Answer:
[tex](x-3)^{2}+(y+2)^{2}=49[/tex]
Step-by-step explanation:
The center-radius form of the equation of a circle is in the format;
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
with the center being at the point (h, k) and the radius being r units.
We simply plugin the values of the center and radius given in order to determine the equation of the circle;
The equation of the circle with center (3, -2) and radius 7 is;
[tex](x-3)^{2}+(y+2)^{2}=49[/tex]
Answer:
[tex](x-3)^2 + (y+2)^2 = 49[/tex]
Step-by-step explanation:
The general equation of a circle has the following form:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Where the point (h, k) represents the center of the circle and r represents the radius
In this case we know that the center is (3, -2) and the radius is 7.
Therefore:
[tex]h=3\\k = -2\\r=7[/tex]
Finally the equation of the circle is:
[tex](x-3)^2 + (y-(-2))^2 = 7^2[/tex]
[tex](x-3)^2 + (y+2)^2 = 49[/tex]
HelppppppI’m only on #11
Answer:14
Step-by-step explanation:Here h(x) is the function of x.So if you put the value of x in the expression,3x-4, you will get the answer of h(x)
h(x)=3x-4
h(6)=3×6-4
= 18-4
=14
All you need to do is just replace the value ,6 with x..
R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)} Select all numbers that are in the domain. -3 -2 -1 0 1 2
Answer:
[tex]-3,\ -1,\ 1[/tex]
Step-by-step explanation:
You are given the relation
[tex]R=\{(-3,-2),\ (-3,0),\ (-1,2),\ (1,2)\}[/tex]
The domain of the relation are all possible inputs and the range of the relation are all possible outputs. In your case,
inputs are: [tex]-3,\ -1,\ 1;[/tex]outputs are: [tex]-2,\ 0,\ 2.[/tex]So,
the domain is [tex]-3,\ -1,\ 1;[/tex]the range is [tex]-2,\ 0, 2.[/tex]Answer:
-3, -1, and 1
Step-by-step explanation:
hope that helps :)
Classify the figure. Name the vertices, edges and bases.
Answer:
The vertices are E , H , G , F , L , K , J , I
The edges are EH , HG , GF , FE , IF , JG , KH , LE , LK , KJ , JL , IL
The bases are EFGH and LIJK
Step-by-step explanation:
* Lets talk about the figure
- It is a trapezoid prism
- It has two bases ( trapezoid bases )
- It has has four side faces (rectangular faces)
- It has has twelve edges
- It has eight vertices
* lets solve the problem
∵ It has 8 vertices
∴ Their names are:
E , H , G , F , L , K , J , I
∵ It has 12 edges
∴ Their names are:
EH , HG , GF , FE , IF , JG , KH , LE , LK , KJ , JL , IL
∵ It has two bases
∴ Their names are:
EFGH and LIJK
Find the x- and y-intercept of the line. x + 4y = 36 x-intercept is 36; y-intercept is 9. x-intercept is 1; y-intercept is 4. x-intercept is 9; y-intercept is 36. x-intercept is 4; y-intercept is 1.
Answer:
see explanation
Step-by-step explanation:
Given
x + 4y = 36
To find the x- intercept, let y = 0 in the equation and solve for x
x + 0 = 36 ⇒ x = 36 ← x- intercept
To find the y- intercept let x = 0 in the equation and solve for y
0 + 4y = 36 ⇒ y = 9 ← y- intercept
Answer:
x-intercept is 36; y-intercept is 9.
Step-by-step explanation:
Given equation of the line,
[tex]x+4y=36[/tex]
For x-intercept ( the point at which the line intersects the x-axis ),
y = 0,
[tex]\implies x+4(0) = 36[/tex]
[tex]x=36[/tex]
⇒ The value of x-intercept is 36,
Now, for y-intercept( the point at which the line interests the y-axis )
x = 0,
0 + 4y = 36
⇒ y = 9
⇒ The value of y-intercept is 9.
Hence, first option is correct.
What is the solution to this equation?
8x - 5 (x-3) = 18
Answer:
x=1
Step-by-step explanation:
We distribute the negative 5 to x minus three to get 8x-5x+15=18. Then, we cancel out the 15 by subtracting it from both sides. This leaves us with 8x-5x=3. When we subtract, we get 3x=3, and when we divide both sides by 3, we get x=1. Hope this helps :)
Why is money as a store of value useful for business owners?
Answer:
B
Step-by-step explanation:
it is a simple exchange for goods and services because, is stores value for later use.
How many times does the graph of 4x = 32 - x2 cross the x-axis?
0
1
2
Answer:
2
Step-by-step explanation:
4x = 32 - x2 would be much clearer if written as 4x = 32 - x^2. Please use
" ^ " to indicate exponentiation.
Rewrite 4x = 32 - x^2 in the standard form of a quadratic: x^2 + 4x - 32
Then the coefficients are a = 1, b = 4 and c = -32.
Find the discriminant. It is b^2-4ac.
Here, b^2-4ac = 4^2 - 4(1)(-32), or 16 + 128, or 144.
Because the discriminant is positive, we know immediately that this quadratic has two real, unequal roots.
So, the answer to this question is "the graph of 4x = 32 - x^2 cross the x-axis in two places."
Answer:
How many times does the graph of 4x = 32 - x2 cross the x-axis?
2
What are the solutions to the equation?
✔ 4, -8
Step-by-step explanation:
2. Janice is buying paint to paint her new apartment. The store sells paint in one-gallon cans. How accurate does her estimate need to be for the amount of paint needed?
3. A city planner is measuring the distance of one city block. Which unit of measure should she use: 1 mile, 1 meter, inch?
When estimating the amount of paint needed, Janice should strive for an accurate estimate to avoid running out of paint or wasting excess. Factors to consider include the size of the apartment, the type of paint, and the need for multiple coats.
Explanation:When estimating the amount of paint needed, Janice should strive for an accurate estimate to avoid running out of paint or wasting excess. Since the store sells paint in one-gallon cans, it is best to estimate in whole gallons. However, if Janice wants a more precise estimate, she can consider the following factors:
The size of the apartment: She can measure the walls and ceiling to calculate the surface area that needs to be painted.The type of paint: Different surfaces require different amounts of paint. For example, a textured wall may require more paint than a smooth wall.Multiple coats: If Janice plans to apply multiple coats of paint, she should account for the extra paint needed.By considering these factors and making an accurate estimate, Janice can ensure that she buys the right amount of paint for her new apartment.
Find the Value of x.
Answer:
x = 6
Step-by-step explanation:
Since the line segment is an angle bisector then the following ratios are equal
[tex]\frac{42}{78}[/tex] = [tex]\frac{6x-1}{10x+5}[/tex] ( cross- multiply )
78(6x - 1) = 42(10x + 5) ← distribute parenthesis on both sides )
468x - 78 = 420x + 210 ( subtract 420x from both sides )
48x - 78 = 210 ( add 78 to both sides )
48x = 288 ( divide both sides by 48 )
x = 6
Marcy determined that her father's age is four less than three times her age. If represents Marcy's age, which expression represents her father's age?
A. 3x - 4
B. x - 4
C. 4x - 3
D. 4 - 3x
The expression that describes his father's age is A. 3x - 4
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Marcy determined that her father's age is four less than three times her age.
Assuming Marcy's age to be x.
∴ The equation that describes her father's age is (3x - 4).
Learn more about numerical expressions here :
https://brainly.com/question/29199574
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The correct expression that represents her father's age is A.[tex]\(3x - 4\).[/tex]
To arrive at this conclusion, let's analyze the given information:
Marcy determined that her father's age is four less than three times her age. Let's denote Marcy's age as x. According to the statement, her father's age can be expressed as three times Marcy's age minus four years.
Mathematically, this can be written as:
[tex]\[ \text{Father's age} = 3 \times \text{Marcy's age} - 4 \][/tex]
Substituting x for Marcy's age, we get:
[tex]\[ \text{Father's age} = 3x - 4 \][/tex]
Now, let's evaluate the other options to confirm that they are incorrect:
B. x - 4: This expression suggests that the father's age is four years less than Marcy's age, which does not match the given information that the father's age is four less than three times Marcy's age.
C. 4x - 3: This expression indicates that the father's age is three years less than four times Marcy's age, which again does not align with the given information.
D. 4 - 3x: This expression would imply that the father's age is calculated by subtracting three times Marcy's age from four, which is not the relationship described in the problem.
Therefore, the only expression that correctly represents the father's age based on the given information is A. [tex]\(3x - 4\).[/tex]
What is the slope of the line represented by the equation y = – – 5x?
Answer:
-5
Step-by-step explanation:
What is the slope of the line represented by the equation y = – – 5x
The equation of the line is given in slope-intercept form. The slope is simply the coefficient of x in the equation.
The slope of the line is thus -5
Which statement most accurately describes this figure?
Answer:
The statement most accurately describes the figure is AB > DB ⇒ A
Step-by-step explanation:
* Lets describe the figure
- AD intersect EC at point B
- There are two triangles ABE and DBC
- B is the mid-point of EC
- AD bisects EC
- EB = BC
- AE = DC
- m∠AEB = 30°
- m∠DCB = 27°
∵ The measure of angle AEB is greater than the measure of
angle DCB
∴ The opposite side to the angle AEB is longer than the opposite
side of angle DCB
∵ AB is the opposite side to angle AEB
∵ BD is the opposite side to angle DCB
∴ AB is longer than BD
∴ AB > DB
* The statement most accurately describes the figure is AB > DB
Vertical? Supplementary? Right? Complementary?
Answer:
D
Step-by-step explanation:
because we know that angle EOD is less the 90 so that means that it is complementary. For AOB it is the same but we can check by adding 35 plus x plus 90 =180 degrees so 35+90=125 x=180-125=55 so x=55 and 55 is less then 90 so it is a complementary angle.
Can sumone answer this easy question? Please
Answer:
Fraction: 70/100
Decimal: 0.7
Percent: 70%
Answer:
The answer is:
Fraction: 7/10
Decimal: 0.7
Percent: 70
Step-by-step explanation:
There are 70 colored squares and 100 squares in total. The fraction is 70/100, which can be simplified to 7/10.
One way to convert the fraction 7/10 to decimals is to divide the numerator (7) by the denominator (10). That gives you the decimal 0.7.
A way you can convert the decimal to percent is to multiply 0.7 by 100. You get 70%. Also, there are 70 colored squares out of 100, so that equals 70%.
I hope this helped! :)
there is a bag filled with 3 blue, 4 red and 5 green marbles. a marble is taken at random. what is the probability of exactly 1 red?
Answer:
P 1 red) = 1/3
Step-by-step explanation:
We have 12 marbles (3+4+5)
P(red) = red marbles/ total marbles
= 4/12 = 1/3
Answer:
4 / 12 or 1/3
Step-by-step explanation:
The total is 3 blue, 4 red and 5 green marbles which is 12 marbles altogether.
There is exactly 4 marbles out of the 12 marbles that are red so the probability of choosing a red is 4 / 12 or 1/3
What is the range of the discrete finite function?
Answer:
Option D
Step-by-step explanation:
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
In plain English, the definition means:
The range is the resulting y-values we get after substituting all the possible x-values.
How to find the range
1.The range of a function is the spread of possible y-values (minimum y-value to maximum y-value)
2. Substitute different x-values into the expression for y to see what is happening. (Ask yourself: Is y always positive? Always negative? Or maybe not equal to certain values?)
3. Make sure you look for minimum and maximum values of y.
4. Draw a sketch! In math, it's very true that a picture is worth a thousand words.
the sixth grade class from Franklin Middle School is going to the zoo on a field trip. there are 270 students who want to go on the field trip. if the school requires one adult for every 15 students, how many adults will be needed for the field trip?
Answer:
18
Step-by-step explanation:
To find the number of adults required, take the number of students and divide by 15
270/15 =18
We require 18 adults
Answer:
18
Step-by-step explanation:
pls mark me brainiest
Which expression is not a polynomial?
А. 8х^10 + 2х^5
B. 5х^5
C. x^5+2
D. 5х^-1 + 4х^-2
Answer:
D.
Step-by-step explanation:
A term in a polynomial is a single number or a number multiplied by any number of variables. A polynomial is a sum of terms.
The only thing that can be done with variables in a polynomial is to multiply them by numbers or other variables. In a polynomial, you cannot: divide by a variable (have a variable in a denominator), have a root of a variable, have a log of a variable, have a variable as an exponent, etc.
All expressions are polynomials except for D. In D., the negative exponents mean division by variables.
If s(x) = x - 7 and t(x) = 4x7 - X+3, which expression is equivalent to (tºs)(x)?
4(x - 72 - x - 7+3
4(x - 72 -(x-7) + 3
(4x²-x+3)-7
(4x? – x+3)(x-7)
Answer:
4(x - 7)² - (x - 7) + 3Step-by-step explanation:
[tex]s(x)=x-7,\ t(x)=4x^2-x+3\\\\(t\circ s)(x)=t\bigg(s(x)\bigg)-\text{exchange x to }\ s(x)=x-7:\\\\(t\circ s)(x)=4(x-7)^2-(x-7)+3[/tex]
Please help asap
Explain your answer
[tex]12=2\cdot7+1\\12=15[/tex]
[tex]LHS\not=RHS[/tex] so no, it isn't on the line.
If A=30°, a=12, b=28 how many triangles can be constructed?
Check the picture below.
recall the ambiguous SSA case, as the "12" side moves, it ends up with two supplementary angles on the base.
Students are given 3 minutes for each multiple-choice question and 5 minutes for each free-response question on a test. There are 15 questions on the test, and students are given 51 minutes to take it.How many multiple-choice questions are on the test?
Answer:
There are 12 multiple choice
Step-by-step explanation:
Let m = multiple choice
f = free response
f+m = 15 since there are 15 questions
3m+5f = 51 since we have 51 minutes and 3 for multiple choice and 5 for free response
We have 2 equations and 2 unknowns
m+f = 15
3m+5f = 51
Multiply the first equation by -3
-3(m+f) = -3*15
-3m -3f = -45
Add this to the second equation
-3m-3f = -45
3m+5f = 51
---------------------
2f = 6
Divide by 2
2f/2 = 6/2
f = 3
There are 3 free response.
m+f = 15
m+3 = 15
Subtract 3 from each side
m+3-3=15-3
m=12
There are 12 multiple choice
Simplify the expression square root of 15•square17
Step-by-step explanation:
[tex]\sqrt{15}\cdot\sqrt{17}=\sqrt{(15)(17)}=\sqrt{255}\\\\\text{Used}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}[/tex]
Thanks for helping plz lmk asap!
For this case we have by definition, that the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
To find the slope two points are needed through which the line passes:
[tex]m = \frac {y2-y1} {x2-x1}\\m = \frac {8-8} {- 5 - (- 2)} = \frac {0} {- 5 + 2} = \frac {0} {- 3} = 0[/tex]
THE equation is of the form:
[tex]y = b[/tex]
We substitute the y coordinate of the point (2,8)
[tex]8 = b[/tex]
Then, [tex]y = 8[/tex]
Answer:
[tex]y = 8[/tex]
What is the diameter of the circle?
[1] units
ANSWER
The diameter is 8 units.
EXPLANATION
A portion of the y-axis is serving as the diameter of the circle.
The portion of the y-axis that intersects the circle at two points.
We can use these intercepts to find the diameter.
There is a y-intercept at y=2 and y=-6.
The distance between the two intercepts is the diameter of the circle.
[tex] |2 - - 6| = |2 + 6| = 8[/tex]
Therefore the radius is 8 units.
Answer: [tex]diameter=8\ units[/tex]
Step-by-step explanation:
By definition, the radius of a circle is the distance from its center to its edge.
We need to remember that diameter of a circle is twice the radius:
[tex]diameter=2(radius)[/tex]
Then, you can observe in the figure that there are 4 units between the center of this circle and its edge, therefore the radius is:
[tex]radius=4\ units[/tex]
Finally, you need to substitute the radius calculated into the formula [tex]diameter=2*radius[/tex] to find the value of the diameter of this circle. Then, this is:
[tex]diameter=2(4\ units)[/tex]
[tex]diameter=8\ units[/tex]
Select the two values of x that are roots of this equation. (This is for apex by the way)
x^2-5x+5=0
Answer:
Step-by-step explanation:
Find the discriminant, b^2-4ac: Here a = 1, b = -5 and c = 5.
Then the discriminant is (-5)^2-4(1)(5) = 5, and so there are 2 real, different roots. The roots are:
-(-5) ±√5
x = ----------------, which correspond to answers A and C.
2(1)
The roots of the equation will be (5 - √5) / 2 and (5 + √5) / 2. Then the correct options are A and C.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have
The quadratic equation is given below.
x² - 5x + 5 = 0
Then the root of the equation is given as
[tex]\rm x = \dfrac{ - (-5) \pm \sqrt{(-5)^2 - 4*1*5}}{2*1}\\\\x = \dfrac{5 \pm \sqrt{25-20}}{2}\\\\x = \dfrac{5 \pm \sqrt5}{2}\\\\x = \dfrac{5 - \sqrt5}{2}, \dfrac{5 + \sqrt5}{2}[/tex]
Thus, the correct options are A and C.
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
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Julie is in a singing competition and needs an average score of 9.1 to make it to the next round. There are four judges. The first three judges gave scores of 8.8, 9.5, and 9.2.
What equation can you solve to determine the lowest score the fourth judge can give for Julie to move on?
Answer:
Solve the equation
[tex]\displaystyle \frac{8.8 + 9.5 + 9.2 + x}{4} \ge 9.1[/tex],
where [tex]x[/tex] is the minimum score of the fourth judge.
At least 8.9 points.
Step-by-step explanation:
Let the score of the fourth judge be [tex]x[/tex].
The average score is the sum of the four judges' score divided by the number of scores. That is:
[tex]\displaystyle \text{Average Score} = \frac{8.8 + 9.5 + 9.2 + x}{4}[/tex].
The minimum average score needs to be greater than or equal to [tex]9.1[/tex]. In other words,
[tex]\displaystyle \frac{8.8 + 9.5 + 9.2 + x}{4} \ge 9.1[/tex].
Multiply both sides of by four.
[tex]8.8 + 9.5 + 9.2 + x = 4\times 9.1[/tex].
Subtract [tex]8.8 + 9.5 + 9.2[/tex] from both sides of the equation:
[tex]x = 4\times 9.1 - (8.8 + 9.5 + 9.2) = 8.9[/tex].
In other words, the minimum score of the last judge is [tex]8.9[/tex] for Julie to move on.
Thank you guys soo much
Answer:
a. 64 tickets.
b. $11.
Step-by-step explanation:
a.[tex]y[/tex] is given as [tex]37[/tex], and the question is asking for the value of [tex]x[/tex].
Solve this equation with respect to [tex]x[/tex].
[tex]0.50x + 5.00 = 37[/tex].
Subtract 5.00 from both sides of this equation:
[tex]0.50x = 32[/tex].
[tex]\displaystyle x= \frac{32}{0.50} = 64[/tex].
In other words, 64 tickets were purchased.
b.[tex]x = 12[/tex], and the question is asking for the value of [tex]y[/tex].
Replace [tex]x[/tex] with 12 and evaluate the expression [tex]y = 0.50x + 5.00[/tex] for [tex]y[/tex].
[tex]y = 0.50\times 12 + 5.00 = 11.00[/tex].
In other words, $11.00 were spent.
Nancy walks 5 blocks to the right, 3 blocks down, 7 blocks to the left, and 1 block up. Each square's side length is 1 block. What are the coordinates of her new position?
Starting coordinates are (2, -3)
A. (1, 5)
B. (0, -5)
C. (-3, 0)
D. (-6, -3)
E. (-4,-4)
Answer:
The coordinates of her new position are (0 , -5) ⇒ answer B
Step-by-step explanation:
* Lets revise some translation
- If the point (x , y) translated horizontally to the right by h units
then the new point = (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
then the new point = (x - h , y)
- If the point (x , y) translated vertically up by k units
then the new point = (x , y + k)
- If the point (x , y) translated vertically down by k units
then the new point = (x , y - k)
* Now lets solve the problem
∵ Nancy start from position (2 , -3)
- She walks 5 blocks to the right and 3 blocks down
∴ Add x-coordinate by 5 and subtract y-coordinate by 3
∵ The starting position is (2 , -3)
∴ The new position is (2 + 5 , -3 - 3) = (7 , -6)
- She walks 7 blocks to the left and 1 block up
∴ Subtract x-coordinate by 7 and add the y-coordinate by 1
∴ The new position is (7 - 7 , -6 + 1) = (0 , -5)
* The coordinates of her new position are (0 , -5)
Answer:
b
Step-by-step explanation:
a patient is to take 60 mg of an antibiotic on day 1, take 45mg on days 2 and 3, take 30mg on days 4 and 5 and take 15 mg on days 6 and 7. how many total mg will the patient take?
Answer:
240mg
Step-by-step explanation:
The patient takes 60mg the first day, 45mg the second and third day, 30mg the fourth and fifth day and 15mg the sixth and seventh day.
The amount of miligrams the patient will take is the following:
mg = 60mg + 2×45mg + 2×30mg and 2×15mg = 240mg
Then, the patient will take in total 240mg!
Answer: [tex]240 mg[/tex]
Step-by-step explanation:
We need to analize the information provided.
On day 1: [tex]60\ mg[/tex]
On day 2: [tex]45\ mg[/tex]
On day 3: [tex]45\ mg[/tex]
On day 4: [tex]30\ mg[/tex]
On day 5: [tex]30\ mg[/tex]
On day 6: [tex]15\ mg[/tex]
On day 7: [tex]15\ mg[/tex]
Then, to find the total mg the patient will take, we need to add the mg of each day. Therefore:
[tex]Total=60\ mg+45\ mg+45\ mg+30\ mg+30\ mg+15\ mg+15\ mg=240\ mg[/tex]