The value of the smaller number is 5
Determining the value of a numberFrom the question, we are to determine the value of the smaller number
Let one of the numbers be x and the other number be y
From the given information,
The difference of two numbers is 1
That is,
x - y = 1
and
Their sum is 11
That is,
x + y = 11
Now, we will solve the equations simultaneously
From the first equation
x - y = 1
x = 1 + y ------------- (3)
Substitute into the second equation
x + y = 11
1 + y + y = 11
1 + 2y = 11
2y = 11 - 1
2y = 10
y = 10/2
y = 5
Substitute the value of y into equation (3)
x = 1 + y
x = 1 + 5
x = 6
Hence, the number is 5
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Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use inverse operations to solve each equation. Explain each step and identify the property used to reach step.
19
=
h
3
−
8
Using the inverse operations, the value of h is 54.
How to use inverse operation to solve equation?An inverse operation can be defined as the operation that undoes what was done by the previous operation.
Therefore, the inverse operation of multiplication is division.
The equation is as follows:
19 = (h/3) - 8
Hence,
add 8 to both sides of the equation
19 = (h/3) - 8
19 + 8 = (h/3) - 8 + 8
27 = h / 3
Multiply both sides of the equation by 3
27 = h / 3
27 × 3 = h / 3 × 3
h = 54
Therefore,
h = 3
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Write an expression for 362 more than the product of 302 and q.
Mathematically we write this as:
=362+(302×q)
The expression is 362+302q
Goodluck.
What is the slope of the line passing through (0, 5) an d(-12, 2)?
m = 1/4 is the slope of the line .
What is slope in plain English?
Slope and slant both refer to an elevation away from a surface or line that is generally straight and used as a reference. Slope is the verb form for an oblique vertical incline: Here, the land abruptly slopes either upward or downhill.The slope-intercept form of an equation is used to represent each time the equation of a line is stated as y = mx + b. M represents the line's slope. Additionally, the y-intercept is at a position where b is the b. (0, b). The slope and y-intercept of the equation y = 3x - 7 are, for instance, 3 and 0, respectively.The slope of a line passing through points ( x₁ , y₁ ) ( x₂ , y₂ ) is defined as
m = y₂ - y₁/x₂ - x₁
if the x coordinates are not equal. The slope is not defined if the x
coordinates are equal because that would require dividing by zero.
here ,
( x₁ , y₁ ) = (0, 5)
( x₂ , y₂ ) = ( -12 , 2 )
m = y₂ - y₁/x₂ - x₁
m = 2 - 5/-12 - 0
m = -3/-12
m = 1/4
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What is 5,028x1/5 (please answer fast)
Answer:
5
028x ·[tex]\frac{1}{5}[/tex]
Explain how to find the product of 3/8 * 7/9. Use complete sentences in your answer.
Answer:
[tex]\frac{3}{8}*\frac{7}{9}=\frac{7}{24}[/tex]
Step-by-step explanation:
Solution with Steps
[tex]\frac{3}{8}*\frac{7}{9}=?[/tex]
For fraction multiplication, multiply the numerators and then multiply the denominators to get
[tex]\frac{3*7}{8*9}=\frac{21}{72}[/tex]
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 21 and 72 using GCF(21,72) = 3
[tex]\frac{21/3}{72/3} =\frac{7}{24}[/tex]
Therefore:
[tex]\frac{3}{8}*\frac{7}{9}=\frac{7}{24}[/tex]
Jake currently has 362 g of sugar and then uses 7 ounces for baking a cake. How many grams (g) of sugar does he have left? 1 ounce = 28 g
Whoever Answers First I will make Brainliest Evaluate
{[(20−32)÷(−6)]2−11}÷(−7)
Please help!!!!!!!! I’ll mark brainliest
The answers to all the equations are:
(A) f(x) = x + 3 when f(4) ⇒ f(x) = 7(B) f(x) = 2x - 9 when f(5) ⇒ f(x) = 1(C) f(x) = -6x + 2 when f(-3) ⇒ f(x) = 20What do we mean by equations?The equals sign is used in mathematical equations to indicate that two expressions are equal.A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation.Using 3x + 5 as an example equals 15.Equations come in a wide variety of forms, including linear, quadratic, cubic, and others.Point-slope, standard, and slope-intercept equations are the three main types of linear equations.So, f(x):
(A) f(x) = x + 3 when f(4)
f(x) = x + 3f(x) = 4 + 7f(x) = 7(B) f(x) = 2x - 9 when f(5)
f(x) = 2x - 9f(x) = 2(5) - 9f(x) = 10 - 9f(x) = 1(C) f(x) = -6x + 2 when f(-3)
f(x) = -6x + 2f(x) = -6(-3) + 2f(x) = 18 + 2f(x) = 20Therefore, the answers to all the equations are:
(A) f(x) = x + 3 when f(4) ⇒ f(x) = 7(B) f(x) = 2x - 9 when f(5) ⇒ f(x) = 1(C) f(x) = -6x + 2 when f(-3) ⇒ f(x) = 20Know more about equations here:
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HELP MEEEEEEEEEEE, Ed's living room is 4 yards wide and 7 yards long. He wants to install yellow carpet that costs $5.00 per square yard. How much will it cost to buy enough carpet for the living room?
It will cost 140 dollars to buy enough carpet for the living room.
What is a rectangle?A rectangle is a four-sided figure in which opposite sides are equal and the diagonals are also of the same length.
Given Ed's living room is 4 yards wide and 7 yards long.
We know that the area of a triangle is the product of its length and width.
∴ The area of Ed's living room is (4×7) sq yards = 28 sq yards.
Also given to install yellow carpet that costs $5.00 per square yard,
∴ For 28 sq yards, the cost of installing a yellow carpet will be,
= (28×5) dollars.
= 140 dollars.
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The ratio of the number of men to the number of woman is 9:5 if there are 63 men how then how many woman are there
Answer:
Step-by-step explation:
if the ratio of 9 contains 63 men then what about the ratio of 5 u do cross multiplication it will be 5 ×63 the answer you get multiply by 9 answer will be 35
A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters. A cylindrical hole cut out of the center has a radius of 6 millimeters.
A cylinder is shown. A smaller cylinder is cut out of the middle of the larger cylinder. Both have a height of 21 millimeters. The diameter of the larger cylinder is 20 millimeters, and the the radius of the smaller cylinder is 6 millimeters.
Which expressions represent the volume of metal needed, in cubic millimeters, to make the pipe? Select two options.
21π(10)2 – 21π(6)2
π(20)2(21) – π(6)2
2,100π – 756π
7,644π
1,344
The expressions that represent the volume of metal needed , to make the pipe are (a)21*π*(10)² - 21*π*(6)² and (c)2100π - 756π .
In the question ,
it is given that
the diameter of the cylindrical metal pipe = 20mm
so the radius of the cylindrical pipe = 10 mm
height of the cylindrical metal pipe = 21mm
Using the formula of Volume of Cylinder = π*r²*h
the volume of cylindrical metal pipe = π*(10)²*21 .....(i)
the height of smaller cylinder = 21mm
radius of the smaller cylinder = 6mm
So, Volume of the smaller cylinder = π*(6)²*21 .....(ii)
the volume of metal needed to make the pipe = Volume of cylindrical metal pipe - Volume of the smaller cylinder .
Substituting the values from (i) and (ii) , we get
volume of metal needed = π*(10)²*21 - π*(6)²*21
= 21*π*(10)² - 21*π*(6)²
hence , option(a) is correct .
Further Simplifying , we get
= 21*100*π - 21*36*π
= 2100π - 756π
hence , option(c) is also correct
Therefore , the expressions that represent the volume of metal needed , to make the pipe are (a)21*π*(10)² - 21*π*(6)² and (c)2100π - 756π .
The given question is incomplete , the complete question is
A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters. A smaller cylinder is cut out of the middle of the larger cylinder. Both have a height of 21 millimeters and the the radius of the smaller cylinder is 6 millimeters.
