Answer:
22 + 5 ÷ 9 = 3
Proof:
27/9
= 3
the number is 22
Factor y2 + 5y + 6.
(y + 6)(y + 1)
(y + 2)(y + 3)
(y + 4)(y + 2)
Answer:
(y + 2)(y + 3)
Step-by-step explanation:
Solve kx + 12 = 3kx for x.
[tex]
kx+12=3kx \\
12=2kx \\
x=\frac{12}{2k} \\
x=\frac{6}{k}
[/tex]
Hope this helps.
Answer: x=6/k
Step-by-step explanation:
kx + 12 = 3kx and subtract k from both sides
12=3kx-kx then simplify
12=2kx, now divide both sides by two
12/2=kx simplify again
6=kx divide next
6/k=x finally, switch sides to get x=6/k
Hope this helps, have a BLESSED and wonderful day, as well as a safe one!
-Cutiepatutie ☺❀❤
Lexie is making a scale drawing of a soccer field that is 120 yards long and 80 yards wide. If the field in Lexie’s drawing is 30 centimeters wide, how long should the field be in the drawing?
9514 1404 393
Answer:
45 cm
Step-by-step explanation:
The ratio of length to width is the same for the drawing as for the field.
length/width = L/(30 cm) = (120 yd)/(80 yd)
L = (30 cm)(3/2) = 45 cm . . . . . . multiply by 30 cm and simplify
The field should be 45 cm long on the drawing.
Final answer:
The soccer field in Lexie's scale drawing should be 45 centimeters long, using a scale factor based on the given width of 30 centimeters and the real soccer field's dimensions.
Explanation:
Lexie is scaling a real soccer field to a drawing, with the real field's dimensions being 120 yards long and 80 yards wide. When converting these dimensions to a scale drawing where the width is 30 centimeters, we need to find the drawing's length. To do this, we will use a scale factor.
First, we find the actual scale factor based on the given dimensions:
Actual width of soccer field = 80 yards
Width in the drawing = 30 centimeters
To convert yards to centimeters, we need to know that 1 yard equals 91.44 centimeters. Given this, the actual width in centimeters is 80 yards * 91.44 cm/yard = 7312 centimeters.
Now, we calculate the scale factor:
Scale factor = Width in the drawing / Actual width in centimeters = 30 cm / 7312 cm
Using this scale factor, we can find the length for the drawing:
Actual length of soccer field = 120 yards
Actual length in centimeters = 120 yards × 91.44 cm/yard = 10972.8 centimeters
Length in the drawing = Actual length in centimeters × Scale factor = 10972.8 cm × (30 cm / 7312 cm)
Calculating this gives us:
Length in the drawing = 45 centimeters
Therefore, the length of the soccer field in Lexie's drawing should be 45 centimeters.
One leg of a right triangle is 12, and the hypotenuse is 20.
The length of the other leg is ___
We can ise Pythagorean triplet which is ( 12 , 16 , 20 )
Therefore the answer is 16.
Step-by-step explanation:
Or we can use Pythagoras theorem , stated as ;
( hyp )^2 = ( adj )^2 + ( opp )^2
hyp ( hypotenuse ) = 20
We can assume the adj ( adjacent ) = 12
By substituting the values ,
20^2 = 12^2 + ( adj )^2
400 = 144 + ( adj )^2
400 - 144 = ( adj )^2
256 = ( adj )^2
Take the square root of both sides
✓256 = adj
16 = adj
Therefore the length of the other leg which is the adjacent( adj ) side is 16.
The length of the other leg is 16
To find the length of the other leg of a right triangle, given one leg is 12 and the hypotenuse is 20, we use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the legs (a and b) is equal to the square of the length of the hypotenuse (c).
This relationship is given by:
a² + b² = c²
1. Here, one leg (a) is 12 and the hypotenuse (c) is 20. So we can write:
12² + b² = 20²
2. Calculating the squares gives:
144 + b² = 400
3. Subtract 144 from both sides to find b²:
b² = 256
4. Finally, take the square root of both sides to find b:
b = √256 = 16
Thus, the length of the other leg is 16.
