Answer:
FIRST OPTION: (-4, -2)
Step-by-step explanation:
Given the inequality [tex]y + x < -5[/tex], substitute each solution given in the options:
1) For (-4, -2) :
[tex](-2)+ (-4) < -5[/tex]
[tex]-6 < -5[/tex] (This is true)
2) For (-3, -2):
[tex](-2)+ (-3) < -5[/tex]
[tex]-5 < -5[/tex] (This is not true)
3) For (-2, -3):
[tex](-3)+ (-2) < -5[/tex]
[tex]-5 < -5[/tex] (This is not true)
4) For (-1, -3):
[tex](-3)+ (-1) < -5[/tex]
[tex]-4 < -5[/tex] (This is not true)
You can observe that (-4, -2) is a solution of [tex]y + x < -5[/tex]
The answer is A.
Hope this helps :)
Find the domain and range of the function f(x)= |x-4|+3
Answer:
B
Step-by-step explanation:
The domain is (- infinity, infinity) (or the set of all real numbers) bc the function goes never ending to the left and right
The range is f(x) is greater than or equal to 3 bc the y value 3 is the turning point. Also, it's "greater than or equal to" bc the graph opens upward
The domain and range of the function f(x)= |x-4|+3 are the set of real numbers and every real number greater than or equal to 3 respectively.
What is the domain and range of a function?The domain of a function is the set of all possible inputs of the function. The range of a function is the set of all possible outputs of that function.
We can find the domain and range as shown below:The function is given:
f(x)= |x-4|+3.
We can substitute any value of x to the given function. This means that the domain of the function is the set of all real numbers.
The lowest value that the given function can have is 3. This is possible only when the value of x = 4.
It cannot go lower than that as a modulus or absolute value is used in the function.
Thus, the range of the function can be defined as the set of all real numbers greater than or equal to 3.
Therefore, we have found that the domain and range of the function f(x)= |x-4|+3 are the set of real numbers and every real number that is greater than or equal to 3 respectively.
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A monument has the shape of a square pyramid. The base has a length of 6ft. The height of a face is 13ft. What is the surface area of the pyramid
The answer is:
The total surface area of the pyramid is:
[tex]TotalSurfaceArea=192ft^{2}[/tex]
Why?To calculate the surface area of a square pyramid, we need to use the following formula:
[tex]TotalSurfaceArea=\frac{1}{2}pl+BaseArea[/tex]
Where,
p, is the perimeter of the base.
l, is the slant of the pyramid.
Base area, is the area of the square base.
Now, from the statement we know that the base has a length of 6 feet, and the height of a face (slant) is 13 feet.
So, calculating, we have:
[tex]BaseArea=BaseLength^{2}=(6ft)^{2} =36ft^{2}[/tex]
[tex]Perimeter=4*side=4*6feet=24feet[/tex]
The total surface area will be:
[tex]TotalSurfaceArea=\frac{1}{2}l+BaseArea[/tex]
[tex]TotalSurfaceArea=\frac{1}{2}*24ft*13ft+36ft^{2}[/tex]
[tex]TotalSurfaceArea=156ft^{2}+36ft^{2}=192ft^{2}[/tex]
Hence, we have the total surface area of the pyramid is:
[tex]TotalSurfaceArea=192ft^{2}[/tex]
Have a nice day!
A house has 3 rectangular countertops. Each countertop is 4 3/8 by 2 2/5 feet. How many square feet of tile is needed to cover all of the countertops?
Answer:
[tex]31\frac{1}{2}ft^2[/tex]
Step-by-step explanation:
From the information given each of the three rectangular countertops has dimension [tex]4\frac{3}{8}[/tex] by [tex]2\frac{2}{5}[/tex] feet.
The area of a rectangular shapes is the product of the dimensions.
Each rectangular countertop has area;
[tex]4\frac{3}{8}\times 2\frac{2}{5}=\frac{35}{8}\times \frac{12}{5} =10\frac{1}{2}ft^2[/tex]
Therefore the number of square feet tiles needed to cover all the countertops is [tex]=3\times 10\frac{1}{2}=31\frac{1}{2}ft^2[/tex]
ANSWER IT CORRECTLY AND ILL GIVE BRAINLIST I think that’s what it’s called
Answer:
y = 8.9
Step-by-step explanation:
Use Pythagoras Theorem a² = b² + c²
In this case a = 12 and c = 8 so,
12² = b² + 8²
( Simplify )
144 = b² + 64
( Minus 64 from both sides to isolate b² )
80 = b²
( Square root to isolate b )
8.94427191 = b
Answer:
8.9
Step-by-step explanation:
The triangle is a right triangle, so we can use the Pythagorean theorem, where a and b are the lengths of the legs (the sides forming the right angle), and c is the length of the hypotenuse (the angle opposite the right angle).
a^2 + b^2 = c^2
y^2 + 8^2 = 12^2
y^2 + 64 = 144
y^2 = 80
y = sqrt(80)
y = sqrt(16 * 5)
y = 4sqrt(5)
y = 8.9
¡¡¡40 POINTS!!!
