[tex]\bf 3\sqrt{8\frac{1}{4}}~\hfill \stackrel{mixed}{8\frac{1}{4}}\implies \cfrac{8\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{33}{4}} \\\\\\ 3\sqrt{\cfrac{33}{4}}\implies 3\cdot \cfrac{\sqrt{33}}{\sqrt{4}}\implies 3\cdot \cfrac{\sqrt{33}}{\sqrt{2^2}}\implies \cfrac{3\sqrt{33}}{2}[/tex]
please help me . Is the roped off area triangle ABC, a right triangle ?
yes a right triangle is and angle that is a angle at 90 degrees. A quick method if you don't ha protractor to measure is to measure the angle on a piece of paper like a posted note or note card since all the angles are 90 on them then see if they match up.
Answer:
Yes
Step-by-step explanation:
It is a right angle because it is 90 degrees.
Also,you can tell its a right angle because the variables a, b, and c
represent the Pythagorean Theorem which is used for finding missing lengths of a right triangle.
I didnt see the part at the bottom but the explanation for that would be
50+40> 30 True 40 squared + 30 squared= 50 squared
50+30> 40 True or 1600+900=2500
40+30> 50 True 2500=2500
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).
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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 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.
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
triangle EFG in which segment EF measures 3 units and segment FG measures 5 units
In ΔEFG, is it possible for segment GE to measure 6 units?
Answer:
Yes
Step-by-step explanation:
It can be 6 units. The rule relating to the sides of the triangle is that you should be able to add two sides and get a length that is longer than the third side. You usually add the lower two numbers because it basically says that it will work for all sides but, if you're still in doubt you just have to compare the numbers.
For Example
3+5 is greater than 6
5+6 is greater than 3
6+3 is greater than 5.
All of these makes sense so 6 can be a possible answer.
In triangle EFG, it is not possible for segment GE to measure 6 units.
Explanation:No, it is not possible for segment GE to measure 6 units in triangle EFG.
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Since segment EF measures 3 units and segment FG measures 5 units, the sum of these two sides is 8 units, which is less than 6 units. Therefore, segment GE cannot be 6 units long in triangle EFG.
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Every evening jenna empties her pockects and puts her change in a jar. one week she had 38 coins, all of them dimes and quarters. when she added them up she had a total of 6.95Every evening jenna empties her pockects and puts her change in a jar. one week she had 38 coins, all of them dimes and quarters. when she added them up she had a total of 6.95
Answer:
17 dimes, 21 quarters
Step-by-step explanation:
I suppose you want to know how many dimes and quarters she had in her jar.
Let's say x = dimes and y = quarters.
We can make the following 2 equations:
1) x + y = 38 (number of coins in the jar)
2) 10x + 25y = 695 (a number of dimes plus a number of quarters sum up to 695 cents)
From 1), we can isolate y: y = 38 - x, and place that value in the second equation:
10x + 25y = 695
10x + 25 (38 - x) = 695
10x + 950 - 25x = 695, then we subtract 950 on both sides and simplify
-15x = -255
x = 17
So, Jenna had 17 dimes.
y = 38 - x, so y = 38 - 17 = 21
And she had 21 quarters.
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
What is the volume and surface area of a right cylinder with a height of 8 and a base diameter of 10?
Answer: Volume is 628.32
Surface Area is 408.41
Step-by-step explanation:
The formula for the surface area is A=2 π r h + 2πr*r
The formula for Volume is V=πr*rh
Good luck!
describe how the graph of the function is related to the graph of f(x)= x^2. g(x)=x^2-5
Answer:
Translation down 5 units.
Step-by-step explanation:
The - 5 results in a shift of the whole graph down 5 units.
Each value of g(x) is 5 units less f(x).
Answer:
a. Translate down 5 units
Step-by-step explanation:
f(x)= [tex]x^{2}[/tex]g(x)=[tex]x^{2}[/tex] -5So g(x) is the transformed function of f(x)
In this situation, only the parameter c affect the f(x) vertically to have g(x), if:
c > 0 function is translate upc < 0 the function is translate upHere, c= -5
So the function is Translate down 5 units
Hope it will find you well.
