Answer:
4
Step-by-step explanation:
Consecutive integers are e.g. 1, 2, 3, 4, ...
So they are 1 units apart.
If we let one of the integers be "x", then the next consecutive one would be "x + 1".
x is the smaller
x + 1 is the larger
of the two...
Now,
The sum of smaller (x) and 2 TIMES larger (x + 1) is 14, so we can write:
[tex]x+2(x+1)=14[/tex]
We use algebra and solve for x:
[tex]x+2(x+1)=14\\x+2x+2=14\\3x=14-2\\3x=12\\x=4[/tex]
So, the two numbers is 4 & 5
smaller of the two numbers is "4"
To find the smaller of two consecutive integers where the sum of the smaller and two times the larger is 14, set up the equation x + 2(x + 1) = 14 and solve for x to find that the smaller integer is 4.
Explanation:To find the smaller of two consecutive integers x, when the sum of the smaller and two times the larger is 14, we can set up a simple algebraic equation. Let x be the smaller integer; then the larger integer is x+1. The equation based on the given information is:
x + 2(x + 1) = 14
Now, let's solve for x:
x + 2x + 2 = 143x + 2 = 143x = 14 - 23x = 12x = 12 / 3x = 4Therefore, the smaller consecutive integer is 4.
What is the value of Negative 3 m n + 4 m minus 3 when m = 2 and n = negative 4?
Answer:
Answer is D
Step-by-step explanation:
engenuity 2022
Answer:
29
Step-by-step explanation:
Complete the inequality.
6 gal ___ 24 qt
Answer:
equal to.
Step-by-step explanation:
1 gallon would equal 4 quarts, So if 6 gallons were presnt multiply 6 and 4 and you get 24 quarts
The quantity in the inequality is the same for both sides, so you would use the equals sign. According to unit conversion, 6 gallons is equal to 24 quarts.
Explanation:The inequality you are trying to solve involves comparing the two quantities in gallons and quarts. One gallon is equivalent to 4 quarts. Therefore, we can multiply 6 gallons by 4 to convert it to quarts:
6 gal * 4 qt/gal = 24 qt
Therefore, the inequality would be: 6 gal = 24 qt
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Which expressions are equivalent to 35+30s-45t35+30s−45t35, plus, 30, s, minus, 45, t?
Answer:
The correct option is B. [tex]5(7+6s-9t)[/tex] and C. [tex](-35-30s+45t)\times (-1)[/tex].
Step-by-step explanation:
Consider the provided expression.
[tex]35 + 30s - 45t[/tex]
Option (A): [tex]7\cdot(5+30s-45t)[/tex]
Open parenthesis.
[tex]35+210s-315t[/tex]
Which is not equal to the provided expression.
Option (B) [tex]5(7+6s-9t)[/tex]
Open parenthesis.
35+30s-45t
Which is equal to the provided expression.
Option (C) [tex](-35-30s+45t)\times (-1)[/tex]
Open parenthesis.
[tex]35+30s-45t[/tex]
Which is equal to the provided expression.
Option (D) [tex]10\times(3.5+3s-4.5)[/tex]
[tex]35+30s-45[/tex]
Which is not equal to the provided expression.
Option (E) [tex](\frac{35}{2}- 15s + \frac{45t}{2}) \cdot(-2)[/tex]
Open parenthesis.
[tex]-35+30s-45t[/tex]
Which is not equal to the provided expression.
Hence, the correct option is B. [tex]5(7+6s-9t)[/tex] and C. [tex](-35-30s+45t)\times (-1)[/tex].
Two boxes are placed in front of you. Box A contains 4 white and 2 black
marbles, and Box B contains 3 white and 7 black marbles. You select one of
the two boxes at random and then select one marble from that box at
random. What is the probability that the marble you select is black?
