simplify the expression 3xy(2x+5y)
8. Susie had $150 in her checking account. She wrote a check for $95 and another check for $85. What was the balance in her account after she wrote the check?
90=20+70 use the distributive property and the GCF OF 20 and 70 to write another related expression for 90 could you write another expression with a different common factor?
Final answer:
To write another expression for 90 using the distributive property and the GCF of 20 and 70, distribute the GCF to each term. Another expression with a different common factor can be written by multiplying each term by a different common factor.
Explanation:
To write another expression for 90 using the distributive property and the GCF of 20 and 70, we can rewrite 90 as (20 + 70). Using the distributive property, we can distribute the GCF to each term inside the parentheses, resulting in 20*(GCF of 20 and 70) + 70*(GCF of 20 and 70). The GCF of 20 and 70 is 10, so the expression becomes 20*10 + 70*10, which simplifies to 200 + 700, equaling 900.
Yes, we can write another expression with a different common factor. Let's say we use the GCF of 20 and 70, which is 10, to rewrite the expression. Instead of multiplying each term by 10, we can multiply 20 and 70 by a different common factor, such as 5. This gives us 20*5 + 70*5, which is equal to 100 + 350, resulting in 450.
Determine the discriminant for the quadratic equation 0 = –2x2 + 3. Based on the discriminant value, how many real number solutions does the equation have?
Discriminant = b2 – 4ac
real number solutions
The positive value of the discriminant implies that there are two real unequal roots and this can be determined by using the formula of the discriminant.
Given :
The quadratic equation is [tex](0=-2x^2+3)[/tex].
The following steps can be used in order to determine the total number of real solutions does the equation have:
Step 1 - Write the given quadratic equation.
[tex]0=-2x^2+0x+3[/tex]
Step 2 - The formula of discriminant is given below:
[tex]D = b^2-4ac[/tex]
where 'b' is the coefficient of 'x', 'a' is the coefficient of [tex]x^2[/tex], and 'c' is the constant.
Step 3 - Now, substitute the values of a, b, and c in the above formula.
[tex]D = (0)^2-4\times (-2)\times 3[/tex]
[tex]D = 24[/tex]
Step 4 - The positive value of the discriminant implies that there are two real unequal roots.
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An object is launched upward with an initial velocity of 64 feet per second from a platform 80 feet high. Write a model for the object? How many seconds until the maximum height is reached? What will be the maximum height? How many seconds until the object hits the ground
The model for the object's motion is [tex]h(t) = -16t^2 + 64t + 80[/tex]. It reaches its maximum height of 144 feet at 2 seconds. The object will hit the ground after 5 seconds.
To model the vertical motion of the object, we use the equation:
[tex]h(t) = -16t^2 + 64t + 80[/tex]
where:
h(t) is the height at time t64 ft/s is the initial velocity80 ft is the initial height[tex]16t^2[/tex] represents the effect of gravity (since the gravitational acceleration is approximately 32 ft/s2, and here it is halved to be per second squared)Time to Reach Maximum Height
The time to reach the maximum height can be found by using the formula:
[tex]t = \frac{v_0}{|g|} = \frac{64}{32} = 2 seconds[/tex]
Maximum Height
Plug t = 2 seconds into the height equation:
[tex]h(2) = -16(2)^2 + 64(2) + 80 = 144 feet[/tex]
Time to Hit the Ground
To find when the object hits the ground (h(t) = 0), solve:
[tex]-16t^2 + 64t + 80 = 0[/tex]
Using the quadratic formula:
[tex]t = \frac{-64\pm\sqrt{64^2-4(-16)(80)} }{2(-16)}[/tex]
Simplifies to:
t = 5 seconds (since the negative value does not make sense in this context)
The object will hit the ground after 5 seconds.
The population of a city in Alabama increases every year by 11.5 percent. If the population in 2011 was 4.8 million, what will its population be in 2016?
A)2.6 million
B)2.76 million
C)8.27 million
D)220 million
!!PLEASE HELP!!
After school, Mike spends from 4:00 to 6:00 doing homework, eating, and playing sports. If he spends 65 minutes on homework and 15 minutes on eating, how much time does he have to play sports?
charlie wants to order lunch for his friend. hell order 5 sandwiches and a $3 kids meals for his little brother. charlie has $28. how much can he spend on each sandwich if they are all the same price?
Answer:4 or less
Step-by-step explanation:
6x+3>27
Simplify by dividing negative three over eight divided by five over nine..
A. negative fifteen over seventy-two.
B. fifteen over seventy-two.
C. negative twenty-seven over forty.
D. twenty-seven over forty.
Answer:
-27/40
Step-by-step explanation:
how do you solve for 2w+8=-3+2w
Commutative property across multiplication for 2x10x7
What three ratios of the lengths of two segments equal?
what is 15.2 rounded to the nearest tenth
Which expression results when the change of base formula is applied to log4(x+2) ?
Answer-
[tex]\frac{\log (x+2)}{\log 4}[/tex] is the correct answer.
Solution-
The formula for change of base in logarithm is given by,
[tex]\log_{b}a=\frac{\log_{c}a}{\log_{c}b}[/tex]
If we take the common base as 'e' , the formula becomes,
[tex]\log_{b}a=\frac{\log a}{\log b}[/tex]
Applying this formula,
[tex]\log_{4}(x+2)=\frac{\log (x+2)}{\log 4}[/tex]
∴ As the first option matches with our answer, hence it is the correct answer.
( In the fourth option a bracket is missing, so it is not the correct option)
(09.05) A golf ball is hit from the ground with an initial velocity of 208 feet per second. Assume the starting height of the ball is 0 feet. How long will it take the golf ball to hit the ground?
The amount of Time that it would take for the golf ball to hit the ground using the given parameters is; 13 seconds
How to solve projectile problems?
We are given;
Initial Velocity = 208 feet per second
Initial height = 0 ft
Now, the general equation to be used here is;
h(t)= -16t² + 208t
Factorizing the equation gives;
h(t) = -16t(t - 13)
At h = 0, we have;
-16t(t - 13) = 0
Thus;
t = 13 seconds
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Given the piecewise function shown below, select all of the statements that are true.
The statements f(1) = 0 and f(-1) = 2 are true based on the piecewise function.
Options B and C are the correct answer.
We have,
The piecewise function:
f(x) = -x + 1, x < 0
f(x) = -2, x = 0
f(x) = x² - 1. x > 0
Now,
f(-2) = 0
False.
When x = -2, we are in the first condition, so f(-2) = -(-2) + 1 = 3, not 0.
f(1) = 0
True
When x = 1, we are in the third condition, so f(1) = (1)² - 1 = 0.
f(-1) = 2
True
When x = -1, we are in the first condition, so f(-1) = -(-1) + 1 = 2.
f(4) = 7
False.
When x = 4, we are in the third condition, so f(4) = (4)² - 1 = 15, not 7.
Therefore,
The statements f(1) = 0 and f(-1) = 2 are true.
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your grandmother is in the hospital and is on a liquid diet. After examining her chart, a mistake is found stating that her weight is 500kg. what is the equivalent weight in pounds
Will the opposite of a opposite always be positive?
Yes, the opposite of an opposite will always return you to the original value, making it positive if you started with a positive number.
The question refers to the concept of opposites in Mathematics. When considering opposite numbers, the opposite of a positive number is negative, and vice versa. To answer the query, let’s break it down into steps.
First Opposite: The opposite of a positive number, say +5, is -5.Second Opposite: The opposite of -5 is, again, +5.So, yes, the opposite of an opposite will always be positive if you start with a positive number. Similarly, the opposite of an opposite will be negative if you start with a negative number, returning to the original number. This concept is crucial in understanding signed numbers and their roles in arithmetic and algebra.
Determine if the number is divisible number 15
A 33 - m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 37 m . Find the length of the shadow. If necessary, round your answer to the nearest tenth.
To solve this, we use Pythagoras' theorem as we have a right-angled triangle formed by the building, its shadow and the line between the top of the building to the end of the shadow. We find that the length of the shadow is approximately 16.7 meters.
Explanation:To solve this problem, we need to apply Pythagoras' theorem because the building, the shadow and the line between the top of the building to the end of the shadow form a right-angled triangle.
Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as:
a² + b² = c²
In this scenario, the height of the building is one side of the triangle (a), the shadow is the other side (b), and the line from the top of the building to the tip of the shadow is the hypotenuse (c).
So, to find the length of the shadow, we rearrange the formula to solve for b:
b = sqrt(c² - a²)
Then, we substitute the known values:
b = sqrt( (37m)² - (33m)²) = sqrt(1369 - 1089) = sqrt(280) = 16.7m
So, the length of the shadow is approximately 16.7 meters.
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What is the answer to 8=56, 7=42, 6=30, 5=20, 3=?
Corresponding range of Celsius temperature C
if the quotient of -20 and 4 is decreased by 3 what number results
quotient is division
-20/4 = -5
-5 -3=
-8
the number is -8
can someone please help me with using the quadratic formula to find the solutions to the equation
What is 7 to the 4 world power in expanded form?
Find the sum of 914 and 878
6×12=(6×7)+(6×_)=answer plz
Anyone know the answer to these problems?
Explain with steps
Correct answer will receive Brainliest
Simplify:-3 1/2-(12 1/4)
Lisa and Alice are playing a game. Each player either receives or has to pay play money based on the result of their apin. The table lists how much a player reieves or pays for various spins.
Answer:
Outcome Bag of Gold Magic Wand
Relative frequency 0.32 0.68
The relative frequency of getting a bag of gold is .......... reasonably close
.32 is close to 30% so
Alison's claim about the theoretical probability is likely to be 2............true
Further, this means that the theoretical probability of getting a magic wand is most likely 3............1 - 30% = 70%
Step-by-step explanation: