Which letters from the table represent like terms? -2x 3 4x 1
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A publisher estimates their costs of publishing a book is from $980,000 to $1,240,000. So far, they have spent $824,000. Which compound inequality correctly expresses how much more the publisher can spend?
$155,850 ≥ x ≤ $415,850
$155,850 ≤ x ≥ $415,850
$155,850 ≥ x ≥ $415,850
$155,850 ≤ x ≤ $415,850
Answer:
[tex]155,850 \leq x \leq 415,850[/tex]
Step-by-step explanation:
A publisher estimates their costs of publishing a book is from $980,000 to $1,240,000.
Let x be the amount publisher can spend
So, [tex]980000\leq x \leq 1240000[/tex]
Now we are given that So far, they have spent $824,000
So, [tex](980000-824000)\leq x \leq (1240000-824000)[/tex]
[tex]156000\leq x \leq 416000[/tex]
So, Option D is true
Hence compound inequality correctly expresses how much more the publisher can spend is [tex]155,850 \leq x \leq 415,850[/tex]
Vanessa made 6 sandwiches for a party and cut them all into fourths. How many 1/4 sandwich pieces did she have?
Estimates 3 2/3 \ 3 2/9
Step by step how to factor:
2y^2+9y+9=0
Solve. 54 ÷ (4 – 1)3
carl puts $1.10 in his piggy bank everyday in month of July (31 days)his total saving was $55.00 at the end of June what is the best estimate for his savaging at the end of June
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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Which expression is the factorization of x2 + 10x + 21?
A) (x + 3)(x + 7)
B) x + 4)(x + 6)
C) (x + 6)(x + 15)
D) (x + 7)(x + 14)
A sum of money is invested at 12% compounded quarterly. About how long will it take for the amount of money to double?
Compound interest formula: (image uploaded V(t) )
t = years since initial deposit
n = number of times compounded per year
r = annual interest rate (as a decimal)
P = initial (principal) investment
V(t) = value of investment after t years
A. 5.9 years
B. 6.1 years
C. 23.4 years
D. 24.5 years
Compound interest is the interest generated overtime on a sum of money invested. The time it will take for the amount of money to double is 5.9 years
How to calculate the compound interest?Compound interest is the interest generated overtime on a sum of money invested. The formula for calculating compound interest is expressed as:
V(t) = P(1+r/n)^nt
where:
t = years since initial depositn = number of times compounded per yearr = annual interest rate (as a decimal)P = initial (principal) investmentV(t) = value of investment after t yearsGiven the following
V(t) = 2P
r = 0.12
n = 4
Substitute
2P = P(1+0.12/4)^4t
2 = (1.03)^4t
ln2 = 4t ln(1.03)
0.6931 = 0.1182t
t = 0.6931/0.1182
t = 5.9 years
Hence the time it will take for the amount of money to double is 5.9 years
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Need help with this problem
Scott has fees taken out of his bank account each month for 3 months. A total of $12 is taken from his bank account.
Drag the numbers to form the equation that represents the change in Scott's bank account each month.
( ? )( ? ) = ( ? )
3, -3, 12, -12, 1/3, -1/3, 4, -4
Show work
A number n is less than 6 units from 0. Write an absolute value inequality
The absolute value inequality which relates to the expression n is less than 6 units from 0 is |n|< 6
The absolute value which stand for 6 units From 0 can be expressed as :
|0 - 6| = 6 (absolute value of any number or expression is always positive)This means that, the number n is less than 6
Therefore, the expression can be written as :
|n| < 6. This means that the absolute value of n is less than 6.
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To write an absolute value inequality when a number n is less than 6 units from 0, use the notation |n| < 6.
Explanation:To write an absolute value inequality, we need to express the distance between the number n and 0 as less than 6 units. This can be done by using the absolute value notation: |n| < 6. In this inequality, the absolute value of n must be less than 6 units.
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Order these fractions from greatest to least. 4/9 , 4/10 , 4/5
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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write an expression 13+ 19+ 17 using mental math
Explanation:
It is convenient to regroup the numbers, and adjust two of them to "make a ten".
= 13 + 17 + 19 . . . . rearrange (swap the order of 17 and 19)
= (10 + 3) + (-3 + 20) + 19 . . . . "make a ten" by adding or subtracting a small number. Here, those adjustments cancel—which is the point of doing it.
= 10 + 20 + 19
= 30 + 19
= 49
Margaret uses 1 3/4 teaspoons of vanilla to make 12 cupcakes. She to wants make 30 cupcakes. how much vanilla will Margaret use?
To make 30 cupcakes Margaret needs 4.375 cups of vanilla.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
Margaret uses 1 3/4 teaspoon of vanilla to make 12 cupcakes
So,
1 3/4 teaspoon vanilla ⇒ 12 cupcakes
(4×1 + 3)/4 teaspoon ⇒ 12 cupcakes
7/4 teaspoon vanilla ⇒ 12 cupcakes
Divide by 12 into both sides,
7/(4×12) teaspoon vanilla ⇒ 1 cupcake
Now multiply by 30 on both sides,
(7 × 30)/(4 × 12)teaspoon vanilla ⇒ 30 cupcake
30 cupcakes ⇒ 4.375 teaspoon vanilla.