Which expressions represent the volume of metal needed, in cubic millimeters, to make the pipe? Select two options.
(a) 21*π*(10)² - 21*π*(6)²
(b) π*(20)²*(21) – π*(6)²
(c) 2100π - 756π
(d) 7,644π
(e) 1,344
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Answer: A & C
Step-by-step explanation: Just did it
Write the given equation in slope-intercept form -10x + 2y = 12
Answer:
x-intercept- (-1.2,0)
y-intercept- (0,6)
Step-by-step explanation:
To find the slope-intercept form, we have to find x and y.
First, find x. Get rid of the 2y, and the equation will look like this.
-10x=12
Now, divide both sides by -10.
12/-10=-1.2
The x-intercept would be (-1.2,0)
To find the y-intercept form, do the same thing.
Get rid of the -10x.
2y=12
Divide by 2 on both sides.
y=6
The y-intercept form would be (0,6)
Hope this helps! :D
True or False
An application of deductive reasoning such that the reasoning is logically correct and undeniably true is a valid argument.
Answer:true
Step-by-step explanation:
y varies inversely as x. y = 18 when x = 5. Find y when x = 3.
Answer:
If the variable
y
varies inversely as the variable
x
, then we can write this relationship as:
y
∝
1
x
Removing the proportionality sign and adding a proportionality constant, we have:
y
=
k
x
If the value of y is 18 when the value of x is 5, then:
18
=
k
5
k
=
18
×
5
=
90
Thus, the equation showing the relationship between the two variables is:
y
=
90
x
Using the above equation, the value of y when x = 3 is equal to:
y
=
90
3
=
30
what expression is equal 4to the -2 power multiplied by 7 to the -2 power
Answer:
Step-by-step explanation:
4^-2 * 7^-2
= 1/4^2 * 1/7^2
= 1/16 * 1/49
- 1/784
3. Which point is closest to -3 on the number line?
Answer: D.
Step-by-step explanation:
-2/20 = -0.1, 0.1 is the closet one to -3
Of the 300 scarves, 200 are not blue.
(d) Write the number of scarves which are blue as a fraction of the total number
of scarves.
The answer will be: 200/300 of scarves are blue. 200/300 also is equal to 2/3. The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
What does "fraction" mean?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.
Reduce the fractions if they aren't already in the lowest terms. Then, all that is required is to multiply the denominator by the denominator and the numerator by the numerator. For instance, multiplying 2 by 7 yields the new numerator, which is 14, when multiplying 2/3 and 7/8. The result of multiplying 3 by 8 is 24.
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sammy buys 5 pounds of oranges for 7.50 at this rate how much would 8 pounds of oranges cost
The cost of 8 pounds of oranges based on the total cost of 5 pounds bought is 12.00
What is the cost for a pound of oranges?
The cost of a pound of oranges based on the rate at which 5 pounds were bought and 8 pounds would also be bought is determined as the amount paid for 5 pounds of oranges divided by the number of pounds of oranges bought
cost per pound of oranges=cost of 5 pounds/5 pounds
cost per pound of oranges=7.50/5
cost per pound of oranges=1.50
Based on the 1.50 per pound, the cost of 8 pounds is the cost per pound multiplied by 8 pounds
cost of 8 pounds of oranges=1.50*8pounds
cost of 8 pounds of oranges=12.00
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Solve for x: -1 < x + 3 < 5
Answer:
Step-by-step explanation:
−1<x+3<5
−1+−3<x+3+ −3<5+−3 (Add -3 to all parts)
Therefore your answer is −4<x<2
Solve for x. Please help!!
