Answer:
x=5 y=-1
Step-by-step explanation:
7x-2y=37
[2(4x+y=19)]=
8x+2y=38
---------------------
15x/15=75/15
x=5
[4(5)+y=19]
y=-1
Final answer:
The solution to the given system of equations using elimination is x = 5 and y = -1. This was achieved by multiplying the second equation by 2 and then adding both equations to eliminate y.
Explanation:
We are given a system of linear equations and are asked to solve it using the method of elimination. We have the following equations:
1) 7x - 2y = 37
2) 4x + y = 19
To eliminate one of the variables, we can multiply the second equation by 2 to make the coefficient of y the same in both equations (but with opposite signs). After this step, our system looks like:
1) 7x - 2y = 37
2) 8x + 2y = 38
Now, adding the two equations will eliminate y, and we get:
7x + 8x = 37 + 38
15x = 75
x = 5
We can then substitute the value of x into one of the original equations to solve for y:
4x + y = 19
4(5) + y = 19
20 + y = 19
y = -1
So, the solution to the system is x = 5 and y = -1.
Which of the following function is graphed below?
Answer:
C
Step-by-step explanation:
We can see that there is a closed dot and the function is going left and it is a cubic function.
Additionally, the only one with a [tex]x^3+n\leq 2[/tex] inequality is C.
25 POINTS + BRAINLIEST
Use the net to find the surface area of the prism.
A. 22 m^2
B. 276 m^2
C. 522 m^2
D. 968 m^2
Answer:
C. 522 m^2.
Step-by-step explanation:
The area of the 3 rectangles in the net
= 10 * (9 + 16.6 + 14)
= 10 * 39.6
= 396. m^2.
The area of the 2 triangles
= 2 * 1/2 * 14 * 9
= 126 m^2.
Total surface area = 522 m^2.
Which of the following histograms would best be approximated by a normal distribution?
Answer:
Choice B is correct
Step-by-step explanation:
The normal distribution has extensive applications in statistics. The distribution is characterized by a symmetric bell-shaped density curve. Most of the observations or data points fall in the middle of the distribution while both the right and left tails are equally longer.
The histogram that can be approximated by a normal distribution must meet the above conditions.
The histogram in alternative A is skewed to the right since most of the values fall in the lower end of the distribution. A skewed distribution is not symmetric.
The histogram in choice C is approximately uniformly distributed since most of the observed values have an approximately equal frequency. Each of the values is approximately equally likely. The uniform distribution is not symmetric.
The histogram in D follows no know pattern and nevertheless it lacks the symmetric property.
The histogram in B is approximately symmetric in distribution since most of the observed data values fall in the middle of the distribution while the left and right tails are nearly equal. This histogram can thus be approximated by a normal distribution.
17.003 - 0.374 please show work
Answer:
16.629
Step-by-step explanation:
Start by setting up the numbers like the first picture. The borrow. To borrow we have to go the whole way over to the 7 since you can't borrow from 0. So the 7 becomes a 6 and the 0 becomes 10. Then the 10 becomes a 9 and the 0 becomes a 10. Then the 10 becomes a 9 and the 3 becomes a 13. Then subtract. Just bring the decimal point down.
78 is 15% of what number
Answer:
520
Step-by-step explanation:
Is means equals and of means multiply
78 = 15% * W
Change to decimal form
78 = .15 *W
Divide by .15 on each side
78/.15 = .15W/.15
520 = W
Answer:
520
Step-by-step explanation:
78/0.15 = 520
Math algebra 1 plsssss helppppp!!!!
Answer:
5. He rented 7 new releases videos
6. 4 3-bedrooms units.
7. length: 37, width: 18
8. 81 dimes, 47 quarters
Step-by-step explanation:
5. Videos
X: New releases
Y: Regular titles
EQ1: x + y = 18 (he rented 18 videos)
EQ2: 3x + 2y = 43 (he paid $43 for the 18 videos)
By EQ1, we can isolate y-value as y = 18 - x
We place this y-value into EQ2:
3x + 2(18 - x) = 43 and we solve:
3x + 36 - 2x = 43
3x - 2x = 43 - 36
x = 7
He rented 7 new releases videos
6. bedroom units
X: 2-bedrooms units
Y: 3-bedrooms units
EQ1: x + y = 7 (they have 7 units)
EQ2: 450x + 650y = 3950 (their monthly renting revenues)
By EQ1, we can isolate x as x = 7 - y (since we're looking for 3-bedrooms units), and place that value in EQ2:
450 (7 - y) + 650y = 3950
3150 - 450y + 650y = 3950
200y = 800
y = 4
So, they have 4 3-bedrooms units.
7. Rectangle
X: length
Y: width
EQ1: x + y = 55 (since perimeter is 110 and includes 2x + 2y)
EQ2: x = 2y + 1 (length is twice the with, plus 1)
Since we are asked to find both values, it doesn't matter by which we begin. By EQ1, we can do x = 55 -y, and place that value in EQ2, to get:
55 - y = 2y + 1
54 = 3y
y = 18
Place y = 18 in EQ1 to find x:
x + 18 = 55
x = 37
8. Dimes and quarters
X: dimes
Y: quarters
EQ1: x = y + 34 (34 more dimes than quarters)
EQ2: 10x + 25y = 1985 (total value of the collection)
Let's place the value of x from EQ1 in EQ2:
10 (y + 34) + 25y = 1985
10y + 340 + 25y = 1985
35y = 1645
y = 47
From EQ1, we then have
x = 47 + 34 = 81
So, we have 81 dimes ($8.10) and 47 quarters ($11.75), for a total of $19.85.
Enter your answer and show all the steps that you use to solve this problem in the space provided.
f(x)+9x^3+2x^2-5x+4 and g(x)=5x^3-7x+4
What is f(x)-g(x)?
Show all of your steps and write your final answer in factored form.
I would like it if you put down all the steps and explanation for I do not understand it. Thank you so much for your help in advance!
Answer:
[tex]\boxed{f(x) - g(x) = 2x(2x^{2} + x + 1)}[/tex]
Step-by-step explanation:
f(x) = 9x³ + 2x² - 5x + 4; g(x)=5x³ -7x + 4
Step 1. Calculate the difference between the functions
(a) Write the two functions, one above the other, in decreasing order of exponents.
ƒ(x) = 9x³ + 2x² - 5x + 4
g(x) = 5x³ - 7x + 4
(b) Create a subtraction problem using the two functions
ƒ(x) = 9x³ + 2x² - 5x + 4
-g(x) = -(5x³ - 7x + 4)
ƒ(x) -g(x)=
(c). Subtract terms with the same exponent of x
ƒ(x) = 9x³ + 2x² - 5x + 4
-g(x) = -(5x³ - 7x + 4)
ƒ(x) -g(x) = 4x³ + 2x² + 2x
Step 2. Factor the expression
y = 4x³ + 2x² + 2x
Factor 2x from each term
y = 2x(2x² + x + 1)
[tex]\boxed{f(x) - g(x) = 2x(2x^{2} + x + 1)}[/tex]
What is the quadratic regression equation that fits these data?
Option: A is the correct answer.
The quadratic equation that fits these data is:
A. [tex]y=2.09x^2+0.33x+3.06[/tex]
Step-by-step explanation:We are given a table of values as:
x y
-4 35
-3 20
-2 12
-1 6
0 2
1 6
2 10
3 24
4 38
From the given data values we see that the points follow a parabolic path this means that the line of best fit will has a quadratic equation.
Also, the line that best represents these data points as is done by the regression calculator is:
A. [tex]y=2.09x^2+0.33x+3.06[/tex]
Which values are the solutions to the inequality below
Answer:
option B 5
option D -6
Step-by-step explanation:
Given in the question an inequality
x² > 16
Step 1
Take square root on both sides of inequality
√x² > ±√16
x < -√16 or x > √16
x < -4 or x > 4
Step 2
-4 > x > 4
x = 5 x > 4 accepted
x = -6 x < -4 accepted
Step 3
x = 4 rejected
x = -1 rejected
There are 858 calories in 13 servings of cereal. If a bowl holds 2 servings, how many calories are in the bowl?
Answer:
132 calories in a bowl that holds 2 servings
Step-by-step explanation:
In order to find what 1 serving equals, you have to divide 858 by 13 and you get 66, but since the bowl holds 2 servings you have to multiply 66 by 2 and you get 132
Answer:
78
Step-by-step explanation:
Subtract 2 serving out of 13 and the then divide 858 by the number.
If x+y = 6, y+z = 7, and z+x = 9, what is the average (arithmetic mean) of x, y, and z?
Answer:
11/3 . . . or . . . 3 2/3
Step-by-step explanation:
Adding the three equations will give 2x+2y+2z:
(x +y) +(y +z) +(z +x) = 6 +7 +9
2x +2y +2z = 22
Dividing by 2 gives the sum of three variables:
x +y +z = 11
The average of x, y, and z is their sum divided by 3:
(x +y +z)/3 = 11/3
Can the numbers 24, 32, 40 be the lengths of the three sides of a right triangle? Explain why or why not.
Answer:
24, 32, 40 can be the lengths of the three sides of a right triangle
Step-by-step explanation:
Pythagoras theorem:
c^2 = a^2 + b^2
40^2 = 1,600
32^2 + 24^2 = 1024 + 576 = 1,600
If the square of the length of the hypotenuse (longest side length) is equal to the sum of the squares of the lengths of the other two sides then it's a right triangle
So
40^2 = 32^2 + 24^2
1,600 = 1,600
24, 32, 40 can be the lengths of the three sides of a right triangle
Stephaine has 3 3/4 bags of soil to put in her garden. Each bag of soil will cover 125.3 ft^2. How many square feet will Stephanie. be able to cover if she uses all these bags of soil?
Answer:
[tex]125.3 \times 3 = 375.9[/tex]
[tex]125.3 \times \frac{3}{4} = 93.975[/tex]
[tex]375.9 + 93.975 = 469.875[/tex]
What is the result of this operation?
the answer is B because you will add and subtract each element with it's corresponding one
The result of this operation is option B. This is obtained by using matrix addition and subtraction.
What is the result of this operation?Adding and subtracting the terms of the matrix since these are matrices with same order. Hence we get,
[tex](\left[\begin{array}{ccc}13&10&7\\6&8&1\\2&5&0\end{array}\right] -\left[\begin{array}{ccc}3&-2&6\\14&-6&11\\8&-12&9\end{array}\right] ) +\left[\begin{array}{ccc}6&10&15\\10&0&9\\1&0&7\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}10&12&1\\-8&14&-10\\-6&17&-9\end{array}\right] +\left[\begin{array}{ccc}6&10&15\\10&0&9\\1&0&7\end{array}\right][/tex]
=[tex]\left[\begin{array}{ccc}16&22&16\\2&14&-1\\-5&17&-2\end{array}\right][/tex]
Thus the required matrix is option B.
Learn more about matrix addition and subtraction here:
brainly.com/question/34923885
#SPJ2
What is the measure of angle K in the circle?
Answer:
The measure of angle k is (1/2)(140°) = 70°.
1. z²-9z=66
2. y²+16y=17
3. 2h²-5h=-1
Hello,
Starting with problem one:
Subtract 66 from both sides.
z2−9z−66=66−66
z2−9z−66=0
Use quadratic formula with a=1, b=-9, c=-66.
z = 9/2+1/2√345
Problem two:
Subtract 17 from both sides.
y^2+16y−17=17−17
y^2+16y−17=0
Factor left side of equation.
(y−1)(y+17)=0
Set factors equal to 0.
y−1=0 or y+17=0
y=1 or y=−17
ANSWER: y=1 or y=−17
Problem 3:
2h^2−5h−(−1)=−1−(−1)
2h^2−5h+1=0
Use quadratic formula with a=2, b=-5, c=1.
ANSWER: h=5/4+1/4√17
Have an amazing day.
What is the value of the function f(x)=3/2x-1/2 when x=6?
Answer:
Option 1
Step-by-step explanation:
In order to find the value of the function at x=6, we have to replace x by 6 in the given function.
[tex]f(x)=\frac{3}{2}x -\frac{1}{2}[/tex]
Replacing(Substituting) x = 6 in above equation we get:
[tex]f(6)=\frac{3}{2} (6) -\frac{1}{2}\\\\f(6)=9-\frac{1}{2}\\\\ f(6)=\frac{18}{2}-\frac{1}{2}\\\\ f(6)=\frac{17}{2}\\\\ f(6)=8\frac{1}{2}[/tex]
Thus, 1st option gives the correct answer.
Answer:
The correct answer is option 1
8 1/2
Step-by-step explanation:
It is given that,
f(x) = 3x/2 - 1/2
We have to find f(x) when x = 6
To find the value of f(6)
we have, f(x) = 3x/2 - 1/2
when x = 6
f(x) = f(6)
f(6) = (3 * 6)/2 - 1/2
= 18/2 - 1/2
= (18 - 1)/2 = 17/2
= 8 1/2
Therefore the correct answer is first option
Need help plz .You have $2500 to invest in two different accounts. In order to save the money you need for college, you need to average 7% interest. If the two accounts pay 7.5% and 6% interest, how much should you invest in each account? Round to the nearest dollar amount.
A)$1667 in 7.5%, $833 in 6%
B)$1833 in 7.5%, $667 in 6%
C)$667 in 7.5%, $1833 in 6%
D)$833 in 7.5%, $1667 in 6%
Answer:
A)$1667 in 7.5%, $833 in 6%
Step-by-step explanation:
Let amount of money invested 6% account = x
Let amount of money invested 7.5% account = y
Then we get equations:
x+y=2500
or x=2500-y ...(i)
6% of x+7.5% of y=7% of (2500)
or 0.06x+0.075y=0.07(2500)
or 60x+75y=175000...(ii)
plug (i) into (ii)
60x+75y=175000
60(2500-y)+75y=175000
150000-60y+75y=175000
-60y+75y=175000-150000
15y=25000
y=$1666.66666667
or y=1667
plug into (i)
x=2500-y=2500-1667=833
Hence final answer is A)$1667 in 7.5%, $833 in 6%
please help i really need help
Answer:
142 degrees
Step-by-step explanation:
Since LON is 180 degrees...
9x - 91 + 6x + 76 = 180
15x - 15 = 180
15x = 165
x = 11
MON = 6(11) + 76
MON = 66 + 76
MON = 142
Please help me with this question I would really appreciate it:Hilda has 72 half dollars.how much is her coin collection worth?
Answer:
36
Step-by-step explanation:
half dollar equals 50 cents.
72/2=35
Answer:
36
Step-by-step explanation:
divide it by two since it says that each are half a dollar meaning 50 cents each.
Which measurement could be a surface area measure? 18 ft. 64.5 m3 27.9 mm2 50 g
Answer:
27.9 mm2
27.9 mm2 = 2.79 × 10^ -5 m2
The circumference of a circle is 50.24 centimeters. Find the area of the circle. (Use 3.14 for π.)
Answer:
help me first
Step-by-step explanation:
Answer:
200.96
Step-by-step explanation:
First, divide 50.24 by the pi (3.14)
50.24 / 3.14 = 16
Second, divide 16 by two (so that the radius is found).
16 / 2 = 8
Now that we have the radius length, solve for the area.
area of circle = πr^2
Area of circle = (3.14) (8^2)
Area of circle = 3.14 x 64
Area of circle = 200.96
Find the inverse of the following function.
For this case we must find the inverse of the following function:
[tex]f (x) = 8 \sqrt {x}[/tex]
For this, we follow the steps below:
We change f (x) to y:
[tex]y = 8 \sqrt {x}[/tex]
We exchange the variables:
[tex]x = 8 \sqrt {y}[/tex]
We solve for y:
[tex]8 \sqrt {y} = x[/tex]
We divide between 8 on both sides of the equation:
[tex]\sqrt {y} = \frac {x} {8}[/tex]
We raise both sides of the equation to the square to remove the root:
[tex]y = (\frac {x} {8}) ^ 2\\y = \frac {x ^ 2} {64}[/tex]
So, the inverse is:[tex]f ^ {- 1} (x) = \frac {x ^ 2} {64}[/tex]
ANswer:
Option C
y - 7x = 6
y +7x = 8
hence y is 7 ,x is 1/7
hope it helps you
use unit multipliers to convert 14 yards per minute to inches per second
Answer:
8.4 in. per seconds
Step-by-step explanation:
14yd=42ft.
42ft=504in per min
504/60=1 min / 60
8.4=1 sec.
Answer:
8.4 inches/second
Step-by-step explanation:
1 yd = 3 ft
1 ft = 12 inches
1 minute = 60 seconds
These are the conversion factors we need to convert 14 yds /minutes to inches per second
14 yds 3 ft
-------- * -------------
minutes yd
The yds cancel and we are left with
42 ft
--------
minutes
42 ft 12 inches
-------- * ------------------
minutes 1 ft
The feet cancel
504 inches
-------------------
minutes
504 inches 1 minute
------------------- *--------------
minutes 60 seconds
The minutes cancel
504 inches
------------------
60 seconds
Simplifying the numbers
8.4 inches
----------------
second
Janice completed the following polynomial addition. Find her error and correct her work.
Answer:
Option B. [tex]9x^{3}-2x^{2}-4x-2[/tex]
Step-by-step explanation:
we have
[tex]7x^{3}-2x^{2} +5[/tex]
[tex]2x^{3}-4x-7[/tex]
Adds the polynomial
Group terms that contain the same variable
[tex](7x^{3}+2x^{3})-2x^{2}-4x+(5-7)[/tex]
Combine like terms
[tex]9x^{3}-2x^{2}-4x-2[/tex]
Janice's error was
[tex]-2x^{2} +5-4x-7=6x^{2}-12[/tex]
so
[tex]-2x^{2}-4x=6x^{2}[/tex]
instead
[tex]-2x^{2}-4x=-2x^{2}-4x[/tex]
and
[tex]5-7=-12[/tex]
instead
[tex]5-7=-2[/tex]
Answer:
B
Step-by-step explanation:
Edge 2022
Find the area of the composite figure and round the nearest tenth
Answer:
The area of the composite figure is 1360 ft.
Step-by-step explanation:
First, you should split up the composite figure into separate shapes.
So to find area of the triangle all the way on the left, you multiply base x height then divide by 2.
30 x 34 = 1020 ÷ 2 = 520.
Then, moving on to next shape, we can break up the trapezoid into a rectangle and a triangle.
To find area of the rectangle you multiply length x width.
16 x 30 = 480.
Finally, we have the last triangle right above the rectangle. Keep in mind that the rectangle does not have a length of 40!
You have to subtract 40 - 16 which equals 24.
30 x 24 = 720 ÷ 2 = 360.
Now that we have all 3 numbers, we simply add them all together and you will get an answer of 1360 ft.
Remember to label your answer!
Answer:
1080 ft^2
Step-by-step explanation:
We are given a composite figure that consists of a triangle and a trapezoid.
We know that the area of these two shapes is given by the following formulas so we will put in the given values to get:
Area of triangle = [tex]\frac{1}{2} \times b \times h[/tex] = [tex]\frac{1}{2} \times 16 \times 30[/tex] = 240 ft^2
Area of trapezoid = [tex]\frac{a+b}{2} h[/tex] = [tex]\frac{16+40}{2} 30[/tex] = 840 ft^2
Area of composite figure = [tex]240+840[/tex] = 1080 ft^2
Your friend can clap his hands 28 times in 12 seconds. How many times can your friend clap his hands in 2.25 minutes?
Answer:
Step-by-step explanation:
x / 2.25 seconds = 28 times / 12 seconds
multiply by sides by 2.25 seconds
x / 2.25 seconds * 2.25 seconds = 28 times / 12 seconds * 2.25 second
x = 2.3333333 times/ second * 2.25 seconds
x = 5.8333
Answer:
315 times
Step-by-step explanation:
We know that the friend can clap his hands 28 times in 12 seconds. First, we need to know how many times can he clap his hands in 1 second:
To do it we have to divide the times he can clap his hands by the time in seconds:
28/12 = 2.333333
He can clap his hands 2.333333 times in 1 second:
Now we want to know how many times will he clap his hands in 2.25 minutes
We have to change 2.25 minutes into seconds:
1 (minute) = 60 (seconds in 1 minute)
2.25 (minutes) * 60 (seconds in 1 minute) = 135 seconds
After we get the seconds he is going to clap his hands, we have to multiply the times he claps times the seconds:
2.3333333 times * 135 seconds = 315
315 times in 2.25 minutes
Please help!!!!! Thanks I will mark brainlest!!
Answer:
Next term doubles
Hope this helps :)
Have a great day !
5INGH
Brainliest please
Step-by-step explanation:
which of exercises 14-19 could you solve mentally
Answer:
piccctures?
Step-by-step explanation: