Answer:
[tex]15x\geq 105[/tex]
Step-by-step explanation:
Hence, the inequality represents how long Johnny needs to work to afford his new bike is
[tex]15x\geq 105[/tex]
What is the inequality?
The relationship between two values that are not equal is defined by inequalities. Inequality means not equal.
Here given that,
Johny earns $[tex]15[/tex] per hour dog walking. So, he wants to earn at least $[tex]105[/tex] to buy a new bike.
So, the inequality is
[tex]15x\geq 105[/tex]
Hence, the inequality represents how long Johnny needs to work to afford his new bike is
[tex]15x\geq 105[/tex]
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If f(x)=4x-1 find f(3)
Answer:
f(3)=11
Step-by-step explanation:
given f(x)=4x-1.............(1)
put x=3
f(3)=[tex]4\times3[/tex]-1
f(3)=12-1
f(3)=11 answer
45 POINTS!! A JCpenny dress originally costs $69.00, but the final price is $20.70. What is the discount percentage? (Example: 50% off $20.00 is $10.00)
Answer:
70%
Step-by-step explanation:
69 - 20.70 = 48.3
48.3 / 69 = 0.7
0.7 x 100 = 70
The discount percentage for the JCPenney dress, discounted from an original price of $69.00 to a final price of $20.70, is calculated to be 70% off.
To calculate the discount percentage for the JCPenney dress, we need to find the difference between the original price and the final price, and then divide that by the original price. We can then multiply the result by 100 to get the percentage.
The original price of the dress is $69.00, and the final price is $20.70. The difference between these two prices is $69.00 - $20.70 = $48.30. This is the amount of the discount.
To find the discount percentage, we divide the discount amount by the original price: $48.30 / $69.00 = 0.7. To convert this decimal to a percentage, we multiply by 100: 0.7 imes 100 = 70%.
Thus, the dress is discounted by 70%.
solve the inequality and graph
2(-6n-5)<-3(4n+2)
thanks!
Answer:
All real numbers are solution for the inequality.
Step-by-step explanation:
Given expression:
[tex]2(-6n-5)<-3(4n+2)[/tex]
Solving the inequality.
Using the distribution.
[tex](2(-6n))+(-2(-5)<(-3(4n))+(-3(2))[/tex]
[tex]-12n-10<-12n-6[/tex]
Adding [tex]12n[/tex] to both sides.
[tex]-12n+12n-10<-12n+12n-6[/tex]
We have,
[tex]-10<-6[/tex]
The above statement is always true and thus the inequality has all real number solutions.
The number line graph for the inequality can be shown.
A baby was born and then began to gain weight at a rate of 1.5 pounds per month. After 4 months, the baby's weight was 16 pounds. Write an equation for the function
W
(
t
)
,
W(t), representing weight, in pounds, of the newborn baby
t
t months after birth.j
Answer: y = (4/3)x + 8
Step-by-step explanation:
If cos x= sin(20 + x)° and 0° < x < 90°, what is the value of x
If cos x= sin(20 + x)° and 0° < x < 90° then value of x is 35 degrees
Solution:
Given that:
[tex]cos x= sin (20 + x)[/tex]
We know that,
[tex]sin (a+b)=sin a \times cos b+cos a \times sin b[/tex]
[tex]cos x= sin (20 + x) = sin 20 cos x + cos 20 sin x[/tex]
[tex]cos x-sin20 \times cos x=cos 20 \times sin x[/tex]
Taking cos x as common,
[tex]cos x(1-sin 20)=cos 20 \times sin x[/tex]
[tex]\frac{(1-sin 20)}{(cos 20)}=\frac{sin x}{cos x }\\\\tan x = \frac{(1-sin 20)}{(cos 20)}[/tex]
By trignometric functions,
sin 20 = 0.34202
cos 20 = 0.939692
So,
[tex]tan x = \frac{1 - 0.34202}{0.939692}\\\\tan x = 0.7002[/tex]
Therefore,
x = arc tan (0.7002)
x = 35 degrees
Therefore value of x is 35 degrees
Method 2:cos x = sin (20 + x)
sin and cos are co - functions, which means that:
cos x = cos [90 - (20 + x)]
cos x = cos (90 - 20 - x)
cos x = cos (70 - x)
Therefore, x = 70 - x
x + x = 70
2x = 70
x = 35
Therefore value of x is 35 degrees
What is the value of y in the equation 2(3y + 7 + 5) = 196 − 16? (1 point) Group of answer choices 13 14 26 28
Answer:
26
Step-by-step explanation:
2(3y+12)=180
3y+12=90
3y=78
y=26
Answer:
Option c) is correct.
