Answer:
SO if f(x)= |x-5|+3 then F(2)= 6
Step-by-step explanation:
These signs | | mean that it is an absolute value equation. SO that means any negative will automatically change to positive values and positive values will stay at positive values. You are supposed to substitute 2 in for x and if you do 2-5 then that is negative 3 but it changes to positive 3 and add three and then f(2)= 6
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.
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]
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.
why should the remainder be less than the divisor
Answer:
or else we can divide again
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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Which is 14% of 50 0.70,7,57,64,or70
Answer:7
Step-by-step explanation: 14%=14/100. (14/100)*50=7
Answer:
7
Step-by-step explanation:
to find your answer multiply .14 (14 as a fraction) by 50 to get 7
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).
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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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!
______________________________________________________
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
Please help; I don't understand how to solve these inequality problems.
For each problem:
Solve the combined inequality.
Explain step by step how you solved it.
State whether the combined inequality is a conjunction or disjunction and explain.
Determine which letter is in the solution.
1. -4≤x+2<1
2. 5x-4>46" or " 4x≤3x+6
3. 10≤2x-4≤20
4. 6-2x≤12" or " 7+2x<-11
5. 5≤2x+1≤11
6. 2/3 x-20≤16" or " x/3+10≥32
7. 10<1/4 (x+1)≤11
Answer:
1. -6 ≤ x < -1, conjunction
2. x > 10 or x ≤ 6, disjunction
3. 7 ≤ x ≤ 12, conjunction
4. x ≥ -3 or x < -9, disjunction
Step-by-step explanation:
These inequalities are called "compound inequalities." Each compound inequality is made up of two simple inequalities.
A compound inequality of the type 5 < x < 8 means x > 5 and x < 8. Since the word between the simple inequalities is "and", it is a conjunction.
A compound inequality of the type "x < 3 or x > 12" uses the word "or" between the simple inequalities. It is called a disjunction.
1.
-4 ≤ x + 2 < 1
Conjunction
For this type of inequality, do what you need to do to get x alone in the middle section. Do the same to all three "sides" of the inequality.
The middle section has x + 2. We want x alone,s o w must subtract 2. We subtract 2 from all three sides.
-4 - 2 ≤ x + 2 - 2 < 1 - 2
-6 ≤ x < -1
2. 5x - 4 > 46 or 4x ≤ 3x + 6
Disjunction
In this type of compound inequality, solve each inequality by itself, and always keep the word "or" between the inequalities.
5x - 4 > 46 or 4x ≤ 3x + 6
5x - 4 + 4 > 46 + 4 or 4x - 3x ≤ 3x - 3x + 6
5x > 50 or x ≤ 6
x > 10 or x ≤ 6
3. Similar to problem 1.
Conjunction
10 ≤ 2x - 4 ≤ 20
Add 4 to all sections.
14 ≤ 2x ≤ 24
Divide all sections by 2.
7 ≤ x ≤ 12
4.
6 - 2x ≤ 12 or 7 + 2x < -11
Disjunction
-2x ≤ 6 or 2x < -18
x ≥ -3 or x < -9
Answer:
1. -6≤x<-1
conjunction
2.x>10 or x≤6
Disjunction
3.7≤x≤12
Conjunction
4.x ≥-6 or x < -6
Disjunction
5.2≤x≤5
Conjunction
6. x ≤ 54 or x≥66
Disjunction
7. 39< x≤43
Conjunction
Step-by-step explanation:
conjunction is "and" like a sandwich between 2 points
disjunction is " or" like boat oars with a gap for the boat in the middle
1. -4≤x+2<1
Subtract 2 from all sides
-4-2≤x+2-2<1 -2
-6≤x<-1
conjunction
2. 5x-4>46" or " 4x≤3x+6
Add 4 to each side Subtract 3x from each side
5x-4+4 > 46+4 4x-3x≤3x-3x+6
5x >50 x≤6
Divide by 5
5x/5 >50/5
x>10 or x≤6
Disjunction
3. 10≤2x-4≤20
Add 4 to all sides
10≤2x-4≤20
10+4 ≤2x-4+4≤20+4
14≤2x≤24
Divide by 2 on all sides
14/2≤2x/2≤24/2
7≤x≤12
Conjunction
4. 6-2x≤12" or " 7+2x<-11
Subtract 6 from each side Subtract 7 from each side
6-6-2x≤12 or " 7-7+2x<-11-7
-2x≤12 2x<-18
Divide by -2 Divide by 2
Flips the inequality
-2x/-2≥12/-2 2x/2 <-18/2
x ≥-6 or x < -6
Disjunction
5. 5≤2x+1≤11
Subtract 1 from all sides
5-1≤2x+1-1≤11-1
4≤2x≤10
Divide all sides by 2
4/2≤2x/2≤10/2
2≤x≤5
Conjunction
6. 2/3 x-20≤16" or " x/3+10≥32
Add 20 from each side Subtract 10 from each side
2/3 x-20+20 ≤16+20 x/3 +10-10 ≥32 -10
2/3 x ≤36 x/3≥22
Multiply by 3/2 on each side Multiply by 3 on each side
3/2 * 2/3x ≤ 36*3/2 x/3*3 ≥22 *3
x ≤ 54 or x≥66
Disjunction
7. 10<1/4 (x+1)≤11
Multiply all sides by 4
4*10<1/4*4 (x+1)≤11*4
40< (x+1)≤44
Subtract 1 from all sides
40-1< (x+1-1)≤44-1
39< x≤43
Conjunction
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.
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.
A group of scientists are studying a new species of insects. They observe the patterns of 6 insects. The scientists find that the insect population, x, is growing exponentiall 20% per month. Which equation can be used to find how many months, t, will it take for there to be a population of 477 insects?
Answer:
(B) [tex]477=6(1+0.20)^t[/tex]
Step-by-step explanation:
we can use formula
[tex]P(t)=P_0(1+r)^t[/tex]
where
Po is the initial population
r is the growth rate
t is the time in months
We are given
initial population of insects
so, Po=6
The scientists find that the insect population, x, is growing exponentially 20% per month
so, r=0.20
now, we can plug these values
[tex]P(t)=6(1+0.20)^t[/tex]
there to be a population of 477 insects
so, P(t)=477
now, we plug it
and we get
[tex]477=6(1+0.20)^t[/tex]
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
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
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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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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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 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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What is the completely factored form of x4 + 8x2 – 9? (x + 1)(x – 1)(x + 3)(x + 3) (x+1)(x+1)(x+3){x^2+9} (x2 – 1)(x + 3)(x – 3) (x + 1)(x + 1)(x + 3)(x + 3)
The complete factor of the expression x⁴ + 8x² – 9 will be (x² + 9), (x - 1), and (x + 1). Then the correct option is B.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The expression is given as,
⇒ x⁴ + 8x² – 9
Factorize the expression, then we have
⇒ x⁴ + 8x² - 9
⇒ x⁴ + 9x² - x² - 9
⇒ x²(x² + 9) - 1(x² + 9)
⇒ (x² + 9)(x² - 1)
⇒ (x² + 9)(x - 1)(x + 1)
The complete factor of the expression x⁴ + 8x² – 9 will be (x² + 9), (x - 1), and (x + 1). Then the correct option is B.
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The complete question is attached below.
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
Find f(6)+5g(-1) given f(x)=-5x+1 and g(x)=-2x2
Answer:
-38
Step-by-step explanation:
Whats the value of 6 in 3.6?
6 is in the tenths place.
Written Form: 0.6
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
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
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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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
How to write z times 5 as an algebraic expression
Answer:
z5
Step-by-step explanation:
Answer:
z is your answer! :)