Answer:Simplifying
(2y + -1)(4y + -3) = 0
Reorder the terms:
(-1 + 2y)(4y + -3) = 0
Reorder the terms:
(-1 + 2y)(-3 + 4y) = 0
Multiply (-1 + 2y) * (-3 + 4y)
(-1(-3 + 4y) + 2y * (-3 + 4y)) = 0
((-3 * -1 + 4y * -1) + 2y * (-3 + 4y)) = 0
((3 + -4y) + 2y * (-3 + 4y)) = 0
(3 + -4y + (-3 * 2y + 4y * 2y)) = 0
(3 + -4y + (-6y + 8y2)) = 0
Combine like terms: -4y + -6y = -10y
(3 + -10y + 8y2) = 0
Solving
3 + -10y + 8y2 = 0
Solving for variable 'y'.
Factor a trinomial.
(1 + -2y)(3 + -4y) = 0
Subproblem 1
Set the factor '(1 + -2y)' equal to zero and attempt to solve:
Simplifying
1 + -2y = 0
Solving
1 + -2y = 0
Move all terms containing y to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + -2y = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -2y = 0 + -1
-2y = 0 + -1
Combine like terms: 0 + -1 = -1
-2y = -1
Divide each side by '-2'.
y = 0.5
Simplifying
y = 0.5
Subproblem 2
Set the factor '(3 + -4y)' equal to zero and attempt to solve:
Simplifying
3 + -4y = 0
Solving
3 + -4y = 0
Move all terms containing y to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + -4y = 0 + -3
Combine like terms: 3 + -3 = 0
0 + -4y = 0 + -3
-4y = 0 + -3
Combine like terms: 0 + -3 = -3
-4y = -3
Divide each side by '-4'.
y = 0.75
Simplifying
y = 0.75
Solution
y = {0.5, 0.75}
Step-by-step explanation:
Answer:
C. 8y² - 10y + 3
Step-by-step explaination:
[tex](2y-1)(4y-3)[/tex]
[tex]2y(4y - 3) - 1(4y - 3)[/tex]
[tex]8 {y}^{2} - 6y - 4y + 3[/tex]
[tex]8 {y}^{2} - 10y + 3[/tex]
3. What is the relative frequency of a
customer 40 years or older getting
information from the Internet?
A 20%
C 50%
B 40%
21. In 4 + In(4x - 15) = In(5x + 19)
Answer:
[tex]x=-30;\quad \:I\ne \:0[/tex]
Step-by-step explanation:
[tex]In\cdot \:4+In\left(4x-15\right)=In\left(5x+19\right)[/tex]
[tex]\:4+In\left(4x-15\right):\quad -11nI+4nxI\\In\cdot \:4+In\left(4x-15\right)\\=4nI+nI\left(4x-15\right)\\\\\:In\left(4x-15\right):\quad 4nxI-15nI\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=In,\:b=4x,\:c=15\\=In\cdot \:4x-In\cdot \:15\\=4nxI-15nI\\=In\cdot \:4+4nxI-15nI\\\mathrm{Simplify}\:In\cdot \:4+4nxI-15nI:\quad -11nI+4nxI\\In\cdot \:4+4nxI-15nI\\\mathrm{Group\:like\:terms}\\=4nI-15nI+4nxI\\\mathrm{Add\:similar\:elements:}\:4nI-15nI=-11nI\\=-11nI+4nxI\\[/tex]
[tex]\mathrm{Expand\:}In\left(5x+19\right):\quad 5nxI+19nI\\In\left(5x+19\right)\\=nI\left(5x+19\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=In,\:b=5x,\:c=19\\=In\cdot \:5x+In\cdot \:19\\=5nxI+19nI\\\\-11nI+4nxI=5nxI+19nI\\\\\mathrm{Add\:}11nI\mathrm{\:to\:both\:sides}\\-11nI+4nxI+11nI=5nxI+19nI+11nI\\Simplify\\4nxI=5nxI+30nI\\\mathrm{Subtract\:}5nxI\mathrm{\:from\:both\:sides}\\4nxI-5nxI=5nxI+30nI-5nxI\\\mathrm{Simplify}\\-nxI=30nI\\[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-nI;\quad \:I\ne \:0\\\frac{-nxI}{-nI}=\frac{30nI}{-nI};\quad \:I\ne \:0\\\mathrm{Simplify}\\\frac{-nxI}{-nI}=\frac{30nI}{-nI}\\\mathrm{Simplify\:}\frac{-nxI}{-nI}:\quad x\\\frac{-nxI}{-nI}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{nxI}{nI}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{xI}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=x\\\mathrm{Simplify\:}\frac{30nI}{-nI}:\quad -30\\\mathrm{Apply\:the\:fraction\:rule}:[/tex]
[tex]\quad \frac{a}{-b}=-\frac{a}{b}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{30I}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=-30\\x=-30;\quad \:I\ne \:0[/tex]
Convert this equation to slope-intercept form:
25x + 10y = 1,000
Answer:
y = -2.5x +100
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
We need to solve for y
25x+ 10y =1000
Subtract 25x from each side
25x-25x+10y = -25x +1000
10y = -25x+1000
Divide each side by 10
10y/10 = -25x/10 +1000/10
y = -2.5x +100
Answer:
y = -2.5x + 100
Step-by-step explanation:
25x + 10y = 1,000
10y = -25x + 1000
y = -2.5x + 100
PLEASE HELP!!!