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]
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
The volume of the sphere is 500/3 π cubic units. What is the value of the radius, x? 4 units 5 units 8 units 10 units
Answer:
The radius of the sphere is 5 units
Step-by-step explanation:
The volume of the sphere with radius r is given by the formula;
[tex]volume=\frac{4}{3}*\pi*r^{3}[/tex]
The volume of the sphere is given as; 500/3 π cubic units
We substitute this value into the formula and solve for r;
[tex]\frac{500}{3}\pi=\frac{4}{3}*\pi*r^{3}\\\\r^{3}=\frac{500}{4}\\\\r=\sqrt[3]{125}=5[/tex]
Answer:
The correct answer is second option
The radius of sphere = 5 units
Step-by-step explanation:
Points to remember
Volume of sphere = (4/3)πx³
Where 'x' is the radius of sphere.
To find the radius of sphere
We have volume is 500/3 π cubic units
(4/3)πx³ = 500/3 π
x³ = (500/3) * (3/4)
= 500/4 = 125
x = ³√125
x = 5 units
The correct answer is second option
The radius of sphere = 5 units
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
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..
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! :)
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.
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:
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
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.
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.
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
What are the zeros of the quadratic function f(x) = 6x2 + 12x – 7?
Answer:
-6 ± √78\6 [0.47196014..., -2.47196014... = x]
Step-by-step explanation:
The roots [zeros] are the x-values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.
Answer:
x = 1 + √74/6 or x = 1 - √74/6
Step-by-step explanation:
Points to remember
Zeros of a quadratic equation ax² + bx + c = 0
x = [-b ± √(b² - 4ac)]/2a
To find the zeros of given quadratic equation
It is given that,
6x² +12x - 7 = 0
Here a = 6, b = -12 and c = -7
x = [-b ± √(b² - 4ac)]/2a
= [-12 ± √(12² - 4*6*(-7))]/2*6
= [12 ± √(144 +168 )]/12
= [12 ± √312]/12
= [12 ± 2√74]/12
= 1 ± √74/6
x = 1 + √74/6 and x = 1 - √74/6
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]
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]
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 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.
URGENT HELP PLEASE HELP ME!!!!!!!!!))
Shari rolls a pair of dice, numbered 1 to 6, 64 times. How many times can she expect to roll an odd number?
Answer:
About 30
Step-by-step explanation:
1ST: see how many odd numbers are in 1-6 (which is 3)
2nd: Divide 64 by 3 (when rounded it equals around 30)
Sarah needs 3 feet of fabric for a project she is working on, but the store only sells the fabric in meters. One meter of fabric costs $1.20. How much will the fabric cost?
Answer:
$1.10
Step-by-step explanation:
1 ft = 0.3048 m
3 ft = 3 * 1 ft = 3 * 0.3048 m = 0.9144 m
$1.20/m * 0.9144 m = $1.09728
Answer: $1.10
Answer:
$ 1.08
Step-by-step explanation:
1 feet = 12 inches
so, 3 feet = 12 x 3 = 36 inches
1 metre = 40 inches
Cost of 1 m of fabric = $ 1.20
cost of 40 inches of fabric = $ 1.20
Cost of 1 inch of fabric = $ 1.20 / 40 = $ 0.03
Cost of 36 inches of fabric = $ 0.03 x 36 = $ 1.08
Thus, the cost pf 3 feet fabric is $ 1.08
Two race cars,car x an y,are at the starting point of a two km track at the same time.car x and car y make one lap every 60 s and every 80 sec respectively.
How long, in minutes, will it take for the faster car to be 5 laps ahead of the slower car?
To find the time for Car X to be 5 laps ahead of Car Y, we calculate the difference in laps completed per minute (0.25 laps) and divide the target difference (5 laps) by this rate, which gives us 20 minutes.
Explanation:The question asks how long it will take for Car X to be 5 laps ahead of Car Y if Car X makes one lap every 60 seconds and Car Y every 80 seconds. To solve this, we need to find the difference in laps completed by the two cars over time, until Car X is 5 laps ahead. Since Car X is the faster car, it takes one lap less time than Car Y to complete a lap.
First, we find out how many laps Car X completes more than Car Y in one minute:
Laps per minute for Car X: 1 lap/60 seconds = 1/60 laps per second * 60 seconds = 1 lapLaps per minute for Car Y: 1 lap/80 seconds = 1/80 laps per seconds * 60 seconds = 0.75 lapsThe difference in the number of laps per minute is 1 lap - 0.75 laps = 0.25 laps per minute for Car X compared to Car Y.
Next, we calculate the time it will take for Car X to be 5 laps ahead:
5 laps / 0.25 laps per minute = 20 minutesTherefore, it will take 20 minutes for Car X to be 5 laps ahead of Car Y.
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: