Answer:
2 inches
Step-by-step explanation:
The area of the frame will be the difference between the area of the picture with frame, and the area of the picture without. We want that difference to be equal to the area of the picture without the frame.
Let x represent the width of the frame. The overall length and width of the picture will be increased by 2x when the frame is added. Then we have ...
a = LW = (8+2x)(12+2x) . . . . area of picture and frame
b = LW = (8)(12) . . . . . . . . . . area of picture
a -b = b . . . . . . desired relationship between areas
Substituting and expanding the expressions for 'a' and 'b', we find ...
a -2b = 0 . . . . subtract b
(8 +2x)(12 +2x) -2(8)(12) = 0
4x² +40x -96 = 0 . . . simplify
x² +10x -24 = 0 . . . . . divide by 4
(x -2)(x +12) = 0 . . . . factor
The positive value of x that makes this true is x = 2.
The width of the frame is 2 inches.
URGENT! WILL GIVE BRAINLY FOR CORRECT ANSWER
Draw the image of \triangle ABC triangle, A, B, C under a dilation whose center is P and scale factor is 2.
Find tan(a-b)
sin a=4/5
tan b=3/4
Give the exact answer, not a decimal approximation.
Answer: 0.2916666665
Step-by-step explanation:
Answer:
[tex]\frac{7}{24}[/tex]
Step-by-step explanation:
By the Pythagorean Theorem, we know
[tex]\cos^2a=1-\sin^2a[/tex].
With this, we can find [tex]\cos a[/tex] by plugging in what we know for [tex]\sin a[/tex]:
[tex]\cos^2a=1-(\frac{4}{5})^2\\~~~~~~~~=1-\frac{16}{25}\\~~~~~~~~=\frac{9}{25}[/tex].
Taking the square root, we get
[tex]\cos a=\frac{3}{5}[/tex] .
Note: there seems to be a problem with the question? It doesn't specify what range [tex]a[/tex] lies in, so we don't know whether [tex]\cos a[/tex] is positive or negative. In this case, I assumed it was positive.
From this, we can find [tex]\tan a[/tex]:
[tex]\tan a=\frac{\sin a}{\cos a}\\~~~~~~~=\dfrac{\frac{4}{5}}{\frac{3}{5}},[/tex]
so [tex]\tan a=\frac{4}{3}[/tex].
Using the [tex]\tan[/tex] difference formula, we know
[tex]\tan (a-b)=\dfrac{\tan a -\tan b}{1+\tan a\tan b}[/tex] .
Plugging in the values we know for [tex]\tan a[/tex] and [tex]\tan b[/tex], we get
[tex]\tan(a-b)=\dfrac{\frac{4}{3}-\frac{3}{4}}{1+\frac{4}{3}\cdot\frac{3}{4}}\\~~~~~~~~~~~~~~=\dfrac{\frac{7}{12}}{1+1}\\~~~~~~~~~~~~~~=\boxed{\frac{7}{24}}~.[/tex]
helppp please please helpppp
Every morning Jessica drinks one fifth of a quart of orange juice how many mornings would Jaze have oranges for if she only has a total of one and 4/5 quarts of orange juice
Answer:
9 more mornings Jessica can drink orange juice
Step-by-step explanation:
1 4/5 = 1/5x
9/5 = 1/5 (divided below)
1/5 1/5
9/5 divided 1/5 = x
x = 9/5 x 5/1 = 45/5
45/5 divide by 5 = 9/1
long division and you get 9
hope this helps!
Answer:
The answer is 9
Step-by-step explanation:
Peter is the owner of a hotel. He has found that when he charges the nightly cost of $139, the average occupancy is 275. In addition, Peter has found that with every $10 increase in the average nightly cost, the hotel occupancy decreases by an average of 22.
Which of the following functions describes the hotel's profit in terms of x, the number of $10 increases over $139?
Answer:
Without price increase, Cost/night = $119
Average occupancy = 372 The revenue will be 119*372 = $44,268
For every $15 price increase, the occupancy decreases by 25. Therefore with x price increases, The revenue will be $(119 + 15x)*(372 25x)
Cost/night = $119 + 15x Occupancy = 372 - 25x
Answer:
The nightly cost with x $15 price increases is $119 + 15x.
The Jackson family drink 4.5 liters of milk each week. If they continue to drink milk at the same rate, how long will it take the Jackson family to drink 49.5 liters of milk?
