Answer:
The solution of the inequality is:
[tex]x>2[/tex]
Step-by-step explanation:
Given inequality:
[tex]-1 >-2(x - 4)-5(4x-7)[/tex]
Solving the inequality.
Using distribution.
⇒ [tex]-1 >(-2x) +((- 4)(-2))+(-5\times4x)+((-5)(-7))[/tex]
⇒ [tex]-1 >-2x +8-20x+35[/tex]
Combining like terms
⇒ [tex]-1 >-2x-20x+35+8[/tex]
⇒ [tex]-1 >-22x +43[/tex]
Adding [tex]22x[/tex] both sides.
⇒ [tex]-1+22x >-22x +43+22x[/tex]
⇒ [tex]-1 +22x> 43[/tex]
Adding 1 both sides.
⇒ [tex]-1+1 +22x> 43+1[/tex]
⇒ [tex]22x>44[/tex]
Dividing both sides by 22.
⇒ [tex]\frac{22x}{22}>\frac{44}{22}[/tex]
⇒ [tex]x>2[/tex]
Thus, the solution of the inequality is:
[tex]x>2[/tex]
Marty's class collected $16.00 in a school-wide penny collection contest.If Tommy's class collected,x, and then multiplied the difference by 2,they would have the same amount of money as Marty's class.How much money did Tommy's class collect?
A.$23.00
B.$13.00
C.$18.00
D.$5.00
Final answer:
Tommy's class collected $8.00.
Explanation:
To find out how much money Tommy's class collected, we can set up an equation:
x * 2 = 16.00
Solving for x, we divide both sides of the equation by 2:
x = 8.00
Therefore, Tommy's class collected $8.00.
of the 20 basketball games so far this year,tracy has attended 14.what percent of basketball games has tracy attended
Answer: Tracey attended 70% of the basketball games.
Step-by-step explanation:
you would multiply 14 by 100then you would multiply 20 by xthat equals 1400=20xthen you divide both sides of the equal sign by 20and get 70%Answer:
70%
Step-by-step explanation:
As a fraction, 14 / 20.
If you multiply the 2 Terms by 5, you would get 70 / 100 which equals 70%.
Best of Luck!
What is the radian measure of the central angle of a circle of radius 1.5 meter that intercepts an arc of length 600 centimeters
Radian measure of the central angle is 4 radian
Solution:
Given that,
A circle of radius 1.5 meter that intercepts an arc of length 600 centimeters
To find: Radian measure of the central angle
Let us find the circumference of circle
The circumference of circle is given as:
[tex]\text{ circumference of circle } = 2 \pi r[/tex]
Where "r" is the radius of circle
[tex]\text{ circumference of circle } = 2 \times \pi \times 1.5 = 3 \pi[/tex]
Therefore circumference of circle = [tex]3 \pi[/tex] meters , which subtends central angle of [tex]2 \pi[/tex] radian
Given that arc of length 600 centimeters. Let us convert 600 centimeter to meter
We know that, to convert centimeter to meter divide the length value by 100
[tex]\text{ 600 centimeter } = \frac{600}{100} \text{ meter } = 6 \text{ meter}[/tex]
Therefore arc of 6 meter will subtend a central angle of:
[tex]\rightarrow \frac{6}{3 \pi} \times 2 \pi = 4[/tex]
Therefore radian measure of the central angle is 4 radian
What is 0.21666667 as a rounded percent
Answer:
23%
Step-by-step explanation: ???
which way is the closest estimate of this product 518 * 5
518x5=2,590, So your estimate is about 2,600, Because we want to round up, So we look in the tens place and we see a nine, so that means we go up on, Also 5 and up means we gonna round up and 5 and below means we gonna round down.
The answer to 518*5 is 2590 or rounded, 3000, or 2600.
You can get your answer my multiplying 518 by 5 and rounding it to the nearest thousands place, hundreds place or tens place.
Hope this helped!
An old house has a basement stairway that has steps with 7.25 inch vertical risers and 7 inch horizontal treads. What is the slope of the stairway? Round to two decimal places.
Answer:
1.04 inch
Step-by-step explanation:
Given: Old house has a basement stairways with 7.25 inch vertical riser and 7 inch horizontal treads.
Remember; horizontal treads is known as run in steps.
Now, calculating the slope of the stairways.
Formula: [tex]Slope= \frac{Rise}{Run}[/tex]
Rise= 7.25 inch
Run= 7 inch.
Subtituting the value in the formula
Slope= [tex]\frac{7.25}{7}= 1.0357 \approx 1.04[/tex] (∵ Round to two decimal)
∴ Slope of stairways is 1.04.
In a 3-digit number, the hundreds digit is four more than the units digit, and the tens digit is twice the hundreds digit. If the sum of the digits is 12, find the three digits. Find the number.
Final answer:
The units digit is 0, the hundreds digit is 4, and the tens digit is 8, making the 3-digit number 480.
Explanation:
The question involves finding a 3-digit number where the hundreds digit is four more than the units digit, the tens digit is twice the hundreds digit, and the sum of the digits is 12. To solve this, we can use algebra.
Let's designate the units digit as 'u'. According to the problem, the hundreds digit will then be 'u + 4'. The tens digit is twice the hundreds digit, which gives us '2(u + 4) = 2u + 8'. Now we can use the information that the sum of the digits equals 12 to create the equation: u + (u + 4) + (2u + 8) = 12.
Simplifying this equation, we get: 4u + 12 = 12, which further reduces to 4u = 0. This indicates that u, the units digit, is 0. Thus, the hundreds digit is 0 + 4 = 4 and the tens digit is 2×4 = 8.
The 3-digit number we are looking for is therefore 480.
1000 into an account that is growing 4.2% per year. What should you do to the pervious years amount
Answer:
The amount into account after a year is $1042
Step-by-step explanation:
Given as :
The principal amount into the account = p = $1000
The amount is growing at the rate = r = 4.2 % per year
Let The Amount into account after 1 year = $A
So, According to question
The amount into account after 1 year = The principal amount × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm 1}[/tex]
Or, A = $1000 × [tex](1+\dfrac{\textrm 4.2}{100})^{\textrm 1}[/tex]
Or, A = $1000 × 1.042
Or, A = $1042
So, The amount into account after a year = A = $1042
Hence,The amount into account after a year is $1042 . Answer
Semicircles
whose centers A
are the midpoints .
of the sides of
square ABCD are .
drawn. If the
measure of each
side of the square
is 4 cm, what is the area, nearest to
the tenth of a sq cm, of the shaded
portion of the figure?
Answer:
The area of the shaded portion of the figure is [tex]9.1\ cm^2[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The shaded area is equal to the area of the square less the area not shaded.
There are 4 "not shaded" regions.
step 1
Find the area of square ABCD
The area of square is equal to
[tex]A=b^2[/tex]
where
b is the length side of the square
we have
[tex]b=4\ cm[/tex]
substitute
[tex]A=4^2=16\ cm^2[/tex]
step 2
We can find the area of 2 "not shaded" regions by calculating the area of the square less two semi-circles (one circle):
The area of circle is equal to
[tex]A=\pi r^{2}[/tex]
The diameter of the circle is equal to the length side of the square
so
[tex]r=\frac{b}{2}=\frac{4}{2}=2\ cm[/tex] ---> radius is half the diameter
substitute
[tex]A=\pi (2)^{2}[/tex]
[tex]A=4\pi\ cm^2[/tex]
Therefore, the area of 2 "not-shaded" regions is:
[tex]A=(16-4\pi) \ cm^2[/tex]
and the area of 4 "not-shaded" regions is:
[tex]A=2(16-4\pi)=(32-8\pi)\ cm^2[/tex]
step 3
Find the area of the shaded region
Remember that the area of the shaded region is the area of the square less 4 "not shaded" regions:
so
[tex]A=16-(32-8\pi)=(8\pi-16)\ cm^2[/tex]
---> exact value
assume
[tex]\pi =3.14[/tex]
substitute
[tex]A=(8(3.14)-16)=9.1\ cm^2[/tex]
if you draw two right triangles using the line as the hypotenuse, do the triangles have to be similar? Why or why not?
Answer:
All the right triangles will be similar.
Step-by-step explanation:
See the attached diagram.
Let us assume any two right triangles are drawn on the line OP, and AB and A'B' as the hypotenuse on the same line OP.
Since the slope of the line OP is constant and assume that it makes x° with the positive x-axis.
Hence, [tex]\tan x = \frac{AC}{BC} = \frac{A'C'}{B'C'}[/tex]
⇒ [tex]\frac{AC}{A'C'} = \frac{BC}{B'C'}[/tex]
Therefore, the sides of the two right triangles are in the same ratio and hence, Δ ABC and Δ A'B'C' are similar.
Hence, all the right triangles will be similar. (Answer)
Find the area of a square if its sides measure 2 2/3m
Answer:
[tex]7\dfrac{1}{9}\ m^2[/tex]
Step-by-step explanation:
If the length of the square side is a units, then the area of the square is
[tex]A=a^2\ un^2.[/tex]
In your case, the side length is
[tex]a=2\dfrac{2}{3}\ m,[/tex]
then the area is
[tex]A=2\dfrac{2}{3}\cdot 2\dfrac{2}{3}\\ \\ \\A=\dfrac{2\cdot 3+2}{3}\cdot \dfrac{2\cdot 3+2}{3}\\ \\ \\A=\dfrac{8}{3}\cdot \dfrac{8}{3}\\ \\ \\A=\dfrac{64}{9}\\ \\ \\A=7\dfrac{1}{9}\ m^2[/tex]
Is x=4 and y=5 perpendicular
Answer:
The statement is true
The lines are perpendicular
Step-by-step explanation:
we have
[tex]x=4[/tex] ----> equation A
The equation A represent a vertical line (is parallel to the y-axis)
The slope is undefined
[tex]y=5[/tex] ----> equation B
The equation B represent a horizontal line (is parallel to the x-axis)
The slope is equal to zero
Remember that
The y-axis and the x-axis are perpendicular lines
so
Line A and line B are perpendicular lines too
therefore
The statement is true
quaker oatmeal is a very popular breakfast cereal .If susan wrapped the entire container with out any overlapping paper what is the minimum amount of wrapping paper that she will need
the cylinders hight is 11
and the dimater is 6
Answer:
263.76
Step-by-step explanation:
To answer this question, we need to know the equation for surface area of a cylinder which can be given as Surface Area=2*pi*[tex]R^{2}[/tex]+2*pi*R*H, where R is the radius of the cylinder (also can be calculated as Diameter/2=6/2=3) and H is the height of the cylinder which is given as 11. Considering pi=3.14, the surface area of the cylinder can now be calculated as 2*3.14*[tex]3^{2}[/tex]+2*3.14*3*11=263.76.
What is the approximate circumference of the circle shown below?
A. 37.8 cm
B. 92.9 cm
C. 46.5 cm
D. 23.2 cm
Answer:c
Step-by-step explanation:
Answer:
Step-by-step explanation:
C
what is the slope of the line that passes through (1,4) and (-3, -3)
Answer: m = 7/4
Step-by-step explanation: Use the slope formula to find the slope m.
Hope this helps you out! ☺
Answer:
7/4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-3-4)/(-3-1)
m=-7/-4
m=7/4
1/3 the weight of a bar of gold plus 30 pounds equals the weight of that bar of gold. How much does the bar of gold weigh?
Answer:
Step-by-step explanation:
Final answer:
To find the weight of the bar of gold, solve the equation (1/3)x + 30 = x, where x represents the weight of the bar. After simplifying, the weight of the bar is found to be 45 pounds.
Explanation:
To solve this problem, let's assume the weight of the bar of gold is x pounds. According to the given information, one-third of the weight of the bar of gold plus 30 pounds equals the weight of the bar of gold. This can be written as:
(1/3)x + 30 = x
To solve for x, we can start by subtracting (1/3)x from both sides of the equation:
(1/3)x + 30 - (1/3)x = x - (1/3)x
This simplifies to:
30 = (2/3)x
To isolate x, we can multiply both sides of the equation by 3/2:
(3/2)(30) = (3/2)(2/3)x
45 = x
Therefore, the bar of gold weighs 45 pounds.
A circle is divided into 6 equal parts. what is the total angle measure of 1 part?
Answer:
[tex]dis \: is \: easy \\ angle \: in \: a \: circle = 360 \\ the \: angle \: is \: divided \: into \: six \: part \\ divide \: the \: 360 \: by \: 6 \\ \frac{360}{6} = 60 \\ therefore \: the \: angle \: of \: one \: part \: \\ = 60 \: degree[/tex]
A hat store sells 900 hats in its first year. If the number of hats it sells in the next year is 50% higher, how many hats will it sell in its second year?
Answer: 1,350 hats
Step-by-step explanation: First, it's important to understand that 50% is equivalent to the fraction 1/2.
So, the next year that hat store will sell 1/2 more hats.
First, we need to divide 900 by 2 which gives us 450.
Now, we simply add 450 to to the number of hats the store sold the first year.
450 + 900 = 1,350
This means that the hat store will sell 1,350 hats the next year.