Carl is on the school track team. To prepare for an upcoming race, he plans to run 217 miles total over the next 31 days.
Write an equation to determine how many miles, m, he needs to run per day, assuming he runs the same amount each day.
How many miles does Carl need to run each day?
The diameter of the circle is 18 m Eugene incorrectly says that the circumference of the circle is about 113.04 m what is the circumference of the circle? What mistake did Eugene make? Use 3.14 for pie
Hi
formula. for circumference of a circle is. : 2πR. if you have the radius.
As the diameter is twice the radius, then circumference is. diameter π
then : 18*π≈ 56.52
the mistake was to take the diameter as the radius.
Final answer:
The circumference of the circle is 56.52 m. Eugene made the mistake of using the radius instead of the diameter to calculate the circumference.
Explanation:
The circumference of a circle can be found using the formula C = πd, where C represents the circumference and d represents the diameter.
In this case, the diameter of the circle is given as 18 m. If we substitute this value into the formula, we get:
C = 3.14 * 18 = 56.52 m
Eugene's mistake was that he used the value of the radius instead of the diameter to calculate the circumference. The correct circumference is 56.52 m, not 113.04 m.
Which describes the correlation show in the scatter plot?
There is a positive linear correlation
There is a negative linear correlation,
There is no positive or negative correlation
There is a nonlinear correlation
Answer:
no positive or negative correlation
Step-by-step explanation:
none looks like |
Positive looks like /
negative looks like \
What operation could you use to find how many centimeters are in 3 meters?
Complete the explanation and the conversion of 3 meters to centimeters.
The operation needed is?
because there are
centimeters in 1 meter.
3 meters?
centimeters.
Answer:
300 centimeters ( cm)
Step-by-step explanation:
The operation is "multiply by 100 the numbers of meters because there are 100 cm in 1 m "
1m=100 cm
3m=3*100 cm=300 cm
There are 100 centimeters in a meter, resulting in 300 centimeters.
The operation needed to convert meters to centimeters is multiplication because there are 100 centimeters in 1 meter. To convert 3 meters to centimeters, you simply multiply 3 meters by the conversion factor of 100 centimeters per meter.
Therefore:
3 meters × 100 centimeters/meter = 300 centimeters
Using this operation and knowing the conversion factor, we find that 3 meters is equal to 300 centimeters.
GIVING BRANLIEST
Which ordered pair is the solution to this system of equations?
y = 4
3x - 2y = 4
Group of answer choices
(0, 6)
(0, 4)
(-4, 4)
(4, 4)
Answer:
(4,4)
Step-by-step explanation:
Answer:
(4,4). You already know the y value is 4, so you just plug that into the second equation. You'd get 3x-8=4, then 3x=12, then x=4. (x,y)=(4,4)
find the length of the third side to the nearest 10th
Answer: 2.8
Step-by-step explanation:
What is equivalent to the expression (x+3)(x-7)+(x+8)(x+3)
Answer:
[tex]2x^2+7x+3[/tex]
Step-by-step explanation:
[tex](x+3)(x-7)+(x+8)(x+3)[/tex]
[tex](x^2-4x-21)+(x^2+11x+24)[/tex]
[tex]x^2-4x-21+x^2+11x+24[/tex]
[tex]2x^2+7x+3[/tex]
What is 90 people to 45 people decrease
Show your work
Answer:
45
Step-by-step explanation:
90 - 45 = 45
4 + 16x - 12(1 + 2x) = ?
Answer:
x=-1.
Step-by-step explanation:
To solve this, we will need to simplify the equation further by distributing the '-12' with the terms inside the parenthesis.
4+16x-12-24x=?
Now, move the numbers to one side with the variable on the other.
-8x=8
x=-1
Answer:
24
Step-by-step explanation:
click on link for step by step explanation
Find the unit rate.
150 mi on 10 gal of gas
A: 15 mi per gal
B: 10 mi per gal
C: 150 mi per gal
The unit rate of miles per gallon is found by dividing the total miles (150 mi) by the total gallons (10 gal), resulting in a unit rate of A) 15 miles per gallon.
To find the unit rate of miles per gallon when given 150 miles on 10 gallons of gas, we divide the total number of miles driven by the number of gallons of gas used. The calculation is as follows:
Write down the given values: 150 miles (mi) and 10 gallons (gal).
Divide the total miles by the total gallons to find the unit rate: 150 mi ÷ 10 gal = 15 mi/gal.
Therefore, the unit rate is 15 miles per gallon, which is option A: 15 mi per gal.
(25 POINTS!)Select all the correct locations
Answer:I go with A,C,E
Step-by-step explanation:
hope this help
A scaled drawing uses a scale factor of 1:25. Is the drawing a reduction or an enlargement? Support your conclusion with an example.
Answer:
Reduction scale
Step-by-step explanation:
Enlarging scale means that the drawing is larger than the actual object. Hence the representative fraction will be greater than unity. For reducing scale the representative fraction is less than unity.
So now looking at 1:25, we see it's a reduction scaling because it's fraction is less than unity.
And what 1:25 means is that 1 on paper while the actual size of the object is 25
Please help me.
Solve for j
–2(j − 42) = –86
Look at the attached picture ⤴
Hope it will help u ....
(04.02 MC)
Solve the system of equations.
5x + y = 9
3x + 2y = 4
Answer:
(2,-1)
Step-by-step explanation:
Multiply first equation by 2:
10x + 2y = 18
Subtract the second equation from this so that the 2y terms cancel:
10x - 3x = 18 - 4
7x = 14
x = 2
Plug into first equation to find y:
5(2) + y = 9
10 + y = 9
y = -1
The answer is (2,-1)
Rectangle A’B’C’D is similar to rectangle ABCD, as shown on the coordinate plane below. Which sequence or transformations maps rectangle ABCD onto rectangle A’B’C’D
The reflection over the [tex]y-axis[/tex] then a dilation by the factor of
[tex]\frac{1}{2}[/tex] with a center of dilation at the origin.
Reflection of the point:Reflecting on the [tex]y-axis[/tex] we get the rectangle A, B, C, D.
A dilation by the factor of [tex]\frac{1}{2}[/tex] with the center of dilation at the origin transforms the rectangle A, B, C, D onto the rectangle A'B'C'D'.
So, the reflection over the [tex]y-axis[/tex] then a dilation by the factor of [tex]\frac{1}{2}[/tex] with a center of dilation at the origin.
The image is attached below.
Learn more about the topic reflection of the point:
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The correct sequence of transformations to map rectangle ABCD onto rectangle A'B'C'D' is a dilation by a scale factor of 1/2. This transformation reduces the size of the original rectangle without additional translation, reflection, or rotation.
The correct sequence of transformations that maps rectangle ABCD onto rectangle A'B'C'D' is:
c. a dilation by a scale factor of 1/2
Here's why:
1. A dilation by a scale factor of 1/2 reduces the size of the original rectangle by half. This transformation scales down all the coordinates by a factor of 1/2. Given the coordinates of ABCD and A'B'C'D', this is the only transformation needed to achieve similarity.
Options a and b involve additional transformations (translation and reflection) that are not required to achieve similarity, and option d introduces a rotation which is not a dilation by itself.
Learn more about sequence of transformations here:
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What is the area of the rhombus?
square units
Answer:
Area = 80
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
Vertical length-16
Horizontal length- 10
make four separate triangles out of the rectangle
each triangle has an area of of 20 (8×5= 40 40/2=20)
multiply by 4
20×4=80
There are 8 flavors of ice cream and
you can have one of 2 kinds of cones
with 4 different kinds of sprinkes on
top. How many combinations are
possible?
Answer:
64
Step-by-step explanation:
you do 8x2x4
Find the area of the parallelogram shown below.
Answer:
The answer is 21
Step-by-step explanation:
The answer is 21 because...
It is hard to explain but for step one you need to take the dotted line and the shape above hat and move it underneath the other shape to make a perfect rectangle.Step two since the dotted line is our new bottom. It has a length of 7. In this step we multiply 3 times 7 Step 3 this is the final step in which 3 times 7 equals 21.Hope this helped :)Find the radius of sphere with a volume of 1372π/3 cubic feet.
Answer:
The radius of the sphere is 7m
Step-by-step explanation:
Given
Volume of a sphere = 1372π/3 m³
Required
The radius.
The volume of a sphere is calculated using the following formula.
V = 4/3 πr³
Where V = volume of the sphere and r represents it's radius.
By substitution;
1372π/3 = 4/3 πr³
Multiply both sides by 3
1372π = 4πr³
Divide through by 4
343π = πr³
Divide through by π
343 = r³
Take cube root of both sides.
r = 7.
Hence, the radius of the sphere is 7m
An actor invests some money at 5% simple interest, and $23,000 more than 3 times the amount at 6% simple interest. The total annual interest earned from the investment is $28,290. How much did he invest at each amount? Use the 6 step method.
Answer:
He invested $117,000 at 5% interests and 3*117,000 + 23000 = $374,000 at 6% interests
Step-by-step explanation:
Let's call x to the some money at 5% simple interest the actor invest. Then, he invested 3x + 23000 dollars at 6% simple interest.
At 5% simple interest, after one year he earned the following interests:
I = P*r*t
I = x*0.05
At 6% simple interest, after one year he earned the following interests:
I = (3x + 23000)*0.06 = 0.18x + 1380
The total annual interest earned from the investment is $28,290, then:
0.05x + 0.18x + 1380 = 28290
x = (28290 - 1380)/0.23
x = $117,000
Dont rip me off for points, if you dont know the answer dont say anything
Answer:
AB = 2 root 13
AC = 4 root 5
Step-by-step explanation:
AB = sqrt[(-4-2)² + (3-7)²]
AB = sqrt(36 + 16)
AB = sqrt(52)
AB = 2sqrt(13)
AC = sqrt[(-8-0)² + (7-3)²]
AC = sqrt(64+16)
AC = sqrt(80)
AC = 4sqrt(5)
sqrt: square root
Determine the intercepts of the line.
The x-intercept of the graph is (0.3, 0).
The y-intercept of the graph is (0, 0.4).
We have,
The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
The intercepts are:
The x-intercept is the point of the line when y = 0,
The y-intercept is the point on the line when x = 0.
Now,
Apply the intercepts concept on the given graph.
From the graph,
The point when x = 0 is 0.4.
The point when y = 0 is 0.3.
Thus,
The x-intercept of the graph is (0.3, 0).
The y-intercept of the graph is (0, 0.4).
Learn more about the equation of a line here:
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Help looks like i forgot to read a ruler
Answer:
the second one
Step-by-step explanation:
Answer:
2nd one is right
Step-by-step explanation:
3 ratios that are equivalent to 3/8
Answer:
30/80 9/24 6/16
Step-by-step explanation:
Answer:
just multiply a fraction equal to 1 for example 2/2
3/8 x 2/2 = 6/16
3/8 x 3/3 = 9/24
3/8 x 4/4 = 12/32
it is equivalent because 2/2 is equal to 1 so it is being multiplied by 1
Step-by-step explanation:
i need help with 4 and 5 please
Answer:
C
Step-by-step explanation:
to find 4, you use the equation [tex]a^{2}+b^{2}=c^{2}[/tex] where the c= hypotenuse, which is the slant of the triangle. Then you width and length can by put as a and b. This gives you [tex]15^{2}+4^{2} = s^{2}[/tex]. Then you solve for s which end up being 15.5.
can someone help me with this?
Sylvie is planning to visit her mother who lives 387 miles away. If
the price of gas ranges from $1.95 to $2.13 per gallon and Sylvie's
car gets 25 miles per gallon, about how much should she plan to
spend on gas for the trip there?
more than $50
$30 to $40
less than $30
$40 to $50
Answer:
$30 to $40
Step-by-step explanation:
387/25= 15.48 (this is how big the tank is)
15.48*2.13= 32.97 (about 33 paying for the highest price)
Sylvie will need approximately 15.48 gallons of gas for her 387-mile trip. With gas prices ranging from $1.95 to $2.13 per gallon, she should plan to spend between $30.20 and $32.96. Therefore, the anticipated cost falls between $30 and $40 that is option B is correct.
To calculate the cost of gas for the trip, we need to follow these steps:
Determine the number of gallons of gas needed for the trip:
Number of Gallons = Total Miles / Miles per Gallon
Number of Gallons = 387 miles / 25 miles per gallon = 15.48 gallons
Calculate the minimum and maximum cost of gas:
Minimum Cost = Number of Gallons * Minimum Price per Gallon
Minimum Cost = 15.48 gallons * $1.95 per gallon ≈ $30.20
Maximum Cost = Number of Gallons * Maximum Price per Gallon
Maximum Cost = 15.48 gallons * $2.13 per gallon ≈ $32.96
Both calculations indicate the cost will fall between $30 and $40. Therefore, the correct answer is: $30 to $40.