Answer:
1) Please find the attached drawing of the archway created with MS Excel
2) The y-intercept is (0, 24)
The x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base is 11
The height of the archway at its highest point = 30.25
Step-by-step explanation:
The given function representing the archway is y = -x² + 5·x + 24
1) Please find attached the required drawing of the archway created with MS Excel
2) The y-intercept is given by the point where x = 0
Therefore, we have, the y-value at the y-intercept = -0² + 5×0 + 24 = 24
The y-intercept = (0, 24)
The x-intercept is given by the point where y = 0
Therefore, the x-values at the x-intercept are found using the following equation;
0 = -x² + 5·x + 24
x² - 5·x - 24 = 0
By inspection, we have;
x² - 8·x + 3·x - 24 = 0
x·(x - 8) + 3·(x - 8) = 0
∴ (x + 3) × (x - 8) = 0
Either (x + 3) = 0, and x = -3, or (x - 8) = 0, and x = 8
Therefore, the x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base = The distance between the x-values at the two x-intercepts
∴ The width of the archway at its base = 8 - (-3) = 11
The highest point of the arch is given by the vertex of the parabola, y = a·x² + b·x + c, which has the x-value of the vertex = -b/(2·a)
∴ The x-value of the vertex of the given parabola, y = -x² + 5·x + 24, is x = -5/(2×(-1)) = 2.5
Therefore;
The y-value of the vertex, is y = -(2.5)² + 5×2.5 + 24 = 30.25 = The height of the archway at its highest point
∴ The height of the archway at its highest point = 30.25.
I need help w this ASAP !!!
hmm...let me think a little bit
Step-by-step explanation:
hmmm ..... i dont know so sorry
i am very very sory
work out the number of ham sandwiches Tina had
Answer:
Number of ham sandwiches Tina made = 60
Step-by-step explanation:
Total number of sandwiches = 480
Fraction of total sandwiches which are Tuna = [tex]\frac{3}{8}[/tex]
Therefore, number of Tuna sandwiches = [tex]480\times \frac{3}{8}[/tex]
= 180
Percentage of beef sandwiches = 35%
Therefore, beef sandwiches = [tex]480\times \frac{35}{100}[/tex]
= 168
Ratio of ham sandwiches (h) and cheese sandwiches (c) = 5 : 6
[tex]\frac{h}{c}=\frac{5}{6}[/tex]
[tex]c=\frac{6}{5}h[/tex] ------(1)
Total number of Tuna sandwiches + Total number of beef sandwiches + Total number of ham sandwiches + Total number of cheese sandwiches = 480
180 + 168 + h + c = 480
h + c = 480 - 348
h + c = 132
Substitute the value of c from equation (1),
[tex]h+\frac{6}{5}h=132[/tex]
[tex]\frac{11}{5}h=132[/tex]
[tex]h=\frac{132\times 5}{11}[/tex]
[tex]h=60[/tex]
Therefore, number of ham sandwiches Tina made = 60
5. Biking at a constant rate, Elise travels
35 miles in 7 hours. If she travels at the
same speed, how far will Elise bike in
9 hours?
A 5 mi
B 44 mi
C 45 mi
D 63 mi
Use the integer tiles to evaluate the following expressions. 6 + 3 = 6 + (–4) = 6 + (–6) =
Given:
The expressions are:
[tex]6+3[/tex]
[tex]6+(-4)[/tex]
[tex]6+(-6)[/tex]
To find:
The value of given expression by using integer tiles.
Solution:
We have,
[tex]6+3[/tex]
Here, both number are positive. When we add 6 and 3 positive integer tiles, we get 9 positive integer tiles as shown in the below figure. So,
[tex]6+3=9[/tex]
Similarly,
[tex]6+(-4)[/tex]
Here, 6 is positive and -4 is negative. It means we have 6 positive integer tiles and 4 negative integer tiles.
When we cancel the positive and negative integer tiles, we get 2 positive integer tiles as shown in the below figure. So,
[tex]6+(-4)=2[/tex]
[tex]6+(-6)[/tex]
Here, 6 is positive and -6 is negative. It means we have 6 positive integer tiles and 6 negative integer tiles.
When we cancel the positive and negative integer tiles, we get 0 integer tiles as shown in the below figure. So,
[tex]6+(-6)=0[/tex]
Therefore, [tex]6+3=9, 6+(-4)=2,6+(-6)=0[/tex].
Answer:
1=9
2=2
3=0
Step-by-step explanation:
What is the fraction for the following decimal expansion? 0.16
OA. 1/6
OB. 2/25
OC. 1/3
OD. 4/25
Answer:
D. 4/25Step-by-step explanation:
As,
0.16
= 16/100
= 4/25. [Taking common factor 4 from both 16 and 100]
What is the approximate value of x. Enter only a numeric answer rounded to the nearest tenth
Answer:
14.9 degrees
Step-by-step explanation:
For this problem you can use Tan∅=o/a and solve for the angle:
15.7 / 59 = 0.2661
Then use inverse tangent of 0.2661 to get 14.9.
Select the correct answer.
Each statement describes a transformation of the graph of y= x. Which statement correctly describes the graph of y=x+7?
OA. It is the graph of y=x where the slope is increased by 7.
ОВ. It is the graph of y= x translated 7 units to the right.
Oc. It is the graph of y= x translated 7 units up.
OD. It is the graph of y= x translated 7 units down.
Answer:
Correct Answer is C
since anything after x decides if it goes up or down like +7 goes up -7 goes down i don't know what would be if it goes sideways
write down five numbers so that the mean is 6 the median is 5 and the mode is 4
Answer:
4,4,5,7,10
Step-by-step explanation:
this can be
4,4,5,7,10
5 is in the middle because 5 is median
4 appeared thrice cause it is the mode
and 10 is just there to give us our mean 6 because it is only 30/5 that gives 6 so we have to find 5 numbers whose sum gives 30
Answer:
The 5 numbers can be: 4, 4, 5, 8, 9.
Step-by-step explanation:
In 4, 4, 5, 8, 9. 5 is the median (The middle number).
The mode is 4 because 4 is the most repeated number.
(4+4+5+8+9)/5 is equal to 30/5 which equals 6. So, 6 is the mean.
Hope this helps! :)
represent the following additions on a number line 3+5=8 3+(-5)
Answer:
8 &-2
Step-by-step explanation:
<-------------------------->
-2-1 0 1 2 3 4 5 6 7 8
________________
-2<8 and 8>-2
SOMEONE PLEASE ANSWER THIS PLZZZ
Answer:
.14
Step-by-step explanation:
A|B (or A given B)= A and B/B
So
Walk to school | senior= (walk to school and senior)/Senior
walk to school and senior= 5
senior= 25+5+5= 35
5/35= .14
simplify (-9)×5×6(-3)
[tex]\bf \large \hookrightarrow \:( - 9) \: \times \: 5 \: \times \: 6 \: \times \: ( - 3) \\ \\ \bf \Large \hookrightarrow \: \: \: - 45 \: \times \: ( - 18) \\ \\ \bf \Large \hookrightarrow \: \: 810[/tex]
What is the value of a+b?
A) 110
B) 125
C) 135
D) 145
Please help!!!!
F= P(1 + r)!
Rearrange the formula to highlight the present value.
P=
[tex]\tt\displaystyle\ P(1+r)!= r*(r-1) *(r-2)*(r-3) ..... *1[/tex]
A line has slope 3 and y–intercept 4.
Answer:
1. 4x + y= 3
Step-by-step explanation:
im sure that is the right answer
Rewrite the equation by completing the square.
Answer:
4(x - [tex]\frac{1}{2}[/tex] )² = 0
Step-by-step explanation:
Given
4x² - 4x + 1 = 0 ( factor out 4 from the first 2 terms )
4(x² - x) + 1 = 0
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² - x
4(x² + 2(- [tex]\frac{1}{2}[/tex] )x + [tex]\frac{1}{4}[/tex] - [tex]\frac{1}{4}[/tex] ) + 1 = 0
4(x - [tex]\frac{1}{2}[/tex] )² - 1 + 1 = 0
4(x - [tex]\frac{1}{2}[/tex] )² = 0
PLS HELP TIMED QUESTION (I'll mark brainiest)
Please show work if possible.
Hello,
[tex]sin(45^o)=\dfrac{\sqrt{2} }{2} \\\\sin(45^o)=\dfrac{a}{c} \\\\\dfrac{\sqrt{2} }{2}=\dfrac{a}{6} \\\\a=6*\dfrac{\sqrt{2} }{2}=3\sqrt{2}\\[/tex]
Answer A
what percent of 98 million is 7740
Answer:
Step-by-step explanation:
x : 100 = 7740 : 98 000 000
x = (7740 * 100)/98 000 000
x = 0.007898 %
A percentage is a hundredth of a number Then [tex]\displaystyle\bf \frac{7740}{98\cdot10^6} \cdot100=\frac{387}{49000} \approx 0,00789\%[/tex]
[tex]solve \: this \: \\ \\ 2a + 5b + 7a + 3b - 2a + 3c[/tex]
Answer:
7a + 8b + 3c
Step-by-step explanation:
Group together like terms and simplifyy
Answer:
7a + 8b + 3c
Step-by-step explanation:
2a + 5b + 7a + 3b - 2a + 3c
= 2a - 2a + 7a + 5b + 3b + 3c
= 7a + 8b + 3c
Find x in the kite below
Answer:
x = 110
Step-by-step explanation:
comment if you want explanation
Answer:
Step-by-step explanation:
Graph 3 points on the line y = x+6
Y=x+6
X+y=8
Answer:
We can first, determine two points on the line:
For:
x
=
0
y
=
0
−
6
y
=
−
6
or
(
0
,
−
6
)
For:
x
=
6
y
=
6
−
6
y
=
0
or
(
6
,
0
)
Next, we can plot these two points on the grid:
graph{(x^2+(y+6)^2-0.125)((x-6)^2+y^2-0.125)=0 [-20, 20, -10, 10]}
Now, we can draw a line through the two points to graph the line for the equation:
graph{(x^2+(y+6)^2-0.125)((x-6)^2+y^2-0.125)(y-x+6)=0 [-20, 20, -10, 10]}
What is the length of DK?
A) 8.5
B) 12.7
C) 7.0
D) 3.5
Answer:
A
8.5 is the answer
If you test is going on so
all the best!
I don't exactly understand
Check this link: https://brainly.com/question/12053038
The same question is explained here :).
Hope it helps.
3. Find the equations of the lines that form the sides to the polygon shown below. What type of polygon is it? Explain your reasoning.
Answer: The question is not complete. the figure is attached below.
The polygon is a rectangle.
Step-by-step explanation:
Line 1 goes through (-2, 3)
hence the slope of line 1 = -3/2
Line 2 goes through (0, 3) (2, 0)
hence the slope of line 2 = -3/2
Line 3 goes through (0, 1) (-3, 1)
hence the slope of line 3 = 2/3
Line 4 goes through (3, 0) (0, -2)
Hence the slope of line 4 = 2/3
therefore -3/2 * 2/3 = -1
Line1 + Line3 Line1 + Line4 Line2 + Line3 Line2+Line4
because, the distance between Line1 and Line2 is not equal to that Line3 and Line4.
The polygon is a rectangle polygon.
Recipe ingredients remain jn a constant ratio no matter how many serving are prepared. Which table shows a possible ratio table for ingredients C and Y for the given number of servings
Answer:
The last table (the bottom one)
Step-by-step explanation:
The ingredients having the same ratio means that, for every number of servings, we should have:
Y/X = constant.
So, for the first table when we have 1 serving, the quotient is:
Y/X = 2/1 = 2
when we have two servings:
Y/X = 3/2 = 1.5
The ratios are different.
Then this is not the correct option.
For the second table, when we have 1 serving the ratio is:
Y/X = 2/1 = 2
when we have two servings:
Y/X = 4/2 = 2
when we have 3 servings:
Y/X = 8/3 = 2.66
This is not the correct option.
For the third table:
1 serving:
Y/X = 2/1 = 2
2 sevings
Y/X = 3/2 = 1.5
This is not the correct option.
fourth table:
1 serving:
Y/X = 2/1 = 2
2 servings
Y/X = 4/2 = 2
3 servings
Y/X = 8/4 = 2
Here we can see that the ratio is always the same, then the ratio remains constant.
This is the table that shows a possible ratio for ingredients X and Y,
Let D be the event that a randomly chosen person has seen a dermatologist. Let S be the event that a randomly chosen person has had surgery for skin cancer. Identify the answer which expresses the following with correct notation: The probability that a randomly chosen person has had surgery for skin cancer, given that the person has seen a dermatologist.Select the correct answer below:A. P(D|S)B. P(D AND S)C. P(S) AND P(D)D. P(S|D)
Given:
D be the event that a randomly chosen person has seen a dermatologist.
S be the event that a randomly chosen person has had surgery for skin cancer.
To find:
The correct notation for the probability that a randomly chosen person has had surgery for skin cancer, given that the person has seen a dermatologist.
Solution:
Conditional probability: Probability of A given B is:
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]
Let D be the event that a randomly chosen person has seen a dermatologist.
Let S be the event that a randomly chosen person has had surgery for skin cancer.
Using the conditional probability, the correct notation for the probability that a randomly chosen person has had surgery for skin cancer, given that the person has seen a dermatologist is P(S|D).
Therefore, the correct option is D.
what expression is equivalent to 96+18
Answer:
114
Step-by-step explanation:
114
Find the area of the square whose length is 3.5 inches?
Answer:
[tex]12.25[/tex]
Step-by-step explanation:
Area of square is
[tex] {s}^{2} [/tex]
where s is the side length.
3.5 is s so the answer is
[tex]3.5 {}^{2} = 12.25[/tex]
Answer:
Area = 12.25 square inches
Step-by-step explanation:
[tex]Given \ length \ of \ a \ side \ of \ the \ square = 3.5 \ inches \\ \\Area \ of \ a \sqaure \ = side \times side = 3. 5 \times 3.5 = 12.25 \ in^2[/tex]
Evaluate each of the following. help plz
Answer:
5!= 120
13!= 6227020800
12!/6!= 665280
10!/7! 3!= 120
5(4!)= 120
Step-by-step explanation:
What is the length of the hypotenuse of the right angle triangle, keep your answer to 1 decimal place a is 9cm and b is 13cm
Answer:
15.8cm
Step-by-step explanation:
\sqrt{9^2+13^2} =15.8113883008
15.8cm
Help, someone please lol
Answer:
2x+5x^2=1
2x+5x*5x=1
2x+25x=1
27x=1
1/27=x
Hope This Helps!!!
Answer:
D. 24
Hope it helps!