Answer:
[tex]a_1=15[/tex]
Step-by-step explanation:
We are talking about arithmetic progression.
Using the formula:
[tex]a_n=a_1+(n-1) \cdot d[/tex]
[tex]a_7=a_1+(7-1) \cdot d[/tex]
[tex]3=a_1+(7-1) \cdot (-2)[/tex]
[tex]3=a_1+(6) \cdot (-2)[/tex]
[tex]3=a_1-12[/tex]
[tex]a_1=15[/tex]
Answer:
[tex]\huge \boxed{a_1=15 }}[/tex]
Step-by-step explanation:
Using the nth term formula:
[tex]a_n=a_1+dn-d[/tex]
[tex]a_7=3 \\ \\ n=7 \\ \\ d=-2[/tex]
[tex]3=a_1+-2(7)-(-2)[/tex]
Simplifying and solving for the first term.
[tex]3=a_1-14+2[/tex]
[tex]3=a_1-12[/tex]
[tex]15=a_1[/tex]
The first term of the sequence is 15.
If y = 7x - 5, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs? (5 points)
О2, 7), (1, 6), (3, 13))
(1, 3), (6, 18), (8, 15))
(о, -5), (2, 9), (-3, -26)
О (-5, 0), (9, 2), (-26, -3)
Answer:
The Third One (0,-5) (2,9)
Step-by-step explanation:
Subtract y2-y1 and x2-x1 and the equation will come out as y=7x-5
does anybody know how to do this
Answer:
Step-by-step explanation:
green tiles you add the x
red tiles is for subtraction
2x-2= 3x + 6 -2x-2
x on one side and numbers on other
2x-3x+2x=6-2+2
-3x=6
x=6/-3 =-2
Another line “r” is perpendicular to the line 3y = 6x + 9. Find the gradient of the line "r" show your working
Answer:
Line r has a gradient of -1/2
Step-by-step explanation:
Perpendicular lines have a gradient of negative reciprocal to each other such that multiplying both the slopes give -1
=> Gradient of this line = 2
=> Gradient of line perpendicular to it = [tex]\frac{-1}{2}[/tex]
Multiplying both gradients:
=> 2 * [tex]\frac{-1}{2}[/tex]
=> -1
(SO They are perpendicular!)
For the parallelogram ABCD the extensions of the angle bisectors AG and BH intersect at point P. Find the area of the parallelogram, if DG = GH, AB = 39 in, GP = 12 in.
Answer:
The area of a parallelogram is 360 in.²
Step-by-step explanation:
Where DG = GH
GP = 12 in.
AB = 39 in.
∠DAB + ∠ABC = 180° (Adjacent angles of a parallelogram)
Whereby ∠DAB is bisected by AG and ∠ABC is bisected by BH
Therefore, ∠GAB + ∠HBA = 90°
Hence, ∠BPA = 90° (Sum of interior angles of a triangle)
[tex]cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{AP}{39} = \dfrac{GP}{GH} =\dfrac{12}{GH}[/tex]
We note that ∠AGD = ∠GAB (Alternate angles of parallel lines)
∴ ∠AGD = ∠AGD since ∠AGD = ∠GAB (Bisected angle)
Hence AD = DG (Side length of isosceles triangle)
The bisector of ∠ADG is parallel to BH and will bisect AG at point Q
Hence ΔDAQ ≅ ΔDGQ ≅ ΔGPH and AQ = QG = GP
Hence, AP = 3 × GP = 3 × 12 = 36
[tex]cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{36}{39}[/tex]
[tex]\angle GAB = cos^{-1} \left (\dfrac{36}{39} \right )[/tex]
∠GAB = 22.62°
[tex]cos(\angle GAB) = \dfrac{36}{39} = \dfrac{12}{GH}[/tex]
[tex]GH = \dfrac{39}{36} \times {12}[/tex]
GH = 13 in.
∴ AD 13 in.
BP = 39 × sin(22.62°) = 15 in.
GH = √(GP² + HP²)
∠DAB = 2 × 22.62° = 45.24°
The height of the parallelogram = AD × sin(∠DAB) = 13 × sin(45.24°)
The height of the parallelogram = 120/13 = 9.23 in.
The area of a parallelogram = Base × Height = (120/13) × 39 = 360 in.²
Answer:
360 in2
Step-by-step explanation:
The figure ABCD is a parallelogram, so the side AB is parallel to the side DC, and that means the angle mBAG is equal the angle mHGP.
The angles mHGP and mAGD are vertically opposite angles, so mHGP = mAGD.
The angle mDAG is equal the angle mBAG, so mDAG = mBAG = mHGP = mAGD
The angles mDAG and mAGD are equal, so the triangle DAG is isosceles, that means the side DG is equal the side DA.
In the same way, we can find that the angle mCBH is equal the angle mBHC, so triangle BCH is isosceles, meaning that side BC (which is equal side AD) is equal side CH, so we have that:
DG + GH + HC = AB = 39
GH + GH + GH = 39
GH = 13
in the parallelogram we have the property:
mDAB + mABC = 180°
We have that mGAB = mDAB/2 and mABH = mABC/2, so using this information for the sum of internal angles of triangle APB, we have:
mGAB + mABH + mBPA = 180
mDAB/2 + mABC/2 + mBPA = 180
(180/2) + mBPA = 180
mBPA = 90°
If the triangle APB is a right triangle, we can find the cosine of the angle mHGP:
cos(mHGP) = GP / GH = 12 / 13
Then, we can find the sine of mHGP using:
sin(mHGP)^2 + cos(mHGP)^2 = 1
sin(mHGP)^2 + 144/169 = 1
sin(mHGP)^2 = 25/169
sin(mHGP) = 5/13
If we draw the height of the triangle GPH relative to the side GH, we have:
sin(mHGP) = height / GP
5 / 13 = height / 12
height = 60/13
The triangles GPH and APB are similar (using the case angle-angle), so we can use this relation to find the height 'h2' of the triangle APB:
height / (h2+height) = GH / AB
(60/13) / (h2 + (60/13)) = 13/39 = 1/3
180 / 13 = h2 + (60/13)
h2 = 120/13
Then the area of the parallelogram is:
Area = AB * h2 = 39 * 120/13 = 360 in2
A password needs to be set up. Which method would have the highest number of
outcomes possible?
Answer:
the permutation of the alphabet or mixed (digits and letters)
Step-by-step explanation:
We are asked which method gives the greatest number of possible results when you want to configure a password, in this case our option is through combinations or permutations.
In a password the order matters, therefore it would be by the permutations method.
When creating a password it can be created with digits or letters, in general terms, digits are in less quantity than letters, therefore the greatest possible number would be through the permutation of the alphabet.
Although if you can do a mixed password, the result could have a higher number of outcomes
Can someone help me with this problem? {18 points}
Answer:
Square = 2
Triangle = 3
Circle = 1
= 7
Step-by-step explanation:
1 square = 2
2 × 2 × 2 = 8
1 triangle = 3
2 × 3 × 3 × 3 = 54
1 circle = 1
2 × 3 × 1 × 1 = 6
1 + 2 × 3 = 7
Penny sells knitted scarves for 12$ each. The cost of supplies to make each scarf is x dollars. How much profit will Penny make if she sells y scarves?
Answer:
If I'm guessing, you're supposed to write an equation. So the answer would be yx + 12y.
Step-by-step explanation:
Answer:
the answer is y(12-x)
Step-by-step explanation:
i took the text and it said i got it right hope i helped have a great day/night and so soorry if i get it wrong byee
how to solve 4(7-3x)=7(4-2x)
Answer:
Step-by-step explanation:
First, you distribute the 4 and 7 to the stuff inside the parentheses 28 - 12x = 28 - 14x then add 28 to both sides -12x = -14x then add 14x to both sides 2x = 0 then divide both sides by 2 x = 0
Answer:
x=0
Step-by-step explanation:
4(7-3x)=7(4-2x)
Distribute
28 -12x = 28 -14x
Subtract 28 from each side
-12x = -14x
Add 14x to each side
-12x+14x = -14x+14x
2x=0
x =0
A number, y, is equal to the difference of a larger number and 3. The same number is one-third of the sum of the larger number and 9. Which equations represent the situation? A. x + y = 3 and x minus 3 y = negative 27 B. x + y = 3 and x minus 3 y = negative 9 C. x minus y = 3 and x minus 3 y = negative 27 D. x minus y = 3 and x minus 3 y = negative 9
Answer:
D. x - y = 3 and x - 3 y = - 9
Step-by-step explanation:
The descriptions above describe the equation of choice D, so I pick this answer.
Answer:
D
Step-by-step explanation:
just took the test
For every 168 ice cream cones made 6 will break.if 392 ice cream cones are made what is the greatest number of cones that will break?
Answer:
Closest answer I could get was 12
hi can anybody help me with this i will mark them as brainliest
Answer:
5.75 cm²
Step-by-step explanation:
→ Utilise the area of a triangle formula
Area of a triangle = 0.5 × Base × Height
→ Identify base and height in the triangle
Base = 4.6 cm
Height = 2.5 cm
→ Substitute in the values into the area of a triangle formula
Area of a triangle = 0.5 × 4.6 × 2.5
→ Simplify
Area of a triangle = 5.75 cm²
Area of a triangle = 1/2 x base x height
= 1/2 x 4.6 x 2.5
= 5.75 sq. cm
Anyone can Answer 20x + 40 = 80 clear x please
Answer:
X=2
Step-by-step explanation:
20x+40=80
20x+40-(80)=0
20x-40=0 20x=40
x=40/20
X=2
How does a male get circumcised?
Answer: the excess skin is surgically removed
Step-by-step explanation:
Answer:
Step-by-step explanation:
two parallel incisions are made around the penis—one upstream from the skin that's set to be removed and one downstream. Then, we unwrap the excess skin from the penis and sew the two remaining edges back together.
the bearing of m from N is 70 degree what is the bearing gor N from M ?
Answer:
250°
Step-by-step explanation:
The bearing of N from M is 70° + 180° = 250°
The average wage for an electrician in CA is $25.47/hour. That is 11% above the national average. What is the national average?
Answer:
$22.95/hour.
Step-by-step explanation:
It is given that the average wage for an electrician in CA is $25.47/hour. That is 11% above the national average.
Let as consider x be the national average.
11% above the national average is
[tex]x+\dfrac{11}{100}x=x+0.11x=1.11x[/tex]
The average wage for an electrician in CA is 11% above the national average. So,
[tex]1.11x=25.47[/tex]
Divide both sides by 1.11.
[tex]x=\dfrac{25.47}{1.11}[/tex]
[tex]x=22.945945...[/tex]
[tex]x=22.95[/tex]
Therefore, the national average is $22.95/hour.
Answer: 22.95
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST
Answer:
3.9
Step-by-step explanation:
cost = 24.40
subtract the cost of beads from the total cost.
24.40-8.8=15.6
divide that by four because there are 4 necklaces
15.6/4=3.9
Which system of inequalities is shown?
Answer:
I'm 90 percent sure the answer is A.
Step-by-step explanation:
Adriana works as a purchasing manager at a trading firm and earns a salary of 60,000 she has deductions of 3000 and tax credit of a 5000 and she pays an annual tax of 6000 what is your annual disposable income 57,000 46,000 55,000 52,000
Answer:
46,000
Step-by-step explanation:
What is the coordinate of point P that lies along the directed line segment from Q(2,5) to R7, 12) and partitions the segment in the ratio of 3 to 2?
Your answer.
0 (3, 42)
O(4.5, 8.5)
O (5,9.2)
O (5,7)
Clear answer
Answer:
Step-by-step explanation:B
The diameter of a sphere is 2 ft. What is the sphere's volume? Round to the nearest tenth.