Lui deposited $3,500 into a savings account. The simple interest is 4%. How much interest will the account earn in 2 years?
Answer:
$280
Step-by-step explanation:
Principal = $3,500
Time = 2 Years
Interest Rate = 4%
Interest = Principal x Time x Interest Rate
Interest = $3,500 x 2 x 0.04
Interest = $280
The height of a tree is a function of its age example
Answer & Explanation:
To determine the age of a tree, first find its diameter by measuring the circumference of the trunk in inches and then dividing that number by pi. Once you have the tree's diameter, look up the growth factor for the type of tree you're measuring, which is how much width it gains annually.
The height and diameter of a tree is a function of its age.
What is meant by growth rate ?Growth rate of a system is defined as the rate at which the system grows by length, breadth, height, etc.
Here,
The growth rate of a tree represents the age of the tree. The measurement of the height and diameter of the tree is used to calculate the age of the tree. These measurements of height and radius of the tree can be considered as a function of its age.
The method of calculating the age of the tree is,
The circumference at a height above 4.5 feet from the ground is measured(breast height).
Dividing the circumference at breast height with pi(3.14), thus we get the diameter at breast height.
Multiplying the diameter with growth factor will give the age of the tree in years.
Hence,
The height and diameter of a tree is a function of its age.
To learn more about growth rate, click:
https://brainly.com/question/17138587
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Question 8 of
Question 8 (2 points)
What values of x satisfy the equation 2x2 + 3x – 10 = 2x + 5
a
x
=3/2 or x=-5
x=-5/2 or x=2
x=10 or x=-1/2
X=-3 or x=5/2
Next Page
Back
Answer:
[tex]x=-3\ or\ \frac{5}{2}[/tex]
Step-by-step explanation:
Given:
Given equation is.
[tex]2x^{2} +3x-10=2x+5[/tex]
Find values of x?
Solution.
[tex]2x^{2} +3x-10=2x+5[/tex]
[tex]2x^{2} +3x-10-2x-5=0[/tex]
[tex]2x^{2} +x-15=0[/tex]
Find the roots of the equation.
compare the above equation with [tex]ax^{2} +bx+c=0[/tex]
Therefore, [tex]a=2,b=1,c=-15[/tex]
[tex]x=\frac{-b\pm\sqrt{(b)^{2}-4ac}}{2a}[/tex]
Put a,b and c value in above equation.
[tex]x=\frac{-1\pm\sqrt{(1)^{2}-4(2)(-15)}}{2(2)}[/tex]
[tex]x=\frac{-1\pm\sqrt{1-8(-15)}}{4}[/tex]
[tex]x=\frac{-1\pm\sqrt{1+120}}{4}[/tex]
[tex]x=\frac{-1\pm\sqrt{121}}{4}[/tex]
[tex]x=\frac{-1\pm\sqrt{(11)^{2}}}{4}[/tex]
[tex]x=\frac{-1\pm 11}{4}[/tex]
For positive sign
[tex]x=\frac{-1+ 11}{4}[/tex]
[tex]x=\frac{10}{4}[/tex]
[tex]x=\frac{5}{2}[/tex]
For negative sign
[tex]x=\frac{-1- 11}{4}[/tex]
[tex]x=\frac{-12}{4}[/tex]
[tex]x=-3[/tex]
[tex]x=-3\ or\ \frac{5}{2}[/tex]
Therefore, the value of [tex]x=-3\ or\ \frac{5}{2}[/tex] satisfy the given equation.
Easy + brainliest
2x(^3) + 10x(^2) − 4x(^2)y − 20xy
factor this pls, (show all work)
Answer:
2x(x + 5)(x - 2y)
Step-by-step explanation:
Given
2x³ + 10x² - 4x²y - 20xy ← factor out 2x from each term
= 2x(x² + 5x - 2xy - 10y)
Factor the first/second and third/fourth terms inside the parenthesis
= 2x(x(x + 5) - 2y(x + 5)) ← factor out (x + 5) from each term in the parenthesis
= 2x(x + 5)(x - 2y)
Which expressions are equivalent to z+(z+6)?
Answer: [tex]2 z + 6[/tex] and [tex]2 (z + 3)[/tex]
Step-by-step explanation:
We have te following expression:
[tex]z+(z+6)[/tex]
Which can be written as:
[tex]z+z+6=2z+6[/tex]
Applying common factor 2 in the right side of the equation:
[tex]z+z+6=2(z+3)[/tex]
All 203 students at Polk School eat lunch at the same time. One
day 19 students were absent. If 8 students sit at each table in
the lunchroom, how many tables were used that day at lunch?
