Find f(6)+5g(-1) given f(x)=-5x+1 and g(x)=-2x2
Answer:
-38
Step-by-step explanation:
A square has a perimeter of 76 inches. Complete parts (a)-(c) (a) what is the length of each side? Each side has length of?
a - side of the square
4a - the perimeter of a square
76 in - the perimeter of a square
The equation:
4a = 76 divide both sides by 4
a = 19 in.
Answer: Each side has length 19 inches.(a) The length of each side is equal to 19 inches.
How to calculate the perimeter of a square?In Mathematics and Geometry, the perimeter of a square can be calculated by using the following formula;
P = 4s
Where:
P is the perimeter of a square.s is the side length of a square.By substituting the given parameters into the formula for the perimeter of a square, we have the following;
Perimeter of a square, P = 4s
76 = 4s
s = 76/4
s = 19 inches.
Therefore, each side has a length 19 inches.
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The circumference of my circle is 45 inches. What is the diameter
Answer:
14.32 inches to nearest thousandth.
Step-by-step explanation:
Circumference = π * d where d = the diameter.
So 45 = π * d
d = 45 / π
= 14.32 inches
The diameter of the circle is 14.33 inches.
What is the area and circumference of a circle?The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.
Given here: The circumference of the circle as 45 inches
We know that Circumference is give by 45=2×3.14×r
2r=14.33 inches
Hence, The diameter of the circle is 14.33 inches.
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Calculate: 0.3 of 14
100% --> 14
30% --> x
100x = 420
x= 420/100
x=4.2
Answer:
The answer is 4.2
Step-by-step explanation:
Always remember that when they use the word of, it means you have to multiply. So 14 times 0.3 is 4.2
Travis can afford a $260-per-month car payment, and he is interested in either a compact car, which costs $10800, or a coupe, which costs 11,300. If he is being offered a 4-year car loan with and APR of 6%, compounded monthly, which car can Travis afford?
Answer: travis can afford the compact car but not the coupe
Step-by-step explanation:
Answer:
Travis can afford the compact car.
Step-by-step explanation:
The EMI formula is :
[tex]\frac{p*r*(1+r)^{n} }{(1+r)^{n}-1 }[/tex]
In first case:
p = 10800
r = 6/12/100=0.005
n = 4*12 = 48
Putting values in the formula we get:
[tex]\frac{10800*0.005*(1+0.005)^{48} }{(1+0.005)^{48}-1 }[/tex]
= $254
We can see that Travis can afford the compact car because the EMI is less than $260.
In second case:
p = 11300
r = 6/12/100=0.005
n = 4*12 = 48
Putting values in the formula we get:
[tex]\frac{11300*0.005*(1+0.005)^{48} }{(1+0.005)^{48}-1 }[/tex]
= $265.75
We can see that the coupe will have an EMI of $265.75 which is higher than the amount that Travis can afford.
Hence, Travis can afford a compact car.
the second step in the process for factoring the trinomial x^2-4x-32
To factor the trinomial x²-4x-32, follow the steps to identify coefficients, find suitable numbers, split the middle term, and factor by grouping. The answer is (x+4)(x-8).
To factor the trinomial x²-4x-32, you can follow these steps:
Identify the coefficients of the quadratic terms: a = 1, b = -4, and c = -32.
Find two numbers that multiply to c (a*c = -32) and add up to b (-4).
Split the middle term using these numbers: x²-4x-32 becomes x²-8x+4x-32.
Factor by grouping: (x²-8x) + (4x-32) = x(x-8) + 4(x-8) = (x+4)(x-8).
In trapezoid ABCD with bases AB and DC , diagonals intersect at point O. Find the length of diagonal BD , if BO=6 cm and: AO/OC = 3/1
Answer:
BD = 8 cm
Step-by-step explanation:
Diagonals of trapezoid divides each other in equal ratio.
if ABCD is a trapezoid and the diagonals AC and BD intersect at point O
then we have
[tex]\frac{AO}{OC} =\frac{OB}{OD}[/tex]
it is given that
[tex]\frac{AO}{OC} =\frac{3}{1}[/tex] and BO=6 cm
so we can write
[tex]\frac{3}{1} =\frac{6}{OD}[/tex]
cross multiply
[tex]3 OD=6[/tex]
divide both side by 3
OD= 2 cm
now we have
BD = BO +OC
BD = 6 cm + 2 cm
BD= 8 cm
Step-by-step explanation:
The ratios of the sides is the same.
