The GCF of numbers is the greatest common factors between the numbers
The GCF of the years is 1
How to determine the GCFThe intervals are given as: 13 years and 17 years
Factor both intervals (i.e. 13 and 17)
13 = 1 * 13
17 = 1 * 17
The common factor between both products is 1
So, we have:
GCF = 1
Hence, the GCF of the years is 1
Read more about GCF at:
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Use the area formula
(b1 + b2) x h ➗ 2 to solve.
If a trapezoid has a base of 8, a base of 3, and a height of 2, What is its area?
Pls help me find my answer
Answer:
11
Step-by-step explanation:
b1 = 8
b2= 3
h = 2
(8+3) = 11
11 x 2 = 22
22 ÷ 2 = 11
Find the coordinates of the point at which the normal to the curve y = x ^ 2 at x = 1 meets the curve again
Answer:
[tex](-\frac{3}{2},\frac{9}{4})[/tex]
Step-by-step explanation:
A normal line is a line perpendicular to the tangent line, so we must take the derivative of the function to find the slope of the tangent line, and then take the opposite reciprocal of this slope, to find the slope of the normal line. The equation of a normal line will be in the form of [tex]y=mx+b[/tex]:
[tex]f(x)=x^2\\\\f'(x)=2x\\\\f'(1)=2(1)\\\\f'(1)=2[/tex]
Hence, the opposite reciprocal is [tex]-\frac{1}{2}[/tex], which is our slope for the normal line. Now, we find the y-intercept by plugging in the given coordinate point [tex](1,1)[/tex] since [tex]f(1)=1^2=1[/tex]:
[tex]y=-\frac{1}{2}x+b\\\\1=-\frac{1}{2}(1)+b\\ \\1=-\frac{1}{2}+b\\ \\b=\frac{3}{2}[/tex]
Thus, the equation of the normal line is [tex]y=-\frac{1}{2}x+\frac{3}{2}[/tex]. Using this information, we can now find the coordinates where the normal of the curve at x=1 meets the curve again:
[tex]x^2=-\frac{1}{2}x+\frac{3}{2}\\ \\ x^2+\frac{1}{2}x-\frac{3}{2}=0\\ \\ 2x^2+x-3=0\\\\(x-1)(2x+3)=0\\\\x=1,\: x=-\frac{3}{2}[/tex]
Since we only care about [tex]x=-\frac{3}{2}[/tex] since [tex]x=1[/tex] was already accounted for, the y-coordinate would be:
[tex]y=x^2\\\\y=(-\frac{3}{2})^2\\\\y=\frac{9}{4}[/tex]
Therefore, the coordinates are [tex](-\frac{3}{2},\frac{9}{4})[/tex].
In the graph attached below, you can see the tangent line [tex]y=2x-1[/tex] and how it is perpendicular to [tex]y=\frac{1}{2}x-\frac{3}{2}[/tex].
the formula E =15h+0.05s represent a salesperson total earnings ,E, where h represents the number of hours she works and s represents the amount of sales in dollars. what is the salesperson totals earnings if she works 36 hours and has sales of 10,000
Answer:
1040
Step-by-step explanation:
substitute the given information
h = 36
s = 10,000
E = 15 x 36 + 0.05 x 10,000
E = 540 + 500 = 1040
1/4c - 1 + 1/4c ≥ 3
Answer please
Answer:
c ≥ 8
Step-by-step explanation:
1/4c − 1 + 1/4c ≥ 3
Step 1: Add 1/4 to 1/4, since they are on the same side of the equation
1/4 + 1/4c - 1 ≥ 3
1/4 + 1/4 = 1 + 1 / 4
= 2/4
= 1/2
Step 2: Put together the equation
1/2c - 1 ≥ 3
Step 3: Add 1 to both sides.
1/2c − 1 + 1 ≥ 3 + 1
1/2c ≥ 4
Step 4: Multiply both sides by 2.
2 × 1/2c ≥ 2 × 4
c ≥ 8
PLEASE SOLVE AND CHECK. SHOW COMPLETE SOLUTION
Answer:
4/3 [tex]\geq[/tex] x
Step-by-step explanation:
[tex](\sqrt{x+4})^ {2} \geq (2\sqrt{x})^{2}\\[/tex]
x + 4 [tex]\geq[/tex] 4x
4 [tex]\geq[/tex] 4x - x
4 [tex]\geq[/tex] 3x
4/3 [tex]\geq[/tex] x
Solution:
[tex]\sqrt{x + 4} \geqslant 2 \sqrt{x} [/tex]
Square both sides.[tex] = > ( \sqrt{x + 4)} ^{2} = (2 \sqrt{x} ) ^{2} \\ [/tex]
In the LHS, square and square root gets cancelled out. In the RHS, do the square.[tex] = > x + 4 \geqslant {2}^{2} x \\ = > x + 4 \geqslant 4x[/tex]
Transpose x to the RHS.[tex] = > 4 \geqslant 4x - x \\ = > 3x \leqslant 4 [/tex]
Now, divide both sides by 3.[tex] = > \frac{3x}{3} \leqslant \frac{4}{3} \\ = > x \leqslant \frac{4}{3} [/tex]
Answer:
[tex]x \leqslant \frac{4}{3} [/tex]
Hope you could understand.
If you have any query, feel free to ask.
Calculate the simple interest on a R5 000 loan for 3 years at 8.5% p.a. interest.
Answer:
R1275
Step-by-step explanation:
simple interest = (5000*3*8.5)/100
simple interest = 127500/100
simple interest = 1275
Find the perimeter of a rectangle with a length of 3.5 meters and a width of 8 meters.
(P=21+2w)
Answer:
23
Step-by-step explanation:
the formula to calculate perimeter of a rectangle is 2(l+b) so its answer will be 23
perimeter of rectangle
=2(l+b)
=2(3.5+8)
=2(11.5)
=23meters
Write the number for one million nine thousand .
thanks for any help!
Answer:
the answer is c
Step-by-step explanation:
Michael bought $75 worth of shoes before the sales tax was added. His sales tax was $5.25. What was the tax rate?
Answer:
7%
Step-by-step explanation:
(2,5) and (3,7)
slope: 2
what is the point slope form ?
what is the slope intercept form ?
Answer:
equation in slope intercept form: y = 2x +1
Step-by-step explanation:
given coordinates = (2,5) and (3,7)find slope,m = (y2 - y1) / (x2 - x1)= (7 - 5) / ( 3 - 2)
= 2
using the formula: y - y1= m( x - x1 ): y = 2x +1
equation in slope intercept form:
[tex]y = 2x +1[/tex]
given coordinates:
[tex](2,5) and (3,7)[/tex]
find slope,m:
[tex]\frac{y2 - y1}{x2-x1}= \frac{7-5}{3-2} = 2[/tex]
using the formula:
[tex] y - y1= m(x-x1) : y-5=2(x-2)[/tex]
[tex]y = 2x +1[/tex]
2:5 ratio. if there are more than 50 marbles in the bag, what is the minimum number of marbles that can be in the bag?
Answer:
sum of ratio term = 2+5
= 7
first we have to find the value of 2 in ratio term
50 x 7/2
175
now, we have to find value of 5 in ratio term
50 x 7/5
70
addition of both the value of 2 and 5 in ratio term
175+70
245
hence, your answer is 245 marbles
plz mark me as brainlist plz bro/sis plz i need 5 brainlist to level up plz
Half as many as 7 more than a number
Answer:
less than twice the number
Step-by-step explanation:
- A total of $12,000 is deposited into two accounts. One
account pays 9% simple interest while the second account
pays 6% simple interest. How much should be invested in
each account so that the total interest after 1 year is $810.
