Answer:
35° and 55°
Step-by-step explanation:
The sum of the angles of a right rectagle is 180°, with a right angle of 90°.
The tell us that A = 2B-15, so:
180° = 90° + A + B
180° = 90° + 2B - 15 + B
180° - 90° + 15 = 2B + B
105° = 3B
B = 105°/3 = 35°
Now, let's find A:
A = 180° - 90° - 35° = 55°
Using the properties of a right triangle and setting up an equation based on the relationship between the two small angles, we find that the angles measure 35 degrees and 55 degrees, respectively.
To solve the problem involving the angles of a right triangle, we recall that the sum of the angles in any triangle is 180 degrees. In a right triangle, one angle is always 90 degrees, which leaves a total of 90 degrees to be shared between the other two angles.
If we let x represent the measure of one of the small angles, then the problem tells us that the other angle is 2x - 15 degrees.
Therefore, we can set up the following equation to solve for x:
x + (2x - 15) + 90 = 180
Combining like terms gives us:
3x - 15 + 90 = 180
3x + 75 = 180
Now, we subtract 75 from both sides of the equation:
3x = 105
Finally, we divide by 3 to find the measure of x:
x = 35
Having found that one of the small angles measures 35 degrees, we can now find the other small angle:
2x - 15 = 2(35) - 15
= 70 - 15
= 55 degrees.
So, the two small angles of the right triangle are 35 degrees and 55 degrees.
Jenny’s Gift Shop sells candles in a variety of packages. The cost per candle is the same in every package. A package of 8 candles costs $12.96. Determine the cost of a package of 3 candles.
Answer:
8 candle = $12.96
1 candle =($12.96/8)
= $1.62
package of 3 candles =3×$(1.62)
: =$4.86
Y/-7=10 solve and check
Always write y in lower case
y/-7 = 10
y = 10(-7)
y = -70
Check:
Let y = -70
(-70)/-7 = 10
10 = 10
Done!
2(2X-3)-10 <_ 6(X-2)
Answer:
x<14/5
Step-by-step explanation:
expand
4x-6-10 < -6x+12
4x-16 < -6x+12
4x < -6x+12+16
4x < -6x+28
4x+6x < 28
10x < 28
x < 28/10
hope this helps
Answer:
[tex]\large\boxed{x\geq-2\to x\in[-2,\ \infty)}[/tex]
Step-by-step explanation:
[tex]2(2x-3)-10\leq6(x-2)\qquad\text{use the distributive property}\ a(b+c)\\\\(2)(2x)+(2)(-3)-10\leq(6)(x)+(6)(-2)\\\\4x-6-10\leq6x-12\\\\4x-16\leq6x-12\qquad\text{add 16 to both sides}\\\\4x\leq6x+4\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\-2x\leq4\qquad\text{change the signs}\\\\2x\geq-4\qquad\text{divide both sides by 2}\\\\x\geq-2[/tex]
Please help me i really need it
Answer:
B and C
Step-by-step explanation:
It can't be A because that would equal 5b.
For C, you multiply 2b by 2 and get 4b.
For B, you add b to 3b to get 4b.
-9.5 as a mixed number
You know that .5 = 0.5 = 5/10 = 1/2.
Mixed number sought: -9_1/2.
The perimeter of a rectangle is 44 m. The length is 4 m more than the twice the
width. Find the dimensions.
Final answer:
The dimensions of the rectangle with a perimeter of 44 m, where the length is 4 m more than twice the width, are 6 m for the width and 16 m for the length.
Explanation:
The perimeter of a rectangle is given as 44 m, and the length (L) is said to be 4 m more than twice the width (W). To find the dimensions, we can set up the following equations based on the properties of a rectangle:
Perimeter P = 2(L + W)
L = 2W + 4
Since the perimeter is 44 m, we can substitute the length expression into the perimeter equation:
44 = 2((2W + 4) + W)
By solving this equation for width (W), we get:
44 = 2(3W + 4)
44 = 6W + 8
36 = 6W
W = 6 m
Now that we have the width, we can determine the length using the expression for L:
L = 2(6) + 4 = 16 m
Therefore, the final answer for the width is 6 m and the length is 16 m.
solve problem y+7=-9
Answer: -16
Step-by-step explanation:
y + 7 = -9
-9 - 7 = -16
-16 + 7 = -9
Critique the reasoning of others. Oriana said that the difference between 9.298 and 3.01 was 8.997.
Was she correct? If not, what error did she make?
Answer: Oriana was not correct, because she didn't line up the decimal points of the numbers [tex]9.298[/tex] and [tex]3.01[/tex]
Step-by-step explanation:
By definition, the "Difference" is the result of a subtraction.
In order to subtract the decimal numbers [tex]9.298[/tex] and [tex]3.01.[/tex], Oriana needed to apply these steps:
1. Write one number under the other. The decimal points must be lined up:
[tex]9.298 \\3.01-\\..........[/tex]
2. Since the decimal numbers must have the same number of decimal places, she needed to add zeros to the right side:
[tex]9.298 \\3.010-\\..........[/tex]
3. Subtract the numbers and put the decimal point in the result:
[tex]9.298 \\3.010-\\..........\\6.288[/tex]
Oriana was not correct, because she didn't line up the decimal points. Her procedure was:
[tex]9.298 \\ 0\ 3.01-\\..........\\8.997[/tex]
For f(x) = 3x +1 and g(x) = х2 - 6, find (f-g)(x).
