Problem 1
Answer: Choice A[tex]f(n) = 59,000\left(1.08^{n-1}\right)[/tex]
---------------------------
Explanation:
The right hand side for choice A is in the form [tex]a(r)^{n-1}[/tex] which is the nth term of a geometric sequence.
a = first term = 59,000 = starting salaryr = common ratio = 1.08 = tells us how the salary increases year to yearThe 1.08 represents an increase of 8% because,
1.08 = 1 + 0.08 = 100% + 8% = 108%
=======================================================
Problem 2
Answer: Choice C[tex]\frac{(y-60)^2}{144} + \frac{x^2}{100} = 1[/tex]
---------------------------
Explanation:
The ellipse is 20 inches wide, which cuts in half to 10 inches. This is the corresponding value plugged into the denominator of the 'x' fraction, as x deals with the horizontal component. So we'll have a^2 = 10^2 = 100 in the denominator under the x term. Only choice C has this, so this is the answer we go for. For the vertical component, we cut 24 in half to get 12, then square it to get 144, which explains the denominator for the y term.
=======================================================
Problem 3
Answer: Choice C30 feet; major axis
---------------------------
Explanation:
Pick the larger denominator 225. Apply the square root to get 15. Then double this value to land on 30. This is the length of the major axis which is the longer axis through the center of the ellipse. The major axis also passes through both foci.
Let's say points P and Q are any two random points on the ellipse. The longest segment PQ can get is 30 feet.
IS IT 60 CAN SOMEONE TELL DID I CLICK IT RIGHT ?
hi how have you been and i think u did get it right
The hypotenuse is NOT located across from the right angle
True or false
The statement, The hypotenuse is NOT located across from the right angle is false.
What is a right angled triangle?
A right-angled triangle is a type of triangle that has an angle that measures 90 degrees. The triangle has three sides. The hypotenuse is the longest side of a right-angled triangle. Other sides are the base and the length. The sum of sides in a a right-angled triangle is 180 degrees.
Please find attached an image of a right-angled triangle. To learn more about a triangle, please check: https://brainly.com/question/9329354
find all complex solutions of 3x^2-6x+1=0
Answer:
[tex]x=\frac{3+\sqrt{6} }{3}, \frac{3-\sqrt{6} }{3}[/tex]
Step-by-step explanation:
Let's see
[tex]\\ \rm\rightarrowtail 3x^2-6x+1=0[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{6\pm \sqrt{36-12}}{6}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{6\pm \sqrt{24}}{6}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{6\pm 2\sqrt{3}}{6}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{3+\sqrt{3}}{6}[/tex]
Given: -3x+y=1. Write the equation In general form Ax + By + C =0.
3x - y = -1
3x = y + 1 = 0
-3x + y -1=0
The given equations are 3x + y - 1 = 0 and 6x + 2y - 2 = 0.
So,
Equation I = (3x + y = 1) and
Equation II = (6x + 2y = 2)
= { 2(3x + y) = 2}
= 3x + y = 2/2
= 3x + y = 1
So, The given equations are 3x + y = 1 and 3x + y = 1.
Thus, there is one equation in two variables.
So, the given equations have an infinite number of solutions.
Answer:
1st option; 3x-y=-1
Step-by-step explanation:
-3x + y = 1
we can divide through by -1 so that the 'x' value is positive:
3x - y = -1
455,757,974,946,454 ×454,942,164,313,233.Plz help.
91929229
7373738292929202010100110010110
Please help with this question
Answer:
D
Step-by-step explanation:
The first equation would have to have a y-intercept of 4, and the second equation would have to have a y-intercept of -1.
-hope it helps
Answer: what the actual fudge is this?? i am a former harvard professer for math and I have never seen such a monstrocity of a math question, but the answer is the first one.
Step-by-step explanation:
-4x +8 = 24
What is the value of x in the equation?
8
4
-4
-8
Answer:
-4x+8=24
24-8
16/-4x
x= -4
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
-4x + 8 = 24
Subtract 8 from both sides to isolate the x.
-4x + 8 = 24
-8 -8
-4x = 16
Divide -4 from both sides to solve for x.
-4x = 16
/-4 /-4
x = -4
How to graph the table
(64/8/ 4 + 7 – 2) • 5 =
Answer:
35
Step-by-step explanation:
Let me know if I got it right
Don has seven pairs of shoes, three pairs of pants, and six shirts. If all items are compatible, how many different outfits can he wear?
Answer:
126
Step-by-step explanation:
There are 126 different ways he can wear the outfit.
What is Combination?The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant." Combining these two words indicates "Selection of things," where the order of the items is irrelevant.
Given:
Number of pairs of shoes= 7
Pants= 3 pairs
Shirts= 6
So, different outfits can he wear
= 7 x 3 x 6
= 21 x 6
= 126
Hence, there 126 different ways he can wear the outfit.
Learn more about combination here:
https://brainly.com/question/8969582
#SPJ5
help please please help
Answer:
24/35
Step-by-step explanation:
Hope this helps!:)
Which pair of triangles can be proven congruent by SAS?
Answer:
The first one
Step-by-step explanation:
SAS postulate says that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, then the one triangles are said to be congruent.
A fish swims 4 feet directly above a scuba diver. The fish suddenly dives to double its depth under the surface of the ocean. The fish dives to a depth of −34 feet.
What is the position of the scuba diver relative to sea level?Choose from the drop-down menu to correctly complete the statement.
The scuba diver is
Choose... 13,21,64,72
feet
Choose... above or below
sea level.
Answer:
21 above is the answer
Step-by-step explanation:
What is the sale price with 15% off? Original price: $110 of bears head phones
Answer:
93.5
Step-by-step explanation:
Yi = 4.0 + 1.5Xi
a. Interpret the Y intercept, b0.
Answer:
Divide each term in Y i = 4 + 1.5 X i by i and simplify.
Y = − 4 i + 1.5 X
Step-by-step explanation:
I need help with this, i did part of it but i'm desperate
Answer:
Let's add more steps.
step 6: angle AEB measures 360 - 90 -90 - 70 - 39 = 71° Reason, AECF is a quadrangonal and three of its angle measures 90, 90, and (70+39)
step 7: angles AEB and ABE are congruent: reason triangle ABE is isosceles since AE is conruent to AB
step 8 Angle BAE measures 180 -71-71 = 38°: by difference from the sum of the internal angles.
step 9: Angle BAD measures 90 - BAE = 90 - 38 = 52° Reason angles BAD and BAE are complementary.
QED
PLEASE HELP ME WITH THIS!!
Answer:
A 3x10^-6
Step-by-step explanation:
Find the greatest common factor of 6a^3b^2c^10 + 20c^10 – 8a^3b^2c^9
Answer: [tex]2c^9[/tex]
Step-by-step explanation:
I'm assuming this is the expression: [tex]6a^3b^2c^{10}+\:20c^{10}\:-\:8a^3b^2c^9[/tex]
[tex]\mathrm{Factor\:}6a^3b^2c^{10}[/tex] (Expand using 2's and 3's as they are the common factor in all terms)
[tex]2\cdot \:3\cdot \:a\cdot \:a\cdot \:a\cdot \:b\cdot \:b\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c[/tex]
[tex]\mathrm{Factor\:}20c^{10}[/tex] (5 needed to expand the coefficient)
[tex]2\cdot \:2\cdot \:5\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c[/tex]
[tex]\mathrm{Factor\:}8a^3b^2c^9[/tex]
[tex]2\cdot \:2\cdot \:2\cdot \:a\cdot \:a\cdot \:a\cdot \:b\cdot \:b\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c[/tex]
Common factors (terms that are in all expressions):
[tex]2\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c[/tex]
Simplify:
[tex]2c^9[/tex]
satellite makes 4 revolutions of the earth in one day. How many revolutions would it make in 6 1/2 days?
does y vary directly with x? if it does write an equation for the direct variation.
Answer:
No it does not
Step-by-step explanation:
Two points simplify to 1/6 whilst the other, 1/5
what is 5÷ 3 1/3 on khan academy
Answer:
1.5
Step-by-step explanation:
Hope this helped!
2 1/2+x=5 1/3 PLEASE HELP
Answer:
Step-by-step explanation:
2 1/2 + x = 5 1/3 Change the mixed numbers to improper fractions
5/2 + x = 16/3 The lowest common multiple is 6. Multiply by 6
5*3 + 6x = 16*2
15 + 6x = 32 Subtract 15 from both sides.
6x = 32 - 15
6x = 17 Divide by 6
6x/6 = 17/6
x = 2 5/6
Check
5/2 + 17/6 = 16/3
15/6 + 17/6 = 32/6
32/6 = 32/6 The question checks.
Three different sets of objects contain 2, 3, and 14 objects, respectively. How
many unique combinations can be formed by picking one object from each
set?
A. 28
B. 42
C. 84
D. 19
Answer:
C) 84
Step-by-step explanation:
Use the Fundamental Counting Principle, which states that if there are p ways to do one thing, and q ways to do another thing, then there are p×q ways to do both things. In this case, we have 2 ways to select one object from the first set, 3 ways to select one object from the second set, and 14 ways to select one object from the third set. So, we multiply and do 2*3*14=84
Therefore, there are 84 unique combinations
If the gross domestic product is currently 12,443.9 billion dollars and grows by 5 percent, how much will it be next year?
Answer:
12,448.9
Step-by-step explanation:
i'm sorry if this is wrong
What is the value of t in the equation 3(t − 4) = 2t + 1?
Answer: 13
Step-by-step explanation:
Distribute t.
Multiply 3 by each value in parentheses to get
3t - 12 = 2t + 1
Add 12 to both sides
3t = 2t + 13
Subtract 2t from both sides
t = 13
Answer:
t = 13
Step-by-step explanation:
[tex]3(t-4)=2t+1\\\\3t-12=2t+1\\\\t-12=1\\\\t=13[/tex]
If a learner’s permit holder is convicted of committing a moving violation, he/she
A must restart the 9 month waiting period to be eligible for a provisional license.
B must complete the Driver Improvement Program on line
C must wait until he/she is 21 to receive a driver’s license.
D none of the above.
Use logarithms to solve the equation 5^x = 3^(2x-1), giving your answer correct to 3 significant figures.
[tex]5^x = 3^{2x-1}\\\\\implies \ln(5^x) = \ln\left(3^{2x-1}\right)\\\\\implies x \ln 5 = (2x-1) \ln 3\\\\\implies x \ln 5 = 2x \ln 3 - \ln 3\\\\\implies 2x \ln 3 - x \ln 5 = \ln 3\\\\\implies x(2 \ln3 - \ln 5) = \ln 3\\\\\implies x =\dfrac{\ln 3}{2 \ln 3 - \ln 5} = 1.87[/tex]
The solution to the equation is x ≈ 1.864 (correct to 3 significant figures).
To solve the equation 5ˣ = 3²ˣ⁻¹ using logarithms, we'll take the logarithm of both sides to bring down the exponent. Since the bases are different (5 and 3), we can use either the natural logarithm (ln) or the common logarithm (log base 10). Let's use the natural logarithm (ln):
Take the natural logarithm (ln) of both sides:
ln(5^x) = ln(3²ˣ⁻¹)
Apply the logarithm rule: ln(a^b) = b * ln(a):
x * ln(5) = (2x - 1) * ln(3)
Expand the equation:
x * ln(5) = 2x * ln(3) - ln(3)
Move the terms with "x" to one side of the equation:
x * ln(5) - 2x * ln(3) = -ln(3)
Factor out "x" from the left side:
x * (ln(5) - 2 * ln(3)) = -ln(3)
Solve for "x":
x = -ln(3) / (ln(5) - 2 * ln(3))
Now, we can calculate the value of "x" using a calculator:
ln(3) ≈ 1.099
ln(5) ≈ 1.609
x ≈ -1.099 / (1.609 - 2 * 1.099) ≈ -1.099 / (1.609 - 2.198) ≈ -1.099 / (-0.589) ≈ 1.864
Therefore, the solution to the equation is x ≈ 1.864 (correct to 3 significant figures).
Learn more about natural logarithm from the link given below.
https://brainly.com/question/29154694
#SPJ2
A tree is 6 feet 7 inches tall. How tall is it in inches?
Answer:
79 inches
Step-by-step explanation:
1 foot equals 12 inches
6 feet = 6*12 = 72 inches
72+7=79
79 inches
Help plz 20 points question is in the pic
s=ut +1/2at
u=10 a= -2 t=1/2
what is the value of s
Answer: 4.5
Step-by-step explanation:
S= ut + 1/2(at)
S= 10(1/2) + 1/2(-2x1/2)
S= 5 + 1/2(-1)
S= 5 + (-.5)
S= 4.5