 2 × 2 × 2
32 = [tex]2^{5}[/tex]
We can write [tex]$\sqrt{2}=2^{1 / 2}$[/tex].
Now,
[tex]$$\begin{array}{r}32 \sqrt{2}=2^a \\2^5 \cdot 2^{1 / 2}=2^a \\2^{5+1 / 2}=2^a \\2^{1 / 2}=2^a \\\end{array}$$[/tex]
Therefore, the value of a = 11/2.
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Meals with a Purpose are selling to-go charcuterie boards. You can purchase a small board or a medium board. On Thursday, Meals with a Purpose sold 10 small charcuterie boards and 12 medium charcuterie boards for a total of $144. On Thursday, Meals with a Purpose sold 5 sold charcuterie boards and 9 medium charcuterie boards for a total of $93.
What is the cost of each small charcuterie boards and one medium charcuterie boards?
The cost of each small charcuterie boards is $6 and one medium charcuterie boards is $7.
How to illustrate the information?A mathematical statement known as an equation is made up of two expressions joined together by an equal sign. It is a formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.
Let small charcuterie boards = c
Let medium charcuterie boards = m
Therefore, the equation will be:
10c + 12m = 144
5c + 9m = 93
Multiply equation i by 5
Multiply equation ii by 10
50c + 60m = 720
50c + 90m = 930
Subtract
30m = 210
m = 210/30
m = 7
Therefore, 5c + 9m = 93
5c + 9(7) = 93
5c + 63 =93
5c = 93 - 63
5c = 30
Divide both sides by 5
c = 30 / 5
c = 6
Therefore, based on the information the cost of each small charcuterie boards is $6 and one medium charcuterie board is $7.
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geometry
through: (1,4), slope=6
Answer:
Step-by-step explanation:
Point slope form y-y₁ = m(x-x₁)
y-4 = 6(x + 1)
y-4 = 6x + 6
y = 6x + 10
If f(x)=7-3 x and g(x)=3 x-7 , what is the value of f(1)+g(1) ?
If f(x)=7-3 x and g(x)=3 x-7 , the value of f(1)+g(1) is 0
What is function composition?A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.
f(x)=7-3 x and g(x)=3 x-7
For, f(1) = 7 - 3(1)
= 7 - 3
= 4
For, g(1) = 3x - 7
= 3(1) - 7
= -4
f(1) + g(1) = 4 - 4
= 0
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Determine whether the given measures define 0,1,2 , or infinitely many triangles. Justify your answers. a=10, b=15, m
We can construct an unlimited number of triangles when given only two sides and no indication of the angle, such as a = 10m and b = 15m
Consider this:
With 10m and 15m side lengths and an angle value ranging from 0 to 360 degrees, how many distinct triangles are possible?
Make one of the triangles with sides of 10 meters, 15 meters, a 30 degree angle, and a third side that may be adjusted to your preferred length using a protractor. A triangle has been built by you.
By changing the length and angle of the third side, we can produce a completely different triangle that is similar to this one.
Keep in mind that you choose the side lengths and angle. This suggests that you might make a different decision. Using the same angles, you can make an infinite number of different triangles.
As a result, using just one angle and one side length, we can create an unlimited number of triangles.
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Given: AB || CD-i AB ≅ DC
Prove: Δ A B E ≅ ΔC D E
We have proved that , the ΔABE is congruent to ΔCDE i.e., ΔABE ≅ ΔCDE
It is given that AB║ CD and AB ≅ DC.
We have to prove that ΔABE is congruent to ΔCDE i.e., ΔABE ≅ ΔCDE.
What is the SAS rule of congruency of triangles ?
SAS axiom states that if two sides and the included angle of one triangle are equal to two sides and included angle of other triangle, then triangles are congruent.
As per the question ;
AB║ CD and AB ≅ DC
The two triangles are ΔABE and ΔCDE
So ,
AB = CD (from given data)
also ;
Included angles of two triangles are equal ;
∴
∠ABE = ∠CDE (from given data)
and
BE = BE (common)
∴ Both triangles are congruent to each other ;
i.e.,
ΔABE ≅ ΔCDE.
by SAS axiom.
Thus , the ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX
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How is diving each side by x>0 by a negative value different from diving each side by a positive value
Yes, the results of dividing X by a negative value and dividing X by a positive value are different. If we divide X by a negative value, the result will be negative, and if we divide X by a positive value, the result will be positive.
For instance:
It is true that 8 > 2 is unequal.
Divide both sides by 2, then:
True inequality also exists when 4 > 1. Due to the fact that we divided by a positive number, the inequality symbol remained.
Let's begin once more with
8 > 2, and apply a -2 to both sides.
-4 > -1 is erroneous. The inequality is no longer valid if the inequality sign changes when both sides are divided by a negative integer. When dividing both sides by a negative integer, the inequality sign must be changed in order to maintain its validity.
8 > 2
Add a -1 to both sides.
True for -4 < -1.
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a -90 degree rotation is the same as
Answer:
Step-by-step explanation:
A 270 degrees anticlockwise rotation is the same result as the rotation of the 90 degrees.