Hello can someone please answer this question i will mark you the Brainliest
Answer:
155 cm2
Step-by-step explanation:
whats a^2=4/25 in square root form
Answer:
a = ± [tex]\sqrt{\frac{4}{25} }[/tex]
Step-by-step explanation:
[tex]a^{2} =\frac{4}{25}[/tex]
[tex]\sqrt{a^{2} } =\sqrt{\frac{4}{25} } \\|a|=\sqrt{\frac{4}{25} \\[/tex]
a = ± [tex]\sqrt{\frac{4}{25} }[/tex]
Do not know what the problem is meaning
Answer:
its b
Step-by-step explanation:
Question: find an equation of a parabola that satisfies the given condition
Problem: horizontal axis; vertex (-1,2) passing through (2,3)
here a subtraction problem that has been solved incorrectly for 44-16=28 choose the addition sentence that check this subtraction problem the choices are 28+16=32 28+44=72 28+16=44 which one is correct
Answer:
Answer:
28+16=44
Step-by-step explanation:
point of correction it has been solved correctly
when subtracting 44 - 16 it gives you 28
=> 44 - 16
=> 28
SO IN ORDER TO CHECK IF THE PROBLEM WAS SOLVE CORRECTLY
you will minus 28 from one of the numbers before the equal sign
the correct option is 28 + 16 equals to 44
=> 28+16=44
Find the measure of the angle marked with a guestion mark using inverse trig
functions. Round your answer to the nearest degree, Enter the number only,
Answer:
37°
Step-by-step explanation:
1. Label the sides: the hypotenuse (the longest, slanted side) is 5 and the adjacent is 4. This means that we are using cosine (CAH)
2. Write out the equation: cosine or cos (?) = adjacent ÷ hypotenuse
3. Substitute in the values: cos (?) = 4 ÷ 5
4. Simplify: cos (?) = 0.8
5. Type this into a calculator to find ?: [tex]cos^{-1}(0.8)[/tex]
? = 36.86989... ≈ 37°
Hope this helps!
25 percent of what is 38?
Answer: 152
Step-by-step explanation:
Let the number = x.
Therefore, x*25% = 38
25% as a decimal is 0.25.
So, 0.25x = 38
We can divide both sides by 0.25:
x = 152
Add and Subtract Decimals
Use the models to solve each equation. Match the letter of each
problem to the corresponding space below to answer the following
riddle.
The more of them you take, the more you leave behind.
What are they?
There are no pictures provided.
( Talking about the models )
You invest 1,000 in one account and 4,000 in another, both accounts have the same interest rate over the same amount of time. How will the interest earned compare?
Answer:
the $4000 WILL EARN 4 TIMES THE AMOUNT OF INTEREST.
Step-by-step explanation:
If both investments have same interest they will grow in the same proportion that the initial amount have.
Use the circle below to answer the question.
Q
R
680
Р
C
S
The Circle is centered at point C. Line segment PQ is parallel to SR.
What is the measure of angle QPS?
The measure of angle QPS in circle C is 112°
What is a circle?
A circle is the locus of a point such that its distance from a fixed point known as the circle center is always constant. The sum of angles in a circle is 360 degrees.
From the circle:
PQ is parallel to SR, hence: ∠PQR + ∠QRS = 180°
∠PQR + 68 = 180
∠PQR = 112°
Also, PS = QR (from the endpoint of the diameter), hence:
∠QPS = ∠PQR = 112°
The measure of angle QPS in circle C is 112°
Find out more on circle at: https://brainly.com/question/24375372
Help with number 4 please
48 boards
Step-by-step explanation:
length of a board = 5½ in = 11/2
Total length should be covered = 22 ft = 264 in (1ft = 12in)
total boards needed = 264 ÷11/2
= 264 × 2/11
= 24 ×2
= 48 boards
Please mark my answer the brainliest and rate me 5 star and follow meplease please please please please please
Which equation, when solved, results in a different value of x than the other three?
8.3=−0.6x+11.3
8 point 3 is equal to negative 0 point 6 x plus 11 point 3
11.3=8.3+0.6x
11 point 3 is equal to 8 point 3 plus 0 point 6 x
11.3−0.6x=8.3
11 point 3 minus 0 point 6 x is equal to 8 point 3
8.3−0.6x=11.3
8 point 3 minus 0 point 6 x is equal to 11 point 3
Answer:
i think it might be c
Step-by-step explanation:
tell me if its wrong or not and brain list please
An instructor wants to create a test that has true-false questions, multiple-choice questions,
and essay questions. He wants the test to have 35 questions, with twice as many multiple-choice
questions as essay questions and with twice as many true-false questions as multiple-choice
questions.
(i). Write a system of equations to represent this problem.
(ii). Hence or otherwise, determine how many of each type of question should the
instructor put on the test?
Let x = multiple choice, y = true/false, z = essay
(i)
where: x + y + z = 35
We need to solve for y first, in order to know how many essay questions there are, since that is our base.
y + 2y + 4y = 35
(ii)
Now to solve:
y + 2y + 4y = 35
7y = 35
[tex]\frac{7y}{y} = \frac{35}{7}[/tex]
y = 5
Therefore, there are 5 essay questions, 10 multiple choice questions, and 20 true/false questions.
10 + 5 + 20 = 35
The equation of the system will be x + y + z = 35 and the number of each type of question should the instructor put on the test will be 5.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
An instructor wants to create a test that has true-false questions, multiple-choice questions, and essay questions.
Let x be the number of essay questions.
Let y be the number of multiple-choice questions.
Let z be the number of true-false questions.
He wants the test to have 35 questions, with twice as many multiple-choice questions as essay questions and with twice as many true-false questions as multiple-choice questions.
x = 2y
z = 4y
1. Then the equation of the system will be
x + y + z = 35
Then we have
2. Then the number of each type of question should the instructor put on the test will be
y + 2y + 4y = 35
y = 5
More about the linear system link is given below.
https://brainly.com/question/20379472
determine the equation of a line that is parallel to the line 2x-3y=12 and passes through the point with coordinates (9,0)
Answer:
5x + 24y =45. (9,0)
5×9 +24×0 = 45
45 =45
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HELP PLS!
Susan's penny bank is 3/4 full. After she removes 280 pennies, it is 1/2 full. How many pennies can Susan's bank hold?
Answer:
390 pennies that susan is holding
Answer:
3/4x-280=x/2
-3/4x-280=x/2 find the common factor for 3/4x-280/1 which is 4 3/4x-280/1 3xby
How do you simplify without using a calculator (-5)(7)+4×5
Answer:
-15 Is the answer
Step-by-step explanation:
(-5)(7)+4×5
= -15
(-5)(7) + 4×5 = -15/1 = -15
Multiple: -5 * 7 = -35
Multiple: 4 * 5 = 20
Add: the result of step No. 1 + the result of step No. 2 = -35 + 20 = -15
Hope this helps.
How do you write 48,600,000 in scientific notation?
Answer:
4.86·10⁷
Step-by-step explanation:
Answer:
4.86 x10^7
Step-by-step explanation:
1. Must be between 1 and 10, the number cannot be 10.
2. Count decimal places to get to the dot.
3. That will be the power at the top of the 10.
4. If number is small, that power will be negative, but positive if number is big. E.g. 0.0001 (small) & 10000 (big)
4.86 x10^7
Hope this helps!
thirty two thousand six hundred and sixty seven in numbers
Answer:
32,667
30,000+2,000+600+60+7
Lily is going to invest in an account paying an interest rate of 5.6% compounded continuously. How much would Lily need to invest, to the nearest cent, for the value of the account to reach $78,000 in 9 years?
NO LINKS!!! Solve each triangle. Part 1a
Answer:
13) C= 95°, a= 0.157, c= 9.86
14) C= 165°, a= 3.35, b= 1.68
15) A= 40°, a= 2, c= 3.06
16) C= 50°, a= 11.8, c= 9.19
Step-by-step explanation:
Please see the attached pictures for the full solution.
Note:
sine rule
[tex] \textcolor{steelblue}{\boxed{{\frac{ \sin A}{a} = \frac{ \sin B }{b} = \frac{ \sin C}{c} }}}[/tex]
∠ sum of ∆
The sum of the angles in a triangle is 180°.
help me please I need it quick
Answer:
it's f(n)= 2n^2+1
Step-by-step explanation:
the blocks are shaped 3,8,15 boxes
because 8-3= 5 and 15-8=7
so there's an addition of 2
2. An expression is shown below.
2V43x
Which value of x makes the expression
equivalent to 14V43?
A.7
B.12
C.49
D.98
3(x-6)-8x+-2+5(2x +1)
Answer:
See below.
Step-by-step explanation:
3x-18-8x-2+10x+5
Combine like terms.
3x-8x+10x
5x
-18-2+5
-15
5x-15
-hope it helps
As Program Director of a Radio Station, you receive a report from an independent service that shows that out of 100 songs played, the same song was played 7 times. Using the Empirical Approach, calculate the probability that song will be played next.
Using an Empirical approach and the probability concept, it is found that there is a 7% probability that song will be played next.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. Using an Empirical approach, these number of outcomes are taken from previous trials.
In this problem, considering the previous 100 songs, the same song was played 7 times, hence:
p = 7/100 = 0.07.
There is a 7% probability that song will be played next.
More can be learned about probabilities at https://brainly.com/question/14398287