Answers
________________________________________________________
Explanation:
________________________________________________________
Given the following equation:
________________________________________________________
" x² + 3x – 54 = 0 " ; Solve for "x" ;
_____________________________________________________
Check if the part of the equation on the "left-hand side" can be "factored":
" x² + 3x – 54 " ;
→ We see the " + 3x " and the " – 54 "
Factors of " -54 " that add up to " +3" ;
Let us try: " -9, 6" ; → " -9 + 6 = -3 " ; → " -3 ≠ +3 ;
Let us try: " 9, -6" ; → " 9 + (-6) = 9 – 6 = 3 " ; YES!
→ {that is: " +9 , -6 "} ;
So, we can rewrite the entire equation:
→ " (x + 9)(x – 6) = 0 " ;
→ " x = -9 " ; or, " x = 6 " ; which is:
→ Answer choice: [A]: " x = 6 " or " x = - 9 " .
______________________________________________________
Related Questions
How many numbers less than 1000 are divisible by 7?
Answers
A store owner paid $15 for a book she marked up the price of the the book by 40% to determine its selling price part A what is the selling price of the book? Part B a customer buys a different book that has an original selling price of $38 the book is discounted 25% the costumer must pay 6% sales tax on the discounted price of the book .what is the total amount the customer must pay for the discounted book
Answers
40% = 0.4
15*0.4 = 6
15 + 6 = 21
The marked up price is $21
B:
To find the discounted price:
25% = 0.25
38*0.25 = 9.5
38 - 9.50 = 28.50
To find the tax and price after tax:
6% = 0.06
28.50*0.06 = 1.71
So tax is $1.71
28.50 + 1.71 = 30.21
Price after tax is $30.21
I'll give you brainliest answer!! Help me. This diagram shows a smaller square inscribed within a larger square.
Answer with supporting work:
Answers
hypotenuse^2 = 3^2 + 4^2
hypotenuse^2 = 9 + 16
hypotenuse^2 = 25
hypotenuse = 5
Therefore, the area of the smaller square is 5 * 5 = 25
7x(x+4)
A. 7x^2+4
B. 7x^2+28x
C.8x+4
D.8x+11
Answers
Use distributive property:
a(b + c) = ab + ac.
7x(x + 4) = (7x)(x) + (7x)(4) = 7x² + 28x
Answer: B. 7x^2 + 28xFind the inverse of the following function. f(x) 8√ x for x > 0
Answers
The inverse of the function f(x) = 8√x for x > 0 is g(x) = x^2/64.
To find the inverse of the function f(x) = 8√x for x > 0, we need to interchange the roles of x and y and solve for y.
Let's start by rewriting the function using y instead of f(x):
y = 8√x
Next, we'll swap x and y:
x = 8√y
To isolate y, we can square both sides:
[tex]x^2 = (8\sqrt y)^2\\\\x^2 = 64y[/tex]
Now, divide both sides by 64:
[tex]x^2/64 = y[/tex]
Simplifying further:
[tex]y = x^2/64[/tex]
Therefore, the inverse of the function f(x) = 8√x for x > 0 is given by [tex]g(x) = x^2/64.[/tex]
To know more about inverse, refer here:
https://brainly.com/question/28595565
#SPJ6
Evaluate the determinant for the following matrix:
-4 -4 -3
3 3 -5
-5 2 -5
A. –203 B. 75 C. –152 D. –263
Answers
Answer:
The determinant of matrix is -203
Step-by-step explanation:
Given the matrix of order 3 i.e
[tex]A=\begin{bmatrix}-4&-4&-3\\ 3&3&-5\\ -5&2&-5 \end{bmatrix}[/tex]
we have to find the determinant of matrix A
[tex]|A|=-4(-5(3)-(-5)(2))-3((-4)(-5)-(-3)(2))+(-5)((-5)(-4)-(-3)(3))\\\\|A|=-4(-15+10)-3(20+6)-5(20+9)\\\\|A|=-4(-5)-3(26)-5(29)\\\\|A|=20-78-145\\\\|A|=-203[/tex]
Hence, the determinant of matrix is -203
Option A is correct.
A tent forms an equilateral triangular prism, with both triangular faces exposed. each side of the triangular face has a length of 196196196 centimeters (\text{cm})(cm)left parenthesis, c, m, right parenthesis, and the tent is 250\,\text{cm}250cm250, space, c, m long. what is the height, in centimeters, of the tent?
Answers
Equilateral Triangular Prism
Each side of the triangular face has a length of 196cm
The tent is 250cm long
I have attached an image of the tent. Since the height of the tent is also the height of the triangle, I will solve for the height of the triangle using Pythagorean theorem.
I divided the equilateral triangle into 2 right triangle. The height then becomes the long leg of the triangle. The hypotenuse is 196cm and the short leg is 98cm, half of one side of the triangle.
a² + b² = c²
a² = c² - b²
a² = (196cm)² - (98cm)²
a² = 38,416cm² - 9,604cm²
a² = 28,812cm²
a = √28,812cm²
a = 169.74cm
The height of the tent is 169.74 centimeters.
Medals and Fan!
Given a segment with endpoints A and B, what figure can you construct using the steps below?
Step 1: Draw a ray with endpoint C.
Step 2. Open the compass to the length of AB
Step 3: With the same compass setting, put the compass point on point C. Draw and arc that intersects the ray. Label the point of intersection D.
A. A perpendicular Bisector
B. A congruent segment
C. an angle bisector
D. a congruent angle,
Answers
help, please simplify.. thank you
Answers
[tex]\bf \cfrac{37(42)\times 10^{-13}}{25(4)\times 10^910^{-15}}\implies \cfrac{1554\times 10^{-13}}{100\times 10^{9-15}}\implies \cfrac{1554\times 10^{-13}}{1\times 10^2\times 10^{9-15}} \\\\\\ \cfrac{1554\times 10^{-13}}{10^{2+9-15}}\implies \cfrac{1554\times 10^{-13}}{10^{-4}}\implies 1554\times 10^{-13}\times 10^4 \\\\\\ 1554\times 10^{-13+4}\implies 1554\times 10^{-9}\implies \cfrac{1554}{10^9}\implies 0.000001554[/tex]
Troy’s canoe is 18 feet long. Ariel’s canoe is 5/6 the length of Troy’s canoe.
What is the length of Ariel’s canoe?
Express your answer in simplest form
Answers
90/6 = 15
it is 15 feet
What exponential function is the best fit for the data in the table?
x f(x)
2 -3
3 0
4 12
A. f(x) = 4(4)^x - 1 + 4
B. f(x) =4(4)^ x - 1 - 4
C. f(x) = 1/4(4)^x -1 + 4
D. f(x) = 1/4(4)^ x - 1 - 4
Answers
There are multiple ways to get to the right answer. You could plot the points on a graphing calculator. Then, graph each function to determine which equation matches the points.
You could also input the x values and see which equation produces the y values in the chart.
On thing to notice is the we have negative output values, there we need to pick either B or D, so the values go beneath the x-axis.
Answer:
option D.
Step-by-step explanation:
Data given in the table is
x 2 3 4
f(x) -3 0 12
Now we will plug in the values of x in the given functions to find the correct exponential function.
For x =2
A). f(x) = 4(4)[tex]^{(x-1)}[/tex] + 4
f(2) = 4(4)[tex]^{2-1}[/tex] + 4 = 4 × 4 + 4 = 20
B). f(x) = 4(4)[tex]^{(2-1)}[/tex] - 4
f(2) = 4(4)[tex]^{2-1}[/tex] - 4 = (4)(4) - 4 = 16 - 4 = 12
C). f(x) = 1/4(4)[tex]^{x-1}[/tex] +4
1/4(4)[tex]^{2-1}[/tex] + 4 = [tex]\frac{1}{4}[/tex] × 4 + 4
= 1 + 4 = 5
D). f(x) = [tex]\frac{1}{4}(4)^{x-1}-4[/tex]
f(2) = [tex]\frac{1}{4} (4)^{2-1}-4=\frac{1}{4}(4)-4[/tex]
= 1 - 4 = -3
We find option D in which f(2) = (-3). so the answer would be option D.
Which of the following statements describes a correct method for solving the equation below?
3x + 3 = 6x
A. Subtract 3x from both sides of the equation, and then divide both sides by 3.
B. Add 3x to both sides of the equation, and then divide both sides by 3.
C. Divide both sides of the equation by 6, and then subtract 3 from both sides.
D. Divide both sides of the equation by 6, and then add 3 to both sides.
Answers
_____
The other choices get you to a place where further work is necessary. They don't really contribute to solving the equation.
3x + 3 = 6x
3x-3x + 3 = 6x - 3x
(3x -3x cancel each other out, leaving you with 3)
3 = 3x
3/3 = 3x/3
1 = x
x = 1
Now Verify-
3x + 3 = 6x
3(1) + 3 = 6(1)
3 +3 = 6
6 = 6
Now can also use the guess and check way. But this is my way of solving it. I hope it helped.
which reason justifies the last step in a proof that ΔEDG≌ΔADC?
Answers
fd is congruet to db
ed is congruent to da
and vertical angles theorem
What is the measure of ∠EGF?
What is the measure of ∠CGF?
Answers
= 1/2(130)
= 65
the measure of ∠CGF = 180 - 65
= 115
This is an isosceles triangle, which means its base angles are congruent. Interior angles of triangle add to equal 180 degrees, so you can make an equation to solve for the measure of the base angles. I'll call the base angles x.
180 = 50 + 2x
130 = 2x
65 = x
That gives you m∠EGF and m∠FGE (65°).
To find m∠CGF, you must know that it and ∠EGF are supplementary (they add to equal 180 degrees). Make another equation setting them to equal 180 using m∠EGF (65°):
180 = 65 + x
115 = x
Answer:
m∠EGF = 65°
m∠CGF = 115°
Yesterday , the snow was 2 feet deep in front of archies house. Today, the snow depth dropped to 1.6 feet because the day is so warm.What is the percent change in the depth of the snow?
Answers
later snow depth = 1.6 feet
change
2 - 1.6
0.4 feet
percentage change
(0.4 / 2) * 100
20 %
Can someone please help me.
The polygons are similar. Write a similarity statement and give the scale factor
Answers
[tex] \frac{4}{3} [/tex]
all you need to so is take one of the sides from the larger figure and divide it by the corresponding side on the smaller figure for example
[tex] \frac{24}{13} [/tex]
which simplifys to your answer
[tex] \frac{4}{3} [/tex]
Many 1/2 inch cubes can fit into a box that is 15 inches tall, 1 1/2 inches wide, and 3 inches long?
Answers
A trapezoid has an area of 150 square meters. If the bases are 14 meters and 16 meters, what us the height of the trapezoid?
Answers
[tex]a = \frac{1}{2} (b1 + b2) \times h[/tex]
In this formula a represents the area and b1 and b2 each represent a base of the trapezoid.
So, we have got the following information
[tex]a = 150[/tex]
[tex]b1 = 14[/tex]
[tex]b2 = 16[/tex]
Filling in the formula gives us:
[tex]150 = \frac{{1} }{2} \times (14 + 16) \times h[/tex]
[tex]150 = \frac{1}{2} \times 30 \times h[/tex]
[tex]150 = 15 \times h[/tex]
Finally we have to divide both sides by 15.
[tex]h = 150 \div 15 = 10[/tex]
Therefore, the height of the trapezoid is 10 meters.
A lake has the capacity to support 10,000 trout. Suppose that the conditions are such that the current population of trout will grow logistically up until it stabilizes at the amount that the lake can support. Currently there are 1,500 trout in the lake. Which of the following is a possible model for P(t), the trout population in t years?
Answers
Answer:
P(t) = 10,000/ (1+9e^-0.48t)
Step-by-step explanation:
i think because it starts at around 1500 for t=1 and then when t=2 and so on it grows exponentially.
Choose the BEST answer.
1. What is a Web page? (1 point)
A single page of a Web site that consists of an HTML document
The entry page of the Web site
Web page that is located in the same group of Web pages or Web Site as th
document
2. What is a home page? (1 point)
A single page of a Web site that consists of an HTML document
The entry page of the Web site
Web page that is located in the same group of Web pages or Web Site as th
document
3. What is the object of storyboarding? (1 point)
To help you visualize your Web site before writing any pages in HTML. To help prevent duplicati
Answers
2. A home page is the entry page of the Web site
3.The object of storyboarding is to help you visualize your Web site before writing any pages in HTML.
Answer:
1)
A single page of a Web site that consists of an HTML document.
2)
The entry page of the Web site.
3)
The object of storyboarding is to help you visualize your Web site before writing any pages in HTML.
Step-by-step explanation:
Web page:
A web page or webpage is a document commonly written in HTML (Hypertext Markup Language) that is accessible through the Internet or other networks using an Internet browser.
Hence, option: A is true.
Home page:
A home page also refers to the first page that appears upon opening a web browser, sometimes called the start page.
Hence, option: B is correct.
( The entry page of the Web site )
object of storyboarding:
The object of storyboarding is to help you visualize your Web site before writing any pages in HTML
You bought a coat at $78.50 and two shirts at $21.99 each. if the sales tax rate is 7%, how much is the total purchase?
Answers
Answer:
The answer is going to be $131.05
Step-by-step explanation:
I just took the test
This figure shows circle O with inscribed ∠XYZ. m∠XYZ=76∘ What is the measure of XYZ?
Answers
now, the inscribed angle is at ∡XYZ and is 76°, that means by the "inscribed angle theorem", the intercepted arcXZ, in red, is twice as much, namely 152°.
keeping in mind that a circle has a total of 360°, and since the red arc has already taken up 152°, the arcXYZ in blue, will pick up the slack from 360° - 152°, namely 208°.
how many fluid ounces are in 3 quarts and 2 cups ?
Answers
1quart= 4 cups
I hope this helped you.
Jennifer is 30 years old. She has $1200 in a checking account, $8000 in a savings account, $6000 in stock investments, $12,000 in a retirement account, and owns a car worth $8000. What is the total value of her liquid assets?
A. $20,000
B. $15,200
C. $23,200
D $25,200
APEX
Answers
Answer:
B.15,200
Step-by-step explanation:
Write the polynomial in standard form. Then name the polynomial based on it's degree and number of terms.
3 - 10x^2 - 7x + 3x^2
Answers
-7x^2 - 7x + 3
This is a trinomial because it has 3 terms.
The degree of this polynomial is 2.
Compare the values of the underlined digits.
34,258 and 47,163
- -
The value of 4 in _________ is______ times the value of 4 in ________
PLEASE ANSWER ASAP IT'S FOR MY SISTER
Answers
In the second number, the "4" is in the ten thousands place - meaning it's
40,000 + 7,163.
40,000/4,000 = 10
The value of 40,000 in the second value is 10x greater than the value of 4,000 in the first value.
In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 3x – 3, and HE = 5y + 4. Find the values of x and y.
x = 5, y = 12
x = 5, y = 9
x = 4, y = 9
x = 9, y = 4
Answers
DH = HF
x + 3 = 3y
GH = HE
3x - 3 = 5y + 4
We then have the following system of equations:
x-3y = -3
3x-5y = 7
Resolving the system graphically we obtain the following values:
x = 9
y = 4
Note: see attached image.
Answer:
The values of x and y are:
x = 9, y = 4
Final answer:
In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 3x – 3, and HE = 5y + 4. Solving the equations yields x = 9, y = 4.
Explanation:
To find the values of x and y in parallelogram DEFG, we'll use the properties of parallelograms. In a parallelogram, opposite sides are equal in length.
Given that DH = x + 3 and HF = 3y, and that DH is opposite to HF, we have:
x + 3 = 3y ...(1)
Similarly, given GH = 3x - 3 and HE = 5y + 4, and that GH is opposite to HE, we have:
3x - 3 = 5y + 4 ...(2)
Now, we have a system of two equations (1) and (2) to solve for x and y.
From equation (1):
x = 3y - 3 ...(3)
Substitute equation (3) into equation (2):
3(3y - 3) - 3 = 5y + 4
9y - 9 - 3 = 5y + 4
9y - 12 = 5y + 4
4y = 16
y = 4
Now, substitute the value of y into equation (3):
x = 3(4) - 3
x = 12 - 3
x = 9
So, the values of x and y are x = 9 and y = 4. Thus, the correct answer is x = 9, y = 4.
A person at ground level measures the angle of elevation to the top of a building to be 74degrees if at this point the person is 34 feet away from the base of the building, then how tall is the building round to the nearest tenth.
Show work
Will give brainliest to best answer
Answers
Let
h---------> building tall
we know that
tan 74°=h/34---------> h=34*tan 74°--------> 34*3.487------> 118.57
h=118.6 ft
the answer is h=118.6 ft
Find the least common multiple of x² + x – 12 and x² + 2x – 15.
Answers
Solution:
we have been asked to find the Least Common multiple of the given polynomial x² + x – 12 and x² + 2x – 15.
To find the least common multiple. Lets first find the factors.
[tex] x^2+x-12=x^2+4x-3x-12\\
\\
x^2+x-12=x(x+4)-3(x+4)\\
\\
x^2+x-12=(x+4)(x-3)\\ [/tex]
[tex] x^2+2x-15=x^2+5x-3x-15\\
\\
x^2+2x-15=x(x+5)-3(x+5)\\
\\
x^2+2x-15=(x+5)(x-3)\\ [/tex]
Hence the LCM of the given set of Polynomials is (x+4)(x-3)(x+5).
The LCM is (x+4)*(x-3)*(x+5)
please help me thank you.
Answers
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Any angle with sides that are radii and a vertex at the center of the circle is a central angle.