A) 4.2 ft3
B) 8.1 ft3
C) 16.8 ft3
D) 33.5 ft3
Answer:
4.19 ft ^3 or A.
Step-by-step explanation:
Answer:
A) 4.2 ft3Step-by-step explanation:
option a is correct ✔✔✔
ANYONE HELP, WILL GIVE BRAINLIEST ANSWER
Write the following phrase as an algebraic expression and simplify if possible. Let x represent the unknown number.
Double a number, minus the sum of the number and two
Answer:
x - 2
Step-by-step explanation:
Rewrite this symbolically: "Double a number, minus the sum of the number and two"
Let x represent the unknown number.
Then: 2x - (x + 2), or 2x - x - 2, or x - 2
can you please tell me what is 7+(-2)=?
Answer:
5
Step-by-step explanation:
Reminder
+ + = +
- + = -
+ - = -
7+(-2)
=7-2
=5
Hope my answer helps
Can you be my friend
[tex]answer = 5 \\ solution \\ 7 + ( - 2) \\ = 7 - 2 \\ = 5 \\ you \: have \: to \: remember \: these \: rules \\ ( + ) \times ( + ) = ( + ) \\ ( - ) \times ( - ) = ( + ) \\ ( + ) \times ( - ) = ( - ) \\ ( - ) \times ( + ) = ( - ) \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
please help, i need to pass. which function represents the inverse of function f below?
Answer:
B
Step-by-step explanation:
If you switch the x and y you can solve for the inverse by solving for y like this:
x=3y+5
3y=x-5
y=(x-5)/3
which can be rewritten as B.
What is the value of [1.1]? –2 –1 0 1
Answer:
The answer is -2.
Step-by-step explanation:
Answer:
-2 :D
Step-by-step explanation:
Just did the test:)
Will Mark Branliest What is the approximate mean absolute value for the data shown in the dot plot? 1.09 0.92 2 6
Answer:
Population size:11
Mean (μ): 6
Mean Absolute Deviation (MAD): 1.09
Two jokers are added to a 52 card deck and the entire stack of 54 cards is shuffled randomly. What is the expected number of cards that will be strictly between the two jokers?
Answer: 52/3
Step-by-step explanation:
Each card has an equal likelihood of being either on top of the jokers, in between them,
or below the jokers. Thus, on average, 1/3 of them will land between the two jokers.
Answer:
52/3
Step-by-step explanation:
The probability that they will be landed on is 52/3
help me pls :((((((((((
Answer:
1040ft
Step-by-step explanation:
17x20
15x8x2
15x20
8x20
add it all up and u will get the ans :)
Evaluate f(-4) for the function f(x) = 5 - X.
Answer:
9Solution,
[tex]f(x) = 5 - x \\ f( - 4) = 5 - ( - 4) \\ \: \: \: \: \: \: \: \: \: \: \: = 5 + 4 \\ \: \: \: \: \: \: \: \: \: = 9[/tex]
hope this helps....
Good luck on your assignment...
I need help pleassseee
Answer:
The length of the radius is 3cm.
Step-by-step explanation:
Given that a circle is inscribed in a square. The side of the circle touches the side of the square which is the diameter. So the diameter of circle is 6cm, in order to find it's radius, you have to duvide it by 2 :
[tex]radius = diameter \div 2[/tex]
[tex]radius = 6 \div 2[/tex]
[tex]radius = 3cm[/tex]
Answer:
[tex]6^{2} - 3^{2} \pi[/tex] = area of the black 7.725666
[tex]x^{2} - r^{2} \pi[/tex]
area of square - area of circle
the diameter of the circle is 6 and half that is the radius = 3
Which is the value of the expression (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed? 1 2 8 10
Answer: B: 2
Step-by-step Explanation
Answer:
C, 8
Step-by-step explanation:
I took the test on edge 2021