Answer:
-21.
Step-by-step explanation:
x^2 + 4x - 21 = 0
To factor this we need 2 numbers whose sum id + 4 and whose produce is -21.
These are - 3 and + 7 , so the factors are:
(x - 3)(x + & = 0
x = 3, -7.
Final answer:
The product of the solutions for the quadratic equation x² + 4x - 21 = 0 is -21, as per Vieta's formulas, which states that the product is c/a.
Explanation:
The question is asking for the product of the solutions of a quadratic equation, specifically x² + 4x - 21 = 0. In the context of the quadratic formula, a = 1, b = 4, and c = -21. The quadratic formula is given by x = [-b ± √(b² - 4ac)] / (2a). However, to find the product of the roots, we can apply Vieta's formulas, which states that the product of the roots of a quadratic ax² + bx + c = 0 is c/a.
For the equation in question, the product of the roots would be c/a = (-21)/1 = -21. This is a straightforward application of a standard property of quadratic equations. Therefore, we don't need to find the individual roots to answer the question about their product, saving time and effort.
Which is the best description of the graph of the function f(x)=60(1/3)^x?
Answer:
what do you mean the best description?
Step-by-step explanation:
Answer:
: the graph has an initial value of 60, and each successive term is determined by multiplying by 1/3
Step-by-step explanation:
f(xequal 6 [1/nitial value x=0, f(x) = 60*[1/3]^0 = 60*1 = 60x=1 ⇒f(1) = 60*[1/3]x=2 f(2) = 60*[1/3]^2 = f(1) * [1/3]x = n f(n) = 60*[1/3]^n=60*[1/3]^(n-1)*[1/3] = f(n-1)*[1/3]
Help, can anybody solve the below
Answer:
1) -3/4
2) 2/3
3) -4/5
4) -1/4
13) 2
14) 0
15) -2/3
16) -3
hope this helps
A room is 12 feet wide. A scale model of the room has a scale of 1 in = 6 ft. What is the width
of the room in the model?
A:6 in
B:2ft
C:1ft
D:2in
Final answer:
To determine the room's width in a scale model, use the scale conversion ratio of 1 in = 6 ft. The width in the model is calculated to be 2 inches.
Explanation:
A room is 12 feet wide. A scale model of the room has a scale of 1 in = 6 ft,
To find the width of the room in the model, we use the scale conversion ratio: 1 inch on the model represents 6 feet in reality. Since the room is 12 feet wide, the width in the model would be 2 inches (12 feet ÷ 6 feet per inch = 2 inches).
Parallel lines e and f are cut by transversal b.
Horizontal and parallel lines e and f are cut by transversal b. At the intersection of lines b and e, the uppercase right angle is (2 x + 18) degrees. At the intersection of lines b and f, the top right angle is (4 x minus 14) degrees and the bottom right angle is y degrees.
What is the value of y?
16
50
130
164
Answer:
130
Step-by-step explanation:
e // f
2x + 18 = 4x - 14
2x = 32
x = 16
y = 180 - (4x - 14) = 180 - (64 - 14) = 130
Using the congruency of the top-right angles, it is found that the value of y is of 130.
---------------------
When two parallel lines are cut by a transversal, the top-right angles are congruent, that is, they have the same measure.In this question, their measures are of (2x + 18)º and (4x - 14)º. Thus, with this, we can find x:[tex]4x - 14 = 2x + 18[/tex]
[tex]2x = 32[/tex]
[tex]x = \frac{32}{2}[/tex]
[tex]x = 16[/tex];
Thus, the measure of the top right angles is given by, in degrees: [tex]4x - 14 = 4(16) - 14 = 64 - 14 = 50[/tex]---------------------
The top-right and the bottom-right angles are supplementary, that is, the sum of their measures is 180º.The measure of the top-right angle is of 50º.The measure of the bottom-right angle is of y.Thus:
[tex]y + 50 = 180[/tex]
[tex]y = 130[/tex]
The value of y is of 130.
A similar problem is given at https://brainly.com/question/16368729
Name the quadrilateral with the most specific name that will describe it.
A) parallelogram
B) isosceles trapezoid
C) square
D) rectangle
Answer: a) parallelogram
Step-by-step explanation:
Top side and bottom side are same lengths/parallel
Angles in a quadrilateral add up to 360 degrees
105+75*2=360
Final answer:
The most specific name for the quadrilateral described is a (C) square because it has equal sides and all right angles, which is more specific than a rectangle, isosceles trapezoid, or a parallelogram.
Explanation:
The question asks to name the quadrilateral with the most specific name. The answer is (C) square. A square is a special type of rectangle with all sides of equal length, which is itself a type of parallelogram. A square is more specific than a rectangle, isosceles trapezoid, or a generic parallelogram because a square has all the properties of these shapes but also has equal sides and all right angles.
the table represents the cost of buying a small piece of land in a remote village since the year 1990
Answer:Linear
Step-by-step explanation:
8. What is the maximum number of
right angles a triangle can have?
Answer:
1
Step-by-step explanation:
180 = 90 + 90 (F)
you must have 3 angles
Answer:
One.
Step-by-step explanation:
A triangle can only have one right angle because all three angles of a triangle MUST add up to be 180 degrees. That means if there are two right angles then the answer would automatically be over 180.
Example:
90+90+1=181
Therefore, a triangle can only have one right angle
In a circle, a chord of 50 cm bisects a chord of 40 cm. Find the length of the longer segment of the 50 cm chord.
Answer:
The length of the longer segment of the 50 cm chord = 40
Step-by-step explanation:
let the length of the longer segment of the 50 cm chord = x
so, the other segment = 50 - x
A chord of 50 cm bisects a chord of 40 cm
using the Intersecting Chords Theorem
so, x(50-x) = 20 * 20
50x - x² = 400
x² - 50x + 400 = 0
(x - 40)(x - 10) = 0
x = 40 or x = 10
So, the the length of the longer segment of the 50 cm chord = 40
Answer:
23cm
Step-by-step explanation:
In the circle below, AB, CD, and EF are the chords of the circle. Chord CD is the diameter of the circle.
= 2√ (142−82)
= 2√ (196 − 64)
= 2√ (132)
= 2 x 11.5
= 23
The rule is applied to ΔFGH to produce ΔF"G"H".
What are the coordinates of vertex F" of ΔF"G"H"?
(4, –1.5)
(4, –0.5)
(–1.5, 4)
(–0.5, 4)
ITS TIMED. I REALLY NEED HELP!!!
Answer:
(4, –1.5)
Step-by-step explanation:
What should Maya do first?
Maya is solving the quadratic equation by completing the
square.
4x2 + 16x + 3 = 0
Isolate the variable x2
Subtract 16x from both sides of the equation.
Isolate the constant.
Factor 4 out of the variable terms.
Answer:
Its C
Step-by-step explanation:
edge 2021
Maya should first isolate the variable [tex]\( x^2 \)[/tex] before completing the square.
The steps to solve the quadratic equation [tex]\( 4x^2 + 16x + 3 = 0 \)[/tex] by completing the square are as follows:
1.*Isolate the variable - To do this, Maya should move the constant term to the other side of the equation by subtracting 3 from both sides:
[tex]\[ 4x^2 + 16x = -3 \][/tex]
2. Factor out the coefficient of -The coefficient of x² is 4. Factor out 4 from the terms involving x
[tex]\[ 4(x^2 + 4x) = -3 \][/tex]
3. Complete the square To complete the square, Maya should add the square of half the coefficient of x t both sides of the equation. Half of 4 is 2, and [tex]\( (2)^2 = 4 \),[/tex]so she should add 4 to both sides:
[tex]\[ 4(x + 2)^2 = 1 \][/tex]
After completing these steps, Maya can proceed to solve the equation by isolating x and taking the square root.
A new statue with a circular base is being unveiled in a downtown park. The statue's base has a radius of 15 feet. What is the area of the base? Round your answer to the nearest whole number. Use 3.14 for π.
The area of the circular base is 707 square feet, calculated using the formula A = πr², where π is 3.14 and the radius is 15 feet.
Explanation:The question asks for the area of a circular base of a statue with a given radius. This is a question of geometry, and the formula for the area of a circle is A = πr², where A represents the area and r represents the radius. In this case, the radius given is 15 feet.
To calculate the area, we insert the value of the radius into the formula, so it becomes A = π(15)². Since we are asked to use 3.14 for π, the calculation becomes: A = 3.14 * 15², which equals 706.5 square feet.
However, since we have been asked to round to the nearest whole number, the final answer would be 707 square feet.
To find the area of the circular base of the statue, we can use the formula A = πr^2, where A is the area and r is the radius. In this case, the radius is given as 15 feet. Plugging this value into the formula, we get:
A = 3.14 * 15^2 = 3.14 * 225 = 706.5 square feet
Rounding to the nearest whole number, the area of the base is approximately 707 square feet.
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9-2: MathXL for School: Practice & Problem Solving KT EDIT
Assignment is past due
9.2.10
Question Help
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement
"And" probabilities can always be determined using the formula P(A and B)=P(A)- P(B).
Choose the correct answer below.
O A. This statement is false, "And" probabilities can only be determined using the formula P(A and B)=P(A). P(BIA).
O B. This statement is false. "And probabilities can be determined using the formula P(A and B) = P(A). P(B) only if A and B are independent. Otherwise, they
can be found using the formula P(A and B)=P(A). P(BIA).
O C. This statement is true.
O D. This statement is false, "And" probabilities can always be determined using the formula P(A and B) = P(A) + P(B).
Answer:the way you put this answer is not readable sorry.
Step-by-step explanation:
The statement is false; the formula to determine "And" probabilities varies depending on whether events are independent or dependent.
Explanation:The statement "And" probabilities can always be determined using the formula P(A and B) = P(A) - P(B) is false. The correct method to determine the probability of two events A and B occurring together, also known as the conjunction, depends on whether the events are independent or dependent. If A and B are independent, the formula is P(A and B) = P(A) × P(B). However, if A and B are dependent, you must use the formula P(A and B) = P(A) × P(B|A), where P(B|A) represents the conditional probability of B given that A has already occurred.
consider the following pair of equations:
x + y = -2
y= 2x + 10
if the two equations are graphed at what point do the lines representing the two equations intersect
Answer:
The lines representing these equations intercept at the point (-4,2) on the plane.
Step-by-step explanation:
When we want to find were both lines intercept, we are trying to find a pair of values (x,y) that belongs to both equations, which means that it satisfies both equations at the same time.
Therefore, we can use the second equation that gives us the value of y in terms of x, to substitute for y in the first equation. Then we end up with an equation with a unique unknown, for which we can solve:
[tex]x+y=-2\\x+(2x+10)=-2\\x+2x+10=-2\\3x+10=-2\\3x=-2-10\\3x=-12\\x=\frac{-12}{3} \\x=-4[/tex]
Next we use this value we obtained for x (-4) in the same equation we use for substitution in order to find which y value corresponds to this:
[tex]y=2x+10\\y=2(-4)+10\\y=-8+10\\y=2[/tex]
Then we have the pair (x,y) that satisfies both equations (-4,2), which is therefore the point on the plane where both lines intercept.
5. A bag contains 4 green marbles and 5 white marbles. Suppose a marble is
randomly selected. What are the odds in favor of picking a white marble?
A 4 to 5
OB 5 to 4
c 4 to 9
D
5 to 9
Answer:
d
Step-by-step explanation:
Mr. Key just his phone bill for the year. The total cost of the bill was $120
What is the unit rate that he paid each month?
O
$12/month
$10/month
O
$1440/year
O
$1/month
Answer:
$10/month
Step-by-step explanation:
Ms. Johnson skates 19.7 miles in 2.8 hours. Estimate her speed in miles per hour.
Answer: 7.04mph
Step-by-step explanation:
[tex]d=19.7mi\\t=2.8h\\v=?[/tex]
Formula:
[tex]d = v*t\\v=\frac{d}{t}\\v=\frac{19.7mi}{2.8h}\\ v=7.04mph[/tex]
The selection from Tales From the Odyssey is told like a short story, not a traditional epic. If it were a traditional epic, what would be true about it?
A. It would be a long poem about heroes.
B. It would be a made-up tale about a war.
C. It would be a factual account of a historical event.
D. It would be a series of poems about imaginary characters.
Extra points! And will mark brainliest
Answer:
I think the answer is A
Step-by-step explanation:
Most Epics are long poems about heroes.
A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 1,808.64 square feet? Use 3.14 for pi.
Answer:
The sprinkler can spread water in a radius of 24 feet.
Step-by-step explanation:
Since the sprinkler sends water in a circular pattern in order to find the distance at which it can spread the water we need to find the radius of the circle. The area of the circle is said to be 1808.64 and it's formula is given by:
area = pi*r²
1808.64 = 3.14*r²
r² = 1808.64/3.14 = 576
r = sqrt(576) = 24 feet
The sprinkler can spread water in a radius of 24 feet.
Drag the correct steps into order to solve the equation -7x + 14 = 56 for x.
Answer:
-7x + 14 = 56
Subtract 14 both sides
-7x + 14 - 14 = 56 - 14
-7x = 42
Divide both sides by -7
(-7x)/(-7) = 42/(-7)
x = -6
To solve for x, you need to isolate/get the variable "x" by itself in the equation:
-7x + 14 = 56 Subtract 14 on both sides
-7x = 42 Divide -7 on both sides to get "x" by itself
x = -6
what is the slope between the points (4,-1) and (-4,3)?
The formula for slope is [tex]\frac{rise}{run} = \frac{y2-y1}{x2-x1}[/tex].
Subtract y1 from y2. (y1= -1, y2 = 3)
3 - -1 = 4
Now subtract x1 from x2. (x1 = 4, x2 = -4)
-4 -4 = -8
Divide the difference between the y coordinates by the difference between the x coordinates.
[tex]\frac{4}{-8}[/tex] or 4 ÷ -8 = -0.5
Answer:The slope between the two points is -0.5.
Hope this helps love :)
The senior class had 100 T-shirts to sell to raise money. They sold 52 T-shirts at $7.75 each. Then they sold the rest for $9.25 each. How much money did they collect overall?
$775.00
$847.00
$925.00
$853.00
Answer:
$847.00
Step-by-step explanation:
First you multiply 52 by $7.75
This gives you $403
Then you subtract 52 from 100 to find the remainder of shirts
This gives you 48
So then you multiply 48 by $9.25
This gives you $444
Then you add $444 and $403 giving you $847.00
Answer:
The answer is B: 847
Step-by-step explanation:
52 x 7.75 = 403
100 - 52 = 48
48 x 9.25 = 444
444 + 403 = 847
is 4 pounds greater than 96 ounces
Answer:
No
Step-by-step explanation:
there are 16 ounces in a pound. 4*16 is is 62.
How many whole numbers are there with not more than 4 digits?
Answer:
Step-by-step explanation:
There are 9,999 positive whole numbers with 4 or less digits and 9,999 negative whole numbers with 4 digits or less and 1 whole number which is neither positive nor negative {0}. This gives us 9,999 + 9,999 + 1 or 19,999 whole numbers composed of 4 digits or less.
Answer:
19999
i think its 19999 because Zero does not have a positive or negative value. However, zero is considered a whole number, which in turn makes it an integer, but not necessarily a natural number. ... They have to be positive, whole numbers. Zero is not positive or negative.
hope this helps
What is the surface area of the rectangular pyramid below?
A rectangular pyramid. The rectangular base has a length of 18 feet and width of 10 feet. 2 triangular sides have a base of 18 feet and height of 14.1 feet. 2 triangular sides have a base of 10 feet and height of 16 feet.
386.9 ft2
593.8 ft2
639.4 ft2
1,053.2 ft2
Answer:
B - 593.8 ft2
Step-by-step explanation:
I also just finish the quiz and got the question right.
To find the base: 10 x 18 = 180
There are 4 lateral face, two each are conguent:
18 x 14.1 = 253.8
253.8 divided by 2 = 126.9
126.9 x 2 = 253.8
Other conguent sides:
10 x 16 = 160
160 divided by 2 = 80
80 x 2 = 160
Finally: 180 + 253.8 + 160 = 593.8 ft2
The required surface area of the rectangular pyramid is 593.8 ft². Therefore, the correct answer is option B.
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
As mentioned in the question, the rectangular pyramid has a rectangular base with dimensions of 18 ft by 10 ft, and four triangular faces. Two of the triangular faces have a base of 18 ft and a height of 14.1 ft, while the other two have a base of 10 ft and a height of 16 ft.
The area of the rectangular base is:
18 ft × 10 ft = 180 ft²
The area of each of the triangular faces is:
(1/2) × base × height
For the first two triangles:
(1/2) × 18 ft × 14.1 ft = 126.9 ft² each
For the second two triangles:
(1/2) × 10 ft × 16 ft = 80 ft² each
The total surface area of the rectangular pyramid is:
180 ft² + 126.9 ft² + 126.9 ft² + 80 ft² + 80 ft² = 593.8 ft²
So, the surface area of the rectangular pyramid is 593.8 ft². Therefore, the correct answer is option B.
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The label on a jacket said it was 80% wool, 14% nylon, and x% other fibers. What is the value of x?
Answer:
6%
Step-by-step explanation:
80%-14%=x%
every % = %
80%-14%=94%
100%-94%=6%
Answer:
6%
Step-by-step explanation:
80% + 14= 94.
94 is 6 digits away from 100, so the answer is 6%.
Look at the following graph of the given equation. Determine whether the equation is a function. Explain why or why not.
y = 2 x + 2
On a coordinate plane, points are at (negative 1, 0), (0, 2), (1, 4), (2, 6).
Answer:
Yes this is a function
Step-by-step explanation:
y = 2x + 2
0 = 2(-1) + 2
0 = -2 + 2
0 = 0
Yes
2 = 2(0) + 2
2 = 0 + 2
2 = 2
Yes
4 = 2(1) + 2
4 = 2 + 2
4 = 4
Yes
6 = 2(2) + 2
6 = 4 + 2
6 = 6
Yes
The equation y = 2x + 2 is a function, because each 'x' value corresponds to a single 'y' value, as per the mathematical definition of a function.
The graph of the equation y = 2x + 2 does indeed represent a function. In mathematics, a function is defined as a relation in which each input (or 'x' value) corresponds to exactly one output (or 'y' value). In the given coordinate pairs, you will notice that each individual 'x' value (such as -1, 0, 1, and 2) corresponds to a single 'y' value. Furthermore, the equation itself, y = 2x + 2, will always yield a single 'y' value for each 'x' value you substitute into it. This aligns with the definition of a function. Hence, the equation y = 2x + 2 is a function.
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Consider the quadratic function fx=x2-8x-4. What is the value of the leading coefficient
Answer:
1
Step-by-step explanation:
Given
f(x) = x² - 8x - 4
The leading term in the expression is x²
with a coefficient of 1 ← leading coefficient
The leading coefficient of a quadratic function of equation fx=x2-8x-4 is 1.
The leading coefficient of a quadratic function is the coefficient of the x² term. In the quadratic function f(x) = x² - 8x - 4, the leading coefficient is 1 because the coefficient of x² is always assumed to be 1 when not explicitly shown.
The roots of the function f(x) = x2 – 2x – 3 are shown. What is the missing number?
x = –1 and x = ____
Answer:
x = -1 and x = 3
Step-by-step explanation:
x² – 2x – 3 = (x - 3) (x + 1) = 0
x = 3 or x = -1
Answer:
The roots of the function f(x) = x2 – 2x – 3 are shown. What is the missing number?
x = –1 and x = 3
Step-by-step explanation:
What is the cube root of b^27
Answer:
b^9
Step-by-step explanation:
We can only subtract or add roots to each other but if we are cubing we can divide them by 3.
How many solutions are there to the equation below?
13x + 195 = 13(x+15)
O
A. 1
OB. o
c. infinitely many