Answer:
x = 1.32, -5.32
Step-by-step explanation:
x^2 + 4x - 7
Set equal to zero
x^2 + 4x - 7 =0
Add 7 to each side
x^2 + 4x =7
Take the coefficient of x and divide by 2
4/2
Square it
2^2 =4
Add to each side
x^2+4x+4 = 7+4
(x+2)^2 = 11
Take the square root of each side
x+2 = ±sqrt(11)
Subtract 2 from each side
x = -2 ±sqrt(11)
x=1.31662
x=-5.31662
To 2 decimal places
x = 1.32, -5.32
At the city museum, child admission is $5.20 and adult admission is $9.10 . On Wednesday, twice as many adult tickets as child tickets were sold, for a total sales of $631.80. How many child tickets were sold that day?
Answer:
54 adult tickets and 27 child ticket
54×9.10+5.20×27=631.80
419.4+104.4=631.80
631.80=631.80 ( so it's the answer)
Determine the smallest integer that makes -3x + 7 - 5x < 15 true.
State the smallest possible value for x in the solution set below as a number only.
Answer:
-1
Step-by-step explanation:
write it in the following manner:
-3x + 7 - 5x = 15
-8x + 7 = 15
-8x = 8
x = -1
Thus, the number has to be smaller than -1.
The smallest integer that makes the given inequality true is 0.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given inequality,
-3x + 7 - 5x < 15
We have to find the value of x.
(-3x - 5x) + 7 < 15
-8x < 8
Dividing whole sides by -1, the inequality sign changes.
x > -1
Smallest possible value is 0.
Hence the smallest posible value is 0.
Learn more about Inequalities here :
https://brainly.com/question/26855203
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What is this problem
Answer:
[tex]m=A-\frac{2n}{Z}[/tex]
Step-by-step explanation:
Multiply by 2:
2n = Z(A - m)
Divide by Z:
[tex]\frac{2n}{Z} =A-m[/tex]
Subtract A:
[tex]-m=\frac{2n}{Z}-A[/tex]
Multiply by -1:
[tex]m=A-\frac{2n}{Z}[/tex]
26x=74 which describe how to solve the equation below
Answer:
x = 37/13
Step-by-step explanation:
26x=74
x=74/26
x=37/13
What are the coordinates of the hole in the graph of the function?
f(x)=x2−3x−10/x−5
Enter your answer in the boxes.
Answer:
Given function f(x) = x + 2
The co-ordinates of ( -2 , 0) , (1 ,3 ),( 2,4)
Step-by-step explanation:
Given function
[tex]f(x) = \frac{x^{2}- 3 x -10 }{x -5}[/tex]
let [tex]y = f(x) = \frac{x^{2}- 3 x -10 }{x -5}[/tex]
The Factor [tex]x^{2} - 3 x - 10[/tex]
x ² - 5 x + 2 x - 10
x ( x -5) + 2 (x-5)
[tex]f(x) = \frac{x^{2}- 3 x -10 }{x -5} = \frac{(x-5)(x+2)}{x-5} = x +2[/tex]
y = x +2
The co-ordinates of ( -2 , 0) , (1 ,3 ),( 2,4)
A psychologist has designed a questionnaire to measure individuals' aggressiveness. suppose that the scores on the questionnaire are normally distributed with a standard deviation of . suppose also that exactly of the scores exceed . find the mean of the distribution of scores. carry your intermediate computations to at least four decimal places. round your answer to at least one decimal place.
Answer: μ = 647.4
Step-by-step explanation:
The question says
"A psychologist has designed a questionnaire to measure individuals' aggressiveness. suppose that the scores on the questionnaire are normally distributed with a standard deviation of . suppose also that exactly of the scores exceed"
And we are told to find the mean of the distribution scores.
Given mean μ = ?
we have from standard normal table that
P(Z > 1.282) = 0.1
Therefore the given Z score of a score of 750 is given thus 1.282.
the z score is given:
x - μ / α = 1.282
750 - μ / 80 = 1.282
Therefore μ = (750 - 80)*1.282 = 647.4
So we have that μ = 647.4
cheers i hope this helped !!!
The slope-intercept form of a line is y = mx + b. Using that equation for a line of best fit, you can substitute an input value to find the output for that point. With this method it is possible to make predictions for data points that may not be shown on a graph.
Answer:
Yes it is
Step-by-step explanation:
If you us a formula you can predict data points that are not on a graph
A cubical block of side 14 cm is surmounted by a hemisphere . what is the greatest radius that the hemisphere can have?
Answer:
9.9cmStep-by-step explanation:
The hemisphere will have its greatest radius along the diagonal of the cube it was surmounted on. The base of the cubical block will be square in nature. Since a cube has all its sides equal, we can find the length of its diagonal using pythagoras theorem as shown.
[tex]hyp^{2} = adj^{2} +opp^{2}[/tex]
Note that the diagonal will be the hypotenuse of the square face which is the longest sides.
Given adjacent = 14cm and opposite = 14cm
[tex]hyp^{2} = 14^{2} +14^{2}\\hyp = \sqrt{196+196} \\hyp = \sqrt{392} \\hyp = 19.8cm[/tex]
The diagonal of the base of the cube is 19.8cm which is equivalent to the greatest diameter of the sphere.
The greatest radius that the hemisphere can have = 19.8/2 = 9.9cm
Drawing diagrams
Circles
Radius rDiameter dRelationship between r and d:Cubes
Length lWidth wHeight hApplication:Let's draw a figure to supplement a visual image to further understand what we need to find. Please refer to the attached image for reference. Please excuse the poor handwriting/drawing. It is also not to scale.
We know that there is a cubical block w/ side measurements of 14 cm. "Surrmounted" means on top. So a hemisphere (half of a sphere) is on top of our block.
If we take a look at our geometrical shape from the top-down angle, we can see that the top would just look like a circle within a square, as depicted in blue.
Labeling our measurements, we can see that the length, width, and height of our cubical block are equal to 14 cm due to the definition of a cube. This extends to the definition of a square as well, so the length and width of our square are also equal to 14 cm.
With the side of the square equal to 14 cm, we know that this is equal to the circle's diameter. So d = 14 cm. We can solve for the radius of the circle/hemisphere by substituting it into the radius formula:
[tex]\begin{aligned}r & = \frac{d}{2} \\& = \frac{14 \ \text{cm}}{2} \\& = \boxed{ 7 \ \text{cm}} \\\end{aligned}[/tex]
Answer:∴ the greatest radius that the hemisphere can have is equal to 7 cm. Any r > 7 cm would result in the hemisphere being over the edge of the cube.
___
Learn more about Geometry: https://brainly.com/question/27732359
___
Topic: Geometry
Unit: Composition of Geometrical Shapes
£90 is divided between Mark, Henry & Gavin so that Mark gets twice as much as Henry, and Henry gets three times as much as Gavin. How much does Mark get?
Answer:
Mark gets £54
Step-by-step explanation:
Let Gavin share=x
Henry=3x
Mark=2(3x)
x+3x+2(3x)=£90
x+3x+6x=£90
10x=£90
x=9
Gavin=x=£9
Henry=3x
=3(9)=£27
Mark=2(3x)
=2(3*9)
=2(27)
=£54
I really need help with this question
Step-by-step explanation:
∠1 = ∠4 = 57° (vertical angles)
∠6 = 123° (same side interior angles are supplementary)
Answer:
The answer is 123
Step-by-step explanation:
Angle 5 is the same measure as angle one, and a straight line measures 180 degrees. Subtract 57 from 180, and you get the remaining angle. 123 degrees.
Can some one plz help me solve this problem! I need help ASAP ! Help me I will mark you as brainlizt!
Answer:
a) y = -5 b) y = -4 c) y = 4 d) y = 11
Step-by-step explanation:
a) (-2+2)²-5
b) (-1+2)²-5
c) (1+2)²-5
d) (2+2)²-5
A high square prism has a length L and width W units. if its height is H Units long the find the lateral surface area of the prism .
Answer:
2(L+W)H
Step-by-step explanation:
The lateral surface area of a prism is the total of the area of the faces. The lateral area of the prism is equal to the perimeter of the base times the altitude.Surface area= 2(L+W)H
Answer:
2(L+W)H
Step-by-step explanation:
The lateral surface area is the total of the area of all the faces of the prism.
Hope this helps!
Please answer correctly !!!!!!! Will mark brainliest answer !!!!!!!!!!
Answer:
625
Step-by-step explanation:
The maximum is the y-coordinate of the vertex. The vertex is (25, 625) so the answer is 625.
PLEASE HELP ME WITH THIS FAST FOR BRAINLIEST!
Answer:
Correct answer = 20 miles
Step-by-step explanation:
The mistake she made was that she made was that she multiplied the amount with 3 instead of dividing it.
The incorrect way -
$60 = 3 × 60 = 90 (Her multiplication is also incorrect as 3 × 60 = 180)
Corrected method -
$60 = [tex]\frac{60}{3}[/tex] = 20 miles
Hope you understood. Please mark my answer as the brainliest.Answer with steps by step please
Answer:
a is 1
Step-by-step explanation:
[tex]a+\dfrac{1}{a}=2[/tex]
Multiply both sides by a:
[tex]a^2+1=2a[/tex]
Move everything to one side:
[tex]a^2-2a+1=0[/tex]
Factor:
[tex](a-1)^2=0[/tex]
By the zero product rule, a is 1.
Therefore, the expression is true, because:
[tex](1)^2+\dfrac{1}{a^2}=a^4+\dfrac{1}{a^4}=1+1=2[/tex]
Hope this helps!
What is the sum of the first five terms of a geometric series with a = 10 andr
= 1/5?
Answer:
12.496
Step-by-step explanation:
Here, to calculate the sum of the first five terms of the series, we use the formula for the sum of terms in a geometric series.
Mathematically, that would be;
Sn = a(1-r^n)/1-r
where Sn = ?
a = 10
r = 1/5 = 0.2
n = 5
Substituting these values into the equation above, we have;
Sn = 10(1-(0.2)^5)/1-0.2
Sn = 10(0.99968)/0.8
Sn = 12.496
Given the function ƒ(x) = 5x^2 − 9x + 18, find ƒ(3). A) ƒ(3) = 31 B) ƒ(3) = 36 C) ƒ(3) = 49 D) ƒ(3) = 85
Answer:
36
Step-by-step explanation:
ƒ(x) = 5x^2 − 9x + 18,
Let x=3
ƒ(3) = 5*3^2 − 9*3 + 18,
=5*9 - 27+18
45 - 27+18
36
-6(4 + 5v) - 3 = -57 solve for V
-6(4 + 5v) - 3 = -57
Use distributive properties
-24 -30V -3 = -57
Combine like terms
-27 -30v = -57
Add 27 to both sides
-30v = -30
Divide both sides by -30
V=1
Answer:
v = 1
Step-by-step explanation:
-6(4 + 5v) - 3 = -57
Add 3 to each side
-6(4 + 5v) - 3+3 = -57+3
-6(4 + 5v) = -54
Divide by -6 on each side
-6(4 + 5v) / -6 = -54/-6
4+5v = 9
Subtract 4 from each side
4+5v-4 = 9-4
5v = 5
Divide each side by 5
5v/5 = 5/5
v =1
the __________ set is the set of elements under consideration
Answer:
SYNTAX PROPERTY
Step-by-step explanation:
Suppose your SAT score is 1490. You look up the average SAT scores for
students admitted to your preferred colleges and find the list of scores below.
Based on your SAT score of 1490, which average score below represents the
college that would be your best option?
Q A. 1470
B. 900
O C. 1420
O D. 1190
THIS IS 1 QUESTION YEAR 9 MATHS PLEASE HELP ME
Here are five shapes.
Two of these shapes have rotational symmetry of order 2
Write down the letter of each of these two shapes.
(2 marks)
A non-standard (but still fair) die has sides 2, 3, 5, 8, 12, 15, 18 and 20. What is P(roll an odd number)?
This is probably very easy but I totally forgot (look at picture)
Answer:
I hope ive done this correctly
Fixed, i see where i went wrong, i done it backwards
Step-by-step explanation:
Determine the value of
f(2) when
f(x)=x² - 5x+2
Answer:
-4
Step-by-step explanation:
Substitute [tex]x = 2[/tex] in to the function
[tex]f(2) = 2^2 -5(2) + 2[/tex]
= -4
What would be the answer and how would i get it?
Answer: c
Step-by-step explanation:
I very easy solve for x> then you take -3 -2 1,0 in order to get your answer
Answer:
x = {-3, -2, -1, 0, 1}
Step-by-step explanation:
We need to find the set that satisfies the inequality x > -4 ∩ x ≤ 1.
∩ means find the members that are common between two sets.
This means that we need to find the set of all integers that satisfy x > -4 and x ≤ 1
So, to find the low end, we find the lowest integer that satisfies x > -4, which is -3.
Now, to find the high end, we find highest integer that satisfies x ≤ 1, which is 1.
So x = {-3, -2, -1, 0, 1}
Pls help emergency will Mark bigbrain
Answer:
C.
Step-by-step explanation:
Volume of a Sphere = [tex]\frac{4}{3} \pi r^3[/tex]
Where volume of sphere = 81 π cm³
So, the equation becomes
81 π = [tex]\frac{4}{3} \pi r^3[/tex]
Answer:
the correct answer is the third row.
Step-by-step explanation
Keeping the properties of exponents in mind to what power must your raise the expression 7 1/2 to get 7 as a result
Answer:
x=2
Step-by-step explanation:
(7^ (1/2))ˣ = 7¹
1/2 *x =1
x =2
simplify this expression
Answer:
option 4
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]
Given
(2 - 5[tex]\sqrt{6}[/tex] ) 3[tex]\sqrt{2}[/tex] ← distribute parenthesis by 3[tex]\sqrt{2}[/tex]
= 6[tex]\sqrt{2}[/tex] - 15[tex]\sqrt{12}[/tex]
= 6[tex]\sqrt{2}[/tex] - 15[tex]\sqrt{4(3)}[/tex]
= 6[tex]\sqrt{2}[/tex] - 15([tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex] )
= 6[tex]\sqrt{2}[/tex] - 15(2[tex]\sqrt{3}[/tex] )
= 6[tex]\sqrt{2}[/tex] - 30[tex]\sqrt{3}[/tex]
What is the rate of change between (6,12) and (8,20)
Step-by-step explanation:
It might be easier thinking of "rate of change" as the slope. Since you'll be finding a slope, then, use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and substitute the values.
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{20-12}{8-6}\\m=\frac{8}{2} \\m=4[/tex]
Answer:
[tex]m=\frac{4}{1}[/tex] or [tex]m=4[/tex]
To approach runway 17 of the Ponca City Municipal Airport in Oklahoma, the pilot must begin a 3° descent starting from a height of 2714 ft above sea level. The airport is 1007 feet above sea level. To the nearest tenth of a mile, how far from the runaway is the airplane at the start of his approach?
Answer:4.
Step-by-step explanation:
