Answer and Step-by-step explanation:
These are the statements that make the question complete:
A. If the base is 24 feet from the wall, the ladder reaches 45 feet up the wall.
B. If the base is 30 feet from the wall, the ladder reaches 40 feet up the wall.
C. If the base is 27 feet from the wall, the ladder reaches 44 feet up the wall.
D. If the base is 14 feet from the wall, the ladder reaches 48 feet up the wall.
Since the ladder leans against a wall, a right angle triangle is formed. Since the ladder is now slant, then it's length becomes the hypothenuse.
The correct statements can be gotten through Pythagoras theorem which says:
A² + B² = C² where C is the hypothenuse and A and B are the other two sides.
Since the hypothenuse is 50, we can test each statement by taking the square of the two sides and add them up, if they are equal to 50² = 2500, then the statement is true.
A. 24² + 45² = 576 + 2025 = 2601 ≠ 2500, therefore it is false.
B. 30² + 40² = 900 + 1600 = 2500, therefore it is true.
C. 27² + 44² = 729 + 1936 = 2665 ≠ 2500, therefore it is false
D. 14² + 48² = 196 + 2304 = 2500, therefore it is true.
From here, statements B and D are true while the rest are all false.
Solve this inequality for x: - 3(x + 3) > 30
Answer:
x<-13
Step-by-step explanation:
−3(x+3)>30
Divide both sides by −3. Since −3 is negative, the inequality direction has changed.
x+3<30/-3
Divide 30 by −3 to get −10.
x+3<−10
Subtract 3 from both sides.
x<−10−3
Subtract 3 from −10 to get −13.
x<−13
Graph for inequality:
In a grid of a backyard, the vertices of a garden are (20, 45), (40, 45), (40, 30), and (20, 30). The coordinates are measured in feet. Find the perimeter of the garden.
it said 14 was wrong so i dont know
Answer:
300 units
Step-by-step explanation:
You did the steps correctly, but you forgot that it does not go by 1s, but goes by 5s. Check your grid!
(I messed up on this too! ^^)
Hope this helps!
Write the equation of the line that passes through the points (4,7) and (8,6). Put
your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
y - 7 = [tex]-\frac{1}{4}[/tex] (x - 4)
Step-by-step explanation:
Find Slope: m = [tex]\frac{y_{2-}y_{1} }{x_{2-}x_{1} }[/tex]
m = [tex]\frac{6-(7)}{8-(4)}[/tex]
m = [tex]\frac{-1}{4}[/tex]
Point Slope Form: y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )
y - 7 = [tex]-\frac{1}{4}[/tex] (x - 4)
Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 28 cards, which was 25% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
Answer:
112
Step-by-step explanation:
28/25%
f(x)=2x^3+ax^2-37x-60
The binomial x-4 is a factor of f(x). Find the value of a.
Given:
The function is
[tex]f(x)=2x^3+ax^2-37x-60[/tex]
The binomial [tex]x-4[/tex] is a factor of f(x).
To find:
The value of [tex]a[/tex].
Solution:
If [tex]x-c[/tex] is a factor of f(x), then [tex]f(c)=0[/tex].
It is given that, [tex]x-4[/tex] is a factor of f(x), then [tex]f(4)=0[/tex].
We have,
[tex]f(x)=2x^3+ax^2-37x-60[/tex]
Substituting x=4, we get
[tex]f(4)=2(4)^3+a(4)^2-37(4)-60[/tex]
[tex]f(4)=2(64)+a(16)-148-60[/tex]
[tex]f(4)=128+16a-208[/tex]
[tex]f(4)=16a-80[/tex]
Now,
[tex]f(4)=0[/tex]
[tex]16a-80=0[/tex]
[tex]16a=80[/tex]
[tex]a=\dfrac{80}{16}[/tex]
[tex]a=5[/tex]
Therefore, the value of a is 5.
h(x) = x^2 + 2 - x
g(x) = 4x + 5
find (h - g) (x/3)
Answer:
x^2 - 15x - 27
---------------------- (Answer C)
9
Step-by-step explanation:
(h - g)(x) is the difference between funcions h and g. Subtract g(x) from h(x) as follows:
x^2 + 2 - x
-(4x + 5)
-------------------
x^2 - 5x - 3 = (h - g)(x)
To find (h - g)(x/3), substitute x/3 for x in x^2 - 5x - 3 = (h - g)(x), obtaining:
(x/3)^2 - 5(x/3) - 3
We must expand this and then combine like terms:
x^2/9 - (5/3)x - 3
The LCD of these three terms is 9. The first term stays as is. The second term becomes (15/9)x. The third term becomes 27/9.
Combining these three terms, all with denominator 9, we get:
x^2 - 15x - 27
----------------------
9
This matches Answer C.
Do the graphs of y=2^x and y=10^x intersect? How many times? Explain. A. Yes; the graphs intersect once at (0, 1). B. Yes; the graphs intersect twice at (0, 1) and (1, 10). C. Yes; the graphs intersect three times at (0, 1), (1, 2), and (1, 10). D. No; the graphs do not intersect.
Solve for 4(3x - y) -2(4y - 5x) =
Answer:22x-12y
Step-by-step explanation:
Can y’all help me with this please will give you the brainliest
Answer and Step-by-step explanation:
A pair of segments that are perpendicular to each other are the line segments:
KI (the letter i) and MJ.
This is because we see that at the intersection T, there a right angle symbol, which means that those 4 angles at the intersection are 90 degrees. When a line meets another line, and it is perpendicular to that line, they form 90 degrees.
So, those line segments are perpendicular.
#teamtrees #WAP (Water And Plant)
Which statement about these triangles is true?
(Image)
A. The dilation is an enlargement
B. The dilation is a reduction
C. It is not a dilation
D. There is not enough information
the answer is D.
there is not enough information
Answer:
d
Step-by-step explanation:
Consider (11 x a) = 11!/a!9! Find the value of a
Answer:
a=√x3x
Step-by-step explanation:
I solved this by combining expressions and isolating the variable a. mabey I did this wrong and this is not what you learned
Can someone please check my answer??!!
¿Me pueden ayudar con esta ecuación? 9 x + (x - 7) = (5 x + 4) - (8 - 3 x) Es que mi profe dice que es 3/2 pero me sale otra cosa... Gracias <3
Responder:
x = 3/2
Explicación paso a paso:
Dada la ecuación
9 x + (x - 7) = (5 x + 4) - (8 - 3 x)
Debemos encontrar el valor de x que satisface la ecuación
9 x + (x - 7) = (5 x + 4) - (8 - 3 x)
Expandir
9x + x-7 = 5x + 4-8 + 3x
Recopile los términos similares;
9x + x-3x-5x = 4-8 + 7
2x = 3
x = 3/2
Responder:
x = 3/2
Explicación paso a paso:
Dada la ecuación
9 x + (x - 7) = (5 x + 4) - (8 - 3 x)
Debemos encontrar el valor de x que satisface la ecuación
9 x + (x - 7) = (5 x + 4) - (8 - 3 x)
Expandir
9x + x-7 = 5x + 4-8 + 3x
Recopile los términos similares;
9x + x-3x-5x = 4-8 + 7
2x = 3
x = 3/2
Por lo tanto, el valor de x que hace que la ecuación sea igual es 3/2
Prove that the square of an odd number is always 1 more than a multiple of 4.
Input note: use 2n +1 as your odd number, and leave your answer in the form
4(...) +1
(4 marks)
Answer:
See explanation.
Step-by-step explanation:
If the odd number is 2n+1 note that n can be any number because any even number plus one will be odd. Let's start by squaring 2n+1 to get:
[tex]4n^2+4n+1[/tex]
Consider xy (x times y). xy is a multiple of both x and y because xy/x = y and xy/y = x. So it doesn't matter what n is it will be a multiple of 4. So now we know that 4n^2 and 4n are both multiples of 4. If we add them together, it will still be a multiple of 4. 2x + 4x = 6x and 6x is still divisible by x.
Now the plus 1 will always make it so it will be one more than a multiple of 4.
2. A landscaper drew a scale drawing of a rectangular yard using the scale, , before beginning to work on the yard.(a) The landscaper plans to put a fence around the entire yard. How many meters of fencing does she need?
Complete question :
A landscaper drew a scale drawing of a rectangular yard using the scale, , before beginning to work on the yard.
(a) The landscaper plans to put a fence around the entire yard. How many meters of fencing does she need? Show your work.
(b) The landscaper plans to create a rectangular garden that is the size of the actual yard. What is the area of the garden?
Answer:
28cm ; 48cm²
Step-by-step explanation:
From the diagram :
Length = 8cm
Width = 6cm
Meters of fencing required :
Perimeter of rectangle :
P = 2(length + Width)
P = 2 (8cm + 6cm)
P= 2(14cm)
P = 28 cm
2.)
Area of rectangle :
Length * width
8cm * 6cm
= 48cm²
HELP A BROTHER OUT PLEASE Which is equivalent to 8s+20t by the distributive property?
Answer:
4(2s +5)
Step-by-step explanation:
.............
Kay's Dessert Shop bakes cookies. The ratio of chocolate chip to sugar cookies baked is always 5 to 2. If she bakes 210 cookies in one day, how many were sugar cookies? 50 points
Answer: 60
Step-by-step explanation:
Given
The ratio of chocolate chip to sugar cookies is 5:2
If she bakes 210 cookies in one day
Suppose she baked x amount of chocolate chips on that day
So, we can write
[tex]\Rightarrow x=\dfrac{2}{5+2}\times 210\\\\\Rightarrow x=\dfrac{2}{7}\times 210=60[/tex]
There were 60 sugar cookies on that day
Can someone help me please and thank you ❤️
Answer:
I think it would be C
He gor A because he thought that since there waz 3 containers that you would just add 2 because there was 3 containers.
Answer:
c
Step-by-step explanation:
❤️
If you had 11 pieces of licorice to share equally among 5 people, how much licorice would each person get?
Answer:
everyone would get 2 and there would be 1 leftover
Step-by-step explanation:
Help me please !!!!!!!!!
13) Are these comparisons TRUE or FALSE? 1/4< 3/4 7/3 > 5/3 2/3 > 2/8
Answer:
They are all correct
Step-by-step explanation:
Answer:
Umm...
Step-by-step explanation:
1/4<3/4 True
7/3>5/3 True
2/3>2/8 True
The value of a car is depreciating
at a rate of 5% per year. In 2015,
the car was worth $32,000. Find
the value of the car in 2018.
Use the coordinates of the labeled point to find the point-slope equation of
the line
Answer:
C.
Step-by-step explanation:
The y-intercept is (0,4) and the slope is -3
So check letter C 4 + 5 = -3(0-3) = 9, it is a true statement
someone please help me
Answer:
AC should be 42
Step-by-step explanation:
35 divided by 7 is 5 same goes with 56 divided by 8 so 6x7 is 42
the Scale factor should be 7:1
Answer:
Line AC's length is 42
Step-by-step explanation:
35 divided by 5 is 7
56 divided by 8 is 7
42 divided by 6 is 7
Isaiah is going to invest $94,000 and leave it in an account for 16 years. Assuming the interest is compounded daily, what interest rate, to the nearest tenth of a percent, would be required in order for Isaiah to end up with $273,000?
Answer:
Step-by-step explanation:
r=6.7
A bakery is makes 120 cookies for St.Patrick's Day. 42% of the cookies have
eprechauns as decorations. How many cookies have leprechaun decorations?
Answer:
50.4 cookies (50 cookies)
Step-by-step explanation:
Make 42% into a decimal = 0.42
0.42x120=50.4
TRANSFORM THE GIVEN QUADRATIC FUNCTION INTO THE FORM y=a(x-h)²+k
1. y=x²+4x+5
Answer:
(x²-2)+1
Step-by-step explanation:
(x²-2)-2²+5
(x²-2)+1
help help i really need it asap
Answer: c
Step-by-step explanation:
Answer:
=0.017+0.00025
=0.01725
=1.725×10^-2
=C
What is the area of the triangle below (in square units)?
1 yd
1 yd
Step-by-step explanation:
The area of a triangle is calculated by multiplying height to the base and that divided by two
1 × 1 ÷ 2 = 1/2 yd^2 or 0.5 y^2
What point would be the reflection across the x-axis for the point, (7,2)?
Answer:-7,2
Step-by-step explanation: It will be because only the X side changes
Answer:
(7,-2)
Step-by-step explanation: