Answers
The solutions to f(x) = 64 is x = 7 and x = –7.
Solution:
Given data:
[tex]$f(x)=x^{2}+15[/tex] – – – – (1)
[tex]f(x)=64[/tex] – – – – (2)
To find the solutions to f(x) = 64.
Equate equation (1) and (2), we get
[tex]x^2+15=64[/tex]
Subtract 15 from both sides of the equation.
[tex]x^2+15-15=64-15[/tex]
[tex]x^2=49[/tex]
[tex]x^2=7^2[/tex]
Taking square root on both sides of the equation, we get
x = ±7
The solutions to f(x) = 64 is x = 7 and x = –7.
Related Questions
In triangle abc the length of side ab is 19 inches and the length of bc is 28 inches. What is the length of ac
Answers
Without knowing the type of triangle or the values of the angles, we can only provide a possible range of values for side AC of triangle ABC, which is between 9 inches (in case of an acute triangle) and 47 inches (in case of an obtuse or right angled triangle). For accurate calculation, more detail is necessary.
Explanation:The question pertains to determining the length of the side AC in a triangle ABC. Given are the lengths AB and BC so without additional details such as the angle values or the nature of the triangle, we cannot definitively determine the length of side AC. Such a calculation usually requires the use of trigonometric calculations or the Pythagorean theorem which applies only to right triangles. However, we can establish a range for the possible length of side AC.
If the triangle ABC is obtuse or a right triangle with the right angle at point B, the length of AC (AB+BC) could be up to 47 inches (19 inches + 28 inches). On the other hand, if it is an acute triangle, the length of AC (BC-AB) would be a minimum of 9 inches (28 inches - 19 inches). Please provide more details or check if it's a right triangle for a more specific calculation.
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The correct option is D (52 inches) satisfies all conditions of the triangle inequality theorem.
To determine which length of side AC could form a triangle with sides AB = 19 inches and BC = 28 inches, we apply the triangle inequality theorem:
1. Triangle Inequality Theorem:
- For any triangle with sides [tex]\( a \), \( b \),[/tex] and [tex]\( c \)[/tex]:
- [tex]\( a + b > c \)[/tex]
- [tex]\( a + c > b \)[/tex]
- [tex]\( b + c > a \)[/tex]
2. Checking the options:
- Option A: 42 inches
- [tex]\( 19 + 42 = 61 > 28 \)[/tex]
- [tex]\( 19 + 28 = 47 > 42 \)[/tex]
- [tex]\( 42 + 28 = 70 > 19 \)[/tex]
- Valid
- Option B: 7 inches
- [tex]\( 19 + 7 = 26 < 28 \)[/tex]
- Invalid (Does not satisfy [tex]\( AB + AC > BC \)[/tex])
- Option C: 49 inches
- [tex]\( 19 + 49 = 68 > 28 \)[/tex]
- [tex]\( 19 + 28 = 47 < 49 \)[/tex]
- Invalid (Does not satisfy [tex]\( AB + BC > AC \)[/tex])
- Option D: 52 inches
- [tex]\( 19 + 52 = 71 > 28 \)[/tex]
- [tex]\( 19 + 28 = 47 < 52 \)[/tex]
- [tex]\( 52 + 28 = 80 > 19 \)[/tex] Valid
3. Conclusion:
- The lengths of side AC that satisfy the triangle inequality theorem and can form a triangle with sides AB = 19 inches and BC = 28 inches are 42 inches and 52 inches.
The complete question is:
In triangle ABC, the length of side AB is 19 inches and the length of side BC is 28 inches. Which of the following could be the length of side AC? A. 42 inches B. 7 inches C. 49 inches D. 52
Consider a distance and time graph whose y-axis is distance and x-axis is time. What do you know about a runner's motion at the time when a segment of the graph is horizontal?
a) The runner is moving at a steady rate.
b) The runner is slowing down.
c) The runner is speeding up.
d) The runner has stopped.
e) The runner is running very slowly
somebody pleaseee help its due in 9 mins
Answers
Answer:
the answer is d.) the runner stopped
Step-by-step explanation:
because the distance is staying the same but the time is changing wich means the runner isn't moving for a period of time.
is milk souring a chemical or physical change
Answers
Answer:
I believe it would be a chemical change as there would be no way to reverse it
The mean of a distribution is 276, while the median is 231. Which of these
statements is likely to be true about the distribution?
Answers
Answer:
The distribution positively skewed
Step-by-step explanation:
We have the mean of a distribution to be 276, while the median is 231.
When compare the mean and median,
we gave
276>231
Since the mean is greater than the median, the distribution is skewed to the right.
