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]
Ben measures the height of two bottles. One is 12 centimeters, and the other is 15 centimeters. In millimeters, what is the difference of the two heights?
Answer:
30 millimeters
Step-by-step explanation:
What is the square root of 360 rounded to the nearest thousandth
weight A weighs 50 pounds. weight B weighs 100 pounds. if A is placed 6 feet from the pivot, how far must B be placed from the pivot in order for the bar to achieve balance?
To achieve balance, the momentum on both sides must be equal so that it cancels out. Momentum is simply the product of mass and distance, therefore:
50 pounds * 6 ft = 100 pounds * X
X = 3 ft
Hence B must be placed 3 ft from the pivot.
greatest common factor for 8x and 40
what are 2 fractions between 3/5 and 4/5?
Which angle pairs are supplementary? Check all that apply
The sum of two angles is equal to [tex]180^\circ[/tex] than the angle pairs are known as supplementary angles. Therefore, from the given diagram angle pairs [tex]\rm \angle 3\;and\;\angle6[/tex], [tex]\rm \angle 5\;and\;\angle6[/tex], [tex]\rm \angle 4\;and\;\angle5[/tex], [tex]\rm \angle 3\;and\;\angle4[/tex] and [tex]\rm \angle 7\;and\;\angle 8[/tex] are supplementary angles. So, the correct options are: B), C), and E).
Given :
[tex]\angle 3 = 90^\circ[/tex]
The sum of two angles is equal to [tex]180^\circ[/tex] than the angle pairs are known as supplementary angles.
From the diagram given in the question it can be clearly observe that if [tex]\angle 3 = 90^\circ[/tex] than [tex]\rm \angle 4,\;\angle 5,\;and\;\angle 6[/tex] are also equal to [tex]90^\circ[/tex].
Than according to the definition of supplementary angles:
[tex]\angle 3 +\angle6 = 180^\circ[/tex]
[tex]\angle 3 +\angle4 = 180^\circ[/tex]
[tex]\angle 4 +\angle5 = 180^\circ[/tex]
[tex]\angle 5 +\angle6 = 180^\circ[/tex]
[tex]\angle 7 +\angle8 = 180^\circ[/tex]
Therefore, angle pairs [tex]\rm \angle 3\;and\;\angle6[/tex], [tex]\rm \angle 5\;and\;\angle6[/tex], [tex]\rm \angle 4\;and\;\angle5[/tex], [tex]\rm \angle 3\;and\;\angle4[/tex] and [tex]\rm \angle 7\;and\;\angle 8[/tex] are supplementary angles.
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Can anyone gimme the answer ASAP please
A powdered drink mix calls for a ratio of powder to water of 1:8 if there are 32 cups of powder how many total of water are needed? explain your reasoning
Josh and Eva are packing first-aid supplies. It takes Josh 12 minutes to fill a box with Bandages. It takes Eva 8 minutes to fill a box with antibiotics. If they start packing boxes at the same time, how long will it be before they start filling a new box at the same time.
What is the recursive formula for this geometric sequence?
Answer: B.
[tex]a_1=2\\a_n=a_n\times(-5)[/tex]
Step-by-step explanation:
The given geometric sequence : 2, -10, 50, -250
The first term of the sequence : [tex]a_1=2[/tex]
The common ratio between the terms :[tex]r=\dfrac{-10}{2}=-5[/tex]
We know that the recursive formula for geometric progression is given by :-
[tex]a_n=a_{n-1}r[/tex]
Then , the recursive formula for the given geometric progression will be :-
[tex]a_n=a_n\times(-5)[/tex]
If mary ellen invest x dollars at 5%, write an equation that describes the total interest
For a one-year investment, the equation is I = x imes 0.05 imes 1.
If Mary Ellen invests x dollars at an interest rate of 5%, we can write an equation that describes the total interest earned on that investment using the simple interest formula. The formula for calculating simple interest is Interest = Principal imes Rate imes Time. Assuming the investment is for 1 year, the equation for the total interest (I) Mary earns would be:
I = x imes 0.05 imes 1
This equation states that the interest Mary earns is equal to the amount of money she invested (x dollars) multiplied by the interest rate (5% or 0.05 as a decimal) and the time the money is invested (1 year).
If Mary Ellen invests $100, the total interest she would earn in one year at a 5% interest rate would be calculated as follows:
I = $100 imes 0.05 imes 1 = $5
in a fish tank 6/7 of the fish have a red stripe on them . if 18 of the fish have red stripes how many total fish are in the tank?
it is 7 kilometers from Kerry's house to the mall. About what is that distance in miles
Calculate the rf value for the reactant b spot. estimate the ruler to the nearest tenth, report the answer using two significant figures.
The fraction model below shows the steps that a student performed to find a quotient. Which statement best interprets the quotient?
There are [tex]\rm 6 \frac{1}{4}[/tex] two - third in [tex]\rm 4 \frac{1}{6}[/tex]. Statement A best interprets the quotient.
What is the definition of a fraction number?A fraction number is a number that represents a portion of a larger number, where the larger number might be any integer. It has the shape of a numerator and a denominator.
The shaded part in step 1 is;
[tex]\rm 4 + \frac{1}{6} = 4 \frac{1}{6}[/tex]
Divide the shaded part with the unshaded part as ;
[tex]\rm \frac{4 \frac{1}{6} }{\frac{2}{3}}\\\\ \frac{25}{6} \times \frac{3}{2} \\\\\ \frac{25}{4} \\\\ 6 \frac{1}{4}[/tex]
There are [tex]\rm 6 \frac{1}{4}[/tex] two - third in [tex]\rm 4 \frac{1}{6}[/tex].
Hence, statement A best interprets the quotient.
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Answer: A
Step-by-step explanation:
Your car is a real gas guzzler getting 15 miles to the gallon on the highway using regular gas which at this time costs $ 4.35/gallon. You have a 25 gallon tank in the car and want to drive to visit a trade show in Memphis, Tennessee which is 1780 miles from Los Angeles. You drive on average 70 miles per hour and spend 2 days and nights at the convention during which time you do not drive your car, You do however check into a hotel room which costs $95.00 per night plus a 12% room tax. Your meals cost a total of $35.00 per day for the 2 days that you are in town. You also decide to leave a tip for the waiter of 20% of your meal bill. On the last day of the trip, you decide to purchase an Apple iPod as a gift for your child and an iPad Tablet for yourself which costs $ 589.00. The iPad costs $589.95 and the iPod costs $ 265.95 plus sales tax of 9.25%. What is the total amount yo will spend for the trip? What are the key elements of the problem and what is the answer?
Angela ordered 2 glass paperweights. The volume of each paperweight is 5 cubic inches, and the density of the glass is 1.5 ounces per cubic inch. Angela can use the calculation below to find the total weight of her order.
2×(5×1.5)
How can Angela simplify the calculation using only the associative property of multiplication?
Drag and drop the appropriate number or expression into each box.
Answer:
[tex](2\times 5)\times 1.5[/tex]
Step-by-step explanation:
Since, according to associative property of multiplication,
a(bc) = (ab)c,
Where a, b and c are any real numbers,
Here, the given expression,
2 × ( 5 × 1.5 ),
By applying the associative property of multiplication,
( 2 × 5 ) × 1.5,
Hence, the appropriate expression in the first box is '(2×5)'
And, the appropriate number in the second box is '1.5'.
Answer:
first box is (2 times 5) next box is 1.5
Step-by-step explanation:
i took K12 test :)
What is the solution to the inequality |x-4|<3
Answer:
The solution of the given inequality [tex]|x-4|<\:3\:[/tex] is [tex]1<x<7[/tex]
Step-by-step explanation:
Given inequality [tex]|x-4|<\:3\:[/tex]
We have to find the solution of the given inequality [tex]|x-4|<\:3\:[/tex]
Using absolute rule, [tex]\mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex], we have,
[tex]-3<x-4<3[/tex]
Rewrite as [tex]x-4<-3\quad \mathrm{and}\quad \:x-4<3[/tex]
Consider , [tex]x-4>-3[/tex]
Adding 4 both side, we have,
[tex]x-4+4>-3+4[/tex]
Simplify, we have,
[tex]x>1[/tex]
Consider , [tex]x-4<3[/tex]
Adding 4 both side, we have,
[tex]x-4+4<3+4[/tex]
Simplify, we have,
[tex]x<7[/tex]
Combining, we have,
[tex]1<x<7[/tex]
Thus, The solution of the given inequality [tex]|x-4|<\:3\:[/tex] is [tex]1<x<7[/tex]
A restaurant used 9.5 ounces of cheese to make 5 slices of pizza. If each slice had the same amount of cheese, how much cheese was on each slice?
Simplify the expression: Sqrt(16 − x^2)
as much as possible after substituting "4 sin x" for x.
Final answer:
Simplify the expression √(16 − x²) by substituting x with '4 sin x' to get 4|cos x|. Use trigonometric identities to arrive at the simplified expression.
Explanation:
The expression to simplify is: √(16 − x²) after substituting '4 sin x' for x.
Step-by-step solution:
Replace x with 4 sin x in the expression: √(16 − (4 sin x)²)
Simplify: √(16 − 16 sin² x)
Apply trigonometric identity: √(16 cos² x) = 4|cos x|
25 POINTS I NEED HELP
What is the sum of the first five terms of the geometric series 2 − 8 + 32 − . . . ?
My clock is 75 inches tall and 28 in wide .What is the ratio of height to wide in fraction form
The ratio of height to wide in the fraction form of the clock is 75/28.
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.
Height of clock = 75 inches.
Width of clock = 28 inches.
The ratio of height to width = Height of clock / Width of clock
So,
The ratio of height to width = = 75/28.
Hence "The ratio of height to wide in the fraction form of the clock is 75/28".
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A car travels at 65 miles per hours. Going through construction it travels at 3/5 this speed. Write this fraction as a decimal and find the speed.
how do you unsquare something? if i know what r squared is how do i find r?
Find the equation of the line that contains the point (3,9) and is parallel to the line y=4x+1. Write the line in slope-intercept form. Graph the lines
The equation of the line parallel to y=4x+1 passing through (3,9) is y=4x-3. It has the same slope of 4 but a different y-intercept, showing that the lines are parallel and do not intersect.
Explanation:To find the equation of the line that contains the point (3,9) and is parallel to the line y=4x+1, we start by noting that parallel lines have the same slope. The given line has a slope of 4, so our new line will also have a slope of 4. The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.
Since we have a point (3,9) and a slope of 4, we can use the point-slope form to find our new line:
y - y₁ = m(x - x₁)
Plugging in our point and slope, we get:
y - 9 = 4(x - 3)
Expanding this, we have:
y - 9 = 4x - 12
Add 9 to both sides to get it into slope-intercept form:
y = 4x - 3
Therefore, the equation of the line parallel to y=4x+1 that passes through (3,9) in slope-intercept form is y = 4x - 3.
When graphing these two lines, you'll notice they never intersect, as they have the same slope but different y-intercepts, which is a distinctive feature of parallel lines.
To find the equation of a line that is parallel to another line, we need to determine the slope of the given line and then use the point-slope form of a linear equation. The equation of the line parallel to y = 4x + 1 and passing through the point (3,9) is y = 4x - 3. The graph of the lines show that they are parallel.
Explanation:To find the equation of a line that is parallel to another line, we need to determine the slope of the given line and then use the point-slope form of a linear equation.
The given line y = 4x + 1 has a slope of 4 because it is in the form y = mx + b, where m is the slope. Since the line we want to find is parallel to this line, it will also have a slope of 4.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point on the line, we can substitute the values (3, 9) and 4 for x1 and m, respectively, to get the equation:
y - 9 = 4(x - 3)
Expanding and rearranging the equation, we get:
y = 4x - 3
Graphing the lines:The graph of the given line y = 4x + 1 is a straight line with a slope of 4 and a y-intercept of 1. The line we found, y = 4x - 3, is also a straight line with the same slope but a different y-intercept. By plotting the two lines on the same graph, we can visually see that they are parallel.
Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. 4log x + 2log y
The simplified expression is log (x⁴y²).
What is a logarithm?Inverse to exponentiation is the logarithm.
The given expression is 4log x + 2log y.
Simplify the expression as follows:
4log x + 2log y
= log x⁴ + log y²
= log (x⁴y²)
Hence, the simplified expression is log (x⁴y²).
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If RS=ST then point S is called the midpoint of .
The statement 3+3=6 serves as a/an _ to the conjecture that the sum of two odd numbers is an odd number .
3 Hundredths + 4 hundredths