Hence "To make 30 cupcakes Margaret needs 4.375 cups of vanilla".
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The sum of two consecutive integers is 65. Find the two integers.
what is 3/4 of 535?????????
pep club members are making spirit buttons. They make 490 spirit buttons in 3 1/2 hours. Find the number of button pep club makes per hour
Answer:
140 button pep club makes per hour.
Step-by-step explanation:
Given : Pep club members are making spirit buttons. They make 490 spirit buttons in [tex]3\frac{1}{2}[/tex] hours.
To find : The number of button pep club makes per hour ?
Solution :
In [tex]3\frac{1}{2}[/tex] hours they make 490 buttons.
i.e. In 3.5 hours they make 490 buttons.
So, In 1 hours they make [tex]\frac{490}{3.5}[/tex] buttons.
In 1 hours they make 140 buttons.
Therefore, 140 button pep club makes per hour.
One card is randomly selected from a deck of cards. find the odds against drawing a blackblack fivefive.
Find the sum of 914 and 878
Factor the difference of two cubes
Consider the equation 3p – 7 + p = 13. What is the resulting equation after the first step in the solution?
Is the value 75+(-75) less than zero, equal to zero, or greater than zero?
Find the area of a triangle that has a base of 10 inches and a height of 7 inches.
A) 8.5 in2
B) 17 in2
C) 35 in2
D) 70 in2
Answer:
C ) 35 in2
Step-by-step explanation:
i did the test
Car X leaves Northtown traveling at a steady rate of 55 mph. Car Y leaves 1 hour later following Car X, traveling at a steady rate of 60 mph. Which equation can be used to determine how long after Car X leaves Car Y will catch up?
The equation that can be used to determine how long after Car X leaves Car Y will catch up is D. 55x = 60(x - 1).
To determine when Car Y will catch up to Car X, we need to find the time it takes for Car Y to cover the same distance as Car X. Since Car Y leaves 1 hour later, it will travel for (x - 1) hours, where x represents the time Car X has been traveling. So, the equation would be:
D. 55x = 60(x - 1)
This equation accounts for the distance traveled by both cars over the same time frame, considering Car Y started an hour later.
Complete question : Car X leaves Northtown traveling at a steady rate of 55 mph. Car Y leaves 1 hour later following Car X, traveling at a steady rate of 60 mph. Which equation can be used to determine how long after Car X leaves Car Y will catch up? A. 55x=60x-1 B.55x=60x C.60x=55x(x-1) D.55x=60(x-1).
If one inch represents 8 feet, what dimensions would you use to make a scale drawing of a building 34 feet by 75 feet?
Please answer and explain!
DIVIDING ALGEBRAIC FRACTIONS
2p/4p^2 divided by 6p^3/6p+3
Gio is solving the quadratic equation by completing the square 5x^2+15x-4=0 What's should gio do first?
Gio should first complete the square by adding and subtracting [tex]\((\frac{3}{2})^2\)[/tex], leading to the equation [tex]\((x + \frac{3}{2})^2 = \frac{25}{4}\).[/tex]
To solve the quadratic equation [tex]\(5x^2 + 15x - 4 = 0\)[/tex] by completing the square, Gio should follow these steps:
1. Make the Coefficient of [tex]\(x^2\) 1:[/tex]
Divide the entire equation by the coefficient of [tex]\(x^2\)[/tex] to make it equal to 1. In this case, divide the equation by 5:
[tex]\[x^2 + 3x - \frac{4}{5} = 0.\][/tex]
2. Move the Constant to the Other Side:
Move the constant term to the other side of the equation:
[tex]\[x^2 + 3x = \frac{4}{5}.\][/tex]
3. Complete the Square:
Add and subtract [tex]\((\frac{3}{2})^2\)[/tex] inside the parentheses to complete the square:
[tex]\[x^2 + 3x + (\frac{3}{2})^2 = \frac{4}{5} + (\frac{3}{2})^2.\][/tex]
4. Factor the Perfect Square Trinomial:
Factor the left side, which now is a perfect square trinomial:
[tex]\[(x + \frac{3}{2})^2 = \frac{25}{4}.\][/tex]
5. Solve for (x):
Take the square root of both sides and solve for (x):
[tex]\[x + \frac{3}{2} = \pm \frac{5}{2}.\][/tex]
6. Isolate (x):
Isolate (x) on one side to find the solutions:
[tex]\[x = -\frac{3}{2} \pm \frac{5}{2}.\][/tex]
Therefore, Gio should first complete the square by adding and subtracting [tex]\((\frac{3}{2})^2\)[/tex], leading to the equation [tex]\((x + \frac{3}{2})^2 = \frac{25}{4}\).[/tex]