Answer:
First,
the age of the son: s
the age of the father is 2 less than 7 times the age of his son: 7s - 2
In 3 years, the sum of their ages will be 52, In 3 years, the age of the sun will
increase 3, so s+3. Also, the age of his
father also increase 3, (7s-2)+3
(s+3)+ [(7s-2)+3] = 52 is the equation.
The correct answer is :
( 7s - 2 ) +3+ ( s + 3 ) = 52 , or 8s + 4 = 52 .
Explanation :Since s is the son's age , " two less than seven times " the son's age would be represented by 7s - 2 .
To represent this in 3 years , we would add 3 : ( 7s - 2 ) +3 .
In 3 years , the son's age , s , would be represented by s + 3 . We are told that the sum of these ages will be 52 ; this gives us ( 7s - 2 ) +3+ ( s + 3 ) = 52 .
To simplify this , combine like terms .
7s + s = 8s ; -2 + 3 + 3 = 4 .
This gives us 8s + 4 = 52 .
In a certain week, the time Lisa spent on
sport was 3 hours less than twice the time
she spent doing her school homework. The
time she spent on reading was of the time
she spent doing her school homework. The
total time she spent on these three
activities was 30 hours in that week. Form
an equation and solve it to find the amount
Answer:
2M + 3 hrs
Step-by-step explanation:
Lisa spent doing her mathematics homework = M hrs
the amount of time spent watching television was 3 hours more than twice the time she spent doing her mathematics homework.
lisa spent on watching television = 2M + 3 hrs
Total time spent on these two activities = M + 2M + 3
= 3M + 3 hrs
3 M + 3 = 30
=> 3M = 27
M = 9
To identify the most efficient model for a windmill, Gandalf Engineering Company designs the windmill shown. The design consists of four right triangles arranged equally around point O such that point O is the midpoint of BF¯¯¯¯¯ and DH¯¯¯¯¯¯.
Deductive Reasoning is the practice of arriving at a mathematical conclusion by simply analyzing the facts using the knowledge of the related concepts.
What is the proof that ∠A ≅ ∠E?Looing at ΔOAB and ΔOEF
It is clear that
OB = OF (O is the midpoint)
∠OBA = ∠OFE = 90°
Therefore
∠AOB = ∠EOF (Vertically Opposite Angles)
⇒ ΔOAB ≅ ΔOEF and
∠ A ≅ ∠E.
QED
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please help with this thank you!
Answer:
3
Step-by-step explanation:
18-15=3
Answer:
first option, 3
Step-by-step explanation:
The interquartile range is the difference between Q3 and Q1.
Q1 is the lower bound of the box = 15
Q3 is the upper bound of the box = 18
Q3 - Q1
= 18 - 15
= 3
IM SO LOST PLS HELP ME
[tex]~~~~~~~c = \dfrac{a^2 +3b}{4}\\\\\implies 4c = a^2 +3b\\\\\implies 3b = 4c-a^2\\\\\implies b = \dfrac{4c-a^2}{3}[/tex]
Answer:
b = [tex]\frac{(4c-a^2)}{3}[/tex]
Step-by-step explanation:
[tex]c=\frac{a^{2}+3b }{4}[/tex]
First, let us multiply both sides by 4.
4c = a² + 3b
Now let us take a² to the left side.
4c - a² = 3b
Now to make b as the subject let us divide both sides by 3.
[tex]\frac{(4c-a^2)}{3} =\frac{3b}{3}[/tex]
Therefore,
b = [tex]\frac{(4c-a^2)}{3}[/tex]
PLEASE HELP!!!!!!!!!
Answer:
CE = 4.6 ft
Step-by-step explanation:
(a)
given 2 secants drawn from an external point to the circle , then
the product of the external part of one secant and the entire secant is equal to the product of the other secant's external part and that entire secant, that is
BE × BC = AB × DB
(b)
substituting given values into the equation
BE × 10 = 3 × 18
10 BE = 54 ( divide both sides by 10 )
BE = 5.4 ft
then
CE = CB - BE = 10 - 5.4 = 4.6 ft
PLEASE HELP ILL MAKE YOU THE BRAINIEST what is the area of the regular polygon
The area of a regular polygon is one-half the product of its apothem and its perimeter. Often the formula is written like this: Area=1/2(ap), where a denotes the length of an apothem, and p denotes the perimeter.
Step-by-step explanation:
#Hopeithelps
james has decided to start saving for a cruise over the summer. his money is currently in the local bank modeled by the function sx equals 102. he is able to do work around the neighborhood to earn extra money that the function would be a x equals eight times x +2 where x is measured in hours. explain how james can we create a function to combine the two and describe any simplification that can be done
In the scenario above, James can we create a function to combine the two by f ( x ) = 8 x + 118.
What is the simplification about?In the question above, to be able to create a function, we have to show that;
s ( x ) = 102
a ( x ) = 8 ( x + 2 )
So, a function that combines the two will be:
f ( x ) = s ( x ) + a ( x ) = 102 + 8 ( x + 2 ) =
= 102 + 8 x + 16
Therefore f ( x ) = 8 x + 118
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Find the following integrals
[tex]\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}[/tex]
[tex] \sf x - \frac{4}{x} + C[/tex]
Step-by-step explanation:
[tex] \sf \longmapsto \int \frac{ {x}^{2} + 4 }{ {x}^{2} }dx \\ \\ \\ \sf \longmapsto \int \frac{ {x}^{2} }{ {x}^{2} } dx + \int \frac{4}{ {x}^{2} } dx \\ \\ \\ \sf \longmapsto \int 1dx + 4 \int \frac{1}{ {x}^{2} } dx \\ \\ \\ \sf \longmapsto x + 4( \frac{{x}^{ -2 + 1}}{ -2 + 1} ) + C \\ \\ \\ \boxed{ \longmapsto x - \frac{4}{x} + C} [/tex]
Find the slope of the line that passes through the points f(4) = 6 and f(-2) = 8.
Answer:
slope = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
given f(4) = 6 and f(- 2) = 8 , then 2 points on the line are
(4, 6 ) and (- 2, 8 )
calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 6 ) and (x₂, y₂ ) = (- 2, 8 )
m = [tex]\frac{8-6}{-2-4}[/tex] = [tex]\frac{2}{-6}[/tex] = - [tex]\frac{1}{3}[/tex]
Change 24 inches into feet given the fact that 1 foot = 12 inches.
Answer:
2 feet
Step-by-step explanation:
1 foot = 12 inches
2 feet=24 inches
Answer:
2 feet
Step-by-step explanation:
12 x 2 is 24.
Solve the formula for a linear equation, y = mx + b, for m. I’m not so great at formulas and it’d be great if someone helped thank you :)
Answer:
See below
Step-by-step explanation:
mx + b = y subtract 'b' from both sides of the equation
mx = y - b now, divide both sides by 'x'
m = (y-b)/x
An investment of $2,375 is made in a 7-year cd that earns 314% annual interest that is compounded continuously. how much will the cd be worth at the end of the 7-year term? round your answer to the nearest cent. do not include the dollar sign.
The worth of the cd at the end of 7 years will be $384,101.79.
What will be the worth of the investment?When an investment earns an interest that is compounded continuously, it means that it earns interest continuously.
The formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rate2375 x (e^3.14) x 7 = $384,101.79
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Complete the equivalent equation for –7x – 60 = x2 + 10x.
(x +
)(x +
) = 0
By algebraic handling and factoring, we conclude that the equivalent equation for the expression - 7 · x - 60 = x² + 10 · x is (x + 5) · (x + 12) = 0.
How to determine the factor form of the given equation
In this question we have a quadratic function which must be factored by algebraic handling:
- 7 · x - 60 = x² + 10 · x
x² + 10 · x + 7 · x + 60 = 0 Compatibility with addition/Modulative property
x² + 17 · x + 60 = 0 Definition of addition
(x + 5) · (x + 12) = 0 x² + (- a - b) · x + a · b = 0/Result
By algebraic handling and factoring, we conclude that the equivalent equation for the expression - 7 · x - 60 = x² + 10 · x is (x + 5) · (x + 12) = 0.
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f(x) = x^2. What is g(x)?
the answer is XG and that is the answer to your question ❓ ok she will he hi she
Explanation:
Normally x = 1 maps to y = f(x) = 1 for the parent function f(x) = x^2
However, the red curve shows x = 1 leads to y = 16 instead. This is a jump of "times 16"
We must multiply the f(x) outputs by 16 to get the g(x) outputs.
g(x) = 16*f(x)
g(x) = 16x^2
REASONING A rectangular box has dimensions of x inches by (x+5) inches by (x−2) inches. The volume of the box is 30x cubic inches. Find the dimensions of the box. Write the dimensions in ascending order.
-33 + 8x = -3 (3x+6) + 2
Answer:
x = 1
Step-by-step explanation:
-33 + 8x = -9x - 18 + 2
8x+ 9x = -18 + 2 + 33
17x = -16 + 33
17x = 17
x = 1
give me brainliest please!
hope this helps :)
can someone help me with this question
Answer:
Step-by-step explanation:
Proof
AB||CD Given
<1 = <2 Given
<2 = <3 Alternate interior angles of Parallel lines
<1 = <3 Substitution for <2 from Given.
AC = AB the sides opposite equal angles are equal
!!!20 POINTS AND BRAINLIEST!!!PLEASE SHOW WORK!!
Describe the graph of y= 3x+14/x-2. Define the horizontal and vertical asymptotes and several points on either side.
The vertical asymptotes are x = 2 and horizontal asymptotes are y = 3 and the parent graph is shifted two to the right and three to the top.
What is hyperbola?It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.
We have a graph of a hyperbola:
[tex]\rm y=\dfrac{\left3x+14\right}{x-2}[/tex]
The above equation represents the hyperbola.
We can write the above equation as:
[tex]\rm y=3+\dfrac{\left20\right}{x-2}[/tex]
The vertical asymptotes: x = 2
The horizontal asymptotes: y = 3
Thus, the vertical asymptotes are x = 2 and horizontal asymptotes are y = 3 and the parent graph is shifted two to the right and three to the top.
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The dual bar chart shows the hair colour of boys and girls in a year group.
What fraction of the red haired students are boys?
Give your answer in its simplest form
The fraction of the red haired students are boys will be 2 / 5.
What is a fraction number?A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.
The dual bar chart shows the hair colour of boys and girls in a year group.
The total number of the boys and girl will be
Total = 6 + 9
Total = 15
Then the fraction of the red haired students are boys will be
⇒ 6 / 15
⇒ 2 / 5
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Help, I still don't understand this question!
What is the measure of ∠BAC, ∠ABC, and ∠ACB?
The answer is:
" m∠BAC = 45° ; m∠ABC, = 64° ; and: m∠ACB = 70° ."
__________
Step-by-step explanation:
To find the measure of ∠BCA {"m∠BCA"} :
<BCA is supplementary to " 110 " ; that is, both, or all, of all the measurements that form a "line or line segment"; or any portions thereof,
that can be written in: "slope-intercept format"
that is, on Cartesian plane: " y = mx + b " ;
in which: "y" is isolated on the "left-hand side" of the equation; as a single, isolated variable;
and in which: "m" is the "slope" (if applicable); and the coefficient to the "x" value'
and in which "b" is the "y-intercept"; or more precisely"
the value of the "y-coordinate"—in: "(x, y)" format —at which:
" x = 0" ; that is, in the format: " (0, b)."
_________________
So, to find
m∠BCA : Subtract our given value, "110" ; from "180" ; as follows:
_________________
" (180 − 110) = 70" ;
__________________
Now: Note a triangle, by definition, has 3 (three) sides and 3 (three) angles—and all three (3) angles of a triangle add up to 180°.
So: We just solved for m∠ACB ; which is: 70° .
Now shall solve for the value of "x" ; & then find the value of all 3 (three) sides of this triangle
Since all angles within a triangle add up to 180: Let's add them up:
" 70 + 3x + 20 + 3x = 180 " ;
Combine the "like terms" on the "left-hand side" of the equation:
" +3x + 3x = 6x " ; "+ 70 + 20 = 90 ";
And rewrite the equation:
" 6x + 90 = 180 " ;
Now, subtract "90" from Each Side of the equation:
" 6x + 90 − 90 = 180 − 90 " ;
to get: " 6x = 90 " ;
Now, divide Each side of the equation by "6" ;
to isolate "x" on one side of the equation ;
and to solve for "x" :
" 6x / 6 = 90 / 6 ;
to get: " x = 15 " ;
________________
Now, we are asked to find:
1) " m∠BAC = 3x " ; Plug in "15" for "x" ; and solve:
"3x = 3(15) = 45 " ;
2) " m∠ABC = "(3x + 20)" ; Plug in "15" for "x"; and solve:
"3(15) + 20 = 45 + 20 = 65 " ;
3) " m∠ACB = 70 " ; (as per our calculated value);
To check our work—do these 3 (three) numbers add up to 180?
"45 + 65 + 70 =? 180 ? " ;
" 110 + 70 = " 180 "? Yes!
__________
So: The answer is as follows:
" m∠BAC = 45° ; m∠ABC, = 64° ; and: m∠ACB = 70° ."
__________
Hope this is helpful to you! Best wishes!
I need help, please. I don’t understand
Answer:
60%
Step-by-step explanation:
So, this question is saying the bowls can be between a diameter of 6.95 and 7.05
Box 1, 3 and 5 are in this margin.
Box 2 and 4 are not.
3/5 boxes can be included.
3/5 is 6/10
6/10 is 60%
Vill all three students complete a sign at the same time? Explain your
no
has 48 chocolate chip cookies, 64 vanilla cookies, and 100 raisin cookies for a
ale. He wants to make bags that have all three cookie flavors and the same
er of each flavor per bag.
ow many bags can he make without having any cookies left over?
NEED HELP ASAP, PLEASE ANSWER THIS
Answer:
Given units of measures of volume:
mm³ = millimeters cubedcm³ = centimeters cubeddm³ = decimeters cubed ⇒ 1 dm³ = 1 literm³ = meters cubed ⇒ 1 m³ = 1000 litersUnits of measure:
mm < cm < dm < m1000 mm = 100 cm = 10 dm = 1 m1. Water in a rectangular pool → m³
2. an ice cube before it melts → cm³
3. a dice → mm³
4. a blackboard eraser → cm³
5. oil in a rectangular box → dm³
To convert liters to cubic meters, divide by 1000:
⇒ 6700 L³ = 67000 L = 6700 ÷ 1000 = 6.7 m³
To convert liters to cubic centimeters, multiply by 1000:
⇒ 28 L³ = 28 L = 28 × 1000 = 28,000 cm³
solve the proportion
Answer:
K=4.44444444444
Step-by-step explanation:
k/6=15/18.
Cross multiply.
k*18=18k.
6*15=80.
18k=80.
18k/18=80/18.
k=4.44444444444
Nevaeh models the volume of a popcorn box as a right rectangular prism. Its dimensions are 5 in by 3 in by 7 1/4 in. How many cubic inches of popcorn would it hold when it’s a quarter full? Round your answer to the nearest tenth if necessary.
The cuboid can hold 27.2 cubic inches of popcorn
What is a right rectangular prism?A right rectangular prism is also called the cuboid. it is a solid three dimensional shape with 6 faces, 12 edges and 8 vertices.
Analysis:
Volume of cuboid = length x width x height
= 5 x 3 x 29/4 = 108.75 cubic inches
When it is quarter full, volume = 1/4 x 108.75 = 27.2 cubic inches
In conclusion, the volume of the cuboid is 27.2 cubic inches.
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Help ASAP
Ben is making a chart in which he is listing the masses of different planetary bodies. He plans to write the masses in scientific notation. Convert the values in scientific notation to standard notation.
The mass of Ganymede is 1.48E23, or , kilograms.
The mass of Pandora is 2.20E17, or , kilograms.
Step-by-step explanation:
I think 2.20e23 because it said bodies not body
Help me if you can please!!!
To solve this, we need to use our trigonometric equations:
⇒ look at the diagram attached
Let's examine what the problem wants:
the length of the side opposite to the 27-degree angleLet's examine what the problem gives us:
the length of the side adjacent to the 27-degree anglethe angle that has a measure of 27-degreesLet's solve:
[tex]tan(27)=\frac{x}{15} \\x=15*tan(27)\\x=7.64[/tex]
Answer: 7.6 (rounded to the nearest tenth)
Hope that helps!
evaluate the exppresion 14x-11y if x=4 and y=3
write Six times a number w is at least -24 as an inequality
Answer:
[tex]6n \geq -24[/tex]
Step-by-step explanation:
First let's provide a variable for "a number" and call it [tex]n[/tex].
So "six times a number" could be written as [tex]6*n[/tex].
"Is at least" in mathematical terms means "greater than or equal to" or
≥
Putting this altogether gives the expression:
[tex]6n\geq -24[/tex]
Round of to the nearest thousand 741,543
Answer:
The correct answer is 742,000
Step-by-step explanation:
Answer:
742,000
Step-by-step explanation:
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