Answer:
The number of tables were used that day at lunch is 23 tables.
Step-by-step explanation:
Given as :
The total number of students in the Polk school = 203
On one day the number of students absent = 19
So, The number of student present on that day = Total student - absent students
I.e The number of student present on that day = 203 - 19 = 184
The number of students sit on each table = 8
Let The number of tables were used that day at lunch = n
So, According to question
The number of tables were used that day at lunch = [tex]\dfrac{\textrm The number of student present on that day}{\textrm Total number of students sit on each table}[/tex]
I.e n = [tex]\frac{184}{8}[/tex]
∴ n = 23 tables
So, The number of tables were used that day at lunch = n = 23 tables
Hence, The number of tables were used that day at lunch is 23 tables. Answer
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
2x + y = 8
y = -x+ 5
O A. (4,1)
O B. (3, 2)
O C. (5,0)
O D. (2,3)
B clearly because u would substitute the x and y with the ordered pairs
What is the standard form of the equation 6, -3 with a slope of two over three
Answer:
The equation of line is y= [tex]\dfrac{2}{3}[/tex] x - 7
Step-by-step explanation:
Given as :
The points as [tex]x_1[/tex] = 6
And [tex]y_1[/tex] = - 3
The slope of the line = m = [tex]\dfrac{2}{3}[/tex]
Now, The equation of line in slope-point form
y - [tex]y_1[/tex] = m × (x - [tex]x_1[/tex])
Or, y - (-3) = [tex]\dfrac{2}{3}[/tex] × (x - 6)
Or, y + 3 = [tex]\dfrac{2}{3}[/tex] × (x - 6)
Or, 3 × (y + 3) = 2 × (x - 6)
Or, 3 y + 9 = 2 x - 12
Or, 3 y = 2 x - 12 - 9
Or, 3 y = 2 x - 21
∴ y = [tex]\dfrac{2}{3}[/tex] x - [tex]\dfrac{21}{3}[/tex]
i.e y = [tex]\dfrac{2}{3}[/tex] x - 7
So, The equation of line = y = [tex]\dfrac{2}{3}[/tex] x - 7
Hence, The equation of line is y= [tex]\dfrac{2}{3}[/tex] x - 7 Answer
Someone please help me with this
Answer:
see explanation
Step-by-step explanation:
(a)
f(0)
Since x = 0 < 5, then
f(0) = x + 4 = 0 + 4 = 4
(b)
f(6)
Since x = 6 meets the condition 5 ≤ x < 7, then
f(6) = 8
complete the equcomplete the equation of the line whose slope is -2 and y intercept is (0,3)ation of the line whose slope is -2 and y intercept is (0,3)
Complete the equation of the line whose slope is -2 and y intercept is (0,3)
Answer:The equation of the line whose slope is -2 and y intercept is (0,3) is y = -2x + 3
Solution:Given that line has slope of -2 and y - intercept of (0, 3)
We have to find the equation of line
The equation of line can be found by using the slope intercept form
The slope intercept form is given as:
y = mx + c
Where "m" is the slope of line and "c" is the y-intercept
Here given that slope = m = -2
y - intercept is the y-coordinate of a point where a line intersects the y-axis.
So here y intercept is (0, 3) and we get c = 3
Substituting the values in slope intercept form we get,
y = -2x + 3
Thus the equation of line is found
What is the domain and range of Y=3X-7.25? can someone please help?
Answer:
Domain and range of the equation
Y = 3X-7.25
will be Set of all Real numbers.
Step-by-step explanation:
Because at any value of x, you will get a respective value of y. For example if you put X=0, then y=7.25. You can put any value of X in the equation and for each value equation will be true and will give respective value of y.
What is the distance in units from (-15, 20) to (-15, - 3) on the coordinate place
O. 17
!. 23
R. 30
V. 35
Answer:
!. [tex]\displaystyle 23[/tex]
Step-by-step explanation:
Use the Distance Formula:
[tex]\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = D \\ \\ \sqrt{[15 - 15]^2 + [-20 - 3]^2} = \sqrt{0^2 + [-23]^2} = \sqrt{0 + 529} = \sqrt{529} = 23[/tex]
Since we are talking about distance, we ONLY want the NON-NEGATIVE root.
I am joyous to assist you anytime.