Darcy harvests 8\dfrac348
4
3
8, start fraction, 3, divided by, 4, end fraction acres of corn every \dfrac56
6
5
start fraction, 5, divided by, 6, end fraction of an hour. Darcy harvests corn at a constant rate
How many acres does she harvest per hour?
Answer:
[tex]10\frac{1}{2}\ \frac{acres}{hour}[/tex]
Step-by-step explanation:
The correct question is:
Darcy harvests 8 3/4 acres of corn every 5/6 of an hour. Darcy harvests corn at a constant rate. How many acres does she harvest per hour?
we know that
To find out the corn rate harvested per hour or the unit rate, divide the number of acres of corn harvested by the total time it takes
so
[tex]8\frac{3}{4} :\frac{5}{6}[/tex]
Convert mixed number to an improper fraction
[tex]8\frac{3}{4}=8+\frac{3}{4}=\frac{8*4+3}{4}=\frac{35}{4}[/tex]
substitute
[tex]\frac{35}{4} :\frac{5}{6}=\frac{210}{20}=\frac{21}{2}\ \frac{acres}{hour}[/tex]
Convert to mixed number
[tex]\frac{21}{2}\ \frac{acres}{hour}=\frac{20}{2}+\frac{1}{2}=10\frac{1}{2}\ \frac{acres}{hour}[/tex]
Answer:
[tex]10\frac{1}{2}[/tex] or [tex]\frac{21}{2}[/tex]
X÷3.7=5? Need help.
Answer:
x = 18.5
Step-by-step explanation:
Multiply 5 and 3.7.
Which equals 18.5.
Check: 18.5 / 3.7 = 5.√
A boat travelled 231 km downstream and back. The trip downstream took 11 hours. The trip back took 77 hours. Find the speed of the boat in still water and the speed of the current
Speed of boat in still water is 12 km/hr and speed of current is 9 km/hr
Solution:
From given,
Downstream distance = 213 km
Time taken for downstream = 11 hours
Thus, speed is given as:
[tex]\text{Downstream speed} = \frac{\text{Downstream distance}}{\text{time taken}}[/tex]
[tex]\text{Downstream speed} = \frac{231}{11} = 21[/tex]
Thus downstream speed is 21 km/hr
Also,
Upstream distance = 213 km
Time taken for upstream = 77 hours
Thus, speed is given as:
[tex]\text{Upstream speed} = \frac{\text{Upstream distance}}{\text{time taken}}\\\\\text{Upstream speed} = \frac{231}{77} = 3[/tex]
Thus upstream speed is 3 km/hr
If the speed downstream is "a" km/hr and the speed upstream is "b" km/hr , then:
[tex]\text{Speed in still water } = \frac{1}{2}(a+b)\\\\\text{Speed of current } = \frac{1}{2}(a-b)[/tex]
Here, a = 21 and b = 3
Therefore,
[tex]\text{Speed in still water } = \frac{1}{2}(21+3) = \frac{24}{2} = 12\\\\\text{Speed of current } = \frac{1}{2}(21-3) = \frac{18}{2} = 9[/tex]
Thus speed of boat in still water is 12 km/hr and speed of current is 9 km/hr
The speed of boat in still water is 12 km/hr as:
Let speed of Boat be 'b' and speed of Current be 'c'.
Distance given is 210 miles.
Therefore speed for downstream = 210 ÷ 10=21 mph
speed for upstream =3mph
Now we can form the two equations as :
i) b+c = 21 ......(i) For downstream
ii) b-c = 3.........(ii) For Upstream
Solving by substitution method :
From equation (ii) c = b - 3 Substitute this value of c in equation
(i) we get b + b - 3 = 21
Therefore b = 12. Now substitute the value of b in any of the equations above (i) or (ii) and get c= 9
b= 12 and c = 9.