Which expression is equivalent to 5x+10y-15?
A.5(x-2y-3)
B.5(x+ 5y-10)
C.5(x+2y-3)
D.5(x+2y-15)
Answer:
C
Step-by-step explanation:
Given
5x + 10y - 15 ← factor out 5 from each term
= 5(x + 2y - 3) → C
Final answer:
After factoring out the common factor of 5 from the expression 5x+10y-15, we obtain the equivalent expression, which is 5(x+2y-3). Option C is correct.
Explanation:
To find an expression equivalent to 5x+10y-15, we need to factor out the common factor in all three terms. The common factor here is 5. By dividing each term by 5, we get:
x (from 5x)2y (from 10y)-3 (from -15)Putting these together within parentheses after factoring out the 5 gives us 5(x+2y-3).
Therefore, the answer is: C. 5(x+2y-3)
1. m’+9 = 58
m
=
2. 7e² = 28
er
d=
3. d? + 6 = 70
4 n - 10 = 62
N=
For this case we must solve each of the equations proposed:
A) [tex]m ^ 2 + 9 = 58[/tex]
Subtracting 9 from both sides of the equation we have:
[tex]m ^ 2 = 49[/tex]
Applying root to both sides of the equation:
[tex]m = \sqrt {49}\\m = \pm7[/tex]
B) [tex]7e ^ 2 = 28[/tex]
We divide between 7 on both sides of the equation:
[tex]e ^ 2 = \frac {28} {7}\\e ^ 2 = 4[/tex]
We apply root to both sides of the equation:
[tex]e = \pm \sqrt {4}\\e = \pm2[/tex]
C) [tex]d ^ 2 + 6 = 70[/tex]
Subtracting 6 on both sides of the equation:
[tex]d ^ 2 = 64[/tex]
We apply root to both sides of the equation:
[tex]d =\pm \sqrt {64}\\d = \pm8[/tex]
D) [tex]\frac {1} {2} n ^ 2-10 = 62[/tex]
We add 10 to both sides of the equation:
[tex]\frac {1} {2} n ^ 2 = 72[/tex]
We multiply by 2 both sides of the equation:
[tex]n ^ 2 = 144[/tex]
We apply root to both sides of the equation:
[tex]n = \pm \sqrt {144}\\n =\pm12[/tex]
Answer:
[tex]m = \pm7\\e = \pm2\\d = \pm8\\n = \pm12[/tex]
A company owns two manufacturing
plants with daily production levels of
8x + 17 widgets and 5x - 7 widgets,
where x represents a minimum
quantity. How many more items does
the first plant produce daily than the
second plant?
Answer:
3x+24 more widgets
Step-by-step explanation:
A company owns two manufacturing plants:
1st plant: 8x+17 widgets;2nd plant: 5x-7 widgets.To find how many more items the first plant produces daily than the second plant, we have to subtract from the number of widgets the first plant produces the second plant produces. So,
[tex](8x+17)-(5x-7)\\ \\=8x+17-5x+7\ [\text{Eliminate brackets}]\\ \\=(8x-5x)+(17+7)\ [\text{Combine the like terms}]\\ \\=3x+24[/tex]
Answer:
3x + 24
Step-by-step explanation:
The question simply requires us to find the difference between the daily production levels of the two plants;
The first plant produces 8x + 17
The second plant produces 5x - 7
The difference between these two expressions will be our required solution;
(8x + 17) - ( 5x - 7) = 8x + 17 - 5x + 7
= 8x - 5x +17 + 7 = 3x + 24
What is the converse of the statement?
"If x - 2 = 5, then x = 7"
ANSWER
"If x=7, then x - 2 = 5"
EXPLANATION
Let
[tex]p \to \: q[/tex]
be a propositional statement.
The converse of this statement is
[tex]q \to \: p[/tex]
In other words, the converse of the statement,
"If p then q" is "If q, then p"
The given given conditional statement is
"If x - 2 = 5, then x = 7"
Therefore the converse is
"If x=7, then x - 2 = 5"
1. Find the mean, median, and mode of this data set.
76, 74, 78, 72, 73, 80, 49, 72, 83
To calculate for this data set, the mean is 73, the median is 74 after sorting the numbers, and the mode is 72 as it appears more than once.
To find the mean, you add up all the numbers in the set and divide by the total count of numbers. For the provided data set:
76 + 74 + 78 + 72 + 73 + 80 + 49 + 72 + 83 = 657There are 9 numbers, so the mean is 657/9 = 73.To find the median, you first sort the data from lowest to highest, then find the middle number. If there is an even number of data points, the median is the average of the two middle numbers.
Sorted data: 49, 72, 72, 73, 74, 76, 78, 80, 83The middle number (fifth in this case) is 74, so the median is 74.The mode is the number that occurs most frequently in the data set. For this set, the mode would be the number that appears more than once.
The number 72 occurs twice, so the mode is 72.two rectangular properties share a common side. Lot is 33 feet wide and 42 feet long. The combined area of the lots is 1,848 square feet .How many feet wide I Lot B
First, find the area of lot A.
To find the area, multiply the length by the width.
33*42=1,386
Now, subtract the area of lot a from the total area. This will give us the area of lot b.
1,848-1,386=462
The area of lot b is 462 square feet.
Finally, divide the area of lot b (462) by its length to find the width. Since they both share a side, we know that it’s length is 42 feet.
462/42=11
Lot b is 11 feet wide.
Hope this helps!
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
well, let's grab a couple of points off the line hmmmm let's see, the lines runs through (0, 4) and also (3,5), so let's use those to get its slope and thus its function.
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5}) ~\hfill slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-4}{3-0}\implies \cfrac{1}{3}[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=\cfrac{1}{3}(x-0)\implies y-4=\cfrac{1}{3}x \\\\\\ y=\cfrac{1}{3}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Each letter of the alphabet is printed on an index card. What is the theoretical probability of randomly choosing any letter except Z? Write your answer as a fraction or percent rounded to the nearest tenth.
The theoretical probability of choosing a letter other than Z is
for z the fraction value is 1/26 and for other letters then Z is 25/26
Which company’s tower holds the most water?
Answer: First Option
Step-by-step explanation:
The formula to calculate the volume of a cylinder is:
[tex]V = \pi(\frac{d}{2})^2*h[/tex]
Where d is the diameter of the cylinder and h is the height.
Notice that the term d is squared. This means that to increase the volume of a cylinder it is more efficient to increase its diameter as well. Therefore, look for the cylinder with the largest diameter among the options.
The first cylinder is 90 ft in diameter and 40 ft in height and its volume is
[tex]V = \pi(\frac{90}{2})^2*40[/tex]
[tex]V=254469\ ft^3[/tex]
You can verify that it is the tank that has the highest volume
If you make $15 per hour and you receive a 10% raise, how much will you be earning after the raise?
Answer:
$16.50/hr
Step-by-step explanation:
Current pay is 1.00($15/hr).
Current pay plus a 10% raise is 1.10($15/hr) = $16.50/hr
After receiving a 10% raise on a $15 per hour wage, you would be earning $16.50 per hour.
If you are currently making $15 per hour and you receive a 10% raise, you can calculate your new hourly wage by first determining the amount of the raise and then adding it to your current wage. To find the raise amount, you multiply your current wage by the raise percentage expressed as a decimal. In this case:
Amount of raise = Current hourly wage imes Raise percentage
Amount of raise = $15 per hour imes 0.10 (since 10% = 0.10)
Amount of raise = $1.50 per hour
Now, you add this raise to your current hourly wage to find your new hourly wage:
New hourly wage = Current hourly wage + Amount of raise
New hourly wage = $15 per hour + $1.50 per hour
New hourly wage = $16.50 per hour
To give an example for comparison, if your job pays $10 per hour and your boss gives you a $2 per hour raise, that is a 20% increase because the percentage change is calculated as $2/$10 = 0.20 or 20%. In your case, the 10% raise increases your wage by $1.50, making it $16.50 per hour after the raise.
Which are the solutions of x2 = -5x + 8?
- 5
-
7
-5 + 17
0 -5 -157 -5 + 157
0-5=17-57 v7
o S-x57.5+, 187
05-55+
IN
SEN
5 -
57
5 + 57
N
Answer:
1.27, -6.27 to the nearest hundredth,
or if you require it in exact form,
-2.5 + √14.25, -2.5 - √14.25.
Step-by-step explanation:
x^2 = -5x + 8
x^2 + 5x = 8
Competing the square:
(x + 2.5)^2 - 6.25 = 8
(x + 2.5) = 14.25
x + 2.5 = +/-√14.25
x = -2.5 + √14.25, -2.5 - √14.25
x = -2.5 + 3.77, -2.5 - 3.77
= 1.27, -6.27.
What is 3 3/4 ft = in yd?
Answer: 1.25
Step-by-step explanation:
Because...
All you have to do is divide the length value by 3
and your answer will be 1.25.
* Hopefully this helps:) Mark me the brainliest:)!!!
Answer:
1.25yd
Step-by-step explanation:
couted through table
If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a _
If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a parallelogram.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a quadrilateral, specifically a parallelogram.
The two identical triangles, when combined in this way, will have their bases aligned and their vertices opposite each other, forming two pairs of parallel sides.
A parallelogram, which is a quadrilateral with opposite sides that are parallel and congruent.
Hence, If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a parallelogram.
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The graph below shows a scatter plot and a linear model of joanna’s height, in inches, for various ages. Use the model to estimate how tall joanna was when she was 11 years old.
Answer:
About 57.5 inches
Step-by-step explanation:
From the points which relates height and age a linear model was made. This allow us to estimate joanna’s height in those years the points are missing. For example, when she was 11 years old, her height was about 57.5 inches.
Answer:
57.5
Step-by-step explanation:
Factor 2x^2 + 7x + 3
Answer: (x - 3) (2x-1)
Answer:
(x+3)(2x+1)
Step-by-step explanation:
I got it right on khan academy.
Find the value of x. Round to the nearest tenth.please help.
Answer:
39.9
Step-by-step explanation:
A good trick to remember is SOH CAH TOA.
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
Here, we're given an angle and the opposite side, and we want to find the adjacent side. So we need to use tangent.
tan 31° = 24 / x
x = 24 / tan 31°
x ≈ 39.9
Simplify 12a2b3 / 3ab PLEASE HELP
12a^2b^3 / 3ab
Factor 3 out of the numerator:
3(4a^2b^3) / 3ab
Cancel out the common factors:
4a^2b^3 / ab
Cancel out the common factors again to get the final answer:
4ab^2
Write the equation of the line represented by the following table
Answer:
y = 100x + 400
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 400) and (x₂, y₂ ) = (1, 500) ← 2 points from the table
m = [tex]\frac{500-400}{1-0}[/tex] = 100
note the line crosses the y- axis at (0, 400) ⇒ c = 400
y = 100x + 400 ← equation of line
The equation of the line represented by the following table in slope-intercept form is y = 100x + 400.
What is slope-intercept form of equation of straight line ?The equation of a straight line in the form y = mx + c where m is the slope of the line and c is its y-intercept is known as the slope-intercept form. Here both the slope (m) and y-intercept (c) have real values. It is known as slope-intercept form as it gives the definition of both the slope and y-intercept.
What is the slope of a straight line using two given coordinates ?Slope of a straight line can be found using two given points say (x1,y1) and (x2,y2).
Slope (m) = (y2 - y1) / (x2 - x1) .
Finding the given equation of straight line -Taking any two arbitrary points, from the table given aside we have x1 = 0, x2 = 1, y1 = 400 and y2 = 500
⇒ Slope (m) = (y2 - y1) / (x2 - x1) .
= (500 - 400)/(1 - 0)
∴ Slope (m) = 100 .
The y-intercept of the line is the value of y coordinate when the value of x = 0. In other words, y-intercept is the point where the curve touches the y-axis.
∴ From the table, y-intercept (c) = 400 .
Thus, we have slope (m) = 100 and y-intercept (c) = 400 .
The equation of straight line is y = 100x + 400 .
Therefore, the equation of the line represented by the following table in slope-intercept form is y = 100x + 400.
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what is another way to write the time half past 7
half an hour past 7, will be 7 plus 30 minutes then 7:30.
we could also come from the other way, and say is 30 minutes before 8 o'clock.
Jenny test grades are 93 89 96 and 98 if she wishes to raise her average to 95 what does she need to score her next test
Answer:
Jenny would have to get a 99 on her next test to raise her average from a 94 to a 95.
Step-by-step explanation:
First you need to find her current average:
93 + 89 + 96 + 98 = 376/4 = 94
Now that you have the current average, all you need to do is find what would be the total of her grades if she had a average of 95. Since her average would be 95, and she would have completed 5 tests, it makes sense to multiply the average by the number of tests:
95 x 5 = 475
Now all you need to do is remove from this number the sum of the original 4 tests, and voila! There is her 5th test score:
475 - 376 = 99
Her 5th test score is 99%.
To raise her average to 95, Jenny needs to score a 99 on her next test.
Explanation:To find out what score Jenny needs to get on her next test, we can use the average formula. We know that Jenny's average score is currently 94 (the average of 93, 89, 96, and 98). Let's call the score she needs to get on her next test 'x'. To raise her average to 95, the sum of all her test scores would be (93 + 89 + 96 + 98 + x) and the number of tests would be 5 (since she has taken 4 tests so far). We can set up the equation (93 + 89 + 96 + 98 + x)/5 = 95 and solve for x:
(93 + 89 + 96 + 98 + x)/5 = 95
Combine like terms and multiply both sides by 5:
376 + x = 475
Subtract 376 from both sides:
x = 99
Therefore, Jenny needs to score a 99 on her next test in order to raise her average to 95.
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What is the equation of line l?
Answer:
y = 3x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (1, 0) ← 2 points on the line
m = [tex]\frac{0+3}{1-0}[/tex] = 3
The line crosses the y- axis at (0, - 3) ⇒ c = - 3
y = 3x - 3 ← equation of line
The equation of line l will be;
⇒ y = 3x - 3
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (1, 0) and (0, -3).
Now,
Since, The equation of line passes through the points (1, 0) and (0, -3).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 3 - 0) / (0 - 1)
m = - 3 / - 1
m = 3
Thus, The equation of line with slope 3 is,
⇒ y - 0 = 3 (x - 1)
⇒ y = 3x - 3
Therefore, The equation of line passes through the points (1, 0) and
(0, -3) will be;
⇒ y = 3x - 3
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what is it 12 - 33/4
Answer: 15/4
Step-by-step explanation:
1. 12/1 - 33/4
2. 48/4 -33/4
3. 15/4
Find the surface area of a square pyramid whose base edge is 6cm and whose slant edge is 5cm
Check the picture below.
so let's notice, the base is a 6x6 square, and triangular faces have a base of 6 and an altitude/height of 5. So we can just get the area of the square and the triangles and sum them up and that's the area of the pyramid.
[tex]\bf \stackrel{\textit{triangles' area}}{4\left[ \cfrac{1}{2}(6)(5) \right]}+\stackrel{\textit{square's area}}{(6\cdot 6)}\implies 60+36\implies 96[/tex]
For this case we have that by definition, the surface area of a regular pyramid, is given by:
[tex]SA = \frac {1} {2} p * l + B[/tex]
Where:
p: Represents the perimeter of the base
l: The inclination height
B: The area of the base
Now, since the base is square we have:
[tex]B = 6 ^ 2 = 36 \ cm ^ 2\\p = 6 + 6 + 6 + 6 = 24 \ cm\\l = 5 \ cm[/tex]
Then, replacing the values:
[tex]SA = \frac {1} {2} 24 * 5 + 36\\SA = 60 + 36\\SA = 96 \ cm ^ 2[/tex]
ANswer
[tex]96 \ cm ^ 2[/tex]
17 points
please show your work
Solve. x^2+5x+6=0
Answer:
x = -2 or x = -3Step-by-step explanation:
[tex]x^2+5x+6=0\\\\x^2+2x+3x+6=0\\\\x(x+2)+3(x+2)=0\\\\(x+2)(x+3)=0\iff x+2=0\ \vee\ x+3=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\x=-2\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3[/tex]
y = x2 + 11x + 24 is equivalent to the graph of which equation? y = (x + 8)(x + 3) y = (x + 4)(x + 6) y = (x + 9)(x + 2) y = (x + 7)(x + 4)
Answer:
First option: [tex]y=(x + 8)(x + 3)[/tex]
Step-by-step explanation:
Given the quadratic equation [tex]y = x^2 + 11x + 24[/tex], you need to factor it.
To do this, you need to find two number that when you add them you get 11 and when you multply them you get 24. These numbers are: 8 and 3.
Therefore, knowing this, you can factor the quadratic equation:
[tex]y = x^2 + 11x + 24\\\\y=(x + 8)(x + 3)[/tex]
Then, [tex]y = x^2 + 11x + 24[/tex] is equivalent to the graph of the equation [tex]y=(x + 8)(x + 3)[/tex], which matches with the first option.
In a bar, three bottles of Fanta cost GHC 6.00 find the cost of ten such bottles of Fanta
Answer:
The cost is GHC 20.00
Step-by-step explanation:
We can write a proportion to solve this
3 bottles 10 bottles
-------------- = -----------
6.00 x
Using cross products
3x = 10 *6
3x = 60
Divide by 3
3x/3 = 60/3
x = 20
The cost is GHC 20.00