The complete statement is that if the equation of the function f(x + 3) = x^2 + 4x − 7, the value of the function f(2) is -10
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the solution to the quadratic equation?A quadratic equations can be split to several equations and it can be solved as a whole
In this case, we have
f(x + 3) = x^2 + 4x − 7
To find f(2), we make use of the following comparison
f(2) = f(x + 3)
This means that
2 = x + 3
Evaluate
x = -1
Substitute x = -1 in f(x + 3) = x^2 + 4x − 7
f(-1 + 3) = (-1)^2 + 4(-1) − 7
This gives
f(2) = -10
Hence, the complete statement is that if the equation of the function f(x + 3) = x^2 + 4x − 7, the value of the function f(2) is -10
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if angle 2 equals (2x+5)degrees and angle 3 equals 85degrees, what is the value of x
Based on the information given, the value of x is 40 degrees
What are corresponding angles?Corresponding angles are defined as any pair of angles which on the same side of one or two lines, there is a cut through by a transversal.
It is also important to note that when a transversal intersects two parallel lines, the corresponding angles of the lines would be equal.
Given the angles;
Angle 2 equals (2x+5) degrees Angle 3 equals 85 degreesWe have that;
Angle 2 = Angle 3
Substitute the values
2x + 5 = 85
collect like terms
2x = 85 - 5
2x = 80
Make 'x' the subject by dividing both sides by 2
2x/ 2 = 80/ 2
x = 40 degrees
Thus, the value of x is 40 degrees
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ar travels on a straight, level road. (a) Starting from rest, the car is going 38 ft/s (26 mi/h) at the end of 4.5 s. What is the car's average acceleration in ft/s²?
The car's average acceleration is 8.44 ft/s².
Acceleration is defined as the rate of change of velocity per unit time. It is usually denoted by the letter a.
Here, we are given that a car travels on a straight road. Starting from rest, the car is going at 38 ft/s (26 mi/h) at the end of 4.5 s.
Acceleration of an object can be calculated using the given formula-
acceleration = velocity/ time
Here, the velocity of the car will be 38 ft/s
and the time is equal to 4.5 seconds.
Thus, putting these formulas in the equation, we get-
acceleration of the car = 38/ 4.5
= 380/ 45
= 8.44
Thus, the car's average acceleration is 8.44 ft/s².
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A print shop borrows $5700 from a credit union for 193 days. The credit union charges simple interest at an annual rate of 12% for this loan. Assume 1/365 each day is
of a year. Answer each part below.
Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
The amount borrowed by the print shop: $5700
Time for which loan is taken: 193 days
Rate of interest: 12%
Day in terms of year is given by: 1/365
The formula for simple interest:
Simple interest = P*R*T/100
where P = principal amount invested
R = rate of interest
T = time in years
Solving the question using the formula we have:
Simple interest = (5700*12*193)/(100*365)
= 13201200/36500
= 361.67 or $362
Interest that will be owed after 193 days will be $362
Amount owed after 193 days will be $5700 + $362 = $6062
Although a part of your question is missing, you might refer to this full question: A print shop borrows $5700 from a credit union for 193 days. The credit union charges simple interest at an annual rate of 12% for this loan. Assume 1/365 each day of a year. Find the interest that will be owed after 193 days. If no payments are made on the loan find the amount owed after 193 days.
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Translate abc with coordinates a(3,4) b(7,7) c( 8,1) 6 units left 7 units down
Answers:
A ' = (-3, -3)
B ' = (1, 0)
C ' = (2, -6)
=====================================================
Explanation:
To translate 6 units to the left, we subtract 6 from each x coordinate.
For point A, we have x = 3 become 3-6 = -3 as the new x coordinate.
Point A also goes down 7 units, in which we subtract 7 from the y coordinate. So the y coordinate of point A, which is 4, becomes 4-7 = -3 as the new y coordinate.
This is how we can write out the work shown for moving point A
[tex](\text{x},\text{y})\to(\text{x}-6,\text{y}-7)\\\\(3,4)\to(3-6,4-7)\\\\(3,4)\to(-3,-3)[/tex]
Point A is at (3,4) and moves to A ' which is at (-3, -3)
Do similar steps for points B and C to get the answers shown above.