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Y is 4 more than the product of 7 and x
Answer:
Let's write this out in an equation.
y = 4 + 7x
The mathematical equation 'Y is 4 more than the product of 7 and x' can be written as 'Y = 7x + 4' where Y is the dependent variable and x is the independent variable. This is a standard form linear equation.
Explanation:The subject of this question is Mathematics, and it appears to be targeted at a Middle School level. The statement 'Y is 4 more than the product of 7 and x' is a mathematical equation that can be written as Y = 7x + 4. Here, '7x' refers to the product of 7 and x, and the '+ 4' indicates that Y is 4 more than this product. It is a linear equation in variable x.
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Type A is 8 feet tall and grows at a rate of 6 inches per year.
Type B is 2 feet tall and grows at a rate of 15 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:
The required time is 8 years.Step-by-step explanation:
Let, it will take x years to be of same height for these trees.
We know that 1 ft = 12 inches.
8 ft = [tex]12\times8 = 96 inch[/tex]. 2 ft = 24 inch.
After x years, the height of type A will be (96 + 6x) inch and the height of type B will be (24 + 15x) inch.
We need find the value of x, for which 96 + 6x = 24 + 15x or, 9x = 72 or, x = 8.
Mark as BRAINLIEST if you are right
Answer:
E
Step-by-step explanation:
7+8+4=19
4/6 + 3/6 + 1/6 = 1 2/6
19 + 1 1/3
20 1/3
A company has a $150 budget to provide lunch for its 20 employees. The options are to provide either roast beef sandwiches, which cost $5 apiece, or tuna sandwiches, which also cost $5 apiece. The company also wants to use the entire budget. Suppose r represents the number of roast beef sandwiches it provides and t represents the number of tuna sandwiches. Which statement is correct?
The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r minus t = 20 and 5 r + 5 t = 150.
The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r + t = 20 and 5 r + 5 t = 150.
The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r minus t = 20 and 5 r + 5 t = 150.
The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r + t = 20 and 5 r + 5 t = 150.
Mark this and return
Answer:
2. The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r + t = 20 and 5 r + 5 t = 150.
Step-by-step explanation:
The total lunch budget of the company = $150
Total number of employees = 20
The cost of 1 roast beef sandwich = $5
The cost of 1 tuna sandwich = $5
r represents the number of roast beef sandwiches provided.
t represents the number of tuna sandwiches provided.
Now, consider the given statements:
Here, total number of sandwiches purchased = Total number of employees
⇒ r + t = 20 .... (1)
Also, as each type of sandwich costs $5.
So, the cost of r roast beef sandwiches = r x ( Cost of 1 beef sandwich)
= r x ( $5) = 5 r
And, the cost of t tuna sandwiches = t x ( Cost of 1 tuna sandwich)
= t x ( $5) = 5 t
Total cost of (r +t) sandwiches = Total Lunch Budget
⇒ 5 r + 5 t = 150 .... (2)
Hence, from (1) and (2) the above situation can be represented as:
r + t = 20
5 r + 5 t = 150
Hence, the company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r + t = 20 and 5 r + 5 t = 150.
Solve for x in the equation x squared + 2 x + 1 = 17.
Answer:
Step-by-step explanation:
x^2 + 2x + 1 = 17
x^2 + 2x = 17 - 1
x^2 + 2x = 16
x^2 + 2x + 1 = 16 + 1
(x + 1)(x + 1) = 17
(x + 1)^2 = 17
x + 1 = sqrt 17
x = -1 (+ - ) sqrt 17
x = -1 + sqrt 17 or x = -1 - sqrt 17 <===
Answer:
x = -1 + square root 17
Step-by-step explanation:
I took the test
Suppose that circles R and S have a central angle measuring 125°. Additionally, circle R has a radius of
2
3
feet and the radius of circle S is
3
4
feet.
If the length of the intercepted arc for circle R is
4
9
π feet, what is the length of the intercepted arc for circle S?
Answer:
The length of the intercepted arc for circle S is (1/2)π ft
goes through (0,0) and is parallel to the y=-5
Answer:
y=0
Step-by-step explanation:
Parallel lines never intersect therefore you need to find what y=-5 would look like on a graph (look at the image for reference, it is the blue line). Because it is a straight line then you just need to find what would make a straight line across the origin, therefore you would have to do y=0 (the red line on the image.)
The reason for putting y=0 or y=-5 is because the y value will ALWAYS stay the same and the x value will continue going on and on, without intersecting.
Tell which quadrant the point (x, y) will be in.
cis negative, yis negative.
Quadrant I
Quadrant IT
Quadrant IV
Quadrant II
Answer:
Look at the picture.
x < 0 and y < 0
Quadrant IIIWhich polynomial is factored completely?
4 (4 x Superscript 4 Baseline minus 1)
2 x (y cubed minus 4 y squared + 5y)
3 x (9 x squared + 1)
5 x squared minus 17 x + 14
Answer:
3x(9x^2+1) or C on edge
Step-by-step explanation:
did the test on edge and i got it right :
The polynomial that is factored completely is 5x^2 - 17x + 14, as it can be fully factored into (5x - 7)(x - 2) using the quadratic formula or factoring by inspection.
Explanation:The question requires us to determine which polynomial is factored completely. We have four options to consider.
4(4x^4 - 1) is not factored completely because the expression inside the parentheses is a difference of squares and can be factored further into (2x^2 + 1)(2x^2 - 1).2x(y^3 - 4y^2 + 5y) is not factored completely because the expression inside the parentheses does not factor further in terms of integer coefficients.3x(9x^2 + 1) cannot be factored further since 9x^2 + 1 is a sum of squares, which is not factorable in the set of real numbers.5x^2 - 17x + 14 is a quadratic equation of the form ax^2 + bx + c. By applying the quadratic formula or through factoring by inspection, we find that it factors completely into (5x - 7)(x - 2).Hence, the polynomial that is factored completely is 5x^2 - 17x + 14.
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Solution please!!!!!
Answer:
All that you would have to do is add 10 more blocks to show that its 10 more than 43
In the figure below, ray was constructed starting from rays and . By using a compass D and G were marked equidistant from E on rays and . The compass was then used to locate a point F, distinct from E, so that F is equidistant from D and G. For all constructions defined by the above steps, the measures of ∠DEF and ∠GEF:
According to the construction described ∠ DEF ≅ ∠GEF by SSS congruence theorem
How to show that the two angles are congruent
Statement Reason
DE ≅ GE given
DF ≅ GF given
EF ≅ FE reflexive property
Δ DEF ≅ Δ GEF SSS congruence theorem
∠ DEF ≅ ∠GEF CPCTC
Is 6(6+x) equivalent to 6x+36
[tex]\text{Hey there!}[/tex]
[tex]\text{Is 6(6 + x) equivalent to 6x + 3?}[/tex]
[tex]\text{Kind of yes, and kind of no}[/tex]
[tex]\text{But in order for you to solve for this equation you have to use the distribute}\\\text{ property}[/tex]
[tex]\text{The distributive property formula is}\rightarrow\text{a(b + c) = a(b) + a(c) = ab + ac}[/tex]
[tex]\text{Let's solve for the equation, shall we?}[/tex]
[tex]\text{6(6 + x)}\\\text{6(6) + 6(x)}\\\text{6(6) = 36}\\\text{36 + 6(x)}\\\text{6(x) = 6x}\\\boxed{\text{\underline{36+6x}}}[/tex]
[tex]\text{36 + 6x}\neq \text{6x+ 36}[/tex]
[tex]\text{So, thus your answer has to be NO}[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
PLEASE HELP < I NEED HELP, TRYING TO MAKE HONOR ROLL
Translate the sentence into an equation.
Five more than the product of a number and 4 is 7.
Use the variable w for the unknown number.
Answer:
5+4w=7
Step-by-step explanation:
Write the polynomial function, in standard form, that has zeros -1, -2, and 3.
Answer:
The sum of the roots of a polynomial is 5/3, the product of the same polynomial is -11. Write the polynomial function in standard form.n:
Answer:
f(x) = x³ - 7x - 6
Step-by-step explanation:
Given that the zeros are x = - 1, x = - 2 and x = 3 then the corresponding factors are
(x + 1), (x +2) and (x - 3)
The polynomial is then the product of the factors, that is
f(x) = (x + 1)(x + 2)(x - 3) ← expand the first pair using FOIL
= (x² + 3x + 2)(x - 3) ← distribute
= x³ - 3x² + 3x² - 9x + 2x - 6 ← collect like terms
= x³ - 7x - 6
Isaac purchased a house for $109,400.00. Every year, Isaac makes improvements so that the value of the house goes up by 3%. Which of the following inequalities can be used to determine the number of years after purchase, t, that the value of Isaac's house will be more than $120,340.00?
The correct inequality is: C. $114,840.00(1 + 0.04)^2 > $115,362.00.
It correctly applies compound interest to determine when the house value exceeds $114,840.00.
To determine the number of years [tex](\( f \))[/tex] after purchase that the value of Isaac's house will be more than $114,840.00, we can use the formula for compound interest.
The formula for compound interest is given by:
[tex]\[ A = P(1 + r)^n \][/tex]
Where:
- A is the future value of the investment/asset.
- P is the initial principal amount (the initial value of the investment/asset).
- r is the annual interest rate (expressed as a decimal).
- n is the number of years the asset is invested for.
In this case:
- [tex]\( P = \$104,400.00 \)[/tex] (the initial value of the house).
- r = 0.04 (the annual rate of increase, which is 4% expressed as a decimal).
- We want to find the value of n when [tex]\( A > \$114,840.00 \)[/tex].
So, the inequality to represent this scenario is:
[tex]\[ \$114,840.00 < \$104,400.00(1 + 0.04)^n \][/tex]
Now, let's compare this inequality with the options provided:
A. [tex]\( \$114,840.00(1 + 0.04)^{n+1} > \$115,362.00 \)[/tex] - This option is incorrect because it uses [tex]\( n + 1 \) instead of \( n \)[/tex] in the exponent.
B. [tex]\( \$114,840.00(0.04)^2 > \$115,362.00 \)[/tex] - This option is incorrect because it uses [tex]\( (0.04)^2 \)[/tex] instead of [tex]\( (1 + 0.04)^n \)[/tex].
C. [tex]\( \$114,840.00(1 + 0.04)^2 > \$115,362.00 \)[/tex] - This option is correct. It uses the correct formula for compound interest and compares it to the threshold value of [tex]\$114,840.00[/tex].
D. [tex]\( \$114,840.00(1 - 0.04)^2 > \$115,362.00 \)[/tex] - This option is incorrect because it uses [tex]\( (1 - 0.04)^2 \) instead of \( (1 + 0.04)^n \).[/tex]
Therefore, the correct inequality is option C:
[tex]\[ \$114,840.00(1 + 0.04)^2 > \$115,362.00 \].[/tex]
Correct question is:
Isaac purchased a house for $104,400.00.
Every year, Isaac makes improvements so that the value of the house goes up by 4% Which of the following inequalities can be used to determine the number of years after purchase, f, that the value of Isaac's house will be more than $114,840.00?
[tex]A. $114,840.00(1+0.04)^r+1 > $115,362.00[/tex]
[tex]B. $114,840.00(0.04)^2 > $115,362.00[/tex]
[tex]C. $114,84000(1+0.04)^2 > $115,362.00[/tex]
[tex]D. $114,84000(1-0.04)^2 > $115,362.00[/tex]
The ____ of Powers property allows you to rewrite xa· xb as xa + b.
Answer:
product
Step-by-step explanation:
Answer:
The Correct Answer is product of powers
Step-by-step explanation:
Which function has the greater rate of change?
Function 1
Function 2
Answer:
Function 1.
Step-by-step explanation:
The rate of change of Function 2 = (18.75 - 14.25)/ (5 - (-1))
= 4.5 / 6
= 3/4 or 0.75.
For Function 1 it is 5/6 or 0.83
So Function 1 has greatest rate of change.
A 30-60-90 triangle has shortest leg 10. The hypotenuse is
Answer:
Hypotenuse = 20
Step-by-step explanation:
As we know that in 30 60 90 triangle
Short leg = X
Hypotenuse = 2X
Perpendicular = X[tex]\sqrt{3}[/tex]
Short leg = X = 10
Hypotenuse = 2X = 10*2 = 20
Final answer:
In a 30-60-90 triangle, the hypotenuse is twice the length of the shortest leg. Therefore, with a shortest leg of 10, the hypotenuse is 20.
Explanation:
The student has asked about the length of the hypotenuse in a 30-60-90 triangle where the shortest leg is given as 10. In a 30-60-90 triangle, the ratios of the sides are 1:√3:2. Since the shortest leg (the one opposite the 30° angle) is known to be 10, we can find the hypotenuse by multiplying the length of the shortest leg by 2.
Thus, the hypotenuse is 20.
To summarize the process, if the shortest leg a is known, then the hypotenuse c is calculated using the formula: c = 2a. Given that a = 10, the calculation would be c = 2 × 10 = 20.
What is 34/8-16/3-14/9=
Answer:
-95/36
Step-by-step explanation: I think that's right.
Which of the graphs below correctly solves for x in the equation −x2 − 3x − 1 = −x − 4?
Graph of quadratic opening downward and linear sloping up to the right. They intersect at point negative 4, negative 2 and point 0, 2.
Graph of quadratic opening upward and linear sloping up to the right. They intersect at point 0, 2 and point 4, 6.
Graph of quadratic opening downward and linear sloping up to the left. They intersect at point negative 3, negative 1 and point 1, negative 5.
Graph of quadratic opening upward and linear sloping up to the right. They intersect at point 2, 0.
Answer:
Graph of quadratic opening downward and linear sloping up to the left. They intersect at point negative 3, negative 1 and point 1, negative 5
Step-by-step explanation:
we have
[tex]-x^{2} -3x-1=-x-4[/tex]
we can separate the expression above into two equations
[tex]y=-x^{2} -3x-1[/tex] ----> equation A
This is a quadratic equation ( vertical parabola) open downward (the leading coefficient is negative)
[tex]y=-x-4[/tex] ----> equation B
This is a linear equation with negative slope (decreasing function).so linear sloping up to the left
The solution of the original expression are the x-coordinates of the intersection point both graphs
using a graphing tool
The intersection points are (-3,-1) and (1,-5)
see the attached figure
Answer: C is the correct choice
Step-by-step explanation:
If each side of the square is 7 units long, how long is the diagonal to the nearest tenth?
I NEED AN ANSWER ASAP
The diagonal of square is 9.90 units long.
Step-by-step explanation:
Given,
Length of each side of square= s = 7 units
Diagonal of square = s√2
Putting s = 7
Diagonal of square = [tex]7*\sqrt{2}[/tex]
Diagonal of square = 7 * 1.414
Diagonal of square = 9.898
Rounding off to nearest hundredth
Diagonal of square = 9.90 units
The diagonal of square is 9.90 units long.
Keywords: square, diagonal
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Answer:
d = 9.9 units
Step-by-step explanation:
The step by step explanation is in the picture below
The width of a rectangle is 4 less than half the length. if l represents the length, which equation could be used to find the width, w?
Answer:
w = I /2 - 4
Step-by-step explanation:
half the length : I /2
4 less than half the length : I /2 - 4
To match the requirements : w= I /2 - 4
How to solve 17=-13-8x
Answer:
Explanation:
add 13 to both sides of the equation.
17+13=−8x.
30=−8x.
divde both sides by −8.
30−8=x⇒x=−308=−154.
As a check.
Step-by-step explanation:
Answer:
Step-by-step explanation:
17 = -13 - 8x....add 13 to both sides
17 + 13 = -13 + 13 - 8x
30 = -8x...now divide both sides by -8
-30/8 = (-8/-8)x
-30/8 = x.....reduce
- 15/4 = x <===