In other words, the the distribution is positively skewed.
Answer:
Positively skewed
Step-by-step explanation:
Kevin will take 4 math tests this term. All of the tests are worth the same number of points. After taking the first 3 tests, his mean test score is 88 points. How many points does he need on his last test to raise his mean test score to 90 points?
Answers
Answer:
Kevin needs 96 points on his last test to raise his mean test score to 90 points.
Step-by-step explanation:
we know that
The mean score is the total of all scores divided by the total number of tests.
Let
x_1 ----> the score in the first math test
x_2 ----> the score in the second math test
x_3 ----> the score in the third math test
x_4 ----> the score in the fourth math test
we have
After taking the first 3 tests, his mean test score is 88 points
so
[tex]\frac{x_1+x_2+x_3}{3} =88[/tex]
[tex]x_1+x_2+x_3=264[/tex] ----> equation A
How many points does he need on his last test to raise his mean test score to 90 points?
so
[tex]\frac{x_1+x_2+x_3+x_4}{4} =90[/tex]
[tex]x_1+x_2+x_3+x_4=360[/tex] ----> equation B
substitute equation A in equation B
[tex]264 + x_4 = 360[/tex]
solve for x_4
[tex]x_4 = 360-264[/tex]
[tex]x_4 = 96[/tex]
Therefore
Kevin needs 96 points on his last test to raise his mean test score to 90 points.
An equiangular triangle can be scalene
Answers
Answer:
No, as a scalene triangle's sides are are different, while an equilateral's sides are all the same.
Hope that helps, :)
Evaluate the logarithm log49 7
Answers
Answer:2
Step-by-step explanation:
Log49 7=Log49/Log7=2Log7/Log7
=2
Type the correct answer in the box. Use a decimal number instead of words.
Find the sum of a finite geometric series.
A ball is dropped from a height of 10 meters. Each time it bounces, it reaches 50 percent of its previous height. The total vertical distance down the ball has traveled when it hits the ground the fifth time is meters.
Answers
2nd-5
3rd-2.5
4th-1.25
5th-0.625
Add all of these together we get 19.375 meters.
I hope this helps!
Is {(-5,1),(4,9),(6,10)} a function
Answers
Help pleaseeeeee. I’m confused. I’ll thank u
Answers
Answer: See Below
Step-by-step explanation:
(b) Make a table of white ovals and black ovals. You will notice that
white starts with 3 and adds 3 to each design → 3 + 3(d - 1) = 3d
black starts with 4 and adds 4 to each design → 4 + 4(d - 1) = 4d
[tex]\begin{array}{c|c|c}\underline{\text{Design \#}}&\underline{\text{white ovals}}&\underline{\text{black ovals}}\\1&3&4\\2&6&8\\3&9&12\\4&3(4)=12&4(4)=16\\5&3(5)=15&4(5)=20\\6&3(6)=18&4(6)=24\\\cdot&\cdot&\cdot\\\cdot&\cdot&\cdot\\\cdot&\cdot&\cdot\\n&3n&4n\end{array}[/tex]
white ovals when design = 30 ---> 3d = 3(30) = 90
black ovals when design = 100 ---> 4d = 4(100) = 400
white ovals when design = 50 ---> 3d = 3(50) = 150
black ovals when design = 50 ---> 4d = 4(50) = 200
TOTAL = 350
**********************************************************************************
(c) Make a table of rods and squares. You will notice that
rods start with 19 and add 12 to each design → 19 + 12(d - 1) = 12d - 7
squares start with 6 and add 4 to each design → 6 + 4(d - 1) = 4d + 2
[tex]\begin{array}{c|c|c}\underline{\text{Design \#}}&\underline{\qquad \text{rods}\qquad }&\underline{\qquad \text{squares}\qquad }\\1&19&6\\2&31&10\\3&43&14\\4&12(4)-7=55&4(4)+2=18\\5&12(5)-7=67&4(5)+2=22\\6&12(6)-7=79&4(6)+2=26\\\cdot&\cdot&\cdot\\\cdot&\cdot&\cdot\\\cdot&\cdot&\cdot\\n&12n-7&4n+2\end{array}[/tex]
rods when design = 15 ---> 12d - 7 = 12(15) - 7 = 173
squares when design = 15 ---> 4d + 2 = 4(15) + 2 = 62
2. What type of transformations moves P (3,-7) to P"(3,7)
Reflection
Rotation
Dilation
None of above
Answers
The type of transformation that moves P (3,-7) to P'' (3,7) is a reflection. The point has been flipped over the x-axis.
Explanation:The type of transformation which moves point
P (3,-7)
to
P'' (3,7)
is a
reflection
. It appears that point P has simply been flipped over the x-axis. The x-coordinate remains unchanged at 3, but the y-coordinate has been reflected to the opposite side of the x-axis, changing it from -7 to 7. So, a reflection over the x-axis is the correct transformation in this case. The transformation that moves point P (3,-7) to P'' (3,7) is a reflection over the x-axis. When a point is reflected in the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. In this case, when the y-coordinate of P changes from -7 to 7, it means that P was reflected over the x-axis.
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Write the quadratic equation in standard form that represents the table below:
20 POINTS IF YOU HELP!
Answers
Final answer:
The quadratic equation in standard form is t² + 14.3t - 20 = 0. It can be solved using the quadratic formula.
Explanation:
The quadratic equation in standard form that represents the given table is:
t² + 14.3t - 20 = 0
Where t represents the variable and the constants are a = 1.00, b = 14.3, and c = -20.0. The solutions to this equation can be found using the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
What is the equation of the line parallel to 3x + 2y = -4 that goes through the point (4, -1)?
Answers
Answer:
y=-3/2x+5
Step-by-step explanation:
3x + 2y = -4
2y=-4-3x /:2
y=-4/2-3x/2
y=-3/2x-2
Slope=-3/2(=m) , because this line is parallel slope is the same, then
y-y1=m(x-x1) ,where
A(4,-1).... x1 =4, y1 =-1
y-(-1)=-3/2(x-4)
y+1=-3/2x+3/2*4
y+1=-3/2x+6
y=-3/2x+6-1
y=-3/2x+5
The park has a circular track with a radius of 7.6 yds. How many whole yards of fencing would they need to purchase to enclose the track? Use = 3.14
Answers
Answer:
48 yards
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=7.6\ yd\\\pi=3.14[/tex]
substitute
[tex]C=2(3.14)(7.6)=48\ yd[/tex]
Answer: 48 yards
Step-by-step explanation:
The circumference of a circle can be calculated with the following formula:
[tex]C=2\pi r[/tex]
Where "C" is the circumference of the circle and "r" is the radius of the circle.
In this case you know that the radius of the circular track is the following:
[tex]r=7.6\ yd[/tex]
Knowing tha radius, you can substitute it into the formula (According to the information given in the exercise, you need to use [tex]\pi =3.14[/tex])
[tex]C=2(3.14)(7.6\ yd)[/tex]
Finally, you need to evaluate.
Therefore, you get that the whole yards of fencing that they need to purchase to enclose the track is:
[tex]C\approx48\ yd[/tex]
Solve fro X -3x + 4 = -8
Answers
Answer:
X = 4
Step-by-step explanation:
Solve for x.
-3x + 4 = -8
Make sure to subtract both sides.
-3x (+4 -4) = -8 - 4
-3x= -12
Divide by -3 on both sides.
-3x/-3 = -12/-3
x = 4Answer:
4
Step-by-step explanation:
-3x + 4 = -8
Subtract 4 from both sides
-3x + 4 - 4 = -8 - 4
-3x = -12
Divide both sides by by -3
x = -12/-3
x = 4
Angle a and angle b are complementary angles. The measure of ∠a is 42°.
Which equation represents this situation with x representing the measure of ∠b ?
A) 90+42=x
B) 42+x=90
C) 42−x=90
D) 90+x=42
Answers
Answer: B) 42 + x = 90
Step-by-step explanation:
A complementary angle always equals 90 degrees. So, with that information, all you have to do is list the measurement of b as x and create an equation. Knowing that the measurement of angle a is 42 degrees, we can now find an equation. So, we would take the measurement of angle a, 42 degrees, and add the measurement of angle b, listed as x, which should equal 90 degrees.
The radius of a circular rug is 5 feet. How much ribbing will you need to buy to go around the
rug? Use 3.14 for pi
Answers
The length around the rug is the circumference.
The formula is C = 2 x PI x r
C = 2 x 3.14 x 5 = 31.4 feet
For this case we must find the perimeter of the circular carpet.
By definition, the perimeter of a circle is given by:
[tex]P = 2 \pi * r[/tex]
Where:
r: It is the radius of the circle
According to the statement we have:
[tex]r = 5 \ ft[/tex]
Substituting:
[tex]P = 2 * 3.14 * 5\\P = 2 * 3.14 * 5\\P = 31.4 \ ft[/tex]
So, you need[tex]31.4 \ ft[/tex]
Answer:
[tex]31.4 \ ft[/tex]
one foot is equal to 1/3 of a yard. What is the decimal equivalent to 1/3? 1.3, 1,
Answers
Answer:
0.33333333333
Step-by-step explanation:
Typing 1/3 in a calculator gives 0.333333333333
Find the values of x and y
Answers
Answer:
x = 12; y = 60
Step-by-step explanation:
The opposite sides of a parallelogram are always equal, so x+3 = 15, making x = 12
The opposite angles of a parallelogram are always equal, making y = 60
what is 2+4 in the world today
Answers
Answer:
i guess it is 6? maybe
Step-by-step explanation:
Answer: I WOULD SAY 24 BUT FOR SOME REASON IT IS 6
Step-by-step explanation:
GIven the equation LaTeX: y=\frac{2}{3}x-1y = 2 /3 x − 1, determine the slope of the line.
Answers
Answer:
The slope of the equation is: [tex]m=\frac{2}{3}x[/tex]
Step-by-step explanation:
Given the equation
[tex]y=\frac{2}{3}x-1[/tex]
As the equation in slope intercept form
[tex]\:y=mx+b[/tex]
Here:
m = slopeb = y - interceptComparing the equation in slope intercept form
[tex]y=\frac{2}{3}x-1[/tex]
so
[tex]m=\frac{2}{3}x[/tex]
Therefore, the slope of the equation is: [tex]m=\frac{2}{3}x[/tex]
Tony needs to ship 12 comedy DVDs, 24 animated DVDs, and 30 musical DVDs. He can pack only one type of DVD in each box and he must pack the same number of DVDs in each box. What is the greatest number of DVDs Tony can pack in each box?
please explain how you found your answer
Answers
The greatest number of DVDs that Tony can pack in each box is 6, which is the greatest common divisor of 12, 24, and 30.
To find the greatest number of DVDs that Tony can pack in each box, we need to determine the greatest common divisor (GCD) of the quantities of each type of DVD. The GCD is the largest number that can evenly divide all the given numbers without leaving a remainder. The numbers of DVDs are 12 (comedy), 24 (animated), and 30 (musical).
Here are the steps to find the GCD:
List the factors of each number:Factors of 12: 1, 2, 3, 4, 6, 12Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30Identify the common factors: 1, 2, 3, 6Find the largest common factor: 6Thus, the greatest number of DVDs Tony can pack in each box is 6.
2) f(x) = x² **
g(x)= 3x – 2
Find f(g(-4)
Answers
Answer:
[tex]f(g( - 4)) = 196[/tex]
Step-by-step explanation:
The functions are;
[tex]f(x) = {x}^{2} [/tex]
and
[tex]g(x) = 3x - 2[/tex]
We want to find
[tex]f(g( - 4))[/tex]
First we find g(-4) to get:
[tex]g( - 4) = 3 \times - 4 - 2[/tex]
[tex]g( - 4) = - 12- 2[/tex]
[tex]g( - 4) = - 14[/tex]
Now
[tex]f(g( - 4)) = f( - 14)[/tex]
This implies that,
[tex]f(g( - 4)) = {( - 14)}^{2} [/tex]
[tex]f(g( - 4)) = {( - 14)} \times - 14[/tex]
[tex]f(g( - 4)) = 196[/tex]
Which transformation(s) affect the horizontal asymptote?
Answers
Answer:
Vertical translations would affect the horizontal asymptote.
Given that two figures are similar, use a scale factor to find the missing length
Answers
The missing length x is 99 m.
Solution:
Given polygons are similar.
If two triangles are similar, then the corresponding sides are in proportion.
[tex]$\Rightarrow\frac{81}{18}=\frac{x}{22}[/tex]
Multiply by 22 on both sides, we get
[tex]$\Rightarrow\frac{81}{18}\times 22=\frac{x}{22}\times 22[/tex]
[tex]$\Rightarrow\frac{9}{2}\times 22=x[/tex]
⇒ 9 × 11 = x
⇒ 99 = x
Switch the sides.
⇒ x = 99
The missing length x is 99 m.
Simplify 4-6+2x-9x-8
Answers
Answer:
x = -10/7
Step-by-step explanation:
Step 1: Combine like terms
4 - 6 + 2x - 9x - 8
-7x - 10
Step 2: Solve for x
-7x - 10 = 0
-7x - 10 + 10 = 0 + 10
-7x / -7 = 10 / -7
x = 10/-7
Answer: x = -10/7
If the sales tax is six 3/4% what is the total cost of a $76.01 item
Answers
the total cost of a $76.01 item is $81.14 .
Step-by-step explanation:
Here we have , sales tax is six 3/4% . We need to find that what is the total cost of a $76.01 item .Let's find out:
Sales tax is actually the extra money we need to give apart from actual cost of item which is given to government or concerned authority .
Tax is 6(3/4)% of cost price i.e.
[tex]Tax = \frac{cost-price(6\frac{3}{4})}{100}[/tex]
⇒ [tex]Tax = \frac{cost-price(6\frac{3}{4})}{100}[/tex]
⇒ [tex]Tax = \frac{(76.01)(6.75)}{100}[/tex]
⇒ [tex]Tax = \frac{513.06}{100}[/tex]
⇒ [tex]Tax = 5.13[/tex]
So, total cost = $76.01 + $5.13
total cost = $81.14
Therefore, the total cost of a $76.01 item is $81.14 .
What is the simplified expression for Negative 2 a squared b + a squared minus 5 a b + 3 a b squared minus b squared + 2 (a squared b + 2 a b)? a squared minus 9 a b + 3 a b squared a squared + 9 a b minus b squared + 3 a b squared 10 a b + a squared minus b squared 3 a b squared + a squared minus b squared minus a b
Answers
Answer:
Its a
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Just did it
8. Chicago, Illinois, has a longitude of 88°W and a latitude of 42°N.
Indianapolis, Indiana, is located at 86°W and 40°N. At this longitude/latitude,
each degree is about 53 miles. Find the distance between Chicago and
Indianapolis.
Chicago, IL
Indianapolis, IN
Lesson 7 Distance on the Coordinate Plane
435
Answers
Answer: 150 miles
Step-by-step explanation:
The distance between Chicago and Indianapolis is approximately 150 miles.
To find the distance between Chicago and Indianapolis using their latitude and longitude coordinates, we can apply the Pythagorean theorem. The distance between two points on the Earth's surface can be approximated by considering the Earth as a flat plane, which is reasonable for relatively short distances like the one between these two cities.
The difference in latitude (north-south distance) between Chicago and Indianapolis is:
[tex]\[ 42N - 40N = 2N \][/tex]
The difference in longitude (east-west distance) between the two cities is [tex]\[ 86W - 88W = 2W \][/tex]
Since each degree is approximately 53 miles, we can calculate the north-south distance and the east-west distance:
North-south distance in miles:
[tex]\[ 2N \times 53 \text{ miles/degree} = 106 \text{ miles} \][/tex]
East-west distance in miles:
[tex]\[ 2W \times 53 \text{ miles/degree} = 106 \text{ miles} \][/tex]
Now, we can use the Pythagorean theorem to find the straight-line distance (the hypotenuse of the right triangle formed by the north-south and east-west distances):
Let [tex]\( d \)[/tex] be the distance between the two cities, then:
[tex]\[ d^2 = (106 \text{ miles})^2 + (106 \text{ miles})^2 \] \\[/tex]
[tex]\[ d^2 = 11236 \text{ miles}^2 + 11236 \text{ miles}^2 \] \\[/tex]
[tex]\[ d^2 = 22472 \text{ miles}^2 \] \\[/tex]
[tex]\[ d = \sqrt{22472 \text{ miles}^2} \] \\[/tex]
[tex]\[ d \approx 150 \text{ miles} \][/tex]
What is the image of Q for a dilation with the center (0,0) and a scale factor of 0.5?
A.) (0.5, 2.5)
B.) (2, 10)
C.) (1, 2.5)
D.) (10, 2)
Answers
Answer: OPTION A.
Step-by-step explanation:
A dilation is defined as a transformation in which the Image (The figure obtained after the transformation) and the Pre-Image (The original figure before the transformation) have the same shape, but they have different sizes.
In this case you know that the dilation is centered at the origin and the scale factor is:
[tex]k=0.5[/tex]
Therefore, the rule is the following:
[tex]Q(kx,ky)[/tex]
You can identify in the figure attached that the point Q is:
[tex]Q(1,5)[/tex]
Therefore, you must multiply its coordinates by the scale factor 0.5 in order to get its Image Q'. This is:
[tex]Q'=(1*0.5,5*0.5)\\\\Q'=(0.5.2.5)[/tex]
Final answer:
The image of point Q for a dilation with a scale factor of 0.5 and center (0,0) is (option A) (0.5, 2.5).
Explanation:
To find the image of point Q, we need to apply the dilation equation: (x', y') = (k * x, k * y), where (x, y) are the coordinates of the original point and k is the scale factor.
In this case, the center of dilation is (0, 0) and the scale factor is 0.5. So, for point Q which has coordinates (x, y), the image coordinates (x', y') will be:
(x', y') = (0.5 * x, 0.5 * y)
Therefore, the image of point Q will be (option A) (0.5, 2.5).