Answer:
It would seem that the third answer would be right but I am only 60% sure if you do not know the answer for sure, choose C but if you would rather get the 100% answer just wait
Step-by-step explanation:
Given points A(−2,0), B(−5,3), C(−9,−1), P(7,6), Q(4,0), and R(−4,4), which of the following proves that △ABC~△PQR?
Answer options:
By the Distance Formula,AB=32–√, BC=42–√, and CA=52–√.Also, PQ=35–√, QR=45–√, and RP=55–√.Therefore, ABPQ=BCQR=CARP=2√5√=10√5, and therefore, △ABC∼△PQR by SAS ∼.
By the Distance Formula,AB=50, BC=32, and CA=18.Also, PQ=125, QR=90, and RP=45.Therefore, ABPQ=BCQR=CARP=25, and therefore, △ABC∼△PQR by SSS ∼.
By the Distance Formula,AB=18, BC=32, and CA=50.Also, PQ=45, QR=90, and RP=125.Therefore, ABPQ=BCQR=CARP=25, andtherefore, △ABC∼△PQR by SAS ∼.
By the Distance Formula,AB=32–√, BC=42–√, and CA=52–√.Also, PQ=35–√ QR=45–√, and RP=55–√.Therefore, ABPQ=BCQR=CARP=2√5√=10√5,and therefore, △ABC∼△PQR by SSS ∼.
Based on the SSS similarity theorem, △ABC ~ △PQR because AB/PQ = BC/QR = CA/RP = √2/√5 = √10/5 (option D).
The SSS Similarity TheoremTwo triangles having three pairs of sides that are proportional can be proven to be similar by the SSS similarity theorem.
If the triangle ABC and triangle PQR are similar, their corresponding sides will be proportional, meaning that: AB/PQ = BC/QR = CA/RP.
Therefore, using the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], the sides of each triangle is found.
Therefore, it shows that:
AB/PQ = BC/QR = CA/RP = √2/√5 = √10/5
Therefore, based on the SSS similarity theorem, △ABC ~ △PQR because AB/PQ = BC/QR = CA/RP = √2/√5 = √10/5 (option D).
Learn more about the SSS similarity theorem on:
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Which of these characteristics do a rhombus and a rectangle always have in common. Choose one.
1). opposite sides with equal length
2).all angles are right angles
3).all sides with equal length
Answer:
A) opposite sides with equal length.
Step-by-step explanation:
Found on another problem answered by Abdulazeez10
The characteristics a rhombus and a rectangle always have in common is opposite sides with equal length.
The right option is opposite sides with equal length
From the question,
We are to determine which of the given characteristics do a rhombus and a rectangle always have in common.
To determine which of the characteristics, we will list some of the characteristics of the two shapes
Characteristics of a Rhombus
All sides are of equal length
Opposite sides are parallel
Opposite angles are congruent
Diagonals intersect perpendicularly
Consecutive angles are supplementary
Characteristics of a Rectangle
Opposite sides are congruent and parallel
Diagonals bisect each other
Each of the interior angles is a right angle
Diagonals are congruent
Now, from above,
We have that all the sides of rhombus are equal in length, which makes the opposite sides to be equal as well.
Also, among the characteristics of a rectangle is that, opposite sides are equal in length
Hence, the characteristics a rhombus and a rectangle always have in common is opposite sides with equal length. The right option is opposite sides with equal length
https://brainly.com/question/12833352
Help please asap and thank you
Answer:
x: 2.25 in
y: 6 in
Step-by-step explanation:
For value of x:
[tex]\tt \frac{x}{9in} =\frac{3in}{12in}[/tex]
Cross-multiply,
[tex]\tt x=2.25in[/tex]
Now, for the value of y:
[tex]\tt \frac{y}{9in} =\frac{8in}{12in}[/tex]
Cross-multiply,
[tex]\tt y=6in[/tex]
This morning, Joe's car had 28.43 gallons of fuel. Now, 3.7 gallons are left. How much fuel did Joe use? Please show step by step.
PART A
a=total amount
c=cans of oil
g=gasoline
a=2.85g+3.15c
PART B
a=2.85(8.4)+3.15(6)
a=23.94+18.90
a=42.84
what fraction is it after subtracting one from both numerator and denominator becomes 5/17
Answer:
6/18
Step-by-step explanation:
To find the answer to that, you reverse the subtraction. Start with 5/17 and add 1 to both numerator and denominator. You get ...
[tex]\dfrac{5+1}{17+1}=\boxed{\dfrac{6}{18}}[/tex]
Wires are usually made from materials, copper and plastic. Explain why
please need this right now because I'm not doing my homework but my teacher said that she's gonna ask me in 20 min so I really need this answer pls pls pls pls pls pls
Answer:
because aluminum and copper are excellent conductors of electricity. the plastic can prevent short circuit while getting on ground or when it brushes against another wire.
A triangle has a side length of 10 inches and a side length of 3 inches. What could be the length in inches of the third side of the triangle?
The ratio of marbles to sticks is 5:8. The ratio of sticks to stones is
5:7. What is the reduced ratio of marbles to stones?
Answer:
25 : 56Step-by-step explanation:
Let the marbles = x, sticks = y, stones = z.
Given:
x / y = 5/ 8and
y / z = 5/ 7Solve for x and z as per above ratios:
x = 5y / 8z = 7y / 5Find the ratio:
x / z = 5y / 8 ÷ 7y / 5x/ z = 5y / 8 × 5 / 7yx / z = 25 / 56Find the domain and range of this relation? (Assume there are arrows at both ends of the relation.)
Answer:
Domain: ( -∞ , ∞ )
Range: ( -∞ , 4 ]
Step-by-step explanation:
Hi there!
The domain tells us the possible x-values of a function. Because there are arrows at the end of each side, it means the graph is travelling infinitely to both the left and the right side. This means the the domain is all real numbers, meaning that for any value of x, there is a real value for y.
( -∞ , ∞ )
The range tells us the possible y-values of a function. Both sides of the graph are travelling infinitely downwards, starting from 4.
( -∞ , 4 ]
I hope this helps!
Given g(x)=−x−2, solve for x when g(x) =0
Answer:
anser is 2x nark me as brainlest please
Graph attached
g(0)=0-2=-227. Find the slope of the line. (1 point)
A.2
B.-2
C.3
D.-1
Answer:
Slope = -2Step-by-step explanation:
Step-1: Choose any two points on the line.
My chosen points: (-3,3) and (0,-3)Step-2: Use y₂ - y₁/x₂ - x₁ to find the slope.
=> -3 - 3/0 - (-3) => -6/3Step-3: Divide.
=> -2 = SlopeHence, the slope is -2.
How do credit cards work? (Own words)
a credit card it like a short term loan and you a a certain amount of credit on it than you have to pay back how ever much credit you used to the credit card company
Step-by-step explanation:
ok im a 100 percent sure but ill give it a shot
Evaluate 14 – 4 – 2h when p=1 and h=4.
Answer:
14 – 4 – 2h = 2
Step-by-step explanation:
14 – 4 – 2h
fill in 4 for h
14 - 4 - 2(4)
14 - 4 - 8
10 - 8
2
hope this helps!!
Write a numerical expression to represent "the difference of 336 and 240 divided
by 8." Then evaluate your expression.
(Don’t ask for a picture)
Answer:
306
Step-by-step explanation:
what is the sum of six hundred seven and two thousand, three hundred ninety three
Answer:
3000
Step-by-step explanation:
Convert them into numbers: 607 + 2393 = 3000.
Answer:
The answer is
→ 3,000 is the sum.
Step-by-step explanation:
Were being asked what is the sum of six hundred seven and two thousand, three hundred ninety three/607 and 2,393
Well if it's asking us for the sum, then we fore SURE have to use addition.
[tex]607+2,393=3,000[/tex]
Therefore, 3,000 is your answer to this question.
Hope this helped! :^)
[tex]48x2y−12xy2−60x2y2[/tex]48x2y−12xy2−60x2y2
