Answer:
81/10
Step-by-step explanation:
1)The sum of two consecutive multiples of 5 is55. Find these multiples.
2)The sum of three consecutive integers is 93. What are the integers?
3)If five is subtracted from three times a number, the result is 10. What is the number?
Part 1
Let the consecutive multiples be 5x and 5x + 5
ATQ
5x + 5x + 5 = 55
10x = 55 - 5
10x = 50
x = 5
Answer is 25 and 30
Part 2
Let the number be x , x + 1, x + 2
ATQ
x + x + 1 + x + 2 = 93
3x + 3 = 93
3x = 93 - 3
x = 90/3
x = 30
The integers are 30,31 and 32
Part 3
Let the number be x
ATQ
3x - 5 = 10
3x = 10 + 5
x = 15/3
x = 5
The number is 5
Answered by Gauthmath must click thanks and mark brainliest
A soccer field is a rectangle 80 meters wide and 100 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?
Answer:
128.06
Step-by-step explanation:
think about the diagonal of the field, breaking up a rectangle into 2 right angled triangles. we are already given the legs of the triangle (80, and 100) and now we have to solve for the hypotenuse (or the diagonal). so use pythagorean theorem :
80^2 + 100^2 = c^2
16400 = c^2
c = 128.06
(8) The average daily temperatures in July of some cities in Texas are shown in the table. Which
of the following fiets the cities from greatest temperature to least temperatura
City
Average Daily
Temperature
Austin
84.52F
Dallas
85.9°F
San Antonio
85 F
Fort Worth
85.31°F
a. Dallas, Fort Worth, San Antonio, Austin
b. Austin, Dallas, San Antonio, Fort Worth
c. Austin, San Antonio, Fort Worth, Dallas
d. Dallas, San Antonio, Fort Worth, Austin
Answer:
A.
Step-by-step explanation:
85.9 > 85.31 > 85 > 84.52
Dallas, Fort Worth, San Antonio, Austin
What point lies on the line with point slope equation y-3=4(x+7)?
Answer:
(-7, 3)
General Formulas and Concepts:
Algebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Identify
y - 3 = 4(x + 7)
↓ Compare to Point-Slope Form
Point (-7, 3)
Slope m = 4
pls help i need both blanks the options for the second one is left, right, up, down PLS HURRY ITS TIMED!!
Answer:
The graph is shifted 7 units right and 5 units up.
1. Determine the sum of the first 53 terms of the following series: 179+173+167+...
2. Determine the sum of the first 19 terms of the following series: 6−12+24−48+...
(1) This series consists of terms of an arithmetic sequence:
179 - 173 = 6
173 - 167 = 6
and so on, so that the n-th term in the series is (for n ≥ 1)
a(n) = 179 - 6 (n - 1) = 185 - 6n
Then the sum of the first 53 terms is
[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = 185\sum_{n=1}^{53}1-6\sum_{n=1}^{53}n[/tex]
[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = 185\times53-6\times\frac{53\times54}2[/tex]
[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = \boxed{1219}[/tex]
(2) This series has terms from a geometric sequence:
-12 / 6 = -2
24/(-12) = -2
-48/24 = -2
and so on. The n-th term is (again, for n ≥ 1)
a(n) = 6 (-2)ⁿ⁻¹
and the sum of the first 19 terms is
[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 + (-2) + (-2)^2 + (-2)^3 + \cdots+(-2)^{19}\right)[/tex]
Multiply both sides by -2 :
[tex]\displaystyle-2\sum_{n=1}^{19}6(-2)^{n-1} = 6\left((-2) + (-2)^2 + (-2)^3 + (-2)^4 + \cdots+(-2)^{20}\right)[/tex]
Subtracting this from the first sum gives
[tex]\displaystyle(1-(-2))\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 -(-2)^{20}\right)[/tex]
and solving for the sum, you get
[tex]\displaystyle3\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 -(-2)^{20}\right)[/tex]
[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -(-2)^{20}\right)[/tex]
[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -(-1)^{20}2^{20}\right)[/tex]
[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -2^{20}\right) = 2-2^{21} = \boxed{-2,097,150}[/tex]
find sine of angle of inclination to the axis is of line y=1/3x√3+3
Answer:
1/2.
Step-by-step explanation:
The inclination of the line to the x axis = 1/3*√3
= √3/3.
This is the tangent of the angle.
The sine of the angle =√3/hypotenuse.
The hypotenuse = √( √3)^2 + 3^2) (By the Pythagoras theorem)
= √12
= 2√3
Therefore the required sine is √3/ 2√3
= 1/2.
I think that's what you want!!
plzzz helpppp due today
Answer:
3 sqrt(3)
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp side / hyp
sin 60 = ZY / 6
6 sin 60 = ZY
6 (sqrt(3) /2) = ZY
3 sqrt(3) = ZY
b. Compare the similar triangle proof from question 3 with the inscribed square
proof. How are they different? Which method was easier for you to understand?
(1 point)
Answer:
i might be wrong but this is what i put
Step-by-step explanation:
In question 3 it was comparing three triangles where now it is using the triangles to find the area of a square instead of proving that they are the same.
Explainnnnnn help me please
Answer:
99cm²
Step-by-step explanation:
area for a triangle = 1/2 x b x h
area = 1/2 x 11 x 18
area = 99cm²
what is the length of de
Answer:
x = 6
Step-by-step explanation:
Since <F = <F, this shows that the triangles are similar. Therefore:
XZ/DF = XY/DE
12/8 = 9/X
Cross multiply
12X = 9*8
12X = 72
X = 72/12
X = 6
Hence the value of x is 6
Quick! HELP! THANK YOU SO MUCH!
If the difference between the interior and exterior angles of a regular polygon is 100°, how many sides does the polygon have?
Answer:
9 sides
Step-by-step explanation:
Sum of the measures of the interior angle of a polygon with n sides:
(n - 2)180
Measure of 1 interior angle of a regular polygon of n sides:
(n - 2)180/n
Sum of the measures of the exterior angles of a polygon, one per vertex:
360
Measure of 1 exterior angle of a regular polygon of n sides:
360/n
(n - 2)180/n = 360/n + 100
Multiply both sides by n.
(n - 2)180 = 360 + 100n
Distribute on left side.
180n - 360 = 360 + 100n
Subtract 100n from both sides.
80n - 360 = 360
Add 360 to both sides.
80n = 720
Divide both sides by 80.
n = 9
Answer: 9 sides
SOMEONE PLEASEEE HELP MEEE OUTTTT!!!
Answer:
cos x= 11/19
x=54.62
Step-by-step explanation:
use cosine to find the angle
This Venn diagram shows the pizza topping preferences for 9 students.
What elements are in A and B?
(Look at picture)
Answer:
I think the answer is C.
Determine which equations have the same solution set as StartFraction 2 Over 3 EndFraction minus x plus StartFraction 1 Over 6 EndFraction equals 6 x. – x + = 6x by recognizing properties, rather than solving. Check all that apply.
Answer:
A, B, F
Step-by-step explanation:
2/3 - x + 1/6 = 6x
Collect like terms
2/3 + 1/6 = 6x + x
(4+1) / 6 = 7x
5/6 = 7x
x = 5/6 ÷ 7
= 5/6 × 1/7
x = 5/42
a) 4 - 6x + 1 = 36x
4 + 1 = 36x + 6x
5 = 42x
x = 5/42
Equivalent to the last step of the simplification above
b) 5/6 - x = 6x
5/6 = 6x + x
5/6 = 7x
This is equivalent to the third step of the simplification
c) 4 - x + 1 = 6x
4 + 1 = 6x + x
5 = 7x
x = 5/7
Not equivalent to any of the steps in the simplification above
d) 5/6 + x = 6x
5/6 = 6x - x
5/6 = 5x
x = 5/6 ÷ 5
= 5/6 × 1/5
x = 5/30
Not equivalent to any of the steps in the simplification above
e) 5 = 30x
x = 5/30
Not equivalent to any of the steps in the simplification above
f) 5 = 42x
x = 5/42
Equivalent to the last step of the simplification above
Simplify each of the following:
a) root25 + root50 - root24 + root49
b) root2(2root8 – 3root32 + 4roor50)
Show your work
Answer:
a)
√25 + √50 - √24 + √49 =5 + 5√2 - 2√6 + 7 = 12 + 5√2 - 2√6b)
√2(2√8 – 3√32 + 4√50) =2√16 - 3√64 + 4√100 = 2*4 - 3*8 + 4*10 = 8 - 24 + 40 = 24Answer:
a.) 12 + 5√2 - 2√6
b.) 24
Step-by-step explanation:
a) √25 + √50 - √24 + √49
√25 + √50 - √24 + √49Calculate the square root .
