Answers
Answer:
x =8
Step-by-step explanation:
The angles are vertical angles which means they are equal
4x+112 = 9x+72
Subtract 4x from each side
112 = 5x+72
Subtract 72 from each side
40 = 5x
Divide each side by 5
40/5 =x
8 =x
Answer: [tex]x=8[/tex]
Step-by-step explanation: Because they are opposite angles, they can be assumed to be equal to each other. Therefore, you can set the two equations equal to each other, creating [tex]9x+72=4x+112[/tex], and from there you can subtract [tex]4x[/tex] as well as [tex]72[/tex] from both sides to get [tex]5x=40[/tex]. Then, divide both sides by [tex]5[/tex] to get [tex]x=8[/tex].
Related Questions
Please answer this correctly
Answers
Answer:
50%
OR
1/2
Step-by-step explanation:
The box and whisker plot shows the time spent from 4 to 6 hours is Quartile 1 to 3 which makes it 50%.
The radius of a circle is 4 miles. What is the length of a 45° arc?
45°
r=4 mi
Give the exact answer in simplest form.
Answers
Answer:
2π miles
Step-by-step explanation:
2πr is the formula for the circumference of a circle.
Using that formula, the circumference for this circle is 8π.
Since the circle's full angle is 360°, we can use a ratio to find out how long the 45° arc is.
° : length
360 : 8π
9 : 0.4π
45 : 2π
The 45° is 2π mi long.
A list of numbers begins iwth the number 6. Each number on the list is 10 more than -2 times the previous terms. what is the fourth number
Answers
Answer:
The fourth term is -18
Step-by-step explanation:
an = -2(an-1) +10
This is the recursive formula
a1 = 6
a2 = -2(a1) +10 = -2(6) +10 = -12+10 = -2
a3 = -2(a2) +10 = -2(-2) +10 = 4+10 = 14
a4 = -2(a3) +10 = -2(14) +10 = -28+10 = -18
problem decoded dude
follow meh
Let f(x)= x^3 −6x^2+11x−5 and g(x)=4x^3−8x^2−x+12. Find (f−g)(x). Then evaluate the difference when x=−3 x=−3 .
Answers
Answer: (f-g)(x)= -138
Step-by-step explanation:
Add 2/7 + 2/7 Is 4/7 the correct answer
Answers
Answer:
Yes
Step-by-step explanation:
The denominator always stays the same
Good Job!
Hope this helps :)
Answer:
yes 4/7 is the answer
Step-by-step explanation:
2/7+2/7
l.c.m is 7
2+2/7
4/7
Please answer this correctly
Answers
Answer:
60%
Step-by-step explanation:
In the spinner there are 5 numbers. 3 of them are odd and 2 of them are even and because each number has 1/5 chance of being chosen, you have a 3/5 chance of choosing an odd number. 3/5 = 60/100 = 60%
Farhan has three pieces of rope with lengths of 140cm, 168cm and 210cm. He wishes to cut all the three pieces of ropes into smaller pieces of equal length and that there is no leftover rope. (i) What is the greatest possible length of each of the smaller pieces of rope? How many smaller pieces of rope can he get altogether?
give correct answer
Answers
Answer:
The greatest possible length is 14 cm.
The total number of smaller pieces is 37.
Step-by-step explanation:
The greatest common factor of these three numbers is 14.
Total number of smaller pieces = 10+12+15 = 37
Best Regards!
What time did they arrive at the airport?
Answers
Answer:
32
Step-by-step explanation:
A rectangle is 4.2 centimetres wide and each diagonal is 8.6 centimetres long. What is the measure of the angle between a diagonal and the shorter side of the rectangle, to the nearest tenth of a degree?
Answers
Answer:
[tex] 60.8^\circ [/tex]
Step-by-step explanation:
First, let's check side lengths.
Using the Pythagorean theorem we can find the length of the other side of the rectangle.
a^2 + b^2 = c^2
4.2^2 + b^2 = 8.6^2
b^2 = 56.32
b = 7.5
The other side of the rectangle measures 7.5 cm, so now we know that 4.2 cm is indeed the shorter side of the rectangle.
For the angle in question, the 4.2 cm side is the adjacent leg.
The diagonal of 8.6 cm is the hypotenuse.
The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.
[tex] \cos \alpha = \dfrac{adj}{hyp} [/tex]
[tex] \cos \alpha = \dfrac{4.2~cm}{8.6~cm} [/tex]
[tex] \alpha = \cos^{-1} \dfrac{4.2~cm}{8.6~cm} [/tex]
[tex] \alpha = 60.8^\circ [/tex]
Angle bisectors $\overline{AX}$ and $\overline{BY}$ of triangle $ABC$ meet at point $I$. Find $\angle C,$ in degrees, if $\angle AIB = 109^\circ$.
Answers
Answer:
<C = [tex]38^{o}[/tex]
Step-by-step explanation:
Given that: <AIB = [tex]109^{o}[/tex]
<AIB + <BIX = [tex]180^{o}[/tex] (sum of angles on a straight line)
[tex]109^{o}[/tex] + <BIX = [tex]180^{o}[/tex]
<BIX = [tex]180^{o}[/tex] - [tex]109^{o}[/tex]
<BIX = [tex]71^{o}[/tex]
But,
<AIB = <YIX = [tex]109^{o}[/tex] (opposite angle property)
<XIB = <AIY = [tex]71^{o}[/tex] (opposite angle property)
Therefore,
[tex]\frac{A}{2}[/tex] + [tex]\frac{B}{2}[/tex] = [tex]71^{o}[/tex] (Exterior angle property)
[tex]\frac{A + B}{2}[/tex] = [tex]71^{o}[/tex]
A + B = [tex]142^{o}[/tex]
A + B + C = [tex]180^{o}[/tex] (sum of angles in a triangle)
[tex]142^{o}[/tex] + C = [tex]180^{o}[/tex]
C = [tex]180^{o}[/tex] - [tex]142^{o}[/tex]
C = [tex]38^{o}[/tex]
Thus, angle C is [tex]38^{o}[/tex].
If a coin is tossed 3 times, and then a standard six-sided die is rolled 4 times, and finally a group of four cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?
Answers
Answer:
67,365,043,200
Step-by-step explanation:
A coin toss has 2 possible outcomes. A coin tossed 3 times has 2³ = 8 possible permutations.
A standard die has 6 possible outcomes. A die rolled 4 times has 6⁴ = 1296 possible permutations.
The number of ways 4 cards can be chosen from a deck of 52 without replacements is 52×51×50×49 = 6,497,400.
The total number of possible outcomes is:
8 × 1296 × 6,497,400 = 67,365,043,200
Five adult tickets and three child tickets for a movie costs £55. The cost of buying two adult tickets and three child tickets is £31. Work out each of the costs of an adult and child ticket.
Answers
Answer:
adult £8child £5Step-by-step explanation:
If you look at the numbers you are given, you see that the first purchase has 3 more adult tickets than the second purchase, and its cost is £24 more. This means an adult ticket costs £24/3 = £8.
Two adult tickets will cost 2×£8 = £16, so three child tickets cost ...
£31 -16 = £15
Each child ticket is then £15/3 = £5.
An adult ticket costs £8; a child ticket costs £5.
Find the original price of a pair of shoes if the sale price is $144 after a 25% discount.
Answers
Answer:
$192
Step-by-step explanation:
1: Subtract the discount from 100% then divide the sale price by this number (100%-25%=75%, $144/75%=$192)
hope this helped
Answer:
$192
Step-by-step explanation:
144 is actually 75% from the original price x:
0.75 x=144
x=144/0.75= $192
check : 192*0.25= $ 48 discount
192-48= $ 144 price of the shoe
how to solve this? please help me
Answers
Answer:
tangent: y = 2x -2normal: y = -1/2x +3Step-by-step explanation:
Differentiating implicitly, you have ...
-y²·dx +(4-x)(2y)dy = 3x²·dx
So, the slope is ...
dy/dx = (3x² +y²)/(2y(4 -x))
At (x, y) = (2, 2), the slope of the curve is ...
dy/dx = (3·2² +2²)/(2·2(4 -2)) = 16/8 = 2
In point-slope form, the equation of the tangent line is then ...
y = m(x -h) +k
y = 2(x -2) +2
y = 2x -2 . . . . equation of tangent line
__
The normal to the curve is perpendicular to the tangent at the same point. The slope of the perpendicular line is the negative reciprocal of the tangent's slope, so is -1/2.
y = (-1/2)(x -2) +2
y = -1/2x +3 . . . equation of normal line
A company borrows $60,000 by signing a $60,000 8% 6 year note that requires equal payments of $12979 at the end of each year. The first payment will record interest expense of $4800 and will reduce principal by
Answers
Answer: $8179
Step-by-step explanation:
The principal is the amount of money that is invested at a particular interest rate.
In this scenario, we are informed that a company borrows $60,000 by signing a $60,000 8% 6 year note that requires equal payments of $12979 at the end of each year.
Since the first payment will record interest expense of $4800, then for us to get the amount that the principal will be reduced by, we subtract the interest expense made from the equal payments that are made at each year end. This will be:
= $12979 - $4800
= $8179
The results of a survey of common allergies was organized into a Venn diagram. Circles D, C, and P overlap. Circle D contains 15. Circle C contains 18. Circle P contains 9. The overlap of circles C and D contains 7. The overlap of circles D and P contains 12. The overlap of C and P contains 10. The overlap of all 3 circles contains 1. Answer the questions about the following sets: D = {x | x is a person allergic to dogs}; C = {x | x is a person allergic to cats}; P = {x | x is a person allergic to pollen} How many people are not allergic to any of the three choices? How many people are allergic to all three choices? How many people are allergic to both dogs and cats but not allergic to pollen? How many people are allergic to cats only?
Answers
Answer:
first blank: 22
second blank: 1
third blank: 7
fourth blank: 18
Step-by-step explanation:
edge 2020
Answer: 22, 1, 7, 18
The results of a survey of common allergies was organized into a Venn diagram.
Circles D, C, and P overlap. Circle D contains 15. Circle C contains 18. Circle P contains 9. The overlap of circles C and D contains 7. The overlap of circles D and P contains 12. The overlap of C and P contains 10. The overlap of all 3 circles contains 1.
Answer the questions about the following sets:
D = {x | x is a person allergic to dogs}; C = {x | x is a person allergic to cats}; P = {x | x is a person allergic to pollen}
How many people are not allergic to any of the three choices?
✔ 22
How many people are allergic to all three choices?
✔ 1
How many people are allergic to both dogs and cats but not allergic to pollen?
✔ 7
How many people are allergic to cats only?
✔ 18
The Environmental Protection Agency must visit nine factories for complaints of air pollution. In how many ways can a representative visit five of these to investigate this week? Since the representative's travel to visit the factories includes air travel, rental cars, etc., then the order of the visits will make a difference to the travel costs.
Answers
Answer:
The number of ways is [tex]\left 9}\atop } \right. P _5 = 15120[/tex]
Step-by-step explanation:
From the question we are told that
The number of factories visited is [tex]n = 9[/tex]
The number of factories to be visited by a representative r = 5
The number of way to visit the 5 factories is mathematically represented as
[tex]\left 9}\atop } \right. P _5 = \frac{9!}{(9-5)!}[/tex]
Where P represents permutation
=> [tex]\left 9}\atop } \right. P _5 = \frac{9 \ !}{4\ !}[/tex]
=> [tex]\left 9}\atop } \right. P _5 = \frac{9 *8*7 * 6 * 5 * 4!}{4\ !}[/tex]
=> [tex]\left 9}\atop } \right. P _5 = 15120[/tex]
Suppose that you buy a two-year 8% bond at its face value.
A. What will be your nominal return over the two years if inflation in 3% in the first year 5 % in the second year. What will be your real return?
B. Suppose that the bond is a TIPS. What will be your real and nominal returns?
Answers
Answer:
Real Rate of Return = 4.9% and Nominal rate = 0.08 or 8%
Real Rate of Return = 2.9% and Nominal rate = 0.081 or 8.1%
real rate = 5 % and Nominal rate = 0.0815 or 8.15%
real rate = 3% and Nominal rate = 0.0815 or 8.15%
Step-by-step explanation:
given data
time period = 2 year
Coupon rate = 8% = 0.08
Inflation rate 1st year = 3% = 0.03
Inflation rate 2nd year = 5% = 0.05
solution
we get here Real Rate of Return that is express as
Real Rate of Return = (Coupon Rate - Inflation rate) ÷ (1+Inflation rate) .........1
so that here 1st year Real return will be
Real Rate of Return = (0.08 - 0.03) ÷ (1+0.03)
solve it we get
Real Rate of Return = 4.9%
and
(1 + nominal rate) = (1 + real rate) × (1 + inflation rate) ............2
(1 + nominal rate) = (1 + 0.049) × (1 + 0.03)
Nominal rate = 0.08 or 8%
and
for 2nd year Real return will be
Real Rate of Return = (0.08 - 0.05) ÷ (1+0.05)
solve it
Real Rate of Return = 2.9%
and
(1 + nominal rate) = (1 + real rate) × (1 + inflation rate) ............3
(1 + nominal rate) = (1 + 0.029) × (1 + 0.05)
Nominal rate = 0.081 or 8.1%
and
now for the bond Treasury Inflation-Protected Securities, we get real and nominal return that is
for 1st year
Real rate = Coupon rate - Inflation ...............4
Real rate = 0.08 - 0.03
real rate = 0.05
and
(1 + nominal rate) = (1 + real rate) × (1 + inflation rate) ................5
(1 + nominal rate) = (1 + 0.05) × (1 + 0.03)
so
Nominal rate = 0.0815 or 8.15%
and for 2nd years it will be
Real rate = Coupon rate - Inflation ....................6
Real rate = 0.08 - 0.05
real rate = 0.03
and
(1 + nominal rate) = (1 + real rate) × (1 + inflation rate) ...................7
(1 + nominal rate) = (1 + 0.03) × (1 + 0.05)
so
Nominal rate = 0.0815 or 8.15%
what is the recursiveformula for this geometric sequence? 4,-12,36,108
Answers
Answer:
a[1] = 4
a[n] = -3·a[n-1]
Step-by-step explanation:
The sequence given is not a geometric sequence, since the ratios of terms are -3, -3, 3 -- not a constant.
If we assume that the last given term is supposed to be -108, then the common ratio is -3 and each term is -3 times the previous one. That is expressed in a recursive formula as ...
a[1] = 4 . . . . . . . . . . . first term is 4
a[n] = -3·a[n-1] . . . . . each successive term is -3 times the previous one
8. Suppose Betty saves $200 each month in her 401(k) account. How much less will her monthly take-home pay be? (Assume a combined 20% state and federal income tax rate, as in the example.)
Answers
Note: Check the file attached below for the complete question
Answer:
Betty's monthly take home is $20 less
Step-by-step explanation:
Betty's monthly income = $2300
Betty's monthly savings = $200
Amount left after savings = $2300 - $200
Amount left after savings = $2100
Federal and State Income tax rate = 20% = 0.2
Tax amount paid = $420
Monthly take home = $2100 - $420
Monthly take home = $1680
Compared to $150 per month savings, Betty's monthly take home is $20 less
multiply and remove all perfect square roots. Assume y is positive. √12
Answers
Answer:
2√3
Step-by-step explanation:
Step 1: Find perfect square roots
√4 x √3
Step 2: Convert
2 x √3
Step 3: Answer
2√3
- 2/3x + 5(3/5 - 3/5x) - 12 divided 6 *2
Answers
Answer: -3 2/3x - 1
Step-by-step explanation:
-2/3x + 5(3/5 - 3/5x) - 12 / 6 * 2
First distribute
-2/3x + 3 - 3x - 12 / 6 * 2
Now divide 12 by 6
-2/3x + 3 - 3x -2 * 2
Now multiply -2 by 2
-2/3x + 3 - 3x - 4
Now subtract 3x from -2/3x
-3 2/3x + 3 - 4
Now subtract 4 from 3
-3 2/3x - 1
Please answer this correctly
Answers
Answer:
Step-by-step explanation:
The 50 people might be random, depending on when the question was done.
The 50 people might be random if there's roughly the same number of men as women, but to accomplish this, Isabella would have to pick a time when men would be out shopping.
The 16 are certainly not random, and the question itself is kind of biased. I would say the answer should be no.
Need help ASAP Thankyou!!!
Answers
Answer:
216
Step-by-step explanation:
To find the volume of the pyramid we have to do length * width * height / 3
The length is 9yd
The width is 8yd
The height is 9yd
So 9 * 9 * 8 = 648
648 / 3 = 216
Alessandro wrote the quadratic equation -6=x2+4x-1 in standard form. What is the value of c in his new equation? c=-6
Answers
Answer:
5
Step-by-step explanation:
To put the equation in standard form, add 6 to both sides.
x^2 +4x -1 +6 = -6 +6
x^2 +4x +5 = 0
The new value of "c" (the constant) is 5.
Answer:
C or 5 for me
Step-by-step explanation:
Which expression is equivalent to Left-bracket log 9 + one-half log x + log (x cubed + 4) Right-bracket minus log 6? log StartFraction 3 StartRoot x EndRoot (x cubed + 4) Over 2 EndFraction log StartFraction 3 StartRoot x EndRoot (3 x + 4) Over 2 EndFraction log StartFraction StartRoot 9 x (x cubed + 4) EndRoot Over 6 EndFraction StartFraction StartRoot log 9 x ( x cubed + 4) EndRoot Over 6 EndFraction
Answers
Answer:
[tex]\log{\dfrac{3\sqrt{x}(x^3+4)}{2}}[/tex]
Step-by-step explanation:
[tex]\log{9}+\dfrac{1}{2}\log{x}+\log{(x^3+4)}-\log{6}=\log{\left(\dfrac{9x^{\frac{1}{2}}(x^3+4)}{6}\right)}\\\\=\boxed{\log{\dfrac{3\sqrt{x}(x^3+4)}{2}}}\qquad\text{matches choice A}[/tex]
__
The applicable rules of logarithms are ...
log(ab) = log(a) +log(b)
log(a/b) = log(a) -log(b)
log(a^b) = b·log(a)
Answer:
A
Step-by-step explanation:
Just did it on edge2020
Which division sentence is related to the product of a/3 (a/3) when A is not equal to 0?
Answers
Answer:
Option 4.
Step-by-step explanation:
Reciprocal of the second fraction turns the product into the division of the two fractions, which equals to 1.
[tex]a/3(a/3)[/tex]
[tex]a/3 \div 3/a=1[/tex]
Two fractions are said to be the reciprocal or multiplicative inverse of each other, if their product is 1.
Answer:
D. a/3 divided by 3/a = 1
Step-by-step explanation:
edge
What is the common difference between successive terms in the sequence?
0.36, 0.26, 0.16, 0.06, –0.04, –0.14, ...
–0.1
–0.01
0.01
0.1
Answers
Answer:
0.1
Step-by-step explanation:
0.36-0.26=0.1
hope u understand
Answer:
A
Step-by-step explanation:
Suppose you want to have $0.5 million saved by the time you reach the age of 30 years and suppose that you are 20 years old now. If you can earn 5% on your funds, how much would you have to invest today to reach your goal?
Answers
Answer:
$306,956,6268
Step-by-step explanation:
Future value, FV = Present value PV [1 + rate]^t
PV = FV/[1 + rate]^t
PV = 500,000/[1.05]^10
PV = $306,956,6268
The function f(x) is given by the set of ordered pairs.
{(8,3), (0, 4), (1, 5), (2, -1), (-6, 10)}
Which is true regarding the function?
f(-3) = 8
f(3) = 5
f(8) = 0
f(-6) = 10
Answers
Answer: f(-6) = 10.
Step-by-step explanation: This above equation is the only one that contains both coordinates of one of the ordered pairs in the correct order, so it is the answer.