Please answer the 2 question in photo [ Brainliest + easy points ]
which expression shows the prime factorization of 36? 2 × 2 × 3 2 × 2 × 3 2 × 3 × 3 2 × 3 × 3 2 × 2 × 2 × 3 × 3 2 × 2 × 2 × 3 × 3 2 × 2 × 3 × 3
Answer:
36 = 2 x 2 x 3 x 3
Answer:
2 2/3 * 2 2/3 = 64/9 = 7 1/9 ≅ 7.1111111
Step-by-step explanation:
The result:
2 2/3 * 2 2/3 = 64/
9
= 7 1/
9
≅ 7.1111111
Spelled result in words is sixty-four ninths (or seven and one ninth).
How do we solve fractions step by step?
Conversion a mixed number 2 2/
3
to a improper fraction: 2 2/3 = 2 2/
3
= 2 · 3 + 2/
3
= 6 + 2/
3
= 8/
3
To find a new numerator:
a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/
3
= 6/
3
b) Add the answer from previous step 6 to the numerator 2. New numerator is 6 + 2 = 8
c) Write a previous answer (new numerator 8) over the denominator 3.
Two and two thirds is eight thirds
Multiple: 8/
3
* 8/
3
= 8 · 8/
3 · 3
= 64/
9
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(64, 9) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - eight thirds multiplied by eight thirds is sixty-four ninths.
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Prove the following inequality.
The proof of the inequality → (a + b)²/2 ≥ 2ab, is given below -
We have the following inequality -
(a + b)²/2 ≥ 2ab
We have to prove it.
What is inequality ?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
According to the question, we have -
Inequality -
(a + b)²/2 ≥ 2ab
Proof -
Starting from the inequality - (a - b)² ≥ 0
(a - b)² ≥ 0
a² + b² - 2ab ≥ 0
a² + b² - 2ab + 2ab ≥ 2ab
a² + b² ≥ 2ab
Add - 2ab on both sides, we get -
a² + b² + 2ab ≥ 4ab
(a + b)² ≥ 4ab
Divide both sides by 2, we get -
(a + b)²/2 ≥ 2ab
Hence Proved.
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Pls help I’m not very smart
Answer:
Blank 1: 97
Blank 2: 73
Step-by-step explanation:
This equation is shown on a straight line, which equals 180.
We can start by adding the two equations which together are equal to 180.
15x + 2 + 10x + 3 = 180
We can simplify it to 25x + 5 = 180
Now we can subtract 5 from both sides to get
25x = 175
Then we can divide both sides by 25 to get x = 7
Now we can plug in x for both angles
Angle RQS is 15x + 2, so 15*7=95 and the +2 is 97.
Angle TQS is 10x + 3 so 10*7=79 and the + 3 is 73
:D
Find x. (Hint: Draw an auxiliary line.)
The angle x will be 98 ⁰
What are alternate interior angle ?
An alternate interior angle is one formed on the inside side of two parallel lines and opposite on the outer side of the transversal when those two parallel lines are intersected by a transversal and they are equal.
Alternate angles between a transverse and parallel lines are equal .
Let the lines are AB and CD and let us draw a transverse line HI parallel to AB and CD, then the angle FEI will be 62 degree as alternate interior angle are equal. and also angle EPC will be supplementary angle of 144 degree that is 36 degree thus forming angle GEI to be 36 degree also as shown in figure below :
Now calculating angle x :
x = 62+ 36
x = 98 ⁰
Therefore, the angle x will be 98 ⁰
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A triangle has two sides of lengths 4 and 7. What value could the length of
the third side be? Check all that apply.
A. 9
B. 5
C. 17
D. 7
E. 3
F.' 11
SULMIT
A=9, B=5 and D=7 are the correct options.
In the *Geometry*, a *triangle* is a closed 2-dimensional figure with 3 angles, 3 sides and 3 vertices. Triangles are considered as a *polygon* with the least number of sides.
a,b and c are the sides of a triangle if it satisfies:
a<b+c , b<a+c and c<b+a
Here, a=4 and b=7
We have to find c
i.e. all those c which satisfies:
4<7+c , 7<4+c and c<4+7=11
AAAAAA. 9 it is true
B.5 it is true
C.17 This is clearly false, since it doesn't satisfies inequality third.
D.7 it is true
EE. 3 it is not true since it doesn't satisfies second inequality.
F.11 This is clearly false, since it doesn't satisfies inequality third
Hence, The correct answer of the given question is A,B and D.
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Get 15 points and 1 Thanks if ur answer is correct.
Answer:
1 3/4
Step-by-step explanation:
OK but what if brainliest instead
Answer:1 3/4
Step-by-step explanati
the shorter leg of a right triangle is 8 less than the hypotenuse. the longer leg is one less than the hypotenuse. find the perimeter
The perimeter of the right triangle is 30 units.