5 + √50 - √24 + 7Simplify the radical expression.
5 + 5√2 - 2√6 + 7Combine like terms.
5 + 7 + 5√2 - 2√6 12 + 5√2 - 2√6b.) √2 ( 2√8 - 3√32 + 4√50 )
√2 ( 2√8 - 3√32 + 4√50 )Simplify the radical expression.
√2 ( 4√2 - 3 × 2²√2 + 20√2)Evaluate the power.
√2 ( 4√2 - 3 × 4√2 + 20√2)Calculate the products.
√2 ( 4√2 -12√2 + 20√2)Combine like terms.
√2 × (4 - 12 + 20 )√2√2 × 12 √ 2Multiply.
2 × 12 24Mrs. Kennedy is teaching an 8th grade class. She is standing 7 meters in front of Catherine. Davis is sitting to Catherine’s left. If Davis and Mrs. Kennedy are 12 meters apart, how far apart are Davis and Catherine?
13.90 meters
5 meters
9.75 meters
4.36 meters
Answer:
9.75 meters
Step-by-step explanation:
Davis and Catherine are approximately 13.90 meters apart.
How to determine distance apartTo find the distance between Davis and Catherine, we can use the concept of right triangles and apply the Pythagorean theorem.
Let's consider a right triangle where the distance between Davis and Mrs. Kennedy is the base, the distance between Mrs. Kennedy and Catherine is the height, and the distance between Davis and Catherine is the hypotenuse.
According to the given information, Mrs. Kennedy is 7 meters in front of Catherine, and Davis and Mrs. Kennedy are 12 meters apart.
Using the Pythagorean theorem, we have:
(Base)² + (Height)² = (Hypotenuse)²
Substituting the given values:
(12)² + (7)² = (Hypotenuse)²
Simplifying the equation:
144 + 49 = (Hypotenuse)²
193 = (Hypotenuse)²
Taking the square root of both sides:
√193 ≈ 13.89 = 13.90
Therefore, Davis and Catherine are approximately 13.90 meters apart.
Learn more about distance at
https://brainly.com/question/26550516
#SPJ2
i need help. i don't understand this at all.
Answer:
Step-by-step explanation:
If this is in terms of angles, 4x+6 must be equal to 90 since it is half of the angle produced by a line (180°) So solving for 4x+6=90, x=21
What is the answer? How to solve?
Answer:
a +73°=90°
a= 90°-73°
a =17°
d+18°=90°
d=90°-18°
d =72 °
Justin packed two suitcases for his trip and compared the weights of the items he packed in each of the suitcase.
Answer:
I am currently taking a unit test and I just got this question. I believe it is the answer but I haven't submitted yet.
Step-by-step explanation:
The answer I chose seems to be the only logical answer.
can i get the answer quick
Answer:
p^3 - 7p^2q^2 + 2pq
Step-by-step explanation:
3pq +5p^2q^2 + p^3 = p^3 + 5p^2q^2 + 3pq
Let the number be x.
x + p^3 + 5p^2q^2 + 3pq + p^3 - pq
= 3p^3 - 2p^2q^2 + 4pq
x + p^3 + p^3 + 5p^2q^2 + 3pq - pq
= 3p^3 - 2p^2q^2 + 4pq
x + 2p^3 + 5p^2a^2 + 2pq
= 3p^3 - 2p^2q^2 + 4pq
x
= 3p^3 - 2p^2q^2 + 4pq - (2p^3 + 5p^2q^2 + 2pq)
= 3p^3 - 2p^2q^2 + 4pq - 2p^3 - 5p^2q^2 - 2pq
= 3p^3 - 2p^3 - 2p^2q^2 - 5p^2q^2 + 4pq - 2pq
= p^3 - 7p^2q^2 + 2pq
Therefore,
p^3 - 7p^2q^2 + 2pq should be added.
3. Rita is applying for a job as an engineer. Hier starting salary at Company will be $30,000 a $300 yearly
raise. Her starting salary at company will be $65.000 with a 5% increase sach year. If Rata is working at a
company for 5 years. Which company should she pick?
Answer:
The 65,000 salary
Step-by-step explanation:
Because the 30,000 salary after 5 years would be 31,500.
30,000+300=30,300
30,300+300=30,600
30,600+300=30,900
30,900+300=31,200
31,200+300=31,500
The 65,000 paying company
65,000x1.05=68,250
68,250x1.05=71.662.5
71,662.5x1.05=75,245.625
75,245.625x1.05=79,007.90625
79,007.90625x1.05=82,958.3015625
her salary after 5 years would be 82,958.3015625
What is the perimeter of this parallelogram? Please help asap!
I got H / 75 but I might be wrong any confirmation
Answer:
30
Step-by-step explanation:
Angle PNM = 180-105
= 75
IF PM = PN then
<PNM = <PMN = 75
<PMN + <PNM + <P = 180 since they form a triangle
75 + 75 + x = 180
150+x = 180
x = 180-150
x = 30
Answer:
<MPN = 40°Step-by-step explanation:
180° - <PNQ = <PNM ( Angles in a straight line )
180° - 105° = 75°
<PMN = < PNM = 75°
<PMN + <PNM + <MPN = 180°
75 ° + 75° + <MPN = 180°
<MPN = 180° - 150°
<MPN = 30°
please solve this please
Answer:
3
Step-by-step explanation:
Wages and salaries
Kelly earns a salary of $68 430 pa how much does he earn each week, each fortnight and each month?
Answer:
Each week = $ 1311.41
Each fortnight = $ 2622.84
Each month = $ 5702.5
Step-by-step explanation:
Given that,
Annual salary of Kelly = $ 68,430
As we know,
There are 52.18 weeks in a year.
So,
Weekly income = Annual salary ÷ no. of weeks in the year
= $ 68,430 ÷ 52.18
= $ 1311.42
Fortnight income = 2 * weekly income
= 2 * $ 1311.42
= $ 2622.84
Each month's income = Annual income ÷ 12(no. of months)
= $ 68,430 ÷ 12
= $ 5702.5
which expression is in the simplest form of 4x^3+x^2+2(x^3-3x^2)
a. 4x^3-6x^2
b. 6x^3-6x^2
c. 2x^3-6x^2
d. 6x^3-5x^2
Answer:
It's D. 6x^3-5x^2
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
4x^3+x^2+2(x^3-3x^2)
4x^3 + x^2 + 2x^3 -6x^2 (Distributed 2 through the parenthesis)
= 6x^3 -5x^2
Answered by Gauthmath
Diagram shows triangle ABC.
Workout the size of angles x,y,z
x= 70*
y= 30*
z= *
Find the product. (-2x^2)^3 ·3x
Answer:
-24 x^7
Step-by-step explanation:
(-2x^2)^3 ·3x
(-2x^2) (-2x^2) (-2x^2)*3x
-8 x^6 *3x
-24 x^7
Given P(B | A)=0.75, P(A ∩ B)=0.15, P(B’)=0.7, find P(A ∪ B)
By definition of conditional probability,
P(B | A) = P(A ∩ B) / P(A)
==> P(A) = P(A ∩ B) / P(B | A) = 0.15/0.75 = 0.2
By definition of complement,
P(B') = 1 - P(B)
==> P(B) = 1 - P(B') = 1 - 0.7 = 0.3
Now by the inclusion/exlcusion principle, we have
P(A U B) = P(A) + P(B) - P(A ∩ B)
==> P(A U B) = 0.2 + 0.3 - 0.15 = 0.35