3OD=OB
Let y be the length of OD
Therefore,
3y=6
y=2,
meaning OD is 2.
OB+OD=DB
BD=6
ANSWER:
BD=8
What is the differnce between the points (-5,-9) and (-5,13)?
Answer:
Step-by-step explanation:
Given that two points (-5,-9) and (-5,13)
We have to find the differences between these points
Both the points have -5 as x coordinate.
But y coordinate is negative for first one while positive for second one.
Also dimension is 9 units down for I point while for ii point it is 13 units up.
The first point lies in the III quadrant while II point lies in the II quadrant.
Both the points are located with a distance of 5 units from x axis to the left of x axis.
But first point is 9 units down y axis and ii point is 13 units up the y axis.
Distance between them is 22 units.
Answer: The difference between the points (-5,-9) and (-5,13) is 22 units.
Explanation:
Since we have given that
(-5,-9) and (-5,13)
As we can see that the points are along the x-axis as the x-coordinate are same in both the points.
So, to find the difference between the points we just need to get the distance between the y- coordinates.
[tex]13-(-9)\\\\=13+9\\\\=22\ units[/tex]
Hence, the difference between the points (-5,-9) and (-5,13) is 22 units.
In the diagram all the angles shown are right angles. The length of AB=4 and BC=5 as indicated in the diagram. What is the perimeter of the entire figure?
Answer: choice C, 18
==============================
Explanation:
We don't know how long each little horizontal piece is, but we do know that the smaller horizontal pieces combine to fully span 5 units across. The top and bottom sides effectively are both 5 units long. Think of a rectangle. Similarly, the same happens with the vertical pieces as well. They combine to get 4.
We have a figure with a perimeter similar to a rectangle that is 4 by 5, the perimeter being 4+5+4+5 = 9+9 = 18
Alternatively, you can use the formula
P = 2*L + 2*W or P = 2*(L+W)
Plug in L = 5 and W = 4 as the length and width to get P = 18 for the perimeter
A 3.5 ft by 5.5 ft mirror is placed in a wooden frame. What is the area of the frame
Answer:
19.25ft
Step-by-step explanation:
area = length x width so 3.5 x 5.5 = 19.25
Answer:
The area of the frame is 19.25 feet.
Step-by-step explanation:
We can see from the information that the wooden frame is a rectangle since length and breadth are unequal.
breadth = 3.5 ft
length = 5.5 ft
The formula for area of a rectangle is = A = L x b
Area = 3.5 * 5.5
Area = 19.25 feet
How to write z times 5 as an algebraic expression
Answer:
z5
Step-by-step explanation:
Answer:
z is your answer! :)
Let f(x) = x2 + 3x − 4 and g(x) = x + 5. Find f(x) ⋅ g(x).
A) x3 + 3x2 + 16x − 20
B) x3 + 5x2 + 14x − 20
C) x3 + 8x2 + 11x − 20
D) x3 + 9x2 + 19x − 20
Answer:
[tex]x^3 + 8x^2 + 11x-20[/tex]
Step-by-step explanation:
f(x) = x^2 + 3x − 4
g(x) = x + 5
To find f(x) * g(x) we multiply f(x) with g(x)
[tex]f(x) * g(x) = (x^2 + 3x -4) * (x+5)[/tex]
First multiply each term in f(x) and multiply with x+5
x^2 times x+5 becomes [tex]x^3+5x^2[/tex]
3x times x+5 becomes [tex]3x^2 + 15x[/tex]
-4 times x+ 5 becomes -4x -20
so f(x) * g(x) = [tex]x^3 + 5x^2 +3x^2 + 15x -4x -20[/tex]
Combine like terms
f(x) * g(x) = [tex]x^3 + 8x^2 + 11x-20[/tex]
Answer: [C]: " x³ + 8x² + 11x − 20 " .