Answer:
(f-g)(x) = -x^2 + 3x + 7
Step-by-step explanation:
Note that -g(x) = -x^2 + 6.
Thus, (f-g)(x) = f(x) + [-x^2 + 6]: Add the following:
f(x) = 3x + 1
-g(x) = -x^2 + 6
--------- ------------------
(f-g)(x) = -x^2 + 3x + 7 (answer)
Which of the following polynomials is equivalent to the expression above?
A) x² + 5
B) x² +7
C) 4x² +7
D) x² + 4x + 7
Answer:
D) x² + 4x + 7
Step-by-step explanation:
2x + 6 + x² + 2x + 1
x² + 2x + 2x + 6 + 1
x² + 4x + 7
The equivalent expression for the given polynomial is x² + 4x + 7.
Option D is the correct answer.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
(2x + 6) + (x² + 2x + 1)
Removing the parenthesis.
2x + 6 + x² + 2x + 1
Adding the like terms.
4x + 7 + x²
x² + 4x + 7
Thus,
The final expression is x² + 4x + 7.
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Select the correct answer.
Anton is approved for overtime at his job. Last week, he worked a total of 45 hours. How many hours of overtime did he work?
3 hours
B. 5 hours
C. 15 hours
D.45 hours
Answer: 15 hours
Step-by-step explanation: full time is 30 hours so if he worked 45 that’s 30+15=45 so 15hrs over time
x + 10 = 2x
PLEASE SHOW EXPLANATION + WORK
Answer:
X=10
Step-by-step explanation:
x+10-10=2x-10
x=2x-10
x-2x=2x-10-2x
-x= -10
-x/-1= -10/-1
x=10
In order for an atom to have a zero charge every proton which has a change of +1, must be matched with an electron which has a change of -1 a helium atom has 2 protons and 2 electrons explain why a helium atom has a zero change
A helium atom has a zero charge because the number of protons equals the number or protons. The positive and negative charges add together to reach zero.
Roselyn wants to drive her car at a speed of 606060 miles per hour for 1.251.251, point, 25 hours. Her car has a fuel efficiency of 151515 miles per gallon.
How many gallons of fuel does Roselyn need for her journey?
Answer:
Hence, there is 5 gallons of fuel Roselyn needed for her journey.
Step-by-step explanation:
Since we have given that
Speed at which Roselyn wants to drive her car = 60 miles per hour
Time taken by her car = 1.5 hours
As we know the formula for "Distance-Speed " :
Her car has fuel efficiency = 15 miles per gallon
Number of gallons of fuel is given by
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Answer:
5 gallons.
Step-by-step explanation:
Roselyn wants to drive her car at a speed of 60 mph
Speed of car, S = 60 mph
She drives for 1.25 hours.
Time travel, t = 1.25 hours
Total distance travel = s × t
= 60 × 1.25
= 75 miles
The fuel efficiency of car is 15 miles per gallon.
[tex]\text{Number of gallon used}=\dfrac{\text{Total distance travel}}{\text{Fuel efficiency}}[/tex]
[tex]\text{Number of gallon used}=\dfrac{75}{15}[/tex]
[tex]=5\text{ gallons}[/tex]
Hence, she needs 5 gallons.
The number 21 is decreased to 15. What is the percentage by which the number was decreased, to the nearest tenth of a percent?
Answer:
Initial Number = x = 21
Number after it is decreased = y = 15
Total decrease form initial to the current number = z = x-y = 21-15 = 6
% of decrease = (z/x) * 100 = (6/21)*100 = 600/21 = 28.5714286 = 28.6 ( correcting it to 10th place)
Step-by-step explanation:
For 21 decreased to 15, the percentage decrease is 28.6%.
The percentage by which a number was decreased can be calculated by finding the difference between the original number and the decreased number, dividing that by the original number, and then multiplying by 100 to get the percentage.
Given number: 21
On reduction, number becomes: 15
To find the percentage decrease:
(21-15)/21 x 100 = 28.6%.
Please help me with this
the answer is true it is a rational number
As a fraction, 2 is 2/1
Oh no, there is always an odd exponent. So it could not have been made by squaring a rational number! This means that the value that was squared to make 2 (ie the square root of 2) cannot be a rational number. In other words, the square root of 2 is irrational.
4 miles 999 feet = in feet
Answer:
approximately = 26394.72
Convert between the 2 units.
Can i plz have the brainliest answer plz!!!!!!!!!!!
If two is added to four times a certain number, the result
is 26. What is the number?
For this sort of question you have to work backwards.
.
26 - 2 = 24.
24 / 4 = 6
.
The number would be 6
The formula for the circumference of a circle is C = 2πr, where r is the radius. Rearrange the formula to solve for r and select the correct option below.
Word expression to match 24-6+3
Answer:
I think itśn 5
Step-by-step explanation:
Given the function below, select all the equalities that are true.
f(x) = x2 + 3
Answer:
a&c
Step-by-step explanation:
because you can multiply to numbers and reach 0 or 2, but no number times another equals 7 and no number times 0 equals three (multiplicative identity of 0)
Which is a possible turning point for the continuous function f(x)? (–6, 8) (-4, 2) (-2, 0) (0,-2)(2,-1)(4,0)(6,4)
The function breaks at (-2,0),(0,-2)&(4,0).So at all these points function i.e triangular curve takes the turn.
That is what kind of continuous function?
A continuous function in mathematics is one whose value does not abruptly change due to discontinuities, or breaches in the continuity of the function.
For example, the function f (x) = 2 sin (x), f (x) = 2 sin (x), and f (x) = 2sin (x) is continuous everywhere. We can sketch its outline without ever lifting our hand. Contrarily, there is a discontinuity at x = 2 x = 2 x = 2 in the function f (x) = 1 x 2 f(x) = frac 1 x 2 f(x) = x 21.
The four points given are (-2,0),(0,-2),(2,-1),(4,0).When you will plot these points on the coordinate axes and join all these points you will get the shape of a triangle. One line lies completely on x axis another two lies below x axis. These two lines intersect at (0,-2).
The meaning of continuity is that there should be no breaking points in the function.
But the function breaks at (-2,0),(0,-2)&(4,0).So at all these points function i.e triangular curve takes the turn.
So this might be also the turning point.
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The possible turning point for the continuous function f(x) from the given list is likely the point (2, -1), where the second derivative y" = 6x - 12 equals zero, indicating a point of inflection.
Explanation:To determine a possible turning point for the continuous function f(x), we need to consider the concept of a point of inflection, which is a point where the concavity of the function changes. According to the excerpts, a point of inflection occurs where the second derivative of the function changes sign or is zero. If we examine the given points, a turning point might be where we can see such a change in concavity or where the f'(x) equals zero.
From the excerpt that gives us the second derivative y" = 6x - 12, we can determine that at x = 2, the second derivative is zero, which signals a possible point of inflection. This would correspond to the point (2, -1) in the list provided. Hence, this is a possible turning point for the function f(x).
there are 18 oranges in box A and 36 in box B, what is the ratio of box A to box B
Answer:
1 : 2
Step-by-step explanation:
Express the ratio as the number of oranges in each box, that is
box A : box B
= 18 : 36
Simplify the ratio by dividing both parts by 18, thus
ratio = 1 : 2 ← in simplest form
Find the slope of the line that passes through the points (-8,-3), (2,3)
Answer:
⅗
Step-by-step explanation:
-y₁ + y₂\-x₁ + x₂ = m
[tex] \frac{3 + 3}{8 + 2} = \frac{6}{10} = \frac{3}{5} [/tex]
I am joyous to assist you anytime.
6 x 7 - 3 + 2 = __
Insert parentheses to make the expression equal 26.
A) 6 x (7 - 3 + 2)
B) 6 x (7 - 3) + 2
C) (6 x 7 - 3) + 2
D) 6 x 7 - (3 + 2)
Answer:
B is the correct answer
Solve the equation for Y 4x-10y = 12
4x - 10y = 12
4x - 12 = 10y
y = (4x - 12)/10
y = 2x/5 - 6/5
cos12sin78+cos78sin12
Sin 12 x cos 78 + cos 12 x sin 78
= sin 12 x cos (90-12) + cos 12 x sin (90-12)
=sin 12 x sin 12 + cos 12 x cos 12
=sin^2 12 + sin^2 12
=1
Find the value of C. m^2+7/12m+c
Use b^2 - 4ac = 0.
Let a = 1
Let b = 7/12
(7/12)^2 - 4(1)c = 0
Take it from here.
This graph displays a linear function. What is the rate of change?
Answer:
rate of change is 5!!! :)
Step-by-step explanation:
Hope this helps!!! :)
The rate of change of the linear function in the graph is: 5
How to find the rate of change of the linear graph?Rate of change problems can generally be approached using the formula R = D/T, or rate of change equals the distance traveled divided by the time it takes to do so.
However, in this case with coordinates, it is expressed as:
Rate of change = (y₂ - y₁)/(x₂ - x₁)
From the graph, we can take two coordinates which are:
(1, -1) and (2, 4).
Thus:
Rate of change = (4 - (-1))/(2 - 1)
= 5/1
= 5
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evaluate 4 square root 9 square root 9 over 4 square root 9^5
[tex]\frac{\sqrt[4]{9}.\sqrt{9}}{\sqrt[4]{9^5}}[/tex]
[tex]\frac{9^\frac{1}{4}.9^\frac{1}{2}}{9^\frac{5}{4}}[/tex]
[tex]\frac{9^\frac{6}{8}}{9^\frac{5}{4}}[/tex]
[tex]9^{\frac{6}{8}-\frac{5}{4}}[/tex]
[tex]9^\frac{-1}{2}[/tex]