Answer:
The probability that the marble you select is black is 0.5167
Step-by-step explanation:
Let,
[tex]E_1[/tex] the probability of selecting one marble from box A
[tex]E_2[/tex] the probability of selecting one marble from box B
[tex]BB_1[/tex] be the probability of selecting black marble from box A
[tex]BB_2[/tex] be the probability of selecting black marble from box B
Now
[tex]P(E_1) = \frac{1}{2}[/tex]
[tex]P(E_2) = \frac{1}{2}[/tex]
[tex]P(BB_1) = \frac{2}{6}[/tex]
[tex]P(BB_2) = \frac{7}{10}[/tex]
P(Selecting a Black Marble ) = [tex](P(E_1) \times P(BB_1))+(P(E_2) \times P(BB_2)) [/tex]
=>[tex](\frac{1}{2} \times \frac{2}{6})+(\frac{1}{2} \times \frac{7}{10}) [/tex]
=>[tex](\frac{2}{12})+(\frac{7}{20}) [/tex]
=>[tex](\frac{1}{6})+(\frac{7}{20}) [/tex]
=>[tex]\frac{20 + 42}{120} [/tex]
=>[tex]\frac{62}{120} [/tex]
=>[tex]\frac{31}{60} [/tex]
=>0.5167
y=-2 y=3x+1 in graph
Answer:
The solution of the system is x=-1, y=-2
Step-by-step explanation:
we have
[tex]y=-2[/tex] ----> equation A
[tex]y=3x+1[/tex] ----> equation B
Solve the system by graphing
Remember that the solution of the system is the intersection point both lines
using a graphing tool
The intersection point is (-1,-2)
see the attached figure
therefore
The solution of the system is x=-1, y=-2
Using the equation y = 3x – 5, what would the output be for an input of 2
Answer:
Step-by-step explanation:
y = 3x - 5.....input values are x and output values are y
so if ur input (x) is 2.....sub 2 in for x and find ur output (y)
y = 3x - 5
y = 3(2) - 5
y = 6 - 5
y = 1 <=== ur output value
The output for the equation y = 3x – 5, is 1.
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
In the linear equation y = 3x - 5 input values are x and output values are y. Put x = 2 as input for output y.
y = 3x - 5
y = 3(2) - 5
y = 6 - 5
y = 1
The output value y is 1.
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John earns $10.26 an hour. How much will he earn if he works for 6.6 hours?
Answer:
he will earn 67.71 dollars, or more precisely 67.716 dollars in 6.6 hours
Step-by-step explanation:
Answer:
$67.72 or 67.71 (depends if you are taking the first 2 decimal points or if you are rounding
Step-by-step explanation:
10.26*6.6
This is done because we have how much he earns per hour and the number of hour he works so we have to multiple them together
The end result would be: 67.716 dollars. The answer varies like I said above
A rhombus has side lengths of 25. What could be the lengths of the diagonals?
Answer:
25√2
For the opposite side, the hypotenuse, a rhombus is always divided by a angle bisector. Therefore you use the 45-45-90 theorem
A baseball player recorded 60 hits in 186 at-bats.What is the ratio of hits to at-bats?
Answer:
10:31
Step-by-step explanation:
Given: A baseball player recorded [tex]60[/tex] hits in [tex]186[/tex] at-bats.
To Find: ratio of hits to at-bats.
Solution:
Total number of hits recorded by baseball player [tex]=60[/tex]
Total number of at-bats [tex]=186[/tex]
Now,
ratio of hits to at-bats [tex]=\frac{\text{total number of hits recorded}}{\text{total number of at-bats}}[/tex]
putting values,
ratio of hits to at-bats [tex]=\frac{60}{186}[/tex]
[tex]=\frac{10}{31}[/tex]
[tex]=10:31[/tex]
Hence the ratio of hits to at-bats is [tex]10:31[/tex]
Solve the triangle. B = 73°, b = 15, c = 10
Incomplete Question, the complete question is
Solve the triangle.
B = 73°, b = 15, c = 10
A. C = 39.6°, A = 67.4°, a ≈ 14.5
B. Cannot be solved
C. C = 44.8°, A = 62.4°, a ≈ 14.5
D. C = 39.6°, A = 67.4°, a ≈ 20.3
Answer:
The Answer is the option A
A. C = 39.6°, A = 67.4°, a ≈ 14.5
Step-by-step explanation:
Given:
In Δ ABC,
∠B = 73°
b = 15
c = 10
To Find:
∠A = ?
∠B = ?
a = ?
Solution:
IN Δ ABC, Sine Rule says that
[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}= \dfrac{c}{\sin C}[/tex]
Substituting the given values we get
[tex]\dfrac{15}{\sin 73}= \dfrac{10}{\sin C}\\\\\sin C=0.6375\\\therefore C=39.6\°[/tex]
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
[tex]\angle A+\angle B+\angle C=180\\\\73+39.6+\angle A=180\\\therefore m\angle A =180-112.6=67.4\°[/tex]
∴ [tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}[/tex]
Substituting the given values we get
∴ [tex]\dfrac{a}{\sin 67.4}= \dfrac{15}{\sin 73}\\\\\therefore a=14.48\approx14.5[/tex]
Therefore,
A. ∠C = 39.6°, ∠A = 67.4°, a ≈ 14.5
Express the ratio below in its simplest form. 3 : 3/ 1 2
Answer:
Step-by-step explanation:
3/12=1/4
3:1/4
What two shapes are quadrilaterals with 2 pairs of parallel sides and no right angles?
Answer:
The answer is totally Rhombus
Answer: A rhombus and a kite
Step-by-step explanation: A rhombus has 4 parallel sides, and have 2 acute angles and two obtuse angles and no right angles. Also a kite is the same way too!
A line includes the points (10,1) and (a,-5) has a slope of 1/3. What is the value of a?
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Where:
[tex](x_ {1}, y_ {1})\ and\ (x_ {2}, y_ {2})[/tex]are two points through which the line passes.
According to the statement we have:
[tex](x_ {1}, y_ {1}) :( 10,1)\\(x_ {2}, y_ {2}) :( a, -5)\\m = \frac {1} {3}[/tex]
Substituting we have:
[tex]\frac {1} {3} = \frac {-5-1} {a-10}\\\frac {1} {3} = \frac {-6} {a-10}\\a-10 = \frac {-6} {\frac {1} {3}}\\a-10 = -18\\a = -18 + 10\\a = -8[/tex]
Thus, the value of a is -8.
Answer:
[tex]a = -8[/tex]
A square has an area of 49 square meters.What is the perimeter of the square?
Answer:
The answer is 28 meters.
Step-by-Step Explanation:
Because the shape is a square, something times itself equals the area.
7 times 7 equals 49. Using this multiplication fact, and also using the fact that the shape is a square, 7+7+7+7=28.
And there you have it, a square with an area of 49 square meters has a perimeter of 28 meters.
The perimeter of the square with an area of 49 sq meters is 28 meters.
What is a square?A square is a 2D figure of which all the sides are of equal length.
We know that area of a square is side multiplied by side.
Given the area of a square is 49 sq meters, So two same numbers that are multiplied by 49 are 7 and 7.
∴ The length of each side of the square is 7 meters.
We also know that the perimeter of a square is 4 times the length of the side.
∴ The perimeter of the given square is (4×7) = 28 meters.
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For the open-ended question below, be sure to show your work and/or explain your reasoning.
Scott has $15.00, and he earns $6.00 an hour babysitting.
a) Write an equation for the amount of money (m) Scott has after a number of hours babysitting (h).
b) After how many hours of babysitting will Scott have $51.00?
a) The equation for the amount of money (m) Scott has after a number of hours babysitting (h) is m = 15 + 6 h
b) Scott will babysitting for 6 hours to have $51.00
Step-by-step explanation:
The given is:
Scott has $15.00He earns $6.00 an hour babysittingWrite an equation for the amount of money (m) Scott has after a number of hours babysitting (h) and find the number of hours of babysitting if Scott have $51.00
a)
∵ Scott has $15.00
∵ He earns $6.00 an hour babysitting
∵ h is the number of hours of babysitting
∵ m is the amount of money that Scott has after h hours
- Equate m by the sum of 15.00 and the product of 6.00 and h
∴ m = 15 + 6 (h)
∴ The equation is m = 15 + 6 h
The equation for the amount of money (m) Scott has after a number of hours babysitting (h) is m = 15 + 6 h
b)
∵ Scott has $51.00
∴ m = 51
- Substitute the value of m in the equation to find h
∵ 51 = 15 + 6 h
- Subtract 15.00 from both sides
∴ 36 = 6 h
- Divide both sides by 6
∴ 6 = h
∴ h = 6 hours
Scott will babysitting for 6 hours to have $51.00
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What is the equation in standard form of the line that passes through the point (1, 24) and has a slope of -0.6.
Answer:
y= -0.6x + 123/5
Step-by-step explanation:
Start with the slope.
Given the slope is -0.6, the equation must be in the form of y=-0.6x+b, where b is the y-intercept.
Now, substitute your values of a and b inside the equation. 24=-0.6+b. given this, b=24.6, which is 123/5.
A pipe that is 12 - feet long is cut into pieces that are 2 feet long. Which step below would give the
number of pieces into which the pipe is cut?
Answer:
Step-by-step explanation:
Number of pieces= total length/ length of one piece
= 12/2 = 6 pieces
YOUR TURN
9. Out of the 25 students in Mrs. Green's class, 19 have a per. Wh
of the students in Mrs. Green's class have a pet?