Answer: x= -16
Step-by-step explanation:
please help meeeeeeeeeeeeeeeeeeeeee
Factor the expression (72a^9b^3-18a^7b^5) completely
After factorizing the expression 72a⁹b³-18a⁷b⁵completely we get the value of a and b will be ±1 and ±2.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,
⇒72a⁹b³-18a⁷b⁵=0 ------(1)
We have to factor in the expression,
⇒72a⁹b³-18a⁷b⁵=0
Take 18a⁷b³ as common,
⇒18a⁷b³(4a²-a²b²)=0
⇒18a⁷b³=0
⇒(4a²-a²b²)=0
⇒4a² = a²b²
⇒b²=4
⇒b=±2
Substitute the value of b in equation 1 we get,
72a⁹b³-18a⁷b⁵=0
72a⁹(2)³-18a⁷(2)⁵=0
576a⁹-576a⁷=0
a²=1
a=±1
Thus, after factorizing the expression 72a⁹b³-18a⁷b⁵completely we get the value of a and b will be ±1 and ±2.
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How to solve one of these - im very confused :(
The graph represents the inequality:
[tex]x<-3[/tex]The reason we used strictly less than (<) is that the circle is not shaded. Therefore, the correct inequality has to be either the first or last.
We will simplify the inequalities to see which one is equivalent.
First Inequality:
[tex]5(4x+3)<10(2x+1)+7[/tex]Expanding the brackets using the distributive property, we have:
[tex]\begin{gathered} 20x+15<20x+10+7_{} \\ 20x+15<20x+17 \end{gathered}[/tex]Subtracting 20x from both sides, we have:
[tex]\begin{gathered} 20x+15-20x<20x+17<20x \\ 15<17 \end{gathered}[/tex]This is not the inequality.
Last Inequality:
[tex]3x+10>5x+16[/tex]Subtract 5x from both sides:
[tex]\begin{gathered} 3x+10-5x>5x+16-5x \\ -2x+10>16 \end{gathered}[/tex]Subtract 10 from both sides:
[tex]\begin{gathered} -2x+10-10>16-10 \\ -2x>6 \end{gathered}[/tex]Divide both sides by -2. Dividing by a negative number will reverse the sign:
[tex]\begin{gathered} \frac{-2x}{-2}>\frac{6}{-2} \\ x<-3 \end{gathered}[/tex]Hence, this is the inequality.
ANSWER: The correct inequality is
[tex]3x+10>5x+16[/tex]IF AB = 6x-9 BC = 3x+17 and AC = 5x+16, find BC
Since the point B is between points A and C, the length BC is 22.25 units
How to determine the numerical length of BC?From the question, we have the following parameters that can be used in our computation:
Length AB = 6x - 9
Length BC = 3x + 17
Length AC = 5x + 16
The above implies that the point B is between points A and C
So, we have the following equation
AC = AB + BC
Substitute the known values in the above equation
So, we have the following equation
5x + 16 = 6x - 9 + 3x + 17
Collect the like terms
So, we have the following equation
5x - 6x - 3x = -9 + 18 - 16
Evaluate the like terms
So, we have the following equation
-4x = -7
Divide by -4
x = 7/4
Substitute x = 7/4 in the equation BC = 3x + 17
So, we have the following equation
BC = 3 x 7/4 + 17
Evaluate
BC = 22.25
Hence, the numerical length of BC is 22.25 units
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18
Select the correct answers from each drop-down menu.
Complete the steps in the proof that show quadrilateral KITE with vertices K(0, -2). I(1, 2). T(7,5), and E(4,-1) is a kite.
Using the distance formula, KI = √√(2 – (-2)² + (1 - 0)² = √17. KE =
-
IT =
and TE=
Therefore, KITE is a kite because
→
In the quadrilateral KITE,
The value of side KI = [tex]\sqrt{17}[/tex]
The value of side KE = [tex]\sqrt{17}[/tex]
The value of side IT = [tex]3\sqrt{5}[/tex]
The value of side TE = [tex]3\sqrt{5}[/tex]
The quadrilateral KITE is a kite because , KI = KE and IT = TE
How are the values of the quadrilateral sides calculated?
K (0,-2) , I(1,2) ,T(7,5) , E(4, -1)
KI = [tex]\sqrt{17}[/tex]
What is the value of side KE ?
K (0,-2) and E(4, -1)
The distance formula is:
[tex]d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }\\\\KE =\sqrt{(4-0)^{2} + (-1 +2)^{2} }\\\\KE = \sqrt{(4)^{2} + (1)^{2} }\\\\KE = \sqrt{16+1} \\\\KE = \sqrt{17}[/tex]
The value of side KE of the quadrilateral = [tex]\sqrt{17}[/tex]
What is the value of side IT ?
I(1,2) and T(7,5)
The distance formula is:
[tex]d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }\\\\IT =\sqrt{(7-1)^{2} + (5-2)^{2} }\\\\IT = \sqrt{(6)^{2} + (3)^{2} }\\\\IT = \sqrt{36+9} \\\\IT = \sqrt{45} =3 \sqrt{5}[/tex]
The value of side IT of the quadrilateral =[tex]3\sqrt{5}[/tex]
What is the value of side TE ?
T(7,5) and E(4, -1)
The distance formula is :
[tex]d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }\\\\TE =\sqrt{(4-7)^{2} + (-1-5)^{2} }\\\\TE = \sqrt{(-3)^{2} + (-6)^{2} }\\\\TE = \sqrt{9+36} \\\\TE = \sqrt{45} =3 \sqrt{5}[/tex]
The value of side TE of the quadrilateral = [tex]3\sqrt{5}[/tex]
The quadrilateral KITE is a kite because :
KI = KE and IT = TE Two sets of a quadrilateral with equal lengths and adjacent edges are kites.To learn more about quadrilaterals, refer:
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Answer:
The answer is in the picture.
Hope this helps!
Step-by-step explanation:
is 26 and 65 relatively prime
No. 26 and 65 both have a common factor of 13, since 26 = 2•13 and 65 = 5•13, so GCD(26, 65) = 13 ≠ 1.
We can also arrive at this using Euclid's algorithm.
65 = 58 + 7 = 2•26 + 13
26 = 2•13 + 0
Since the last remainder is zero, the previous remainder is the GCD.
a human resources representative claims that the proportion of employees earning more than $50,000 is less than 40%. to test this claim, a random sample of 700 employees is taken and 305 employees are determined to earn more than $50,000. the following is the setup for this hypothesis test: $ h0: p
The test is one of the form Hₐ < ; that means is a right tail test, and the value z(p) is bigger than our critical value (z(c) = 1.64) so we rejecte H₀
According to problem ststement : We need to solve an Hypotesis test proportion so:
H₀ P₀ = 0,4 and Hₐ < 0,4 ( Alternative hipotesis)
From a random sample of 700 employes 305 are determined to earn more than $ 50000
Proportion pₐ = 305/700 = 0,4357 pₐ = 0,4357
proportions are p = 0.4 and q = 0,6
We will asume a confidence level of 95 % hence α= 1-0,95 α = 0,05
so from z table we find z(c) = 1,64
Therefore we must calculate our z(p) = ( pₐ-p₀) ÷√(p*q)/n
Calculating z(p) = 0,0357 /0,01851 ⇒ z(p) 1.9286
Our test is one of the form Hₐ < ; that means is a right tail test, and the value z(p) is bigger than our critical value (z(c) = 1.64) so we rejecte H₀
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A quantity with an initial value of 200 grows continuously at a rate of 55% per day.
What is the value of the quantity after 1 week, to the nearest hundredth?
The value of the quantity after 420 minutes is 1.739
How to calculate the amount of the quantity?
In mathematics, the amount of the quantity can be measured with the help of the exponential function by using its standard equation. But the measured quantity should grow continuously.
According to the question, the growth of the quantity is growing continuously which illustrate the exponential function.
The given parameters are:
Initial value, a = 200; Rate, r = 55%
An exponential growth function is represented as:
y = a(1 + r)^x
Substitute the value in the equation
y = 200(1 + 55%)^x
After 1.55 minutes, x = 7 * 60
So, we have:
y = 200(1 + 55%)^(7 * 60)
Evaluate the expression
y = 1.739
Hence, the value of the quantity after 420 minutes is 1.739
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How do you find this??
Answer:
Step-by-step explanation:
If-4y² − x³ + 4 = 0 then find dy/dx in terms of x and y.