How to find the perimeter of a right triangle?The shorter leg of the right triangle is 8 less than the hypotenuse. The longer leg is one less than the hypotenuse.
Let's break the information into smaller chunk.
The shorter leg of a right triangle is 8 less than the hypotenuse.
The longer leg is one less than the hypotenuse.
The hypotenuse is the longest side of a right triangle.
Therefore,
let
the hypotenuse = x
short leg = x - 8
long leg = x - 1
Applying Pythagorean theorem in the given right triangle.
c² = a² + b²
where
c = hypotenusea and b are the other legs.(x - 1)² + (x - 8)² = x²
(x - 1)(x - 1) + (x - 8)(x - 8) = x²
x² - x - x + 1 + x² - 8x - 8x + 64 = x²
2x² - 18x + 65 = x²
x² - 18x + 65 = 0
(x - 13)(x - 5) = 0
Therefore,
x = 5 and x = 13
13² - 5² = a²
169 - 25 = a²
a = √144
a = 12
So, the hypotenuse is 13, the shorter leg is 5 and the longer leg is 12.
perimeter of the right triangle = 13 + 5 + 12 = 30
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There is quite literally not one moment where I was taught this that I remember answer correctly for 69 points. Answer choices are 15, 20, 23, 25, and 18.
It should be noted that based on the information given, the square root of 225 will be A. 15.
What is the square root?It should be noted that a number y such that y² = x, or a number y whose square is x, is referred to as the square root of a number x in mathematics. For instance, since 4² = 16, 4 and -4 are the square roots of 16.
It should be noted that in this case, the square root of 225 will be:
= ✓225
= 15
Therefore, it should be noted that based on the information given, the square root of 225 will be 15.
In conclusion, based on the information, the correct option is A.
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Can yall help me with this
Answer:
8 feet
Step-by-step explanation:
Since it is 2 inches and 1 inch is equal to 4 feet, you just multiply 2 inches by 4 feet which will give you 8 feet.
Hope that helps
find f(-2)
i need help
Answer:
f(-2) = -1
Step-by-step explanation:
wwwwwwwwwwww
Answer: f(-2) = 5
Step-by-step explanation: In this piecewise function, when x is less than -1, the equation is -3x-1. -2 is less than -1 so we use the first equation. -3(-2)-1= 6-1 = 5.
your friend says that you can write any equation in slope-intercept form. is your friend correct? explain.
Answer:
almost.
Step-by-step explanation:
You can write almost every linear equation in slope-intercept form.
Slope-intercept form is:
y = mx + b
So every line except a vertical line can be written in the form y=mx+b.
This form cannot be used when m is undefined.
which two cards show reflection, rotation, or translation?
Answer:
1 & 4
Step-by-step explanation:
because 3 & 5 is a reflection, 2 & 6 is a translation.
( 2x+7) - (2x - 4) please help me with this answer because it is in big ideas math
Answer:
11
Step-by-step explanation:
You want to simplify (2x+7) - (2x - 4).
Distributive propertyThe distributive property tells you the factor outside parentheses applies to every term inside parentheses. It is used for the purpose of removing parentheses.
(2x+7) - (2x - 4) = 2x +7 -(2x) -(-4) = 2x +7 -2x +4
Like termsTerms that have the same variable (or product of variables) are "like terms." Their coefficients can be combined. (This is another use of the distributive property.)
2x +7 -2x +4 = 2x -2x +7 +4 = (2 -2)x +(7 +4) = 0x +11
= 11 . . . . simplified form of the given expression
Given negative four and one sixth times negative three and fifteen hundredths, determine the product.
The resulting product of the expression is 13 1/8
Product of fractionsFractions are written as a ratio of two integers
Given the following expression
-4 1/6 * -3 15/100
Convert to improper fraction to have:
-25/6 * -315/100
-1/6 * -315/4
315/24
13 1/8
Hence the resulting product of the expression is 13 1/8
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Find the measure of ∠ b ?
Answer:
38 degrees
Step-by-step explanation:
Angle 38 and b are the same.
Enlarge triangle A by scale factor 1.5 with centre (0,2)
Scale factor 1.5
Let O (0,2) as the centre of enlargement
A (0, 0)
B (-2, 0)
C (-2, 4)
Step 1:
First draw lines from point O through A, B and C, as shown in the image attached below
Step 2:
Measure the length O A and multiply it by 1.5 to get the distance from O of the image point A';
<=> O A' = 1.5 × O A.
<=> OA' = 1.5 * [tex]\sqrt{2^2}[/tex]
<=> OA' = 1.5*2
<=> OA' = 3
Mark the point A' on the diagram
Step 3:
The images B' and C' can then be marked in a similar way and the enlarged triangle A' B' C' can then be drawn.
OB' = 1.5OB
<=> OB' = 1.5 *[tex]\sqrt{( 2^2+2^2}[/tex]
<=> OB' = 1.5*2[tex]\sqrt{2}[/tex]
<=> OB' = 3[tex]\sqrt{2[/tex]
OC' = 1.5*[tex]\sqrt{2^2+2^2}[/tex]
<=> OC' = 1.5*2[tex]\sqrt{2[/tex]
<=> OC' = 3[tex]\sqrt{2}[/tex]
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20 +? =100 ÷ 4
Help
Answer:
5
Step-by-step explanation:
Both answers equal 25.
The measure of an angle is 56.3°. What is the measure of its complementary angle?
Answer:
33.7
Step-by-step explanation:
Complementary angles are angles that when added, sum up to 90*
First, make the equation, x being the missing angle
90*= x + 56.3
Rewrite the equation to find the missing angle
90 - 56.3 = x
x= 33.7
Answer:33.7°
Step-by-step explanation:
To find the complement of an angle, subtract that angle's measurement from 90 degrees. The result will be the complement
90° - 56.3°
=33.7°
The circumference is 25 ft I have to find what X is for my radius
R= -4x-5
The value of x based on the information given about the circumference is 2.24.
How to illustrate the information?It should be noted that the circumference is calculated as:
= 2πr
where
π = 3.142
r = radius = 4x - 5.
Circumference = 25
Therefore, circumference = 2πr.
(2 × 3.142)(4x - 5) = 25
6.284(4x - 5) = 25.
25.136x - 31.42 = 25
Collect like terms
25.136x = 25 + 31.42
25.136x = 56.42
x = 56.42 / 25.136
x = 2.24
Therefore, the value of x based on the information given about the circumference is 2.24.
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find the indicated value for the given function. f(4) =|2x-7|
Answer: 1
I did this problem a couple times and got 1 every time
3. Select all the equations that match the diagram.
X+5\x+5\x+5
a.
x+5=18
b. 18÷3=x+5
C. 3(x+5)= 18
d. x+5=-18
e. 3x+5= 18
The equations that match the diagram are 18 ÷ 3 = x + 5 and 3(x + 5) = 18
How to select all the equations that match the diagram?The given parameters are
Expression = x+5\x+5\x+5
Value = 18
The above means that
Expression = Value
So, we have
x + 5 + x + 5 + x + 5 = 18
Evaluate the sum
So, we have
3x + 15 = 18
Factor out 3
So, we have
3(x + 5) = 18
Divide both sides by 3
So, we have
x + 5 = 18 ÷ 3
Hence, the equations that match the diagram are 18 ÷ 3 = x + 5 and 3(x + 5) = 18
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Best painters charges $100 to paint a room and $15 per can of paint used. Top Painters charges $75 to paint a room and $30 per can of paint used. Which equation could be used to find the number of cans of paint (p) for which the cost of the two companies is the same?
a) 45p = 175
b) p(100 + 15) = p(75 + 30)
c) 100p + 15 = 75p + 30
d) 15p + 100 = 30p + 75
d. 15p + 100 = 30p + 75
What is the equation of the line?
y=-12+1
Oy=2x-1
O y=-2z+1
Oy=-z-1
Answer:
y = -1/2 x + 1.
Step-by-step explanation:
The slope is -1/2.
The y intercept is at y = 1
So, it's
y = -1/2 x + 1.
Please answer this math equation.
The table that represents the linear function is table (B)
How to determine the linear function?As a general rule, a linear function is any function that has a constant rate of change
This means that as the function independent value changes by a constant, the function dependent value changes by a constant
In other words, as the function x value changes by a constant, the function y value changes by a constant
Using the above as a guide, we can see the table B represents a linear function
This is so because, as x increases by 3, the y value decrease by -2
Hence, the table that represents the linear function is table (B)
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during math class, you find the length of a right triangle's hypotenuse with a theorem created long ago. who do you have to thank for that theorem?
The length of a right triangle's hypotenuse with a theorem created long ago is c² = a² + b², where 'c' = the hypotenuse of the right triangle and 'a' and 'b' are the other two legs.
We need to find the length of a right triangle's hypotenuse with a theorem created long ago.
What is a Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
The Pythagoras theorem equation is expressed as, c² = a² + b², where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
Therefore, the length of a right triangle's hypotenuse with a theorem created long ago is c² = a² + b², where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs.
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