Answer:
[tex]\frac{19}{25}[/tex] or [tex]76%[/tex]
Step-by-step explanation:
As a fraction: [tex]\frac{19}{25} \\[/tex] it can't be simplified further
As a percentage: [tex]\frac{19}{25} =0.76[/tex]
Trent lifts weights 7 days a week. He spends 18 minutes lifting weights on Monday, 29 minutes on Tuesday, 40 minutes on Wednesday, and 51 minutes on Thursday. If this pattern continues, how many minutes will Trent lift weights on Saturday?
Answer:
73 minutes
Step-by-step explanation:
Find a pattern in the sequence.
The sequence is 18, 29, 40, 51.
29 - 18 = 11
40 - 29 = 11
51 - 40 = 11
The pattern is add 11 each day.
If 51 is Thursday, 51 + 11 is Friday.
51 + 11 + 11 is Saturday.
51 + 11 + 11 = 73
Therefore Trent will lift weights for 73 minutes.
When 18 is subtracted from the square of a number, the result is 3 times the number. Find the negative solution.
Answer: x = -3
Step-by-step explanation:
Let the number be x , that is the square of x is [tex]x^{2}[/tex].
From the first statement :
[tex]x^{2}[/tex] - 18 = 3x
writing the equation in a standard quadratic format , we have
[tex]x^{2}[/tex] - 3x - 18 = 0
Factorizing , we have
(x - 6 )(x + 3 ) = 0
x - 6 = 0 or x + 3 = 0
Therefore :
x = 6 or x = -3
Therefore , the negative solution implies x = -3
Answer:-3
Step-by-step explanation:
If P= (-1,5), Find:
Rx=1 (P)
([?],[])
Answer:
The reflection will be on the point (3, 5).
Step-by-step explanation:
For a given point (x, y) reflection along the line x = k, the co-ordinates will be:
[tex]$ R_{x = k} (x, y) = (2k - x, y) $[/tex].
Here, we have (x, y) = (-1, 5)
Reflection across the line x = 1, we have:
[tex]$ R_{x = 1} (-1, 5) = (2(1) - (-1), 5) $[/tex]
= (3, 5)
Hence, the reflection of the point (-1, 5) would be the point (3, 5).
Write a fraction equivalent to 4/18
Answer:
Its 2/9, sorry I can't show the explanation I have to do my work.
Step-by-step explanation:
2/9 is a fraction equivalent to 4/18.
What are the fractions?A fraction is a portion of a whole. In mathematics, the number is define as a quotient, in which the numerator is divided by the denominator.
In a simple fraction, two are integers. A complex fraction has a fraction in the numerator or denominator.
In a proper fraction, the numerator is less than the denominator.
To determine equivalent fraction to 4/18
Divide by 2, then we get,
4/18 = 2/9.
Therefore, a 2/9 fraction is equivalent to 4/18.
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Suppose you invested $1200 for 6 years. You earned $396 in simple interest at the end of the 6 years what is the annual interest rate
Answer:
rate of interest=R=5.5%
Step-by-step explanation:
given principle=P=$1200
simple interest=S.I=$396
time=T=6 years
simple interest=[tex]\frac{P\times R\times T}{100}[/tex]
$396=[tex]\frac{1200\times R\times 6}{100}[/tex]
$396=[tex]72\times R[/tex]
R=[tex]396\div 72[/tex]
R=5.5%
rate of interest=R=5.5% answer
Graph the equation using the point and the slope.
y-5= 1/5
(x-5)
Use the graphing tool to graph the equation. Use the point contained in the equation when drawing the line.
Answer:
The graph in the attached figure
Step-by-step explanation:
we have the equation of the line in point slope form
[tex]y-5=\frac{1}{5}(x-5)[/tex]
where
the point is (5,5)
the slope is m=1/5
Remember that
The formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)
so
To graph the line
1. Plot the point (5,5).
2. From that point, count right 5 units and up 1 unit and plot a second point.
3. Draw a line through the two points
so
The new point is (5+5,5+1) ----> (10,6)
Plot the points (5,5) and (10,6) and draw a line through the two points
The graph in the attached figure
Given f(x) = 364-27, what is the value of f(16)
Answer:
f(16)=337
Step-by-step explanation:
A recipe for ricotta cheese calls for 3/4 cup of whole milk for every 1/8 teaspoon of salt how much whole milk should be used for every teaspoon of salt
Answer:
6 cups of whole milk is used for every teaspoon of salt.
Step-by-step explanation:
Given:
A recipe for ricotta cheese calls for 3/4 cup of whole milk for every 1/8 teaspoon of salt.
