Answer:
A
Step-by-step explanation:
Given
x² - 14x = 0
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 7)x + 49 = 0 + 49
(x - 7)² = 49 ( take the square root of both sides )
x - 7 = ± [tex]\sqrt{49}[/tex] = ± 7 ( add 7 to both sides )
x = 7 ± 7 , thus
x = 7 + 7 = 14 or x = 7 - 7 = 0
What is the constant rate of change in the function y=5x?
1/5
x
5
1
Answer:
5
Step-by-step explanation:
The rate of change is the slope
y = 5x
The slope is the constant in front of the x
The constant rate of change is 5
Which of the following is an example of a function
whose graph in the xy-plane has no x-intercepts?
A) A linear function whose rate of change is not
B) A quadratic function with real menos
© A quadratic function with no real xeros
D) A cubic polynomial with at least one real zero
Answer: Option C.
Step-by-step explanation:
A function goes trough the x-axis when f(x) = 0 for some value of x.
For example, when we say that a quadratic function has no real zeros, this means that the determinant is less than zero, so the roots of the equation:
a*x^2 + b*x + c = 0
are complex roots, this means that for the function:
f(x) = y = a*x^2 + b*x + c
there is not a real number x such f(x) = 0
So the correct option is C.
The quadratic function with no real zeros is an example of a function whose graph in the xy-plane has no x-intercepts.
What is x-intercept?The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the x-axis.
The example of a function whose graph in the xy-plane has no x-intercepts has to find out.
X-intercept is the point over the graph where,
[tex]y=f(x)[/tex]
Here, x is the roots of the function.
For no value of x-intercepts, the function become,
[tex]y=0[/tex]
[tex]f(x)=0[/tex]
Here, the zeros and roots are the same, where function become equal to zero.
Thus, the quadratic function with no real zeros is an example of a function whose graph in the xy-plane has no x-intercepts.
Learn more about the x-intercept here;
https://brainly.com/question/8018800
The width of a rectangle is 2 less than twice its length. If the area of the rectangle is 182 cm 2 , what is the length of the diagonal?
Answer:
20.93cm
Step-by-step explanation:
The shape of the solid is rectangle
Area = length × width
But the width (w) = 2 times the length minus 2
W = 2L - 2
A = L × (2L - 2)
Area of the rectangle = 182cm²
A = 2L² - 2L
182 = 2L² - 2L
2L² - 2L - 182 = 0
L² - L - 91 = 0
Solving the equation using quadratic formula,
A = 1, b = -1, c = -91
L = [-b±√(b² - 4ac)]/2a
L = [-(-1) ± √((-1)² - 4*1*(-91))] / 2(1)²
L = [1 ± √(1² + 364)] / 2
L = [1 ± √(365)] / 2
L = (1 ± 19.10) / 2
Note : Since we're working with length, we can't have a negative value as a solution hence we would not test both sides
L = (1 + 19.10) / 2 = 10.05cm
Width = 2L - 2
W = 20.1 - 2 = 18.10cm
Length = 10.05cm
Width = 18.10cm
Diagonal of the rectangle = ?
To find the diagonal, we'll use pythagorean theorem,
A = diagonal
B = length
C = width
a² = b² + c²
a² = (10.05)² + (18.10)²
a² = 110.25 + 327.61
a² = 437.86
a = √(437.86)
a = 20.93cm
The diagonal of the rectangle is 20.93cm
Please help I will mark brainliest
Answer:
1 acute angle
2 acute angle
Step-by-step explanation:
less than 90° acute angle
more than 90° obtuse angle
90° right angle
A box contains cards that are numbered from 1 to 100. What is the probability of randomly selecting a number that is less than 12?
1 / 100
1 /12
11 / 100
12 / 100
Answer:
1/100
Step-by-step explanation:
The box contains 100 cards numbered from 1-100
Since there are 100 cards and one of each number, the probability of pulling 12 is 1/100 like any other card.
Hope it helps!
Answer:
1/100
Step-by-step explanation:
The box contains 100 cards numbered from 1-100
Since there are 100 cards and one of each number, the probability of pulling 12 is 1/100 like any other card.
Hope it helps!
Eric, Cam, and Brooke are playing a game of mini golf on a computer. The computer program for the game stores
objects in terms of x and y coordinates. All coordinate values are in meters.
The players are shooting at the hole, which is located at (3,2). After hitting their initial shots, Eric's golf ball is at
(-6,6), Cam's golf ball is at (8,-6), and Brooke's golf ball is at (10,8).
If the player whose ball is farthest from the hole should shoot next, which player should shoot next?
Answer:
Eric
Step-by-step explanation:
First, we determine the distance of each player to the hole using the distance formula.
Given points [tex](x_1,y_1)$ and (x_2,y_2)[/tex]
Distance[tex]=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Eric
The hole is at (3,2)
Eric's golf ball is at point (-6,6)
Distance=[tex]\sqrt{(-6-3)^2+(6-2)^2}[/tex]
[tex]=\sqrt{(-9)^2+(4)^2}\\=\sqrt{97} \\\approx 9.85[/tex]
Cam
The hole is at (3,2)
Cam's golf ball is at point (8,-6)
Distance=[tex]\sqrt{(8-3)^2+(-6-2)^2}[/tex]
[tex]=\sqrt{(5)^2+(-8)^2}\\=\sqrt{89} \approx9.43[/tex]
Brooke
The hole is at (3,2)
Brooke's golf ball is at point (10,8)
[tex]Distance=\sqrt{(10-3)^2+(8-2)^2}\\=\sqrt{(7)^2+(6)^2}\\=\sqrt{85} \approx 9.22[/tex]
Since Eric's ball is the farthest from the hole, Eric should shoot next.
Answer: Erick
Step-by-step explanation: 9.85
HALF LIFE The half-life of Zn-71 is 2.4 minutes. If one had 100.0 g at the beginning,
how many grams would be left after 7.2 minutes has elapsed?
A: 50.0 grams
B: 100.0 grams
C: 8.5 grams
D: 12.5 grams
Answer:
7.2 / 2.4 = 3 half-lives
(1/2)3 = 0.125 (the amount remaining after 3 half-lives)
100.0 g x 0.125 = 12.5 g remaining
Hope this Helped! :)
The image of a triangle after it has been dilated with a center of dilation at the origin has vertices at A prime(12, –6), B prime(–24, –12), and C prime. If the pre-image of B prime, point B, has coordinates of (–18, –9) and the pre-image of C prime, point C, has coordinates of (–13.5, 18), which statements are true? Check all that apply. The coordinates of C prime are (27, 18). The coordinates of C prime are (–18, 24). The scale factor is 1 and one-third. The scale factor is 1 and one-fifth. The scale factor is Three-fourths. The coordinates of A are (16, –8). The coordinates of A are (9, –4.5).
Answer:
C is (-18, 24)
Scale factor --> 1 1/3
A is (9, - 4 1/2) *4 1/2 is also 4.5
Brainliest please, I need a few more :D
The true statement are; The coordinates of C prime are (–18, 24). The scale factor is 1 1/3 . The coordinates of A are (9, –4.5).
How to find if a pair of figure is not dilated version of each other?Dilation of a figure will leave its sides get scaled (multiplied) by same number.
Thus, suppose if a rectangle is dilated, and its sides were of length = L and width = W, then its dilated version would be having length = Ln, and width = Wn where n is the factor of scaling.
At image B (-24, -12) and pre image B (-18, -9),
we can work out the scale factor by (-24/-18) and (-12/-9) both equal 4/3
Using the scale factor to go from the pre image to the image,
We can find C coordinate by pre image C by the scale factor.
C is (-13.5 x 4/3) and (18 x 4/3)
C is (-18, 24)
So, The scale factor is 4/3, which is the mixed numeral of 1 1/3.
To find the pre image of point A;
A is (12/(4/3)) and (-6/(4/3))
A is (9, - 4 1/2)
Hence, the true statement are;
The coordinates of C prime are (–18, 24).
The scale factor is 1 1/3 .
The coordinates of A are (9, –4.5).
Learn more about dilation here:
https://brainly.com/question/27212783
#SPJ5
3) A box of chocolates contains four milk
chocolates and four dark chocolates. You
randomly pick a chocolate and eat it.
