Answer:
10(3/2x-22+3y)
Step-by-step explanation:
A rectangle is enlarged by a factor of 6 that originally has the area of 20in squared. What is the area of the enlarged rectangle?
A: 120in squared
B: 720in squared
C: 2,400in squared
D: 14,400in squared
Answer:
The person on top is wrong the answer is 14,400 in.² or D
Step-by-step explanation:
The correct option is B. 720in squared. The area of the rectangle, when enlarged by a factor of 6, scales by the square of 6, resulting in an enlarged area of 720 square inches.
To determine the area of a rectangle after it has been enlarged by a factor, we need to understand how area scales with respect to the linear dimensions. When a shape is enlarged by a factor, the area scales by the square of that factor.
Given:
→ Original area = 20 square inches
→ Enlargement factor = 6
Steps to Find the Enlarged Area:
→ Calculate the scaling factor for the area:
= 6²
= 36.
→ Multiply the original area by this scaling factor:
= 20 in² * 36
= 720 in².
Therefore, the area of the enlarged rectangle is 720 square inches, which corresponds to answer choice B.
[tex]x^{2} - x - 6 \div {x}^{2} - 4[/tex]
[tex]\bf x^2-x-6\div x^2-4\implies \cfrac{x^2-x-6}{x^2-4}\implies \cfrac{(x-3)(x+2)}{\underset{\textit{difference of squares}}{x^2-2^2}} \\\\\\ \cfrac{(x-3)~~\begin{matrix} (x+2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{(x-2)~~\begin{matrix} (x+2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{x-3}{x-2}[/tex]
A large map of the United States uses a scale of $2 \text{ cm} = 2.5\text{ km}$. On the map, the distance between two cities is 1 meter. What is the actual distance between the two cities (in kilometers)? PLZ ANSWER NOW CORRECTLY FAST ILL GIVE 40 POINTSS!!!!!!! PLZZZZZZZZZZZZZZZZZZZZZ
Answer: (AoPS)
125
Step-by-step explanation:
A distance of 1 meter is 50 times 2 cm, so the actual distance between the two cities is 50 times 2.5 km, which is 125 km.
To find the actual distance between two cities on a map given a scale, convert the map distance to real-world distance using the scale ratio.
The actual distance between two cities on the map can be calculated as follows:
Given scale: 2 cm = 2.5 kmDistance on the map: 1 meterConvert meters to centimeters (1 meter = 100 cm)Use the scale to convert centimeters on the map to kilometers in realitySo, the actual distance between the two cities is 1.25 kilometers.
Twenty-seven less than twice a number is -1
Answer: 13
Step-by-step explanation:
2x-27=-1
2x=26
X=13
The expression of the given mathematical phrase Twenty-seven less than twice a number is -1 is 2x - 27 = -1 and that number will be 13.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
As per the given,
Twenty-seven less than twice a number is -1
Let's say that number is x.
Twice of x = 2x
27 less will be 2x - 27
It is equal to -1.
2x - 27 = -1
2x = -1 + 27
2x = 26
x = 13
Hence "The expression of the given mathematical phrase Twenty-seven less than twice a number is -1 is 2x - 27 = -1 and that number will be 13".
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Can u help me solve this
Explanation:
Rewrite the left side in terms of sine and cosine, then rearrange.
[tex](1+\tan^2{A})+(1+\dfrac{1}{\tan^2{A}})=\dfrac{1}{\sin^2{A}-\sin^4{A}}\\\\(1+\dfrac{\sin^2{A}}{\cos^2{A}})+(1+\dfrac{\cos^2{A}}{\sin^2{A}})=\\\\\dfrac{\sin^2{A}+\cos^2{A}}{\cos^2{A}}+\dfrac{\sin^2{A}+\cos^2{A}}{\sin^2{A}}=\\\\\dfrac{1}{\cos^2{A}}+\dfrac{1}{\sin^2{A}}=\\\\\dfrac{\sin^2{A}+\cos^2{A}}{(\sin^2{A})(\cos^2{A})}=\\\\\dfrac{1}{(\sin^2{A})(1-\sin^2{A})}=\dfrac{1}{\sin^2{A}-\sin^4{A}} \qquad\text{Q.E.D.}[/tex]
2. Write and solve an equation to find the value of x.
3.8, 4.2, 5.3, x; mean 4.8
Answer:
5.9
Step-by-step explanation:
The mean means arithmetic average (some people just say average here).
The average of 4 numbers is the sum of those 4 numbers divided by the number of numbers which is 4 in this case.
So we have this formula:
[tex]\frac{3.8+4.2+5.3+x}{4}=4.8[/tex]
Multiply both sides by 4:
[tex]3.8+4.2+5.3+x=4(4.8)[/tex]
Simplify:
[tex]13.3+x=19.2[/tex]
Subtract 13.3 on both sides:
[tex]x=19.2-13.3[/tex]
Simplify:
[tex]x=5.9[/tex]
What is the product of (3a + 2)(4a? - 2a + 9)?
1223 - 2a + 18
12a3 + 6a +9
12a3 - 6a+ 23a + 18
1223 + 2a + 23a + 18
Answer:
The answer is 12a^3+2a²+23a+18 ....
Step-by-step explanation:
The given terms are:
(3a + 2)(4a² - 2a + 9)
Now multiply each value of second bracket with the first bracket:
=4a²(3a+2) -2a(3a+2)+9(3a+2)
=12a^3+8a²-6a²-4a+27a+18
Solve the like terms:
=12a^3+2a²+23a+18
Therefore the answer is 12a^3+2a²+23a+18 ....
6. A square is inscribed in a circle. The sic
length of the square is 4 centimeters,
Calculate the area of the shaded region.
Answer:
9.13 cm^2.
Step-by-step explanation:
The diagonal of the square = the diameter of the circle.
The length of the diagonal = 4√2 cm (because we have a 45-45-90 triangle), so the radius of the circle is half of this = 2√2 cm.
The area of the shaded part = area of the circle - area of the square
= π (2√2)^2 - 4^2
= 25.13 - 16
= 9.13 cm^2.
7. How much 6% solution can you make by diluting 350 mL of a 15% solution
Answer:
We know that the formula to mix chemical solutions is: C1V1 = C2V2
where C represents the concentration of the solute, and V represents volume in milliliters or ml.
In this case, we have:
0.06V1 = 0.15×350
Solving for 'V1' we have:
V1 = (0.15×350)/0.06 = 52.5/0.06 = 875
Therefre I can make 875 mL of a 6% solution by diluting 350 mL of a 15% solution.
Mary Stevens earns $6 an hour at her job and she is entitled to time and a half for overtime and double time on holidays. Last week she worked 40 hours of regular time ,6 1/2 hours of over time and 8 hours of holiday time. how much did she earn?
Answer:
$394.5
Step-by-step explanation:
40 x 6 = 240
6.5 x 9 = 58.5
(6 x 2) x 8 = 96
240 + 58.5 + 96
the measure of angle 6 =(11x +8) degrees and measure of angle 7(12x-4)degrees what is the measure of angle 4
40
48
132
140
Answer:
Answer is m∠4=40
Step-by-step explanation:
According to the image which i have posted below,we first want to take note that m∠6 & m∠7 are vertical angles. Vertical angles are equal to each other, therefore m∠6 is equal to m∠7.
m∠6 = m∠7 (vertical angles)
11x + 8 = 12x – 4
12x - 11x = 8 + 4
x = 12
so
m∠6 = 11x + 8
m∠6 = 11(12) + 8
m∠6 = 132 + 8
m∠6 = 140
m∠4 = 180 - m<6
m∠4 = 180 - 140
m∠4 = 40
Answer is m∠4=40....
Given the coordinate points of the preimage, use the transformation given to provide the points of the image. W(3,3) V(3,4) U(5,4) Rotation: 90∘ counterclockwise about the origin. W′( , ) V′( , ) U′( , )
Answer:
W'(-3,3) V'(-4,3) U'(-4,5)
Step-by-step explanation:
The mapping for 90 degrees counterclockwise rotation is;
[tex](x,y)\to (-y,x)[/tex]
The given points have coordinates: W(3,3) V(3,4) U(5,4)
[tex](x,y)\to (-y,x)[/tex]
This implies that:
[tex]W(3,3)\to W'(-3,3)[/tex]
[tex]V(3,4)\to V'(-4,3)[/tex]
[tex]U(5,4)\to U'(-4,5)[/tex]
The required points of the image are:
W'(-3,3) V'(-4,3) U'(-4,5)
Since 2002, the number of a telephone company’s customers using a landline has been decreasing by 10% per year. Which of these statements are correct? Select all that apply.
1. To find the number of landline customers in 2004, you can multiply the number of landline customers in 2002 by 0.81.
2. To find the number of landline customers in 2004, you can subtract the product of 0.2 and the number of landline customers in 2002 from the number of landline customers in 2002.
3. To find the number of landline customers in 2003, you can multiply the number of landline customers in 2002 by 0.9
4. To find the number of landline customers in 2003, you can subtract the product of 0.1 and number of landline customers in 2002 from the number of landline customers in 2002.
1 and 3 I believe are the correct answers
Answer:
Option 1 , Option 3 and Option 4 are correct.
Step-by-step explanation:
Number of customers using landlines decreases 10% per year.
Let x be the umber of customers using landlines in 2002.
⇒ Number of customer using landlines in 2003 = [tex]x-\frac{10}{100}\times x[/tex]
= [tex]x-0.1x[/tex]
= 0.9x
Number of customers using landlines in 2004 = [tex]0.9x-\frac{10}{100}\times 0.9x[/tex]
= [tex]0.9x-0.1\times0.9x[/tex]
= [tex]0.9x-0.09x[/tex]
= [tex]0.81x[/tex]
Therefore, from this Option 1 , Option 3 and Option 4 are correct.
What is the relationship between the values of m and n plotted on the number line below?
On a plotted graph, 'm' commonly represents the slope indicating how much the line rises or falls for each step across. On the other hand, 'n' usually demonstrates the y-intercept - the point where the line crosses the y-axis.
Explanation:The relationship between the values of m and n plotted on a number line depends on the mathematic law or concept being applied. But in many cases, such as on a graph, 'm' typically represents the slope while the 'n' value shows the y-intercept.
Slope (m) shows how much a line moves up or down along the y-axis for each step across the x-axis ('run'). The equation for this is ∆y/∆x meaning the change in y over the change in x. For example, if the slope (m) is three, each time the x value increases by one, the y value will rise by three.
The y-intercept (n) is the point where the line crosses the y-axis. This is the value of y when x = 0.
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Find the domain the function graphed below. Express in interval notation.
Domain:
The domain of the function can be written as [-1,2]-{2}, therefore the function is defined from -1 to 2 except 2.
What are the domain and range of a function?• Domain is the set of values for which the given function is defined.
• Range is the set of all values which the given function can output.
What is the domain of the given function?Since the dark point of the function show that is the beginning of the function therefore the function will be defined from that point to all values of x but will not be defined at the point where there is a blank dot, also, the function is defined till the line is drawn.
Thus, the domain of the function will be,
Domain: [-1,2]-{2}
Hence, the domain of the function can be written as [-1,2]-{2}, therefore the function is defined from -1 to 2 except 2.
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A recipe calls for 3 1/2 cups of sugar. If you want to make only 1/3 of the recipe, how much sugar should you use?
Answer: 1 1/6 cups of sugar
Step-by-step explanation:
First let’s convert 3 1/2 into an improper fraction: 7/2
Then we multiply 7/2 by 1/3: 7/2*1/3=7/6
Then finally we convert 7/6 into a mixed number, so your answer will be 1 1/6
Which equation is y=9x^2+9x-1 re-written in vertex form
Answer:
A. y = 9(x +1/2)^2 - 13/4.
Step-by-step explanation:
y = 9x^2 + 9x - 1
y = 9(x^2 + x) - 1
y = 9 [ (x + 1/2)^2 - 1/4] - 1
y = 9 (x + 1/2)^2 - 9/4 - 1
y = 9(x +1/2)^2 - 13/4.
Answer: First Option
[tex]y = (x+\frac{1}{2}) ^ 2 -\frac{13}{4}[[/tex]
Step-by-step explanation:
For a quadratic function of the form:
[tex]y = ax ^ 2 + bx + c[/tex]
The vertex form of the equation is:
[tex]y = (x-h) ^ 2 + k[/tex]
Where the vertex is the point (h, k) and [tex]h =-\frac{b}{2a}[/tex]
In this case the equation is: [tex]y=9x^2+9x-1[/tex]
So:
[tex]a=9\\b=9\\c=-1[/tex]
Therefore:
[tex]h =-\frac{9}{2*(9)}[/tex]
[tex]h =-\frac{1}{2}[/tex]
[tex]k=9(-\frac{1}{2})^2+9(-\frac{1}{2})-1\\\\k=-\frac{13}{4}[/tex]
Finally the equation in vertex form is:
[tex]y = (x+\frac{1}{2}) ^ 2 -\frac{13}{4}[[/tex]
Suppose a life insurance policy costs $24 for the first unit of coverage and then $6 for each additional unit of coverage. Let C(x) be the cost for insurance of x units of coverage. What will 10 units of coverage cost?
Answer:
C(x) =24+6(z-1) where z is the total of units sold.
Therefore if z=10 units, the answer is: C(x)=24+6(10-1)
Or 24+6(9)
Or $78
Step-by-step explanation:
Answer:
10 Units would cost $78
Step-by-step explanation:
We will be using the following equation to solve this problem
[tex]C(x) = 24+6(x-1)[/tex]
Where x will be the amount of units of coverage that are sold. The equation subtracts 1 from the amount of units sold (since the first unit costs $24) and multiplies that by $6 which is the cost per unit. Then it adds $24 to that, which gives us the total cost.
Since we sold 10 units of coverage we plug that into the equation
[tex]C(10) = 24+6(10-1)[/tex]
[tex]C(10) = 24+6(9)[/tex]
[tex]C(10) = 24+54[/tex]
[tex]C(10) = 78[/tex]
So 10 units of coverage sold would cost $78
PG¯¯¯¯¯¯¯¯=9 in. The radius of the circle is 41 inches. Find the length of CT¯¯¯¯¯¯¯.
A. 40
B. 9
C. 80
D. not enough information
See the attached picture for the solution.
Answer:
Option: C is the correct answer.
C. 80
Step-by-step explanation:
PG=9 in. The radius of the circle is 41 inches.
We know that the side CT is given by:
CT=CS+ST
The side CS is calculated by using the Pythagorean Theorem in ΔCSP
i.e.
[tex]CP^2=CS^2+SP^2\\\\i.e.\\\\[/tex]
as CP is the radius of the circle
and SP=PG=9 in.
i.e.
[tex]41^2=9^2+CS^2\\\\i.e.\\\\1681=81+CS^2\\\\i.e.\\\\CS^2=1681-81\\\\i.e.\\\\CS^2=1600\\\\i.e.\\\\CS=40\ units[/tex]
and
similarly in right angled triangle ΔPST
we have:
[tex]TP^2=ST^2+PS^2\\\\i.e.\\\\41^2=9^2+ST^2\\\\i.e.\\\\ST=40\ units[/tex]
Hence,
[tex]CT=CS+ST\\\\i.e.\\\\CT=40+40\\\\i.e.\\\\CT=80\ in.[/tex]
Find f(-2) for f(x) = 2 • 3 ^x
А. -18
B. 2/9
C. 1/18 D. -36
Answer:
2/9
Step-by-step explanation:
We have [tex]f(x)=2 \cdot 3^x[/tex] and are asked to find [tex]f(-2)[/tex].
[tex]f(-2)[/tex] means to replace x with -2 and evaluate the expression named f.
Let's do that:
[tex]f(x)=2 \cdot 3^x[/tex]
[tex]f(-2)=2 \cdot 3^{-2}[/tex]
[tex]f(-2)=2 \cdot \frac{1}{3^2}[/tex]
[tex]f(-2)=2 \cdot \frac{1}{9}[/tex]
[tex]f(-2)=\frac{2}{9}[/tex]
Answer:
2/9
Step-by-step explanation:
Given:
[tex]f(x)=2*3^x[/tex][tex]f(-2)[/tex]We'd substitute x with -2:
[tex]2 *3^{-2}[/tex]
Using order of operations, we'd solve the exponent first:
[tex]3^{-2}=.111[/tex](repeating)
Multiply by 2:
.111(repeating) * 2 = 2/9
Our answer is 2/9
WILL GIVE BRAINLEIST NEED TO TURN IN BY 9 P.M. PLS HURRY SUPER EASYIdentify the equation that does not belong with the other three. Explain your reasoning.
A. 6+x=9 B. 15=x+12 C. x+9=11 D. 7+x=10
Answer:
C. x + 9 = 11
Step-by-step explanation:
We are trying to identify which of the equations does not match with the others. In this case, solve for x in each equation:
Option A):
6 + x = 9
Subtract 6 from both sides:
6 (-6) + x = 9 (-6)
x = 9 - 6
x = 3
Option B):
15 = x + 12
Subtract 12 from both sides:
15 (-12) = x + 12 (-12)
15 - 12 = x
x = 3
Option C):
x + 9 = 11
Subtract 9 from both sides:
x + 9 (-9) = 11 (-9)
x = 11 - 9
x = 2
Option D):
7 + x = 10
Subtract 7 from both sides:
x + 7 (-7) = 10 (-7)
x = 10 - 7
x = 3
---------------------------------------------------------------------------------------------------------
As you can tell, all the equations end with x = 3 as there answers except C. x+9=11, making (C) your answer.
~
How much would $600 be worth after 10 years, if it were invested at 4% interest compounded continuously? (Use the formula below and round your answer to the nearest cent.)
A(t)=P•e^rt
Answer:
$895.09
Step-by-step explanation:
Applying the given formula:
A = $600e^(0.04*10), or
= $895.09
We find that the answer is $895.09.
Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest from the previous.
How to find how much would $600 be worth after 10 years, if it were invested at 4% interest compounded continuously?
Hint: Use the formula below and round your answer to the nearest cent.)
A(t)=P•e^rt.
Applying the given formula:
A = $600e^(0.04*10),
or
= $895.09.
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Evaluate 5(x - 1) - 2 when x = 3.
O A. -4
Ос.
O D.O
Answer:
8
Step-by-step explanation
First you have to plug in 3 for x:
5(3-1)-2
Then using PEMDAS you would simplify that:
5(2)-2
10-2
8
The second number in an ordered pair of numbers that corresponds to a point on a coordinate system is the ?
Answer:
See below.
Step-by-step explanation:
The y-coordinate , giving the value of the function at this point. It is a part of the range of the function.
Answer:
It is the y-value
Step-by-step explanation:
Took the test on edg.
For f(x) = 2x+1 and g(x) = x2 - 7, find (f+9)(x).
Answer:
[tex]\large\boxed{(f+g)(x)=x^2+2x-6}[/tex]
Step-by-step explanation:
[tex](f+g)(x)+f(x)+g(x)\\\\f(x)=2x+1,\ g(x)=x^2-7\\\\(f+g)(x)=(2x+1)+(x^2-7)=2x+1+x^2-7=x^2+2x-6[/tex]
Some people might be confused while applying the three theorems related to segments in circles. They might not be sure which segments to multiply. What helpful hints would you recommend they use to figure out which segments to multiply for each of the three theorems?
Answer:
1.Intersecting segments theorem
In this scenario, two secant segments intersect each other inside the circle.The relationship is that the product of the segment pieces of one segment is equal to the product of the segment piece of the other.
Hint⇒identify the corresponding segment pieces for multiplication
2.Two secant segments that intersect outside circle
In this scenario the product of the whole secant with its external part is equal to the product of the other whole secant segment with its external part.
Hint ⇒identify the segment pieces outside the circle and the whole segments that include the external parts
3.One secant and one Tangent
In this case, the relation is that the product of whole segment with its external part is equal to square of the tangent segment.
Hint⇒ Identify the tangent segment and the whole secant segment that has an external part.
Hope this Helps.
Evan has an exam worth fifteen percent of his grade. He has an overall grade of 84.7 percent. The exam has 40 questions. How many questions does he need to get right in order to pass with an overall grade of 70?
Answer:
He needs to get 1 right
Step-by-step explanation:
1/40 is equal to .025. This means the other 39/40 incorrect ones are worth .975(97.5%). If we multiply the .975 by the 15 percent of his overall grade, we get 14.625. When you subtract this from the overall grade, you get 70.075, which is just above a 70%.
For this case we have that the general qualification is 70, of it Evan has accumulated 84.7%. Making a rule of three:
70 ----------> 100%
x -------------> 84.7%
Where "x" represents the rating that Evan has accumulated:
[tex]x = \frac {84.7 * 70} {100}\\x = 59.29\\70-59.29 = 10.71[/tex]
Evan is missing 10.71 to get 70.
In percentage, we have to:
100% -84.7% = 15.3%
Now we have that the exam represents 15% of the grade, this is divided into 40 questions.
It is observed that Evan must correctly answer the 40 questions of the exam, so he would get 15%. Even so, it would lack a 0.3% note to reach 70.
Answer:
He must answer the 40 questions correctly.
1. A plane flew 3,200 miles in 5 hours.
How fast was it flying?
Use the formula d = rt.
Answer:
640 miles per hour.
Step-by-step explanation:
I calculated this by 3200/5
Is this appropriate?
If P(A) = 0.60 and P(B) = 0.20, then A and B are independent events if
Answer:
[tex]P(A\cap B)=0.12[/tex]
Step-by-step explanation:
If two events, A and B are independent, then [tex]P(A\cap B)=P(A)\times P(B)[/tex], otherwise the two events are dependent.
If P(A)=0.60 and P(B) =0.20, then A and B are independent events, if
[tex]P(A\cap B)=0.60\times 0.20[/tex]
[tex]\implies P(A\cap B)=0.12[/tex]
Therefore the best complete is:
If P(A) = 0.60 and P(B) = 0.20, then A and B are independent events if [tex]P(A\cap B)=0.12[/tex]
Answer:
Step-by-step explanation:
p(a and b) = 0.12
PLEASE HELP 30 POINTS!! AND BRAINLIEST ASAP
What is an equation of the line that is perpendicular to 3x+y=−5 and passes through the point (3, −7) ?
Enter your equation in the box.
Answer:
y = 1/3x -8
Step-by-step explanation:
3x+y=−5
First we need to get the equation in slope intercept form to find the slope
Subtract 3x from each side
3x-3x+y=-3x−5
y = -3x-5
The slope is -3
We want a line perpendicular. Perpendicualr lines have slopes that are the negative reciprocal. Take the negative reciprocal
m new = - (1/-3) = 1/3
The slope of the new line is 1/3
We have the slope (1/3) and a point (3,-7)
We can use the point slope form for the equation of a line
y-y1 = m(x-x1)
y--7 = 1/3 (x-3)
y+7 = 1/3 (x-3)
or if we want the slope intercept form
Distribute
y+7 = 1/3x -1
Subtract 7 from each side
y+7-7 = 1/3x -1-7
y = 1/3x -8