Now, to find the cup of whole milk should be used for every teaspoon of salt.
So, to get the cup of whole milk used we use unitary method:
For every 1/8 teaspoon of salt cup of whole milk used = 3/4 cup.
Thus for every teaspoon of salt cup of whole milk used = 3/4 ÷ 1/8.
[tex]=\frac{3}{4}\times \frac{8}{1}[/tex] (changing the division to multiplication the fraction reciprocals.)
[tex]=\frac{24}{4}[/tex]
[tex]=6\ cups.[/tex]
Therefore, 6 cups of whole milk is used for every teaspoon of salt.
What is the domain of f(x) = 3x - 2?
{x|x>0}
O {x\x<0}
{x\ x = 0}
{x | x is a real number}
{x | x is a real number} is the domain of the function.
Determining the domain of a function.The collection of all conceivable input values (x) for which a function can be defined is known as the domain.
There are no limitations on the input values for f(x) = 3x - 2. Since there are no denominators, square roots, or other operations that could make the function undefined, it is defined for all real numbers.
The domain of f(x) = 3x - 2 is thus:
x is a real number | x.
This indicates that the function f(x) can take any real number as an argument.
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A $40.00 skateboard is discounted 30%. If sales tax is 5%, what is the amount of tax paid?
Answer:
$1.40
Step-by-step explanation:
Data provided in the question
Skateboard price = $40
Discounted percentage = 30%
Sales tax rate = 5%
By considering the above information, the amount of tax paid is
For computing the amount of tax paid, first we have to determine the price after considering the given discount percentage which is shown below:
= Skateboard price - Skateboard price × discounted percentage
= $40 - $40 × 30%
= $40 - $12
= $28
Now the amount of tax paid is
= $28 × 5%
= $1.40
Ron walked 3 3/4 km on monday,4 1/3 km on Wednesday. What distance did he walk in all
Answer:
Ron walked a total of 8 1/12 km
Step-by-step explanation:
Answer:
[tex]8\frac{1}{12} \; km[/tex]
Step-by-step explanation:
Distance walked by Ron on Monday = [tex]3\frac{3}{4} \; km[/tex]
Distance walked by Ron on Wednesday = [tex]4\frac{1}{3} \; km[/tex]
Now we will convert the given mixed fractions into improper fractions.
As we know that, a mixed fraction is composed of a whole number and a proper fraction.
Now,.
[tex]3\frac{3}{4} =\frac{3\times4+3}{4}=\frac{15}{4}[/tex]
[tex]4\frac{1}{3} =\frac{4\times3+1}{3} =\frac{13}{3}[/tex]
So, distance walked by Ron on Monday = [tex]\frac{15}{4}\; km[/tex]
Distance walked by Ron on Wednesday = [tex]\frac{13}{3} \; km[/tex]
Now, to find the total distance walked by Ron, we will add the distances walked by him on Monday and Wednesday.
So,
[tex]3\frac{3}{4} +4\frac{1}{3} =\frac{15}{4}+ \frac{13}{3}[/tex]
Now, we will find the LCM of the denominators of the given fractions.
The prime factorisation of 4 and 3 is,
4 = 2 × 2
3 = 3
So, LCM (3, 4) = 2 × 2 × 3 = 12
Now, we will convert each of the given fractions into their equivalent fractions with denominator 12.
[tex]\frac{15}{4}=\frac{15\times3}{4\times3}=\frac{45}{12}[/tex]
[tex]\frac{13}{3}=\frac{13\times4}{3\times4}=\frac{52}{12}[/tex]
So,
[tex]\frac{15}{4}+\frac{13}{3}=\frac{45}{12} +\frac{52}{12}=\frac{45+52}{12}=\frac{97}{12}[/tex]
Now, we will convert [tex]\frac{97}{12}[/tex] into improper fraction.
Now, 97 = 96 + 1 = 12 × 8 + 1
So, when '97' is divided by '12', then we get '8' as the quotient and '1' as the remainder.
So,
[tex]\frac{97}{12} = 8\frac{1}{12}[/tex]
Hence, Ron walked a total distance of [tex]8\frac{1}{12}[/tex] km in both the days.
The roots of a quadratic equation are -7 and 1. Write an equation that could represent this function. Give your answer in standard form and factored form.
Answer:
X^2+6X-7=0
Step-by-step explanation:
To identify the quadratic equation use the following method
(X-a)(X-b)=0
Where
a=-7
b=1
(X+7)(X-1)=0
X^2+7X-X-7=0
X^2+6X-7=0