Then you randomly pick another piece.
The first piece is milk chocolate and the
second piece is dark chocolate.
Are the events independent or dependent?
What is the probability?
Answer:
dependent and 2/7
Step-by-step explanation:
dependent because you didn't replace it.
1/2 times 4/7 which is 4/14 which equals to 2/7
Evaluate 6p, when p=4
Answer:
24
Step-by-step explanation:
6(4) = 24
Answer:
24
Step-by-step explanation:
What is the area of the triangle shown below?
Answer:
48
Step-by-step explanation:
Split it into 2 right triangles flip one around and you have a rectangle who's area is equal to 10x6.
a=6
c=2
b=?
Solve for b:
What do the stage directions at the end of the excerpt indicate?
Answer:
The stage direction at the end of an excerpt are used to provide information about how the characters should move or speak on stage.
Answer:
The stage direction at the end of an excerpt are used to provide information about how the characters should move or speak on stage.
Step-by-step explanation:
can someone help me find the area please?
Answer:
The area would be 48 m.
Step-by-step explanation:
need help with this question
Answer:
x=-7,y=10,p=53°,k+w=90°,k=45°,w=45°
Step-by-step explanation:
hope this helps
Sharice buys a vintage video game for $10, then marks up the price 40%. How much did she raise the price?
Answer:
By 4 dollars so the final price is 14$
Step-by-step explanation:
Answer:She raised the price $4.
Step-by-step explanation: Multiply 10 and .40 to get $4.
Can I please get help with this math problem?
Percentages less than 100% definition
Answer:
fractions
Step-by-step explanation:
Answer:
A number or ratio expressed as a fraction of 100
Step-by-step explanation:
Use outside of percentages but reused under 100 when explained.
Steepness of a hill or gradient of a line = rise/run x 100
On a graph the numbers go from 0 for flat, to 100% at 45 degrees, to infinity as it approaches vertical.
Percentage is Tangent of a circle as where it meets it angle it always is intercepted by the circumference or new angle and becomes less than 180 as it forms a leg of a shape, or a side and 1% represents 100 x 0.01000033334% in Radians as another example. we multiply by 100 and get 1 Rad or a 180 degree line. Broadness of usefulness in percentage is the ratio so 1% of a radian can be the decimal above, and 100% of 1 rad = 180/pi =57.2957 We find a semi-circle has an arc length of pi*r and also that it is 180 degrees. From that you can conclude that the number of degrees in a radian is 180/pi and shows 50% of the circle but 100% of 1 radian.
PLEASE HELP
Results of a blood test are normally distributed with a mean of 6.2 and a standard deviation of 1.5. What is the probability that a patient has a blood test result less than or equal to 8.3?
Answer:
91.92%
Step-by-step explanation:
Given that:
Mean (μ) = 6.2, standard deviation (σ) = 1.5
Z score is a measure in statistics to determine the relationship of a measured value with the mean. It is given by the equation:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
To calculate the probability that a patient has a blood test result less than or equal to 8.3, we need to calculate the z score of 8.3
For x = 8.3, the z score is:
[tex]z=\frac{x-\mu}{\sigma}=\frac{8.3-6.2}{1.5} =1.4[/tex]
From the probability distribution table:
P( x ≤ 8.3) = P(z < 1.4) = 0.9192 = 91.92%
What is the area of the regular pentagon with 5 inch sides and an apothem that measures 4.2 inches?
Answer:
43.01m^2
Step-by-step explanation:
[tex]A=\frac{1}{4} \sqrt{5(5+2\sqrt{5}) } a^2\\[/tex]
This is the formula for a pentagon
Answer:52.2in
Step-by-step explanation:
Did it on a test and got it correct
show work please. need asap.
Answer:
129 = QRX
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
49+80 = QRX
129 = QRX
Answer:
129°
Step-by-step explanation:
Exterior angle = sum of interior angles
Angle QRX = 49 + 80
= 129°
please please help! will give brainliest and points!
Which is an example of dependent events?
choosing two socks from a drawer of black and white socks without replacement
choosing two numbered slips from a hat with replacement
rolling a die three times
spinning a spinner two times
Answer:
choosing two socks from a drawer of black and white socks without replacement
Step-by-step explanation:
Dependent events have results that depend on each other. When I take one sock out, there are less socks in the drawer to pick from. The probability of picking a certain sock changes because the number of socks are different when I do not put the sock back. That makes the events dependent.
When I put the sock back, the probability goes back to what it was before I took the sock, and now the results do not depend on each other, so when they are replaced, they are independent
Answer:
choosing two socks from a drawer of black and white socks without replacement
Step-by-step explanation:
choosing two socks from a drawer of black and white socks without replacement are dependent events because the available options for the second selection depends on which colour was the first sock
Find the area of a circle with a diameter of 4.
Either enter an exact answer in terms of or use 3.14 for i and enter your answer as a decimal.
Answer:
12.57
Step-by-step explanation:
help !!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Find the range of the data in the box plot below.
Answer:
Range: 20
General Formulas and Concepts:
Statistics
Range - the difference between the highest and lowest pointStep-by-step explanation:
Step 1: Define
Find values from box-and-whisker plot.
Highest point recorded = 25
Lowest point recorded = 5
Step 2: Find Range
Set up: 25 - 5Subtract: 20which of the following is equivalent to the expression below?
(a²-2b²+3)-(4b²+5)+(3a²+4)
A: 4a²-6b²+12
B: 4a²-6b²+2
C: 4a²+2b²+2
D:4a²+2b²+12
Answer:
4a^2−6b^2+2 so B
Step-by-step explanation:
Question 15
2 pts
The daily caloric intake for a group of women follows a normal distribution with a mean of
1,750 calories and a standard deviation of 200 calories. What is the z-score for a woman
who had a daily intake of 2,100 calories?
2,091
-1.75
1.75
1.09
Question 16
2 pts
What is it called when you get a positive test result for a disease that you do not have?
False Negative
Margin of Error
Accuracy
True Positive
False Positive
Answer:
1. Z = 1.75
2. False Positive
Step-by-step explanation:
1. mean = 1750 calories
standard deviation, sd = 200 calories
value of interest, x = 2,100
z-score is computed as follows:
Z = (x - mean)/sd
Z = (2100 - 1750)/200
Z = 1.75
2. A false positive happens, when a negative case is detected as a positive case
The image shows parallel lines cut by a transversal. The expressions represent unknown angle measurements. What is the value of x?
Answer: 6
Step-by-step explanation:
16x + 4 = 15x + 10
X = 6
Whats 67 + 90 + (40 x 6)
Answer:
397
Step-by-step explanation:
67 + 90 + (40 x 6)
PEMDAS
Parentheses first
67 + 90 + 240
Then add
157+240
397
I AM GIVING BRAINLIEST
A pan has an original price of $32 but is marked down by 15 percent. Which equation shows the new price of the pan?
Answer:
The first choice is correct
Step-by-step explanation:
$32.00 x 15% = 4.80. 32.00-4.80=27.20. Another way to work it is the first choice, subtracting 15% from 100% and then multiplying 85% by $32.00. Same answer
What is the distance between the points (0,5) and (8,0)?
Please help ASAP! I NEED VERIFIED ANSWER AND EXPLANATION! THIS DEPENDS ON MY GRADE! I WILL BE MARKING BRAINLIEST ANSWER!!
Answer:
[tex]\sqrt{89}[/tex]
Step-by-step explanation:
distance = [tex]\sqrt{(x_{2}- x_{1})^{2} + { (y_{2} - y_{2} } ){^2} }[/tex]
Let:
(x₁ , y₁) = (0 , 5)
(x₂ , y₂) = (8 , 0)
Plug in the corresponding numbers to the corresponding variables:
Remember to follow PEMDAS. Solve the parenthesis first:
distance = [tex]\sqrt{(8- 0)^{2} + { (0 - 5 } ){^2} }[/tex]
distance = [tex]\sqrt{(8)^2 + (-5)^2}[/tex]
Solve for the powers next:
distance = [tex]\sqrt{(8)^2 + (-5)^2}[/tex]
distance = [tex]\sqrt{64 + 25}[/tex]
Simplify:
distance = [tex]\sqrt{64 + 25}[/tex]
distance = [tex]\sqrt{89}[/tex]
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