The value of y in the given equation is 26 ie., y=26
Step-by-step explanation:
Given equation is
[tex]2(3y+7+5)=196-16[/tex]
Now to the find the value of y in the above equation.
To find y simplify the above equation
[tex]2(3y+7+5)=196-16[/tex]
[tex]2(3y+12)=180[/tex]
Now apply distributive property
[tex]6y+24=180[/tex]
[tex]6y=180-24[/tex]
[tex]=\frac{156}{6}[/tex]
Therefore y=26
Option c) is correct.
The value of y in the given equation is 26 ie., y=26
The average height of a giraffe and a baby giraffe is 6m. If the baby giraffe has a height which is 2/3 that of the giraffe, what is the height of the baby giraffe?
To find the height of the baby giraffe given the average height of it and a giraffe is 6m, and it is 2/3 the giraffe's height, first solve for the giraffe's height to find it is 7.2m. Then, calculate 2/3 of this to get the baby giraffe's height, which is 4.8m.
Explanation:The question asks to determine the height of a baby giraffe given the average height of a giraffe and a baby giraffe together is 6m, and the baby giraffe's height is 2/3 that of the giraffe's height. Let X be the height of the giraffe. Then, the baby giraffe's height would be 2/3 X. Given the average of these two heights is 6m, the equation to find the height of the baby giraffe is:
(X + (2/3)X) / 2 = 6
By solving this equation:
First, find a common denominator to add X and 2/3 X, which gives us (3/3)X + (2/3)X = (5/3)X.Then, multiply both sides by 2 to eliminate the division by 2, resulting in (5/3)X = 12.Finally, multiply each side by 3/5 to solve for X, which gives X = 12 * (3/5) = 7.2m.Since the baby giraffe is 2/3 the height of the giraffe, its height is 2/3 * 7.2 = 4.8m.Hence, the height of the baby giraffe is 4.8m.
Which rule represents the translation from the pre-image,
ДАВС, tо thе іmаge, ДАВ'C'?
x x
оооо
x x
(x, y) — (х + 7, y+6)
О (x, y) — (х+7, у– 6)
=(x – 6, y + 7)
о(x, y) — (х+6, y+7)
Answer:(x,y)-(x+7,y+6)
Step-by-step explanation:
There are 80 grams of salt in a 32% solution. Find the weight of the solution.
Answer: 250 grams.
Step-by-step explanation:
Let x be the weight of the solution.
Given : There are 80 grams of salt in a 32% solution.
That means , 32% of x = 80 grams
[tex]\Rightarrow\ 0.32x=80[/tex] [convert percent into decimal by dividing it by 100]
[tex]\Rightarrow\ x=\dfrac{80}{0.32}=\dfrac{8000}{32}=250[/tex]
i.e. Total solution = 250 grams.
Hence, the weight of the solution = 250 grams.
Which equation can be use to solve for x in the parallelogram below ?
Answer:
Below.
Step-by-step explanation:
I can't read it very well but one equation might be
2x + 8 = 3x - 12
(because the opposite sides of a parallelogram are congruent.
Explanation:
Opposite angles of a parallelogram are equal.
B. (3x - 12)° = (2x + 8)°
This equation can be used to solve x.
3x - 12 = 2x + 8
3x - 2x = 12 + 8
x = 20°
Verification:
3(20) - 12 = 2(20) + 8
60 - 12 = 40 + 8
48° = 48°
Hence, verified.
10 POINTS!
How can the figure be cut so that the resulting cross section is a trapezoid?
i'll give brainliest
Answer:
Angular cut
Step-by-step explanation:
If you cut it horizontally, the cross-section would be a square.
If you cut it vertically, it would be result as a triangle.
If you cut angular, it would result as a trapezoid.
Answer: Horizontal cut
Step-by-step explanation:
62,591 + 7.1 X 10-2 in standard notations
help ill give you 20 points
Answer:
The top left graph is the correct one.
Step-by-step explanation:
The graph of y = 1/2x - 4 will rise to the right , have a slope of 1/2 and pass through the point (0, -4) on the y-axis.
Since the inequality sign is 'less than or equal to' the line will be continuous and the shading will be below this line.
What kind of Theorem is this? AAS, SAS, SSS, ASA, HL, or NP?
Answer:
SAS
Step-by-step explanation:
WX = ZY
ANGLE W = ANGLE Y (90 DEGREE)
YZ = YZ
SAS CONGRUENCY
I hope this answer is correct
Anyways do confirm
Marcos make his famous salad Jackson by mixing 5 1/4 ounces of olive oil with one and a half ounces of vinegar. How much vinegar should Marco mix with a 28 ounce bottle of olive oil to make his salad dressing? How much salad dressing will he make?
Answer:
8 ounces of vinegar
36 ounces of dressing
Step-by-step explanation:
Marco makes his famous salad Jackson by mixing 5 1/4 ounces of olive oil with 1 1/2 ounces of vinegar.
Olive oil Vinegar
5 1/4 1 1/2
28 x
Write a proportion:
[tex]\dfrac{5\frac{1}{4}}{28}=\dfrac{1\frac{1}{2}}{x}\\ \\5\dfrac{1}{4}\cdot x=28\cdot 1\dfrac{1}{2}\ [\text{Cross multiply}]\\ \\\dfrac{21}{4}x=28\cdot \dfrac{3}{2}\\ \\\dfrac{21 x}{4}=42\\ \\x=42\div \dfrac{21}{4}\\ \\x=42\cdot \dfrac{4}{21}\\ \\x=2\cdot 4\\ \\x=8\ ounces[/tex]
Marco will make
[tex]28+8=36[/tex] ounces of dressing
You and your guest have eaten in a restaurant which had excellent service. Your bill comes to $23.00. If you leave exactly a 15% tip, what would the amount of the tip be?
Answer:
23*0.15=$3.45
Step-by-step explanation:
23*0.15=$3.45
Which ordered pair is a solution of the equation?
-3x+4y=14
A- Only (2,5)
B- Both (2,5) and (4,6)
C-Neither
Final answer:
The ordered pair (2,5) satisfies the equation -3x+4y=14, making it the correct solution, while the ordered pair (4,6) does not satisfy the equation.
Explanation:
To determine which ordered pair is a solution to the given linear equation -3x+4y=14, we need to plug in the x and y values from each pair into the equation and see if the equation holds true.
For the ordered pair (2,5), substituting x with 2 and y with 5 gives us:
-3(2) + 4(5) = -6 + 20 = 14Since the equation is satisfied, (2,5) is a solution to the equation.
For the ordered pair (4,6), substituting x with 4 and y with 6 gives us:
-3(4) + 4(6) = -12 + 24 = 12Since -12 + 24 does not equal 14, the equation is not satisfied, and hence, (4,6) is not a solution to the equation.
Therefore, the correct answer is A- Only (2,5)
Find the maximum value of P=3x+2y subject to the following constraints:
Please help me!!!
Answer:
maximum value of P is 33
Step-by-step explanation:
Sketch the lines represented by the constraints
5x + y = 16
with intercepts ([tex]\frac{16}{5}[/tex], 0) and (0, 16)
2x + 3y = 22
with intercepts (11, 0) and (0, [tex]\frac{22}{3}[/tex])
The solutions to both are below the lines.
Solve 5x + y = 16 and 2x + 3y = 22 simultaneously to find the point of intersection at (2, 6)
The coordinates of the vertices of the feasible region are
(0, 0), (0, 16), (2, 6), 11, 0)
Evaluate the objective function at each vertex
P = 3(0) + 2(0) = 0 + 0 = 0
P = 3(0) + 2(16) = 0 + 32 = 32
P = 3(2) + 2(6) = 6 + 12 = 18
P = 3(11) + 2(0) = 33 + 0 = 33
The maximum value of P is 33 when x = 11 and y = 0
What is the opposite of the number of 5 and 1/2
Answer:
the answer will be -5 and 1/2
Answer:
5 is a regular number and 1/2 is a fraction
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Step-by-step explanation:
what is y equals negative five over two times negative two
Answer:
y = - 5/2 * - 2
y = 10/2
y = 5
Step-by-step explanation:
Jordan built her cat Tuna a new scratching post. She needs to cover the post with carpet.
How much carpet does Jordan need to cover the surface of the post, including the bottom?
Answer:
3800 square centimeters
Step-by-step explanation:
We need to find the surface of the rectangular prism shown.
The surface area is the area of all the surfaces (including the bottom and top).
There are 6 surfaces, top and bottom is squares and 4 sides are rectangles.
The area of square is side * side, and
The area of rectangle is length * width
Top Area = 10 * 10 = 100
Bottom Area = 10 * 10 = 100
Area of 1 side = 90 * 10 = 900
Hence, area of 4 of these same sides is: 900 * 4 = 3600
Total Surface Area = 3600 + 100 + 100 = 3800
Total Carpet Needed = 3800 square centimeters
Answer:
3800
Step-by-step explanation:
Rewrite x2 − 6x + 7 = 0 in the form (x − a)2 = b, where a and b are integers, to determine the a and b values.
Answer 1: a = 4 and b = 3
Answer 2: a = 3 and b = 2
Answer 3: a = 2 and b = 1
Anwser 4: a = 1 and b = 4
Answer:
Therefore values of a and b are
[tex]a=3\ and\ b = 2[/tex]
Step-by-step explanation:
Rewrite [tex]x^{2}-6x+7=0[/tex] in the form
[tex](x-a)^{2}=b[/tex]
where a and b are integers,
To Find:
a = ?
b = ?
Solution:
[tex]x^{2}-6x+7=0[/tex] ..............Given
Which can be written as
[tex]x^{2}-6x=-7[/tex]
[tex](\frac{1}{2} coefficient\ of\ x)^{2}=(\frac{1}{2}\times -6)^{2}=9[/tex]
Adding half coefficient of X square on both the side we get
[tex]x^{2}-6x+9=-7+9=2[/tex] ...................( 1 )
By identity we have (A - B)² =A² - 2AB + B²
Therefore,
[tex]x^{2}-6x+9=x^{2}-2\times 3\times x+3^{2}=(x-3)^{2}[/tex]
Substituting in equation 1 we get
[tex](x-3)^{2}=2[/tex]
Which is in the form of
[tex](x-a)^{2}=b[/tex]
On comparing we get
a = 3 and b = 2
Therefore values of a and b are
[tex]a=3\ and\ b = 2[/tex]
Answer 2: a = 3 and b = 2
The area of a mirror is 225 Square inches, it's width is
[tex]13 \frac{3}{4} [/tex]
inches. Will the mirror fit in a space that is 15 inches by 16 inches? Explain.
NO. The mirror will not fit in a space that is 15 inches by 16 inches
Solution:
Given that area of mirror is 225 square inches
[tex]width = 13\frac{3}{4} \text{ inches }[/tex]
Converting the above mixed fraction we get,
[tex]width = 13\frac{3}{4} = \frac{13 \times 4 + 3}{4} = \frac{55}{4} \text{ inches }[/tex]
Let us find the length of mirror
The area of mirror is given as:
area of mirror = length x width
Substituting the given values,
[tex]225 = length \times \frac{55}{4}\\\\length = 225 \times \frac{4}{55}\\\\length = 225 \times 0.0727\\\\length = 16.36[/tex]
Thus length of mirror is 16.36 inches
Will the mirror fit in a space that is 15 inches by 16 inches?
NO. The mirror will not fit in a space that is 15 inches by 16 inches
Because length of mirror is 16.36 inches whereas the given space is 15 inches long
16.36 > 15 so the length of mirror will not fit inside the space
Also width of mirror is [tex]\frac{55}{4} = 13.75[/tex] inches which is less than the given space whose width is 16 inches
13.75 < 16 so the width of mirror will not fit inside the space
What is 6532 rounded to the nearest thousand
Answer:
7000
Step-by-step explanation:
because 6532 is closer to 7000 then 6000.
A bookstore carries 72 magazines. 50% of the magazines are women's magazines. How many women's magazines does the bookstore carry?
Answer:
36
Step-by-step explanation:
72/2=36 50% of 72 is 36
Answer:
36
Step-by-step explanation:
72 divided by 2 to get a quotient of 36
A department Store sells a pair of shoes with an 87% markup. If the store sells the shoes for 192.61 dollars then what is their non-markup price?
Answer:
$103
Step-by-step explanation:
192.62 divided by 1.87
answer is $103
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If the markup price of the shoes is $192.61 then the original price of the shoes will be equal to $25.04.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the given information in the question,
Let the original price of the shoes is x.
Markup Price = $192.61, which is 87% more than the original price.
Price markup = 192.61 × 87/100 = $167.57
Original Price, x = $192.61 - $167.57
x = $25.04.
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A line has a slope of - 2/3 and passes through the point (-3, 8) what is the equation of the line
Answer:
y - 8 = (-2/3)(x + 3)
y - 8 = (-2/3)x - 2
y = (-2/3)x + 6
Identify all sets to which the number belongs.
-0.249851765....
a. integer
b. irrational
c.rational, integer, whole
d.rational, integer, whole, natural
Option B
-0.249851765 is a irrational number
Solution:
Given number is -0.249851765
We have to classify the number
Let us first understand about irrational, real, whole, integer and rational numbers
Integers:An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043
Every integer can be expressed as a decimal, but most numbers that can be expressed as a decimal are not integers. If all the digits after the decimal point are zeroes, the number is an integer. If there are any non-zero digits after the decimal point, the number is not an integer.
Thus -0.249851765 has non zero digits after decimal point. So it is not a integer
Whole numbers:Whole numbers are positive numbers, including zero, without any decimal or fractional parts. Negative numbers are not considered "whole numbers."
But the given number -0.249851765 is negative number. So it is not a whole number
Natural numbers:A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc. Natural numbers are also called "counting numbers" because they are used for counting.
A decimal is a natural number if it is non-negative and the only digits after its decimal points are zero
So the given number -0.249851765 is a negative number and so it is not a natural number
Rational numbers:A rational number is a number that can be expressed as a fraction (ratio) in the form [tex]\frac{p}{q}[/tex] where p and q are integers and q is not zero.
The rational numbers includes all positive numbers, negative numbers and zero that can be written as a ratio (fraction) of one number over another.
When a rational number fraction is divided to form a decimal value, it becomes a terminating or repeating decimal.
So -0.249851765 is not a rational number
Irrational number:An irrational number is real number that cannot be expressed as a ratio of two integers.
When an irrational number is expressed in decimal form, it goes on forever without repeating
So the given number -0.249851765 is irrational number
We can conclude that:
-0.249851765 is a irrational number, So Option B is correct
Carol's monthly take home pay is $1500.she spends $250.a month on food. What the ratio of food costs to take home dollars
Answer:
The answer is 6 ratio because when you divide these two number then the anwer is 6
Answer:
ratio of food costs to take away home 1:6
Step-by-step explanation:
$1500: $250
150:25
30:5
6:1
A boat travels upstream for 2 hours. the return trip only takes 1.7 miles because the boat travels 2.5 miles faster downstream. How far does the boat travel one way?
Answer:
the boat travel one way = 2 x 14.16 = 28.32 miles
Step-by-step explanation:
the return trip only takes 1.7 miles (?) ... is it 1.7 hours (?)
the boat travels 2.5 miles (per hour ?) faster downstream
I calculate it on the assumption of my guess stated above ...
X: represent the boat speed / hour
distance one way = 2X
and Distance also = 1.7 * (x + 2.5 ) on return
2x = 1.7 x + 1.7 * 2.5 = 1.7x + 4.25
0.3 x = 4.25
x = 14.16
the boat travel one way = 2 x 14.16 = 28.32 miles