______________________________________________________
Step-by-step explanation:
______________________________________________________
Given: " f(x) = x² + 3x − 4 " ; and
" g(x) = x + 5 " ;
Find: " f(x) ⋅ g(x) " :
______________________________________________________
f(x) ⋅ g(x) =
" (x² + 3x − 4) (x + 5) " ;
↔ " (x + 5) (x² + 3x − 4) " ;
______________________________________________________
Note: " (a + b) (c + d + e) = ac + ad + ae + bc + bd + ae " ;
______________________________________________________
→ " (x + 5) (x² + 3x − 4)
= (x * x²) + (x * 3x) + (x*-4) + (5*x²) + (5*3x) + (5*-4) " ;
= (x³) + (3x²) + (-4x) + (5x²) + (15x) + (-20) ;
= x³ + 3x² − 4x + 5x² + 15x − 20 ;
→ Combine the "like terms" :
+ 3x² + 5x² = + 8x² ;
− 4x + 15x = + 11 x ;
______________________________________________________
→ And rewrite:
______________________________________________________
→ " x³ + 8x² + 11x − 20 " ;
______________________________________________________
→ which is: Answer choice: [C]: " x³ + 8x² + 11x − 20 " .
______________________________________________________
Hope this helps!
Best wishes!
______________________________________________________
solve for m 1/3=12-m
Answer:
m = 35/3 or 11 2/3
Step-by-step explanation:
1/3=12-m
Subtract 12 from each side
1/3 - 12 = -m
Get a common denominator
1/3 - 12*3/3 = -m
1/3 - 36/3 = -m
-35/3 = -m
Multiply by -1
-1* -35/3 = -1 *-m
35/3 = m
Changing to a mixed number
3 goes into 35 11 times with 2 left over
11 2/3
[tex]12-m=\dfrac{1}{3}\qquad\text{subtract 12 from both sides}\\\\-m=-11\dfrac{2}{3}\qquad\text{change the signs}\\\\\boxed{m=11\dfrac{2}{3}}[/tex]
Find 6% of $5900000 to the nearest cent
Answer:
$354,000
Step-by-step explanation:
Since six percent in decimal is .06, all we have to do is multiply that by 5900000. When multiplied this would leave our answer to be $354,000. This is the answer unless we're missing any decimals, that would relate to the part of the question where it says round to the nearest cent.
An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. tall, and the initial velocity of the ball is 40 ft per sec. The height s of the ball in feet is given by the equation s equals negative 2.7 t squared plus 40 t plus 6.5s=−2.7t2+40t+6.5 , where t is the number of seconds after the ball was thrown. Complete parts a and b. a. After how many seconds is the ball 12 ft above the moon's surface?
Answer:
0.14 s
Step-by-step explanation:
s = -2.7 t² + 40t + 6.5
Let s = 12
12 = -2.7t² + 40t + 6.5 Subtract 12 from each side
-2.7t² + 40t + 6.5 - 12 = 0
-2.7t² + 40t - 5.5 = 0
Apply the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a = -2.7; b = 40; c = -5.5
[tex]x = \frac{-40\pm\sqrt{40^2 - 4\times (-2.7) \times (-5.5)}} {2(-2.7)}[/tex]
[tex]x = \frac{-40\pm\sqrt{1600-59.4}}{-5.4}[/tex]
[tex]x = \frac{-40\pm\sqrt{1540.6}}{-5.4}[/tex]
[tex]x = \frac{-40\pm 39.25}{-5.4}[/tex]
x = 7.41 ± 7.27
x₁ = 0.14; x₂ = 14.68
The graph below shows the roots at x₁ = 0.134 and x₂ = 14.68.
The Moon’s surface is at -12 ft. The ball will be 12 ft above the Moon’s surface (crossing the x-axis) in 0.14 s.
The second root gives the time the ball will be 12 ft above the Moon’s surface on its way back down.
How many ounces of iodine worth 30 cents an ounce must be mixed with 50 ounces of iodine worth 18 cents an ounce so that the mixture can be sold for 20 cents an ounce?
Answer:
10 ounces
Step-by-step explanation:
10 ounces of iodine are worth 30 cents so the mixture can be sold for 20 cents an ounce.
What are arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Let n be the ounces of 30 cents worth of iodine.
To determine the mixture to be worth 20 cents per ounce.
The value of 50 ounces of 18-cent iodine is
⇒ (50)(18) = 900 cents of iodine.
A (50+n) mixture of iodine is produced by combining 50 ounces of 18-cent iodine with n ounces of 30-cent iodine.
Similarly, n ounces of 30-cent iodine is worth 30n.
So, the price of 50+n ounces of 20-cent iodine (50+n)20
⇒ 30x + 900 = 1000 + 20x
Rearrange the likewise terms and apply the arithmetic operations,
⇒ 10x = 100
⇒ x = 10
We can estimate that in order to sell the mixture for 20 cents per ounce, we should combine 10 ounces of iodine worth 30 cents.
Hence, 10 ounces of iodine are worth 30 cents so the mixture can be sold for 20 cents an ounce.
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Two fair coins are flipped at the same time. What is the probability that both will display tails?
Answer:
2 out of 4. 2/4
Step-by-step explanation:
There are 2 sides to each coin, there are two coins so all sides add up to 4.
The probability that both coins will display tails is:
P = 0.25
How to get the probability?
A fair coin has two possible outcomes, tails and heads, both with the same probability.
Then the probability of getting tails is:
p = 0.5
So, the probability for each coin (of getting tails) is:
p₁ = 0.5
p₂ = 0.5
The joint probability (this is, the probability that both of the above events happen at the same time) is the product between the individual probabilities:
P = p₁*p₂ = 0.5*0.5 = 0.25
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Whats the value of 6 in 3.6?
6 is in the tenths place.
Written Form: 0.6
The square base has side lengths of 10 millimeters. The height of one triangular face is 15 millimeters. Find the total surface area of the square pyramid.(if you can answer it thanks!)
Answer:
The total surface area of the square pyramid is [tex]SA=400\ mm^2[/tex]
Step-by-step explanation:
we know that
The surface area of a square pyramid is equal to the area of the square base plus the area of four triangular faces
so
[tex]SA=10^{2} +4[\frac{1}{2}(10)(15)][/tex]
[tex]SA=400\ mm^2[/tex]
Hari's weekly allowance varies depending on the number of chores he does. He received $20 in allowance the week he did 22 chores, and $12 in allowance the week he did 6 chores. Write an equation for his allowance in slope-intercept form.Hari's weekly allowance varies depending on the number of chores he does. He received $20 in allowance the week he did 22 chores, and $12 in allowance the week he did 6 chores. Write an equation for his allowance in slope-intercept form.
The slope-intercept form of the equation, which represents how much allowance Hari receives based on the number of chores he does, is y = 0.5x + 9. Here, the slope of 0.5 represents the amount Hari earns per chore, and 9 is the base amount Hari receives irrespective of the chores.
Explanation:The given scenario provides us with two points (22, $20) and (6, $12) where the number of chores is the x-coordinate and the allowance is the y-coordinate. We can use these points to find the slope of the line:
Slope (m) = (y2 - y1) / (x2 - x1)= ($20 - $12) / (22 - 6) = $8 / 16 = $0.5,
Next, we use the slope and one of the points to find the y-intercept: y = mx + b so $20 = ($0.5 * 22) + b, solving for b gives us b = $20 - $11 = $9, which is our y-intercept.
So, the equation of the line in slope-intercept form is y = 0.5x + 9
This equation states that Hari earns $0.5 per chore and gets a guaranteed $9 even if he does no chores.
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Gustave measured his pace and determined that for him, s steps make up one mile. One day Gustave walked 6300 steps, which was 3 miles. Write an equation to describe this situation.
Answer:
6300 = s * 3
s=2100
Step-by-step explanation:
s =steps per mile
steps = steps per miles * miles
6300 = s * 3
This is the equation.
Divide each side by 3.
6300/3 = s3/3
2100 /s
Answer:
6300/3=s
s=2100
Step-by-step explanation:
six thousand three hundred over 3 equals s
s equals two thousand one hundred
A 12 foot basketball hoop has a shadow 9.6ft long. How long is the shadow of a 6ft adult standing next to the basketball hoop?
Answer:
The adults shadow is 4.8 ft
Step-by-step explanation:
We can use ratio's to solve this problem
12 ft hoop 6ft adult
-------------- = -----------------
9.6 ft shadow x ft shadow
Using cross products
12 * x = 9.6 * 6
12x = 57.6
Divide each side by 12
12x/12 = 57.6 /12
x = 4.8 ft
Jenna bought a bike for $200. The value of the bike decreases by 5% each year. Write an equation to model the situation.
I'm not sure if this is correct.
200/5x
Answer:200-10x= y
Step-by-step explanation:
5%= .05 so 200*.05= $10 Per year
so the equation would look something like
200-10x= y
x= how old the bike is
y= is your answer
Mike is 3 years old.joe is 6 times as old as mike whict equation shows how to find Joe's age?
Answer:
3x6=18
Step-by-step explanation:
3x6=18
6 times as old is the same as saying TIMES by 6 :)
Joe's age can be found using the equation 'Joe's Age = 6 * 3', as Joe is 6 times as old as Mike, and Mike is 3 years old.
Explanation:The question presents a situation where Joe is 6 times as old as Mike. We know that Mike is 3 years old, so to find Joe's age, we need to multiply Mike's age by 6. This situation can be expressed by the following equation: Joe's Age = 6 * Mike's Age.
Replacing 'Mike's Age' with the given value (3 years), we get: Joe's Age = 6 * 3
Therefore, the equation to find Joe's age is Joe's Age = 6 * 3.
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why should the remainder be less than the divisor
Answer:
or else we can divide again
A shop has a sale that offers 20% of all prices.
On the final day the reduce all the sale prices by 25%.
Linz buys a radio on the final day.
Work out the overall percentage reduction on the price of the radio.
Answer:
40% reduction
Step-by-step explanation:
To answert this, we need to find how much of the price is each percentage. This can be found my subtracting the percent from 100:
Sale price: 100 - 20 = 80
Last day price: 100 - 25 = 75
Now we need to multiply these two values together, remembering to divide both numbers by 100 first:
80 ÷ 100 = 0.8
75 ÷ 100 = 0.75
0.8 * 0.75 = 0.6
Then multiply by 100 to find the percentage:
0.6 * 100 = 60
60% is the end price, but to find the overall reduction we need to subtract this value from 100:
100 - 60 = 40
So there was a 40% reduction on the price.
are the following figures similar
Answer:
Yes, they are similar. The answer you would click is Yes, the corresponding sides are proportional.
Step-by-step explanation:
The second figure is a dilation of the first, making them similar. The dilation is by a factor of 2 and a half.
If you were going to use the quadratic formula to solve the following equation and b=15, what number would you use as the value for the variable ‘a’?
-15x+22=12x^2
Answer:
You would use a = 12
Step-by-step explanation:
The b value is the coefficient that is in front of the x term, that does not have an exponent of 2. It's simply the x term (not the x^2 term)
We're told that b = 15 is used, but we see that -15 is in front of the x term. To fix this contradiction, add 15x to both sides so that you move the x term to the right side
-15x+22 = 12x^2
-15x+22+15x = 12x^2+15x
22 = 12x^2+15x
Now subtract 22 from both sides to move that term over as well
22-22 = 12x^2 + 15x - 22
0 = 12x^2 + 15x - 22
12x^2 + 15x - 22 = 0
12x^2 + 15x + (-22) = 0
The last equation is in the form ax^2 + bx + c = 0 with
a = 12, b = 15, c = -22
Mike has a stack of 10 cards numbered from 1 to 10. He randomly chooses a card and without replacing it, randomly chooses a seconds card. What is the probability that Mike would pick two cards that are prime numbers?
Answer:
2/10
Step-by-step explanation:
2/10
The probability that Mike would pick two prime numbers from the stack of 10 cards without replacement is 2/15.
Explanation:The probability of picking two prime numbers from a stack of 10 cards without replacement can be calculated by finding the probability of picking a prime number on the first draw and a prime number on the second draw, given that the first draw was successful.
There are four prime numbers among the 10 cards (2, 3, 5, and 7). So, the probability of picking a prime number on the first draw is 4/10.
Since we do not replace the first card, there are now 9 cards left in the deck, with 3 prime numbers. So, the probability of picking a prime number on the second draw, given that the first draw was successful, is 3/9.
To find the overall probability, we multiply the probabilities of the individual events: (4/10) * (3/9) = 12/90 = 2/15.
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Area and Perimeter of a rectangle that is 92 meters long and 18 meters wide
a= 92(18) =1656
Area= 1656m
p= 2(92+18) =220
Perimeter= 220m