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]
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.
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]
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
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
Pure gold has a density of 19.32 g/cm². If you have
37 grams of pure gold, what is the volume of your sample?
Round to four significant digits.
0.5222 cm^3
1.915 cm^3
2.216 cm^3
19.15 cm^3
Answer:
1.915
Step-by-step explanation:
volume= mass/density
37g/19.32=1.91511387
to four significant digits... 1.915
find the length of the third side to the nearest 10th
Answer: 2.8
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.
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
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
Complete the following statements for the cosine
function shown in the graph.
The minimum value is
The maximum value is
First Part:
The minimum value is -0.75
The maximum value is 0.75
Second Part:
The amplitude is 0.75
Third Part:
An equation for this function is y = 0.75cos(x)
The minimum value of the graph is -0.75 and maximum value is 0.75, amplitude is 0.75, and function for the graph is y = 0.75cosx.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a graph shown in the picture.
From the graph, we can see that:
The minimum value = -0.75
The maximum value = 0.75
The amplitude = 0.75
And the graph of the function:
y = 0.75cosx
Where y ∈ [-0.75, 0.75]
Thus, the minimum value of the graph is -0.75 and maximum value is 0.75, amplitude is 0.75, and function for the graph is y = 0.75cosx.
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True or false: 4 (2x + y + 6) is equivalent to 8x + 4y + 24.
A true
B false
Answer:
A) true
Step-by-step explanation:
when you use the distributive property with the equation 4(2x + y + 6) you get 8x + 4y + 24
What is 90 people to 45 people decrease
Show your work
Answer:
45
Step-by-step explanation:
90 - 45 = 45
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.
(25 POINTS!)Select all the correct locations
Answer:I go with A,C,E
Step-by-step explanation:
hope this help
Pleas look at photo and answer!!
Answer:
B
Step-by-step explanation:
Answer:
the answer is the second one
Step-by-step explanation:
___ probability is the predicted ratio of favorable outcomes to the total number of outcomes.
Answer:
theoretical probability
Answer:
Theoretical Probability
Step-by-step explanation:
The answer is Theoretical Probability
Write a recursive formula for the perimeter of the
nth figure.
an = an- 1 + 6 where a = 4
an = n2 where ay = 1
an = an- 1 + 9 where a1 = 4
DONE
Answer:
Option A
Step-by-step explanation:
So in other words, an = an-1 + 6 where a1 = 4. Correct on Ed 2020!
Answer:
A
Step-by-step explanation:
Write an equation that is perpendicular to y=4x- 10 and goes through the point (4,2)
Answer:
y = (-1/4)x + 3
Step-by-step explanation:
The slope of our equation is 4, so to find the slope of the perpendicular equation, we have that:
m1 * m2 = -1
Where m1 is the slope of the first equation and m2 is the slope of the perpendicular equation.
So, we have that:
4 * m2 = -1
m2 = -1/4
So the second equation is y = (-1/4)x + b
If the second equation goes through the point (4,2), for x = 4 we have y = 2, then:
2 = (-1/4)*4 + b
2 = -1 + b
b = 3
So the perpendicular equation is:
y = (-1/4)x + 3
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).
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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
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)
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
Solve the equation below showing all steps.
3/4 (x + 3) = 9
Answer:
x=9
Step-by-step explanation:
3/4(x+3)=9
3/4x+2 1/4=9
3/4x=6 3/4
x=9
Hope this helped :)
Answer:
9
Step-by-step explanation:
3(x+3) =9/4
3(x+3)=9×4
3(x+3)=36
x+3= 3/36
x+3=12
x=12−3
x=9
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 \
Evaluate.
−27125−−−−√3
−925
−35
925
35
Evaluate.
−27125−−−−√3
−925
−35
925
35
Evaluate.
−27125−−−−√3
−925
−35
925
35
The given expression can be solved as -3/5.
The given expression is [tex]\sqrt[3]{\frac{-27}{125} }[/tex].
Here, 27 and 125 can be written as
27 = 3×3×3 = 3³
125 = 5×5×5 = 5³
Now, [tex]\sqrt[3]{\frac{-3^3}{5^3} }= ({\frac{-3^3}{5^3})^{\frac{1}{3} }[/tex]
= -3/5
Therefore, the given expression can be solved as -3/5.
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"Your question is incomplete, probably the complete question/missing part is:"
Evaluate: [tex]\sqrt[3]{\frac{-27}{125} }[/tex]
What is the greatest common factor and least common multiple of 4 and 10?
Answer:
The greatest common factor of 4 and 10 is 2, and the Least common multiple of 4 and 10 is 20
Step-by-step explanation:
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?
can someone help me with this?